Intermetallic Chemistry (Pergamon Materials Series, Volume 13)

Intermetallic Chemistry PERGAMON MATERIALS SERIES Series Editor: Robert W. Cahn FRS Department of Materials Science ...

Author: Riccardo Ferro | Adriana Saccone

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Intermetallic Chemistry

PERGAMON MATERIALS SERIES

Series Editor: Robert W. Cahn FRS Department of Materials Science and Metallurgy, University of Cambridge, Cambridge, UK Vol. 1 Vol. 2 Vol. 3 Vol. 4 Vol. 5 Vol. 6 Vol. 7 Vol. 8 Vol. 9 Vol. 10 Vol. 11 Vol. 12

CALPHAD by N. Saunders and A. P. Midownik Non-Equilibrium Processing of Materials edited by C. Suryanarayana Wettability at High Temperatures by N. Eustathopoulos, M. G. Nicholas and B. Drevet Structural Biological Materials edited by M. Elices The Coming of Materials Science by R. W. Cahn Multinuclear Solid-State NMR of Inorganic Materials by K. J. D. MacKenzie and M. E. Smith Underneath the Bragg Peaks: Structural Analysis of Complex Materials by T. Egami and S. J. L. Billinge Thermally Activated Mechanisms in Crystal Plasticity by D. Caillard and J. L. Martin The Local Chemical Analysis of Materials by J. W. Martin Metastable Solids from Undercooled Melts by D. M. Herlach, P. Galenko and D. Holland-Moritz Thermo-Mechanical Processing of Metallic Materials by B. Verlinden, J. Driver, I. Samajdar and R.D. Doherty Phase Transformations Examples from Titanium and Zirconium Alloys by S. Banerjee and P. Mukhopadhyay

Intermetallic Chemistry

R. Ferro and A. Saccone Department of Chemistry, University of Genoa, Italy

Amsterdam • Boston • Heidelberg • London • New York • Oxford Paris • San Diego • San Francisco • Singapore • Sydney • Tokyo Pergamon is an imprint of Elsevier

Pergamon is an imprint of Elsevier The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands First edition 2008 Copyright © 2008 Elsevier Ltd. All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (44) (0) 1865 843830; fax (44) (0) 1865 853333; email: [email protected]. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress For information on all Pergamon publications visit our web site at books.elsevier.com Typeset by Charon Tec Ltd (A Macmillan Company), Chennai, India www.charontec.com Printed and bound in Great Britain 08 09 10 10 9 8 7 6 5 4 3 2 1 ISBN: 978-0-08-044099-6

Contents Editorial Foreword Preface

xxiii xxv

CHAPTER 1 Introductory survey 1.1. A presentation of the book and remarks on its contents CHAPTER 2 Phase diagrams in alloy systems 2.1. Preliminary remarks 2.2. Some characteristic, T vs. x, binary phase diagrams 2.2.1 Mutual solid solubility of the component metals in alloy systems 2.2.1.1 Mutual solid-state solubility: a simple structural representation – order/disorder 2.2.1.2 Trends in mutual solid solubility 2.2.1.3 Electronegativity, Mendeleev number, Miedema parameters 2.2.1.4 Partial mutual solubility in the solid state 2.2.2 Inter-crossing of two-phase equilibria 2.2.2.1 Phase rule, ‘Building Blocks’ in binary system diagrams, Invariant equilibria 2.2.2.2 Solubility Diagrams: effects of atomic properties on mutual solubility 2.2.3 Trends in mutual liquid solubilities 2.2.4 Formation of intermediate phases in alloy systems 2.2.4.1 Trends in the formation capability of binary compounds 2.3. Examples of more complex phase diagrams 2.3.1 Ternary phase diagrams 2.3.2 Variable pressure phase diagrams 2.3.2.1 Partial pressure as a variable 2.3.3 Equilibrium and reaction rate 2.3.3.1 Stable, metastable and unstable states: a simple analogy v

1

7 8 8 10 11 12 21 22 24 28 30 33 38 40 41 45 48 51 54

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Contents

2.3.3.2 Spinodal decomposition Remarks on phase diagram determination and evaluation 2.4.1 Experimental determination of phase diagrams 2.4.1.1 Polythermal methods 2.4.1.2 Isothermal methods 2.4.1.3 Recent developments and prospects of X-ray powder diffraction methods 2.4.1.4 The diffusion couple technique in phase diagram determination 2.4.1.5 The characterization and 3D representation of materials microstructure 2.4.2 Assessment and calculation of phase diagrams 2.4.2.1 Assessment of phase diagrams 2.4.2.2 Calculation, thermodynamic optimization of phase diagrams References

2.4.

CHAPTER 3 Sructural characteristics of intermetallic phases 3.1. Preliminary remarks 3.2. Liquid intermetallic phases 3.2.1 Recent investigations on liquid alloys 3.3. Intermetallic compound chemistry in the solid state 3.4. Identification of the intermetallic (solid) phases 3.5. Composition and compositional formula of the intermetallic phase 3.5.1 Order of citation of element symbols in the formula 3.5.2 Indication of constituent proportions 3.6. Crystal structure of the solid phase and its standard representation 3.6.1 General remarks, unit cell description 3.6.1.1 Crystallographic nomenclature (Bravais lattices, crystal classes, space groups) 3.6.1.2 The unit cell content 3.6.1.3 Common crystal–chemical formulae. Unit cell volumes and interatomic distances 3.6.2 Shortened version of the standard description: structural types 3.6.3 Structure types and unit cell Pearson symbol 3.7. Alternative and complementary descriptions of the crystal structures of the solid phases 3.7.1 Lattice complexes

56 58 58 59 59 62 64 66 67 67 68 75

81 82 85 87 88 89 89 90 94 94 96 101 105 113 115 116 116

Contents

3.7.2 3.7.3

3.8.

3.9.

Alternative structural descriptions and symbols Coordination and dimensionality symbols in the crystal coordination formula 3.7.3.1 Coordination number and packing geometry 3.7.4 The concept of coordination number 3.7.5 Atomic environment definition (and symbols) and corresponding coordination numbers and polyhedra 3.7.6 Layer stacking sequence description and symbols 3.7.7 The cP4-AuCu3 type: an example of the use of alternative and complementary structural notations and symbols 3.7.8 Structure trivial names and Strukturbericht symbols Structure families: degenerate structures, derivative structures, ‘superstructures’ 3.8.1 Defect and filled-up derivative structures 3.8.1.1 Tetrahedral and octahedral holes in closepacked structures 3.8.2 Order–disorder transformation 3.8.3 Examples of substitutional superstructures 3.8.4 Examples of interstitial superstructures: Hägg phases 3.8.4.1 Interstitial hydrides 3.8.4.2 Interstitial carbides and nitrides 3.8.4.3 Hägg rules 3.8.4.4 Miscellaneous examples of interstitial superstructures 3.8.5 Remarks about a ‘second kind’ of superstructures Structure families: ‘recombination structures’, modular aspects of crystal structures 3.9.1 Modular aspects of crystal structures 3.9.2 Homeotect structure types, polytypic structures 3.9.2.1 Close-packed element structure types 3.9.2.2 Equiatomic tetrahedral structure types (Carborundum structure types) 3.9.2.3 Laves phases 3.9.2.4 A few general remarks about homeotect structures 3.9.3 Assembly of polyhedra 3.9.3.1 Tetrahedrally close-packed structures. Frank–Kasper structures 3.9.3.2 Structures based on frameworks of fused polyhedra: Samson phases 3.9.4 Recombination structures, intergrowth structure series

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3.10. Group–subgroup relations between space groups for the representation of crystal–chemical relationships 3.11. Quasi-periodic crystals 3.11.1 Modulated structures 3.11.2 Composite crystals 3.11.2.1 Nowotny phases, chimney-ladder structures 3.11.2.2 Combination of commensurate and incommensurate periodic ‘substructures’ 3.11.3 Quasicrystals 3.11.3.1 Notes on the crystallography of quasiperiodic structures 3.11.3.2 Types of quasicrystals and examples of alloy systems showing their formation 3.11.3.3 Structural relations between quasicrystals and other intermetallic phases 3.12. Amorphous alloys, metallic glasses 3.12.1 Structure of metallic glasses 3.12.2 Examples of metallic systems with glass-forming capability References

CHAPTER 4 Intermetallic reactivity trends in the Periodic Table 4.1. Introduction 4.2. The Periodic Table and its structure 4.2.1 The Periodic Table and the electron configurations of the elements 4.2.1.1 Remarks about the structure of the Periodic Table 4.2.1.2 The electronic structure of the atoms 4.2.2 Blocks and subdivisions of the Periodic Table 4.2.2.1 ‘Blocks’ of the Periodic Table 4.2.2.2 Comments on some trends and on the ‘Divides’ in the Periodic Table 4.2.2.3 ‘Geochemical’ subdivision of the Periodic Table 4.2.2.4 Superconducting elements in the Periodic Table 4.2.2.5 ‘Technological’ subdivision of the Periodic Table 4.3. Trends in the Periodic Table: the role of the atomic dimensions as a factor controlling the structure of intermetallic phases

189 190 190 193 193 197 198 200 203 204 206 209 211 212

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Contents

4.3.1 4.3.2

4.4.

Introduction Atomic dimensions, interatomic distances in the intermetallic phases 4.3.2.1 Atomic radii and volumes. (Pauling’s rule, Vegard’s and Biltz-Zen’s formulae) 4.3.2.2 Relationship between formV and formH for selected groups of alloys. Gschneidner’s formulae 4.3.2.3 Atomic dimensions and an example of stability multi-diagrams 4.3.2.4 Partial molar (atomic) volume 4.3.2.5 Geometrical considerations about intermetallic crystal structures Remarks on the chemical bond factor and valence-electron counting rules 4.4.1 Introduction 4.4.2 Normal valence compound rule 4.4.2.1 ‘Tetrahedral structures’ 4.4.2.2 Valence compounds: notes for a classification (VEC and partial VEC) 4.4.3 Polyanionic compounds 4.4.3.1 Zintl phases: an introduction 4.4.3.2 Zintl phases: remarks on their definition 4.4.4 ‘Cluster’ compounds 4.4.4.1 Cluster compounds: introductory remarks 4.4.4.2 Cluster compounds and remarks on the ‘2e, 2c bonding scheme’ 4.4.4.3 Wade electron counting rules: borane-like cluster nomenclature 4.4.4.4 Electron-precise, electron-deficient and electron-rich clusters 4.4.4.5 Interstitial atoms in clusters 4.4.4.6 Condensed and high nuclearity cluster compounds 4.4.4.7 From clusters towards solid state intermetallics 4.4.4.8 Problems in the relations between complex intermetallic alloys and clusters 4.4.4.9 Thermochemistry of cluster compounds

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Contents

4.4.5 4.4.6 4.4.7

‘Hume–Rothery phases’ and VEC VEC and stability multi-diagrams. Brewer diagrams New developments in electronic counting in intermetallic compounds 4.4.7.1 Stability maps and correlation diagrams

References

CHAPTER 5 Elements of alloying behaviour systematics 5.1. Introductory notes 5.1.1 Symbols and nomenclature 5.2. Alloys of hydrogen 5.2.1 Introduction 5.2.2 Intermetallic chemistry of hydrogen 5.2.2.1 Remarks on the systematics of hydrogen reactivity with the elements 5.2.2.2 Examples of phase diagrams of metal–hydrogen systems 5.2.2.3 Comments on the crystal structures of typical hydrogen–metal phases 5.2.2.4 Notes on the application of metal hydrides 5.3. Alloys of the alkali metals (1st group metals) (Li, Na, K, Rb, Cs, Fr) 5.3.1 Introduction 5.3.2 The alkali metals: a summary of their atomic and physical properties 5.3.3 The alkali metals: remarks about their general chemical properties and reactivity 5.3.4 Intermetallic chemistry of the alkali metals 5.3.4.1 Phase diagrams of alkali metal alloys 5.3.4.2 Melting point trend in the binary alkali metal alloys 5.3.4.3 Remarks on the crystal chemistry of the alkali metal alloys 5.3.4.4 A glance through complex intermetallic compounds of the alkali metals 5.4. Alloys of the alkaline earth metals and of the ‘divalent’ rare earth metals (Ca, Sr, Ba, Ra, Eu, Yb) 5.4.1 Introduction 5.4.2 The alkali earth metals and Eu and Yb: a summary of their atomic and physical properties

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Contents

5.4.3

5.5.

5.6.

The alkali earth metals and Eu and Yb: remarks about their general chemical properties and reactivity 5.4.4 Intermetallic chemistry of the alkaline earth metals and of Eu and Yb 5.4.4.1 Phase diagrams of the alkaline earth metals and of Eu and Yb 5.4.4.2 Melting point trend in the binary alkaline earth metal alloys 5.4.4.3 Remarks on the crystal chemistry of the alloys of the alkaline earth metals and of Eu and Yb Alloys of the metals of the 3rd group of the Periodic Table (Sc, Y, La, Ln, Ac, An) 5.5.1 Introduction 5.5.2 Lanthanide and actinide concept, lanthanide contraction 5.5.3 Rare earth metals 5.5.3.1 Rare earth metals: occurrence and preparation 5.5.4 Actinides 5.5.4.1 Actinides: occurrence and preparation 5.5.5 The 3rd group metals: a summary of their atomic and physical properties 5.5.5.1 The rare earth metals 5.5.5.2 The actinides 5.5.6 The 3rd group metals: remarks about their general chemical properties and reactivity 5.5.6.1 The rare earth metals 5.5.6.2 The actinides 5.5.7 Intermetallic chemistry of the 3rd group metals 5.5.7.1 Phase diagrams of the 3rd group metals 5.5.7.2 Remarks on the stability of the binary alloys of the 3rd group metals (melting point and formation enthalpy trends) 5.5.7.3 Further remarks on the actinide alloys 5.5.7.4 Remarks on the crystal chemistry of the alloys of the 3rd group metals Alloys of the metals of the 4th group of the Periodic Table (Ti, Zr, Hf) 5.6.1 Introduction 5.6.2 The 4th group metals: a summary of their atomic and physical properties 5.6.3 The 4th group metals: remarks about their general chemical properties and reactivity

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383 387 390 393 393 394 395

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Contents

5.6.4

5.7.

5.8.

5.9.

Intermetallic chemistry of the 4th group metals 5.6.4.1 Phase diagrams of the 4th group metals 5.6.4.2 Melting point trend in the binary alloys of the 4th group metals 5.6.4.3 Remarks on the alloy crystal chemistry of the 4th group metals 5.6.4.4 Notes on the applications of the 4th group metals Alloys of the metals of the 5th group of the Periodic Table (V, Nb, Ta) 5.7.1 Introduction 5.7.2 The 5th group metals: a summary of their atomic and physical properties 5.7.3 The 5th group metals: remarks about their general chemical properties and reactivity 5.7.4 Intermetallic chemistry of the 5th group metals 5.7.4.1 Phase diagrams of the 5th group metals 5.7.4.2 Melting point trend in the binary alloys of the 5th group metals 5.7.4.3 Remarks on the alloy crystal chemistry of the 5th group metals Alloys of the metals of the 6th group of the Periodic Table (Cr, Mo, W) 5.8.1 Introduction 5.8.2 The 6th group metals: a summary of their atomic and physical properties 5.8.3 The 6th group metals: remarks about their general chemical properties and reactivity 5.8.4 Intermetallic chemistry of the 6th group metals 5.8.4.1 Phase diagrams of the 6th group metals 5.8.4.2 Remarks on the melting point trends in the binary alloys of the 6th group metals 5.8.4.3 Notes on the alloy crystal chemistry of the 6th group metals Alloys of the metals of the 7th group of the Periodic Table (Mn, Tc, Re) 5.9.1 Introduction 5.9.2 The 7th group metals: a summary of their atomic and physical properties 5.9.3 The 7th group metals: remarks about their general chemical properties and reactivity

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Contents

5.9.4

Intermetallic chemistry of the 7th group metals 5.9.4.1 Phase diagrams of the 7th group metals 5.9.4.2 Remarks on the alloy crystal chemistry of the 7th group metals 5.10. Alloys of the metals of the 8th, 9th and 10th groups of the Periodic Table (Fe, Co, Ni, Ru, Os, Rh, Ir, Pd, Pt) 5.10.1 Introduction 5.10.1.1 Metals of the iron family 5.10.1.2 Metals of the platinum family 5.10.1.3 Platinum family metals preparation 5.10.2 The metals of the 8th, 9th and 10th groups: a summary of their atomic and physical properties 5.10.3 The metals of the 8th, 9th and 10th groups: remarks about their general chemical properties and reactivity 5.10.4 Intermetallic chemistry of the metals of the 8th, 9th and 10th groups: general remarks 5.10.4.1 Phase diagrams of the iron family metals 5.10.4.2 Phase diagrams of the platinum family metals 5.10.4.3 Remarks on the alloys crystal chemistry of the metals of the 8th, 9th and 10th groups 5.10.4.4 Notes on the application of the metals of the 8th, 9th and 10th groups and their alloys 5.10.4.5 Iron and steel: Steel production, the Fe–C phase diagram, TTT diagrams, martensite 5.11. Alloys of the metals of the 11th group of the Periodic Table (Cu, Ag, Au) 5.11.1 Introduction 5.11.2 The 11th group metals: a summary of their atomic and physical properties 5.11.3 The 11th group metals: remarks about their general chemical properties and reactivity 5.11.4 Intermetallic chemistry of the 11th group metals 5.11.4.1 Phase diagrams of the 11th group metals 5.11.4.2 Remarks on the alloy crystal chemistry of the 11th group metals 5.11.4.3 Notes on the applications of the alloys of the 11th group metals

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457 457 459 460 460 460 464 466

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Contents

5.12. Alloys of Be, Mg, Zn, Cd and Hg 5.12.1 Introduction 5.12.2 Be, Mg, Zn, Cd and Hg: a summary of their atomic and physical properties 5.12.3 Be, Mg, Zn, Cd and Hg: remarks about their general chemical properties and reactivity 5.12.4 Intermetallic chemistry of Be, Mg, Zn, Cd and Hg 5.12.4.1 Phase diagrams of the Be, Mg, Zn, Cd and Hg alloys 5.12.4.2 Remarks on the melting point trends in the binary alloys of Be, Mg and of the 12th group metals 5.12.4.3 Remarks on the crystal structures of selected alloys of Be, Mg and of the 12th group metals 5.12.4.4 Notes on the application of Be, Mg, Zn, Cd, and Hg alloys 5.12.4.5 Magnesium alloys: standard ASTM alloy designation 5.13. Alloys of the elements of the 13th group of the Periodic Table (B, Al, Ga, In, Tl) 5.13.1 Introduction 5.13.2 B, Al, Ga, In, Tl: a summary of their atomic and physical properties 5.13.3 The 13th group elements: remarks about their general chemical properties and reactivity 5.13.4 Intermetallic chemistry of the 13th group elements 5.13.4.1 Phase diagrams of the 13th group elements 5.13.4.2 Remarks on the crystal chemistry of the triel elements (Al, Ga, In, Tl) 5.13.4.3 Notes on the applications of aluminium alloys 5.13.4.4 Remarks on some commercial aluminium alloys 5.14. Alloys of the elements of the 14th group of the Periodic Table (C, Si, Ge, Sn, Pb) 5.14.1 Introduction 5.14.2 The 14th group elements: a summary of their atomic and physical properties 5.14.3 Intermetallic chemistry of the 14th group elements 5.14.3.1 Phase diagrams of the 14th group elements 5.14.3.2 Remarks on the alloy crystal chemistry of the 14th group elements

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473 473 476 478 479 479 482 484 485 485 486 491 492 494 494 500 501 501 502

Contents

5.14.3.3 Notes on some peculiar applications of diamond 5.14.3.4 Joining processes: tin-containing soft solders 5.15. Alloys of the elements of the 15th group of the Periodic Table (N, P, As, Sb, Bi) 5.15.1 Introduction 5.15.2 The 15th group elements: a summary of their atomic and physical properties 5.15.3 Intermetallic chemistry of the 15th group elements 5.15.3.1 Phase diagrams of the 15th group elements 5.15.3.2 Notes on the crystal chemistry of selected alloys and compounds of the 15th group elements 5.16. Alloys of the elements of the 16th group of the Periodic Table (O, S, Se, Te, Po) 5.16.1 Introduction 5.16.2 The 16th group elements: a summary of their atomic and physical properties 5.16.3 Intermetallic chemistry of the 16th group elements 5.16.3.1 Phase diagrams of the 16th group elements 5.16.3.2 A few notes about simple binary compounds of the 16th group elements 5.17. General remarks on the systematics of the binary alloys of the metals 5.18. Complex alloys: a few notes and remarks about their systematics References

CHAPTER 6 Laboratory preparation of intermetallic phases 6.1. Introduction 6.2. Notes about procedures and instruments frequently used in an intermetallic chemical laboratory 6.2.1 Heating, thermal treatments 6.2.1.1 Laboratory furnaces 6.2.1.2 Crucibles, refractory materials 6.2.2 Miscellaneous, special processing techniques and heat treatments 6.2.2.1 Quenching (from the solid state) 6.2.2.2 Super-Quenching (quenching from the liquid) 6.2.2.3 Thixoforming, semi-solid processing 6.2.2.4 Temperature measurements 6.2.3 Laboratory equipment: a few additional remarks

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531 531 531 532 539 542 544 545 546 546 551

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6.3.

6.4.

6.5.

Contents

Purity problems, the role of impurities 6.3.1 Introductory remarks 6.3.2 Formation of impurity-stabilized phases 6.3.3 Examples of preparation of high-purity materials 6.3.3.1 Silicon 6.3.3.2 Rare Earth metals 6.3.4 Effects of impurities on alloy properties and on the synthesis control 6.3.5 Effects of interstitial impurities on phase equilibria Direct synthesis of the intermetallic phases 6.4.1 Introduction 6.4.2 Melting (reaction in the liquid state) 6.4.2.1 Examples of reactions and synthesis by melting 6.4.3 High-temperature liquid intermetallic solution growth of single crystals and quasicrystals 6.4.4 Solid-state synthesis 6.4.4.1 Direct synthesis from component powders 6.4.4.2 Direct synthesis from the solid components by ‘mechanical alloying’ 6.4.4.3 Combustion synthesis 6.4.4.4 Field-activated, self-propagating, hightemperature synthesis 6.4.4.5 Co-reduction of mixed oxides 6.4.4.6 Fast, solid state, microwave-assisted, synthesis 6.4.4.7 ‘Extraction’ of a phase from a mixture Synthesis in solvents (under fluxes) 6.5.1 Synthesis of intermetallic phases in liquid sodium 6.5.2 Synthesis in mercury solution 6.5.3 Synthesis in liquid aluminium 6.5.3.1 Al as solvent: the synthesis of beryllides as an example 6.5.3.2 Synthesis in liquid Al: Al as a reactive solvent 6.5.4 Synthesis in liquid gallium (reactive solvent) 6.5.5 Synthesis in liquid indium 6.5.6 Synthesis in tin flux 6.5.7 Synthesis in lead flux 6.5.8 Single-crystal preparation and growth by NaCl/KCl flux reaction 6.5.9 Synthesis in alkali chalcogenide reactive flux 6.5.10 Synthesis in alkali poly-chalcogenide flux

552 552 553 553 553 554 556 560 560 560 561 563 565 566 566 567 569 573 573 573 574 575 577 577 578 578 578 579 579 580 580 581 581 581

Contents

6.5.11 Synthesis in liquid NH3 Reactions with the gas phase 6.6.1 Physical vapour deposition 6.6.2 Chemical vapour deposition 6.6.3 Vapour phase transport 6.6.4 Chemical transport reactions as a new variant of the phase composition control 6.6.5 Single-crystal preparation by means of chemical transport reactions. (Ni–Sn–S compounds as an example) 6.6.6 Synthesis of metastable Al and Ga monohalide solutions and subsequent preparation of large Al and Ga clusters 6.7. Synthesis of intermetallic phases by exchange reactions (metathesis reactions) 6.7.1 Metathesis (exchange) reactions 6.7.1.1 Solid-state metathesis reactions 6.7.1.2 Metathesis reactions in solution 6.7.2 Coupled reductions 6.7.2.1 Oxide coupled reduction with a metal and hydrogen 6.7.2.2 Preparation of ‘base’ metals by coupled reduction with platinum group metals 6.7.2.3 Oxide coupled reduction with boron and sulphur 6.8. Electrodeposition and electrolytic reduction (electrowinning) 6.8.1 Electrochemical reduction 6.8.2 Electrodeposition of alloys. Ag–Bi alloys as an example of electro co-deposition 6.8.3 Preparation of amalgams: electrochemical reduction on an Hg cathode 6.8.4 Preparation of transition metal compounds with non-metals by electrolytic reduction of fused salts 6.9. Special techniques 6.9.1 Sono-chemical techniques 6.9.2 Shock-induced and shock-assisted reactions in powder mixtures 6.9.3 Sputtering 6.9.4 Pulsed laser ablation deposition technique (PLAD technique) 6.10. Synthesis of nano-structured metals and alloys 6.10.1 Synthesis of nano-structured alloys by the inert gas evaporation technique

6.6.

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6.10.2 Synthesis of nano-structured alloys via mechanical deformation 6.10.3 ‘Precursor’ preparation by solution chemistry 6.10.4 Synthesis of nano-structured alloys by chemical vapour deposition and chemical vapour condensation 6.10.5 Synthesis of nano-structured alloys from organometallics 6.10.6 ‘Nanowires’ 6.10.7 ‘Nano-structures’: comments on an example of extreme microstructure 6.11. Examples of preparation routes of groups of compounds with non-metals 6.11.1 Borides 6.11.1.1 Borothermic reduction of oxides enhanced by electron-beam bombardment 6.11.1.2 Borides from metallic fluxes 6.11.1.3 Application of carbo-thermal reduction 6.11.2 Carbides 6.11.3 Phosphides and polyphosphides 6.12. The synthesis of InAs: examples of alternative routes of preparation 6.12.1 Introduction 6.12.2 Preparation of InAs by direct synthesis from the elements 6.12.3 InAs equilibrium with the liquid 6.12.4 Synthesis of InAs (and III–V semiconductors) by solid-state metathesis 6.12.5 Synthesis of InAs by reaction of indium halides 6.12.6 Synthesis of InAs by hydrothermal route 6.12.7 Single source precursors in the synthesis of triels monopictides 6.12.8 The liquid-encapsulated Czochralski process and the growth of III–V crystals References CHAPTER 7 Families of intermetallic structure types: a selection 7.1. Introduction and statistical remarks 7.2. A prototype directory of selected intermetallic structures 7.2.1 On the schematic representations of crystal structures 7.2.1.1 Structure and structure component sections: the tI2-αPa, cI2-W, cF8-ZnS and tI8-NbAs types as examples

597 597 598 598 598 599 600 600 602 602 602 603 604 606 606 607 607 607 608 608 609 609 610

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Contents

7.2.1.2

7.3.

7.4.

Structure and structure component projections: the cP1-Po, cI2-W and hP3-AlB2 type structures as examples 7.2.2 Examples of common structure types and of their characteristic fragments 7.2.3 Polyhedra projections Unary structures 7.3.1 General remarks 7.3.2 Metallic element structures 7.3.2.1 The close-packed element structure types (Mg, Cu, La, Sm types) and simple derivative types 7.3.2.2 The body-centred cubic W-type structure 7.3.2.3 Two body-centred tetragonal structures (In- and Pa-type structures) 7.3.2.4 Special structural types of selected metals 7.3.2.5 A few comments about uranium and plutonium elemental structures 7.3.3 A selection of non-metallic elemental structures 7.3.3.1 Boron: remarks on its crystal structure 7.3.3.2 The 8 – eat rule 7.3.3.3 Typical structures of elements of the 15th group (As, Sb, Bi) 7.3.3.3.1 As, hR6, structural type 7.3.3.4 Comments on other structures of 15th group elements 7.3.3.5 Typical structures of 16th group elements 7.3.3.6 Remarks on the structures of 17th group elements (I2) Binary structures: a selection of common prototypes 7.4.1 Preliminary remarks 7.4.2 Simple 1:1 prototypes and derivative structures 7.4.2.1 Introduction 7.4.2.2 cP2-CsCl, cF8-NaCl and cF16-NaTl types and NaTl-related structures 7.4.2.3 Simple binary tetrahedral structures and polytypes (ZnS-sphalerite, cF8-ZnS and ZnS-wurtzite, hP4-ZnO, structural types) 7.4.2.4 hP2-WC and hP4-NiAs types and examples of NiAs-derivative structures

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7.4.2.5

7.4.3

7.4.4

oS8-CrB and oP8-FeB structure types (two triangular prism-based structures, similar in coordination) 7.4.2.6 AuCu(I), tP2, and AuCu(II), oI40, structural types (ordered derivatives in the Cu–Au system) 7.4.2.7 oS16-CeAl and oP16-DyAl structure types 7.4.2.8 FeSi, cP8, structural type 7.4.2.9 The tI8-NbAs type (and related structures) and the tI8-NbP type Remarks on structures of some 1:2 compounds 7.4.3.1 Introduction 7.4.3.2 CaF2 type (and its ordered AgMgAs-derivative structure) 7.4.3.3 Laves phases 7.4.3.4 tI6-CaC2 and MoSi2-type structures 7.4.3.5 oI12, CeCu2 and KHg2 structural descriptions (an exercise on isotypism and ‘normalization’ of crystal structure data) 7.4.3.6 Co2Si (PbCl2), oP12, and TiNiSi, oP12, structural types 7.4.3.7 CuAl2, tI12, structural type 7.4.3.8 Cu2Sb, tP6, structural type 7.4.3.9 Fe2P, hP9, structural type 7.4.3.10 TiSi2, oF24, structural type 7.4.3.11 UPt2, oS12, structural type 7.4.3.12 MoPt2, oI6, structural type 7.4.3.13 FeS2, cP12, structural type (pyrite) 7.4.3.14 The AlB2, hP3, type and its structural family 7.4.3.15 αThSi2, tI12, and LaPtSi, tI12, structural types 7.4.3.16 Rge2x (rare earth ‘digermanides’): an example of a family of compounds with structures related to the ‘coordination similar’ AlB2 and ThSi2 types Examples of structure types with a 1:3 stoichiometry 7.4.4.1 Introductory remarks 7.4.4.2 A polytypic structure family consisting of close-packed stacking of layers composed of triangular and kagomè nets (the hP8-Ni3Sn, cP4-AuCu3, hP16-TiNi3, hP24-VCo3, hP24-PuAl3 and hR36-BaPb3, types)

666 668 669 671 671 673 673 674 676 680

680 683 685 685 686 687 687 687 688 688 697

701 703 703

703

Contents

The βTiCu3, oP8, structural type (a Ni3Sn-type related structure) 7.4.4.4 The tP4-Ti3Cu, tI8-TiAl3 and tI16-ZrAl3 type structures: tetragonal derivatives of the cP4AuCu3 type 7.4.4.5 Cr3Si, cP8, structural type: an example of ‘tetrahedrally close-packed’ phases 7.4.4.6 Na3As, hP8, structural type (and the ‘bond factor’) 7.4.4.7 Fe3Co, P16, structural type A Selection of more common intermetallic prototypes having more complex stoichiometries and structures 7.5.1 Examples of protoypes corresponding to high stoichiometric ratios 7.5.1.1 Th6Mn23, cF116, structural type 7.5.1.2 Fe4N, cP5, structural type 7.5.1.3 BaAl4, tI10, structural type and BaAl4derivative types 7.5.1.4 MoNi4, tI10, structural type 7.5.1.5 CaCu5, hP6, structural type 7.5.1.6 CaB6, cP7 structural type (a cross-reference note) 7.5.1.7 Th2Ni17, hP38, structural type 7.5.1.8 Th2Zn17, hR57, structural type 7.5.1.9 BaHg11, cP36, structural type 7.5.1.10 ThMn12, tI26, structural type and ThMn12derivative types 7.5.1.11 NaZn13, cF112, structural type 7.5.1.12 Relationships among prototypes with high stoichiometric ratios 7.5.2 γ-brass: Cu5Zn8, cI52 structural type 7.5.3 Tetrahedrally close-packed phases, Frank–Kasper phases (cross-reference note) 7.5.3.1 Zr4Al3, hP7, structural type (a tetrahedrally close-packed phase) 7.5.3.2 σ Cr-Fe, tP30, structural type (a tetrahedrally closepacked phase) 7.5.3.3 W6Fe7, hR39, structural type (μ phase) (a tetrahedrally close-packed phase) 7.5.4 Samson phases (a cross-reference note) 7.5.5 Chevrel phases, structures containing Me6X8 clusters (cross-reference note)

xxi

7.4.4.3

7.5

708

709 711 712 713 714 714 714 715 715 721 721 723 723 724 725 726 727 728 728 729 729 730 731 731 731

xxii

Contents

7.5.6

A miscellany of stoichiometries and prototypes (short notes) 7.5.6.1 Selected structures corresponding to a binary 5:4 stoichiometry 7.5.6.2 Selected structures corresponding to a binary 5:3 stoichiometry 7.5.6.3 A selected structure corresponding to the binary 3:4 stoichiometry 7.6. Remarks about the crystal structures of a few oxygen compounds. Examples of oxides and minerals 7.6.1 Introduction 7.6.2 Ta4O, oP5, structural type 7.6.3 Al2O3, hR30, structural type (and derivative FeTiO3, ilmenite type) 7.6.4 TiO2, tP6, structural type (rutile) 7.6.5 ReO3, cP4, structural type 7.6.6 CaTiO3, cP5, structural type (perovskite) 7.6.7 BeAl2O4, oP28, structural type (chrysoberil) 7.6.8 Garnet, yttrium iron garnet, cI160, structural type 7.6.9 MgAl2O4, cF56, structural type (spinel) 7.6.10 Olivines References Appendix Index

731 732 734 737 738 738 738 738 739 741 742 743 744 745 747 748 751 757

Editorial Foreword The draft of this remarkable book reached me in the mid-December 2006. As I was reading through it, a message from Prof. Saccone informed me that Prof. Ferro had died suddenly and unexpectedly on 28 December. The two authors of the book, Prof. Ferro and Saccone, had been close scientific collaborators for many years. I first came to know them when, in the early 1990s, I was advised to invite them to contribute a chapter on intermetallic compounds to the fourth edition of my Physical Metallurgy, which duly appeared in 1996. Since then I have come to appreciate fully the remarkable team of solid-state chemists built up in Genoa by Prof. Ferro and Saccone. Their approach to the borderlands of crystal chemistry and metallurgy is unique and very impressive. This book, Intermetallic Chemistry, which has been several years in preparation, encapsulates their joint approach, and I regard its publication as a fitting memorial to a truly remarkable man. Robert W. Cahn (Series Editor) January 2007

On December 28, 2006 Professor Ferro suddenly died. After working for so many years under his direction, I feel indebted not only for his valuable scientific advice, but above all for the precious example he gave me through his dedication to science and teaching. Intermetallic compound chemistry, the subject matter of this book, is the focal point of Prof. Ferro’s scientific activity and the subject to which he has dedicated his professional life. Assisting Prof. Ferro in the preparation of this book has been for me a great honour. It is my hope that this book will be able to convey to the reader not only a systematic view of a complex matter, but also a feeling of the human touch given to it by Prof. Ferro. Adriana Saccone February 2007

Preface This book is an attempt to give an introductory account of the intermetallic chemistry of the elements for both undergraduate and graduate students. Intermetallic chemistry is strictly related to, or even a part of, both inorganic chemistry and solid-state physics. These subjects are dealt with and discussed in depth in a number of treatises. We have therefore decided to give pride of place to specific chemical phenomena and to the factual, experimental basis of our theme. We are not aware, indeed, of any other book especially dedicated to these subjects. The decision to write this book arose as a consequence of our being involved, since the beginning of our activity at the University of Genoa, in intermetallic chemistry both as researchers and teachers. In this university, indeed, for 70 years or so, several research groups have been studying and continue to study various aspects of alloy physical chemistry, creating an environment in which the handling of metals is natural and spontaneous, and for which we are very grateful to all the colleagues who made it possible. The founder of this line of activity was Aldo Iandelli, and we wish, on this occasion, to express our thanks to him for his teaching and for having introduced us to various aspects (preparative, structural, etc.) of alloy and phase diagram sciences. R.F. would also like to express his gratitude in memory of the late Ostwald Kubaschewski, who encouraged him to consider experimental thermodynamics in the investigation of alloys and helped to insert him in a broad European scientific community. We are very much indebted to the Series Editor, Robert W. Cahn, for his patience, continuous encouragement and precious suggestions. The responsibility for any errors in the book is naturally ours. However, the prestige and competence of R.W. Cahn have been an important point of reference and guidance. His scientific contributions to Materials and Intermetallics Science, his teaching and organizing ability have established an authoritative scientific activity in which we are very proud to be involved. Riccardo Ferro Adriana Saccone (Dipartimento di Chimica Università di Genova)

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Chapter 1

Introductory Survey

1.1. A PRESENTATION OF THE BOOK AND REMARKS ON ITS CONTENTS

Intermetallic science has a long and interesting history. Several interrelated topics can be considered within this subject, both from a basic viewpoint and with a view to their potential for future applications. These topics are closely connected with, or even part of, other disciplines such as physics, chemistry, metallurgy, materials science and technology, engineering. Emphasis will be given in this book to the chemical aspects of this science, that is to the mutual reactivity of the metals, and to the formation and characteristics of intermetallic compounds. Intermetallic chemistry is closely connected to the subject matter of inorganic chemistry: several groups of substances, for instance, may be conveniently presented in the systematic descriptive sections of both subjects. There are, however, several distinctive features which justify separate specific treatment. We just underline here a few characteristics of intermetallic chemistry which, we believe, are peculiar to the domain of descriptive chemistry and to which special chapters are dedicated in this book. In first place the relevance of the phase equilibria aspects in the description of the alloying behaviour of the elements (that is, of the mutual reactivity among metals) has to be underlined. It is typical indeed of many intermetallic systems to form several compounds (generally not obeying common simple stoichiometric rules), often homogeneous in a certain range of compositions. The stability and extension of these phases in terms of temperature and composition (that is their saturation limits or, in other words, their coexistence equilibria with other phases) are important points in their characterization and are given a convenient presentation and rational description through phase diagrams. The same diagrams are a useful tool in discussing preparation and purification methods (crystallization processes, solid-state synthesis, etc.). On the other hand, these phase diagrams are also a necessary reference point in the description of the conditions and processes which may result in the formation of alloys not in a true equilibrium state (metastable alloys, glassy (amorphous) alloys, quenching processes, etc.). A chapter about phase diagrams of alloy systems has therefore been included. It is not of course intended to fully discuss this subject and its theoretical basis and systematics: several chapters in various textbooks and specialized treatises are available on this matter. It is intended as a 1

2

Intermetallic Chemistry

presentation of the subject through a collection of examples and a presentation of some typical aspects of alloying behaviour mainly concerning the mutual reactivity of the metals involved. This behaviour may result in the formation of more or less extensive (terminal and/or intermediate) solid solutions, of stoichiometric intermetallic compounds, etc. An indication is given of the regularity that we notice when comparing the appearance of a specific phase diagram type with the position in the Periodic Table of the elements involved. A short description of some effects of transformation rate is included in the same chapter. Finally we draw attention to the fact that problems concerning phase diagram determination, assessment and thermodynamic optimization have a rapidly increasing relevance in several fields of materials science and especially in intermetallic chemistry. A few notes and references to these points conclude this chapter. Another characteristic point is the special attention that in intermetallic science, as in several fields of chemistry, needs to be dedicated to the structural aspects and to the description of the phases. The structure of intermetallic alloys in their different states, liquid, amorphous (glassy), quasi-crystalline and fully, three-dimensionally (3D) periodic crystalline are closely related to the different properties shown by these substances. Two chapters are therefore dedicated to selected aspects of intermetallic structural chemistry. Particular attention is dedicated to the solid state, in which a very large variety of properties and structures can be found. Solid intermetallic phases, generally non-molecular by nature, are characterized by their 3D crystal (or quasicrystal) structure. A great many crystal structures (often complex or very complex) have been elucidated, and intermetallic crystallochemistry is a fundamental topic of reference. A great number of papers have been published containing results obtained by powder and single crystal X-ray diffractometry and by neutron and electron diffraction methods. A characteristic nomenclature and several symbols and representations have been developed for the description, classification and identification of these phases. In one chapter (Chapter 3) general definitions are included, general structural characteristics of intermetallic phases are presented and some of their features discussed. Attention is given to nomenclature and to alternative and complementary methods of presenting crystal–chemical data, which could be especially useful in underlining peculiar structural features. Concepts such as coordination and linkage type and dimensionality of the structure (3D network, 2D layers or slabs, 1D fibres or individual molecules or atoms) are presented and discussed together with different criteria used in the description (analysis) of several groups of intermetallic structures. Examples are reported of structures described in terms of atomic layer stacking or of packing of atomic clusters or polyhedra or in terms of atomic environment types. It is also underlined that several intermetallic phases are known which have the same (or a similar) stoichiometry and crystallize in the same structure type,

Introductory Survey

3

which is generally named after the formula of the first representative identified: the ‘prototype’. A brief account, moreover, is given of such fundamental concepts such as derivative and degenerate structures (and superstructures), modular aspects of crystal structures (recombination structures) and a short description of a few special groups of alloys (quasicrystals, amorphous alloys). In another chapter concerning the intermetallic crystallochemistry (Chapter 7), a number of selected structural prototypes are described presenting some of their typical features and commenting on their distribution among different types of alloys. Attention is especially given to relationships between different prototype structures, and examples of their possible grouping in structural ‘families’ are underlined. This chapter, therefore, could possibly be used as a first draft of a gazetteer of intermetallic structure types and could be considered as an introduction (partial and provisional indeed!) to the descriptive systematics of intermetallic crystal chemistry. Another chapter (Chapter 4) is entitled ‘Intermetallic reactivity trends in the Periodic Table’. The Periodic Table, indeed (or Periodic Law or Periodic System of Chemical Elements), is acknowledged to play an indispensable role in several different sciences. Especially in inorganic chemistry it represents a fundamental classificatory scheme and a means of systematizing data with a clear predictive power. Inorganic chemists have traditionally made considerable use of the Periodic Table to understand the chemistry of the different elements. With a few exceptions (as detailed in the same chapter), metallurgists and intermetallic chemists have made little use of this Table to understand and describe the properties of metals and alloys: we believe, however, that it may be a useful tool also in the systematics of descriptive intermetallic chemistry (as exemplified in the subsequent chapter (Chapter 5)). In several paragraphs of Chapter 4, therefore, different aspects of the Periodic Table and of its characteristic trends are summarized. Attention is especially given to a few selected elemental parameters (and to their changes along the Table) which may act as reference factors in the definition and classification of the intermetallic behaviour, that is in the determination of phase structures, phase equilibria, etc. in the various alloys. To illustrate these points a number of graphs, ‘stability maps’ and ‘correlation diagrams’ have been used. Parameters such as ‘atomic dimension’ or ‘electronegativity’ have been considered. Especially relevant parameters, however, strictly related to the structure and layout of the Periodic Table are represented by electron configuration, valence electron number, group number, etc. of the different elements. Some attention is consequently given to these concepts. As an example the relationships between crystal structure and the number of valence electrons per atom (or per formula) in various classes of compounds (or solid solution phases) observed by Hume-Rothery, Brewer, Parthé, Zintl, Mingos, Hoffmann are considered. These rules, which may also serve as an introduction to a theoretical treatment of bonding, represent one of the criteria used in the

4

Intermetallic Chemistry

description and classification of some ‘families’ of intermetallic compounds. It will often be noticed, however, that in a certain family several compounds may be grouped, having for instance similar crystallographic features, but showing different properties and bonding mechanisms (we could say with different ‘percentages’ of a metallic or ionic–covalent character). A connection therefore between intermetallic chemistry and other sections of inorganic chemistry becomes evident. To this end the particular role played by the Zintl phases and ‘cluster’ chemistry is underlined. The alloying behaviour systematics of intermetallic systems is then discussed in a special chapter (Chapter 5), presenting a description of the intermetallic reactivity of each element, or group of elements, in the order of their position in the Periodic Table. It was not possible, of course, to give a complete treatment for all the elements; some particular aspects have therefore been selected together with information about general trends. An aspect of the alloying behaviour which may be considered relevant for each pair of metallic elements is their capability to form intermediate phases (intermetallic compounds); schemes (maps) giving summaries of this capability have been prepared for different elements and collected in Chapter 5. The trends of these maps, observed on passing through the different families of metals, and of similar diagrams concerning the mutual solubility in the liquid and solid states have been discussed. Owing to the complexity of an in-depth description of the intermetallic chemistry of all the groups of elements, generally only the simplest combinations (the binary ones) have been described in some detail. Nevertheless, without any claim to completeness, a few indications have also been presented about some families of more complex alloys (ternary or multi-component systems and compounds). These are especially intended to give at least a rough idea of the richness and variety of a disciplinary approach by no means as yet fully investigated and exploited. In the same chapter (Chapter 5), as an introduction to the paragraphs dedicated to the various groups of metals, the values relevant to a number of elementary properties have been collected. These are atomic properties (such as metallic and ionic radii, ionization energies, electronegativities, Mendeleev number, chemical scale, Miedema parameters, etc.), crystal structure and lattice parameters data of the allotropes of the elements, and selected thermodynamic data (melting and boiling temperatures and enthalpies, etc.). All these data indeed represent reference values in the discussion of the alloying behaviour of the elements. A chapter dedicated to the laboratory (small scale) preparation methods of intermetallics has then been included (Chapter 6). In the preparation of intermetallic phases, indeed (or, more generally, of alloys), in comparison to other chemical compounds a number of interesting and significant peculiarities are pointed out, for instance, those related to their high melting points, insolubility in many common solvents, etc. The presentation of selected examples of preparative methods, therefore,

Introductory Survey

5

can be useful for discussing some general points on the reactivity and chemical properties of metals and alloys. In a number of cases special references must be made to the phase diagram characteristics of the alloys involved and to considerations based on kinetic principles. Examples of the effects of different heat treatments are considered and mention is made of the preparation of metastable alloys, glassy alloys, etc. As a conclusion to this introductory survey we underline a few points which are probably already clear for the reader. Intermetallic science includes so many topics and is related to so many fundamental and applied problems that a different content selection and sequence could be easily envisaged for a book on this subject. We hope that the reader, who of course is forced to accept the book structure we adopted, will be at least partially helped by the lists of general cross-references and reading suggestions that we have inserted.

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Chapter 2

Phase Diagrams in Alloy Systems

2.1. PRELIMINARY REMARKS

In the field of inorganic chemistry an important group of substances and transformations is represented by the intermetallic compounds (or phases) and by the reactions among metallic elements. As for many other materials, phase diagrams are roadmaps not only for the description of these substances and of their reactions, but also for their processing and for research and development planning. The systematic experimental determination of phase diagrams, their assessment and compilation and their thermodynamic optimization and calculation are the essential steps in the development of materials science and make up one of the bases of the intermetallic disciplines. A few general and introductory remarks about these topics will follow, discussing the aspects of typical (binary and more complex) phase diagrams. As pointed out for instance by Pelton (1991), many thermodynamic variables may be used and plotted on phase diagrams to show equilibrium states: on this basis he presented and discussed general rules for classifying phase diagrams. It is well known that in material science and metallurgy the diagrams based on plots of temperature vs. composition (T vs. x) are commonly used. By using these diagrams it is possible to summarize and explain many aspects of the alloying behaviour of mixtures of two, three or more metals. A short collection of (T/x) phase diagrams of binary intermetallic systems, generally taken from the well-known Massalski et al. (1990) and Okamoto (2000) compilations, will be described here in order to present the types of mutual reactivity in such systems. Characteristic types of phase diagrams will be discussed and a preliminary indication will be given of their occurrence in the alloys of different metal groups. On this basis it will be feasible to establish a starting point for a possible classification of the different alloys. In particular, mainly by using special maps (Pettifor maps), a summary will be given of the diagram types formed by the different pairs of metals. Of course it will be impossible, in a few pages, to give a complete description of phase diagram science, and only an outline of some noteworthy aspects will be presented. Notice that the phase diagrams presented first are equilibrium diagrams. These represent an important reference point and describe the final state (stable state) which can be reached in a reaction of the substances involved. Slow (or very 7

8

Intermetallic Chemistry

slow) establishment of the equilibrium state can however be observed in several circumstances, resulting often in non-equilibrium phase transformations and also giving rise to real diagrams showing deviations from the equilibrium diagrams (see § 2.3.3). 2.2. SOME CHARACTERISTIC, T VS. x, BINARY PHASE DIAGRAMS

The diagrams that will be mainly considered are those concerning the behaviour of the alloys in the liquid and solid states; that is, melting and solid-state transformation diagrams. A number of different diagram types can be defined and classified on the basis of the different mutual solubility of the components (in the liquid and in the solid state with the formation of more or less extended liquid and/or solid solutions) and of their reactivity, resulting in the formation of various, so-called ‘intermediate phases’. 2.2.1 Mutual solid solubility of the component metals in alloy systems The systems V–Mo and Cs–Rb presented in Fig. 2.1 are a first example of phase diagrams. The first system concerns refractory (high melting) alloys, the second one very low melting (close to room temperature) alloys. However, both diagrams are representative of the melting behaviour of binary systems in which the two components are mutually and completely (in all proportions) soluble with each other in the liquid and in the solid state. The composition/temperature field is subdivided into three regions, as for instance in Fig. 2.1(a), at low temperature there is a single phase field (S) where all the temperature and composition values are collected for which only one solid phase is stable (a continuous solid solution field between Mo and V). In a similar way, another single-phase field (L) exists at high temperature: the two components show, indeed, a mutual complete solubility in the liquid state also. For intermediate temperatures there is a third region corresponding to a twophase field (coexistence of the solid and liquid phases): this defines for each composition the temperature range in which one phase transforms into the other. A similar aspect (complete solubility both in the liquid and in the solid state) is shown by the system Cs–Rb, for which however, owing to a larger deviation from the ‘ideal solution’ behaviour, a different trend of the melting temperatures can be noticed (see Fig. 2.1(b): in this case the melting temperatures decrease down to a minimum by adding one component to the other). Also in this case, at higher temperatures, a continuous single-phase field is present from one component to the other, corresponding to the liquid phase, as well as complete solid solubility at

9

Phase Diagrams in Alloy Systems (b) 2623

Temperature (°C)

Temperature (°C)

(a)

2500 L 2300 S

2100 1910

20

40

60

40 L

28.39 20

S

10

80

V

39.48

20 Mo

40

60

Cs

80 Rb

at.%

at.%

Temperature (°C)

(c) 842

L

769 700

β

547 443

400 300

α 20

40

60

Sr

80 Ca

at.%

Figure 2.1. Examples of melting phase diagrams of binary systems showing complete mutual solubility in the solid and in the liquid states (L liquid field, S solid field). The melting behaviour of the Mo–V, Cs–Rb and Ca–Sr alloys is presented. Notice the different ranges of temperature involved. The melting points of the pure metal components are shown on the corresponding vertical axes. The Cs–Rb is an example of a system showing a minimum in the melting temperature. In the Sr–Ca system complete mutual solid solubility is shown in both the allotropic forms α and β of the two metals.

lower temperatures. For intermediate temperatures, depending on the concentration, the two-phase region of coexistence (transformation) of the two phases (melting of the alloys) can be seen. Notice that according to a commonly employed nomenclature, the curve limiting the liquid field is called the liquidus. Similarly the other curve is called the solidus. Fig. 2.1(c) shows a similar, but slightly more complex diagram. It is the diagram of the alloys formed by Ca and Sr: these metals are completely soluble in the liquid state and crystallize in a solid phase forming a solution in the complete range of compositions. These two elements, however, besides being mutually completely soluble in their high-temperature forms (βCa and βSr), dissolve together completely in their low-temperature modifications also (see the structural data of the

10

Intermetallic Chemistry

elements in Chapter 5). In the diagram, therefore, we have in this case the region corresponding to the continuous liquid solution and two regions corresponding to the two solid, α and β, solutions. Between the mentioned single-phase fields, the two two-phase fields (very narrow in this case) correspond to the liquid–solid (β) equilibrium and, respectively, to the solid-state α–β transformation. 2.2.1.1 Mutual solid-state solubility: a simple structural representation – order/ disorder. In a number of systems such as the previously described V–Mo and Cs–Rb, continuous solid solutions are formed in the whole range of compositions, characteristics and structures of which will be discussed in more detail in Chapter 3. These result from two metals having the same crystal structure, which is maintained for all the intermediate compositions, due to a continuous random substitution of the atoms of one kind for another and vice versa. Fig. 2.2 gives a schematic two-dimensional (2D) representation of this random substitution. In Fig. 2.2(a) and (b) two ‘substances’ are presented, formed by white and black atoms, having however the same structure (the same arrangement of the atoms). In Fig 2.2(c) and (d) the same structure, in which, however about 20% and 50% respectively of white atoms have been replaced by black ones, can be seen. An equivalent representation is given in Fig. 2.2(e) and (f) in which the random distribution of the two species in all the positions is simulated by the intensity of the

(a)

(c)

(e)

(b)

(d)

(f)

Figure 2.2. 2D models of crystalline metals.

Phase Diagrams in Alloy Systems

11

colour (intermediate between those of the pure elements) assigned to the ‘atoms’. All the discs are equivalent: each one corresponds to the same probability (20%, 50%, etc.) of being black or white. This random distribution can be related to the possibility of gradually changing the overall composition while maintaining the same structure. Therefore, in this case, it is possible to find a continuous solid solution, ranging from 0% to 100% B (in all the intermediate alloys there is equivalence of all the atomic sites whose average occupation gradually changes from pure A to pure B). This generally corresponds to the fact that both A and B have the same crystal structure, which is maintained along the complete composition range, and similar values of the atomic radii (for instance 134.6 and 140.0 pm in the specific case of V and Mo, both bodycentred cubic) and of the Mendeleev number (54 for V, 56 for Mo), etc., so that they can play a similar role inside the structure and substitute each other. The simple structural models built by collections of discs can also be useful for the description of other frequently found behaviour: Fig. 2.3(a) and (b) present cases in which we still have substitution of the two atoms but in an ordered way, causing in Fig. 2.3(a) the formation of atomic ‘clusters’ and in Fig. 2.3(b) the formation of a new substance (a ‘solid compound’) of a well-defined composition and not of a phase field having a continuously changing composition. In Fig. 2.4, finally, different types of solid solutions (and intermediate phases) are modelled. The solid, metallic, structure of an element A is simulated in Fig. 2.4(a), while the molecular (diatomic) structure of a non-metal B in the gas phase is given in Fig. 2.4(b). The interstitial (ordered and disordered) introduction of the small atoms B in the interstices of the structure of element A is indicated in Fig. 2.4(c) and (d). 2.2.1.2 Trends in mutual solid solubility. On the basis of the similarities generally shown by the elements involved in the formation of continuous (substitutional) (a)

(b)

Figure 2.3. Schemes of ordered substitutions. (a) Model of cluster formation. (b) Ordered distribution of the two types of atoms.

12

Intermetallic Chemistry (a)

(b)

(c)

(d)

Figure 2.4. Interstitial formation of a solid phase. The dissolution in the interstices of the structures of the metal (a) of the atoms of the gas (b) gives a solid solution (c) or an ordered phase (d).

solid solutions, it is possible to identify the element pairs which form phase diagrams such as those shown in Fig. 2.1. The map shown in Fig. 2.8, where the elements are ordered according to their ‘Mendeleev number’, summarizes this behaviour by means of codes. All the element pairs forming simple phase diagrams are represented by square boxes. Emphasis has been given in this map to the metal combinations showing complete mutual solid solubility (black boxes). Notice that these pairs crowd around the diagonal line where elements, having similar element parameter values, combine with each other. For the meaning of the Mendeleev number, see § 2.2.1.3. 2.2.1.3 Electronegativity, Mendeleev number, Miedema parameters. A few semi-empirical ‘parameters’ and ‘scales’ which are useful as reference data in the systematic description (or even prediction) of the alloying behaviour of the different metals will be presented here also as an introduction to the following paragraphs. The closely related basic concepts of chemical periodicity and electron configurations will be reminded in Chapter 4. Electronegativity and the so-called Mendeleev number are two parameters, basically empirical at least in their initial definitions, which, however, proved to be very

Phase Diagrams in Alloy Systems

13

useful for simple classifications of the chemical behaviour of the elements, for a preliminary evaluation of bond energies, etc. The definition of electronegativity dates back to 1932 to an analysis carried out by Pauling of the energies of covalent–ionic bonds. More recent was the proposal by Pettifor (1984) of the introduction of a ‘chemical scale’ of the elements based on a new parameter, the Mendeleev number, which is useful, mainly in intermetallic chemistry, in the systematic description of the structures of compounds and of the types of phase diagrams adopted by the different metals. The Miedema’s parameters and the Miedema model and formula proved to be useful in an approximate evaluation of the formation enthalpy of alloys, in the estimate of the formation capability of intermetallic compounds, etc. 2.2.1.3.1 Electronegativity. Electronegativity was first defined by Pauling (1932) who also suggested a method for its determination. In the words of Pauling himself (Pauling 1967) it may be pointed out that the values of the difference Δ between the energy D(A–B) of the bond between two atoms A and B and the energy expected for a normal covalent bond, assumed to be the arithmetic mean of the bond energies D(A–A) and D(B–B) increases as the two atoms A and B become more and more unlike with respect to the qualitative property that chemists call electronegativity, the power of an atom in a molecule to attract electrons to itself. Thus Δ increases rapidly in the sequence HI, HBr, HCl, HF in which the halogen changes from iodine, which is recognized by its general chemical properties to be only a little more electronegative than hydrogen, to fluorine, the most electronegative of all the elements. Pauling found that the bond energy, in kcal/mol, for a bond A–B is given approximately by the equation: Δ D(A–B) 1⁄2 [D(A–A) (B–B)] 23(ηA ηB)2 (It would be 96.49 (ηA ηB)2 in kJ/mol) In this equation ηA and ηB are values of electronegativity assigned to atoms A and B. In the original formulation of the electronegativity scale, the electron volt was used as the unit of energy: this use accounts for the approximate factor 23 in the equation. (1 eV 1.60217653(14) 1019 J, Avogadro number 6.0221415(10) 1023 mol1). On the basis of this equation, systematically considering all the available thermochemical data and arbitrarily assigning to the most electronegative element, fluorine, a value of about 4, Pauling was able to prepare a complete electronegativity scale. This is shown in Table 2.1. Several definitions of electronegativity have since been proposed and various methods for its evaluation suggested. A reliable compilation extensively used in discussing metallurgical behaviour is that by Teatum et al. (1968).

14

Intermetallic Chemistry

Table 2.1. The electronegative scale as reported by Pauling (1967). H 2.1 Li Be 1.0 1.5

B 2.0

C 2.5

N O 3.0 3.5

F 4.0

Na Mg Al 0.9 1.2 1.5

Si 1.8

P S 2.1 2.5

Cl 3.0

K Ca 0.8 1.0

Sc 1.3

Ti V Cr 1.4 1.6 1.6

Mn 1.5

Fe Co 1.8 1.8

Ni Cu Zn Ga Ge 1.8 1.9 1.6 1.6 1.8

As Se 2.0 2.4

Br 2.8

Rb Sr 0.8 1.0

Y 1.2

Zr Nb Mo Tc 1.4 1.6 1.8 1.9

Ru Rh 2.2 2.2

Pd Ag Cd In Sn 2.2 1.9 1.7 1.7 1.8

Sb Te 1.9 2.1

I 2.5

Cs Ba 0.7 0.9

La–Lu Hf Ta W 1.1–1.2 1.3 1.5 1.7

Re 1.9

Os Ir 2.2 2.2

Pt Au Hg Tl Pb 2.2 2.4 1.9 1.8 1.8

Bi Po 1.9 2.0

At 2.2

Fr Ra 0.7 0.9

Ac 1.1

Np–No 1.3

Th Pa U 1.3 1.5 1.7

2.2.1.3.2 The Mendeleev number and a ‘scale’ for ordering the chemical behaviour of the elements. In order to stress the chemical character of the elements and to simplify the description of their behaviour, Pettifor (1984, 1985, 1986) created a new chemical scale (χ) which orders the elements along a simple axis. The progressive order number of the elements in this scale (the so-called Mendeleev number) may also be considered. The Mendeleev numbers M (which, of course, are different from the atomic numbers) start, according to Pettifor, with the least electronegative elements He 1, Ne 2, … and end with the most electronegative ones … N 100, O 101, F 102 up to H 103. The Mendeleev number (M) and the correlated ‘chemical scale χ’ are shown in Table 2.2. The chemical meaning of these parameters may be deduced not only by their relation to the Periodic Table. By using them, in fact, excellent separation of similar structures is achieved for numerous AmBn phases with a given stoichiometry within single 2D MA/MB maps (see Fig. 2.5). The same parameters are also very useful for a systematic presentation of some general trends in the alloying behaviour (see the maps shown in Figs. 2.8, 2.22 and 2.23). Notice, however, that in more recent papers, on the basis of a progressive improvement of the structure maps, slightly different versions of the chemical scale were reported without however any substantial modification to its meaning and application. On the basis of the Pettifor scale, the suggestion has also been made that in the formulae of the compounds the element E with a lower value ME (or χE) is quoted first. This will generally be adopted here (see § 3.5).

15

Phase Diagrams in Alloy Systems Table 2.2. Chemical order of the elements, according to Pettifor (1986). (a) Mendeleev number of the elements arranged in alphabetical order Ac 48 Ag 71 Al 80 Am 42 Ar 3 As 89 At 96 Au 70 B 86 Ba 14 Be 77 Bi 87

Bk 40 Br 98 C 95 Ca 16 Cd 75 Ce 32 Cf 39 Cl 99 Cm 41 Co 64 Cr 57 Cs 8

Cu 72 Dy 24 Er 22 Es 38 Eu 18 F 102 Fe 61 Fm 37 Fr 7 Ga 81 Gd 27 Ge 84

H 103 He 1 Hf 50 Hg 74 Ho 23 I 97 In 79 Ir 66 K 10 Kr 4 La 33 Li 12

Lr 34 Lu 20 Md 36 Mg 73 Mn 60 Mo 56 N 100 Na 11 Nb 53 Nd 30 Ne 2 Ni 67

No 35 Np 44 O 101 Os 63 P 90 Pa 46 Pb 82 Pd 69 Pm 29 Po 91 Pr 31 Pt 68

Pu 43 Ra 13 Rb 9 Re 58 Rh 65 Rn 6 Ru 62 S 94 Sb 88 Sc 19 Se 93 Si 85

Sm 28 Sn 83 Sr 15 Ta 52 Tb 26 Tc 59 Te 92 Th 47 Ti 51 Tl 78 Tm 21 U 45

V 54 W 55 Xe 5 Y 25 Yb 17 Zn 76 Zr 49

(b) The elements (El) arranged in the Mendeleev number (M) order and related chemical scale χ M

El

χ

M

El

χ

M

El

χ

M

El

χ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

He Ne Ar Kr Xe Rn Fr Cs Rb K Na Li Ra Ba Sr Ca Yb Eu Sc Lu Tm Er Ho Dy Y Tb

0.00 0.04 0.08 0.12 0.16 0.20 0.23 0.25 0.30 0.35 0.40 0.45 0.48 0.50 0.55 0.60 0.645 0.655 0.66 0.67 0.675 0.6775 0.68 0.6825 0.685 0.6875

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

Gd Sm Pm Nd Pr Ce La Lw No Md Fm Es Cf Bk Cm Am Pu Np U Pa Th Ac Zr Hf Ti Ta

0.69 0.6925 0.695 0.6975 0.70 0.7025 0.705 0.7075 0.71 0.725 0.715 0.7175 0.72 0.7225 0.725 0.7275 0.73 0.7325 0.735 0.7375 0.74 0.7425 0.76 0.775 0.79 0.82

53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78

Nb V W Mo Cr Re Tc Mn Fe Ru Os Co Rh Ir Ni Pt Pd Au Ag Cu Mg Hg Cd Zn Be Tl

0.83 0.84 0.88 0.885 0.89 0.935 0.94 0.945 0.99 0.995 1.00 1.04 1.05 1.06 1.09 1.105 1.12 1.16 1.18 1.20 1.28 1.32 1.36 1.44 1.50 1.56

79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103

In Al Ga Pb Sn Ge Si B Bi Sb As P Po Te Se S C At I Br Cl N O F H

1.60 1.66 1.68 1.80 1.84 1.90 1.94 2.00 2.04 2.08 2.16 2.18 2.28 2.32 2.40 2.44 2.50 2.52 2.56 2.64 2.70 3.00 3.50 4.00 5.00

16

Intermetallic Chemistry

Figure 2.5. Simplified version of Pettifor’s map for AB compounds. The component elements are arranged along the axes according to their Mendeleev number (M). As an example, the existence regions of the NaCl, CsCl and cubic ZnS type phases are evidenced.

2.2.1.3.3 Miedema’s model and parameters and ‘prediction’ of compound formation capability. A semi-empirical approach to the evaluation of the compound formation capability and of the heats of formation of alloys was proposed by Miedema and co-workers. This resulted in a model which became very popular and, especially because there was scarcity of experimental data, was frequently used in the evaluation, even if approximate and several times incorrect, of the formation enthalpies. The model suggested for energy effects in alloys is well known: essentially it is based on the definition of two parameters. By assigning two coordinates

17

Phase Diagrams in Alloy Systems 7

Work function of the elements

6

5

4

3

2 Non-transition element Transition element 1 0

1

2

3

Electronegativity (Pauling scale)

Figure 2.6. The approximate linear relationship between Φ* (Miedema 1973) and the electronegativity η (Pauling scale) as illustrated by de Boer et al. (1988).

(ϕ and nWS, to be defined below) to each transition element it was possible to build a map in which a clear separation was observed between all those binary alloys with positive heats of formation and those with negative values (Miedema 1973). Successive steps in the formulation of the model have been described, for instance, by Niessen et al. (1983) and by de Boer et al. (1988). The enthalpy of formation of solid and liquid binary alloys was described as proportional to the expression: f [P(ΔΦ*)2 Q(ΔnWS1/3 ) 2 R] where f is a concentration (and molar volumes) dependent function, ΔΦ* Φ*A Φ *B where Φ*i is the work function of each element, closely related to its electronegativity (see Fig. 2.6) (the values initially tabulated by Miedema, however, have been slightly readjusted by amounts comparable to the experimental uncertainty of work function values), nWS is the electron density at the boundary of the Wigner–Seitz cell for each element. P, Q and R are constants for specific groups of elements (their values are related to the position in the Periodic Table of the

Table 2.3. Miedema model. The values of the model parameters Φ*, nws1/3 and V 2/3. H 5.20 1.50 1.42 Li 2.85 0.98 5.53

El Φ* n ws1/3 V 2/3

Be 5.05 1.67 2.88

Na 2.70 Mg 3.45 0.82 1.17 8.27 5.81 K 2.25 0.65 12.77

Ca 2.55 0.91 8.82

Al 4.20 1.39 4.64

Si 4.70 1.50 4.20

P 5.55 1.65 4.15

S

Ga 4.10 Ge 4.55 1.31 1.37 5.19 4.60

As 4.80 1.44 5.20

Se

Cr 4.65 1.73 3.74

Rb 2.10 Sr 2.40 0.60 0.84 14.65 10.48

Y 3.20 1.21 7.34

Zr 3.45 1.41 5.81

Nb 4.05 1.64 4.89

Mo 4.65 Tc 5.30 1.77 1.81 4.45 4.21

Ru 5.40 Rh 5.40 Pd 5.45 1.83 1.76 1.67 4.06 4.10 4.29

Ag 4.35 Cd 4.05 1.36 1.24 4.72 5.53

In 3.90 1.17 6.28

Sn 4.15 1.24 6.43

Sb 4.40 1.26 6.60

Te

Cs 1.95 0.55 16.86

La 3.17 1.18 7.98

Hf 3.60 1.45 5.65

Ta 4.05 1.63 4.89

W 4.80 1.81 4.50

Os 5.40 Ir 5.55 1.85 1.83 4.15 4.17

Au 5.15 Hg 4.20 1.57 1.24 4.70 5.83

Tl 3.90 1.12 6.67

Pb 4.10 1.15 6.94

Bi 4.15 1.16 7.20

Po

Ce3 3.18 Pr 3.19 Nd 3.19 Pm 3.19 Sm 3.20 1.19 1.20 1.20 1.21 1.21 7.76 7.56 7.51 7.43 7.37 Th 3.30 1.28 7.32

Pa 3.60

U 3.90 Np 3.85 Pu 3.80 1.51 1.44 5.57 5.26

Zn 4.10 1.32 4.38

O

V 4.25 1.64 4.12

Pt 5.65 1.78 4.36

Cu 4.45 1.47 3.70

N 6.86 1.65 2.56

Ti 3.80 1.52 4.82

Re 5.20 1.85 4.28

Co 5.10 Ni 5.20 1.75 1.75 3.55 3.52

C 6.24 1.77 2.20

Sc 3.25 1.27 6.09

Ba 2.32 0.81 11.32

Mn 4.45 Fe 4.93 1.61 1.77 3.78 3.69

B 5.30 1.75 2.80

Eu3 3.20 Gd 3.20 Tb 3.21 Dy 3.21 Ho 3.22 Er 3.22 1.21 1.21 1.22 1.22 1.22 1.23 7.36 7.34 7.20 7.12 7.06 6.98

Tm 3.22 Yb3 3.22 Lu 3.22 1.23 1.23 1.24 6.90 6.86 6.81

Ce4 3.25 1.34 6.36

Eu2 2.50 0.88 9.43

Yb2 2.58 0.92 8.52

19

Phase Diagrams in Alloy Systems Average number of intermediate phases ΔH 75 75 ΔH 40 40 ΔH 20 20 ΔH 10 10 ΔH 4 4 ΔH 0 0 ΔH 5 0

1

2

3

4

5

6

Figure 2.7. The relation, suggested by de Boer et al. (1988), between the average number of stable intermediate phases in a binary system and the formation enthalpy predicted for the equiatomic composition.

elements involved). In the same model (Miedema and Niessen 1982) the volume variation during the formation of the intermetallic compound is evaluated as proportional to (ΔΦ*)[(Δ(nWS)1]). Miedema’s parameters are collected in Table 2.3. The existence of an approximate relation between the average number of stable intermediate phases in a binary system and the calculated extreme values of the enthalpies of formation was also suggested (see Fig. 2.7). Although the way to predict formation enthalpies of alloys was introduced as an empirical one and several discrepancies may be noticed between calculated and measured values, it is important to observe that the model incorporates basic physics. A quantum-mechanical interpretation of Miedema’s parameters has already been proposed by Chelikowsky and Phillips (1978). Extensions of the model to complex alloy systems have been considered. As an interesting application we may mention the discussion on the stabilities of ternary compounds presented by de Boer et al. (1988). In the case of the Heusler-type alloys XY2Z, for instance, the stability conditions with respect to mechanical mixtures of the same nominal composition (XY2Z, XY2Z, XYYZ, etc.) have been systematically examined and presented by means of diagrams. The Miedema’s parameters, ΔΦ*, Δn WS1/3, moreover, have been used as variables for the construction of structural maps of intermetallic phases (Zunger 1981, Rajasekharan and Girgis 1983). According to Rajasekharan and Girgis on a ΔΦ*, Δn WS1/3 map, considerable resolution is obtained among the binary systems in which different structure types occur. The points corresponding to the systems in which the Laves phases (or the phases of types such as Cr3Si, TiAl3, etc.) occur show linear relationships on the

20

Intermetallic Chemistry

Figure 2.8. A map presenting the mutual solubility in the solid state of the different metals. A selection of the elements is ordered along the two axes according to their values of the Mendeleev number. Each square box identifies a metal pair. The meaning of the codes inserted in the boxes is explained by the diagrams on the right. Notice that the crowding of the metal pairs showing complete solid solubility is along the diagonal of the figure corresponding to close values of their Mendeleev numbers.

map. The good separation, moreover, between the line connecting the Cr3Si-type phase points and that of the Laves phase points, can be related to the almost total exclusion of the Cr3Si-type phases from the 250 binary systems containing Laves phases and that of the Laves phases from the 90, or so, binary systems in which a Cr3Si-type phase occurs.

21

Phase Diagrams in Alloy Systems (b)

1100

1064.43

900 700 500 300 Ni

20

40

60

80

Temperature (°C)

Temperature (°C)

(a) 1455 1300

1769.0 1600 1400 1200 1000 800 600

Au

20

Pt

40

at.%

Au

(d) 842

800 727 600 500

443

400 300 20

40

60

at.%

80

Ca

Temperature (°C)

Temperature (°C)

80

at.%

(c)

Ba

60

0

Tc Ti

2

1 α A

3

β x2 4

x1

B

at.%

Figure 2.9. Examples of melting phase diagrams of binary systems showing complete mutual solubility in the liquid state and, at high temperature only, in the solid state. By lowering the temperature, however, the continuous solid solution decomposes into two phases. In (d) a schematic representation of NiAu or PtAu type diagrams is shown as formed by two generic components A and B.

As a conclusive comment to the Miedema model, especially with reference to the enthalpy evaluation, we have to underline that while it may be useful in order to define a reference behaviour, however, its approximate (in a way qualitative) character cannot be forgotten. A critical discussion on the application and limits of this model has been published for instance by Chen et al. (2004); see the comments on the thermochemistry of the Laves phases in § 3.9.3, see also a few more remarks on this subject in § 4.4.7.1. 2.2.1.4 Partial mutual solubility in the solid state. Fig. 2.9 shows different examples of binary systems for which there is still a complete miscibility in the liquid state, but only a limited mutual solubility in the solid state, depending on the temperature. The Ni–Au system, for instance, still has complete mutual solid solubility but only at high temperature, that is, by decreasing the temperature, de-mixing

22

Intermetallic Chemistry

into two different solid phases occurs from the homogeneous solid solution field in the whole composition range. Actual phase diagrams are presented in Fig. 2.9(a)–(c). A schematic representation of this behaviour for a generic A–B pair of metals is shown in Fig. 2.9(d). For a curve such as 3-1-0 (and/or 4-2-0) the name solvus is often used. At T Tc (Tc is the critical consolute temperature) it is possible through a single-phase field, by continuously changing the composition, to move from A to B, without cutting any equilibrium line. At lower temperature, for instance Ti, the single-phase alloys α phase (A-based solid solution of B in A) and β phase (B-based single-phase alloy) exist for x x1 and for x x2, respectively. For the intermediate compositions the equilibrium structure corresponds to heterogeneous alloys consisting in mechanical mixtures of two different solid phases: mutually saturated α phase (A-based) and β phase (B-based) having (at the Ti temperature) the x1 and x2 compositions, respectively. A few remarks about the decomposition mechanism will be found in § 2.3.3 and Fig. 2.38, where there are also a few notes about the so-called spinodal decomposition. A similar behaviour (complete mutual solubility in the liquid state and partial solubility in the solid state) is presented also by the Pt–Au and Ba–Ca systems (Fig. 2.9(b) and (c)). Notice in the Pt–Au diagram the closeness (mainly for compositions near 40 at.% Au) between the melting and the de-mixing equilibria. The Ba–Ca diagram has a different appearance because Ca (in its high-temperature form) and Ba are completely mutually soluble, while only a partial solid solubility is observed for Ba in the low-temperature modification of Ca.

2.2.2 Inter-crossing of two-phase equilibria The diagrams shown in Fig. 2.10 exemplify a slightly more complex behaviour (for the corresponding nomenclature see the following § 2.2.2.1). In these cases the demixing equilibria involving the solid solutions cross the melting equilibria. As a consequence, at a certain well-defined temperature a three-phase, invariant, equilibrium is established while, in the solid state, completely separated terminal phases (A-based and B-based solid solutions) are found (see for instance the Cubased and the Ag-based terminal solid solutions in the Cu–Ag system of Fig. 2.10(a)). In this system there is the eutectic solidification of a liquid (having 61.1 at.% Ag at 779°C) into two solid phases respectively Cu-rich (4.9 at.% Ag) and Agrich (85.9 at.% Ag). In the Ru–Ni system there is a peritectic transformation involving the liquid and the two, Ru-based and Ni-based, solid solutions; in Fig. 2.10(c) the peritectic transformation involves the liquid and two solid solutions: one based on the high-temperature form of Co and the other corresponding to the solution between Re and the low-temperature form of Co. In the system Ti–W the continuous solid solution stable at high temperature decomposes on lowering the temperature through a eutectic-type reaction into

23

Phase Diagrams in Alloy Systems (b) 2334

1084.87 1000

Temperature (°C)

Temperature (°C)

(a)

961.93

800 600 400

Cu

20

40

60

80

2000 1600

1455

1200 800

Ag

20

Ru

at.%

40

60

80

(c)

(d) 3422 Temperature (°C)

Temperature (°C)

3186 2500 2000 1495

1500 1000 500 Re

Ni

at.%

422 20

40

60

80

3000 2500 2000 1670 882

Co

20

Ti

at.%

40

60

80

W

at.%

Temperature (°C)

(e) 1855

1755 1600 1360 1000

863

600 200 Th

20

40

60

80

Zr

at.%

Figure 2.10. Examples of binary systems characterized by complete mutual solubility in the liquid state and, depending on temperature and/or composition, partial solubility in the solid state and presenting (in certain composition ranges) an invariant (three-phase) reaction (eutectic in the Cu–Ag, peritectic in the Ru–Ni and Re–Co and eutectoidal in Ti–W (one) and in Th–Zr (two)).

nearly pure Ti and a solid solution of Ti in W. In Fig. 2.10(e) (Th–Zr system) there are, in the solid state, two subsequent eutectic-type decomposition reactions of a solid solution into two solid phases. Notice that the name eutectoid is used for a three-phase eutectic-type reaction involving three solid phases.

24

Intermetallic Chemistry (b)

(a) Temperature (°C)

1414 1300 1064.43 900 700 500 300 Au

20

40 60 at.%

80

1900 1700 1500 1300 1135 900 776 668

Si

1863

U

20

40 60 at.%

80

Cr

Figure 2.11. The Au–Si diagram is an example of a simple eutectic system with complete mutual solubility in the liquid state and no (or negligible) solubility in the solid state; at a temperature of 363°C the liquid having the composition of 18.6 at.% Si solidifies with the simultaneous crystallization of the practically pure gold and silicon mechanically mixed. In the Cr–U system a slightly more complex situation due to the solid-state transformations of uranium is shown.

Extreme cases of solid solubility are shown in Fig. 2.11. In particular notice the system Au–Si for which, owing to a negligible solubility in the solid state, the terminal phases are practically coincident with the pure elements. Several pairs of elements show the behaviour exemplified by these figures. These have also been collected in the map of Fig. 2.8. 2.2.2.1 Phase rule, ‘Building Blocks’ in binary system diagrams, Invariant equilibria. Previously we made some remarks about specific features of the phase diagrams and the existence of ‘invariant’ equilibria, mainly referring to the diagrams of Fig. 2.10. A short summary of these items and of the relevant nomenclature is given here. To this aim a well-known starting point is the phase rule (Gibbs phase rule). (a) Phase rule, variance The phase rule is: VCP2 where V is the variance (the number of degrees of freedom) of the system, C is the number of the so-called ‘independent’ components (the minimum number of species needed to define the composition of all the phases of the system) and P is the number of phases in equilibrium. An explanation of this rule can be summarized as follows. The description of a thermodynamic system formed by C components present in P phases needs the specification of temperature, pressure and composition of all the P phases.

25

Phase Diagrams in Alloy Systems

1

a b

T

2

T

1

c

V at.% Mo a = liquid; b = liquid + solid; c = solid

V

Mo

at.%

1

a b

2

d

c e

T

1

i

h

Pt

2

T

f g

2

1

2

at.%

Ag

2

1

Pt

at.%

Ag

a = liquid; b = liquid + (Pt); c = (Pt); d = liquid + (Ag); e = (Pt) + (Ag); f = (Ag); g = (Pt) + Ag15Pt17; h = Ag15Pt17; i = (Ag) + Ag15Pt17

a

1 d

b

c

e T

f

l m Zr

h

1 T 2

g

n at.%

V

2

2

i

1 Zr

2

1

2

1

2

2 at.%

V

a = liquid; b = liquid + (βZr); c = liquid + (V); d = liquid + ZrV3; e = (βZr); f = (βZr) + ZrV3; g = (V) + ZrV3; h = ZrV3; i = (V); l = (βZr) + (αZr); m = (αZr); n = (αZr) + ZrV3 1 = single-phase fields;

2 = two-phase fields

Figure 2.12a. ‘Building blocks’ of binary phase diagrams: examples of single-phase (two-variant) and two-phase (mono-variant) fields. In the figure the indication is given of the phases existing in the various fields and respectively of their number. The phase equilibrium composition in the twophase fields is defined by the boundary (saturation) lines of the single-phase regions. (Pt), (Ag), (V, Mo), etc. are short symbols for indicating solid solution phases based on Pt, Ag, etc.

The composition of each phase is known when the concentrations of C 1 components in the phase have been defined. Thus, for all the phases, there are P(C 1) concentration variables. In principle, we have to add P values for the temperature of the different phases and P values of pressure to obtain the total number,

26

Intermetallic Chemistry The two-phase fields correspond to two types Transformation

Mixing–de-mixing

α α

T1

Ti

T2

Tm β

Tf

α′

x1

β′

α′ + α″

x 2′ x 1′

x 1′′ x 2′′

Figure 2.12b. ‘Building blocks’ of binary phase diagrams: examples of two-phase (mono-variant) reactions. On the left the transformation, on cooling, from the α phase to β is shown. For the composition x1 in equilibrium conditions the transformation starts at temperature Ti and ends at Tf. Notice that at an intermediate temperature as Tm only a partial transformation has been carried out: a certain quantity of α (having the composition corresponding to α ) will coexist with β ( of composition β ). On the right, the α phase undergoes, on cooling, a de-mixing in the two α and α phases having at temperature T1 the compositions x 1 and x1, at temperature T2 the compositions x 2, x2, etc.

P P P(C 1) P(C 1), of variables. For equilibrium conditions to exist, however, several relationships between the stated variables must occur. Each of the P phases must be at the same temperature and pressure so there are P 1 equalities of temperature and P 1 of pressure. As for the concentration, the C values of each component in each phase must be related to the corresponding C values in the other phases (technically this means the same activity of each component in all the phases): so C(P 1) relations are found. The total number of equilibrium conditions, therefore, is given by: (P 1) (P 1) C(P 1) (P 1)(C 2) The variance (V, degree of freedom) of the system is defined as the maximum number of variables which may be independently altered without disturbing the equilibrium state of the system. It is given by the difference between the total number of variables and the total number of equations among these variables defined by the equilibrium conditions. Therefore: V P(C 1) (P 1)(C 2) C P 2

27

Phase Diagrams in Alloy Systems The three-phase equilibria correspond to two types of reactions, represented by the following equations conventionally written in order to indicate (from left to right) the transformation occurring on cooling. α → ← β+γ

λ+ϕ→ ←χ

1st class equilibrium

2nd class equilibrium

α γ

β

ϕ

λ

χ

2

3

1

T Hf

at.%

Ru Zr

at.%

V

Three 1st class equilibria Two 1st class equilibria One 2nd class equilibria

Ca

at.%

Pb

Three 1st class equilibria Two 2nd class equilibria

Figure 2.13. ‘Building blocks’ of binary phase diagrams: examples of three-phase (invariant) reactions. In the upper part the general appearance, inside a phase diagram, of the two types of invariant equilibria is presented, that is, the so-called 1st class (or eutectic type) and the 2nd class (or peritectic type) equilibria. In the lower part the various invariant equilibria formed by selected binary alloys for well-defined values of temperature and composition are listed. In the Hf–Ru diagram, for instance, three 1st class equilibria may be observed, 1: (βHf) : (αHf) HfRu (eutectoid, three solid phases involved), 2: L : βHf HfRu (eutectic), 3: L : HfRu (Ru) (eutectic).

The reader interested in a more complete and rigorous demonstration of the Gibbs rule may consult for instance the books by Gokcen and Reddy (1996) or Hillert (1998) where a classification of the different systems (reacting, non-reacting, etc.) to which the rule can be applied is also presented. (b) Phase rule and the ‘building blocks’ in the T/x diagrams of binary systems. In the specific case of binary (C 2) systems, V 4 P. If, however, we consider systems at constant pressure (isobaric conditions), as is usual when studying solidification, melting processes, the number of variables decreases by one and the variance decreases to V C P 1, that is, for a two-component system, V 3 P.

28

Intermetallic Chemistry

As a consequence in a two-component phase diagram, at constant pressure, it is possible to have: – single-phase, bi-variant (P 1, V 2) fields; – two-phase, mono-variant equilibria (P 2, V 1); – three-phase, invariant (zero-variant) equilibria (P 3, V 0). Negative values of V will correspond to non-equilibrium systems. The aspects of these fields and equilibria are characteristic; they can be considered the fundamental ‘building blocks’ of each phase diagram (see Figs. 2.12(a) and 2.12(b) and 2.13). Each phase diagram, indeed, can be described as an assembly, subjected to well-defined rules, of a certain number of such blocks. 2.2.2.2 Solubility Diagrams: effects of atomic properties on mutual solubility. The effect on mutual solubility of the atomic properties of the components (and therefore of their relative positions on the map shown in Fig. 2.8) may be considered on the basis also of different diagrams. An introductory example to this subject is the well-known diagrams developed by Darken and Gurry (1953) for solid solution prediction. In such a diagram (as shown in Fig. 2.14) all elements may be included. The two coordinates represent the atomic size, generally the radius corresponding to the coordination number (CN) 12, and the electronegativity of the elements. The electronegativity, previously introduced in § 2.2.1.3, is a characteristic elemental parameter which may be used as a convenient chemical coordinate. In the original Darken and Gurry diagram (Fig. 2.14) the values proposed by Gordy (1946) were used. In order to classify the solid solubility of the different elements in a given metal, in the Darken and Gurry map, the region with the selected metal (Mg, for instance, in Fig. 2.14) in the centre is considered. Generally, elements having high solubility lie inside a small region around the selected metal. As a rule of thumb an ellipse is drawn in the diagram, with the selected metal in the centre, for instance with 0.3 electronegativity unit difference on one axis and 15% atomic radius difference on the other axis. For those elements for which there is a low or a negligible solubility, a larger region has to be considered. In the original chapter by Darken and Gurry a number of discrepancies between mapped and observed values were also discussed. For a review of the application of the Darken and Gurry method to predict solid solubility see Gschneidner Jr. (1980). An improvement of the method by means of simultaneous use of rules based on the electronic and crystal structures of the metals involved is also presented. Notice that, in a way, the Darken and Gurry diagram corresponds to a row, or to a column, of the map reported in Fig. 2.8.

29

Phase Diagrams in Alloy Systems

Au

3.0

0 –5 at.% 5 –10 at.% >10 at.%

Mu

Electronegativity

2.5

2.0

B

1.5

1.0

Cu Cr Mo As Ni V Ag Nb Sb Bi Fe Ge Sn Ti Zr Pb Be In Ga Al Ti Y La Zn Sc Mg Cd Ca Sr Hg Ba Na Li

0.5

100

150 200 Radius (CN 12) (pm)

Figure 2.14. Darken and Gurry diagram. In a map of the electronegativity vs. radius, the different metals are collected. For a selected metal (Mg in this example) a region corresponding to a range of 0.3 electronegativity units and 15% atomic radius difference is evidenced. The different symbols corresponding to a more or less large solubility in Mg are shown on the right of the figure.

In the general case a complex behaviour may be expected for the extension of the terminal solid solutions which, for a pair of metals M1, M2, also depends on the stoichiometry and stability of the M1 (or, respectively, M2) richest phase. However a certain regularity of the dependence of the mutual solid solubility on the position of the metals involved in the Periodic Table may be observed. This can be related to the so-called Hume-Rothery rules (1931): First rule: Effect of the size factor. If the atomic sizes of the two components differ more than 15%, extended solid solution formation is not expected. Second rule: Effect of the electrochemical nature. If the electrochemical characteristics of the two elements are similar, solid solution formation may be expected, otherwise compound formation is more probable. Third rule: Effect of the valence electrons. Generally a higher-valence metal is more soluble in a lower-valence metal than the contrary. A combination of the effects of the three factors should, of course, be considered in order to make reliable predictions. As for the third rule (about the valence-electron

30

Intermetallic Chemistry Metal Y 11

10

9

8

7

6

5

4

Cu Ag Au Ni Pd Pt Co Rh Ir Fe Rn Os Mn Tc Re Cr Mo W V Nb Ta Ti Zr Hf Ti

4

Zr Hf V

5

Nb Ta Cr

6

Mo W

Metal X

Mn

7

Tc Re Fe

8

Ru Os Co

9

Rh

Alloy X–Y Larger solid solubility in Y

Ir

10

Ni

Larger solid solubility in X

Pd

Similar solid solubility in X and Y

Pt

11

Cu

Negligible solid solublity

Ag

Complete mutual solid solubility (at least at HT)

Au

Figure 2.15. Relative extent of the mutual solid solubility in binary alloys of transition metals, ordered according to their group number in the Periodic Table. The group number is reported on the left and on the top of the figure.

factor) this has been discussed by Goodman et al. (1983) considering the trend summarized in a map such as that shown in Fig. 2.15. As for different concepts introduced by Hume-Rothery, see also § 4.4.5. 2.2.3 Trends in mutual liquid solubilities All the phase diagrams reported above show a complete mutual solubility in the liquid state. The formation of a single phase in the liquid state corresponds to behaviour frequently observed in intermetallic (binary and complex) systems. Examples, however, of a degree of immiscibility in the liquid state are also found in selected intermetallic systems. Fig. 2.16 shows a few binary systems in which such immiscibility can be observed (existence of miscibility gaps in the liquid state). All the three

31

Phase Diagrams in Alloy Systems

Temperature (°C)

(a)

(b) 1800

300 250 200 150 100

271.442 2L

600 29.7741 Ga

20

40 60 at.%

80

200

Bi

29.7741 Be

(c)

Temperature (°C)

2L

1400 1289 1000

20

40 60 at.%

80

Ga

(d) 2L

700 600 500 400 300 200 97.8

660.452

1200 1064.43 1000

2L 2L

800 600 400

221

200 Na

20

40 60 at.%

80

Al

Au

20

40 60 at.%

80

Se

Figure 2.16. The diagrams presented in this figure show certain ranges of de-mixing in the liquid state. We see in the Ga–Bi system a miscibility gap that, at the temperature of 222°C extends from 8.5 to 61.5 at.% Bi. A much larger region of existence of two liquids is observed in the Be–Ga system. In the Na–Al system finally the immiscibility region practically includes the whole composition range from 0% to 100%. In this case the two metals are completely insoluble in the liquid state (as well as in the solid state). The melting temperatures of the two metals (Na and Al in this example) are practically unaffected by the addition of the other component. The diagram consists of three superimposed two-phase fields corresponding to the coexistence of solid Na with solid Al, liquid Na with solid Al and liquid Na with liquid Al. For (d) see the text.

simple diagrams Ga–Bi, Be–Ga and Na–Al show practically negligible solid solubility and also immiscibility in the liquid state. The diagram Na–Al in Fig. 2.16(c) corresponds to extremely small solubilities: the solubility of Na in Al has been evaluated in less than 0.002 at.%, while that of Al in Na is practically zero. A summary of all the metal pairs showing partial or complete immiscibility in the liquid state is presented in the map of Fig. 2.17. In the same figure metal pairs giving solid–gas equilibria are also shown. The solid–gas equilibria are especially observed in systems in which there is a large difference in the boiling points of the components (see for instance the systems formed by the alkali metals with refractory metals such as Cr, Mo, V, etc.). Several groups of systems forming miscibility

32

Intermetallic Chemistry MB Rh Pa Li Be Tb Ga Si S U La P Pd Co Ca Zn Na Y Cu Cd Pt O Ge B As Se Ti V Cr Mn Os Al Tm Ce Np Sr K Ag Hg Sb Te Ac Hf Nb Mo Tc Ru Sm Pu Ni Ba Eu Lu Rb N In Sn Cs C Po Ra Yb Sc Au Mg Bi Tl Gd Am Ir Th Zr Ta W Re Fe Pb H C Po Bi

Te Sb

N Se As

O S P

B Si Ge Sn Ga Al In Tl Be Zn Cd Hg Mg Cu Ag Au Pd Pt Ni Ir Rh Co Os Ru Fe Mn Tc Re Cr Mo W V Nb Ta Ti MA Hf Zr Ac Th Pa U Np Pu Am La Ce Sm Gd Tb Y Tm Lu Sc Eu Yb Ca Sr Ba Ra Li Na K Rb Pb

(a)

(b)

L L1 L2

LG

L1 B

GA

T

AL

AB A

G

AB B

A

B

Figure 2.17. Liquid–liquid and solid–gas equilibria in intermetallic systems. In a map based on the so-called Mendeleev number coordinates the different binary combinations are represented. Only those combinations have been coded for which the existence of liquid miscibility gaps (or of solid–gas equilibria) is known. (In the same systems, other equilibria, the formation of compounds, etc. may be present). For many systems data are lacking: probably in the bottom-left corner of the figure many more boxes could be added to those representing miscibility gap. Notice that the solid–gas equilibria are relevant to systems formed by metals with a large difference between their boiling temperatures.

gaps can be noticed: such as many systems of the alkali metals and several systems given by the alkali-earth and rare-earth metals (see in the systematic part, in Chapter 5, the description of the interesting behaviour of ytterbium). Another group of systems showing a liquid miscibility gap is given by the combinations

Phase Diagrams in Alloy Systems

33

with several semi-metals or non-metals (see the right-hand side of the map). Among these systems there are a few characterized by the formation of two miscibility gaps (generally placed on the two sides of some intermediate compounds): these are generally sulphur or selenium systems such as Ag–S, Al–S, Au–Se, Co–Se, Cr–S, Cu–S, Cu–Se, Ga–S, Hg–S, Hg–Se, In–Se, K–S, Na–S, P–Sn, S–Sb, S–Sn, S–Tl, S–W, S–Zn, Se–Tl. In these systems three different liquid phases can be defined: two terminal phases which include as limit composition one of the components and one intermediate phase. This behaviour may be related to the change vs. the composition of the bond characteristics: covalent bond for the molecular element on one side of the system, metallic on the other side and ionic–covalent for the intermediate compounds. At high temperature we generally have the closure of the immiscibility and the continuous liquid solution. An example of this type of diagram is given in Fig. 2.16 (d). At high temperature the gold-rich and the selenium-rich liquid phases and around 50 at.% another liquid phase are highlighted. At low temperature the peritectic formation of AuSe can be noticed. These different bonds, at least up to a certain temperature, are maintained in the liquid state, which also favours de-mixing. The Te–S system is peculiar: it is a simple eutectic-type diagram and shows (like an island completely surrounded by the single-phase field of the liquid) a small ‘oval’ insolubility region situated between 37 and 41.5 at.% S and between two critical temperatures (upper Tc 740°C and lower Tc 690°C). This behaviour (often observed for instance in organic systems) among the different pairs of elements has been described only for Te–S. The diagrams of Fig. 2.16 may be considered examples of systems showing not only small (or very small) solubility in the solid state, but also a degree of insolubility in the liquid state (existence of miscibility gaps in the liquid state). The diagram shown in Fig. 2.16(c) corresponds to the extreme case where practically complete insolubility exists both in the solid and in the liquid state. 2.2.4 Formation of intermediate phases in alloy systems A different, more complex, alloying behaviour is illustrated in a number of figures (Figs. 2.18–2.21) where several examples of alloy diagrams are presented which are typically characterized by the formation, through a range of different mechanisms, of intermediate phases. In the field of solid-state chemistry an important group of substances is represented by the intermetallic compounds and phases. In binary and multicomponent metal systems, in fact, several crystalline phases (terminal and intermediate, stable and metastable) may occur. A few introductory remarks about these substances will be presented in relation to the mentioned figures. Simple schematic phase diagrams of binary alloy systems are shown in Fig. 2.18 in which the formation of one intermediate solid phase may be noticed. In these

34

Intermetallic Chemistry (b) 1064.43 1000

938.3

800 650

Mg

20

40 60 at.%

80

Temperature (°C)

Temperature (°C)

(a)

800

400

Ge

Au

20

40 60 at.%

80 Sb

(d) 1064.43

961.93

20

40 60 at.%

80

Temperature (°C)

Temperature (°C)

(c) 1769 1600 1400 1200 1000 800 600 Pt

630.755

600

800 600 400 271.442

200

Ag

Au

20

40 60 at.%

80

Bi

Temperature (°C)

(e) 1200 1000 800 600 400 Zn

20

40 60 at.%

80

Te

Figure 2.18. Examples of binary phase diagrams in each of which one stoichiometric phase is formed. In the Mg–Ge system we have the congruently melting Mg2Ge (33.3 at.% Ge); in Au–Sb, AuSb2 is formed through a peritectic reaction. In the Pt–Ag system one compound at 47 at.% Ag with stoichiometry Pt17Ag15 is formed via a solid state reaction (Pt) (Ag) : Pt17Ag15. In the Au–Bi system the compound Au2Bi is stable in a restricted range of temperature only: it is formed by a peritectic reaction (371°C) and, at a lower temperature (116°C), it is decomposed according to the eutectoidal reaction: Au2Bi : (Au) (Bi). In the Zn–Te system, finally, we have the congruently melting compound ZnTe. In this system a miscibility gap in the liquid state may also be noticed.

35

Phase Diagrams in Alloy Systems (b)

800 700 600 500 400 300

449.57

231.9681

Sn

20

40 60 at.%

80

Temperature (°C)

Temperature (°C)

(a) 2400 2231 2000 1743 1600 1400 1200 1000

Hf

Te

20

40 60 at.%

80

Ru

(d) 1910

1855 1600 1400 1200 1000 863 20

40 60 at.%

80

V

Temperature (°C)

Temperature (°C)

(c)

Zr

2334

3020 2600 2200 1910

1800 1400 1000 Ta

20

40 60 at.%

80

V

Figure 2.19. Examples of systems in which intermediate phases corresponding to small composition ranges are formed. These are SnTe (congruent melting), HfRu (congruent melting), ZrV2 (peritectic formation) and TaV2 (formed through a solid-state reaction).

diagrams we observe the formation of an intermediate phase, which generally crystallizes with a structure other than those of the constituent elements, and which has a negligible homogeneity range. Thermodynamically, the composition of any such phase is variable. In a number of cases, however, the possible variation in composition is very small. Invariant composition phases or stoichiometric phases, or ‘compounds’ proper, also called ‘point compounds’ in binary alloys, are represented by a point on the composition axis. In Fig. 2.19, on the contrary, we observe that intermediate solid phases with a variable composition are formed (non-stoichiometric phases). In the diagrams shown here we see therefore examples both of terminal and intermediate phases. (For instance, the Hf–Ru diagram shows the terminal solid solutions of Ru in α and βHf and of Hf in Ru and the intermediate compound containing about 50 at.% Ru). These phases are characterized by homogeneity ranges (solid solubility ranges), which, in the case of the terminal phases, include the pure components and which, generally, have a variable temperature-dependent extension.

36

Intermetallic Chemistry (b)

2400

Temperature (°C)

Temperature (°C)

(a)

2092

2000 1600 1135 776 668 U

20

40 60 at.%

80

1200 1000 842 600 400 200

327.502

Ca

B

20

40 60 at.%

80

Pb

(c) 1455

Temperature (°C)

1400 1300 1200 1100 1000 900 819 20

Yb

40 60 at.%

80

Ni

(d) 1200 1084.87

Temperature (°C)

1064.43

800 (Au, Cu)

AuCuII

400

AuCu3II AuCuI

AuCu3I

Au3Cu Au

20

40

60 at.%

80

Cu

Figure 2.20. Examples of systems in which several intermediate phases are formed. In the U–B system there are the three congruently melting compounds UB2, UB4, UB12, in the Ca–Pb system Ca2Pb and CaPb3 (congruently melting), Ca5Pb3 and CaPb (peritectic formation). The Yb–Ni system shows quite different interactions in the different parts of the phase diagram: in the Yb-rich region we have no compounds and a miscibility gap in the liquid state, while several point compounds are formed in the Ni-rich region. Completely different is the Au–Cu system in which the continuous solid solution, stable at high temperature, gives on cooling various ordered intermediate phases through ordering processes.

37

800 400

Au

Temperature (°C)

Temperature (°C)

1200

20

40 60 at.%

80

Mn

1200 1000 800 600 400 200 Mn

20

40 60 at.%

80

Ga

1800 1600 1400 1200 1000 800 Er

Temperature (°C)

Temperature (°C)

Phase Diagrams in Alloy Systems

20

40 60 at.%

80

20

40 60 at.%

80

Ge

1400 1200 1000 800 600 400 200 Mn

Ni

Figure 2.21. Phase diagrams of the systems Au–Mn, Er–Ge, Mn–Ga, Mn–Ni.

More complex situations will be shown in the following and some typical examples of ternary (or multi-component) alloy phase diagrams presented. In Figs. 2.20 and 2.21 a selection of binary alloy systems which give various types of phase diagrams characterized by the formation of intermediate phases is given. These systems and their phase diagrams have been arranged in order of their increasing complexity. A few specific comments may be helpful. In the U–B and in the Ca–Pb systems we notice the formation of several stoichiometric compounds (UB2, UB4, UB12 and, respectively, Ca2Pb, Ca5Pb3, CaPb, CaPb3, possibly having quasi-polar, salt-like, bonds). In the Yb–Ni system we have the formation of a number of compounds in the Ni-rich region, no compounds and a miscibility gap in the liquid state in the Yb-rich region. The Au–Cu system is a typical example of formation of intermediate phases by ordering in the solid state: at high temperature we have a continuous solid solution. Fig. 2.21 shows a few examples of very complex systems characterized by the formation of several (point and solution range) intermediate phases often involved in a number of different formation and decomposition reactions. The crowded sequence of intermediate compounds of interrelated structures is noteworthy in the Au-rich region of the Au–Mn system. A similar situation (however, not yet well defined) may

38

Intermetallic Chemistry

be observed in the Ge-rich region of the rare earth–germanium systems (for instance Er–Ge). The Mn–Ga and Mn–Ni systems show a number of solid-state reactions involving several solid solution intermediate phases. 2.2.4.1 Trends in the formation capability of binary compounds. A few general comments about the formation of intermediate phases in binary alloy systems can be made by using maps similar to those previously employed in Fig. 2.8 in order to give a summary of the mutual solubility. In Figs. 2.22 and 2.23 all the binary combinations are mapped as a function of the Mendeleev numbers of the two elements involved. The compound formation capability is represented in Fig. 2.22 by means of a few codes, whereas in Fig. 2.23 an indication is given of the thermal stability of the intermediate phases. To this end, values correlated to the so-called Raynor Index (Raynor 1972, 1974) are coded in this figure. This index IR is defined as follows (for a generic phase or compound having the composition AxB(1x)):

IR

Tm ( Ax B(1 x ) ) xTm ( A) (1 x )Tm ( B )

In the formula Tm(S) is the melting point in Kelvin of the substance S. The pairs of elements forming compounds have been mapped; both those having at least one compound with IR 1 and those for which IR 1. An outline of the intermediate phase formation and behaviour may be obtained through a look at both maps. All the systems, for instance, shown in Figs. 2.1 (V–Mo, Cs–Rb, Sr–Ca), 2.9 (Ni–Au, Pt–Au, Ba–Ca), 2.11 (Au–Si, U–Cr) and 2.16 (Ga–Bi, Be–Ga, Na–Al) will be represented as non-compound systems in the map of Fig. 2.22. The system Au–Cu (Fig. 2.20(d)) corresponds to the formation of a certain number of intermediate phases (in Fig. 2.22) and low values of IR in the Fig. 2.23. The system Ca–Pb (Fig. 2.20(b)) on the contrary is represented by the existence of several intermediate phases and high values of IR, etc. As already suggested and discussed by several authors, such as Pettifor (1984, 1986), Villars et al. (1989), etc., these maps highlight a regular trend in the formation of binary compounds. In the lower-left corner of the map those systems are represented obtained by combinations among elements of the first four groups of the Periodic Table. No intermediate compounds are generally observed in these systems. On the other hand, several compounds are observed in systems given by elements having high

Phase Diagrams in Alloy Systems

39

MB Rh Pa Li Be Tb Ga Si S U La P Pd Co Ca Zn Na Y Cu Cd Pt O Ge B As Se Ti V Cr Mn Os Al Tm Ce Np Sr K Ag Hg Sb Te Ac Hf Nb Mo Tc Ru Sm Pu Ni Ba Eu Lu Rb N In Sn Cs C Po Ra Yb Sc Au Mg Bi Tl Gd Am Ir Th Zr Ta W Re Fe Pb H C Po Bi

Te Sb

N Se As

O S P

B Si Ge Sn Ga Al In Tl Be Zn Cd Hg Mg Cu Ag Au Pd Pt Ni Ir Rh Co Os Ru Fe Mn Tc Re Cr Mo W V Nb Ta Ti MA Hf Zr Ac Th Pa U Np Pu Am La Ce Sm Gd Tb Y Tm Lu Sc Eu Yb Ca Sr Ba Ra Li Na K Rb Pb

The phase diagram has been determined and no intermediate phase has been observed. Only one intermediate phase is formed (either by crystallization from the liquid or by ordering in the solid state). Several intermediate phases are formed ( 2).

Figure 2.22. Compound formation capability in binary systems. The different element combinations are mapped on Mendeleev number coordinates and those systems are indicated in which the formation of intermediate phases has been observed (either from the liquid or in the solid state). Blank boxes indicate systems for which no certain data are available. Notice that the compound-forming alloys are crowded in a region corresponding to a large difference in the Mendeleev numbers of the elements involved (for instance, basic metals with semi-metals).

electronegativity differences, such as those reported in the higher (left and central) part of the map. Similar information about the mutual reactivity of the different types of elements may be obtained from Fig. 2.23, where, with a similar format, an indication of the Raynor Index is mapped.

40

Intermetallic Chemistry

Figure 2.23. Raynor Index map. In this map only the systems forming intermediate phases are coded. The two diagrams show the codes used in the map. In the first diagram the index IR for all the compositions is less than 1 (the melting points in the diagram are lower than the averaged melting points of the components). In the second diagram, for a certain range of compositions IR is higher than 1. Notice that the high values of the Raynor Index correspond to the metal pairs showing high compound formation capability (compare with Fig. 2.22).

2.3. EXAMPLES OF MORE COMPLEX PHASE DIAGRAMS

In the preceding paragraphs we have seen a few examples of phase equilibria occurring in binary systems represented by means of 2D diagrams built, at constant pressure (isobaric), on temperature/composition axes for which the phase rule

41

Phase Diagrams in Alloy Systems C

C (a)

(b)

a b

b′ b

a

P1 P2

X c = 0.5

b

c′ c

P3

a

P

c A

a′

P4

X c = 0.25

c B X

a ′+ b ′+ c ′ = CX a +b + c = AB = AC = BC

A

XA /XB = 1 XA /XB = 1 / 3

B

P 1 = A 0.25 B 0.25 C 0.5 ( = ABC 2) P 2 = A 0.125 B 0.375 C 0.5 ( = AB 3C 4) P 3 = A 0.375 B 0.375 C 0.25 ( = A 3 B 3C 2) P 4 = A 3B 9C 4

Figure 2.24 The Gibbs triangle for the representation of the composition in a ternary system.

reduces to V 2 P 1 3 P. More complex systems and representations may be considered in several cases. Just as an indication a few examples will be given here. 2.3.1 Ternary phase diagrams More complex representations are needed when considering more than two components. In the three-component case, the so-called Gibbs triangle is employed for the representation of the composition (see Fig. 2.24(a)). On the vertices the pure components (A, B, C) are represented, on the edges the binary compositions pertaining to the systems A–B, B–C, and C–A. In the interior of the triangle the ternary compositions are defined for a given point according to two coordinate systems. In the so-called contravariant system, distances are measured parallel to the sides of the triangle (a b c AB, taken as unit); in the other system, the covariant one, the quantities are measured by the perpendicular distances from point P to the sides (a b c CX, which is taken as the unit). Examples of compositions and their representation in the Gibbs triangle are shown in Fig. 2.24(b). Notice that along a straight line parallel to one axis (for instance A–B), the concentration of the third component (C) is constant. On the other hand, straight lines radiating from one vertex (C in this case) correspond to a constant ratio of the components placed in the two other vertices (A and B). If we consider three-component (ternary) systems, for instance, we have C 3 and, according to the phase rule, the variance is given by V C P 2 5 P or in

42

Intermetallic Chemistry

Temperature

(a)

T2 TE

A

C

T1

B

α

(b) A

C ∗

γ

α

(c) A

C

∗

∗

T = T2 β

γ

T = T1

β B

B (d) A

C E

B

Figure 2.25. A hypothetical ternary diagram presenting a ternary eutectic (at temperature TE) is shown in (a); two isothermal sections (at T2 and T1) are presented in (b) and (c) where the shaded regions represent single-phase fields, the ruled ones represent two-phase fields and those marked by an asterisk three-phase fields. The segments shown in the two-phase fields are supposed to be ‘tie-lines’ (co-nodes) connecting the points representing the compositions (experimentally determined) of the two phases in equilibrium at the given temperature. The three-phase fields are triangles (tie-triangles) the vertices of which correspond to the compositions of the three coexisting phases. In (d) a projection of the ‘liquidus’ is shown. The projections of the valleys meet in the ternary eutectic (LE : α β γ).

43

Phase Diagrams in Alloy Systems

the simpler and very common case of an investigation carried out at constant pressure V C P 1 4 P. In Fig. 2.25 a perspective view of a 3D temperature/ composition diagram is given. Isothermal sections of the diagram are given in Fig. 2.25(b) and (c), and a projection of equilibrium lines in Fig. 2.25(d). In the case of a ternary system, the formation of several, binary and ternary, stoichiometric phases, and different types of variable composition phases can be observed. One may differentiate between these phases by using terms such as ‘point compounds’ (or point phases), that is, phases represented in the composition field by points, ‘line phases’, ‘field phases’, etc. A simple example of a real ternary diagram is shown in Fig. 2.26, where the isothermal section, determined at 200°C, of the Al–Bi–Sb system is shown together with the relevant binary diagrams: Al–Bi showing a miscibility gap in the liquid state and complete insolubility in the solid state, Bi–Sb with complete mutual T (°C)

600 1000

1000 500

900

400

600

800 700

300

600

Al

10

30

50

70

90

at.% Bi

Bi

Bi

10

30

50

70

90

at.% Sb

Al

Sb

10

30

50

70

at.% Sb

90

Sb

Bi

80

20

60

40

40

∗

60

+

20

80

Al

20

40

60

80

Sb

AlSb

Figure 2.26. Isothermal section of the Al–Bi–Sb phase diagram at 200°C. In the triangle marked by the asterisk, three phases (coincident with the two elements Al and Bi together with the compound AlSb) are observed. In the other triangle two-phase alloys are formed. A few tie-lines are shown. The alloy marked by ‘’, for instance, contains the compound AlSb together with a (Bi, Sb) solid solution of composition marked by ‘䊊’.

44

Intermetallic Chemistry

T (°C) 1300

1300 600

900

900

500

500

400 307 200

Al

10

30

50

70

90

at.% Si

Si

Si

10

30

50

70

90

at.% Zn Si

Zn

Al

30

50

70

at.% Zn

90

Zn

80

20

60

40

40

60

∗

∗ 20

80

Al

10

20

40

60

80

Zn

Figure 2.27. Isothermal section at 307°C of the Al–Zn–Si diagram. The boundary binary systems are shown. The isothermal section at 307°C is marked on the binary Al–Zn diagram. The corresponding single-phase (thick segment) and two-phase regions are indicated in the base edge of the triangle. By additions of Si (immiscible in the solid state in the other two elements) two- and three-phase fields are formed. (*) three-phase region. In the two-phase region on the left examples of tie-lines are presented.

solubility in the solid and liquid states and Al–Sb presenting the formation of only one intermediate compound and no appreciable solid solubility. No ternary intermediate phases are present. The ternary Al–Bi–Sb triangle is composed by two triangular regions. The first, Al–Bi–AlSb, includes all the compositions corresponding to AlSb with additions of Al and Bi, that is, AlSb mixed with an excess of elemental (unreacted) Al and Bi. The second triangle, AlSb–Bi–Sb, includes compositions corresponding to AlSb with additions of Bi and Sb. In this case the resulting alloys are two-phase, that is, AlSb together with the second phase represented by the solid solution (Bi, Sb). The Al–Zn–Si is another example of simple ternary system; its isothermal section at 307°C is shown in Fig. 2.27 together with its boundary binaries. Si, in the solid state, is practically insoluble in Al or in Zn and in their binary solutions. In the

45

Phase Diagrams in Alloy Systems O

20 80

Mg

∗

τ1

SiO2

τ2

60

O

∗

MgO ∗

60

%

at. %

∗

∗

a t.

40

∗ 40

80

∗

20

MgO+ L+ Gas

Mg

20

∗

40

60

80

Si

at.% Si

Figure 2.28. Isothermal section of the Mg–Si–O diagram at a temperature of 1280°C and a pressure of 105 Pa. Two ternary point compounds are formed (τ1 Mg2SiO4, forsterite, and τ2 MgSiO3, protoenstatite). Notice along the Mg–Si edge, owing to the high temperature, the large range of the liquid phase (thick line). The three-phase regions are marked by ‘*’. A few tielines are indicated in the two-phase field (MgO liquid). The two-phase regions between point phases are represented by segments (linear regions of negligible thickness). In the oxygen-rich region gaseous O2 is present in equilibrium with the solid phases MgO and τ1, or τ1 τ2, or τ2 SiO2.

different fields of the ternary Al–Zn–Si composition triangle we have the binary (single or two phase) Al–Zn alloys with the mechanical addition of solid Si. Examples of isothermal sections of more complex, not only intermetallic, ternary systems are presented in Figs. 2.28 and 2.29. These systems show several point, line and field compounds. The isothermal sections are subdivided into numerous single, two- and three-phase regions. The three-phase regions, marked by an asterisk, are triangles (tie-triangles) the vertices of which give the compositions of the three coexisting phases either point compounds or saturated solid solutions. 2.3.2 Variable pressure phase diagrams Hydrostatic pressure is a variable that obviously affects phase equilibria. Atmospheric pressure may generally be considered negligible and therefore neglected in

46

Intermetallic Chemistry Al (a)

10 90

∗

Mg

30

τ

Al2Er

∗

∗

%

Al3Mg2 ∗ 50 ∗

∗

∗

AlEr ∗

∗

70

Al2Er3 AlEr2

∗

∗

30

∗

90

∗

10

∗

10

Mg

Al

Al12Mg17

Al3Er a t.

at. %

∗

30

50

70

90

Er

Er5Mg24 ErMg2 ErMg at.% Er Cu

(b) 20

∗

at.

τ4

Al

20

Al3Ti

∗

40

CuTi2 ∗

60

AlTi

20

∗

∗

40

Cu

τ1 τ2

CuTi

∗

∗

80

∗

Cu3Ti2

∗

∗

∗

60

∗

∗

60

Al2Cu

∗

τ3

%

AlCu

∗

Cu4Ti

at.

%

Al

∗

40 Al2Cu3

80

80

Ti

AlTi3

at.% Ti

Figure 2.29. Isothermal sections of ternary phase diagrams: (a) Al–Er–Mg system at 400°C, Saccone et al. (2002) and, (b) Al–Cu–Ti system at 540°C from Villars et al. (1995). A number of single-phase regions (dark grey) may be noticed, both extending from binary compounds and as ternary intermediate phases (τ) in the Al–Er–Mg system and the four phases τ1 τ2 τ3 and τ4 in the Al–Cu–Ti system. The three-phase fields are marked by an asterisk, in the Al–Er–Mg system a few tie-lines are indicated in the two-phase fields.

47

Phase Diagrams in Alloy Systems (a)

(b)

0

Solid −2 Gas Triple point

−3

15 Pressure (GPa)

−1 log10P (bar)

ε

Liquid

γ

10

5

α

L

δ −30

0

30

Temperature (°C)

500

1000 1500 2000

Temperature (°C)

Figure 2.30. Typical one-component systems: (a) Room temperature, room pressure region of the well-known P/T phase diagram of water (notice the logarithmic scale of pressure). (b) P–T phase diagram of elemental Fe. The fields of existence of the different forms of Fe are shown: α (body-centred cubic Fe), γ (face-centred cubic), δ (body-centred cubic, high-temperature form isostructural with α), ε (hexagonal close packed), L (liquid Fe). The gas phase field, owing to the pressure scale and the not very high temperatures considered, should be represented by a very narrow region close to the T axis.

the construction of metallurgical phase diagrams. There are diagrams, however, in which the state variable pressure is explicitly considered, such as those concerning alloys of volatile components, especially those at high or very high temperatures, and, of course, those related to investigations under great pressure. A few figures are here presented as a kind of ‘aide-memoire’ on this subject. Figs. 2.30 and 2.31 show diagrams in which the state variable pressure is explicitly considered. Fig. 2.30 shows two typical one-component systems. In Fig. 2.31(a) and (b), on the other hand, the equilibria relevant to a simple two-component system are represented. As an example of more complex systems and descriptions, the Ni–Mg system is shown in Fig. 2.32 (adapted from Levinsky 1997). In (a) an isobaric section of the diagram is shown (a low pressure has been considered in order to have a certain extension of the gas phase which consists essentially of Mg vapour). In Fig 2.32(b) there is an isothermal section of the diagram at 700°C. Notice, for different values of pressure, the change in the sequence of phases stable at different compositions. A value of the pressure close to atmosphere is approached at the top of the figure. In Fig 2.32(c) the usual T/x diagram is shown. This can be considered an isobaric phase diagram if pressure is relatively low but still higher than the sum of the equilibrium partial pressures of the components.

48

Intermetallic Chemistry (a)

(b)

SB, LB Pressure

Pressure

,G

L α,

G S B,

SA, LA

G+L

S+ L

,G LB

,G LA

G S A,

G+ S Temperature A

Compo

sition

e

mp

B Te

ure rat

Figure 2.31. Schematic representation of the P/T equilibria in a simple two-component system (forming continuous solid and liquid solutions). In (a) a perspective view of the P–T–X diagram is shown; in (b) its projection on the P/T plane. Notice the two single-component systems represented, for instance, for the component B by the three lines SB/G (sublimation line of B representing the gas/solid equilibrium), SB/LB (melting equilibrium of B) and the boiling line LB/G. The solid solution is indicated by α. Notice in (a) the isobaric and isothermal sections of the diagrams (compare with Fig. 2.1).

For a discussion of the role of non-hydrostatic pressure in phase equilibria investigations, the effects of applied stress and their consequences in metallurgy, geology, etc. see Cahn (1989). 2.3.2.1 Partial pressure as a variable. As mentioned in § 2.1, many types of thermodynamic variables may be used in the construction of phase diagrams. The various rules of construction, based on the laws of chemical thermodynamics, which apply to the different types of phase diagrams have been discussed in several books and papers (for instance, Pelton and Schmalzried 1973, Okamoto 1991, Pelton 1991). Following a classification proposed by Pelton, the various, bidimensional, phase diagrams may be subdivided into three types as follows: Type 1 are potential/potential phase diagrams. The potentials considered in chemical thermodynamics are: temperature (thermal potential), pressure (mechanical potential) and the chemical potentials of the N components μ1, μ2, μ3, …, μN. The P/T diagrams are examples of type 1 diagrams.

49

Phase Diagrams in Alloy Systems (a)

NiMg2

800

Ni2Mg

T (°C)

1000

600

400

Ni

20

40

60

80

at.% Mg

Mg

NiMg2

(b)

2

Ni2Mg

log p (Pa)

3

1

Ni

20

40

60

80

Mg

at.% Mg (c)

1000

600

200

20

NiMg2

Ni2Mg

T (°C)

1400

40

60

Ni

80

Mg at.% Mg

Figure 2.32. (a) Ni–Mg system. Isobaric section of the diagram at p 103 Pa (from Levinsky 1997). (b) Ni–Mg system. Isothermal section of the diagram at 700°C (from Levinsky 1997). (c) Ni–Mg system. T/x diagram at a pressure nearly constant and equal to the ambient.

50

Intermetallic Chemistry

Type 2 are represented by the plotting of one potential vs. the composition (for instance T vs. x at constant P or P vs. x at constant T, etc.). Type 3 are composition/composition phase diagrams, such as the isobarothermal sections of ternary systems shown in Figs. 2.25–2.27. Another example of type 2 diagrams may be represented by chemical potential/ composition diagrams. A version of such diagrams, useful with systems in which gaseous components are involved, is given by partial pressure vs. composition diagrams. A simple case, taken from Pelton and Thompson (1975), is shown in Fig. 2.33, where isothermal equilibria in the ternary system Ni–Co–O are presented. The plot of log pO2 vs. the molar fraction nCo/(nCo nNi) describes the oxidation behaviour of the alloys formed by Co and Ni, showing a complete mutual solid solubility. The oxidation product, formed at high values of pO2 is made up of the solid solution of NiO and CoO, also showing a complete mutual solubility. Notice that the general features of this diagram are similar to those of the diagram presented in Fig. 2.1(a) and in the first example of Fig. 2.9. In both cases we have two single-phase fields separated by a twophase field; the passage through them depends on the value of the ‘potential’ (thermal potential, temperature in one case, partial pressure of oxygen in the other). In both

− 6.6

3

log pO2 (atm)

(Ni, Co)O (s) − 7.0

2

y − 7.4

− 7.8

Ni

1 (Ni, Co) (s)

20

x1

40

60

x2

80

Co

at.% Co

Figure 2.33. Ni–Co–O phase diagram (isothermal section at 1600 K). log pO2 (oxygen partial pressure) is plotted against the molar fraction in the metallic alloy. The metallic alloy, (Ni, Co) solid solution is stable in (1) and the mixed oxide (Ni, Co)O solid solution in (3). In the intermediate region (2) we have coexistence of alloy and oxide. For the value of the partial oxygen pressure corresponding to y, within the two-phase field, we will have the alloy of composition x1 in equilibrium with an oxide containing the two metals in the ratio x2.

51

Phase Diagrams in Alloy Systems

cases the two-phase field is delimited by two boundary lines (saturation curves) and within this field horizontal segments (tie-segments) connect the points (on the boundary lines) representing the two coexisting phases. 2.3.3 Equilibrium and reaction rate In previous paragraphs, a description has been given of equilibrium diagrams and transformations. Phase diagrams have come to be of great help in the preparation and investigation of alloys, ceramic materials, etc. Increasing attention is dedicated worldwide to the experimental determination of phase equilibria data, to their computation, compilation and assessment. For a given system a detailed description of the different phases and of their stability ranges of temperature and composition is indeed essential information for the evaluation of both basic and applicative properties. Notice, however, that in real situations, if for instance an alloy is subjected to a rapid change of temperature, it is possible that transformations occur which do not correspond to a sequence of true equilibrium states. It is possible that some transition will be missed or shifted to a different temperature or that a phase stable in a certain range of temperature (or pressure) will be retained in different conditions. In Table 2.4, as an aide-memoire, an indication is given of how the rate of temperature

Table 2.4. Average cooling rate as a parameter for material formation in different states. Cooling rate (Ks1)

Type of process

Materials

Method of realization

1010

Very slow crystallization

Minerals single crystals

Geological processes

107–104

Controlled crystallization

Natural and synthetic single crystals

Crystal growth from solutions, gels and by coarsening of solids

102–1

Common cooling

Metals, alloys, etc.

Furnace cooling

1–103

Quenching

Oxides, silicates, chalcogenides, metals, alloys

Casting, immersion

105–108

Freeze-in by ultrafast cooling

Metals

Melt splatting or spinning techniques

1011

Disordering on surfaces

Layers on materials

Vapour deposition, laser surface melting, ion beam modification

52

Intermetallic Chemistry 100

Temperature (K) (arbitrary scale)

E K

M

0

0

0.5

1.0

Molar fraction

Figure 2.34. For a hypothetical binary system, possible trends of equilibrium (E) and kinetic (K) phase diagram are shown. (M) indicates the appearance of transformations which could be observed in a metastable situation (adapted from Chvoj et al. 1991).

change in a material may be a deciding factor for the formation of a given structure and the acquisition of a certain set of properties. These points will be considered further on in Chapter 6, about alloy preparation methods. In some cases comprehensive information about the real behaviour is included in the phase diagrams themselves, obtaining the so-called kinetic and metastable phase diagrams. Following Chvoj et al. (1991), an example of such diagrams is presented in Fig. 2.34. The kinetic phase diagram (K) can correspond to a shift of the equilibrium phase diagram (E) to a lower temperature (under-cooling of the system). A metastable phase diagram (M) changes the character of the phase transitions. It would be possible, during its realization, to prepare new materials with new properties which cannot be obtained in near equilibrium conditions. A real example of such diagrams is reported in Fig. 2.35. Fig. 2.35 shows the equilibrium phase diagram of the system In–Pb (continuous lines) together with a metastable diagram. The procedure adopted in the determination of this phase diagram is briefly described here: it may be useful as an example

53

Phase Diagrams in Alloy Systems

20

40

Mass% Pb 60

80

Temperature (°C)

300

250

200

150 (In) In

δ 20

(Pb) 40

60 at.% Pb

80

Pb

Figure 2.35. In–Pb diagram. The equilibrium diagram is shown (continuous line) together with a metastable solidus (dotted line).

of the significance of such diagrams and also of the difficulties often met in this kind of experimental investigation. The diagram was determined by Evans and Prince (1978). While performing thermal analysis they obtained a precise reproducible determination of the liquidus during solidification with a cooling rate of 1–1.5°C/min. They underlined the problems encountered in determining the solidus. During cooling from the liquidus, solidus temperatures were indeed obtained initially which do not correspond to the equilibrium curve (see the dotted line in Fig. 2.35). The solidified alloys were then annealed for several hours just below their measured solidus. On reheating, melting was observed at a higher temperature than previously measured. The samples were then re-annealed just below the new observed temperature before reheating. This cycle was repeated until the solidus temperature became reproducible (continuous line in Fig. 2.35). Metastable phases and equilibria may be obtained by fast cooling.

54

Intermetallic Chemistry

Temperature (°C)

1000

AuSb2

500 Es

Em1

ζ

Π

Em2

0 −100 20

Au

(Au)

60

40 at.% Sb

ζ

AuSb2 Π

80

Sb

Sb

Figure 2.36. Au–Sb system. The continuous line represents the (equilibrium) phase diagram containing the peritectic melting AuSb2 compound and a eutectic equilibrium (Es). Dotted lines represent equilibria (and phases) which may be observed on rapid cooling. The sequence of phases (ζ, AuSb2, π) detected in fast-quenched alloys and their composition ranges are shown in the lower part of the figure.

Considerations about metastable diagrams involving very rapid quenching from the liquid state date back to the work by Duwez (1967). An interesting contribution to this subject is summarized in Fig. 2.36. It shows the equilibrium diagram of the Au–Sb alloys and the sequence of phases observed by fast quenching (Giessen and Willens 1970, Massalski 1989). 2.3.3.1 Stable, metastable and unstable states: a simple analogy. A simple mechanical model is shown in Fig. 2.37: a block on a stand may be in different equilibrium states. In A and C the centre of gravity (G) of the block is lower than

55

Gravitational potential energy

Phase Diagrams in Alloy Systems

B

B C′

A′

C

A′

A

A Position G

A

A′

B

C C′

B

A′

A

Figure 2.37. A simple mechanical system and its equilibrium states. Different positions of a block on a stand and the corresponding values of the gravitation potential energy are shown. Point G is the centre of gravity of the block. In A there is stable equilibrium, in C metastable, in B unstable. In A e C a transformation is taking place.

in any nearby position: the gravitational potential energy is a minimum. If the block position is slightly disturbed it will spontaneously (natural process) revert to its previous position (corresponding to a stable equilibrium). In B, on the contrary, G is higher than in any nearby position: the gravitational potential energy is a maximum and this corresponds to an unstable equilibrium. Position C does not correspond to the lowest minimum of the energy: following a small displacement, the block will return to the initial position whereas large displacements will move the block to the more stable position A. In A there is an (absolutely) stable equilibrium and in C a metastable equilibrium. For this mechanical system the stability conditions and the trends of spontaneous (natural) processes are related to minima (relative or absolute) of the gravitational potential energy. For physico-chemical systems, with materials in a closed system considered at constant temperature and pressure, the role of equilibrium indicator is played by the Gibbs free energy. The free energy of a multiphase system is given by ΣniGi where n i is the number of moles of the ith phase and Gi its molar free energy. The molar Gibbs free energy of a phase is related to its molar enthalpy Hi, molar entropy S i and absolute temperature T: Gi Hi TS i. The equilibrium state of the system corresponds to the minimum of the ΣniGi function.

56

Intermetallic Chemistry

2.3.3.2 Spinodal decomposition. An important kind of transformation involving non-equilibrium states corresponds to the so-called spinodal decomposition. This can be observed in phase diagrams such as those previously presented in Fig. 2.9(a), (b), (d), and may be described by the scheme shown in Fig. 2.38. In Fig. 2.38(a), a possible trend of the Gibbs energy of mixing in the solid state is shown for various temperatures (T1, T2, T3, T4): the corresponding de-mixing equilibria (miscibility gap) are presented in the lower part of the same figure. A curve of the ΔmixG such as that shown for T Tc (for instance T4) corresponds to minimum values for all the compositions. The single-phase alloy is stable. As T decreases, the ΔmixG values become less and less negative (however, they are always negative as xA : 1 and xB : 1) so the curves (below the critical, consolute, temperature Tc) show a peculiar trend with two minima. Common tangent lines (b1 b1 , b2 b2 , etc.) to these two parts of the curves define segments, the points of which correspond to ΔmixG values lower than those of the curves themselves. These tangent lines, therefore, define regions for which a two-phase, solid–solid, alloy is more stable than a singlephase one (in other words they define the ends of the tie-lines in the miscibility gap, the binodal points). These points connected by a continuous line in the lower part of 2.38(a) result in the miscibility gap itself. The inflection points we notice in the curves (points S) are the spinodal points; if we plot these points in the phase diagram we obtain the spinodal curve (dotted line in Fig. 2.38(a)). It is not part of the phase diagram but it gives important information on the phase transformation kinetics. Single-phase alloys, as obtained for instance by quenching from the one-phase region, within the two branch of the spinodal curve are unstable, while in the regions between the spinodal and the equilibrium (binodal) curves they are metastable. A simple explanation for this behaviour can be understood from an examination of Fig. 2.38(b) and (c). On the right (in Fig. 2.38(b)) a complete phase diagram is shown of alloys which, at low temperature in the solid state, are involved in a demixing equilibrium. Both the miscibility gap and the spinodal curve are represented. On the right, in the lower part of the figure (Fig. 2.38(c)) an enlarged portion of the ΔG vs. composition curve for a given temperature is shown. Notice the different composition scale in comparison with Fig. 2.38(a) and (b). We may now consider the different behaviour, on cooling from the single-phase field, of alloys placed in different ranges of compositions within the miscibility gap. To this end, on the ΔmixG curve, on both sides of the inflection point S, short segments connecting two points placed close to each other have been drawn (xm1 xm2 and xu1 xu2 respectively). The points of these segments represent the ΔmixG of two-phase alloys. In the composition range between the maximum and the spinodal (xs) a two-phase alloy, such as a mixture xu1 xu2, has therefore an overall free energy lower than that of any single-phase alloy of an intermediate composition, which is therefore unstable.

57

Phase Diagrams in Alloy Systems (a)

(b)

T1 b1

b1

S1

S1

T2

A

T3

b1

b1 S1

S1

xB

Free energy

Temperature

Tc

b2

b2

A

xb xs

B

xB

(c)

T4

T2 T1

α

b2

b2

T4 T3

L+α

Temperature

ΔG mixing (arbitrary units)

L

Δu S

t

Δm

B xb xm1 xs xm2

xu1 xu2

xB

Figure 2.38. Miscibility gap in the solid state. A possible trend of the Gibbs energy of mixing in the solid state is shown in (a) for various temperatures. The points b1 b1 , b2 b2 , etc. (and the corresponding binodal tangent lines) define the stable two-phase equilibrium and the corresponding tie-line. Plotting these points in the phase diagram results in the de-mixing curve (miscibility gap) presented in the lower part of the figure and in (b). The inflection points of the curves (points S) are the ‘spinodal points’; these points plotted in the phase diagram give the ‘spinodal curve’ (dotted line). On the right, a part of the Gibbs free energy of mixing curve is shown with the spinodal inflection S; xm1 and xm2 correspond to two compositions within the metastable region, xu1 and xu2 to two compositions in the unstable region. Δm, Δu are the free energy changes (increase or decrease) for an initial de-mixing process (t is a part of the line tangent to the minima b and b ).

In the region between the spinodal and the binodal points, on the contrary, the algebraic summation of the Gibbs free energies of two points such as xm1 and xm2 is higher than that of a single alloy of intermediate composition. At atomic scale, however, random shifts in the positions of atoms may result in local regions of compositional inhomogeneity, eventually leading to macroscopic phase separation.

58

Intermetallic Chemistry

The energy increase related to a compositional fluctuation resulting in a two-phase splitting may be considered as an energy threshold of activation of the de-mixing process. The spinodal curve thus defines a kinetic limit, not a phase boundary line. 2.4. REMARKS ON PHASE DIAGRAM DETERMINATION AND EVALUATION

The definition of the phase diagrams of different groups of substances such as the various alloy systems is an important step both in basic and applied sciences (materials science, metallurgy). Several interconnected activities may be related to this point such as experimental determination of phase diagrams, calculation (and prediction) of phase diagrams, their assessment, compilation, etc. A large number of reviews and books concerning different aspects of theory, measurement and application of phase diagrams and several compilations of binary and ternary system diagrams have been published; a selection of them is given in the reference list. 2.4.1 Experimental determination of phase diagrams The experimental methods of determining phase diagrams will be only briefly commented upon, in order to give an idea of the problems involved and of the connection between phase diagram science and other disciplines. A few special points will be considered in Chapter 6, dedicated to the preparation of intermetallics. It must however be pointed out that a sound experimental definition of a phase diagram can be obtained from the results of a number of concerted investigations such as thermal analysis, thermodynamic analysis, micrographic examination and phase analysis and identification by means of techniques such as X-ray diffraction measurements, microprobe analysis, etc. Among these methods, the old ‘classical’ thermal analysis techniques play a relevant role. This has been illustrated by different authors. Examples taken from the investigation of binary systems, rather than complex ones, are more frequently considered. This is because of the easier interpretation in such cases of the observed thermal effects and of the prominent role that thermal analysis methods may play in the definition of simple systems, while the ever-increasing complexity of systems being investigated requires the use of more and more auxiliary complementary techniques even if thermodynamic modelling may be very useful in simplifying the time-consuming experimental work. Emphasis has already been placed on the different experimental methodologies, for instance by Hume-Rothery et al. (1953) who stressed the need to use different complementary techniques in the definition of ternary or more complex systems. The necessity of combining thermal analysis with microscopic techniques was especially highlighted, for example, in the determination of solid ← → liquid equilibria.

Phase Diagrams in Alloy Systems

59

In any case, going back to the beginning of the past century we may mention the pioneering investigation carried out by Parravano and Sirovich (1912) and Parravano (1914) in the determination by thermal analysis of the phase diagrams of quaternary alloy systems, such as Cu–Fe–Mn–Ni, Bi–Cd–Pb–Sn, Ag–Au–Cu–Ni. Considering now a few common methods and techniques for the experimental definition of a phase diagram, it may be useful to refer to their usual classification into two groups: polythermal and isothermal methods. 2.4.1.1 Polythermal methods. The temperature of an alloy sample is progressively changed, generally at a well-defined and controlled heating or cooling rate, as some properties of the sample itself are continuously measured. This could be either the volume, or the length, of the sample, or its electric conductivity, or its X-ray diffraction pattern, etc. A continuous trend is generally observed within a certain phase field, while some discontinuity or trend change may be noticed on crossing one of the characteristic lines of the diagram. One of the main techniques of this group is thermal analysis in which the cooling or heating curves themselves are analysed and of which several variants are known (thermal analysis proper, differential thermal analysis, differential scanning calorimetry, etc.). A scheme of such a technique is presented in Fig. 2.39. In principle two similar crucibles containing respectively a sample of the alloy under investigation and an inert reference specimen are cooled (or heated) together in a furnace. By means of conveniently inserted thermocouples it is possible to follow: (1) the continuous reference temperature trend of the reference specimen, (2) the temperature trend of the specimen under examination and (3) the temperature difference (ΔT ) between the two. If, at a certain temperature, there is a change in the structure of the sample (that is, if a boundary line in the corresponding phase diagram is crossed), a variation in the slope of the temperature vs. time curve is recorded. As a consequence the ΔT vs. time curve (or vs. temperature) shows a deviation from the baseline. The temperatures at which such deviations are observed are used to build the phase diagram. For the Cu–Mg alloy system, as an example, the phase diagram is shown in Fig. 2.40 together with the corresponding T/ΔT graphs obtained from the thermal analysis of two selected alloys. 2.4.1.2 Isothermal methods. In principle these methods imply the preparation of a certain number of alloy specimens of different compositions and their examination at the same given temperature. Important methods are those based on observations carried out under a microscope. An example of such an analysis is given in Fig. 2.41 where the photomicrographs of two alloys of the Cu–Mg phase diagram are shown. These pictures, taken with a reflection microscope, allow identification

60

Intermetallic Chemistry (a)

(b) To T R

S

Temperature (T )

TS

R

F Time (t ) (c) t (or T ) TR

0 TS −TR

TS

Figure 2.39. A sketch of a type of differential thermal analysis ‘head’ is shown in (a). The two small crucibles (internal diameter 4–6 mm) contain the sample (S) and the reference (R, inert material). The junctions of two thermocouples (TS, TR) are inserted in the crucibles. They give the temperature of the sample and the ΔT between sample and reference. The DTA head is inserted inside a furnace (F), the heating and cooling regime of which may be conveniently controlled. In (b) typical trends of temperature vs. time are presented: T0 is the controlled furnace temperature trend, TR is the T trend of the inert reference specimen, TS is the trend observed for a sample undergoing some transformation. The corresponding differential curve (ΔT vs. time (or vs. temperature)) is shown in (c).

of the phases and their morphology which may be related to the specific transformations undergone by the alloy. For the alloy marked ‘1’, on cooling, the liquidus curve was intercepted at a relatively high temperature and there was a fair temperature interval during which for the Mg crystals it was possible to grow within the remaining part of liquid. The solidification finally ended at the eutectic temperature. At this temperature the eutectic crystallization occurs (L ← → (Mg) Cu2Mg) in isothermal conditions, where the simultaneous separation of the two solid phases results in a fine mixture

61

Phase Diagrams in Alloy Systems 1084.87

2

1 797

800

725 568 485

500 400

(Mg)

0 10 Mg

20

30

552 MgCu2

700 650 600

2

Temperature

1

(Cu)

900

Mg2Cu

Temperature (°C)

1000

40 50 60 at.% Cu

70

80

90 100 Cu

ΔT

Figure 2.40. Phase diagram of the Mg–Cu alloy system. For the alloys marked (1) (at 5 at.% Cu) and (2) (at 20 at.% Cu), the DTA curves are shown on the right. Notice that, on cooling, a sharp thermal effect due to the invariant eutectic transformation is observed. At higher temperature the crossing of the liquidus curves is detected. (The coordinates of the eutectic point are 485°C and 14.5 at.% Cu.)

(a)

(b)

Figure 2.41. Microscopic examination of Mg–Cu alloys. The micrographs of the same two alloys considered in Fig. 2.40 are shown. Small pieces of the alloys were polished by using finer and finer abrasive powders (Al2O3, diamond) in order to obtain a shiny surface. This appears as a continuous white surface under a metallographic reflection microscope. When the sample, however, is gently etched by using a convenient reactant (in this specific case a dilute water–alcoholic solution of HNO3) phases of different chemical composition (here Mg and the compound CuMg2) are differentiated. The more reactive phase (in this case Mg) is more deeply etched, losing its brilliance, and it appears dark under the microscope.

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of intermixed small crystals of the two solids. For the alloy marked ‘2’, notice the primary crystallization of Cu2Mg (white crystals) in small amounts, owing to the proximity of the alloy to the eutectic composition. Notice the larger quantity of ‘eutectic mixture’ which is identical to that observed in Fig. 2.41(a). The composition of alloy 2 is indeed closer to the eutectic than that of alloy 1. The above comments also highlight the fact that alloy morphology could provide information about the aspect of the phase diagrams and the type of transformation to which the alloy was subjected. A rich bibliography is available, as also are atlases. The observation under a light microscope may be complemented by examination under an electron microscope, possibly equipped with microanalysis devices to analyse point by point the composition of the sample and of its constituent phases. Several different methods are available for carrying out an analysis of the samples. Among the different techniques employed in solid-state physical chemistry, the diffractometric ones certainly play a relevant role; powder X-ray diffractometry, for instance, has been and is systematically used not only for the determination of the crystal structure of the various phases, but also, as an analytical tool, for their identification in complex samples. In the diffraction patterns obtained from a series of alloys having gradually changing compositions, it is indeed possible, even in a routine investigation, to recognize the groups of reflections characteristic of each phase and to follow their appearing or vanishing at certain compositions. Moreover, small changes in the diffraction angles of these reflections, characteristic of each single phase, are due to progressive variations of the unit cell dimensions and may be related to the formation of solid solution ranges. On the other hand, an accurate analysis of these diffraction patterns, possibly combined with single crystal diffractometry (and/or electron diffractometry, etc.), will give information about the formation mechanism of the solid solution phase (ordered or disordered substitution, structure modulation, etc.). Isothermal examination can be more easily carried out at room temperature. However, special instruments (microscopes, diffractometers, etc.) and techniques can be used for high- (or low-) temperature work. In a number of cases, an investigation carried out on samples annealed at the selected temperature, and then quenched, could be an alternative to direct hightemperature examination. It is possible indeed that the structure which is stable at high temperature is maintained on quenching. 2.4.1.3 Recent developments and prospects of X-ray powder diffraction methods. In the preceding paragraph a few comments have been made about diffractometry and its uses in the analysis of materials. However it is not possible to give here an account of this subject: its principles and underlying theories, its experimental techniques and

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related interpretation and application methods are fully described in several treatises, such as the book series edited by the International Union of Crystallography (IUCr), while references are often contained in books of General or Physical Chemistry, Materials Science, etc. In this paragraph, therefore, we will give only a few reading suggestions with special attention to the powder diffraction methods. Recent developments and prospects of these methods have been discussed in a chapter by Schneider et al. (2001). It was underlined that these methods are widely applied for the characterization of crystalline materials (phase identification, quantitative analysis, determination of structure imperfections, crystal structure determination and analysis of 3D microstructural properties). Phase identification was traditionally based on a comparison of observed data with interplanar spacings and relative intensities (d and I) listed for crystalline materials. More recent search–match procedures, based on digitized patterns, and Powder Diffraction File (International Centre for Diffraction Data, USA.) containing powder data for hundreds of thousands substances may result in a fast efficient qualitative analysis. The determination of the amounts of different phases present in a multi-component sample (quantitative analysis) is based on the so-called Rietveld method. Procedures for pattern indexing, structure solution and refinement of structure model are based on the same method. The Rietveld method (1967, 1969) was originally conceived as a method of refining crystal structures using neutron diffraction data. The powder diffraction data are recorded in digitized form, that is, as numerical intensity values, yi at each of several thousands equal increment in the pattern. Depending on the method the increments may be for instance in the scattering angle 2θ, typically with a step size from 0.01° to 0.05°, for the fixed wavelength X-ray technique. A best (leastsquares) fit to all the yi is sought; the quantity minimized, by means of a suitable computer program, in the least-square refinement is the residual: Sy Σiwi(yi yci)2 where wi 1/yi, and yi observed intensity at the i step and yci calculated intensity at the i step, and the sum is over all data points. The calculated intensities depend on several parameters which may be refined and defined: these include the structural characteristics (the cell parameters, see Chapter 3) of the phase, its quantity in a multiphase sample, etc. In a paper by Albinati and Willis (1982) the application of the Rietveld method in neutron and X-ray powder diffraction was discussed considering the different experimental techniques of obtaining the diffraction patterns. For a detailed description of the method and its applications see a reference publication (Young 1995). See also Jenkins and Snyder (1996). A frequently used calculation program for the

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quantitative Rietveld refinement of the X-ray and neutron diffraction data is the ‘FULLPROF’ program (Rodriguez-Carvajal 1993, Roisnel and RodriguezCarvajal 2001) whereas general program packages for handling diffraction data are for instance SHELXL-97 (Sheldrick 1997) and the Nonius Kappa package (1998). Notice, finally, that from an instrumental point of view the development of diffraction methods may be based on the availability of fast detectors and high brightness X-ray (and also neutron) sources. By using synchrotron X-ray radiation owing to its high intensity it is possible to study reactions on a sub-second time-scale and for instance follow the transformation kinetics in a self-propagating solid-state ‘combustion’ reaction. Various applications and expected breakthrough have been discussed by Schneider et al. (2001). 2.4.1.4 The diffusion couple technique in phase diagram determination. Several techniques and methods based on different experimental arrangements and relying on the measurement of various properties have been devised and applied to the determination of phase diagrams. Many of them have a long history, well-founded basis and have been used in the analysis and definition of thousands of phase diagrams. Short outlines of some important methods have been reported in the previous paragraphs; as a conclusion to this subject just another technique will be mentioned in the following. It is the elegant diffusion couple technique which has become more and more popular due to the improvement and increased availability of methods (such as the EPMA, electron probe micro-analysis) for point microanalysis. This technique proved to be a reliable tool in the investigation of isothermal sections of ternary systems by itself or in combination with more traditional methods of equilibrated alloys. In principle the preparation of a solid-state diffusion couple consists in bringing two (or more) materials in such intimate contact that, when maintained at a conveniently high temperature, each diffuses into the other. To this end, small blocks (discs for instance) of the component materials are polished flat on the bonding surfaces and clamped together. They are then annealed, in vacuum or inert atmosphere, at the selected temperature and eventually quenched. The resulting morphology which develops during the solid-state inter-diffusion and reaction can be examined by using standard metallographic methods. A schematic illustration of the method, and of the correlation between binary phase diagram and the one-phase layers formed in a diffusion couple, is shown in Fig. 2.42 adapted from Rhines (1956). The one-phase layers are separated by parallel straight interfaces, with fixed composition gaps, in a sequence dictated by the phase diagram. The absence, in a binary diffusion couple, of two-phase layers follows directly from the phase rule. In a ternary system, on the other hand (preparing for instance a diffusion couple between a block of a binary alloy and a piece of a third

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Phase Diagrams in Alloy Systems

T (°C)

1200

800

β (Cu)

γ

(Cu)

ε

β′

400

Cu

δ

20

40

60

80

at.% Zn

γ

ε

Zn

(Zn)

Figure 2.42. The Cu–Zn system: phase diagram and microstructure scheme of the diffusion couple obtainable by maintaining Cu and Zn blocks in contact for several days at 400°C. Shading indicates subsequent layers, each one corresponding to a one-phase region. The two-phase regions are represented by the interfaces between the one-phase layers (adapted from Rhines 1956).

component), it is possible to develop two-phase areas in the diffusion zone because of the higher degree of freedom. A systematic description of the diffusion couple technique and of its application to phase diagram determination has been presented by Kodentsov et al. (2001). The use of different modifications of the method and of its applications to the investigation of ternary systems are described and discussed. A summary is also given of the experimental procedures and of the micro-analytical techniques to be used in the determination of concentration profiles along a diffusion couple sample and in the local analysis of small areas of interest. Different measurement techniques have been mentioned such as the Auger electron spectroscopy, the secondary ion mass spectrometry, the Rutherford backscattering spectrometry, the glancing angle X-ray diffraction, EPMA and analytical electron microscopy. Especially interesting for the examination of bulk diffusion couple is the EPMA.

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With this technique, under an especially equipped electron microscope, highenergy electrons are focused on a fine probe and directed at the point of interest in the specimen. The electrons interacting with the sample atoms cause the emission of the characteristic X-rays, which are detected and identified for qualitative analysis and used, generally through suitable standardization, to perform also a quantitative analysis. As concluding remarks about these techniques, their increasing interest and the advantages of their combination with other techniques, we may mention, as an example, that within the European research project COST 535, concerning the ‘Thermodynamics of Alloyed Aluminides’, a meeting (Düsseldorf, December 2004) was dedicated to ‘The Diffusion Couple Technique’, presenting the principles of the method and the results obtained in the examination of several alloy systems. Zhao (2004) has developed an efficient variant of the diffusion couple technique (the ‘diffusion multiple approach’). A general treatment of a diffusion-controlled growth of a stoichiometric intermetallic in reaction between two two-phase alloys has been introduced by Paul et al. (2006). A reaction couple in which a layer of Co2Si is formed during interdiffusion from its adjacent saturated phases was used as a model system. In the discussion it has been emphasized that the diffusion couple is undoubtedly one of the most efficient and versatile techniques in solid-state science: it is therefore desirable to have alternative theories that enable us to deduce the highest possible amount of information from the data that are relatively easily attainable in this type of experiments. 2.4.1.5 The characterization and 3D representation of materials microstructure. Concerning micro-analytical techniques and their improvement, and their application to microstructural material investigation, interesting developments have been discussed and reported (Uchic et al. 2002) in the proceedings of a symposium dedicated to the characterization and representation of materials microstructure in 3D. Materials structure was intended to mean not only morphological and topological information, but also chemical and crystallographic information on various dimensional scales. It was observed that a common practice is to examine 2D planar sections of a material microstructure and then to make inferences (using stereological procedures) about the true spatial morphology, distribution and connectivity of the microstructure elements. It was underlined, however, that the need for inference could be reduced if one can obtain a direct 3D sampling of the microstructure. Advances towards this end in both destructive and non-destructive techniques have been described and discussed. The following are examples of methods which have been considered: 3D characterization by serial sectioning; focused ion beam tomography; X-ray micro-tomography; 3D X-ray crystal microscopy; computer

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reconstruction of 3D microstructure based on orthogonal observation sections; new stereological methods of analysis.

2.4.2 Assessment and calculation of phase diagrams 2.4.2.1 Assessment of phase diagrams. Selection, designing and planning of materials are relevant subjects from a fundamental point of view but, of course, are also interrelated basic topics in material science and engineering. Study and classification of preparation methods and of constitutional and fundamental properties followed by an investigation of application and performance characteristics are essential aspects of such topics and procedures. Among the basic properties of a given material the constitutional characteristics play a special preliminary role: indeed the structural and thermodynamic properties define the existence and the stability conditions (stability ranges of temperature, of composition, etc.) of the various phases of which the material consists. In other words, this means that one essential requirement in the evaluation and prediction of the performance of a material is the knowledge of its phase diagram, and we actually notice an ever-increasing attention to several aspects of phase diagram science in metallurgy but also in ceramurgy, polymer science, etc. A first problem, after the experimental analyses, is related to the collection (critical collection, assessment) of the experimental data. Different problems however have to be faced in the assessment procedures (data availability and reliability, agreement among data obtained by different authors and by using different methods, coherence of experimental data and trends with general principles and rules, etc.). Notice that a presently accepted version of a phase diagram generally is the result of a comparison and selection among the (often partial) data published for the given systems in several tens (in some cases hundreds) of papers. This of course is a problem common to several disciplines; as regards however alloy systems and related topics, such as intermetallic structures, a wide bibliography is available, a selection of which is collected in the reference list. Important steps towards an optimization of the procedures in order to make available to the community of chemists, physicists and material scientists sound databases for metallic phase description, transformation and equilibria have been performed in the course of time. A significant indication of this fact is given, for instance, by the growth in the number of publications, reference books and journals in which data relevant to phase diagrams are systematically reported and assessed, such as ‘Constitution of Binary Alloys’ Hansen and Anderko (1958), Elliott (1965), Shunk (1969), ‘Binary Alloy Phase Diagrams’ Massalski et al. (1990), ‘Phase Diagrams for Binary Alloys, Desk Handbook’ Okamoto (2000), ‘Multicomponent Alloy Constitution Bibliography 1955–1973’ Prince (1978), ‘Handbook of Ternary Alloy Phase Diagrams’ Villars

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et al. (1995), Pauling File (Villars et al. 2004 and subsequent editions), etc. Another clear indication of the relevance of these data and of their reliability is given by the different actions, often organized on an international basis, devoted to the assessment and critical evaluation of phase equilibria data. We may mention the activity of several institutions and bodies such as IAEA (International Atomic Energy Agency, Vienna) which, in special issues of its ‘Atomic Energy Review’ dedicated to various metals of nuclear interest, has published critical collections of physico-chemical properties of their compounds and alloys. APDIC, that is the Alloy Phase Diagram Commission which coordinates an international program on the subject and periodically publishes reports on the Journal of Phase Equilibria (now Journal of Phase Equilibria and Diffusion), MSIT® that is the Material Science International Team under the direction of G. Effenberg (MSI, Stuttgart) systematically organizes the collection, assessment and publication of the data (phase diagrams, phase crystal structures, thermodynamics) of large groups of ternary alloys. Several, critically evaluated, ternary alloy systems which have undergone a thorough review process have been previously published in the series ‘Ternary Alloys – A Comprehensive Compendium of Evaluated Constitutional Data and Phase Diagrams’; promoted by Petzow and Effenberg (1988 et seq., 19 volumes) and are now under publication in the New Series of ‘Landolt-Börnstein’ (Effenberg and Ilyenko 2004). A systematic contribution to the metals and alloys properties is given by the multi-volume ASM Handbooks (ASM International). See also in the following paragraphs on ‘Thermodynamic calculation’ (§ 2.4.2.2), some information concerning international efforts in critically collecting data about intermetallic systems. As a conclusion to these notes on the assessment and compilation of intermetallic data, we mention a few examples of papers in which criteria to be followed in order to ‘extract’ from literature data the ‘best’ version of a phase diagram have been discussed. These are Morral and Gupta (1991) (a figure of merit for predicted phase diagram), Okamoto and Massalski (1991, 1993) (thermodynamically improbable phase diagrams and guidelines for binary phase diagram assessment). See also various comments in several chapters in Cahn (2001). 2.4.2.2 Calculation, thermodynamic optimization of phase diagrams. The knowledge of phase equilibria, phase stability, phase transformations is an important reference point in the description and understanding of the fundamental properties of the alloys and of their possible technological applications. This interest has promoted a multi-disciplinary and multi-national effort dedicated not only to experimental methods, but also to techniques of optimization, calculation and prediction of

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phase diagrams, that is to the so-called CALPHAD methods (CALculation of PHAse Diagrams) (see Figure 2.43). Several approaches to this problem have been considered starting from the first calculations carried out by van Laar (1908) and the contributions given by Meijering

THEORETICAL CALCULATIONS Quantum mechanics, statistical thermodynamics, etc.

ESTIMATES According to CHEMICAL CRITERIA Periodic properties, Pettifor stability maps, Gschneidner relations, etc.

EXPERIMENTS Phase identification and characterization: Optical and electron microscopy, X-ray diffractometry, dilatometry, resistometry, etc.

Optimization

First principles or semiempirical calculations

Selection of suitable THERMODYNAMIC MODELS (with adjustable parameters) for the phases

EXPERIMENTS Thermal analysis, calorimetry, emf, vapour pressure measurements

EVALUATION OF PARAMETERS by error minimization procedures Models cannot reproduce input data: NEW MODELS NEEDED

Data added to DATA BASES, BOOKS, etc.

Analytical expression of THERMODYNAMIC FUNCTIONS of the phases

Calculation CALCULATED THERMODYNAMICS AND PHASE EQUILIBRIA

Input data insufficient for determination of adjustable parameters: NEW EXPERIMENTS NEEDED

EVALUATION OF PARAMETERS by error minimization procedures GRAPHICAL PRESENTATION of phase diagrams, thermodynamic functions, etc.

APPLICATIONS

Figure 2.43. Optimization, calculation, prediction of phase diagrams: an indication of the working scheme of the CALPHAD method is shown.

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(1963). Since the systematic introduction of electronic computers, however, and with special attention to metal systems, it is worth mentioning the pioneering work and the comprehensive summary already presented by Kaufman et al. (see Kaufman and Bernstein 1970) and the more recent discussion by Massalski (1989). The role of a thermodynamic approach is well known: a thermodynamic check, optimization and prediction of the phase diagram may be carried out by using methods such as those envisaged by Kubaschewski and Evans (1958), described by Kaufman and Nesor (1973), Ansara et al. (1978), Hillert (1981) and very successfully implemented by Lukas et al. (1977, 1982), Sundman et al. (1985). The knowledge (or the prediction) of the intermediate phases which are formed in a certain alloy system may be considered as a preliminary step in the more general and complex problem of assessment and prediction of all the features of phase equilibria and phase diagrams. See also Aldinger and Seifert (1993). It should be remembered that the CALPHAD approach is based on the hypothesis that, for all the phases and structures existing across the complete alloy system, entire Gibbs energy vs. composition curves may be constructed even by extrapolation into regions where they are unstable or metastable. A particular case concerns the pure component elements for which the relative Gibbs energy for the different crystal structures (the so-called lattice stabilities) must also be established and defined as a function of temperature (and pressure). Evidence relevant to the phase stability problem has been given by Massalski (1989). The so-called compound energy formalism was constructed by Hillert and Staffansson (1970) in order to describe models of the thermodynamic properties of phases with two or more sublattices showing a variation in composition, which therefore belong to the class of solution phases. A review of this formalism and a summary of its applications have been recently published by Hillert (2001) and Frisk and Selleby (2001). Finally, the significant progress and the limits of the ab initio, first-principle, calculations (Hafner 1987, 1989, Colinet 2003, Pettifor 2003), and the usefulness of a number of semi-empirical approaches have to be pointed out. Several schemes and criteria have been suggested to forecast and/or optimize the data concerning certain properties. In the following a short outline will be reported on some prediction methods based on selected correlations between elemental properties and structure formation. A significant review of several aspects of the phase diagram computation (phase diagram calculations in teaching, research and industry) has been published by Chang (2006). The relationship between the characteristic features of a phase diagram and the relative thermodynamic stabilities of the phases involved has been there underlined and exemplified. Representative examples of binary, ternary and highorder alloy systems have been presented. Moreover a number of applications have

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been illustrated. A first example was concerned with a rapid and efficient approach for generating a thermodynamic description of the quaternary Mo–Si–B–Ti system for identifying potential alloy compositions possibly exhibiting desirable microstructures for high-temperature applications. A second example concerned computations intended to define optimum compositions of Ti additions to glass-forming quaternary (Al, Cu, Ni, Zr) alloys in order to improve their glass-forming ability. The identification, through computational thermodynamics, of potential binary alloys with a tendency to form, via rapid quenching processes, glass or amorphous alloy thin films was also presented together with a discussion of possible applications of such materials. Another example examined consisted in the use of computational thermodynamics for selecting convenient filler metals to minimize cracks in welding multi-component aluminium alloys, and finally it was shown that computational thermodynamics can replace experimentation in procedures such as the certification of alloys for commercialization. (The alloy Ti6Al4V, that is, the Ti-based alloy with 6 mass% Al and 4 mass% V, was especially employed to illustrate this point.) Another relevant aspect of Chang’s review and of the included description of the CALPHAD approach is also the presentation of the continuing need to improve the thermodynamic phase models and a summary of the most useful ones. (i) Ab initio, first-principle calculations. The ab initio calculations are intended to obtain for the compounds their total energies, having only as input data the atomic numbers of the component elements and their atomic positions in the unit cell of a given crystal structure. From the computed energies, heats of formation, lattice parameters, relative stabilities of their structures, etc. may be derived for the compounds. Major problems are presented by calculations concerning liquid alloys and disordered solid solutions. From a combination of these results the calculation of first-principle (binary) phase diagrams could also be performed. Several relevant examples of review papers dedicated to this subject are available. See for example: Pettifor (1977), Saunders et al. (1988), Hafner (1992), Miodownik (1992), Turchi and Sluiter (1993), Carlsson and Meschter (1994), Turchi (1994), Pettifor et al. (1995), de Fontaine (1996). The state of the art has been summarized by Colinet (2003) who reported a description of the ab initio calculation methods of energies of formation for intermetallic compounds and a review of the aluminium-based compounds studied. In its conclusions, this paper underlined that the complete ab initio calculation of complex phase diagrams is not close at hand. However, calculation of phase diagrams in systems, where experimental data are missing, could, in the future, be performed by combination of CALPHAD routines and ab initio calculations of formation energies or mixing energies.

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A relevant contribution to the presentation of ab initio methods and of their application is a paper by Curtarolo et al. (2005). In the introduction the work by de Fontaine (1994) and the paper by Sluiter et al. (1988) are mentioned which contain full bibliographic references to the ab initio studies on binary and ternary phase stability until that date and, respectively, the earliest complete ab initio computation of a binary phase diagram. Curtarolo et al. (2005) presented the results of a first-principle study for 80 binary systems comparing these data with those contained in experimental compilations. According to their introductive remarks, 14 080 total energies on 176 crystal structures in these 80 binary alloys were computed. The energies were computed in the so-called local density (LDA) or generalized gradient approximation (GGA) to density functional theory which were considered standard approaches to first-principle studies on solids. As general references, see for instance: Perdew and Zunger (1981), Perdew and Wang (1992), Vanderbilt (1990), Kresse and Furthmuller (1996), Kresse and Joubert (1999). The formation energy for each structure was determined with respect to the most stable structure of the pure elements. It was underlined that to determine the ground state of a system one needs to find as a function of composition, the ordered compounds that have energy lower than any other structure or any linear combination of structures corresponding to the given composition. The set of ground state structures forms, in a energy vs. composition diagram, a convex hull (all other structures have an energy that falls above the set of tie-lines connecting the energy of ground states). This convex hull may be considered a representation of the Gibbs free energy of the alloy at zero temperature. As a specific example mention can also be given to the work carried out by Ghosh on the alloys of the fourth group metals (Ghosh and Asta 2005, Ghosh et al. 2006). In Fig. 2.44 the ab initio calculated enthalpy of formation of the Ti–Zn intermetallics is shown. The following introductive sentences may be quoted from the abstract of this work: ‘The total energies and equilibrium cohesive properties of 48 intermetallics in the Ti–Zn system are calculated from first principle employing electronic density functional theory, ultra-soft potentials and the GGA. Selected experiments are also performed to determine the heat of formation by direct reaction calorimetry and to measure the isotropic elastic moduli by pulse-echo technique. In alloys containing 50 at.% or less Ti, where it was possible to synthesize nearly single-phase specimens, the calculated heats of formation agree within a few kJ/mol of the direct reaction calorimetry data, while the calculated isotropic elastic constants agree within 5% of the experimental values’. (ii) Semi-empirical methods and rules. The prediction of the phase diagram aspect and/or of the thermodynamic function values has been the subject of a number

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Phase Diagrams in Alloy Systems

Enthalpy of formation (ΔH f) (kJ/atom)

10

5

0

6

−5

−10 5

1 2

−15

−20 Ti

3 20

40

60 at.% Zn

4 80

Zn

Figure 2.44 The Ti–Zn system. The calculated enthalpy of formation of the intermetallics and the resulting convex hull are shown according to Ghosh et al. (2006). Experimental values of about 22–19 kJ/mol of atoms were measured in the composition range 50–75 at.% Zn. The calculations yield a ground state convex hull defined by the following structures: (1) Ti3Zn–L12; (2) Ti2Zn–C11b; (3) TiZn–B19; (4) TiZn3–L12; (5) Ti3Zn22–tP100; (6) TiZn16–oS68.

of papers. Several empirical or semi-empirical rules and formulae have been proposed which may be useful in order to have a first, even if approximate, description of the characteristics of a given system. Notice that this kind of relations may be substantially more convenient when used in the description (in the comparison) of the properties of well-defined limited groups of similar alloys. Examples of such relations have been presented in § 2.2.1.3 describing the Pettifor parameters and maps, the evaluation of the heat of formation according to Miedema, etc. A few more examples have been collected in Chapter 4. (iii) Thermodynamic calculation. In the last few years several improvements and developments in phase properties ‘modelling’, together with an increasing availability of numerical methods and computer software, have allowed a systematic application of thermodynamic analysis to phase diagrams. As sketched in the scheme presented in Fig. 2.43, it is possible to perform an assessment of all the available experimental data (phase diagram measurements, but also thermodynamic data) to represent the Gibbs energy of all the phases (as function

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of temperature and composition) by means of ‘optimized equations’. An optimized version of the phase diagrams can then be calculated from these equations. The data can be interpolated and extrapolated, it is also possible to obtain an estimate of ternary and more complex diagrams, starting from the optimized data of the binary systems involved. These techniques, generally known as CALPHAD methods, minimize the number of experimental determinations to be carried out for a full phase diagram definition, and are therefore important in the analysis of complex systems. There are several computer programs available for performing the CALPHAD optimization, starting from the cited work by Kaufman and Bernstein (1970). A detailed presentation of the CALPHAD method with the description of thermodynamic models, computational methods and a discussion of the extensions and applications of these methodologies is available as an authoritative reference book by Saunders and Miodownik (1998). A very recent treatise on this subject is ‘Computational Thermodynamics’ by Lukas et al. (2007). Some guidelines for thermodynamic optimization of phase diagrams have been published by Kumar and Wollants (2001). One of the first programs is the Lukas program described by Lukas et al. (1977, 1982), which has modules to perform thermodynamic optimization of phase diagrams. A short reference list of recent frequently used programs (generally available for a fee) is given below: ● Thermo-Calc (Sundman et al. 1985, Andersson et al. 2002). It features a wide spectrum of thermodynamic models, databases and modules making it possible to perform calculations on most problems involving phase equilibria (phase transformation, stable and metastable equilibria, etc.). The calculations are performed using databases produced by an expert evaluation of experimental data. There are thermodynamic databases available for many different systems and applications. ● DICTRA (Diffusion simulation software) (Borgenstam et al. 2000). DICTRA (coupled with Thermo-Calc) is a software for the simulation of diffusion in multi-component alloy systems (processes which can be simulated are for example the homogenization of alloys, micro-segregation during solidification, carburizing, and decarburizing, of steels, etc.). © ● FactSage (Bale et al. 2002) which resulted from the fusion of the FACTWin/F*A*C*T and the ChemSage/SOLGASMIX (Eriksson and Hack, 1990) thermochemical packages (see www.crct.polymtl.ca and www. gtt-technologies.de). ● Pandat software package and applications (Chen et al. 1993). Pandat is a software package for multi-component phase diagram calculations. Given a set of thermodynamic parameters for all phases in a system and a set of user constraints, Pandat automatically calculates the stable phase diagram without

Phase Diagrams in Alloy Systems

●

●

75

requiring prior knowledge of the diagram. Details and applications have been described by Chen et al. (2002, 2003): in particular, as an example, an application using PanEngine (the calculation engine of Pandat) was given for coupling micro-modelling to predict microstructure and micro-segregation of aluminium alloys. MTDATA (Dinsdale et al. 1988, Davies et al. 2002). It is a software/database package for calculating multi-component phase diagrams. Depending on the data available, it finds applications in chemistry, metallurgy, geochemistry, materials science (interactions for instance between liquid and solid alloys, matte, slag and gas phase can be treated) (www.ues-software.com/mcpa/ homepage.htm). DATABASES (thermodynamic and diffusion). The calculations require a database for the material systems of interest. For the commercially important materials, databases have been developed by teams of experts critically assessing all experimental phase equilibria and thermodynamic data and, for the complex systems relevant for applications, by extrapolating from binary, ternary and quaternary subsystems. Databases, generally available for a fee, often together with software packages, have been prepared for several types of materials and systems. Typical examples are: a database developed for Fe-rich alloys containing data for up to 15 components, and 55 types of phases or similar databases for Mg-rich, Al-rich, Ni-rich, Ti-rich alloys. Other databases are available for different types of materials: semiconductors, solder alloys, ceramic systems, slag, molten salts, etc. The thermodynamic optimization of a complex system (with the implied assessment of its subsystems) generally requires the cooperative complementary lasting commitment of several experts. An answer to this request has been given by a number of international research projects; as an example, a few so-called European COST projects (European COoperation in the field of Scientific and Technical research). COST actions active in the specific field are, for instance, the COST 531 and 535 Actions. The former is dedicated to the investigation of Pb-free soldering alloys, that is, of low melting alloy systems which, for soft soldering, could replace the alloys of Pb owing to the toxicity of this element. The latter is dedicated to the experimental and computational investigation of complex aluminium alloy systems.

REFERECES

Albinati, A. and Willis, B.T.M. (1982) J. Appl. Crystallogr, 15, 361. Aldinger, F. and Seifert, H.J. (1993) Z. Metallkd, 84, 2.

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Andersson, J.-O., Helander, T., Höglund, L., Shi, P.F. and Sundman, B. (2002) Calphad, 26, 273. Ansara, I., Bernard, C., Kaufman, L. and Spencer, P. (1978) Calphad, 2, 1. Bale, C.W., Chartrand, P., Degterov, S.A., Eriksson, G., Hack, K., Ben Mahfoud, R., Melancon, J., Pelton, A.D. and Peterson, S. (2002) Calphad, 26, 189. Borgenstam, A., Engström, A., Höglund, L. and Ågren, J. (2000) J. Phase Equilib., 21, 269. Cahn, R.W. (1989) Angew. Chem. Int. Ed. Engl. Adv. Mater., 28, 1128. Cahn, R.W. (2001) The Coming of Materials Science, Pergamon Materials Series, Vol. 5 (Pergamon, Oxford). Carlsson, A.E. and Meschter, P.J. (1994) Ab initio calculations. In: Intermetallic Compounds. Vol. 1: Principles, eds. Westbrook, J.H. and Fleischer, R.L. (J. Wiley & Sons, Chichester), p. 55. Chang, Y.A. (2006) Metall. Mater. Trans. B, 37B, 7. Chelikowsky, R. and Phillips, J.C. (1978) Phys. Rev., B17, 2453. Chen, S.-L., Chou, K.C. and Chang Y.A., (1993) Metall. Trans., B21, 287. Chen, S.-L., Daniel, S., Zhang, F., Chang, Y.A., Yan, X.-Y., Xie, F.-Y., Schmid-Fetzer, R. and Oates, W.A. (2002) Calphad, 26, 175. Chen, S.-L., Zhang, F., Daniel, S., Xie, F.-X., Yan, X.-Y., Chang, Y.A., Schmid-Fetzer, R. and Oates, W.A. (2003) JOM, 55, 48. Chen, X.Q., Wolf, W., Podloucky, R. and Rogl, R. (2004) Intermetallics, 12, 59. Chvoj, Z., Sestak, J. and Triska, A. (ed.) (1991) Kinetic Phase Diagrams. Non Equilibrium Phase Transitions (Elsevier Science, Amsterdam). Colinet, C. (2003) Intermetallics, 11, 1095. Curtarolo, S., Morgan, D. and Ceder, G. (2005) Calphad, 29, 163. Darken, L.S. and Gurry, R.W. (1953) Physical Chemistry of Metals (McGraw-Hill Book Company, New York). Davies, R.H., Dinsdale, A.T., Gisby, J.A., Robinson, J.A.J. and Martin, S.M. (2002) Calphad, 26, 229. de Boer, F.R., Boom, R., Mattens, W.C.M., Miedema, A.R. and Niessen, A.K. (1988) Cohesion in Metals, Transition Metal Alloys (North-Holland, Amsterdam). de Fontaine, D. (1994) Solid State Physics, eds. Ehrenreich, H. and Turnbull, D., (Academic Press, San Diego), Vol. 47, p.33. de Fontaine, D. (1996) MRS Bull., 21 (8), 16. Dinsdale, A.T., Hodson, S.M., Barry, T.I. and Taylor, J.R. (1988) Proceedings of 27th Annual Conference of Metallurgists, Vol. 11 (CIM, Montreal), p. 59. Duwez, P. (1967) Trans. ASM Quart., 60, 605. Effenberg, G. and Ilyenko, S. (ed.) (2004) Landolt-Börnstein, Numerical Data and Functional Relationships in Science and Technology, Physical-Chemistry. Ternary Alloy Systems: Phase Diagrams, Crystallographic and Thermodynamic Data. Critically evaluated by MSIT® (Springer Verlag, Berlin). Elliott, R.P. (1965) Constitution of Binary Alloys, 1st Supplement (McGraw-Hill Book Company, New York). Eriksson, G. and Hack, K. (1990) Metall. Trans., B21, 1013.

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Evans, D.S. and Prince, A. (1978) Metal Sci., 12, 600. Frisk, K. and Selleby, M. (2001) J. Alloys Comp., 320, 177. Ghosh, G. and Asta, M. (2005) Acta Mater., 53, 3225. Ghosh, G., Delsante, S., Borzone, G., Asta, M. and Ferro, R. (2006) Acta Mater., 54, 4877. Giessen, B.C. and Willens, R.H. (1970) Phase Diagrams, ed. Alper, A.M. (Academic Press, New York), Vol. 3, p. 103. Gokcen, N.A. and Reddy, R.G. (1996) Thermodynamics, 2nd Edition (Plenum Press, New York). Goodman, D.A., Bennett, L.H. and Watson, R.E. (1983) Scripta Metall., 17, 91. Gordy, W. (1946) Phys. Rev., 69, 604. Gschneidner Jr., K.A. (1980) Theory of alloy phase formation, Proceedings of 108th AIME Annual Meeting, ed. Bennett, L.H. (New Orleans, LA, USA). Hafner, J. (1987) From Hamiltonians to Phase Diagrams (Springer, Berlin). Hafner, J. (1989) Cohesion and Structure, ed. Pettifor, D.G. and de Boer F.R. (NorthHolland, Amsterdam) Vol. 2. Hafner, J. (1992) Electron Theory in Alloy Design, ed. Pettifor, D.G. and Cottrell, A.H. (Institute of Materials, London). Hansen, M. and Anderko, K. (1958) Constitution of Binary Alloys (McGraw-Hill Book Company, New York). Hillert, M. (1981) Physica B, 103, 31. Hillert, M. (1998) Phase Equilibria, Phase Diagrams and Phase Transformations (Cambridge University Press, Cambridge). Hillert, M. (2001) J. Alloys Comp., 320, 161. Hillert, M. and Staffansson, L.-I. (1970) Acta Chem. Scand., 24, 3618. Hume-Rothery, W. (1931) The Metallic State (Oxford University Press, New York). Hume-Rothery, W., Christian, J.W. and Pearson, W.B. (1953) Metallurgical Equilibrium Diagrams, The Institute of Physics (Chapman & Hall Ltd., London). Jenkins, R. and Snyder, R.L. (1996) Introduction to X-ray Powder Diffractometry (J. Wiley & Sons Inc., New York). Kaufman, L. and Bernstein, H. (1970) Computer Calculation of Phase Diagrams with Special Reference to Refractory Metals (Academic Press, New York). Kaufman, L. and Nesor, H. (1973) Ann. Rev. Mater. Sci., 3, 1. Kodentsov, A.A., Bastin, G.F. and Van Loo, F.J.J. (2001) J. Alloys Comp., 320, 207. Kresse, G. and Furthmuller, J. (1996) Comput. Mater. Sci., 6, 15. Kresse, G. and Joubert, D. (1999), Phys. Rev., B59, 758. Kubaschewski, O. and Evans, E. (1958) Metallurgical Thermochemistry, 3rd Edition (Pergamon Press, New York). Kumar, K.C. and Wollants, P. (2001) J. Alloys Comp., 320, 189. Levinsky, Y. (1997) Pressure Dependent Phase Diagrams of Binary Alloys, (ASM International, Materials Park, OH, USA), Vol. 2. Lukas, H.L., Henig, E.-Th. and Zimmermann, B. (1977) Calphad, 1, 225. Lukas, H.L., Fries, S.G. and Sundman B. (2007) Computational Thermodynamics (Cambridge University Press, Cambridge).

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Lukas, H.L., Weiss, J. and Henig, E.-Th. (1982) Calphad, 6, 229. Massalski, T.B. (1989) Metall. Trans., 20A, 1295. Massalski, T.B., Okamoto, H., Subramanian, P.R. and Kacprzak, L. (1990) Binary Alloy Phase Diagrams, 2nd Edition (ASM International, Materials Park, OH, USA), Vols. 1–3. Meijering, J.L. (1963) Philips Res. Rep., 18, 318. Miedema, A.R. (1973) J. Less Common Met., 32, 117. Miedema, A.R. and Niessen, A.K. (1982) Physica, 114B, 367. Miodownik, A.P. (1992) Structural and Phase Stability of Alloys, eds. Moran-Lopez, J.L. et al. (Plenum Press, New York), p. 65. Morral, J.E. and Gupta, H. (1991) Scripta Metall., 25, 1393. Niessen, A.K., de Boer, F.R., Boom, R., De Chatel, P.F., Mattens, W.C.M. and Miedema, A.R. (1983) Calphad, 7, 51. Nonius Kappa CCD Program Package (1998) Nonius, Delft, The Netherlands. Okamoto, H. (1991) J. Phase Equilib., 12, 623. Okamoto, H. (2000) Phase Diagrams for Binary Alloys, Desk Handbook (ASM International, Materials Park, OH, USA). Okamoto, H. and Massalski, T.B. (1991) J. Phase Equilib., 12, 148. Okamoto, H. and Massalski, T.B. (1993) J. Phase Equilib., 14, 316. Parravano, N. (1912) Gazz. Chim. Ital., 42, 593. Parravano, N. (1914) Gazz. Chim. Ital., 44, 279. Parravano, N. and Sirovich, G. (1912) Gazz. Chim. Ital., 42, 1630. Paul, A., Kodentsov, A.A. and van Loo, F.J.J. (2006) Intermetallics, 14, 1428. Pauling, L. (1932) J. Am. Chem. Soc., 54, 3570. Pauling, L. (1967) The Chemical Bond, 3rd Edition (Cornell University, Ithaca). Pelton, A.D. (1991) Thermodynamics and phase diagrams of materials. In: Phase Transformations in Materials, Vol. 5: Materials Science and Technology: A Comprehensive Treatment, eds. Cahn, R.W, Haasen, P. and Kramer, E.J. (VCH, Weinheim). Pelton, A.D. and Schmalzried, H. (1973) Metall. Trans., 4, 1395. Pelton, A.D. and Thompson, W.T. (1975) Prog. Solid State Chem., 10, 119. Perdew, J.P. and Wang, Y. (1992) Phys. Rev., B45, 13244. Perdew, J.P. and Zunger, A. (1981) Phys. Rev., B23, 5048. Pettifor, D.G. (1977) Calphad, 1, 305. Pettifor, D.G. (1984) Solid State Commun., 51, 31. Pettifor, D.G. (1985) J. Less Common Met., 114, 7. Pettifor, D.G. (1986) J. Phys. C: Solid State Phys., 19, 285. Pettifor, D.G. (2003) Acta Mater., 51, 5649. Pettifor, D.G., Aoki, M., Gumbsch, P., Horsfield, A.P., Nguyen-Manh, D. and Vitek, K. (1995) Mat. Sci. Eng., A192/193, 24. Petzow, G. and Effenberg, G. (eds.) (1988 et seq.) Ternary Alloys. A Comprehensive Compendium of Evaluated Constitutional Data and Phase Diagrams (VCH, Weinheim). Prince, A. (1978) Multicomponent Alloy Constitution Bibliography 1955–1973 (The Metals Society, London). Rajasekharan, T. and Girgis, K. (1983) Phys. Rev., B27, 910.

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Chapter 3

Structural Characteristics of Intermetallic Phases

3.1. PRELIMINARY REMARKS

In the previous chapter some questions concerning intermetallic systems were analyzed by using as examples various types of phase diagrams. We have seen in many systems the formation, in the liquid and/or in the solid state, in stable or metastable conditions, of different types of phases: non-stoichiometric phases, homogeneous in certain ranges of composition, which in the case of terminal phases include the constituents themselves, and/or stoichiometric phases. Large fields of homogeneity (extensive solubility) are generally met in the liquid state, for which the most frequent behaviour in metallic systems corresponds to the formation of a ‘continuous’ solution ranging from one component to the other. See for instance the singlephase field of the continuous liquid solution in a variety of phase diagrams such as those depicted in Figs 2.1 and 2.9. In a few cases, at least for certain temperature ranges, more than one liquid phase may be formed in a given system. See for instance Figs 2.16 and 2.18(e). The situation in the solid state is generally more complex. Several examples of binary systems were seen in which, in the solid state, a number of phases (intermediate and terminal) are formed. See for instance Figs 2.18–2.21. Both stoichiometric phases (compounds) and variable composition phases (solid solutions) may be considered and, as for their structures, both fully ordered or more or less completely disordered phases. This variety of types is characteristic for the solid alloys. After a few comments on liquid alloys, particular attention will therefore be dedicated in the following paragraphs to the description and classification of solid intermetallic phases. In this chapter, general aspects and structural properties of crystalline solid phases are described, and a short introduction is given to modulated and quasicrystal structures (quasi-periodic crystals). Elements of structure systematics with the description of a number of ‘structure types’ are presented in the subsequent Chapter 7. Finally, both in this chapter and in Chapter 6, dedicated to preparation techniques, characteristic features of typical metastable phases are considered with attention to amorphous and glassy alloys. 81

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r (μΩ cm)

400

300

200

100

Li

20

40

60

at.% Pb

80

Pb

Figure 3.1. Li–Pb system: averaged values (in the temperature range between 400°C and 800°C) of the resistivity of the liquid alloys (Van der Lugt 1996).

3.2. LIQUID INTERMETALLIC PHASES

A summary of the general alloying behaviour in the liquid state for the different binary alloys was presented in the previous chapter and described with the map shown in Fig. 2.17. Very often a single liquid phase exists with a continuous trend of properties in the complete range of compositions from one component to the other. However, in several cases, for certain compositions, extrema in the physical properties of the liquid are observed when these are plotted as a function of the composition. According to Van der Lugt (1996) a liquid compound can be identified at these points. See the trend of the resistivity of the liquid Li–Pb alloys presented in Fig. 3.1: a sharp peak is observed at 21 at.% Pb and the formation of an octet compound, Li4Pb has been suggested. In the Li–Pb phase diagram a number of solid compounds are formed around 20 at.% Pb. Notice that the ‘octet rule’ is a concept of the chemical bonding description based on the assumption that, in the formation of compounds, atoms exhibit a tendency for their valence shell either to be empty or to have a full complement of eight electrons (octet) as in Li4Pb (4 1 1 4) : 8 electrons (see also Chapter 4). Further evidence of the peculiar behaviour of the liquid at this composition may be obtained by measuring several other properties. Enthalpies of mixing of liquid Li–Pb alloys were determined by Predel and Oehme (1979) over the entire concentration range through calorimetric investigations (see Fig. 3.2).

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83

xPb

ΔH (kJ/mol at)

Li

0.2

0.4

0.2

0.4

0.6

0.8

0.6

0.8

Pb

–10

–20

–30

50

dΔH /dx

0

–50

–100

–150

Li

xPb

Pb

Figure 3.2. Li–Pb system: trend of the mixing enthalpy, ΔH, of the liquid alloys (after Predel and Oehme 1979) and dΔmixH/dx vs. composition.

A minimum is observed for xPb 0.22. The deviation of this system from regular behaviour was explained by the existence of associates in the alloy melts. An associate having this composition (Li7Pb2) was assumed and a good agreement was obtained between the values calculated on this basis and the experimental values. In a more general way, according to Sommer (1978, 1982), it may be noticed that thermodynamic quantities show peculiar trends in the same concentration ranges where solid-state intermetallic phases or compounds exist. It has been suggested that this behaviour can be described by considering the liquid alloy as

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consisting of some ‘associated atoms’ which are in dynamic equilibrium in a number of binary alloy melts with compound-forming tendency and with anomalies in their concentration dependence. These are for instance a more or less clearly defined triangular shape of the mixing enthalpies vs. concentration, a temperature dependence of ΔH values associated with positive ΔCp values, etc. A comparison between the behaviour in the liquid and in the solid state is schematically presented in Fig. 3.3 for a number of alloys of the alkali metals with Tl

Sn

Pb

Bi

Li

Na

K

Rb

Cs

A

2L

at.% Me

2L

2L

2L

2L

A

Me

A

Me

A

Me

Me

Figure 3.3. Schematic representation of the diagrams for the alkali metals with a selected number of elements of the p-block. In each box the solid intermediate phases are represented in the positions approximately corresponding to their compositions (long bars: congruent melting phases; short bars: non-congruent phases). In the top part of each box every mark corresponds to a characteristic composition of the liquid phase for which the formation of an ‘associate’ (‘liquid compound’) may be suggested, for instance by the presence of an extremum in the trend of some property of the liquid phase. The symbol 2 L shown for certain ranges of compositions in a few diagrams indicates the presence of a miscibility gap in the liquid state, that is: two liquid phases.

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a few elements of the last groups of the periodic table (13th and subsequent groups) called p-block elements. General characteristics of alloys such as those presented in Fig. 3.3 have been discussed by Fässler and Hoffmann (1999) in a paper dedicated to ‘valence compounds at the border of intermetallics (alkali and alkaline earth metal stannides and plumbides)’. Examples showing gradual transition from valence compounds to intermetallic phases and new possibilities for structural mechanisms and bonding for Sn and Pb have been discussed. Structural relationships with Zintl phases (see Chapter 4) containing discrete and linked polyhedra have been considered. See § 3.12 for a few remarks on the relationships between liquid and amorphous glassy alloys. A number of features and characteristics of liquid alloys have been discussed in a review by Van der Lugt and Verkerk (2002). It was underlined that the molten, so-called, Zintl phases make up an interdisciplinary subject with three main components: crystal chemistry of Zintl ions, the physics of liquids and the electron theory in disordered materials. According to van der Lugt and Verkerk (2002), Zintl ions (see also § 4.4.3) are polyanions formed by anion clustering in ionic alloys and two categories may be distinguished: those that fit the so-called Zintl–Klemm concept and those that are electron deficient. The Zintl–Klemm ions (octet compounds) may be described as formed by an electronegative element of the nth group which accepts an electron (from the electropositive component) obtaining the electron configuration typical of an element of the (n 1)th group. Typical examples described are for instance KPb, RbPb containing the (Pb4)4 ion analogous, isoelectronic, with P4, As4. In NaSb, KSb, infinite Sb chains may be identified similar to Te chain. As an example of an electron-deficient structure Me8Tr11 compounds are considered (containing some Me K, Rb, Cs metals and (Tr11)7 ions with Tr Ga, In, Tl. Physical properties and detection of liquid Zintl compounds have been discussed and problems of gradual development of stoichiometries in non-clustering liquid ionic alloys, and their agreement with those persisting in the solid, have been considered. Neutron diffraction techniques and the results of their applications (Ga, Tl, alkali alloys) have been described.

3.2.1 Recent investigations on liquid alloys In a special issue (4/2006) of the International Journal of Materials Research (formerly Zeitschrift für Metallkunde) a number of papers have been collected which have been dedicated to liquid alloys and their properties. A short summary of these, even without any claim to be systematic, highlights some research problems into liquid metals and alloys.

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Liquid–liquid interfacial tension, and density difference, in the immiscible (monotectic) alloy (Al34.5Bi65.5)95Si5 (mass%) have been measured by Kaban and Hoyer (2006). Addition of Si to the binary Al–Bi alloy increases the interfacial tension between the Al-and Bi-rich liquid phases. Surface tension and density of liquid alloys have been studied by Moser et al. (2006). Measurements by maximum bubble pressure and dilatometric techniques were carried out in an extensive range of temperatures on liquid alloys close to the ternary eutectic Sn3.3Ag0.76Cu with different Sb additions, which decrease surface tension and density. The experimental data were discussed in comparison also with values calculated on the basis of different models. The velocity of sound has been measured (Tsuchiya 2006) as a function of temperature to investigate structural changes in molten As–Sb alloys. The velocity of sound was measured with a standard pulse technique: piezoelectric ceramic, operated at about 8.8 MHz, were used to produce and detect the sound pulse. The overall profile of temperature dependence of the sound velocity in the different alloys changes smoothly from Sb to As. The results indicate that a tendency to change structures in the super-cooled state develops with increasing As fraction. The results are in agreement with previous observations that molten As changes rapidly its structure in the under-cooled state and it is already in the high-temperature side of an assumed liquid–liquid transition at the melting point. Trends, in the periodic table, for liquid–liquid transition have been summarized and discussed. By using a thermodynamic model based on the formation of self-associates, as proposed by Singh and Sommer (1992), Akinlade and Awe (2006) studied the composition dependence of the bulk and surface properties of some liquid alloys (Tl–Ga at 700°C, Cd–Zn at 627°C). Positive deviations of the mixing properties from ideal solution behaviour were explained and the degree of phase separation was computed both for bulk alloys and for the surface. A first-principle approach has been used by Singh and Ali (2006) in a study of liquid Na–Cd alloys. The Na–Cd diagram is characterized by the formation of two congruently melting compounds (Na2Cd11, melting point 364°C, and NaCd2, 384°C). As for the liquid alloys (at, say, 400°C), it has been observed, and confirmed by several experimental and theoretical investigations, that these alloys exhibit transformation to an ordered phase at large contents of Cd. The entropy of mixing vs. composition variation is S-shaped: it is negative towards the Cd-rich region and positive towards the Na-rich region. Previously (Singh et al. 1991) a description of liquid Na–Cd alloys (close to the melting temperature) in terms of chemical complexes (Na 2Cd M NaCd2) was proposed and employed to give an explanation of the composition-dependent asymmetry of the thermodynamic properties. A first-principle approach based on a pseudo-potential perturbation scheme (with the Gibbs–Bogoliubov variation technique) was used by Singh and Ali (2006); they

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found that the deepening of the structural part of the entropy around the composition xNa 0.33 is responsible for the S-shaped entropy and suggests the existence of short-range order in the liquid. Finally, a paper may be mentioned concerning surface and transport properties of Au–Sn liquid alloys (Novakovic et al. 2005). The surface tension measurements on molten Au and Au–Sn alloys over the whole composition range were performed by using a special drop method (Passerone and Ricci 1998). The sample, placed in a special sapphire crucible, was introduced at the centre of a chamber, in a horizontal furnace heated by a high-frequency generator coupled to a graphite heater. The surface tension was measured by decreasing the temperature step by step in the range 1200–1000°C. Resting on a levelled substrate, the sample was illuminated by an aligned light source and its image analysed by means of specific software which allows fast automatic acquisition of the surface tension data and other parameters (temperature, oxygen partial pressure). The temperature dependence of the surface tension of the liquid alloys exhibits a negative trend for all compositions. The thermodynamic functions of mixing show an asymmetrical behaviour at the equiatomic composition that corresponds to the energetically favoured compound AuSn. The applicability of the ‘complex formation model’ was examined and discussed in the framework of statistical mechanical theory in conjunction with ‘quasi-lattice theory’ to describe surface and transport properties of Au–Sn liquid alloys.

3.3. INTERMETALLIC COMPOUND CHEMISTRY IN THE SOLID STATE

In the previous chapter we looked at some questions concerning solid intermetallic phases both terminal (that is solubility fields which include one of the components) and intermediate. Particularly we have seen, in several alloy systems, the formation in the solid state of intermetallic compounds or, more generally, intermetallic phases. A few general and introductory remarks about these phases have been presented by means of Figs. 2.2–2.4, in which structural schemes of ordered and disordered phases have been suggested. On the other hand we have seen that in binary (and multi-component) metal systems, several crystalline phases (terminal and intermediate, stable and also metastable) may occur. Several phase diagrams of binary alloy systems have been shown (see for instance Fig. 2.18) in which the existence of intermediate phases may be noticed. In these systems we have seen the formation of AmBn phases, which generally crystallize with structures other than those of the constituent elements, and which have negligible homogeneity ranges. Thermodynamically, the composition of any such phase is variable. In a number of cases, as those exemplified in Fig. 2.19, the possible variation in composition is very small (invariant composition phases or

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stoichiometric phases, or ‘compounds’ proper, also called ‘point compounds’ in binary alloys). In Fig. 2.21, on the contrary, we observed in a number of systems that solid phases with a variable composition were formed (non-stoichiometric phases). In the reported diagrams we saw examples of both terminal and intermediate phases. These phases are characterized by homogeneity ranges (solid solubility ranges) which, in the case of the terminal phases, include the pure components and which, generally, have a variable temperature-dependent extension. In the older literature, stoichiometric and non-stoichiometric phases were often called ‘daltonides’ and ‘berthollides’, respectively. These names, however, are no longer recommended by the Commission on the Nomenclature of Inorganic Chemistry (International Union of Pure and Applied Chemistry, IUPAC), Leigh (1990). More complex situations were shown in Figs. 2.26 and 2.27, where some typical examples of isobarothermal sections of ternary alloy phase diagrams were presented. In the case of ternary systems, several binary and ternary stoichiometric (Fig. 2.28) phases and/or different types of variable composition phases (Fig. 2.29) may be found. We may differentiate between these phases by using terms such as: ‘point compounds’ (or point phases, that is, phases represented in the composition triangle, or more generally in the composition simplex by points), ‘line phases’, ‘field phases’, etc. As a starting point in the description of the solid intermetallic phases it is useful to recall that their identification and classification requires information about their chemical composition and structure. To be consistent with other fields of descriptive chemistry, this information should be included in specific chemical and structural formulae built up according to well-defined rules. This task, however, in the specific domain of the intermetallic phases, or more generally in the area of solidstate chemistry, is much more complicated than for other chemical compounds. This complexity is related both to the chemical characteristics (formation of variable composition phases) and to the structural properties, since the intermetallic compounds are generally non-molecular in nature, while the conventional chemical symbolism has been mainly developed for the representation of molecular units. As a consequence there is no complete, or generally accepted, method of representing the formulae of intermetallic compounds. Some details and questions about these points will be discussed in the next paragraphs. These will then be used for a description of selected common phases and a presentation of a few characteristic features of intermetallic crystal chemistry. 3.4. IDENTIFICATION OF THE INTERMETALLIC (SOLID) PHASES

The identification and characterization of an intermetallic solid phase requires the determination and analysis of a number of points, which in the following paragraphs will be defined and discussed with a few details, starting with attention to

Structural Characteristics of Intermetallic Phases

89

crystalline phases, while glassy alloys, quasi-periodic structures, quasicrystals will be briefly presented in § 3.11 and 3.12. A number of points are relevant for a full crystallochemical characterization; for each of them a few noteworthy remarks will be presented in the following. To this end, crystallographic conventions, nomenclature and symbols will be used. For a summary of these and of the corresponding definitions the most important reference book is International Tables for Crystallography (Hahn 2002). The following features and aspects will be considered: (a) Chemical composition (and the homogeneity composition range and its temperature and pressure dependence). (b) Structure type (or crystal system, space group, number of atoms per unit cell and list of occupied atomic positions). (c) Values of a number of parameters characteristic of the specific phase within the group of isostructural phases (unit cell edges, occupation characteristics and, if not fixed, coordinate triplets of every occupied point set). (d) Volumetric characteristics (molar volume of the phase, formation volume contraction or expansion, space-filling characteristics, etc.). (e) Interatomic connection characteristics (local atomic coordination, long-distance order, interatomic distances, their ratios to atomic diameters, etc.). (f) Relationships with other phases and structure types (comparison of the phase structural data with those relevant to other isostructural phases; comparison of the crystallochemical characteristics of the phase with those of other compounds formed by the same elements). Clearly, not all the data relevant to the aforesaid points are independent of each other. The strictly interrelated characteristics listed under (d) and (e), for instance, may be calculated from the data indicated in (b) and (c), from which the actual chemical composition of the phase can also be obtained. 3.5. COMPOSITION AND COMPOSITIONAL FORMULA OF THE INTERMETALLIC PHASE

As in the other fields of inorganic chemistry, simple compositional formulae are often used for intermetallic phases; these, for instance, Mg2Ge, ThCr2Si2, etc., are useful as quick references, especially for simple, stoichiometric, compounds. The following remarks may be noteworthy. 3.5.1 Order of citation of element symbols in the formula The symbol sequence in a formula (LaPb3 or Pb3La) is of course arbitrary and, in particular cases, it may be a matter of convenience. Alphabetical order has often

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been suggested (for example by the IUPAC, Leigh 1990) and may be especially convenient in phase indexes, directories, etc. A symbol sequence based on chemical properties, however, may be more useful when, for instance, compounds with analogous structures have to be compared (Mg2Ge and Mg2Pb). A symbol quotation order based on a parameter introduced by Pettifor (1984, 1986) has been suggested (see for instance Petzow and Effenberg 1988 et seq.) and will also be used here. In fact, in order to stress the chemical character of the elements and to simplify their description, Pettifor (1984, 1985, 1986), as described in the § 2.2.1.3 and in the enclosed tables, created a new chemical scale (χ) which orders the elements along a simple axis. The progressive order number of the elements in this scale, the so-called Mendeleev number, can also be considered. These Mendeleev numbers M, which, of course, are different from the atomic numbers, start, according to Pettifor, with the least electronegative elements He 1, Ne 2, … and terminate with the most electronegative ones … N 100, O 101, F 102 up to H 103. On the basis of the Pettifor scale, the suggestion has been made that the element E with a lower-value ME (or χE) is quoted first in the formulae of its compounds. This will be generally adopted here and, therefore, we will prefer formulae such as PbCl2, ZnS, NiAs, MnCu2Al, etc. (instead of, for instance, Cl2Pb, AsNi, etc.). Notice, however, that for a quick reference the alphabetical order has been used in the formula index of Chapter 7.

3.5.2 Indication of constituent proportions No special comments are needed for stoichiometric compounds (LaPb3, ThCr2Si2, etc.). A more complex notation is needed for non-stoichiometric phases. Selected simple examples are given below, and more detailed information will be reported when discussing crystal coordination formulae: (a) Ideal formulae: While considering a variable composition phase, it is often possible to define an ‘ideal composition’ (and formula) relative to which the composition variations occur (or are considered to occur). This composition may be that for which the ratio of the numbers of different atoms corresponds to the ratio of the numbers of the different crystal sites in the ideal (ordered) crystal structure (as suggested by IUPAC, Leigh 1990). These formulae may be used even when the ‘ideal composition’ is not included in the homogeneity range of the phase (Nb3Al for instance shows a homogeneity range included between 18.6 and 21.5 at.% Al at room temperature and which hardly reaches 25 at.% Al at 1940°C). At the peritectic formation temperature of 2060°C the composition of the phase is about 22.5 at.% Al.

Structural Characteristics of Intermetallic Phases

91

(b) Approximate formulae: A general notation which has been suggested by IUPAC when only little information has to be conveyed, and which can be used even when the composition variation mechanism is unknown, is to put the sign (read as ‘circa’ or ‘approximately’) before the formula; for instance In2Bi. (c) Variable composition formulae: (Ni,Cu) or NixCu1x (0 x 1) are the equivalent representations of the continuous solid solution between Ni and Cu, homogeneous in the complete range of compositions; other examples are: Ce1xLaxNi5 (0 x 1); (Ti1xCrx)5Si3 (0 x 0.69 at 1000°C); etc. Similar formulae may also be used in more complicated cases to convey more information: AmxBnxCp (… x …) (phase involving substitution of atoms A for B). A1xB may indicate that there are A-type vacant sites in the structure. LaNi5Hx (0 x 6.7) indicates the solid solution of H in LaNi5 (d) Site occupation formulae: According to the Recommendations of the Commission on the Nomenclature of Inorganic Chemistry (Leigh 1990), additional information may be conveyed by using a more complex symbolism; suggestions have also been made about the indication of site occupation and of their characterization. These points will be discussed in more detail in the following sections. However for the indication of site occupation, the following criteria have been suggested by the Commission. The site and its occupancy are represented by two right lower indexes separated by a comma. The first index indicates the type of site; the second one indicates the number of atoms in this site. (AA, for instance, means an atom A on a site occupied by A in the ideal structure, whereas AB represents an atom A in a site normally (ideally) occupied by B). A formula such as: MM,1x NM,xMN,xNN,1x or (M1xNx)M(MxN1x)N represents a disordered alloy, whereas the ideal composition is MN with an ideal MMNN structure and in which the ‘M sites’ are occupied by (1 x) M atoms and xN atoms. In this notation vacant sites may be represented by 䊐 or by v. A species occupying an interstitial site, which is unoccupied in the ideal structure, is indicated by the subscript i. The following examples of alloy formulae have been reported: MgMg,2xSnMg,xMgSn,xSnSn,1x indicates a partially disordered alloy (related to the ‘ideal’ formula Mg2Sn) with some of the Mg atoms on Sn sites, and vice versa; (Bi2xTex)Bi(BixTe3x)Te indicates the composition changes from the ideal Bi2Te3 formula; AlAl,1PdAl,xPdPd,1x䊐Pd,2x shows that in the phase (corresponding to the ideal composition PdAl), every Al is on an Al site, but x Pd atoms are on Al sites, (1x) Pd atoms in Pd sites and 2x Pd sites are vacant.

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This type of description and formulae may be especially useful when considering thermodynamic properties of the phase, and when dealing with solid solution models and quasi-chemical equilibria between point defects. More details about this point may be found in the book on the calculation of phase diagrams by Saunders and Miodownik (1998). In their description of ‘thermodynamic models for solution and compound phases’ they presented the sublattice model reminding us that, to this end, a sublattice phase can be envisaged as being composed of interlocking sublattices on which the various components can mix. It is usually crystalline in nature, but the model can also be extended to consider ionic liquids when mixing on particular ionic sublattices is considered. The model, as used in applied thermodynamics, is phenomenological in nature and does not define any crystal structure within its formulation. However, it has been noticed that the fruitful extension of this concept to the modelling of complex intermetallic phases, such as the so-called σ, μ, χ and Laves phases, may be simplified if a coherent crystallographic approach is used and due consideration is given to the classification of the possible sites corresponding to the sublattices presumed on the basis of their symmetry, coordination, etc. (Ansara et al. 1997, Ferro and Cacciamani 2002) and to the differentiation of their occupation on the basis, for instance, of their atomic dimensions. (e) Polymorphism descriptors: Several substances may change their crystal structure because of external conditions such as temperature and pressure. These different structures (polymorphic forms) may be distinguished by using special designators of the stability conditions. If the various crystal structures are known, explicit structural descriptors may obviously be added. According to a simple but systematic notation, the different temperature modifications are indicated by lower case letters in parenthesis behind the phase designation, with (h) high-temperature modification, (r) room temperature modification and (l) low-temperature modification; h1, h2, etc. represent different high-temperature modifications. In the description of a number of modifications which are stable at different temperatures, the letters are used in the sequence h2, h1, r, l1, l2, …, corresponding to the decreasing stability temperature. Similarly a form stable only under high pressure can by described by the symbol HP. Table 3.1 shows a few examples of this notation. In this case, of course, the temperature and composition ranges of stability explicitly indicated for all the phases give additional or more detailed information. The Greek letters assigned to the phases of the systems may be considered as arbitrary (‘pseudonyms’ of the formula or synonyms). Similarly to what can be observed for several common alloys of practical interest, these symbols often date back to the first investigation of the

93

Structural Characteristics of Intermetallic Phases

Table 3.1. An example of crystallochemical description of an alloy system. Binary solid phases in the Al–Cu system. Phase/ ideal formula/ temperature range (°C)

Pearson symbol/ prototype

Lattice parameters (pm) (composition at.% Cu)

Maximum composition range (at.% Cu)

(Al) 660.452 Θ, Al2Cu 592 η1, AlCu 624–560

cF4 Cu tI12 Al2Cu o*32

a 404.96 (at 298 K)

0–2.5 32.05 to 32.6

η2, AlCu 563

mC20

ζ1, Al4Cu5 590–530

oF88 (83.3)

ζ2, Al4Cu5 570

oI24 (20.5)

ε1, Al4Cu5 958–850 ε2, AlCu1x 850–560 δ, Al3Cu2 686 γ0, Al4Cu9 1040–800 γ1, Al4Cu9 900 β AlCu3 1049–567 α2 AlCu3 363 (Cu) 1084.6

c**

a 606.7 (at 33 at.%) c 487.7 a 410 b 1202.4 (at 49.8 at.%) c 865 a 1206.6 b 410.5 (at 49.8 at.%) c 691.3 β 55.04° a 812.7 b 1419.9 c 999.3 a 409.7 b 703.1 c 997.9 –

hP6 (6x) Ni2In hR*

a 414.6 (at 57.4 at.%) c 506.3 –

55.0–61.1

cI52 Cu5Zn8 cP52 Al4Cu9 cI2 W Related to the tI8 TiAl3 type cF4 Cu

–

63–69

a 870.23 (at 68 at.%)

62.5–68.5

a 294.6

69.5–82

a 366.8 c 368.0 a 365.4 (at 85 at.%) a 361.46 (at 100 at.%) (at 298 K)

76.5–78

49.8–52.4

49.8–52.3

55.2–56.8

55.2–56.3

59.4–62.1

59.3–61.9

80.3–100

alloy involved when the precise identification and the chemical and crystallographic definition of a phase were much more uncertain. In several cases, however, Greek characters, sometimes assigned in alphabetical order according to the composition, are still used as short alloy symbols (see § 3.7.8). In connection with this

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Intermetallic Chemistry

group of descriptors other indicators such as (am), (vt), etc. for amorphous, vitreous substances are sometimes used. For instance: SiO2(am) amorphous silica; Si(am)Hx amorphous silicon doped with hydrogen. For general remarks on amorphous, glassy metastable phases (see § 3.12).

3.6. CRYSTAL STRUCTURE OF THE SOLID PHASE AND ITS STANDARD REPRESENTATION

3.6.1 General remarks, unit cell description The characterization, the full identification, of a phase requires a complete and detailed description of its structure. As examples, consider the data, obtained from X-ray diffraction experiments, reported in Table 3.2 for stoichiometric and variable composition phases. An explanation of the various symbols used will be given in the following paragraphs. For a general reference to symbols, definitions and

Table 3.2a. Examples of crystallographic description of phase structures: stoichiometric or nearly stoichiometric compounds. Cell dimensions in picometres. CsCl (stoichiometric compound) – Primitive cubic; a 411.3 pm; space group Pm 3m, N. 221 1 Cs in (a): 0, 0, 0 1 1 Cl in (b): ⁄2, 1⁄2, 1⁄2 The two special (a) and (b) Wyckoff positions have no free coordinate parameter. The two occupancy parameters are 100%. The Pearson symbol is cP2. Mg2Ge (stoichiometric compound) – Face-centred cubic; a 638.7 pm; space group Fm 3m, N. 225 1 1 1 1 1 1 Atomic positions: (0, 0, 0; 0, ⁄2, ⁄2; ⁄2, 0, ⁄2; ⁄2, ⁄2, 0) 4 Ge in (a): 0, 0, 0 1 8 Mg in (c): ⁄4, 1⁄4, 1⁄4; 1⁄4, 1⁄4, 3⁄4 No free parameters in the atomic positions of Mg and Ge. In this case the two occupancy parameters have been found to be 100%. The Pearson symbol is cF12 (CaF2 is considered the prototype of this structure). MoSi2 (nearly stoichiometric compound) Body-centred tetragonal; a ⫽ 319.6–320.8 pm and c 785–790 pm, according to the composition; space group I4/mmm, N. 139 Atomic positions: (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) 2 Mo in (a): 0, 0, 0 4 Si in (e): 0, 0, z; 0, 0, z–; (z 0.333) The Si position has the free parameter z, for which, in this particular case, the value 0.333 has been determined; the two occupancy parameters are 100%. The Pearson symbol is tI6.

Structural Characteristics of Intermetallic Phases

95

nomenclature see ‘The International Tables of Crystallography’ (Hahn 2002). These data, their symbolic representation, and the table itself correspond to what may be called the normal (reference) description. It is adopted in all the compilations and atlases of crystal structures. From this description, however, alternative (and/or complementary) presentations of the structure and different symbolic representations can be deduced. These are often differently defined for specific groups of compounds and may be useful to obtain a clearer view of the atomic assembly and/or to make an easier comparison between different compounds. In other words it must be underlined that there is no ideal way of describing all structure types. The most appropriate way of description depends on the structure itself but also on a number of points we are interested in emphasizing (comparison with other structural types, comparison with other compounds of the same element, etc.). These points will be discussed in a few subsequent sections after the presentation of the ‘conventional’ description.

Table 3.2b. Examples of crystallographic description of phase structures: non-stoichiometric compounds. Cell dimensions in picometres. Mo2N (non-stoichiometric phase, partial occupancy) Body-centred tetragonal; a 420.0 pm, c 801 pm; space group I41/amd, N. 141. Atomic positions (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) 4N in (a): 0, 0, 0; 0, 1⁄2, 1⁄4 (occupancy parameter 0.75) 8 Mo in (e): 0, 0, z; 0, 1⁄2, 1⁄4z; 1⁄2, 0, 3⁄4z; 1⁄2, 1⁄2, 1⁄2z; (occupancy parameter 1) The occupancy parameter of N is 75% that is three atoms are statistically distributed in the four positions. The real stoichiometry corresponds to Mo2N0.75 and in the unit cell there are 11 atoms instead of the ideal value of 12. The Mo position has the free parameter z for which, in this particular case the value 0.258 has been determined. The Pearson symbol is tI12 (11). Pt3Cd0.6Zn4.4 (Pt5CdZn7) (non-stoichiometric phase with partial substitution of Cd and Zn atoms) Hexagonal, a 705.0 pm, c 279.2 pm; space group P31 m, N. 157. 1 2 Me1 in (b): ⁄3, 2⁄3, z; 2⁄3, 1⁄3, z; (occupancy parameter 1) 3 Me2 in (c1): x, 0, z; 0, x, z; x–, x–, z; (occupancy parameter 1) 3 Pt in (c2): x, 0, z; 0, x, z; x–, x–, z; (occupancy parameter 1) The (b) and (c) positions are statistically occupied by mixtures of Cd and Zn atoms indicated as Me1 and Me2 and estimated to have the average composition 12 at.% Cd and 88 at.% Zn. The 5 (Me1 Me2) atoms correspond therefore to about 0.6 Cd atoms and 4.4 Zn atoms. All the positions have free parameters and there are two sets of atoms in one type of Wyckoff positions (the position c). These two sets (here marked c1 and c2), however, are different owing to the different values of the free parameters x and z. The following values of the parameters have been determined: z 0.50 for the (b) position, x 0.735 and z 0.5 for the first group of c (c1 occupied by Me2); x 0.358 and z 0.0 for the position c2 (occupied by Pt atoms). The Pearson symbol is hP8.

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3.6.1.1 Crystallographic nomenclature (Bravais lattices, crystal classes, space groups) The following information is generally included in a ‘usual’ crystallographic description: ●

●

Crystallographic system It defines the coordinate system (and metrical relationships between the lattice parameters of the adopted unit cell: for instance, cubic: a b c, α β γ 90°; tetragonal: a b c, α β γ 90°, etc.). The specific values (in picometres, for instance) of the unit cell dimensions are related to the crystal system (see Table 3.3 and Fig. 3.4). The absolute value of the unit cell edges and of related quantities such as interatomic distances, atomic diameters, etc. are generally given in nanometres (1 nm 109 m) or picometres (1 pm 1012 m). In the past a non-SI unit, the angstrom was usually employed by crystallographers. (1 Å 1010 m). Bravais point lattice type The space lattice of a crystal is a representation of its translation repetition. The parallelepiped built upon the three translations selected as unit translations is defined as the unit cell. The lattice may be built up by setting unit cell on unit cell in an infinite framework of unit cells, all the corners of which form a point lattice. These points may be considered also as endpoints of vectors radiating from the origin of the coordinate system and resulting from a combination of the basis vectors a, b and c. If no other lattice points are contained in the interior of the unit cell this is said to be primitive. In the non-primitive lattices other lattice points exist resulting from the so-called centring translations characteristic of the different lattice types: these are C (base centred): 1⁄2 (a b), I (body centred): 1⁄2 (a b c), F (face centred: 1⁄2 (a b), 1 ⁄2 (a c), and 1⁄2 (b c) and R (rhombohedral cell on a hexagonal basis): 1 ⁄3 (a b c) and 1⁄3 (a 2b c). The centring translations are summarized by the following triplets, which have to be added to the representative coordinate of any point in order to obtain all the translational equivalent points: C: I: F: R:

(0, 0, 0), (1⁄2, 1⁄2, 0) (0, 0, 0), (1⁄2, 1⁄2, 1⁄2) (0, 0, 0), (1⁄2, 1⁄2, 0), (1⁄2 , 0, 1⁄2), (0, 1⁄2, 1⁄2) (0, 0, 0), (2⁄3, 1⁄3, 1⁄3), (1⁄3, 2⁄3, 2⁄3)

(double-primitive cell) (double-primitive cell) (four-fold primitive cell) (triple-primitive cell)

The combination of the point lattices constructed on the basis of the crystallographic systems with the possible centring translation results in the 14 so-called Bravais lattice type, illustrated in Fig. 3.4. Substituting (decorating) each lattice

Table 3.3. Classification of space groups (from Hahn 2002). Crystal family

Symbol

Crystal system

Crystallographic point groups (crystal classes)

Number of space groups

Triclinic (anorthic)

a

Triclinic

– 1, 1

Monoclinic

m

Monoclinic

2, m, 2/m

13

Orthorhombic

o

Orthorhombic

222, mm2, mmm

59

Tetragonal

t

Tetragonal

Hexagonal

h

Trigonal

– 4, 4 , 4/m – 422, 4mm, 4 2m, 4/mmm – – 3, 3, 32, 3m,3m

2

Cubic

c

Cubic

– 6, 6 , 6/m – 622, 6mm, 6 2m 6/mmm – 23, m3 – 432, 43m, m3m

Restriction on cell parameter None b-unique setting α γ 90° α β γ 90°

Bravais lattices

Parameters to be determined (*) a, b, c α, β, γ a, b, c β a, b, c

aP mP mS (mC, mA, mI) oP oS (oC, oA, oB) oI oF tP tI

68

ab α β γ 90°

a, c

18

ab α β 90°, γ 120° abc αβγ ab α β 90°, γ 120° abc α β γ 90°

a, c

hP (hexagonal axes)

a, α

hR (rhombohedral axes) hP

7 Hexagonal

Conventional coordinate system

27

36

a, c

a

cP cI cF

According to Hahn (2002), mS and oS are the standard setting independent symbols for the centred monoclinic and the one-face-centred orthorhombic Bravais lattices. Symbols between parentheses oC, oA, etc. represent alternative settings of these Bravais lattices. (*) is the angle between the y and z axes (b, c parameters) and the angle between the x and z axes (a, c parameters) and the angle between x and y axes (a, b parameters).

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Intermetallic Chemistry

c P

t P

c I

t I

o P

h P

o I

m P

c F

h R

o C

m C

o F

a P

Figure 3.4. The crystal systems and the Bravais lattices illustrated by a unit cell of each. All the points which, within a unit cell, are equivalent to each other and to the cell origin are shown. Notice that, in the primitive lattices the unit cell edges are coincident with the smallest equivalence distances. For the rhombohedral lattice, described in terms of hexagonal axis, the symbol hR is used instead of a symbol such as rP. In the construction of the so-called Pearson symbol (§ 3.6.3), oS and mS will be used instead of oC and mC.

point with an atom, or a group of atoms, results in a periodic array of atoms (atom groups) that is in a (periodic) crystal structure. Criteria adopted in the choice of the unit cell are illustrated by the bi-dimensional example reported in Fig. 3.5. The different unit cell types, and the corresponding crystal systems and lattice types, are listed in Table 3.3, and illustrated in Fig. 3.4.

Structural Characteristics of Intermetallic Phases B

a (a)

α

99

(c)

A

a a (b)

α a

Figure 3.5. A bi-dimensional lattice of points is shown which can be built on the basis of the translation units a (the shortest one) and the corresponding unit cell. The origin of the cell is arbitrary (for inst. (a) or (b)): it contains 1 point. A more symmetric cell (c) may be built with the edges A and B, however it is double primitive centred rectangular, containing two equivalent points.

In the following a few selected formulae useful in common crystallographic calculations have been collected. ●

Space groups The space group describes the spatial symmetry of the structure on a microscopic (atomic) level, and is represented by means of the Hermann–Mauguin symbol composed of a letter representing the lattice type (P primitive; I body centred, etc., see Table 3.3 and Fig. 3.4) followed by the symbols of the symmetry elements ordered according to their positions relative to the axes (for – instance Pm3 m is the symbol of the space group of the CsCl structure). As usual, – the space group is also identified by the serial number (221 for Pm3m) listed in several compilations and atlases such as the International Tables, which is the fundamental reference book for crystallography (Hahn 2002). It may be mentioned that in 2D and 3D the possible rotations (the symmetry axes) that superimpose an infinitely periodic structure on itself are limited to angles 360°/n with n 1, 2, 3, 4 or 6. Notice that for non-periodic, noncrystalline, quasi-crystalline structures, other symmetry axes are possible. See § 3.11.3 and Fig. 3.45 on quasi-periodic crystals.

The numbers 2, 3, 4 and 6 are used as symbols of the corresponding axes of – – – symmetry while the symbols 3, 4 and 6 (3 bar, 4 bar, etc.) are used for the threefour- and six-fold (roto) inversion axes, corresponding to a counter-clockwise rotation of 360°/n around an axis followed by an inversion through a point on the axis. – The centre of symmetry (inversion through a point) is represented by 1 and the plane of symmetry (mirror symmetry) by the letter m. The inversion operation

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Intermetallic Chemistry

and the ‘mirror operation’ are called improper symmetry operations, because they do not relate congruent asymmetric objects but change the hand (chirality) of the objects turning from the right-hand form to the left-hand one. Notice that any asymmetric object (that is which has no symmetry itself) can exist in both a right-handed and a left-handed forms. Any two thus related objects are called enantiomorphous. All the possible combinations of these symmetry elements result in 32 crystallographic point-group symmetries or crystal classes; their symbols are listed in Table 3.3. Notice that in putting together the symbols to denote the symmetries of any crystal classes the convention is to give the symmetry of the principal axis – first: for instance 4 or 4 , for tetragonal classes. If there is a plane of symmetry per– pendicular to the principal axis, the two symbols are associated as in 4 m or 4/m (4 over m), then the symbols for the secondary axes, if any, follow, and then any other symmetry planes. In a symbol such as 4/mmm, the second and third m refer to planes parallel to the four-fold axis. Notice that the symmetry operations of each point group by continued repetition always bring us back to the point from which we started. Considering, however, a space crystalline pattern, additional symmetry operations can be observed. These involve translation and therefore do not occur in point groups (or crystal classes). These additional operations are glide planes which correspond to a simultaneous reflection and translation and screw axis involving simultaneous rotation and translation. With subsequent application of these operations we do not obtain the point from which we started but another, equivalent, point of the lattice. The symbols used for such operations are exemplified as follows: a, b or c (axial) glide reflection through a plane with a glide vector 1⁄2 a, 1⁄2 b or 1⁄2 c. n (diagonal) glide reflection through a plane with a glide vector such as 1⁄2(a b). d (diamond) glide reflection through a plane with a glide vector such as 1⁄4(a b). np (n sub p) n-fold screw axis: 21, 31, 32, 41, 42, 43, 61, 62, 63, 64, 65. Right-handed screw rotation of 360°/n around an axis, with screw vector (p/n)t, where t is the shortest lattice translation vector parallel to the screw axis. Conventionally a righthanded axis is one whose screw motion is clockwise when looking up along the – axis. An illustration of the 41, 42 and 43 axes in comparison with the axes 4 and 4 is shown in Fig. 3.6. Notice that pairs of axes such as 31 and 32, 41 and 43 or 61 and 65 are identical except for the sense of the screw motion; such pairs are therefore enantiomorphous. Taking into account these symmetry operations together with those corresponding to the translations characteristic of the different lattice types (see Fig. 3.4), it is possible to obtain 230 different combinations corresponding to the 230 space groups which describe the spatial symmetry of the structure on a microscopic

101

Structural Characteristics of Intermetallic Phases 4

4

41

42

43

t

y, x x, y x, y y, x 4

x,y, z

y, x, z

x, y, z

y, x, z

4 41 42 43

x,y, z x,y, z x,y, z x,y, z

y, x, z y, x, z + y, x, z + y, x, z +

x, y, z x, y, z + x, y, z x, y, z +

y, x, z y, x, z + y, x, z + y, x, z +

Figure 3.6. An indication is given of the equivalent points generated (from a generic point of – coordinates x, y, z) by the action of the axes 4 and 4 and of the 41, 42 and 43 screw axes. A perspective view of the graphical symbols used in the International Tables (Hahn 2002) for the different axes is shown. (t is the shortest translation vector in the direction of the axes). The projection (along these axes) on the base plane of the equivalent points is also shown: notice that the same projection is obtained in all the cases illustrated. The coordinates of all the equivalent points in the different sets are listed. Notice that the x, y, z coordinates are fractional coordinates: they indicate the positions along the corresponding directions as fractions of the constants a, b and c (in these examples c t).

level. The numbers of space groups associated with each crystal class are given in Table 3.3. 3.6.1.2 The unit cell content. To complete the description of the crystal structure, the list of the atoms contained in the unit cell and their coordinates (fractional coordinates related to the adopted system and unit cell edges) are then reported. These are usually presented in a format such as M El in n: x, y, z. In the MoSi2 structure, also reported in Table 3.2, and in Fig. 3.7, for instance, four silicon atoms

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1

785 = c 654

0.83

523

0.67

393

0.5

262

0.33

131

0.17

Z

d/pm 638 = c

1 0.91

579 378

0.59

260

0.41

0

0

MoSi2 Mo or Ca

59 0

0.09 0

CaC2 Si or C

Figure 3.7. Unit cell schematic representations of the isopointal structures of MoSi2 and CaC2 (see also Chapter 7). Absolute and fractional rounded values of the vertical coordinate are shown. Notice that due to the different values of the c/a ratios and of the z parameters the two structures (corresponding to the same space group and the same occupation of Wyckoff positions) result in different coordination and atomic grouping. In CaC2 we have the formation of C—C, dumbbell, discrete groups. The C—C distance corresponds (see text, § 3.6.2) to (1–2z) c 0.1864 638 pm 118.9 pm. This distance and the corresponding C radius of 59.5 pm are in good agreement with the bond length for bond order 3, found for instance in acetylene.

(that is: M El 4 Si) are in the position set coded as e (in the so-called Wyckoff notation) and corresponding, in this specific case, to the four positions (the four coordinate triplets) 0, 0, z; 0, 0, –z ; 1⁄2, 1⁄2, 1⁄2 z; 1⁄2, 1⁄2, 1⁄2 z. Such entries correspond to one of the Wyckoff positions characterized by well-defined site symmetry and by a multiplicity M. For each Wyckoff position, M is the number of equivalent points (positions) in the unit cell with the same site symmetry. Notice, indeed, that a ‘space group’ is a group of symmetry elements. If an atom is placed in a quite general position in the unit cell it is multiplied by the symmetry elements and thus other atoms, exactly equivalent to the first, are found at other positions precisely related to those of the first. Each space group has its own characteristic number of equivalent general positions. This is the highest multiplicity Mmax of the given space group and corresponds to the lowest site symmetry (each point is mapped onto itself only by the ‘identity operation’). In this ‘general position’ the coordinate triplets of the Mmax sites include the reference triplet indicated as x, y, z (having three variable parameters, to be experimentally determined). In a given space group, moreover, it is possible to have several special positions. In this case, points (atoms) are considered which

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are located on symmetry elements (without translations) or at the intersection of several such symmetry elements. Each point will be mapped onto itself by at least one of these symmetry operations: we will have as a consequence a reduction in the number of different equivalent points in the unit cell generated by all the characteristic symmetry operations. The multiplicity of these positions will be lower than Mmax (M in a special position is a divisor of that of the general position). Specific constraints are imposed on the coordinates of each point of a special position leading to triplets such as x, y, 0 (that is z 0) or x, x, z (that is x y), with two variable parameters, or x, 1⁄2, 1⁄2 or x, x, 0 (with one variable parameter) or 0, 0, 0 or 1 ⁄2, 1⁄2, 0 (with no variable parameter). In the International Tables of Crystallography, for each of the 230 space groups the list of all the Wyckoff positions is reported. For each of the positions (the general and the special ones) the coordinate triplets of the equivalent points are also given. The different positions are coded by means of the Wyckoff letter, a, b, c, etc., starting with a for the position with the lowest multiplicity and continuing in alphabetical order up to the general position. In the examples reported in Table 3.2 it is also shown that, for the positions with free parameters, the specific values of the parameters themselves (experimentally determined) should be given in order to present a complete description of the structure. Notice that, for instance in the case of the MoSi2 structure, the different atomic positions in the unit cell (in the space group I4/mmm) are the following: 2 Mo in 0, 0, 0 and in 1⁄2, 1⁄2, 1⁄2 and 4 Si in 0, 0, z; in 0, 0, –z ; in 1⁄2, 1⁄2, 1⁄2 z and in 1⁄2, 1⁄2, 1⁄2 z corresponding (on the basis of the experimental value z 0.333) to 0, 0, 0.333; 0, 0, 0.667; 1⁄2, 1⁄2, 0.833; 1⁄2, 1⁄2, 0.167. These positions have been described, according to the International Tables of Crystallography conventions, explicitly indicating the centring translations (0, 0, 0; 1⁄2, 1⁄2, 1⁄2), characteristic of body-centred lattices (I-space groups), before representative coordinate triplets. The symbol means that, in order to obtain the complete set of Wyckoff positions, the components of these centring translations have to be added to each of the listed triplets. A similar presentation has been used for the Mg2Ge structure description. Notice that in the description of the content of the unit cell, the atomic coordinates are given for the first cell from the chosen origin, and are formulated modulo 1: thus, for instance, x, y, z is written (x–, –y , –z ) rather than 1 x, 1 y, 1 z and the following equivalences could be considered as typical examples: — 1 1⁄4 1⁄4; 1⁄2 3⁄4 1⁄4; 0.1 0.1 1 0.1 0.9; 1 0 Notice however that in the analysis of a given structure, in order to evaluate coordination and atomic distances, the atomic positions in several adjacent cells may be relevant, and therefore values of x, y, z higher than 1 or lower than 0 should be

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(b)

(c)

0

0 1/2

0 0

(d)

(e)

(g) (f)

Figure 3.8. Crystal structure of CsCl. The positions of the centres of the atoms in the unit cell are shown in (a). In (b) the same cell is described by means of its characteristic sections taken at the height 0, 1⁄2, and 1 of the third axis. In (c) a projection of the cell on its square basis is presented: the values of the third (fractional) coordinate are indicated. In (d) the shortest interatomic distances are shown: dCs–Cl a3/2 411.3 0.866025…. 356.2. In (e) the subsequent group of interatomic distances (d a 411.3) involving six atoms in the adjacent cells is presented. A group of eight cells is represented in (f) to suggest that the actual structure of CsCl corresponds to a threedimensional infinite repetition of unit cells and to show that the coordination around the white atoms is similar to that around the black ones shown in (d). The unit cell of the CsCl structure is shown as a packed spheres model in (g).

considered (see § 3.7.7). Finally, in Table 3.2 some more examples are reported as an introduction to more complex, partially disordered, structures (random distribution of different atom types in the same positions, partial occupancy of certain positions). Considering now the simple structure of CsCl as an illustration, we see that the ‘crystallographic description’ reported in Table 3.2 corresponds to the atom arrangement shown, with alternative representations, in Fig. 3.8. More generally, from

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105

descriptions such as those reported in Table 3.2, the interatomic distances may be computed and, consequently, the coordinations and grouping of the various atoms may be derived. An example of this computation will be presented in § 3.7.7. A systematic listing of the crystal data relevant to all the known phases has been reported in a number of fundamental reference books such as Pearson (1967), Landolt-Börnstein (1971), Villars and Calvert (1985), Villars and Calvert (1991), etc. or crystal structure databases. For the criteria to be followed in the preparation and presentation of coordinate lists, especially when complex structures are involved, see Parthé and Gelato (1984). Their paper describes a proposal for a standardized presentation of inorganic crystal structure data with the aim of recognizing identical, or nearly identical, structures from the similarity of the numerical values of the atom coordinates. Different, equivalent, but not easily recognizable, descriptions could, in fact, be obtained by shift of origin of the coordinate system, rotation of the coordinate system, inversion of the basis vector triplet (see also Parthé et al. 1993). As an example of different descriptions of the same structural type see the KHg2, oI12 structural type in Chapter 7. The description of KHg2, as obtained from the original literature data, is reported; it is also shown that this structure is isotypic with the CeCu2 type, for which an apparently different description was given in the literature. 3.6.1.3 Common crystal–chemical formulae. Unit cell volumes and interatomic distances. In the analysis and description of a structure some calculation may be useful. A few common formulae are collected here. 3.6.1.3.1 Volume of the unit cell (Vcell ). This may be calculated from the unit cell constants by using the following formulae. From this the density (ρ) of the compound may be obtained: ρ Mcell/Vcell, where Mcell is the mass of the matter in the unit cell, that is the sum of the masses of all the atoms contained. The mass of an individual atom is calculated in grams by the ratio of the atomic molar mass and the Avogadro number. General case (Triclinic):

Vcell abc 1 cos2 α cos2 β cos2 γ 2 cos α cos β cos γ

Monoclinic:

Vcell abc sin β

Rhombohedral: Vcell a3 1 3 cos2 α 2 cos3 α Hexagonal:

Vcell a 2 c

Orthorhombic: Vcell abc

3 2

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Tetragonal: Cubic:

Intermetallic Chemistry

Vcell a2c Vcell a3

3.6.1.3.2 Examples of alternative descriptions of the unit cell In a number of cases, in order for instance, to compare a given atomic distribution and arrangement with several others, it may be useful to use different descriptions of the same structure (to refer to different, but obviously equivalent, unit cells). The transformations (of the unit cell constants and, consequently, of the coordinates of the atomic positions) are described, for the general case, for instance, in the International Tables (Hahn 2002). A few, frequently used, transformation formulae of the unit cell constants are reported here. Description of a rhombohedral unit cell in terms of the equivalent, triple-primitive, hexagonal cell (see Fig. 3.9). (Rhombohedral axes: ar and α; Hexagonal axes: ah and ch) Rhombohedral → hexagonal

ah ar 2 1 cos α 2ar sin

α 2

ch ar 3 1 2 cos α Cell volume

Vh 3Vr

Hexagonal → rhombohedral

ar sin

1 (3ah2 ch2 ) 3 3

α 2 2 3 ch2 ah2

0

0 2 3

1 3

ch ar ah

ar

1 3

0

0

2 3

ar

ah

0

ah

0

2 3

1 3

0

Figure 3.9. The relation between a primitive rhombohedral cell and an equivalent tripleprimitive hexagonal cell is shown. The cell orientations have been selected according to the criteria adopted by the International Tables (Hahn 2002).

Structural Characteristics of Intermetallic Phases

107

A detailed example of the alternative descriptions of a given compound, both in terms of its hexagonal unit cell and of the corresponding rhombohedral primitive cell is presented in Chapter 4: the rhombohedral compound Mo6PbS8 (the prototype of the family of the so-called Chevrel phases) is described and unit cell constants and atomic positions are listed for its conventional hexagonal cell and for the rhombohedral primitive cell. The rhombohedral cell has a nearly cubic shape (αr 90°) when ch/ah (3/2) 1.2247… Description of a hexagonal unit cell (ah, ch cell edges) in terms of an orthohexagonal cell (equivalent orthorhombic cell a0, b0, c0) (see Fig. 3.10). Hexagonal : ortho-hexagonal

a0 ah b0 ah 3 c0 ch

Cell volume

Vh a2hch

3 2

V0 a0b0c0 V0 2Vh Number of atoms in the cell

N0 2Nh

a0

ah

b0

Figure 3.10. The relation between a hexagonal cell and an equivalent orthorhombic cell is shown by means of their projections on the a, b plane.

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Description of a cubic (primitive, body centred or face centred) unit cell (ac) in terms of the equivalent, primitive rhombohedral, (ar, ) and triple-primitive hexagonal, cells (ah, ch). See Fig. 3.11. Primitive cubic:

ar ac

α 90°

ah ac 2 Cell volume

Vr Vc

ch ac 3 ch/ah 1.225 … Vh 3Vc 3Vr

Number of atoms in the cell

Nr Nc

Nh 3Nc 3Nr

Body-centred cubic (doubly primitive):

ar ac

3 2

ah ac 2 Vr

Number of atoms in the cell

Nr

Face-centred cubic (quadruply primitive):

ar ac

ar

ch ac

1 V 2 c

Cell volume

α 109°28 12

Vh

1 N 2 c 2 2

Nh

3 2

ch/ah 0.612

3 V 3Vr 2 c 3 N 3N r 2 c

α 60°

ar ar ac

Figure 3.11. Relation between a face-centred cubic cell (of edge ac and quadruple primitive) and its equivalent primitive rhombohedral cell

ar ac

2 2 , α 60º.

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Structural Characteristics of Intermetallic Phases

ah ac Cell volume

Vr

Number of atoms in the cell

Nr

2 2

1 V 4 c

ch ac 3 Vh

1 N 4 c

Nh

ch/ah 2.449 …

3 V 3Vr 4 c 3 N 3N r 4 c

Transformation (deformation) of a face-centred cubic unit cell into a body-centred cubic cell. A face-centred cubic cell (having a unit edge a0), ‘compressed’ along an axis, when the reduction corresponds to a face-centred tetragonal cell with a c/a ratio a 1/ 2 , becomes a body-centred cubic cell with an edge: a 0 (see Fig. 3.12). 2

Notice that, in the tetragonal system, there is no face-centred lattice: if, to a simple tetragonal lattice, we add extra lattice points at the centres of the cell faces, the lattice (and the cell) obtained may be described in terms of a body-centred unit cell with a square base whose edges are 1/ 2 times the length of the original (pseudoface-centred) cell (see Fig. 3.12). Some ambiguity may be found in literature concerning this point; for a few compounds, indeed, descriptions in terms of the two cells have been reported. A description of what possibly is the first example of such a misunderstanding has been vividly described in the brilliant book The Coming of Materials Science by Cahn (2001). M. Polanyi, in an account of his own

ac = c t

at ac

Figure 3.12. A face-centred cubic cell (edge ac) can be described in terms of a body-centred tetragonal cell with a c/a ratio having the value 2 (at ac 2 /2, ct ac). By a convenient compression along the c axis, the body-centred tetragonal cell can be transformed into a body-centred cubic cell.

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Intermetallic Chemistry

research, described how he in 1923, together with H. Mark, determined the crystal structure of white tin (βSn, tI4). Just after this study they received a visit from a colleague, who had independently determined the same structure. The colleague strongly maintained that Polanyi’s structure was wrong. And, in Polanyi’s words: ‘only after hours of discussion did it become apparent that his structure was actually the same as ours, but looked different because he represented it with axes turned by 45° with respect to ours’. Nevertheless it may be observed that, in some specific cases, reference to a pseudo-face-centred tetragonal cell may be useful, for instance to compare the structure under examination with a face-centred cubic structure. 3.6.1.3.3 Interatomic distances. Relevant data in the description and evaluation of the characteristics (coordination) of a structure are the values of the interatomic distances. A summary of the formulae to be used for their calculation is given here. In the general case, the distance d1–2 between points (atoms) 1 and 2 having, in the unit cell, along the axes x, y, z the fractional coordinates x1, y1, z1 and x2, y2, z2 may be calculated, from the crystallographic constants a, b, c, α, β, γ (defined as in Table 3.3) according to the following equation: 2 a2(x2 x1)2 b2(y2 y1)2 c2(z2 z1)2 2ab(x2 x1)(y2 y1)cos γ d12 2bc(y2 y1) (z2 z1)cos α 2ca(z2 z1) (x2 x1)cos β

(triclinic axes) which simplifies to: d 212 a2(x2 x1)2 b2(y2 y1)2 c2(z2 z1)2 2ca(z2 z1)(x2 x1)cos β (monoclinic axes) and respectively to: d 212 a2[(x2 x1)2 (y2 y1)2] c2(z2 z1)2 a2(x2 x1) (y2 y1) (hexagonal axes) (γ 120°) that is: d 212/a2 [(x2 x1)2 (y2 y1)2 (x2 x1) (y2 y1)] c2/a2(z2 z1)2 (hexagonal axes)

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Structural Characteristics of Intermetallic Phases

or to: d 212 a2[(x2 x1)2 (y2 y1)2 (z2 z1)2] 2a2[(x2 x1) (y2 y1) (y2 y1) (z2 z1) (z2 z1) (x2 x1)] cos α (rhombohedral axes) For orthoclinic axes (rectangular) we have: d 212 a2(x2 x1)2 b2(y2 y1)2 c2(z2 z1)2

(orthorhombic)

d212 a2[(x2 x1)2 (y2 y1)2] c2(z2 z1)2

(tetragonal)

that is: d212/a2 [(x2 x1)2 (y2 y1)2] c2/a2(z2 z1)2

(tetragonal)

and: d 212 a2[(x2 x1)2 (y2 y1)2 (z2 z1)2]

(cubic)

that is d 212/a2 (x2 x1)2 (y2 y1)2 (z2 z1)2 (constant for fixed parameter positions). 3.6.1.3.4 Plane and direction indices. Reference to the three coordinate axes (crystallographic axes) must also be made, in order to indicate (to identify) the position of a plane and the direction of a line. A plane is identified by its equation or by three parameters. These are related to the plane intercepts on the three chosen crystallographic axes (z, y, z) with reference to their own unit lengths (a, b and c). The three indices, generically defined by the three letters h, k and l are defined by the ratios: h: k : l aA : Bb : Cc : where a, b and c are the unit cell edges and A, B and C are the plane intercepts (see Fig. 3.13). The symbol of the plane is (hkl) with the three indexes (reduced to the smallest relative prime integers) within round brackets. If a plane is parallel to an axis the corres-ponding index is zero. So the indices (100), (010) and (001) represent the faces of the unit cell. The direction of a line, passing through the origin, is indicated by a similar symbol [uvw], within square brackets, defined by: u: v: w xa : yb : zc where a, b and P P P c are the unit cell edges and xP, yP and zP are the coordinates of an arbitrary point on the line. So [010] is the symbol of the direction (of the axis) y.

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Intermetallic Chemistry (a)

z C=c

B=1 2b b

y

A=a x ∞

z

(b) ∞

c

y B=b

A=a x

∞

z

(c) ∞

c +u y

A=a

−u

B=b=a

x

Figure 3.13. Crystallographic index of a plane. The plane shown in (a) has the intercepts: A a, B –12 b and C c. Its symbol is (121). The plane (110), parallel to the z-axis, is shown in (b). In (c) the plane (110) is shown in the hexagonal system. The full index h, k, i, l, with reference to the axes – x, y, u (all coplanar) and z, is (1120). Notice the negative intercept on the axis u. See text.

Notice that, for reasons of symmetry, in the hexagonal system a somewhat redundant index type may be used for plane identification. It is customary to define an auxiliary axis u at 120° to x and y and 90° to z (and with the same unit length of the x and y axes). As a consequence instead of indices (hkl) for a face, indices (h, k, i, l) are used, where the index i is related to the axis u in the same way

Structural Characteristics of Intermetallic Phases

113

as h and k are related to the axes x and y (see Fig. 3.13 (c)). It can be shown that the index i is not independent from h and k and that h k i 0. In a way, it is therefore a matter of personal choice whether three or four symbols are used.

3.6.2 Shortened version of the standard description: structural types Several intermetallic phases are known which have the same (or a similar) stoichiometry and crystallize in the same crystal system and space group with the same occupied point positions. Such compounds are considered as belonging to the same structure type. About 30 000 intermetallic phases have been described. These, however, may be grouped in about 2800 types. The reference to the structure type may be a simpler and more convenient way of describing the structure of the specific phase. The structure type is generally named after the formula of the first representative identified: the ‘prototype’. Expressions such as: ‘KCl has the NaCl structure type’ are frequently used. Trivial names and symbols may also be found in several cases. The various representatives of a specific structure type generally have different unit cell edges, different values of the occupancy parameters and of the free coordinates of the atomic positions and, in the same atomic positions, different atoms. However, if these differences are small, the general pattern of the structure may be considered unaltered. On the other hand, of course, if these differences become larger, it might be more convenient to describe the situation in terms of a ‘family’, instead of a single structural type, of different (more or less strictly interrelated) structural (sub) types. According to Parthé and Gelato (1984), some structures may not really be isotypic but only isopointal, which means that they have the same space group and the same occupation of Wyckoff positions with the same adjustable parameters, but different unit cell axial ratios and/or different values of Wyckoff free parameters and different atom coordinations. An interesting example may be given by the structures of MoSi2 (reported in Table 3.2a) and CaC2. In this compound, Ca and C are respectively in the same positions as Mo and Si in the same space group I4/mmm: 2 Ca in (a): 0, 0, 0; 1⁄2, 1⁄2, 1⁄2; 4 C in (e): 0, 0, z; 0, 0, –z ; 1⁄2, 1⁄2, 1⁄2, z; 1⁄2, 1⁄2, 1⁄2 z. The unit cell dimensions, however, correspond to a 388 pm, c 638 pm (c/a 1.644 instead of 2.463 as in MoSi2) and the free parameter z has the value 0.4068 (instead of 0.333). These differences result in two different space arrangements (see Fig. 3.7). Diatomic groups, such as C2, clearly evident in CaC2 and in a number of isostructural dicarbides and peroxides, are not formed in MoSi2. Very

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interesting general comments and definitions on this question have been proposed, for instance, by Pearson (1972), and more recently by Lima de Faria et al. (1990). According to these authors, two structures are isoconfigurational (configurationally isotypic) if they are isopointal and similar with respect to the corresponding Wyckoff positions and their geometrical interrelationships (same or similar positional coordinates, same or similar values of the unit cell axial ratios, c/a, a/b, b/c and cell angles α, β, γ). Isotypism is found particularly with inorganic compounds. This behaviour has been discussed by Parthé et al. (1993). It has been underlined that it is not always simple to explain why two compounds adopt the same atom arrangement. The following examples have been presented: ●

●

●

●

The isotypism of Gd4Ni6Al23 and Y4Ni6Al23 may be easily explained because Gd and Y (elements of the same group of the Periodic Table) have comparable electron configuration and nearly the same atomic dimensions. Li2SiO3 and LiSi2N3 are isotypic, even if not in a rigorous sense, owing to slightly different distortions of the coordination polyhedra. They adopt an adamantine structure type, for which particular values of the electron concentration may be relevant even if obtained with elements from different parts of the Periodic Table. GdNi and NiB represent another couple of isotypic compounds. The role (the position in the crystal structure), however, of the same atom, Ni, in the two compounds is exchanged. In NiB, the Ni atoms are those centring the trigonal prism formed by Gd atoms. A reason for the existence of this structure type could possibly be related to the atomic size difference of the elements involved or, perhaps, to their relative position in the Pettifor chemical scale. The last and most intriguing example reported by Parthé et al. (1993) is the couple of compounds Pu31Rh20 and Ca31Sn20. For the present, the isotypism of these compounds of unusual stoichiometry is unexpected and cannot be explained.

As a conclusion to these comments, we may mention that two structures are defined as crystal-chemically isotypic if they are isoconfigurational and the corresponding atoms (and bonds) have similar chemical/physical characteristics. These concepts and their historical development were summarized in a contribution by Laves (1944), translated and reported by Hellner (1979), in which conditions for calling crystal structures ‘equal’ (isotypism), ‘similar’ (homeotypism) or ‘different’ (heterotypism) are discussed and exemplified. Finally we have to observe that, when considering phases having certain polar characteristics (salt-like ‘bonding’), the concepts type and antitype may be useful.

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115

Antitypic phases have the same site occupations as the typical ones, but with the cation–anion positions exchanged, or more generally some important physical/ chemical characteristics of the corresponding atoms interchanged. As examples, the structure types CaF2 and CdI2 and their antitypes (exemplified by Na2S and Ti2O, respectively) may be considered. Notice, however, that for a structure such as the CsCl type, it does not matter whether we describe it as 1 Cs in 0, 0, 0 and 1 Cl in 1⁄2, 1⁄2, 1⁄2, or as 1 Cs in 1⁄2, 1⁄2, 1⁄2 and 1 Cl in 0, 0, 0. In this case the two descriptions are undistinguishable (see Fig. 3.8): they correspond to a mere shift of the origin of the reference axes. The CsCl type is its own antitype. Similar considerations are also valid for other structures such as the NaCl, ZnS types, etc.

3.6.3 Structure types and unit cell Pearson symbol The use of the so-called Pearson notation (Pearson 1972) is highly recommended (IUPAC, Petzow and Effenberg 1988 et seq, Leigh 1990, Villars et al. 1995) for the construction of a compact symbolic representation of the structure of the phase. As far as possible, it should be completed with a more detailed structural description by using the prototype formula which defines, as previously mentioned, a certain structure type. The Pearson symbol is composed of a sequence of two letters and a number. The first (small) letter corresponds to the crystal system of the structure type involved; the second (capital) letter represents the lattice type (see Table 3.3). The symbol S is generally adopted to indicate ‘side centred faces’ instead of the C used in the past. The symbol is completed by the ‘ideal’ number of the atoms, corresponding to the full occupation of all the sites, in the unit cell. This is possibly followed, within brackets, by the real number of atoms present, due to vacancies, in the cell. A symbol such as tP10 represents a structure type, or a group of structure types, corresponding to 10 atoms in a primitive tetragonal cell. A symbol such as tI12 (11.5) represents a structure corresponding to a body-centred tetragonal unit cell ideally containing 12 atoms when all the sites are fully occupied, but in which however, on average only 11.5 atoms are present, due to a partial occupation of some atomic positions. In this book, the Pearson symbol will be used throughout and the convention has been adopted indicating in every case the number (ideal or effective) of atoms contained in the chosen unit cell. In the case, therefore, of rhombohedral substances for which the data of the (triple primitive) hexagonal cell are generally reported, the number of atoms is given which is in the hexagonal cell and not the number of atoms in the equivalent rhombohedral cell (Ferro and Girgis 1990). So, for instance,

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at variance with Villars and Calvert (1985, 1991), hR9 (and not rP3 or hR3) is given for the Sm-type structure. If the structure is not known exactly, the prototype indication cannot be added to the Pearson symbol. In some cases, moreover, only incomplete Pearson symbols (such as o?60, cF?, etc.) can be used. Criteria similar to Pearson’s for the unit cell designation were used by Schubert (1964) and Frevel (1985). According to Parthé et al. (1993), a standardization procedure is necessary in the presentation of the relevant data characteristic of a crystal structure (see also Parthé and Gelato 1984). A convenient description of the structure types is then possible using the ‘Wyckoff sequence’ (the letters of the occupied Wyckoff sites). This allows a finer classification of structure types and offers suggestions not only for recognizing isotypic structures but also possible structural relationships like substitution, formation of vacancy or filled-in structure variants.

3.7. ALTERNATIVE AND COMPLEMENTARY DESCRIPTIONS OF THE CRYSTAL STRUCTURES OF THE SOLID PHASES

…..O, be some other name! What’s in a name? That which we call a rose By any other name would smell as sweet; ….. (Shakespeare, ‘Romeo and Juliet’ 2, II, 41–43).

In the previous paragraphs a brief account has been given of the fundamental aspects of the crystallographic description of the structures and structure types of solid phases. A number of symbols and names have been defined and their application to intermetallic compounds exemplified. It must, however, be underlined that both for historical reasons and for the need to improve classification and interpretation of the structural characteristics of intermetallic phases, other symbols and nomenclature criteria have been invented. Some of them have a mathematical basis, others are more colloquial. A selection of these criteria will be given in the following. 3.7.1 Lattice complexes A description which in some simple cases could be considered alternative to those exemplified in Table 3.2 is based on the lattice complex concept. Listing the symbols of the lattice complexes occupied by the different atoms in a structure (for instance, symbol P for the point 0, 0, 0 and its equivalent points), provides in fact

Structural Characteristics of Intermetallic Phases

117

a means of describing and classifying structures. This may be especially convenient for relatively simple structures particularly in the cubic system. A lattice complex may be defined as an arrangement of equivalent points that are related by space group symmetry operations including lattice translations (Pearson 1972). The same lattice complex may occur in different space group types and may have more than one location in regard to a chosen origin for the unit cell. The number of degrees of freedom of a lattice complex, normally, is the same as that of any of its Wyckoff positions and is the number of coordinate (free) parameters x, y, z, that can vary independently. According to its number of degrees of freedom a lattice complex is called invariant, uni-, bi- or tri-variant. The invariant lattice complexes in their characteristic Wyckoff positions are represented mainly by capital letters. Those with equipoints at the nodes of the Bravais lattice are designated by their appropriate lattice symbols. Lattice complexes, from different crystal families that have the same coordinate description for their characteristic Wyckoff positions, receive the same symbol: for instance, lattice complex P corresponding to coordinate 0, 0, 0. In such a case, unless it is obvious from the context which lattice is meant, the crystal family may be stated by a small letter, preceding the lattice complex symbol as follows: c cubic, t tetragonal, h hexagonal, o orthorhombic, m monoclinic, a anorthic triclinic. Other invariant complexes are designated by letters that recall some structural features of a given complex, for instance D from the diamond structure, E from the hexagonal close-packing. Examples of two-dimensional (2D) invariant complexes are G (from graphite layer) and K (from kagomé net). A short list of invariant lattice complex symbols is reported in the following. For a complete list, for a more systematic description and formal definition, see the International Tables of Crystallography, Hahn (2002). ●

●

●

●

Lattice complex P: (multiplicity 1; multiplicity is the number of equivalent points in the unit cell) Coordinates 0, 0, 0. (crystal families: c, t, h, o, m, a). Lattice complex I: (multiplicity 2) Coordinates 0, 0, 0; 1⁄2, 1⁄2, 1⁄2 (crystal families: c, t, o). Lattice complex J: (multiplicity 3) Coordinates 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0 (crystal families: c). Lattice complex F: (multiplicity 4) Coordinates 0, 0, 0; 0,1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2; 1⁄2, 0 (crystal families: c, o).

118 ●

●

●

●

●

●

●

●

Intermetallic Chemistry

Lattice complex Y: (multiplicity 4) Coordinates 1⁄8, 1⁄8, 1⁄8; 7⁄8, 5⁄8, 3⁄8; 5⁄8, 3⁄8, 7⁄8; (crystal families: c). Lattice complex W: (multiplicity 6) Coordinates 0, 1⁄2, 1⁄4; 1⁄2, 1⁄4, 0; 1⁄4, 0, 1⁄2; (crystal families: c). Lattice complex D: (multiplicity 8) (D from ‘Diamond’) Coordinates 0, 0, 0; 1⁄2, 1⁄2, 0; 1⁄2, 0, 1⁄2; 1 ⁄4, 1⁄4, 1⁄4; 3⁄4, 3⁄4, 1⁄4; 3⁄4, 1⁄4, 3⁄4; (crystal families: c, o). Lattice complex S: (multiplicity 12) Coordinates 3⁄8, 0, 1⁄4; 1⁄4, 3⁄8, 0; 0, 1⁄4, 3⁄8; 7 ⁄8, 1⁄2, 3⁄4; 3⁄4, 7⁄8, 1⁄2; 1⁄2, 3⁄4, 7⁄8; (crystal families: c) Lattice complex T: (multiplicity 16) Coordinates 1⁄8, 1⁄8, 1⁄8; 3⁄8, 1⁄8, 3⁄8; 1⁄8, 3⁄8, 3⁄8; 5 ⁄8, 5⁄8, 1⁄8; 7⁄8, 1⁄8, 7⁄8; 1⁄8, 7⁄8, 7⁄8; 3 ⁄8, 7⁄8, 5⁄8; 3⁄8, 5⁄8, 7⁄8; 5⁄8, 7⁄8, 3⁄8; (crystal families: c, o). Lattice complex E: (multiplicity 2) Coordinates 1⁄3, 2⁄3, 1⁄4; 2⁄3, 1⁄3, 3⁄4 (crystal families: h). Lattice complex G: (multiplicity 2) (G from ‘Graphite’ layer) Coordinates 1⁄3, 2⁄3, 0; 2⁄3, 1⁄3, 0 (crystal families: h). Lattice complex R: (multiplicity 3) Coordinates 0, 0, 0; 1⁄3, 2⁄3, 2⁄3; 2⁄3, 1⁄3, 1⁄3 (crystal families: h).

⁄8, 7⁄8, 5⁄8

3

0, 1⁄2, 3⁄4;

⁄2, 3⁄4, 0;

1

⁄4, 0, 1⁄2

3

0, 1⁄2, 1⁄2 1 ⁄4, 3⁄4, 3⁄4

1

⁄8, 0, 3⁄4; 5 ⁄8, 1⁄2, 1⁄4;

3

⁄8, 3⁄8, 1⁄8; 7 ⁄8, 7⁄8, 1⁄8; 7 ⁄8, 3⁄8, 5⁄8;

1

3

⁄4, 1⁄8, 0; 0, 3⁄4, 1⁄8 1 ⁄4, 5⁄8, 1⁄2 1⁄2, 1⁄4, 5⁄8

⁄8, 5⁄8, 5⁄8; 7 ⁄8, 5⁄8, 3⁄8;

⁄8, 1⁄8, 5⁄8 5 ⁄8, 3⁄8, 7⁄8 5

The coordinates indicated in the reported partial list of invariant lattice complexes correspond to the so-called ‘standard setting’ and to related standard representations. Some of the non-standard settings of an invariant lattice complex may be described by a shifting vector, defined in terms of fractional coordinates, in front of the symbol. The most common shifting vectors also have abbreviated symbols: P⬘ represents 1⁄2, 1⁄2, 1⁄2 P (that is the coordinates which are obtained by adding 1 ⁄2, 1⁄2, 1⁄2 to those of P, that is: coordinates 1⁄2, 1⁄2, 1⁄2), J⬘ represents 1⁄2, 1⁄2, 1⁄2 J (coordinates 1⁄2, 0, 0; 0, 1⁄2, 0; 0, 0, 1⁄2); F ⬙ represents 1⁄4, 1⁄4, 1⁄4 F (coordinates 1⁄4, 1⁄4, 1⁄4; 1⁄4, 3⁄4, 3⁄4; 3 ⁄4, 1⁄4, 3⁄4; 3⁄4, 3⁄4, 1⁄4) and F ⬙⬘ represents 3⁄4, 3⁄4, 3⁄4 F. It can be seen, moreover, that the complex D corresponds to the coordinates F F ⬙.

Structural Characteristics of Intermetallic Phases 0

0

0

0 4

0

0

4 4

0

0

0

P

4

I 0

4 0

0 26

7

5 5

1

3

4

4

26 0

0 26 0

Y∗

3

6

5

1

3

5

7

6

7

3

1

5

3

1

7

5

2

3

7

5

1

5

7

1

3

6

5

1

3

7

7

5

3

1

2

37 4

0

15 0

4

37

T

2

6

6

2

04 04

0

04 04

P2

0

4

04

4

4

04

0

04

0

4

04

4

6

2

2

6

J∗ 1

3

0

4 7

4

0

1

1

2 6 2 6

15 4

0

37 0

S∗

4

15

04

6

2

2

6

6

2

2

6

15 0

4

37 4

0

15

04 26

26

26

26

04

2 6

4 3

V

6 2 6 2

37 0

4

15 4

V∗

0

37

04

2 6 2 6

04 26

04 26

04

P2′

2

5

26 04

04

6

+

S

3

04

7

6

3

7

04

4 2

0

4

5

Y ∗∗

1 0

2

1

F″

4

4 26 4 W∗

+

4

D

0

4

4

2

0

4 26 4 3 7

6

W

1

0

6 0

4

3

4

F

2 4

4

+Y

0

0

4

4

5 7

4

J

26 1

4

0

119

04 26

04

04

I2

Figure 3.14. Projections of unit cells are shown which correspond to cubic invariant complexes in their standard setting. The numbers indicate, in eighths of the unit cell edge a, the positions of the points along the third axis (perpendicular to the drawing). Therefore: four represents a point at a height of 4/8 (1⁄2 a) and 26 represents two superimposed points at heights respectively of 2/8 and 6/8 of the edge. A few examples of representations with enlarged cells are shown (P2, P2 , I2). Notice that with reference to these cells the shifting vector between P2 and P2 is 1⁄4, 1⁄4, 1⁄4.

The signs and as superscripts in front of the letters (for instance Y, Y ) indicate enantiomorphic forms. The superscript * (‘star’) indicates a complex that may be built up as a combination of two complexes of the same kind shifted against each other by 1⁄2, 1⁄2, 1⁄2 (W* W 1⁄2, 1⁄2, 1⁄2 W W W ) or as a combination of two enantiomorphic forms (see the examples shown in Fig. 3.15). Other representations may be obtained by subdividing the unit cell into a number of similar subcells. In the cubic system the subdivision is made along the three axes by the same factor which is used as a subscript in the new lattice complex

120

Intermetallic Chemistry 7 3 1 5 5

7

3

1

3

−

Y′

1

5

7 −

Y∗

5 1 3

1

5

7

3

7

3

1

5

3

7

5

1

5

1

3

7

Y

∗∗

7 −

Y 3

7 5 1 1

3

7

5 7

5

1

3

+

Y∗

+

Y′

1 5 7 3 +

Y

Figure 3.15. An example of relations between invariant lattice complexes with the symbols of their representations.

symbol: P2, P4, I2, etc. In the cubic system where all axes have to be changed by the same factor, we have P222 P2, etc. A schematic representation of cubic lattice complexes is given in Figs 3.14 and 3.15; this could also be useful as an indication of possible combinations and ‘splitting’. Such relations may be useful while comparing different structures and studying their interrelations and possible transformations (order–disorder transformations, etc.) A short list of examples of structure descriptions in terms of combination of invariant lattice complexes is here reported. (Compare with the structure descriptions in Chapter 7.) CsCl-type structure: P P (Cs in 0,0,0; Cl in 1⁄2, 1⁄2, 1⁄2); NaCl-type structure: F F ; ZnS (sphalerite) type structure: F F; NaTl-type structure: D D ; AuCu3-type structure: P J; CaF2-type structure: F F F F P ; 2 Fe4Ntype structure: P J P ; Li3Bi-type structure: F F F F F F P ; 2

Structural Characteristics of Intermetallic Phases

121

Cr3Si-type structure: W I; AgMgAs-type structure: F F F; CaTiO3-type structure: P P J; Cu2Mg-type structure: T D. For a few element structures: Cu type structure: F; W-type structure: I; α-Po-type structure: P; Mg-type structure: E; C-diamond-type structure: D. As a simple example of transformations, the β M β transformation in the Cu–Zn system may be mentioned. At high temperature the equiatomic alloy has the cI2-W-type structure with Cu and Zn atoms distributed at random in the two equivalent positions. On cooling, the stable structure corresponds to an ordered disposition of the two species in the two positions (no longer equivalent) of the cell assuming the cP2-CsCl type structure. In terms of lattice complexes the transformation may be represented by the equation I : P P⬘. Similarly the ordering into the AuCu3-type structure of a disordered Cu-25 at.% Au solid solution (facecentred cubic cF4-Cu type) corresponds to the equation: F : P J. The reported combinations of original or transformed invariant lattice complexes are also indicated as connection patterns or construction patterns or frameworks (or Bauverbände in the German literature, according to Laves 1930). These patterns are homogeneous if they may be described by the parameters of one point position; heterogeneous if, for their description, the parameters of two or more independent point positions are necessary. This terminology may give a short informative description of the crystal structure and it is especially useful for cubic substances. For its use in a systematic description and classification of cubic structures see Hellner (1979). For non-invariant complexes and/or in crystal systems with symmetry lower than cubic, the geometrical configuration of the complex (and the coordination) may change significantly with free parameter values and with axial ratios and angles between the crystal axes. 3.7.2 Alternative structural descriptions and symbols All the requisite structural information for a solid phase is contained (either explicitly or implicitly) in the description of its unit cell. A number of features, however, which are especially relevant for chemical–physical considerations, such as local coordination geometries, the existence of clusters of atoms or chains or layers, etc., are not self-evident in the aforementioned structural descriptions and can be deduced only by means of a more or less complicated series of calculations. Another point which should be underlined is that the same structure can be differently viewed and described (Parthé and Gelato 1984, Franzen 1986). The simple rocksalt structure, for instance, can be viewed as a cubic close-packed set of anions with cations in octahedral holes, as XY6 octahedra sharing edges, as a stacking sequence of superimposed alternate triangular nets, respectively, of X and Y atoms

122

Intermetallic Chemistry

or as a cubic-close-packed structure of a metal with non-metals in octahedral interstices. As a further example the cubic Cu structure, for instance, could be conveniently compared with those, hexagonal, of Mg, La and Sm, or from another point of view, with the tetragonal AuCu, and cubic AuCu3 structures. In the two cases, one could choose a different description and representation of the aforementioned Cu structure. In the different cases, some criteria may therefore be useful in order to give explicit information on the characteristic structural features in a systematic and simple way. In the following sections some details will be given on a few complementary, alternative notations.

3.7.3 Coordination and dimensionality symbols in the crystal coordination formula Several attempts have been made at designing special formulae which (possibly in a convenient linear format) may convey explicit information on the connections and coordination of each atom. One interesting approach was aimed at giving information about the local coordination geometry. A detailed discussion of these attempts and of their development (through the work, inter alios, of Niggli 1945, 1948, Machatschki 1938, 1953, Lima de Faria and Figueiredo 1976, 1978, Parthé 1980, Jensen 1984) may be found in a review by Jensen (1989), who presented and systematically discussed a flexible notation for an interpretation of solid-state structures. A short description of Jensen’s notation will be given below. A report by the International Union of Crystallography Commission on Crystallographic Nomenclature (Lima de Faria et al. 1990) presents a concise description of similar alternative notations, a summary of which is in Table 3.4. The symbols suggested by Jensen, based on Niggli’s proposals, describe the ‘local coordination’ by means of coordination number ratios. For instance, a formula AEm/n will indicate a binary compound where m is the coordination number (defined as the nearest-neighbour number (NNN)) of atoms E around A and n is the similarly defined coordination number of A around E. However, for alternative definitions of coordination and coordination numbers, see the following paragraphs. In simple binary structures, in which no other relevant coordinations (or bonds) can be considered, the ratio m/n will be equal to the stoichiometric compositional ratio. For instance, we will write NaCl6/6 to represent the hexa-coordination (in this case octahedral coordination) of Cl around Na (and vice versa) in sodium chloride. Similarly we will have: ZnS4/4; PH3/1; CsCl8/8; CaF8/4; UCl9/3; etc. Moreover, it is possible to add modifiers to the coordination numbers in order to specify not only topological but also geometrical characteristics of the primary coordination sphere.

123

Structural Characteristics of Intermetallic Phases Table 3.4. Suggested notations for common coordination geometries (from Lima de Faria et al. 1990). Coordination polyhedron around atom A Single neighbour Two atoms collinear with atom A Two atoms non-collinear with atom A Triangle coplanar with atom A Triangle non-coplanar with atom A Triangular pyramid with atom A in the centre of the base Tetrahedron Square coplanar with atom A Square non-coplanar with atom A Pentagon coplanar with atom A Tetragonal pyramid with atom A in the centre of the base Trigonal bipyramid Octahedron Trigonal prism Trigonal antiprism Pentagonal bipyramid Monocapped trigonal prism Bicapped trigonal prism Tetragonal prism Tetragonal antiprism Cube Anticube Dodecahedron with triangular faces Hexagonal bipyramid Tricapped trigonal prism Cuboctahedron Anticuboctahedron (twinned cubooctahedron) Icosahedron Truncated tetrahedron Hexagonal prism Frank – Kasper polyhedra with 14 vertices 15 vertices 16 vertices

Complete symbol

Alternative simplified symbols

[1l] [2l] [2n] [3l] [3n] [4y]

[1] [2] [2] [3] [3] [4]

[4t] [t] [4l] or [4s][s] [4n] [5l] [5y]

[4] t [4] s [4] [5] [5]

[5by] [6o] [o] [6p] [p] [6ap] [ap] [7by] [6p1c] [6p2c] [8p] [8ap] [8cb] [cb] [8acb] [acb] [8do] [do] [8by] [6p3c] [12co] [co] [12aco] [aco]

[5] [6] [6] [6] [7] [7] [8] [8] [8] [8] [8] [8] [8] [9] [12] [12]

[12i] [i] [12tt] [12p]

[12] i [12] [12]

[14FK] [15FK] [16FK]

[14] [15] [16]

o p ap

cb acb do

co aco

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Intermetallic Chemistry

A set of symbols was proposed by Donnay et al. (1964) who suggested adding one or two letters to the coordination number, to indicate the geometry: y, pyramidal; l, planar; c, cubic; etc. Detailed descriptions of the coordination polyhedra are obtained by means of the Lima de Faria et al. (1990) symbols presented in Table 3.4. An advantage of the Lima de Faria symbolism is the existence of two alternative, complete and simplified sets of symbols. The simplified symbols give only a numerical indication, without any distinction between different geometries; the complete symbols, clearly distinguishable from the previous ones, contain a description of the coordination polyhedron beside the numeric indication. A selection of the Lima de Faria symbols, together with Jensen’s suggestions, will be used here. According to Jensen, the dimensionality of a structure (or of a substructure of the same) is indicated by enclosing its compositional formula in square brackets d and prefixing an appropriate symbol . The dimensionality index, d, may be: d 0 for a discrete molecular (cluster, ring) structure, d 1 for a 1D, infinite chain structure, d 2 for a 2D, infinite layer structure and d 3 for an infinite 3D, - framework structure. More complex symbols such as d_d or d d d will represent intermediate dimensionality (between d and d⬘) or, the dimensionality indexes of different substructures (d ⬘ and d ⬙ ) followed by that of the overall structure (d). A few examples: Molecular structures

0 [HI],

Linear structures

1 [BeCl ] 2

Layer structures

2 [C]

graphite, 2 [As]

Framework structures

3 [C]

diamond

Substructures

0 Ca[CO ] 3 1 K[PO ] 3

0 [CO ] 2

(finite ions)

(infinite anionic PO 3 chain), etc.

If, in an A–B structure, one wishes to show not only the A/B coordination but also the B/B, or A/A, self-coordinations, this is done, according to the suggestion by Jensen, via the use of a composite dimensionality index and the relative positions of the various ratios and brackets in the formula, with the last un-bracketed ratio always referring to the B/A coordination. So, for instance, 0_ 3 [( H 2O)4/4 ] is 03 a compact form for [( H 2O)(H 2O)4/4 ] to indicate the molecular packing in the 323 ice structure. The formula 23 Al[B3 / 3 ]12 / 6 or [Al8 by / 8 by ][B31 / 31 ]12 p/6p

Structural Characteristics of Intermetallic Phases

125

corresponds to a more or less detailed description of the AlB2-type structure where the coordination of B around Al is 12 (12p: hexagonal prismatic) and that of Al around B is 6 (6p: trigonal prismatic). The self-coordinations are bipyramidal for Al/Al (8by: hexagonal bipyramidal) and trigonal-planar (3l) for B/B (the B atoms form a 2D hexagonal net). Considering as a further example the compounds AB having the CsCl- type structure, according to Jensen, the two descriptions 3 [AB 333 [A 8 / 8 ] (with and without the indication of the self 6 / 6 ][B6 / 6 ]8/8 and coordination) may also be used to suggest the bonding type (metallic if the A–A and B–B interactions substantially contribute to the overall bonding, ionic or covalent, if mainly A–B interactions have to be considered). More complex examples of the use of this notation may be given by the structures of typical fluorides for which ionic-type coordination formulae are here reported: oP16-YF3:

3 [YF F ] 8 / 3 1/ 3

hP8-LaF3:

3 [LaF F ] 8/ 4 3/ 3

cF16-BiF3:

3 [BiF F 8 / 4 6 / 6 ].

In all these cases the sum of the numerators of the coordination ratios gives the total coordination (of two groups of F atoms) around the metal atom. The sums of the ratios give the stoichiometric coefficients. Another example is represented by the hP6-Ni2In structure ( 3 [InNi6 / 6 Ni5 / 5 ]) described in Chapter 7. A detailed example (AuCu3) of the application of the aforementioned notation to the description of a simple intermetallic structure will be presented in § 3.7.7. A few more examples will be included in the following descriptions of a number of typical structures (see Chapter 7). 3.7.3.1 Coordination number and packing geometry. On the basis of the previous definition of the coordination number (as the number of first neighbours), and of the corresponding coordination geometries (as listed in Table 3.4) some additional remarks may be useful for the particular case of packing of hard sphere atoms. If we have N hard spheres (of radius rS) forming a close-packed polyhedron, another sphere (of smaller radius rC) can fit neatly into the central hole of the polyhedron if the radius ratio has a well-defined value (see also § 3.8.1.1). The ideal radius ratio (rC/rS) for a perfect fit is: 0.225.. (in a regular tetrahedron, CN 4), 0.414.. (regular octahedron CN 6), 0.528.. (Archimedean trigonal prism CN 6), 0.645… (Archimedean square antiprism CN 8), 0.732.. (cube CN 8), 0.902… (regular icosahedron CN 12), 1 (cuboctahedron and twinned cuboctahedron CN 12).

126

Intermetallic Chemistry

For hard spheres, coordination numbers higher than 12 require smaller spheres to cluster around a larger one. Hard spheres of the same radius however, will not fit exactly with all the neighbours in these clusters: two or more types of surrounding spheres (with slightly different values of rS) are needed. It is only possible therefore to define an average rC/rS radius ratio for the best fit. This average ratio is higher than 1 and ranges from 1.2 to 1.3 for CN 14–16.

3.7.4 The concept of coordination number In the description of ‘crystal coordination formulae’ a coordination number was introduced, defined as the NNN of atoms X around the atom Y under consideration. It may be underlined indeed that the determination of the local coordination geometry of an atom in a structure is clearly an important point in the definition of that atom’s contribution to the bulk material properties and in the characterization of the structure itself. Several properties, for instance, atomic size, atomic valence and magnetic properties and species stability and reactivity, are known to be coordination, and coordination number, dependent. However, it can be noticed that the term coordination number (CN) may be used in two ways in crystallography (Frank and Kasper 1958). That is, according to one definition, the coordination number, as previously mentioned, is the number of nearest neighbours to an atom. According to the other, the definition of the coordination should be based on an ‘interpretation’ of the structure, which depends not only on an evaluation of the interatomic distances to assign bonding vs. non-bonding contacts, but on considerations on the bonding mechanism (Jensen 1989). These considerations are particularly important when thinking of metallic phases where it may be difficult to make distinctions between X–X, X–Y or Y–Y contacts. So, for instance, when considering the bodycentred cubic structure of the W-type, some authors define the coordination number as 8, in agreement with the nearest-neighbours definition, but others prefer to regard it as 14 (including a group of six atoms at a slightly higher distance). More generally, in many cases of intermetallic compounds, unlike a high number of covalent compounds (compare for instance with the illustrative example of a carbon atom in the diamond structure), we cannot speak of ‘bonds’ of an atom ‘directed’ to (and ‘saturated’ with) a well-defined group of atoms. As a consequence the coordination number (or ligancy) of a central atom which is easily obtained by enumerating the neighbours (and which, of course, has an important role in the description of the crystal structure and of its geometrical characteristics), very often is not clearly and immediately related to the bonding mechanism of the intermetallic phase. In other words, there are many cases in which the enumeration procedure alone gives only a very partial representation of the bonding. Moreover, there are numerous cases where the criteria for the enumeration

Structural Characteristics of Intermetallic Phases

127

(a)

d2

3/4 c

1/4 c a

a

(b)

z = 1/4

d1

z = 3/4

(c) Cd Zn

hp2-Mg type

R = d 2 /d1

1.10

1.05

1.00

0.95

Mg

e Fe(HP) a Ti

Re

a Yb

a Li

b AI(HP) a Tl a Be b Ba e Co 1.60

1.70 c /a

1.80

1.90

Figure 3.16. The hexagonal unit cell (edges a and c) of Mg is shown in (a). The cell contains two atoms in the positions: 1⁄3, 2⁄3, 1⁄4 and 2⁄3, 1⁄3, 3⁄4. Around each Mg atom there are 6 Mg on the same plane (at a distance d1) forming a regular hexagon, six other near atoms are at a distance d2 (three on each of the over and underlying layers). The value of the first distance is given by d1 a, and the second –– 1 by d2 (a2/3 c2/4) ⁄2; if c/a 8/3 1.632993… then d1 d2. In (b) at level 1⁄4 c and 3⁄4 c, sections of nine adjacent cells are shown. In (c), the ratio d2/d1 is given as a function of c/a for several hexagonal, Mg-type, elements. Notice the clustering of the points round the ideal value and the deviation shown by Zn and Cd.

procedure may be ambiguous. For an introductory description of this point, see for instance: Carter (1978), O’Keeffe (1979). Another example may be represented by the hexagonal close-packed hP2-Mg type structure where, according to the first —– definition, CN is 6 unless the axial ratio c/a has exactly the ‘ideal’ value (8/3)

128

Intermetallic Chemistry

(1.63299…), in which case it is 12. See Fig. 3.16 and the arrangement of the white balls around the black one in the scheme 12-d of Fig. 3.18. In the previously mentioned example of the Mg-type structure (Fig. 3.16), the mentioned definition of CN is seldom applied with rigour, that is, the CN in the hP2-Mg type structure is generally regarded as 12, even with c/a slightly different from the ‘ideal’ value, as not only the first group, but also the very close second group of distances are considered together. More difficulties arise in less symmetrical structures and when there is a high coordination number. Near neighbours with slightly different interatomic distances are often found, and it may be difficult to determine unambiguously how many atoms should be considered as coordinating the central one. As regards the second method of coordination evaluation, several schemes for the calculation of an ‘effective’ coordination have been proposed. According to Frank and Kasper (1958), the computation of the coordination number can be based on the definition of the ‘domain’ of an atom in a structure. This is the space in which all points are nearer to the centre of that atom than to any other. It is a polyhedron (Voronoi polyhedron, Voronoi cell, Wigner–Seitz cell), each face of which is the plane equidistant between that atom and a neighbour. Every atom whose domain has a face in common with the domain of the central atom is, by the Frank–Kasper definition, one of its neighbours. The counting of the faces of the domain polyhedron gives the number of neighbours: the set of neighbours is the ‘coordination shell’. The coordination polyhedron, of course, is the polyhedron whose edges are the lines joining all the atoms in the coordination shell. The domain (Voronoi) polyhedron and the coordination polyhedron, therefore, stand in dual relationship, each having a vertex corresponding to each face of the other. According to the Frank–Kasper definition, the coordination number is unambiguously 12 in the hexagonal close-packed metals and assumes the value 14 in a body-centred cubic metal. Generally in several complex metallic structures this definition yields reasonable values such as 14, even when the nearest-neighbour definition would give 1 or 2. According for instance to O’Keeffe, however, this definition may lead to some difficulties. The value 14 for the body-centred cubic structure, higher than that of closest packing, does not seem entirely reasonable; the difficulty becomes more acute in a structure such as that of diamond for which a very high value, 16, is computed according to the mentioned definition. For a better quantification of the coordination number, several alternative schemes have been proposed. For example, a simple procedure is to identify a gap in the list of interatomic distances and to add atoms up to this gap. A similar procedure (O’Keeffe 1979) may be to add atoms to the coordination polyhedron in order of increasing interatomic distances and to stop when the next addition would

Structural Characteristics of Intermetallic Phases

129

result in a non-convex polyhedron. Brunner and Schwarzenbach (1971) suggested cutting off the coordinating atoms at the largest gap in the list of the interatomic distances (maximum gap rule). This rule was used by Daams et al. (1992) and Daams and Villars (1993, 1994, 1997) to define the so-called atomic environment type (AET) (see § 3.7.5) and to identify the atoms which are assumed to form the coordination polyhedron. We should however mention another more complex suggestion, which is to weight the contribution of the atoms according to a weight that decreases with interatomic distances (Bhandary and Girgis 1977) or according to a bond strength of the Pauling type (Brown and Shannon 1973). More complex relations are used, and non-integral coordination numbers may of course be obtained. In relation to the previously reported Frank–Kasper proposal, O’Keeffe (1979) suggested that coordinating atoms contribute faces to the Voronoi polyhedron around the central atom, and their contributions are weighed in proportion to the solid angle subtended by that face at the centre. By using this definition, increasing values of the (weighted) CNW coordination number are obtained for the structures: diamond (4.54), simple cubic (6), bodycentred cubic (10.16), face-centred cubic (12) (in agreement with the increasing packing density). A more refined weighting scheme has been suggested by Carter (1978) on the basis of the following assumptions. The interactions of a central atom with its neighbour are considered as being measured by a certain parameter Ai (ΣAi Atot, finite). The CNW as a function of all the Ai should satisfy the following conditions: ● ● ●

● ●

●

CNW(Ai) is dimensionless and 1 if any neighbours with non-zero Ai exists; CNW(Ai) is a continuous function of the Ai (its slope may not be); if N interactions exist such that A1 A2 … AN, for all neighbours with nonzero Ai, then CNW(Ai) N; if some of the Ai are unequal, then CNW(Ai) N; if m of the Ai are equal and large and N ⫺ m are equal and small, then: m CNW(Ai) N; The formula proposed by Carter for the quantification is: 1/CNW ΣNl (wiAi /Σ wjAj)2

(where wi are finite weighing factors). Definitions and measures of Ai might include bond strengths, bond energies, bond orders, etc. As an example, the structure of the CsCl-type has been discussed by Carter using several criteria of evaluation of Ai. In a geometrical approach a weighted coordination number as a function of atomic radii difference was described.

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Intermetallic Chemistry

We may finally mention the so-called ‘effective coordination number’ ECoN, proposed by Hoppe (1979) and Hoppe and Meyer (1980) computed by means of a rapidly converging function of the distances. According to Hoppe’s scheme, which can be related to Brunner’s suggestions previously mentioned, individual contributions ECoNj of all neighbours to the coordination number are summed together. Each contribution ECoNj quickly becomes small to the point of vanishing with increasing atomic distances dj according to an expression such as ECoNj exp(1 (d j/dm)6), where dm is a reference distance (the ‘mean fictive’ atomic size) which has to be determined beforehand from the structure. The trend of the ECoN has, for instance, been discussed as a function of the axial ratio c/a for the hexagonal closest packing of spheres (hP2-Mg structure). Values of ECoN ranging from, for example, 11.94 (for c/a 1.57 as Ho or Er) to 12.02 (for the ‘ideal’ c/a value, 1.633...) and to 11.02 (c/a 1.856, as for Zn) or to 10.74 (c/a 1.886, as for Cd) have been computed. ECoN for different Laves phases have been presented. For a number of NaCl- and CsCl-type compounds, moreover, values have been given to show the dependence of ECoN as a function of varying ionic radii. For a discussion on the ‘effective coordination number’, its relation to atomic size, bond strength, Madelung constant, etc., see also Simon (1983). For a computation of the heats of formation based on the so-called effective coordination, see a formula by Kubaschewski and Evans (1958), and for a discussion on its application and limits, see Borzone et al. (1993).

3.7.5 Atomic environment definition (and symbols) and corresponding coordination numbers and polyhedra With reference to some questions discussed in the previous paragraph and with special regard to the problem of an ‘efficient’ and simple definition of coordination and of an ‘optimal’ description of the local geometric characteristic, some details and aspects of the contributions given by Daams et al. (1992) and Daams and Villars (1993, 1994, 1997) in a series of reviews may be considered. They faced the problem of the classification of intermetallic structural types, reporting a complete description of the geometrical atomic environments found in the structural types of cubic, rhombohedral, hexagonal and tetragonal intermetallic compounds, respectively. As mentioned in the previous paragraphs, to define an atomic environment they used the maximum gap rule. The Brunner–Schwarzenbach method was considered, in which all interatomic distances between an atom and its neighbours are plotted in a histogram such as those shown in Fig. 3.17. The height of the bars is proportional to the number of neighbours, and all distances are expressed as reduced values relative to the shortest distance. In the specific case of CsCl, having a 411.3 pm,

131

Structural Characteristics of Intermetallic Phases Interatomic distances (pm) in CsCI (from CI in Atom

x

y

z

Distance

Cs Cs Cs Cs Cs Cs Cs Cs Cl Cl Cl Cl Cl Cl

0 1 0 0 1 1 0 1 1/2 1/2 1/2 1/2 −1/2 3/2

0 0 1 0 1 0 1 1 1/2 1/2 −1/2 3/2 1/2 1/2

0 0 0 1 0 1 1 1 −1/2 3/2 1/2 1/2 1/2 1/2

356.2 356.2 356.2 356.2 356.2 356.2 356.2 356.2 411.3 411.3 411.3 411.3 411.3 411.3

,

,

)

25 20 15 n 10 5 0 1.0

1.5

2.0

2.5

2.0

2.5

d /d min

Interatomic distances (pm) in CsCI (from Cs in 0, 0, 0) Atom

x

y

z

Distance

Cl Cl Cl Cl Cl Cl Cl Cl Cs Cs Cs Cs Cs Cs

1/2 1/2 1/2 −1/2 1/2 −1/2 −1/2 −1/2 0 −1 0 1 0 0

1/2 1/2 −1/2 1/2 −1/2 1/2 −1/2 −1/2 0 0 0 0 −1 1

1/2 −1/2 1/2 1/2 −1/2 −1/2 1/2 −1/2 1 0 −1 0 0 0

356.2 356.2 356.2 356.2 356.2 356.2 356.2 356.2 411.3 411.3 411.3 411.3 411.3 411.3

25 20 15 n 10 5 0 1.0

1.5 d /d min

Figure 3.17. Interatomic distances in CsCl. The distances are given for the CsCl compound (cubic, cP2-CsCl type, a 411.3 pm) with Cs and Cl in the representative positions 0, 0, 0, and 1⁄2, 1⁄2, 1⁄2 respectively, white and black atoms in Fig. 3.8. In the tables the first two groups of distances (in pm) are given as positions of each atom around the reference atom. Notice that not only atoms in the reference cell but also those in the adjacent cells must be considered (see Figs. 3.8 (d)–(f)). At the right side, the corresponding histograms using the ‘reduced distances’ d/dmin are shown: the first two ‘bars’ summarize the data contained in the table.

the minimum distance is that between positions such as 0, 0, 0 and 1⁄2, 1⁄2, 1⁄2, that is dmin (a3)/2 356.2 pm. The subsequent interatomic distance is 411.3 pm (see Fig. 3.8e). In the histograms similar for the two atoms, we have 8 atoms at d1 dmin 356.2 pm (d1/dmin 1), 6 atoms at d2 a(d2/dmin 2/3 1.1547…), etc.

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Intermetallic Chemistry

In most cases a clear maximum gap is revealed (here the gap between the second and the third bar). The atomic environment is then constructed with the atoms to the left of this gap (8 6 in the example of CsCl). To avoid in particular cases bad or ambiguous descriptions, however, a few additional rules have been considered. When for instance two (or more) nearly equal maximum gaps were observed, a selection was made in order to keep, in a given structure type, the number of different AET as small as possible. A convexity criterion for the environment polyhedron was also considered. The coordination polyhedron has to be defined as the maximum convex volume around only one central atom enclosed by convex faces with all coordinating faces lying at the intersections of at least three faces. This rule was especially used where no clear maximum gap was detectable. The different AET were characterized by a polyhedron code based on the number of triangles, squares, pentagons, hexagons, etc. that join each other at the different vertices (coordinating atoms). The polyhedron code gives the number of equivalent vertices with the number of faces in the above-mentioned sequence as an exponent. For example, a quadratic pyramid has four corners adjoining two triangles and one square (no pentagons or hexagons) and one corner adjoining four triangles: its code, therefore, is 42.1.0.014.0.0.0 (or briefly 42.114.0 with coordination number 5). The cube, eight equivalent vertices, adjoining three squares, has the code 80.3, the octahedron 64.0 and the so-called Frank–Kasper polyhedra have the codes 125.0; 125.026.0; 125.036.0 and 125.046.0 (with coordination numbers, CN, 12, 14, 15 and 16, respectively). Several polyhedra occurring in intermetallic crystal structures are shown in Fig. 3.18. Daams et al. (1992) have analysed all the cubic structure types reported in Villars and Calvert (1985), after excluding all oxides and a few types with improbable interatomic distances, thus leaving 128 structure types representing 5521 compounds. Their analysis showed that these cubic structure types have 13 917 atomic environments (point sets). Of those environments, 92% belong to one of the 21 most frequently occurring AET, which are those reported in the following list (see also Fig. 3.18): 43.0 (tetrahedron); 42.114.0; 64.0 (octahedron); 35.034.013.0; 80.3 (cube); 65.034.0; 5.0 4.0 6.0 3.0 2.2 0.3 5.0 4.0 6.0 8 2 ; 6 4 ; 9 2 ; 8 2 1 ; 125.0 (icosahedron); 122.2 (c.p. cubic) and 122.2 (c.p. hexagonal) (the same code describes the cubic as well as the hexagonal atomic environment of the ideal close-packing); 102.225.0; 105.026.014.0; 112.224.1; 125.026.0; 80.360.4; 125.036.0; 125.046.0; 126.064.0. Of the 5521 compounds crystallizing in the mentioned 128 structure types, 46% belong to a single-environment group (structures in which all atoms have the same type of environment), 37% have two environment types, 9% three and the rest four or more environments (98% of the cubic compounds crystallize in structure types with 1, 2, 3 or 4 AET).

133

Structural Characteristics of Intermetallic Phases

1#a

1 2#a

4#a

4

4-a

2

43.0

3#a

3

5-a

42.114.0

6-a

64.0 8-a

80.3

8-b

83.1

8-d

45.044.0 9-a

65.034.0

9-b

45.043.114.0

Figure 3.18a. AET (According to Daams and Villars 1992, 1993, 1994, 1997). The polyhedra corresponding to frequently observed AET are shown together with their codes. The Frank–Kasper (FK) polyhedra are indicated (see § 3.9.3.1). Notice the same code 122.2 of the two polyhedra describing the cubic (c) as well as the hexagonal (h) atomic environments of the two ideal close-packed structures.

In another paper (Daams and Villars 1993), the results of a similar classification of the rhombohedral intermetallic structure types were shown. The 195 rhombohedral structure types reported in Villars and Calvert (1991) were analysed; 51 types had improbable interatomic distances or correspond to oxides with no intermetallic representatives and were excluded. The remaining 144 types (corresponding to 1324 compounds) were considered. It was observed that 14 AET are greatly

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Intermetallic Chemistry

10-c

85.024.0

11-b

85.024.016.0

12-a

125.0

FK 12-b

122.2(c)

12-d

122.2(h)

13-a

105.026.014.0

14-a

125.026.0

14-b

80.360.4

15-a

125.036.0

FK 16-a

125.046.0

FK 17-d

125.056.0

20-a

125.0 86.0

FK

Figure 3.18b. (Continued)

preferred. Out of 6356 investigated point sets 71% belong to one of these 14 frequent AET, which are those reported in the following list: 3 (loose triangle); 43.0; 64.0; 61.2 (trigonal prism); 80.3; 65.034.0; 64.043.0; 92.220.3; 125.0; 122.2 (cubic type); 105.026.014.0; 125.026.0; 80.360.4; 125.046.0. Compare this list with the previous one of the cubic compounds: notice that several AET are reported in both lists. Of the 1324 rhombohedral compounds crystallizing in one of the 144 types, 19% belong to a single-environment group, 15% combine two environment types, 25% three environments, 34% four, and the remaining 7%, five or more environments (93% of the rhombohedral compounds crystallize in structure types with 1, 2, 3 or 4 environment types).

Structural Characteristics of Intermetallic Phases

135

The results of a similar analysis of the intermetallic hexagonal structure types have been reported by Daams and Villars (1994). Of 442 structure types, 315 (clearly intermetallic and correctly refined) were considered. In this case too it was observed that a small group of atomic environments is greatly preferred. The 23 AET most frequently occurring in the 315 hexagonal structure types are reported in the following list (to be compared with those previously reported for cubic and rhombohedral structure types): 3; 43.0; 4; 64.0; 61.2; 35.034.013.0; 80.3; 65.034.0; 64.043.0; 65.034.016.0; 92.220.3; 85.024.015.0; 125.0; 122.2 (cubic); 122.2 (hexagonal); 105.026.014.0; 64.133.032.219.0; 125.026.0; 122.226.0; 65.063.029.0; 125.036.0; 125.046.0; 125.086.0. The 3 and 4 codes correspond to ‘irregular’ AET. The reference atom is not included in the plane (volume) of the polygon (polyhedron) formed by the 3 (4) coordinating atoms. Out of 20 131 point sets investigated (belonging to 5646 compounds crystallizing in one of the aforementioned 315 hexagonal structure types), 81% (16 392) belong to one of these 23 AET. Of the 5646 compounds, 14% belong to a singleenvironment group; 35% combine two environment types; 32% three; 11% four and the rest (7%) five or more (93% of the hexagonal compounds crystallize in structure types with 1, 2, 3 or 4 AET). The results of the analysis of the intermetallic tetragonal structure types have also been reported and described by Daams and Villars (1997); 404 structure types were analysed. The analysis showed that 294 (clearly intermetallic and correctly refined) were possible with 4264 compounds and 17 157 point sets. In this case too it was observed that a small group (23) of atomic environments is greatly preferred. The 23 AET most frequently occurring in the 294 tetragonal structure types are reported in the following list (to be compared with those previously reported for the other systems): 1; 2; 3; 43.0; 4; 42.114.0; 64.0; 80.3; 83.1; 45.044.0; 65.034.0; 45.043.114.0; 85.024.0; 5.0 4.0 6.0 8 2 1 ; 125.0; 122.2 (cubic); 105.026.014.0; 125.026.0; 80.360.4; 125.036.0; 125.046.0; 125.056.0; 125.086.0. Out of 17157 point sets investigated, 83% (14 194) belong to one of these 23 AET. Of the 4264 compounds crystallizing in one of the mentioned 294 structure types, 16% belong to a single-environment group (that is to structures in which all atoms have the same type of environment); 17% combine two environment types; 42% three; 13% four and the rest (12%) five or more (88% of the tetragonal compounds crystallize in structure types with 1, 2, 3 or 4 AET). As a result of these analyses, several relations between structure types have been shown and discussed. Emphasis has been given to the fact that apparently, in all the structure types considered, ‘Nature prefers one of the most symmetrical AET. Remarkably these AETs are often found equally in single-environment and polyenvironment groups, meaning that even in complex structures, symmetrical

136

Intermetallic Chemistry

arrangements are preferred’. The formation of the geometrically simplest structure types containing a small number of different AET was also noted. The results of these analyses can be compared with the Stability Principles stated by Laves (§ 4.3.2.5). Concluding this section, we may mention a paper by Daams and Villars (1993) concerning an atomic environment classification of the chemical elements. Critically evaluated crystallographic data for all element modifications (and recommended atomic volumes) have been reported. Special structural stability diagrams were used to separate AET stability domains and to predict the structure (in terms of environment types) of hitherto unknown high-pressure and high-temperature modifications. Reference to the use of AET in thermodynamic (CALPHAD) modelling and calculation has been made by Ferro and Cacciamani (2002). A summary of this analysis of the atomic environments is shown in Fig. 3.18, where the most common frequently occurring AET are depicted with their symbols and codes. References to the so-defined AET and the corresponding coordination number, indicated as CNE, are reported for various prototype structures listed in Chapter 7. As a final remark we have to observe that the numbers of compounds, point sets, environment types, etc. evaluated at a certain time are continuously increasing, nevertheless they are sufficiently large to justify the general conclusions drawn.

3.7.6 Layer stacking sequence description and symbols A large group of structures of intermetallic phases can be considered to be formed by the successive stacking of certain polygonal nets of atoms or, in more complex cases, by the successive stacking of characteristic ‘slabs’. There are layer structures, for instance C graphite, CdI2, etc., in which bi-dimensional substructures formed by one or more atomic planes may be identified because distances between atoms of different slabs are clearly larger than those within each slab, and structures (for instance cubic, hexagonal close-packed structures) which can be conveniently regarded and described as a number of close-packed atomic planes piled one on top of the other. These structural characteristics can be easily represented by using specific codes and symbols, which can be very useful for a compact presentation and comparison of the structural features of several structures. Many different notations have been devised to describe the stacking pattern (for a summary see Parthé 1964, Pearson 1972). A few of them will be presented here. As an introduction to this point we consider Figs 3.19 and 3.20 where typical simple close-packed structures are shown and described as built from the

Structural Characteristics of Intermetallic Phases B

C B

137

C

A

A A

I

II

III

Figure 3.19. Close-packed bi-dimensional arrangement of equal spheres. Their centres, marked by A, are in the nodes of a triangular net. The points B and C may correspond to the nodes of similar triangular nets in different relative positions. On the right a few spheres of three superimposed layers in the hexagonal close-packing are shown. In this structure the spheres of the layer III are just above those of the layer I. A lateral view of the same arrangement is shown in Fig. 3.20.

superimposition of close-packed atomic layers. If spheres of equal sizes are packed together as closely as possible on a plane surface, they arrange themselves as shown in Fig. 3.19. Their centres are in the nodes of a triangular net. Each sphere is in contact with six others. Such layers can be stacked to give 3D close-packed arrays. If we label the positions of the centres of the spheres in one layer as A, then an identical layer can be superimposed on the first so that the centres of the spheres of the second layer are vertically above the positions B (for two layers, it is insignificant whether we choose the positions B or the equivalent position C). When we superimpose a third layer above the second (B), we have two alternatives: the centres of the spheres may be above either the A or the C positions. The two simplest sequences of layers will thus correspond to the superimpositions ABABAB… and ABCABCABC… (more complex sequences may of course be considered). The sequence ABAB…, corresponding to the so-called hexagonal close-packed structure (hP2-Mg type structure), is shown in Fig. 3.20. The sequence ABCABC… having a cubic symmetry is shown in Fig. 3.21. It is the cubic (face-centred cubic) close-packed structure, also described as cF4-Cu type structure. A more complete representation of different layer sequences, which can be used not only for the description of close-packed structures, may be obtained by using

138

Intermetallic Chemistry A A

C

B

B

A

A

B

C

A

B

B

1 3/4

A

1/4 0

B

c

A

A

1

C

2/3

B

1/3

A

0 Cu

Mg A

1

A

B

0.89

C

A

0.78

A

B

0.67

B

C

0.55

A

1

B

0.45

C

3/4

C

0.33

A

1/2

A

0.22 0.11 0

c

B

1/4

C

A

0

A

La

ch

c

Sm

Figure 3.20. A lateral view of different stacking sequences of triangular nets. They correspond to some typical close-packed structures. The first layer sequence shown corresponds to a superimposition according to the scheme ABABAB… (equivalent to BCBCBC… or CACACA… descriptions) characteristic of the hexagonal close-packed, Mg-type, structure. With reference to the usual description of its unit cell, the full stacking symbol indicating the element, the relative B position of the superimposed layers and their distance is Mg1/4 MgC3/4.The other sequences correspond to the schemes: ABC.ABC…. (Cu, cubic), ABAC.ABAC…. (La, hexagonal), ACACBCBAB…. (Sm, hexagonal). For Cu the constant ch of the (equivalent, non-conventional) hexagonal cell is shown which may be obtained by a convenient re-description of the standard cubic cell (see § 3.6.1.3). ch ac3, body diagonal of the cubic cell.

layer position symbols (stacking symbols) together with the indication of the relative spacings between the layers. Fig. 3.22 shows a network of atoms which can be considered as a triangular net, T net that is the 36 net. We may incidentally notice that the Schläfli Notation PN

139

Structural Characteristics of Intermetallic Phases

Figure 3.21. The face-centred cubic close-packed structure (Cu type). On the left a block of eight cells is shown (one cell darkened). On the right a section of the structure is presented: it corresponds to a plane perpendicular to the cube diagonal. Notice that the plane is the same presented on the left in Fig. 3.19. The sequence of the layers in this structure is shown in Fig. 3.20 in comparison with other close-packed elemental structures. a1

a2

C

B

A

A : 0,0

B:

1 3

,

2 3

C:

2 3

,

1 3

Figure 3.22. The triangular, 36, net of points and the corresponding bi-dimensional cell. The selected coordinate system corresponds to an inter-axial angle of 120°. The conventional order used in labelling the unit cell edges along the equivalent x and y axes (a1, a2) is indicated. On the right different positions (relative to the cell origin) are shown for the point net with the corresponding coding (stacking symbols). A: the representative point in the x, y plane (a, b plane with b a) has the coordinate 0, 0; B: the plane coordinate doublet of the representative point is 1⁄3, 2⁄3; C: the coordinate doublet of the reresentative point is 2⁄3, 1⁄3.

140

Intermetallic Chemistry

describes the characteristics of each node in the network, that is the number N of P-gon polygons surrounding the node. In the reported 36 net all the nodes are equivalent: their polygonal surrounding corresponds to 6 triangles. More complex symbols are used for nets containing non-equivalent nodes: for instance, the symbol 32434 3242 (2:1) means that, in the given net, two type of nodes, 32434 and 3242, occur with a relative 2:1 frequency. A symbol such as 3242 means that the given node is surrounded, in this order, by two triangles and two squares. In the case of the simple 36 triangular net, the symbols A, B, C relate the positions of the nodes to the origin of the cell, which is defined as in Fig. 3.22. In the layer stacking sequence full symbol, the component atoms occupying the layers are written on the base line, with the stacking symbols as exponents and the layer spacings in the form of suffixes, denoting the fractional height of the repetition constant along the direction perpendicular to the layers. In the case of Mg, for instance, with reference to the standard choice of the unit cell origin (two equivalent atomic positions for the two Mg atoms in 1⁄3, 2⁄3, 1⁄4 and 2⁄3, 1⁄3, 3⁄4), the symbol will be MgB1⁄4 MgC3⁄4 (which, with a zero point shift, is equivalent to MgA0 MgB1⁄2). a1

a2

c

b

a

a:

2 3

,

1 3

;

1 3

,

2 3

b : 0, 0 ;

2 3

,

1 3

c : 0, 0 ;

1 3

,

2 3

Figure 3.23. Hexagonal, 63, net of points. a, b and c are the codes corresponding to the different positions relative to the cell origin. Notice that the unit cell contains two points (every point in a corner is in common with four adjacent hexagonal cells). The coordinate doublets of the points are reported.

141

Structural Characteristics of Intermetallic Phases

The symbol CuA0 CuB1⁄3 CuC2⁄3, on the other hand, represents the cubic Cu structure as a stacking sequence of triangular layers viewed along the direction of the unit cell diagonal, which is perpendicular to the layers themselves. A few other nets, based on the hexagonal cell, are of frequent structural occurrence. Following Pearson’s suggestions (Pearson 1972), the corresponding sequences of stacking symbols which have a wide application are here presented. Fig. 3.23 shows the hexagonal (honeycomb) 63 net (H net) and the stacking symbols (a, b, c) used for relating the different positions of the nodes to the cell origin. Notice that two nodes are contained in the unit cell. A simple structure which can be described in terms of superposition of (even if far away, not close-packed) hexagonal layers is that of graphite: Cb1⁄4 Cc3⁄4. The hexagonal net is also called ‘graphitic’ net. Fig. 3.24 shows the three-way bamboo weave net, known as kagomé, a net of triangles and hexagons (K net, the 3636 net of points). The different positions of the nodes (three nodes in the unit cell) are represented by the symbols (α, β, γ) shown. Fig. 3.25 shows the similarly defined nine primed symbols (A , B , C , a , b , c , a1

a2

α

β

γ

α:

1 2

, 0; 0,

1 2

;

1, 1 2 2

β:

1 6

,

1 3

;

2, 5; 1 3 6 6

,

5 6

γ:

1 3

,

1 6

;

5 6

,

1 6

;

5 6

,

2 3

Figure 3.24. The ‘kagomé’, 3636, net of points. The codes α, β, γ corresponding to the different positions of the net (relative to the hexagonal cell origin) are shown. Notice that the unit cell contains three points of the net (every point in an edge belongs to two adjacent cells). For the different positions the coordinate doublets of the three points are reported.

142

Intermetallic Chemistry a2

a1

c′

C′

B′ b′ A′

C′

1 3

2 3 2 3 2 3

, 1 ; 0, 2 ;

B′ 0,,

3 1; 3

3

1 , 0; 3 1, 2; 3 3

A′ 0, 0;

,0 , ,

a′

2 3 1 3 1 c′ 0, 0; 0,, 3 ;

1, 3

0;

1 3

, 2;

2 3

, 1;

2 3

,

2 3

2 b′ 0, 0; 0,, 3 ;

2, 3

0;

1 3

, 1;

1 3

, 2;

2 3

,

1 3

1 3

1, 3

0;

2, 3

1 3

, 1;

2 3

,

2 3

a′ 0,,

β′

γ′

1 2 1 3

, 0; 0,, ,

1; 6

5, 6

1 6

,

2; 3

0,,

5; 6

1 6 2 3

;

1, 1 2 2

;

;

2, 5 3 6

;

2, 1 3 6

;

1, 1 6 6

;

1, 5 2 6

;

1, 1 3 2

;

1 6 1, 2 2 3

;

1, 2 1, 3

;

, 0; 0,, ,

1; 2

1 2 1 6

;

3

3

0;

3 3 3

a2

a1

α′

; 0,, 2 ;

3

1 6 5 6

;

1 6 5 6

,

1; 3 2 3

1, 5; 6 6

5 6 1 2

, 0;

5, 1; 6 2

,

1 3

1 6 5 6

,

1; 2 5 6

,

,

5, 1; 6 3

α′

β′

γ′

Figure 3.25. Stacking symbols applicable to larger unit cells. A , B , C : three nodes in the unit cell of a triangular net; a , b , c : six nodes of a hexagonal net in the unit cell; α , β , γ : nine nodes of a kagomé net in the unit cell. The coordinate doublets are indicated.

α , β , γ ) used for larger cells containing, respectively, 3, 6 and 9 atoms of the 36, 63 and kagomé nets. Several structures, especially hexagonal, rhombohedral and cubic ones, may be conveniently described in terms of stacking triangular, hexagonal and/or kagomé layers of atoms. Examples will be given in the following sections. The specification

Structural Characteristics of Intermetallic Phases

143

of the spacing between the layers is useful in order to compare different structures, to recognize the close-packed ones (A, B, C symbols with appropriate layer distances) and to deduce atomic coordinations. We have to notice, however, that the A, B, C notation previously described is not the only one devised. Several different symbols have been suggested to describe stacking patterns. For a description of the more frequently used notations see Parthé (1964), Pearson (1972). A very common notation is that by Jagodzinski (1954). This notation involving h and c symbols is applicable only to those structure type groups which allow not more than three possible positions of the unit layer (or more generally of the ‘unit slabs’; see also the polytypic structures in the following paragraph). The h and c notation cannot therefore be applied, for instance, to disilicide types. The letters h and c have the following meaning: ●

●

the letter h is assigned to a unit slab, whose neighbouring unit slabs (above and below) are displaced sideways, in the same direction by the same amount: for instance ABABA or CBCBCB hhh hhhh (h comes from hexagonal: this is the stacking sequence of the simple hexagonal structures such as hP2-Mg, hP4-ZnS wurtzite and hP12-MgZn2 types). the letter c, on the other hand, is assigned to unit slabs whose neighbouring slabs have different sideways displacements: for instance ABCABC or CABCAB cccc cccc (c comes from cubic: this is the stacking sequence found in cubic structures such as cF4-Cu, cF8-ZnS sphalerite and cF24-Cu2Mg types).

To denote the stacking sequence of the different structures it is sufficient to give only one identity period of the h, c symbol series. For instance: cF4-Cu, c (instead of ABC); cF8-ZnS sphalerite, c; hP4-ZnS wurtzite, h; hP4La, hc; hR9-Sm, hhc. As can be seen from the previously reported examples, the identity period of the h, c symbols is generally shorter than the A, B, C, … letter sequence. The h, c, … symbols may be condensed, for example, hcchcchchc to (hcc)2(hc)2. If the number of c letters in a Jagodzinski symbol is divided by the total number of letters one obtains the percentage of ‘cubic stacking’ in the total structure. Another common notation for describing stacking of close-packed 36 nets (T nets) is that devised by Zhdanov (1945) (a number notation equivalent to Jagodzinski’s notation). A short description of the Zhdanov symbol is the following: a ‘’ is assigned if the order between a layer and its previous partner follows the

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sequence corresponding to any two subsequent layers in the face-centred cubictype structure, that is A : B, B : C, C : A. Otherwise a ‘’ is assigned. For instance, the sequence ‘ ’ (shortened 33) corresponds to ABCACB. Finally, as another simple example of description (and symbolic representation) of structures in terms of layer stacking sequence, we now examine structures which can be considered as generated by layer networks containing squares. A typical case will be that of structures containing 44 nets of atoms (Square net: S net). The description of the structures will be made in terms of the separation of the different nets, along the direction perpendicular to their plane, and of the origin and orientation of the unit cell. Fig. 3.26 shows the different symbols, in this case numbers, suggested by Pearson (1972) which will be used to indicate origin and orientation of the nets. These numbers will be reported as exponents of the symbols of the atoms forming the

a

a′

a′

a

1

2

0, 0

0,

5

1 2,

0; 0,

3

1 2

6

1 2

1 1 3 3 4, 4 ; 4 , 4

4

1 2,

0

7

3 1 1 3 4, 4 ; 4 , 4

1 1 2, 2

8

0, 0;

1 1 2, 2

Figure 3.26. The bi-dimensional square, 44, net of points. Different numerical codes are shown for the different positions of the representative point in the unit square (bi-dimensional unit cell). In 1–4 the unit square contains one point. In 5–8 a larger square cell is considered with axes at 45° to the net alignment (and edges equal to 2 times the repeat unit of the net): it contains two representative points. For the different positions the corresponding bi-dimensional coordinate doublets are reported.

Structural Characteristics of Intermetallic Phases

145

different nets. In this case too the relative height of the layers will be indicated by a fractional index. A few symbols of square net stacking sequences are the following: Po01: the simple cubic cell of Po (containing 1 atom in the origin) corresponds to a stacking sequence of type 1 square nets. W10W41/2: the body-centred cubic structure of W (1 atom in 0, 0, 0 and 1 atom in 1 ⁄2, 1⁄2, 1⁄2) corresponds to a sequence of type 1 and type 4 square nets at the heights 0 and 1⁄2, respectively. Note, however, that for a full description of the structure, either in the hexagonal or the tetragonal case, the inter-layer distance must be taken into account not only in terms of the fractional coordinates (that is, the c/a axial ratio must be considered). For more complex polygonal nets, their symbolic representation and use in the description, for instance, of the Frank–Kasper phases, see Frank and Kasper (1958) and Pearson (1972). 3.7.7 The cP4-AuCu3 type: an example of the use of alternative and complementary structural notations and symbols As a conclusion to the nomenclature and symbols defined in the preceding paragraphs and as an introduction to their application in the description and discussion of selected crystal structures, it may be useful to underline some of their characteristics by means of an example. The structural type cP4-AuCu3 will be used to this – end. AuCu3 is primitive, cubic. The space group is Pm3m (N. 221 in the International Tables for Crystallography, Hahn 2002). In the unit cell there are 4 atoms in the following positions: 1 Au in (a) 0, 0, 0; 3 Cu in (c) 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2 1⁄2, 0; Its structure can be described as derivative of that of Cu (face-centred cubic, – cF4) for which, in the space group Fm3m (N. 225), four Cu are in the positions (a): 0, 0, 0; 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0. On passing from Cu to AuCu3 we have the splitting of the four Cu equivalent positions into two sets of positions (1 3), the structure is no longer face centred (cP4 instead of cF4) and corresponds to another space group. (In the lattice-complex symbolism this ‘splitting’ corresponds to the equation F : P J, as described in § 3.7.1.) Several phases are known to have this structure; a short selection is presented in the following list with indicative values of the lattice parameter (unit cell edge length): HfPt3 LaIn3 La3In Mn3Pt MnZn3 Ni3Al

a 398.1 pm a 473.9 pm a 511 pm a 383.3 pm a 386 pm a 360.9 pm

Ti3Hg TiZn3 UPb3 USn3 YAl3 Y3Al

a 416.5 pm a 393.2 pm a 479.1 pm a 460.3 pm a 432.3 pm a 481.8 pm

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(b)

(c)

0, 1, 1

(d)

0, 0, 1

1 1 1• 2, 2,

1, 1, 1

1, 0, 1

0, 1, 0 1 1 , 2 2

1, 1, 0

0, 1, 1

1 1 1• 2, 2,

1, 1, 1

0, 0, 0 1 1 , 2 2

,0 • 1, 0, 0

0, 2, 1

1 3 1• 2, 2,

1, 2, 1

0, 1, 0 1 3 , 2 2

,0 • 1, 1, 0

0, 2, 0

,0 • 1, 2, 0

Figure 3.27. Unit cell of the cP4-AuCu3 type structure. In (a) a ‘packing’ model, in (b) the positions of the atom centres, in (c) the same unit cell viewed along the cube diagonal are illustrated. In (d) as an introduction to the exercises reported in the text, a selection of the relevant coordinate triplets is shown both in the cell at the origin and in two adjacent cells.

Notice that for this structure type, examples are known of compounds, such as Y3Al and YAl3, in which the same elements alternatively occupy either the (a) or the (c) Wyckoff positions and exchange their roles in the structure. As for the prototype itself, AuCu3, a 374.84 pm. In the following, while discussing the characteristics of this structural type, reference to this value will be made. Its unit cell is shown in Fig. 3.27, by using different drawing styles and in different perspective views. The structure is shown in Fig. 3.28, where the 3D sequence of the atoms is suggested by presenting a small group (eight) of contiguous cells. The subsequent Figs. 3.29 (a)–(d) correspond to an analysis of the structure carried out in order to show the different local atomic arrangements (coordinations around the atoms in the two crystal sites). In the analysis of a structure, however, it is also necessary to take into consideration the values of the interatomic distances. It may be useful to consider both

Structural Characteristics of Intermetallic Phases

147

Figure 3.28. cP4-AuCu3 type structure. A block of eight unit cells is shown (Au: white; Cu: grey). (a)

(b)

(c)

(d)

Figure 3.29. Analysis of the cP4-AuCu3 type structure. Typical fragments of a few adjacent cells are depicted in order to show the different coordinations (Au: white; Cu: grey). (a) and (b) coordination around Au, (c) and (d) coordination around Cu. (a) octahedral coordination of 6 Au around Au, (b) cuboctahedral coordination of 12 Cu around Au (c) tetragonal prismatic coordination of 8 Cu around Cu, (d) square coordination of 4 Au around Cu. Notice that the overall coordination of 8Cu 4Au around Cu (c) and (d) is similar to the coordination of 12 Cu around Au (b).

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absolute and so-called ‘reduced’ values of the interatomic distances. In the case of the AuCu3 phase, the minimum interatomic distance corresponds to the Au–Cu distance (Au in 0, 0, 0 and Cu in 0, 1⁄2, 1⁄2) which is the same as the Cu–Cu distance between Cu in 0, 1⁄2, 1⁄2 and Cu in 1⁄2, 0, 1⁄2. This distance is given by (a2)/2. For the AuCu3 phase a 374.8 pm and, therefore, dmin 265.0 pm. This value (absolute value of the interatomic distance) could be compared, for instance, to the value 272 pm, sum of the radii of Cu and Au, as defined for a coordination number of 12, or to the value 256 pm of the Cu–Cu distance in the metal (Cu atomic ‘diameter’). Reduced interatomic distances (dr d/dmin) may be defined as the ratios of the actual distance values to the minimum value. A first set of interatomic distances (and the corresponding coordination, taken as the number of nearest-neighbour atoms) which can be considered in the AuCu3 phase is that related to the Au coordination around Au atoms (see Fig. 3.29(a)): Considering Au in 0, 0, 0 as the reference atom, the next neighbours Au atoms are the six Au shown in Fig. 3.29(a), corresponding to the same Wyckoff position – and having, in comparison with the reference atom, the coordinates 0, 0, 1; 0, 0, 1; – – 0, 1, 0; 0, 1, 0; 1, 0, 0; 1, 0, 0, all at a distance d a 374.8 pm, that is at a reduced distance dr d/dmin 1.414. Notice that in the analysis of the structure it may be necessary to consider not only the positions of the atoms in the reference cell but also those in the adjacent cells. Notice also that, in a simple cubic structure without free positional parameters such as the AuCu3 type, the reduced distances are independent of the values of the lattice parameters and are the same for all the isostructural compounds. In the same group of Au–Au interatomic distances a subsequent set is represented by distances such as those between Au0, 0, 0 and Au0, –1, 1 (or Au0, –1,1–, Au0, 1, –1, Au1,0,1, etc.). This set corresponds to 12 atoms (all at an absolute distance of a2 530.1 pm, that is, at a reduced distance dr d/dmin 2.000). A second set of interatomic distances (and coordination) corresponds to the Cu coordination around Au atoms. Considering as the reference atom, the atom Au in 0, 0, 0, the next neighbours Cu atoms are the 12 Cu reported in Fig. 3.29 (b), in the – – – – – – – – coordinates: 0, 1⁄2, 1⁄2; 0, 1⁄2, 1⁄2; 0, 1⁄2, 1⁄2; 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0; – – – – – 1 ⁄2, 1⁄2, 0; 1⁄2, 1⁄2, 0; 1⁄2, 1⁄2, 0, all at a distance d a 2 /2 265.1 pm, corresponding to a reduced distance d/dmin 1.000. The subsequent sets of Au–Cu distances correspond to 24 atoms at d 459.1 pm (dr d/dmin 3 1.732), 24 Cu at d 592.7 pm (dr 2.236), etc. A third group of interatomic distances (and coordination) is that corresponding to the Cu coordination around Cu atoms. Selecting among the Cu atoms (all equivalent to each other) the atom Cu in 1⁄2, 1⁄2, 0 as the reference atom, the next

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Structural Characteristics of Intermetallic Phases

neighbouring Cu atoms are the eight Cu atoms in: 1⁄2, 0, 1⁄2; 0, 1⁄2, 1⁄2; 1, 1⁄2, 1⁄2; 1⁄2, 1, 1⁄2; – – – – 1 ⁄2, 0, 1⁄2; 0, 1⁄2, 1⁄2; 1, 1⁄2, 1⁄2; 1⁄2, 1, 1⁄2 (see Fig. 3.29(c)); all at a distance d a— 2/2 265.1 pm, corresponding to a reduced distance d/dmin 1.000. The subsequent sets of Cu–Cu distances correspond to six Cu atoms, in coordinates such – as: 1⁄2, 1⁄2, 1; 1⁄2, 1⁄2, 1; 3⁄2, 1⁄2, 0; etc. at a distance d 374.8 pm (dr 1.414), 16 Cu atoms at d 459.1 pm (dr 1.732), 12 Cu atoms at d 530.1 pm (dr 2.000), 16 Cu atoms at 592.7 pm (dr 2.236), etc. The fourth (and last) type of interatomic distances (and coordination) characteristic of the AuCu3 structure is given by the Au coordination around the Cu atoms. Considering as the reference atom one of the three equivalent atoms Cu in the Wyckoff position (c), for instance, the atom in 1⁄2, 1⁄2, 0, the next neighbours Au atoms are 4 Au in 0, 0, 0; 1, 0, 0; 0, 1, 0 and 1, 1, 0 (see Fig. 3.29 (d)); all at a distance d a2/2 265.1 pm, that is, at a reduced distance d/dmin 1.000. Subsequent sets of Cu–Au distances correspond to a group of 8 Au atoms (in coordinates such as 0, 0, 1; 1, 0, 1; 0, 1, 1; etc.) at a distance d 459.1 pm (reduced distance d/dmin 1.732), to a group of 8 Au, at a distance d 592.7 pm, d/dmin 2.236, etc. Considering now all the atoms (Cu and Au) surrounding an Au atom (or respectively a Cu atom) we may prepare characteristic histograms such as those in Fig. 3.30 where, the number of surrounding atoms is plotted as a function of the reduced interatomic distance from a given atom. Lists of coordinating atoms, with distances from the references atom, coordination polyhedra, and next neighbour histograms are presented systematically by Daams et al. (1991) for all the known prototypes. 25

Cu

25

Cu

20

Au

20

15 n

Au

Au

Cu 10

Cu

Cu

15 n

Cu

Au 10

5

Au

0 1.0

1.5

Cu 5

2.0

2.5

0 1.0

Cu

1.5

2.0

d /dmin

d /dmin

Coordination around Au

Coordination around Cu

2.5

Figure 3.30. Analysis of the cP4-AuCu3 type structure. Coordination and interatomic (reduced) distances. The total number (n) of near-neighbour atoms around Au and Cu are plotted as a function of their reduced distances from the reference atom. The symbols of the surrounding atoms are indicated. Notice the similarity between the two histograms.

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As a conclusion to the description of the different coordinations, we may observe that those corresponding to the first distance sets are summarized in the 333 symbol 333 [A6/6][B8/8]12/4 ( [Au6/6][Cu8/8]12/4 for the prototype or, in more detail, 333 [Au6o/6o][Cu8p/8p]12co/4l). In terms of polyhedra packing, therefore, this structure may be described as a 3D arrangement of cubo-octahedra. On terms of atomic environments, on the other hand, according to the definitions adopted in § 3.7.5 we have the following data for the types of polyhedra surrounding each atom, and the nature of their vertices. Around Au in (a) a polyhedron 122.2 made up of 12 Cu atoms (that is a coordination CNE 12). Around Cu in (c) a polyhedron 122.2 made up of 8Cu 4Au atoms (that is a coordination CNE 12). In Fig. 3.27 (c), on the other hand, it is suggested that, for the same structure, an alternative description may be obtained and, according to Pearson, symbolized. In this figure the structure is viewed along the cube diagonal: it corresponds to a stacking sequence of triangular and kagomé nets, with the symbol AuA0Cuα0 AuC1/3Cuγ1/3AuB2/3Cuβ2/3. In this symbol we have the same number of triangular (A, B, C) Au atom nets and of kagomé (α, β, γ) Cu atom nets. These two net types are characterized by the presence of 1 and 3 points (atoms) in the unit ‘tile’ (Figs. 3.22 and 3.24). This, of course, corresponds to the overall 1:3 stoichiometric ratio. The same structure, viewed along the unit cell edge direction, corresponds to a square net stacking sequence (see Fig. 3.26). The stacking symbol is Au10Cu40Cu51/2. These different symbols may be useful when comparing this structure with other structural types: for instance with the cF4-Cu type or the tP2AuCu(I) type (Au10Au40Cu51/2 as square net stacking) or the hP8-Ni3Sn type (SnB0.25Niβ0.25 SnC0.75Niγ0.75 as triangular and kagomé net stacking). With reference to a description in terms of lattice-complex combination, the AuCu3-type structure corresponds to a combination of P and J complexes (AuCu3: P J). According to Hellner (1979), this structure may be considered as pertaining to an F-family as a consequence of the particular splitting, previously described, of the points of the F complex. A few other comments on the AuCu3-type structure and some remarks on the relationship with other structural types will be reported in the following Chapter 7.

3.7.8 Structure trivial names and Strukturbericht symbols As a conclusion to the presentation of the rational nomenclature and symbolism of the intermetallic phases, it must be mentioned that a number of trivial names and symbols have been used and, due to historical reasons, are still in use both as indicators of a single phase in specific systems, or as descriptors of certain structural types or of families of different interrelated structural types.

Structural Characteristics of Intermetallic Phases

151

Trivial symbols and names. Among these, Greek (and Roman) letters have been used; often in order to indicate actual phases in specific systems, for instance in a given binary system, phase α, β, γ, etc., in alphabetical order according to the increasing composition from one component to the other, while in unary systems α, β, etc., symbols have been used to denote different allotropic forms. Obviously this notation (or other similar ones such as τ1, τ2, τ3, denoting ‘1st’, ‘2nd’, etc., phase) may be useful as a quick reference code while discussing and comparing phase properties of alloys in a single specific system, but in general cannot be used as a rational criterion for denoting structural types. In a few cases, however, certain Greek and Roman letters have assumed a more general meaning as symbols of groups of similar phases: for instance, the name ‘γ phases’ which is an abbreviation of a sentence such as ‘phases having the γ-brass (the γ-Cu–Zn) type structure’. In a number of cases such a general meaning has been attributed also to names of scientists as in: Laves-type phases, Heusler phases, etc. A short list of these names and letters, in alphabetical order, is included in the formula index in Chapter 7. Strukturbericht symbols. These correspond to a pre-war designation adopted by the editors of the Strukturbericht publications (and later Structure Reports) in abstracting crystal structure determination. This designation is no longer recommended by the IUPAC, but it is still used, especially in papers concerning thermodynamics and phase diagram studies. According to this designation, each structure type is represented by a symbol generally composed of a letter (A, B, C, etc.) and a number. The letter is related to the stoichiometry; A: unary phases (or believed to be unary); B: binary compounds having a 1:1 stoichiometry; C: binary 1:2 compounds, etc. In every class of stoichiometries, the different types of structures are distinguished by a number and/or a letter. An equivalence table between the Strukturbericht designation and the Pearson symbol especially relevant to intermetallic phases can be found in Appendix at the end of Chapter 7.

3.8. STRUCTURE FAMILIES: DEGENERATE STRUCTURES, DERIVATIVE STRUCTURES, ‘SUPERSTRUCTURES’

As clearly pointed out, for instance, by Bärnighausen (1980), one of the main objectives of crystal chemistry is to order the profusion of structure types and to show the general principles involved. To this end relations between cognate structures evidently play an important role. The structures corresponding to different types may often be interrelated on the basis of some transformation or construction schemes. These schemes can be used as criteria for classifying structure types and showing structural relationships.

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A few selected types of such relationships between different structures will be presented in this paragraph and in the following ones (§ 3.9 and 3.10). Examples will be considered of possible (virtual and/or real) transformation mechanisms from one structure type to another (degenerate, derivative structures); examples will also be discussed of groups of structures interrelated because based on the assembly of similar blocks and fragments (recombination structures). A derivative structure can be considered as being obtained from a reference structure by ordered atomic substitution, subtraction or addition processes or by unit cell distortions (or both). The opposite kinds of transformation correspond to the so-called degeneration processes. A derivative structure has fewer symmetry operations than the reference structure (a degenerate structure has more). A derivative structure has either a larger cell or a lower symmetry (or both) than the reference structure. It is possible, for instance, that a set of equipoints of a certain structure (considered as the reference structure) has to be subdivided into two (or more) subgroups in order to obtain the description of another (‘derivative’) structure. The structure of the Cu type (cF4 type), for instance, corresponds to four Cu atoms in the unit cell, placed in 0, 0, 0; 1⁄2, 1⁄2, 0; 1⁄2, 0, 1⁄2; 0, 1⁄2, 1⁄2, whereas in the cP4-AuCu3 type structure the same atomic sites are subdivided into two groups with an ordered distribution, in another space group, of the two atomic species (1 Au atom in 0, 0, 0, and 3 Cu atoms in 1⁄2, 1⁄2, 0; 1⁄2, 0, 1⁄2; 0, 1⁄2, 1⁄2). (See also in § 3.7.1 the corresponding description in terms of lattice complexes.) The AuCu3-type structure can, therefore, be considered as a derivative structure of the Cu type. On the other hand, if we consider the AuCu3 type as the reference structure, we may describe the Cu type as a degenerate structure. The aforementioned subdivision of a set of equipoints in more groups can be described in this case in terms of similar cubic cells both of the original and of the derivative structures. Notice, however, that in the case of Cu the conventional cubic cell is face centred. It is not primitive: it corresponds to four (rhombohedral) primitive cells, whereas, in the case of AuCu3 the primitive unit cell is larger and it is identical to the cube. Because of the observation that these ordering processes may lead to a cell larger than the original one, they are also referred to as forming superstructures (also called superlattices) (Barrett and Massalski 1966) of the original structure. An example where, due to ordering, we observe perhaps in a more immediate way, the increase of the unit cell size (formation of a multiple cell) is the MnCu2Altype structure (representative of the so-called Heusler alloys) which can be considered a derivative structure (superstructure) of the cP2-CsCl type, which in turn is a superstructure of the W-type structure, corresponding to a non-primitive cubic cI2

Structural Characteristics of Intermetallic Phases

153

(a)

(b) Al Mn Cu

Figure 3.31. cF16-MnCu2Al type structure (representative of the ‘Heusler type’ alloys). The unit cell is shown in (a), an eighth of the cell is shown in (b). It degenerates into a cP2-CsCl type cell if the atoms at the cube corners (Mn and Al) are equivalent. If all the atoms were equivalent there would be a further degeneration into the cI2-W type.

cell (see Fig. 3.31). Notice that the ordering may not lead to a multiple cell, if the symmetry of the ordered structure is reduced relatively to the original one. Nevertheless the name superstructure is generally used, especially when we have a disordered solid solution involved, regardless of whether there is multiplication of the edges of the cell or not. A contribution to the study of order–disorder interrelations between structures and to their classification into two groups on the basis of the presence/absence of a difference in the translational symmetry (unit cell edge variations) has been made by Wondratschek and Jeitschko (1976) and by Albering et al. (1994). The detectability of the two types of ordering by means of X-ray diffraction studies has also been discussed. Albering et al. (1994) especially studied the hP3-AlB2 type structure and its derivatives. A few of these are presented in Fig. 3.32. The main features of several deformation and substitution derivatives of the AlB2 type were discussed by Gladyshevskii et al. (1992). A more complex case of structure interrelation

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Intermetallic Chemistry (a)

(b) AlB2 Al

B

(c) ThAuSi Au

Si

(d) Er2RhSi3 Rh

Si

Figure 3.32. hP3-AlB2 type and derivative structures. (a) Two sections of the AlB2 unit cell at the height 0 (Al atoms) and 1⁄2 c (B atoms) are shown. (b) The corresponding hexagonal net of the B atoms is presented; a projection, on the plane a, b, of the unit cell is superimposed. (c) The hexagonal net (at z 1⁄2) of the atoms Au and Si in the hP3-ThAuSi type cell. (d) The hexagonal RhSi3 net (at z 0) in the hP24-Er2RhSi3 cell: notice, in comparison with AlB2 the larger unit cell and compare this hexagonal net with those shown in (b) and (c).

which can be presented in terms of, albeit ‘formal’, substitution is that which can be exemplified by considering structures such as those of NaCl (Fig. 3.33) and FeS2 or CaC2 (see the description of the CaC2 structure and a comparison with that of MoSi2 in § 3.6.1.2).

Structural Characteristics of Intermetallic Phases

155

Figure 3.33. cF8-NaCl type structure. The positions in the unit cell of two types of atoms are indicated. Notice that interchanging the positions of Na and Cl corresponds to a shift of the origin: the two dispositions are undistinguishable; the NaCl type is its own antitype.

These structures may be compared. The cP12-FeS2 type may be described as having Fe atoms in the sodium ion positions and the centres of the discrete S2 dumb-bell groups at the chlorine ion positions. The passage from one structure containing spherical atoms to another in which atomic groups substitute single atoms will generally result in a symmetry reduction. A clear example is the tI6-CaC2 type which can also be compared with the NaCl type: the positions of Na and Cl atoms may be related to those of calcium and of the C2 groups, respectively. In this case, however, the long axes of the C–C groups are all aligned in one direction so that the unit cell is tetragonal instead of cubic. In a similar way, for instance, the K2PtCl6 structure may be considered essentially the same as the CaF2 antitype: the K ions are in the F ion positions and the centres of the PtCl6 octahedral groups are in the Ca ion positions.

3.8.1 Defect and filled-up derivative structures Derived structures may also be formed by the ordered introduction of vacant sites. As an example, consider the hP3-CdI2 type structure (see Chapter 7) which can be related to the hP4-NiAs type structure in which the set of equivalent points 0, 0, 0 and 0, 0, 1⁄2 is considered as being subdivided into two groups (each of one site) 0, 0, 0 (occupied by one atomic species) and 0, 0, 1⁄2 (vacant). We can therefore regard the hP3-CdI2 type structure as a defect derivative form of the hP4-NiAs type (see § 7.4.2.4.3). Similar considerations may be extended to include (besides substitution and subtraction) ordered addition of atoms. In this case stuffed or filled-up derivative

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Intermetallic Chemistry

structures are considered in which extra atoms have been added in an ordered way, on sites unoccupied in the reference structure. The hP6-Ni2In structure, which is a stuffed derivative structure of the previously mentioned NiAs structure is an example. Another interesting example is the face-centred cubic-derivative interstitial cP5-Fe4N phase. It may be described as corresponding to the following atomic – – positions in the Pm3m (or P4 3m) space group: 1 Fe in (a): 0, 0, 0; 1 N in (b): 1⁄2, 1⁄2, 1⁄2 and 3 Fe in (c): 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0. This filled-up superstructure may therefore be described in terms of the occupation by N of an interstice (centred in 1⁄2, 1⁄2, 1⁄2) of a Cu-type (or AuCu3-type) structure. The N atom is octahedrally surrounded by 6 Fe atoms. This structure could also be described as a deficient NaCl-type derivative structure: the Fe atoms are in the same positions as the Na atoms in NaCl and one out of the four Cl positions is occupied by the N atoms. As a footnote to these observations, we also have to mention that frequently structural distortions (axial ratio and/or inter-axial angle variations) accompany the formation of derivative structures, especially because of the ordered distribution of atoms of different sizes or of vacant sites. 3.8.1.1 Tetrahedral and octahedral holes in close-packed structures. Derivative structures may be obtained from a parent structure by ordered substitution or by ordered addition of atoms. For a systematic description of the derivative structures which can be obtained from the close-packed structure by ordered filling-up, it may be useful to consider that in the closest packing of equal spheres there are, among the spheres themselves, essentially two kinds of interstices (holes). These are shown in Fig. 3.34. The smallest holes surrounded by a polyhedral group of spheres are those marked by T. An atom inserted in this hole will have four neighbours whose centres lie at the vertices of a regular tetrahedron (tetrahedral holes). The larger holes (octahedral holes) are surrounded by octahedral groups of six spheres. In an infinite assembly of close-packed spheres the ratios of the numbers of the tetrahedral and octahedral holes to the number of spheres are, respectively, 2 and 1. Considering the Cu-type structure (in which the four close-packed spheres are in 0, 0, 0; 0, 1⁄2, 1⁄2; 1⁄2, 0, 1 ⁄2; 1⁄2, 1⁄2, 0) the centres of the tetrahedral and octahedral holes have the coordinates: Four octahedral holes in: ⁄2, 1⁄2, 1⁄2; 1⁄2, 0, 0; 0, 1⁄2, 0; 0, 0, 1⁄2;

1

Two sets of 4 tetrahedral holes in: ⁄4, 1⁄4, 1⁄4; 1⁄4, 3⁄4, 3⁄4; 3⁄4, 1⁄4, 3⁄4; 3⁄4, 3⁄4, 1⁄4;

1

and in: ⁄4, 3⁄4, 3⁄4; 3⁄4, 1⁄4, 1⁄4; 1⁄4, 3⁄4, 1⁄4; 1⁄4, 1⁄4, 3⁄4.

3

Structural Characteristics of Intermetallic Phases

157

O

T

T

O

Figure 3.34. Holes in the closest packing of equal spheres. Two superimposed layers of spheres are shown (continuous and dotted lines). Tetrahedral (T) and octahedral (O) holes are indicated.

Several cubic structures, therefore, in which (besides 0, 0, 0; 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0) one or more of the reported coordinate groups are occupied could be considered as filled-up derivatives of the cubic close-packed structures. The NaCl, CaF2, ZnS (sphalerite), AgMgAs and Li3Bi-type structures could, therefore, be included in this family of derivative structures. For this purpose, however, it may be useful to note that the radii of small spheres which fit exactly into tetrahedral and octahedral holes are, respectively, 0.225.... and 0.414... if the radius of the close-packed spheres is 1.0. For a given phase pertaining to one of the aforementioned types (NaCl, ZnS, etc.) if the stated dimensional conditions are not fulfilled, alternative descriptions of the structure may be more convenient than the reported derivation schemes. Notice, moreover, that one face-centred cubic cell of atoms X in which all the interstices are occupied (the octahedral by X and the tetrahedral by Z atoms) is equivalent to a block of 8 XZ, CsCl-type cells (see Fig. 3.31). This relationship (and others with other structures such as Li3Bi and MnCu2Al) should be kept in mind when considering, for instance, phase transformations occurring in ordering processes. Similar considerations may be made with reference to the other simple closepacked structure, that is to the hexagonal Mg-type structure. In this case two basic derived structures can be considered: the NiAs type with occupied octahedral holes and the wurtzite (ZnS) type with one set of occupied tetrahedral holes (compare with the data given with an origin shift in § 7.4.2.3.2). For a few more comments about ‘interstices’ and interstitial structures see § 3.8.4. See Fig. 3.35.

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Intermetallic Chemistry 1/2

0

1/2

0

1/2

0

1/4 , 3/4 1/4 , 3/4 0 1/2

0

1/2

0

1/ 2

1/2

0

1/4 , 3/4 1/4 , 3/4

0

1/2

Four c.p. spheres in:

Eight tetrahedral holes in: , , , ,

0, 0, 0 , 0, 0, , , ,0

, , , ,

, , , ,

0

1/2

Four octahedral holes in:

, , , ,

0, 0, , 0, 0 0, , 0 , ,

y 0, 1/2

x

0, 1/2

5/8, 7/8

1/4 1/8, 3/8

3/4

0,1/2 Two spheres in: , ,

, ,

Four tetrahedral holes in: , ,

, 8 , 58

, ,

, 8 , 78

0,1/2 Two octahedral holes in: 0, 0, 0 0, 0,

Figure 3.35. Position of the holes in closest packing. Unit cell projections are shown for the cubic and hexagonal sphere closest packing. Coordinates of the spheres and of the tetrahedral and octahedral holes are given. The values indicated inside the drawing correspond to the third coordinate (along the vertical axis); when two values are given, these correspond to two positions along the same vertical line.

3.8.2 Order–disorder transformation In a number of metal systems for a given range of compositions, depending for instance on temperature, it is possible to observe alloys having both a certain degenerate structure and a corresponding (more or less) ordered derivative structure. The transformation from one structure to the other corresponds to a real process (order–disorder transformation). A large number of solid solutions become ordered at low temperature. In the specific case, for instance, of the Au–Cu system, an alloy with the AuCu3 composition at high temperature has the disordered cF4-Cu type structure. The two atomic species are equally distributed in

Structural Characteristics of Intermetallic Phases

159

the four atomic sites, which are therefore equivalent: each one is occupied by Au with a 25% probability and by Cu with a 75% probability. This random distribution may also be related to the possibility of gradually changing the overall composition of the alloy while maintaining the same structure and giving the formation of solid solutions. For the Au–Cu alloys we have, at high temperature, a continuous solid solution ranging from Au to Cu, both having the same cF4-Cu type structure: in all the intermediate alloys we have the equivalence of all the atomic sites whose occupation gradually changes from pure Cu to pure Au. By lowering the temperature we have ordering processes corresponding to a change from a nearly random distribution of atoms among the structure sites into more ordered arrangements where certain sites are predominantly occupied by one kind of atom. In the specific case of the AuCu3 composition we have the transformation from the cF4-Cu type into the described derivative type (cP4-AuCu3 type) structure. Typical examples of ordering processes are also the transformation from the β to β phases in the Cu–Zn system (from cI2-W type to cP2-CsCl type) and the ordering of the FeAl phase in the CsCl-type structure. Notice that ordering in these metallic phases may be an extremely sluggish process requiring slow cooling and/or long annealing of the alloys. Alloy samples with different degrees of ordering can be obtained by quenching at various cooling times. As a consequence, the effects of ordering on a number of properties have been studied. Alloys such as AuCu3 and Fe3Al have been the subject of many of these studies. The Au–Cu system, in particular, was the first system for which a superstructure was shown to exist (Johansson and Linde 1925). As a result, a very large volume of work has been carried out on the ordered AuCu and AuCu3 phases. The description of the Au–Cu system, reported by Okamoto et al. (1987) (see Fig. 2.20 (d)), can be considered as a reference for the review and assessment, not only of the specific system, but also of the investigation methods and discussion criteria of general interest. The following topics are covered in the paper by Okamoto et al. (1987). Au–Cu phase diagram, Au3Cu, AuCu, AuCu3 ordered phases (phase boundaries determination by X-ray studies, electrical resistometry, electron microscopy), crystal structure determination by X-ray and electron diffraction methods, nature of ordering transformation in AuCu, short-range order, anomalous behaviour in AuCu3 at high temperatures (specific heat, thermal expansion measurements, etc.). Kinetic studies carried out by measuring gradual shift and intensity variation of the X-ray lines from a disordered to an ordered (superlattice) structure on samples after different quenching and annealing are also reported. For a review on site preference of substitutional additions to CsCl-type intermetallic compounds see Kao et al. (1994). In this work dilute additions to NiAl, FeAl and CoAl are especially discussed. The addition of a third element to ordered Ni3Al (cP4-AuCu3 type) occurring in different ways (Ochiai et al. 1984) is another

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example where Sb, Si, Ge and Ga atoms replace preferably Al, while Cu and Co replace Ni. For a discussion on the trends of lattice parameter and volume changes consequent on disordering some types of structure see Bhatia and Cahn (2005). They observed that, when the more electropositive constituent of the alloy is a simple metal, a strong correlation may be observed between the volume increase on disordering and the formation volume of the ordered alloy. As a conclusion to this section, notice that a systematic description of ordering processes in alloys and of the superstructures which can be generated has been presented, for instance, by Khachaturyan (1983) in the framework of a theoretical treatment of structural transformation in solids. Two groups of superstructures have been specially considered: substitutional and interstitial.

3.8.3 Examples of substitutional superstructures A first group of superstructures, described in several paragraphs of this chapter and of Chapter 7, must be mentioned; these include the types tP2-AuCu(I), cP4AuCu3 and tP4-Ti3Cu which can be considered face-centred cubic-based substitutional ordered superstructures. A few more interrelated structures that may be described as substitutional superstructures of the cP4-AuCu3 type are schematically shown in Fig. 3.36. A full description of these different prototypes is given in the specific paragraphs of Chapter 7. In this figure characteristic projections of their unit cells are collected: in addition to AuCu3 itself, the tI8-TiAl3, tI16-ZrAl3, oI6-MoPt2 and tI10-MoNi4 types are depicted. tI8-TiAl3 (c/2a 1.12) has a unit cell composed of two distorted, AuCu3-type related, subcells stacked one above the other along the c direction. tI16-ZrAl3 (c/4a 1.08) has a unit cell corresponding along the c direction to four superimposed face-centred cubic subcells. oI6-MoPt2 (b/a 3.00) also is a close-packed superstructure based on pseudoface-centred cubic sub-cells. The tI10-MoNi4 type is another superstructure based on face-centred cubic pseudo-cells. In the projection shown in Fig. 3.36, inside the true cell, the pseudocubic subcell (aps 362 pm, cps 356.4 pm) has been evidenced by dotted lines. Close-packed layers can be identified in this structure: they are stacked in a 15 close-packed repeat sequence. Like the Au–Cu system, also the alloy system Cu–Pt is characterized by a phase diagram with the face-centred cubic continuous solid solution stable at high temperature and, for different composition ranges, a number of ordered superstructure phases stable at lower temperatures. CuPt(I), for instance, is a complex, slightly

161

Structural Characteristics of Intermetallic Phases Au Cu

AuCu3

0

.5

0

.5

0

.5 Zr

.5

0

.5

0

.5

0 Al

0

.5

0

.5

0

.5

0

.5

0

Ti Al

TiAl3

0

.5

0

.5

0

.5

.5

0

.5

0

.5

0

0

.5

0

.5

0

.5

.5

0

.5

0

.5

0

0

.5

0

.5

0

.5 ZrAl3

Mo Ni

.5

0

0

.5

0

.5

0

.5

0

.5

0

.5 0

MoNi4

.5

0

.5

0

.5

0

.5

0

.5

Pt .5

Mo

.5

MoPt2

Figure 3.36. cP4-AuCu3 type structure and examples of its substitutional superstructures. The projections of the unit cells of a number of interrelated structures are shown. cP4-AuCu3 projected on the face a, a; tI8-TiAl3 projected on the face a, c; tI16-ZrAl3 projected on the face a, c; tI10MoNi4 projected on the face a, a; oI6-MoPt2 projected on the face a, b. The values of the fractional coordinates along the third axis are indicated: notice, however, as reported in the text, the different c/a values.

distorted superstructure made up of eight face-centred cubic pseudo-cells (it is hR96 type with 32 atoms in the corresponding primitive rhombohedral cell which is slightly distorted in comparison with the original face-centred cubic cell: αrh 90°–91° according to the composition). In the same system other superstructures have been described for compositions around Cu3Pt5 (also called rhombohedral CuPt(II) type), Cu3Pt (cP4-AuCu3 type for compositions from 9 to 24 at.% Pt and tP8-Cu3Pd type at 23 to 28 at.% Pt), CuPt3 (orthorhombic), etc.

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Intermetallic Chemistry

Another example of a superstructure based on a close-packed structure but related to the hexagonal close-packed one is that corresponding to the hP8-Ni3Sn prototype. Just as the AuCu3 type can be derived by ordering the Cu-type structure, so the Ni3Sn type can be obtained from the hP2-Mg type. Details of this structure and of some stacking variants are described in Chapter 7. 3.8.4 Examples of interstitial superstructures: Hägg phases In previous paragraphs it was observed that derivative structures may be obtained by the addition of atoms to certain parent structures. It was also mentioned that these extra atoms may be added on sites unoccupied in the reference structure, obtaining stuffed or filled-up derivative structures. The particular case of unoccupied sites corresponding to holes (interstices) in a structure was previously presented while discussing the example of the holes (tetrahedral and octahedral) in close-packed structures. In addition to what was reported in § 3.8.1.1 about the radii of small spheres which exactly fit into tetrahedral and octahedral holes, the values relevant to other polyhedral environments are given in Table 3.5. It must be underlined, however, that these are geometry-based considerations and concepts which may be very useful for the description of the structure types and their comparison and for classification purposes, but do not necessarily correspond to real chemical processes, even if in some cases (with certain elements) the insertion of atoms in the interstices of clusters or of a sphere packing can actually be performed. In the metal chemistry field, the uptake of hydrogen by some metals giving metal hydrides is an important example of an effective interstitial insertion. 3.8.4.1 Interstitial hydrides. A few different kinds of compounds may be obtained from the reaction of hydrogen with the metals (see Chapter 5). The term interstitial hydrides generally concerns non-stoichiometric phases with variable hydrogen content. During the absorption of hydrogen by a certain metal, a change in the properties of the metal itself occurs, which often may result in a phase change so Table 3.5. Radii of the cavities formed at the centres of some polyhedral metal arrangements where the metal atoms are hard spheres of radius 1.000 (the metal–metal bond lengths, that is the polyhedral edges, are 2.000). Tetrahedron Trigonal prism Square antiprism Cube Icosahedron Anticubooctahedron

0.225 0.528 0.645 0.732 0.902 1.000

Octahedron Capped octahedron Dodecahedron Tricapped trigonal prism Cuboctahedron

0.414 0.592 0.668 0.732 1.000

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Structural Characteristics of Intermetallic Phases

that the packing of the metal atoms in the final hydride may be different from that in the pure metal, generally being however still one of the packings characteristic for metal structures. Hydrogen compounds of the elements from the 3rd to 5th transition metal groups, including lanthanides and actinides, and of Cr, Ni, Pd and possibly Mg can be considered interstitial hydrides. The packing density of H atoms is generally very high in the hydrogen-rich metal hydrides. In some cases it is higher than in pure liquid hydrogen (for instance MgH2). A number of metals such as Mg (and alloys as LaNi5 and its ternary derivatives) easily take up and release hydrogen: so they can be used as reservoirs for hydrogen storage. The Pd–H system. Quoting from the detailed and comprehensive review by Manchester and Pitre (1994) it can be said that this system is the paradigm of metal hydrogen systems, the longest studied, the easiest to activate for hydrogen absorption and probably the richest in the number of physically interesting phenomena observed. A T/x projection from the P–T–x surface is shown in Fig. 3.37. The separation between the two phases (so-called α and α phases) and the twophase field may be noticed. The mutual saturation limits at room temperature are

Mass percent hydrogen 0.05

0.1

0.2

0.3

0.4

0.5

0.6 0.7

T = 293°C Critical point: X = 22.5 at.% H = 0.27 mass% H

350 300 Temperature (°C)

250 200

α

α′

150 100 50 0 −50 5

10

15 20 25 30 Atomic percent hydrogen

35

40

Figure 3.37. Pd–H phase diagram. T–X projection (onto a plane at constant pressure P 100 Pa) obtained from the experimental P–x isotherms. Because of hysteresis the data obtained in absorption or desorption experiments are slightly different.

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Intermetallic Chemistry

2 at.% H and 37.5 at.% H, respectively. There is no difference between the α and α phases above the critical temperature where we have a region of continuous solid solutions. Ordered phases stable at low temperature (200°C to 230°C) have been described also for this system. 3.8.4.2 Interstitial carbides and nitrides. Metals such as thorium, uranium, titanium, zirconium, hafnium, vanadium, niobium, tantalum, chromium, molybdenum, tungsten give carbides and nitrides, generally corresponding to solid solution phases around compositions such as Me2X and MeX, which are generally described as typical interstitial phases. Their similar packing geometry is characteristic. These carbides (and nitrides) frequently give together extended fields of solid solutions. Brewer type diagrams (see Chapter 4) for combinations of 4th and 5th column transition metals with 2nd period p-elements were presented by Engel (1969). For several monocarbides (MeC or, more generally, MeC1x) and mono-nitrides (MeN or MeN1x) a cF8-NaCl type crystal structure has been described corresponding to two sets of four sites (F F in the lattice-complex symbolism) occupied, respectively, by the Me atoms and, with a more or less large number of vacancies, by the C atoms. The atomic arrangement of one of these sets of positions is the same as that of the close-packed cF4-Cu type structure. The other set corresponds to the coordinates of the octahedral holes existing in the Cu-type structure. If the second elemental species (the non-metal) has sufficiently small atomic dimensions, an alternative description of the structure is therefore that of considering a certain number of atoms X inserted in a disordered or more or less ordered way in the interstices (holes) of a close-packed Me structure. The mentioned MeC1x(and MeN1x) compounds are characterized by very strong bonds; their hardness is very high (values close to that of diamond have been observed) and they have very high melting points (among the highest known) corresponding, for instance for the 1:1 compositions, to: TiC (3070°C), ZrC (3430°C), HfC (3950°C), VC (2660°C), TaC (3970°C), Ta2N (3000°C), ZrN (decomposes in liquidgas at 3410°C). A few more details about these systems are summarized in the following data as taken from the compilation by Okamoto (2000). Ti–C: In this system one intermediate phase is formed with a homogeneity range extending, depending on temperature, between 32 and 50 at.% C, in short named TiC (or, better, TiC1x) and having a NaCl-type structure. Zr–C: One intermediate phase ZrC (36–50 at.% C) NaCl type. Hf–C: One intermediate phase HfC (34–49.5 at.% C) NaCl type. V–C: Several intermediate phases: VC (37.4–48 at.% C), NaCl type, a few V2C phases (in the range 27–34 at.% C) and V4C3, V6C5, V8C7.

Structural Characteristics of Intermetallic Phases

165

Nb–C: Two intermediate phases NbC (37.7–49 at.% C), NaCl-type and Nb2C (29–33.5 at.% C), NiAs-type. Ta–C: Two intermediate phases TaC (38–49 at.% C), NaCl type and Ta2C (28–33 at.% C) hP3-Fe2N type. Ti–N: The system is complex with several intermediate phases; among them TiN (28 to 50 at.% N), NaCl-type. Zr–N: The system shows the ZrN phase, homogeneous in the 40–50 at.% N composition range with the NaCl-type structure. Solid solutions of N in αZr (up to 25 at.%) and in βZr (up to 5 at.%) have been described. Hf–N: The system is complex with several intermediate phases Hf3N2, Hf4N3, HfN (40–52.5 at.% N), NaCl-type. V–N: The system contains two intermediate phases: VN (that is VN1x, homogeneous between 38.4 and 50 at.% N), NaCl-type and the hexagonal hP9 V2N1y (28–34 at.% N). The VN1x phase, at high temperature (up to the melting point 2340°C), shows a large homogeneity field (33–50 at.% N). The composition changes result from variation in the number of vacancies on sites in the N sublattice, with x being the fraction of sites randomly vacant. At lower temperature, in the composition range 43–46 at.% N, an ordering of the N atoms has been observed, resulting in a tetragonal superstructure containing 32 V atoms and 26 N atoms in the unit cell. A number of metastable phases have been also described. Nb–N: The system contains the intermediate phases: NbN (TiAs-type), Nb2N (V2N-type) and the tetragonal Nb4N3. Ta–N: The system contains the so-called δ phase (high-temperature phase homogeneous between 40 and 50 at.% N, NaCl-type), Ta2N (21–35 at.% N, Fe2N-type) and TaN (CoSn-type). W–N: The so-called γ phase (29.5 to 41.5 at.% N) is stable between 283°C and 1875°C and has the NaCl-type structure. WN (50 at.% N) has the hP2-WC type structure. Several other phases, probably metastable, have been described. 3.8.4.3 Hägg rules. It was Hägg (1930, 1931) who remarked that a number of hydrides, borides, carbides, nitrides and oxides could be described in terms of metal atoms in sphere packing with the smaller B, C, N, O atoms in the octahedral interstices or the still smaller H atoms in the tetrahedral interstices (see § 3.8.1.1). He empirically found, on the basis of the atomic radius ratio, RX/RMe, between the non-metal and metal atoms, a number of regularities in the formation of several hydrides, borides, carbides and nitrides. The generally non-stoichiometric compounds are now called Hägg phases. Considering a large number of transition elements Me, he observed that: ‘Alle untersuchten Phasen, wo RX/RMe 0.59 ist, zeigen einfache Strukturen’ that is: All the phases studied for which RX/RMe 0.59 show ‘simple’ structures. A number of these ‘simple’ structures have been described

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Intermetallic Chemistry

6.00

Density (g/cm3)

5.60

5.20

4.80

0.2

0.6

Ti2O3

TiO

Ti2O

4.40

1.0 TiOx (x)

1.4

1.8

Figure 3.38. Experimental densities of titanium oxides (continuous lines). The upper dotted line gives the values computed for a 100% occupancy of the cation sites in the NaCl structure type (from Hyde and Andersson 1989).

in the previous paragraphs. The different behaviour generally noticed for the oxides was attributed to their different bonding (ionic) mechanism. In the Ti–O system, as an example, γTiO (high-temperature form, homogeneous in the composition range 35–55 at.% O) has the NaCl-type structure. Other forms of the monoxide βTiO, αTiO, βTi1xO, αTi1xO have ordered structures based on γTiO. In the structure there are atoms missing from some of the sites. According to what is summarized by Hyde and Andersson (1989), in TiO0.64 36% of the oxygens are missing, in TiO1.26, which can be represented also with the stoichiometry Ti0.79O, 20% of the Ti atoms are missing and in TiO both kinds of atoms are missing (15% of each) (see Fig. 3.38). As a final example, we may mention the NaCl-type phases formed in the V–O systems. The VO1 x phase is homogeneous in the composition range 42–57 at.% O. Lattice parameter determination in combination with density measurements evidenced that, in the structure, vacancies occur in both V and O sublattices through the entire range of composition. At the stoichiometric composition VO there are 15% of sites vacant in each sublattice. 3.8.4.4 Miscellaneous examples of interstitial superstructures. tP3-FeNiN, a 283.0, c 371.3 pm, c/a 1.312. Space group P4/mmm, N. 123. 1 Fe in (a) 0, 0, 0; 1 N in (c) 1⁄2, 1⁄2, 0 and 1 Ni in (d) 1⁄2, 1⁄2, 1⁄2.

Structural Characteristics of Intermetallic Phases

167

This structure can be considered a superstructure of the AuCu(I) type with 1 N atom inserted in an octahedral interstice. This structure, as the previously described cP5-Fe4N type, can be considered an interstitial ordered phase. oP5-Ta4O: a 719.4, b 326.6, c 320.4 pm. Space group Pmmm, N. 47. 1 Ta in (a): 0, 0, 0; 1 Ta in (b): 1⁄2, 0, 0; 1 O in (h): 1⁄2, 1⁄2, 1⁄2, 2 Ta in (l): x, 1⁄2, 1⁄2 and –x , 1⁄2, 1⁄2 (with x 0.225). The cell can be described as formed by two superimposed slightly distorted body-centred cubic subcells of the metal atoms. The O atom is surrounded by a slightly compressed Ta atom octahedron.

3.8.5 Remarks about a ‘second kind’ of superstructures In the preceding paragraphs examples of a number of so-called superstructures have been considered. Generally, it has been observed that a derivative structure has fewer symmetry operations than the reference structure: it has either a larger cell or a lower symmetry (or both) than the reference structure. Typically the passage from the reference structure to the derivative structure (superstructure) may be related to the fact that a set of equipoints of a certain structure (the reference one) has to be subdivided into two (or more) subsets in order to obtain the description of the other structure. The structure of the Cu type (cF4 type), for instance, corresponds to 4 Cu atoms in the unit cell, placed in 0, 0, 0; 1⁄2, 1⁄2, 0; 1⁄2, 0, 1 ⁄2; 0, 1⁄2, 1⁄2, whereas in the cP4-AuCu3 type structure the same atomic sites are subdivided, in another space group, into two sets with an ordered distribution of the two atomic species (1 Au atom in 0, 0, 0 and 3 Cu atoms in 1⁄2, 1⁄2, 0; 1⁄2, 0, 1⁄2; 0, 1⁄2, 1⁄2). Apart from this type of superstructure, which could then be described as superstructure of the first kind, another type of structure derivation can be considered: an example could be given by the relation between the CaCu5 and the CeCo3B2 structures. Both hP6-CaCu5 and hP6-CeCo3B2 structures are hexagonal, in the same space group (P6/mmm, N. 191), with the following occupation of the same sites: 1 Ca, or respectively, 1Ce 2 Cu, or respectively, 2 B 3 Cu, or respectively, 3 Co

in (a) 0, 0, 0; in (c) 1⁄3, 2⁄3, 0; 2⁄3, 1⁄3, 0; in (g) 1⁄2, 0, 1⁄2; 0, 1⁄2, 1⁄2; 1⁄2, 1⁄2; 1⁄2;

For the two compounds the lattice parameters are a 508.2 pm (CaCu5), a 505.7 pm (CeCo3B2), c 407.8 pm (CaCu5), c 303.6 pm (CeCo3B2), c/a 0.802 (CaCu5), c/a 0.600 (CaCo3B2)

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Intermetallic Chemistry

We notice that in the second structure we have the occupation of the same sites and a similar shape of the unit cell. The CeCo3B2-type structure can therefore be considered as a superstructure of the second kind of the CaCu5 type (Gladyshevskii and Bodak 1995). Other examples of pairs of structures having the same space group and the same assembly of Wyckoff sites orderly occupied but with a different atomic distribution (different stoichiometric ratio) are given by: cI58-α-Mn : cI58-Ti5Re24(χ phase); cI58-α-Mn : cI58-Mg17Al12; hP12MgZn2 : hP12-U2OsAl3. Notice that not in all the compilations and not by all the researchers are such structural variants considered as separate structure types. It seems however useful to speak of, say, the cI58-Ti5Re24 type structure when the elements are orderly distributed in selected sites of the Mn type, whereas it could really be more appropriate to speak of the cI58 α -Mn type even in the case of a binary combination (a solid solution) in which all the sites of this structure are occupied, at random in the same proportion, by the different components. 3.9. STRUCTURE FAMILIES: ‘RECOMBINATION STRUCTURES’, MODULAR ASPECTS OF CRYSTAL STRUCTURES

Tantum elementa queunt permutato ordine solo, T. Lucreti Cari Liber primus De Rerum Natura, 827 (So much may be obtained by changing only the component arrangement) (Titus Lucretius Caro ‘On the nature of Things’)

3.9.1 Modular aspects of crystal structures A very general, mainly geometric, approach to the description and classification of the different inorganic structures can be based on a systematic construction of complex structural types by means of a few operations applied to some building units. As suggested by Andersson and Hyde (1982), Hyde and Andersson (1989) a formal description and classification of the various crystal structures could be obtained in terms of a classification of the building units and of the construction mechanism. Building units correspond to packets of points (atoms) (blocks, clusters, bounded in three dimensions) or to groups of lines (rods, columns bounded in two dimensions, infinite in the third) or to groups of planes (slabs, sheets, layers, lamellae bounded in only one dimension, infinite in the other two). Structures may then be constructed from such portions by discontinuous symmetry operations (translation, reflection or their combinations) repeated in a parallel way or by similar symmetry operations repeated in a cyclic way, involving rotation (see, for instance, Figs. 3.39(a)–(d)).

Structural Characteristics of Intermetallic Phases

169

Figure 3.39. AlB2-type derivative structures generated by cyclic repetition of blocks of AlB2-type columns. The projections of the unit cells (all having nearly the same c parameter) on the x, y plane are presented. (a) hP22-Ce6Ni2Si3 (a 1211.2 pm, c 432.3 pm); (b) The arrangement of the building blocks of the hP22-Ce6Ni2Si3 structure around the z axis (63 symmetry axis). (c) hP40Ce5Ni2Si3 (a 1612.0 pm, c 430.9 pm); (d) hP64-Pr15Ni7Si10 (a 1988.1 pm, c 425.5 pm); rare earth atoms (Ce, Pr): white circles; Si (and Si Ni): black circles; small circles: atoms at level z 1⁄4, large circles at level z 3⁄4. Ni atoms at level 0 and level 1⁄2: double circles; Ni atoms at level 1 ⁄4, 3⁄4: grey circles.

Emphasis to a similar approach has been given by Zvyagin (1993). He pointed out that many crystal structures can be represented as a composite of certain standard ‘construction modules’ and various combinations, distributions and arrangements of these. The simplest example of a modular structure is the densest packing

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Intermetallic Chemistry

of identical atoms; the atomic planes represent the construction modules forming various structures owing to a variation of the two possible placements of the successive plane relative to the preceding one. A classification of the different structures can be based on: ● ● ● ● ●

module types (sheets, rods, blocks); dimension of the modules; variety of module type (single or mixed-module structures); relative number of module types; arrangement of adjacent modules (variations in these arrangements, periodicity/ aperiodicity of successive variations, etc.).

Principles and types of modular series have been summarized in a book by Ferraris et al. (2004). A hierarchical classification of structure has been introduced as well as the application of modularity to structure description and modelling. The order/disorder theory has been presented as fundamental to developing a systematic theory of polytypism, dealing with structures based on both ordered and disordered stacking of one or more layers. The structures of a great number of compounds (minerals, complex oxides, salts, etc.) have been described and discussed. Strictly related to this kind of description are the concepts of Recombination Structures and of Intergrowth Structure Series, to be discussed in the following see § 3.9.4. 3.9.2 Homeotect structure types, polytypic structures According to Parthé (1964), two different structure types of the same formula XmYn are called homeotect structure types if every X atom has the same number of nearest X neighbours and the same number of nearest Y neighbours, and, conversely, if every Y atom has the same number of nearest X and Y neighbour atoms. It is possible for several structure types to have this feature. All the different structure types of equal composition, which have (for corresponding atoms) the same kind of surroundings, form a set of homeotect structure types. The term polytypic structure is also used to denote the relationships observed with homeotect structures. According to Parthé (1964) all structure types which belong to a homeotect set can be described as different stacking variants of identical structural unit slabs (minimal sandwiches). All structure types of a set are constructed by stacking identical unit slabs one on top of another. The various types differ only in the relative horizontal displacement of these units. The vertical unit cell edges of the different types are integer multiples of a common unit which is the height of the unit slab characteristic for the homeotect structure type set. All structure types which belong to a homeotect set have the same space-filling curve (see § 4.3.2.5).

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A few important examples of groups of homeotect structure types will be described in the following sections. A short list follows, in which the Jagodzinski–Wyckoff notation of the stacking pattern has been inserted according to the previously given indications. 3.9.2.1 Close-packed element structure types. The structures of the close-packed metals are a simple well-known example of homeotect structure types. We have seen that the following metals can be considered as reference types. Mg type (h), Cu type (c), La type (hc), Sm type (hhc). (See § 3.7.6 and Figs 3.20, and 3.21). Their polytypic nature may be represented by a series of close-packed stacking variants of similar triangular atomic nets (A, B, C nets) corresponding to the following symbols: hP2-Mg type: MgB0.25MgC0.75. That is BCBCBC..... or CACACA in short: (BC) cF4-Cu type: Cu0ACuB0.33CuC0,67 (ABC) B A C hP4-La type.: LaA (ABAC) 0 La 0.25La 0.5La 0.75. A C A hR9-Sm type: Sm0 Sm 0.11Sm 0.22SmC0.33SmB0.45SmC0.55SmB0.67 (ACACBCBAB) SmA0.78SmB0.89 Details about these structure types and lists of metals belonging to them are presented in § 7.3.2.1. 3.9.2.2 Equiatomic tetrahedral structure types. (Carborundum structure types). To this group pertain the diamond-type structure, the wurtzite (h) and the sphalerite (c) types, and the large family of SiC polytypes (such as hc, hcc, hccc, hcchc, … (hcc)5(hccc)(hcc)5hc … (hchcc)17(hcc)2, … (hcc)43hc…). These are all examples of a family of ‘tetrahedral’ structures which have been described by Parthé and will be briefly presented in Chapters 4 and 7. The cF8-C (diamond) structure type, and the cF8-ZnS (sphalerite), hP4-ZnO (ZnS wurtzite) are described in §7.3.3.2 and 7.4.2.3, respectively. 3.9.2.3 Laves phases. hP12 MgZn2 type (h), cF24 Cu2Mg type (c), hP24 Ni2Mg type (hc), Laves polytypes (hhc, hhccc, etc.). The Laves phases form a homeotect structure type set (a family of polytypic structures). In all of them, described in terms of a hexagonal cell, three closely spaced 36 nets of atoms are followed (in the z direction of the same cell) by a 3636 net. The 36 nets are stacked on the same site as the kagomé 3636 nets which they surround. For instance: β-BAC-γ-CAB in the ‘two slabs’ MgZn2-type (h) structure, β-BAC-γ-CBA-α-ACB in the ‘three slabs’ MgCu2-type (c) structure,

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α-ABC-γ-CBA-α-ACB-β-BCA in the ‘four slabs (hc)’ Ni2Mg-type structure, etc. However, the Laves phases, like Frank–Kasper structures (see Table 3.6), can also be described by alternative stacking of pentagon-triangle main layers of atoms and secondary triangular layers, parallel to (110) planes of the hexagonal cell. Layer stacking symbols (K 3T slabs formed by kagomé and triangular nets) of the main types of Laves phases: hP12-MgZn2 (two slabs type structure (h) β-BAC-γ-CAB) γ B β B A C C ZnA 0 Mg 0.06Zn 0.25Mg 0.44Zn 0.50Mg 0.56Zn 0.75Mg 0.94 cF24-Cu2Mg (three slabs type structure (c) β-BAC-γ-CBA-α-ACB) MgA0Cuα0.13MgA0.25CuC0.29MgB0.33Cuβ0.46MgB0.58CuA0.63MgC0.67Cuγ0.79MgC0.92CuB0.96 hP24-Ni2Mg (four slabs type structure (hc) α-ABC-γ-CBA-α-ACB-β-BCA) Niα0MgA0.09NiB0.13MgC0.16Niγ0.25MgC0.34NiB0.37MgA0.41Niα0.50MgA0.59NiC0.63MgB0.66 β Ni0.75 MgB0.84NiC0.87MgA0.91 Details about general crystallography of the Laves phases and alternative descriptions and their polytypes and variants are given in § 7.4.3.3 whereas some information about their occurrence and thermodynamics is reported in § 3.9.3.1.3. 3.9.2.4 A few general remarks about homeotect structures. Other important sets of homeotect structure types are those related to disilicide structure types (MoSi2, CrSi2, etc.), cadmium halide structure types, etc. (See Parthé 1964, Hyde and Anderson 1989), or presented by certain groups of compounds such as rare earth trialuminides (Van Vucht and Buschow 1965). From a general point of view, polytypism may be considered a special case of polymorphism: the 2D translations within the layers are essentially preserved whereas the lattice spacings normal to the layers vary between polytypes and are indicative of the stacking period (Guinier et al. 1984). As evidenced by Zvyagin (1987), various forms of polytypic structures may be distinguished, including, besides close-packing of like and unlike atoms, polytypes of tetrahedral, octahedral and prismatic layers packed according to the laws of closest packings. Complex silicate structures, for instance, may be considered, which are characterized by a great variety in the orientation and displacements of the layers and also structures in which 2D layers are conjoined with 1D bands and island groups. The aforementioned papers (Guinier et al. 1984, Zvyagin 1987) also contain suggestions and recommendations on the nomenclature and symbolism for use in the general case of either simple or complex polytypic structures. Another method for describing polytypic structures has been suggested by Bokii and Laptev (1994). The polytypic structures, described by means of special unit

Structural Characteristics of Intermetallic Phases

173

cell diagrams and crystal–chemical formulae, are distinguished by the number and type of Wyckoff positions. 3.9.3 Assembly of polyhedra Several intermetallic phase structures can be described in terms of an assembly of building blocks consisting of a collection of coordination polyhedra. A classification of types of intermetallic structures based on the coordination number, configurations of coordination polyhedra and their method of combination has been given by Kripyakevich (1963). According to Kripyakevich, a coordination polyhedron of an atom is the polyhedron, the vertices of which are defined by the atoms surrounding this atom: a coordination polyhedron should have a form as close as possible to a sphere, that is, it should be convex everywhere and have the maximum number of triangular faces. At the vertices of a coordination polyhedron of a given atom (in addition to atoms of different elements) there can also be atoms of the same kind. A considerable variety of coordination polyhedra exists. In some cases, plane coordination polygons have to be considered. The number of vertices may vary from 3 to 24. Generally, the structure consists of atoms with different coordination numbers; according to Kripyakevich, structures are most conveniently classified according to the type of coordination polyhedron of the atoms with the lowest coordination number. An important contribution to the structure analysis of intermetallic phases in terms of the coordination polyhedra has been carried out by Frank and Kasper (1958). They described several structure types (Frank–Kasper structures) as the result of the interpenetration of a group of polyhedra, which give rise to a distorted tetrahedral close-packing of the atoms. Samson (1967, 1969) developed the analysis of the structural principles of intermetallic phases having giant unit cells (Samson phases). These structures have been described as arrangements of fused polyhedra rather than the full interpenetrating polyhedra. The principle of describing structures in terms of polyhedron packing has been considered by Girgis and Villars (1985). To this end they consider, in a given structure, the coordination polyhedra of all the atomic positions; structures are then described by packing the least number of polyhedra types. All the atoms in the unit cell are included in the structure-building polyhedra. The polyhedra considered should not penetrate each other. According to Girgis and Villars (1985) structures are then classified mainly on the basis of the following criteria: ● ● ●

Number of polyhedra types employed in the description of the structure. Characteristics of the polyhedra (number of vertices, symmetry). Types of polyhedra packing (either 3D distribution of discrete polyhedra sharing corners, edges or faces, or layer-like distribution of polyhedra).

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Examples of structures described by packing of one polyhedron type are: cP4-AuCu3 type, 3D arrangement of cubooctahedra (coordination number, CN, 12) and tP30-σ(Cr,Fe) type, layer-like arrangement of icosahedra (CN 12). For a general approach to the problem of structure descriptions in terms of polyhedron packing, a paper by Hawthorne (1983) should also be consulted. The following hypothesis is proposed: crystal structures may be ordered or classified according to the polymerization of those coordination polyhedra (not necessarily of the same type) with the higher bond valences. The linkage of polyhedra to form ‘clusters’ is then considered from a graph-theoretical point of view. Different kinds of isomers are described and their enumeration considered. According to Hawthorne, moreover, it has to be pointed out that many classifications of complex structures recognize families of structures based on different arrangements of a fundamental building block or module (see § 3.9.4). If this building module is a tightly bound unit within the structure it could be considered, for instance, as the analogue of a molecule in an organic structure. Such modules can be considered the basis of structural hierarchies that include, for instance, simple and complex oxides and complex alloy structures. These modules can be considered as formed by polymerization of those coordination polyhedra that are most strongly bonded and may be useful for a classification and systematic description of crystal structures. As a conclusion to this section it is worth mentioning the ‘atomic environments’, defined and coded by Daams et al. (1992). A short description of this topic has been given in § 3.7.5 together with some remarks about the classification of AET and their description and coding in terms of coordination polyhedra. 3.9.3.1 Tetrahedrally close-packed structures. Frank–Kasper structures. A number of structures of several important intermetallic phases can be classified as tetrahedrally close-packed structures. According to Shoemaker and Shoemaker (1969), in packing spheres of equal size the best space filling is obtained in the cubic or hexagonal close-packed structures, or in their variants. In those arrangements there are tetrahedral and octahedral holes (see the comments on this point reported in the description of the cF4-Cu-type structure in § 3.8.1.1). The local mean atomic density (the average space filling) is somewhat higher at the tetrahedral holes than in the larger octahedral ones. A more compact arrangement might, therefore, be obtained if it were possible to have only tetrahedral interstices. It is, however, impossible to fill space with regular tetrahedra throughout. By introducing some variability in the sphere dimensions it is possible to obtain packing containing only tetrahedral holes. The tetrahedra are now no longer regular: the ratio of the longest tetrahedron edge to the shortest, however, need not exceed about 4/3 in a given structure. The corresponding crystal structure can be considered to be obtained from the space filling

Structural Characteristics of Intermetallic Phases

175

of these tetrahedra which share faces, edges and vertices. In structures containing atoms of approximately the same size and within the aforementioned limits of edge-length ratio, the sharing of a given tetrahedron edge (that is, an interatomic link ligand) either among 5 or 6 tetrahedra has to be considered the most favoured situation, according to the systematic analysis of these structures carried out by Frank and Kasper (1958, 1959). On the assumption that only 5 o 6 tetrahedra may share a given edge, the number of tetrahedra that share a given vertex is limited to the values 12, 14, 15 and 16. The 12 (or 14, 15, 16) tetrahedra that are assembled around a point share this point as a common vertex, and form, around this point, a coordination polyhedron with triangular faces. The radii of this polyhedron are the edges shared among 5 or 6 component tetrahedra and connect the central atom with the polyhedron vertices, five-fold or six-fold vertices, that is vertices in which 5 or 6 faces meet. The four possible Frank–Kasper coordination polyhedra are included in Fig. 3.18 (and coded 12a, 14a, 15a, 16a) and correspond to the following properties: Coordination 12 (regular, or approximately regular, icosahedron): 12 vertices (12 five-fold vertices) and 20 faces. Coordination 14: 14 vertices (12 five-fold and 2 six-fold) and 24 faces. Coordination 15: 15 vertices (12 five-fold and 3 six-fold) and 26 faces. Coordination 16: 16 vertices (12 five-fold and 4 six-fold) and 28 faces. For symbols used in the coding of the vertex characteristics see § 3.7.5. Several structures (Frank–Kasper structures) can be considered in which all atoms have either 12 (icosahedral), 14, 15 or 16 coordinations. These can be described as resulting from the polyhedra included in Fig. 3.18. These polyhedra interpenetrate each other so that every vertex atom is again the centre of another polyhedron. All structures in this family contain icosahedra and at least one other coordination type. Frank and Kasper demonstrated that structures formed by the interpenetration of the four polyhedra contain planar or approximately planar layers of atoms: primary layers made by tessellation of triangles with hexagons and/or pentagons, and intervening secondary layers of triangles and/or squares. For a classification and coding of the nets and of their stacking, see Pearson (1972) and also Shoemaker and Shoemaker (1969) or Frank and Kasper (1958, 1959). A short summary of structural types pertaining to this family is reported in Table 3.6; for a few of them some details or comments are reported in the following § 7.5.3. 3.9.3.1.1 cP8-Cr3Si type structure. This structure is also called W3O or β-W type (it was previously believed to be a W modification instead of an oxide) or A15 type.

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Table 3.6. Examples of tetrahedral close-packed structures. Structural type

Unit cell dimensions (rounded values) for the reported prototype (pm)

Percentage of atoms in the centre of a polyhedron with CN 12

14

15

16

cP8-Cr3Si (also called β-W (W3O) type or A15 type phase)

a 456

25

75

tP30-σCr46Fe54* σ phases

a 880 c 456

33

53

13

hR39-W6Fe7 μ phases

a 476 c 2562

55

15

15

hP7-Zr4Al3

a 543 c 539

43

28

28

oP52Nb48Ni39Al13* M phases

a 930 b 493 c 1627

55

15

15

15

oP56Mo21Cr9Ni20* P phases

a 1698 b 475 c 907

43

36

14

7

hR159Mo31Cr18Co51* R phases

a 1090 c 1934

51

23

11

15

cI162-Mg11Zn11Al6* Bergman phases

a 1416

61

7

7

25

a 704 a 522 c 856

67 67

a 482 c 1583

67

Laves Phases: cF24-Cu2Mg hP12-MgZn2 hP24-Ni2Mg

15

33 33 33

* For these phases the reported formulae generally correspond to an average composition within a solid solution field. This also in relation to a (partially) disordered occupation of the different sites.

– Cubic, space group Pm3n, N. 223. Atomic positions: 2 Si in (a) 0, 0, 0; 1⁄2, 1⁄2, 1⁄2 6 Cr in (c) 1⁄4, 0, 1⁄2; 3⁄4, 0, 1⁄2; 1⁄2, 1⁄4, 0; 1⁄2, 3⁄4, 0; 0, 1⁄2, 1⁄4; 0, 1⁄2, 3⁄4. This structure type is observed for many phases formed in the composition ratio 3:1 by several transition metals with elements from the III, IV, V main group (or with Pt metals or Au). Phases having this structural type are, for instance, Mo3Al,

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177

Nb3Al, V3Al, Ta3Au, Ti3Au, Cr3Pt, Cr3Os, Cr6AlSi, V6AlSn, Nb6GaGe, etc. A number of compounds with this structure have been found to have significantly high superconducting transition temperature, Tc (among the highest known, before the discovery of the families of superconducting complex oxides, such as Ba2YCu3O7x or Bi2(Ca,Sr)3Cu2O9x,etc.). Examples of superconducting, Cr3Si type, phases are: Nb3Ge (Tc 23.2 K, sputtered films), Nb3Ga (Tc 20.7 K, bulk), Nb3Sn (Tc 18.1 K), V3Si (Tc 16.8 K), V3Ga (Tc 14.1 K), Nb3Au (Tc 11.5 K), Nb3Pt (Tc 9.2 K), Mo3Ir (Tc 8.8 K), etc. The Cr3Si-type structure does not always remain stable in these materials down to 0 K, yet the change in crystal structure, when it occurs (for instance, with a tetragonal structure formed at low temperature as a result of a martensitic transformation) does not seem to be correlated with Tc. Solid solutions in general have lower Tc values than the stoichiometric compounds. Other superconducting intermetallic phases belonging to different structural types are, for instance, LuRh4B4 (Tc 11.7 K, YPd5B3Cx (Tc 23 K), quaternary lanthanum nickel boro nitrides, etc. See Cava et al. (1994a, b). Another recently discovered (Nagamatsu et al. 2001) superconductor (with a remarkably high transition temperature, Tc 39 K) is MgB2 (AlB2 type, a 308.5 pm, c 352.3 pm, c/a 1.142). 3.9.3.1.2 σ-phase type structure (tP30-σ Cr–Fe type). In the space group P42/mnm, N. 136, the two atomic species, Cr and Fe, are distributed in several sites with a nearly random occupation. Also owing to different preparation methods and heat treatments, different atom distributions have been proposed in the literature. The following distribution is one of those reported in Daams et al. (1991): two atoms in sites (a) (with a 12% probability for Cr and 88% for Fe), 4 atoms (75% Cr, 25% Fe) in sites ( f ), 8 atoms (62% Cr, 38% Fe) in a set (i), 8 atoms (16% Cr, 84% Fe) in another set (i) and 8 atoms (66% Cr, 34% Fe) in ( j). The structure can be considered as made up of primary hexagon-triangle layers containing 3636 3262 and 63 nodes (in a 3:2:1 ratio) at height 0 and 1/2 separated (at height 1/4 and 3/4) by secondary 32434 layers (that is layers, in which every node is surrounded, in order, by: 2 triangles, 1 square, 1 triangle and 1 square). As pointed out by Pearson, by studying the near-neighbours diagrams (see § 4.3.2.5), the σ phase structure is a good example of a structure which is controlled by the coordination factor: all the known phases are closely grouped around the intersection of lines corresponding to high coordination numbers. The most favourable radius ratio for the component atoms is included between 1.0 and 1.1. It is also possible that the electron concentration plays some role in controlling the phase stability. The different phases are grouped in the range 6.2–7.5 electrons (s, p and d) per atom.

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3.9.3.1.3 Laves phases and derivative structures: cF24-Cu2Mg (and cF24Cu4MgSn and cF24-AuBe5), hP12-MgZn2 (and hP12-U2OsAl3) and hP24Ni2Mg types. Many binary and complex solid solutions Laves phases are known. They form one of the largest groups of intermetallic compounds. Their fundamental and applicative properties have been object of extensive researches: some space will therefore be dedicated to this group of compounds. A crystal–chemical description of the main Laves structure types and of some of their derivatives is included in Chapter 7 and summarized in Table 3.7. A few data on their occurrence, stability, etc. are discussed in this paragraph. General remarks. In a description of the principal Laves types, a few more remarks can be made concerning higher-order Laves polytypes. An interesting example is given by the Li–Mg–Zn alloys (Melnik and Kripyakevich 1974, Mallik 1987). This system is one of the richest in Laves phases among the known ternary systems. It contains, besides MgZn2, eight ternary compounds Ln (the index n denotes the number of slabs) in the following sequence: L2: MgZn2 L8: Mg(Li0.07Zn1.93) L14: Mg(Li0.11Zn1.89) L9: Mg(Li0.20Zn1.80) L10: Mg(Li0.23Zn1.77) L4: Mg(Li0.25Zn1.75) L 4: Mg(Li0.50Zn1.50) L 3: Mg(Li0.56Zn1.44) L3: Mg(Li0.77Zn1.23)

(hP), (hP), (hP), (hR), (hP), (hP), (hP), (hR), (cF),

a 521.4 pm; a 521.3 pm; a 521.5 pm; a 522 pm; a 522.3 pm; a 522.7 pm; a 1046 pm; a 1051 pm; a 522.6 pm;

c 856.3 pm (2 428.1) c 3422 pm (8 427.8) c 5989 pm (14 427.8) c 3841 pm (9 426.8) c 4278 pm (10 427.8) c 1709 pm (4 427.3) c 1705 pm (4 426.3) c 1285 pm (3 428.3) c 1290 pm (3 430)

Notice that the structures with n 3 and 4 exist not only in an ordinary form L4, Ni2Mg, and L3, Cu2Mg-type cubic (a 744.8 pm, here described in terms of an equivalent set of hexagonal axes), but also with doubled unit cell edge a (Ni2Mg type and Cu2Mg type superstructures L 4 and L 3). It may be useful to mention that depending for instance on the temperature, different Laves-type structures can be observed in the same chemical system. An example is the Ti–Cr system for which three different structures have been described: αTiCr2 (MgCu2 type, homogeneous in the composition range 63–65 at.% Cr), stable from room temperature up to 1220°C; βTiCr2 (MgZn2 type, homogeneous from 64 to 66 at.% Cr), high-temperature phase stable from 800°C up to 1270°C. Notice that the α and β forms, which can coexist in the temperature range from 800°C up to 1220°C have slightly different compositions and are stable with an excess of Ti atoms.

Table 3.7. Summary of the crystal structure data of the three most important Laves phases (see § 7.4.3.3). Pearson symbol and prototype

Space group symbol and number

Lattice parameters (pm)

Wyckoff positions (WP)

Representative coordinates x, y, z of the 1st WP

Occupancy

Coordination polyhedron code

Average polyhedron radius (pm)

AET

cF24 Cu2Mg

Fd-3 m 227

a 699.0

8a 16d

0, 0, 0 5/8, 5/8, 5/8

Mg Cu

125.0, 46.0 125.0

293.0 268.5

16-a 12-a

hP12 MgZn2

P63/mmc 194

a 517.0 c 850.0

2a 4f 6h

0, 0, 0 1/3, 2/3, .063 0.830, 0.660, 1/4

Zn Mg Zn

125.0 125.0, 46.0 125.0

282.4 306.9 281.5

12-a 16-a 12-a

hP24 Ni2Mg

P63/mmc 194

a 480.5 c 1577.0

4e 4f(1) 4f(2) 6g 6h

0, 0, 0.094 1/3, 2/3, 0.844 1/3, 2/3, 0.125 1/2, 0, 0 0.167, 0.334, 1/4

Mg Mg Ni Ni Ni

125.0, 46.0 125.0, 46.0 125.0 125.0 125.0

285.3 285.3 261.3 261.4 261.4

16-a 16-a 12-a 12-a 12-a

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A γTiCr2 (Ni2Mg type, 65–66 at.% Cr) form has also been described either as a high temperature phase (stable from 1270°C up to the melting point, 1370°C) or, probably, as a metastable phase occurring only in quenched samples. Typically, binary Laves compounds AM2 are formed in several systems of A metals such as alkaline earths, rare earths, actinides, Ti, Zr, Hf, etc., with M Al, Mg, VIII group metals, etc. Laves phases are formed also in several ternary systems either as solid solution fields extending from one binary phase (or possibly connecting the binary phases of two boundary systems) or as ‘true ternary’ phases, that is forming homogeneity fields not connected with the boundary systems. Examples of true ternary phases may be observed in systems such as Nb–Ni–Al, Ta–Ni–Al, where no Laves phases exist in any of the boundary binary systems and a MgZn2-type phase Ta(Ni,Al)2 (or Nb(Ni,Al)2) is formed within the composition range Ta(Ni1xAlx)2 (with 0.15 x 0.75). Laves phases: stability, occurrence. The importance of the geometrical factor in determining the stability of these phases has been pointed out (Pearson 1972). In a simplified description, Laves phases AM2 of the MgCu2 type may be presented as cubic face-centred packing of large spheres A which form tetrahedral holes that are occupied by tetrahedra of smaller spheres M. The ideal value of the radius ratio rA/rM is 1.225. The values experimentally observed for the various Laves types range from 1.05 to 1.7. The role of the electron concentration in controlling the differential stability of the different Laves phase types has also been suggested. By studying, for instance, solid solutions of Cu2Mg and MgZn2 with Ag, Al, Si (Laves and Witte 1936, Klee and Witte 1954), it was observed that for an average VEC (valence electron concentration) between 1.3 and 1.8 e/a (s, p, electrons per atom) the Cu2Mg structure is generally formed, and for VEC values in the range from 1.8 to 2.2 e/a, generally the MgZn2-type structure is obtained. The Ni2Mg type can be observed for intermediate values of VEC between 1.8 and 2.0. Notice, however, that such a simple correlation (or similar ones for transition metal Laves phases) is only valid for a restricted number of alloy systems. A systematic analysis of structure and stability of binary and ternary Laves phases, or Friauf–Laves phases, has been performed by Stein et al. (2004, 2005). By reviewing a large number of experimentally determined phase diagrams with Laves phases, a number of general conclusions have been obtained. These may be summarized in the following points: ●

If in a binary system, at a specific composition, both a cubic and a hexagonal Laves phase are formed, and then generally it is the Cu2Mg type which is stable at low temperature and the MgZn2 (or Ni2Mg) type at higher temperature.

Structural Characteristics of Intermetallic Phases ●

●

●

181

If in a binary system, at a given temperature but different compositions, both a cubic and a hexagonal Laves phase are formed, then generally the Cu2Mg- type occurs around the stoichiometric composition and the other polytypes at offstoichiometric compositions. The hexagonal Ni2Mg-type phase generally occurs in a binary or ternary system as an additional phase together with a Cu2Mg and/or a MgZn2-type phase. Laves phases occurring in ternary systems, the binary subsystems of which contain no Laves phases, generally pertain to the hexagonal MgZn2-type structure.

Stein et al. (2005) observed also that, in binary and ternary systems, the homogeneity regions of different Laves phases are generally separated by two-phase fields which are very narrow and of difficult determination. Laves phases, stability, thermodynamics, thermodynamic modelling. A review of the data concerning the enthalpies of formation of binary Laves phases has been reported by Zhu et al. (2002) and subsequently commented by Chen et al. (2004). For the different main types of binary Laves phases, Zhu et al. (2002) reported the radius ratio of the involved metals, the axial ratio c/a of the hexagonal phases and the experimental data available (ΔH and ΔS of formation). According to their analysis, the examination of the experimental data indicate that both geometric and electronic factors are important in stabilizing Laves phases and that in these phases there are metallic, covalent and ionic bonds or a mixed metallic–covalent–ionic bond. They claimed, moreover, that the enthalpies of formation for binary transition metal lanthanide Laves phases as calculated by the semi-empirical Miedema model (see § 2.2.1.3) are found to be in good agreement with the available experimental data. In the paper however by Chen et al. (2004), objections were raised especially to the suggestion that the Miedema model is suitable for a quantitative prediction of the formation enthalpies of the Laves phases. It was observed that discrepancies in the order of 20–80 kJ/mole are common. As an alternative route, ab initio calculations based on density functional theory were suggested to provide accurate enthalpies of formation for Laves phases. As for the thermodynamic modelling of Laves phases, this has been successfully performed for several alloy systems. Especially using the sublattice model (see § 2.4.2.2) a number of phase diagrams containing Laves phases have been calculated taking into account homogeneity ranges and polytypism. A few details will be reported here giving special attention to the Cu2Mg type. According to an analysis performed by Ferro and Cacciamani (2002), the preferential site occupancies observed in MgCu2-type phases are summarized in Table 3.8. The atoms preferentially present in each site type are indicated.

Table 3.8. cF24-MgCu2 type Laves phases. (preferential site occupancies). Reference element

Atoms in the Wyckoff position 8a

Atoms in the Wyckoff position 16d

Cs,Rb,K Na Li Ba Sr Ca Yb Eu Sc Y Ln(III) An Zr Hf Ti Ta Nb

Cs,Rb,K Na Li Ba Sr Ca Yb Eu Sc Y Ln(III) An Zr Hf Ti Ta Nb

Bi Ag,Au,Pt Pt Al,Pd,Pt Al,Ir,Pd,Pt,Rh Al,Ni,Pd,Pt,Rh Al,Co,Fe,Ir,Ni,Pt,Rh Al,Ir,Ni,Pd,Pt,Rh Al,Co,Fe,Ir,Ni Al,Co,Fe,Ir,Mn,Pt,Rh Al,Co,Fe,Ir,Mg,Mn,Ni,Os,Pt,Rh,Ru Al,Co,Fe,Ir,Mn,Ni,Os,Pt,Rh,Ru,Zn Co,Cr,Fe,Ir,Mo,Ni,V,W,Zn Co,Cr,Fe,Mo,Ni,V,W,Zn Be,Co,Cr Be,Co,Cr,V Be,Co,Cr

V W Mo Cr Mn Fe Ru Os Co Rh Ir Ni Pt Pd Au Ag Cu Mg

Hf,Ta,Zr Hf,Zr Hf,Zr Hf, Nb,Ta,Ti,Zr An, Ln(III),Y An,Hf,Sc,Ln(III),Y,Yb,Zr An,Ln(III) An,Ln(III) An,Hf,Nb,Sc,Ta,Ti,Ln(III),Y,Yb,Zr An,Ca,Eu,Sr,Ln(III),Y,Yb An,Eu,Sc,Sr,Ln(III),Y,Yb,Zr An,Ca,Eu,Hf,Sc,Ln(III),Yb,Zr An,Ba,Ca,Eu,Li,Na,Sr,Ln(III),Y,Yb Ba,Ca,Eu,Sr Bi,Na,Pb Na Mg Ln(III)

V W Mo Cr Mn Fe Ru Os Co Rh Ir Ni Pt Pd Au Ag Cu Mg

Ag Cu Mg

Ag Cu Mg

Be Be Cu

Zn Be Al

An,Hf,Zr Ag,Cu,Nb,Ta,Ti An,Ba,Ca,Eu,Sc,Sr,Ln(III),Y

Zn Be Al

Pb Bi

Pb Bi

Au Au

Bi

Cs,K,Rb

Bi

Structural Characteristics of Intermetallic Phases

183

For a number of elements, listed in the first column according to their chemical order, their MgCu2-type compounds are reported. (Ln(III) and An mean trivalent lanthanides and actinides, respectively). For all the compounds an indication is given of the preferential occupancy of the different Wyckoff Position (WP) by the metals involved. (for example Na preferentially occupies the Wyckoff Position 8a when combined with Ag, Au or Pt, that is in NaAg2, NaAu2 and NaPt2). It results that atoms belonging to the earlier groups of the Periodic Table and, more precisely from group 1 to the Nb group (including lanthanides, actinides and Pb), generally occupy the positions with higher coordination (that is, in MgCu2, the Wyckoff Position 8a with an environment coordination CNE 16). On the other hand, elements from V to Au and Zn, Be and Al prefer to occupy the lower coordination sites. A few atoms (Ag, Cu, Mg and Bi) are found to occupy either positions with CNE 12 or 16, depending on the partner element. In multi-component systems, elements preferentially occupying the same site are generally allowed to substitute each other forming more or less extended substitutional solid solutions. Similar considerations have been found to be valid for the hP12-MgZn2 and hP24-Ni2Mg structures. Only two different AET (see § 3.7.5) and, correspondingly, two different coordination polyhedra are present in each structure. Moreover, in the three structures the same 1:2 ratio is found between sites with coordination 16 and 12 and, finally, polyhedra with the same AET and the same average radius are preferentially occupied by the same element. A sublattice model suggested by this structure analysis is reported in Table 3.9 where sublattices are denoted by the symbols identifying the characteristic AET (16-a and 12-a in this case) and sorted according to the decreasing coordination. Sublattice ratios are determined by the ratio between the total multiplicities of the WPs included in each sublattice. This model can be considered as a crystallographic justification of the long time adopted model simply based on stoichiometric considerations. It is also in agreement with the analysis carried out by Ansara et al. (1997) who examined the same problem by a similar, although less general, approach. Stein et al. (2005) observed on the basis of their systematic analysis that the site occupancies in ternary Laves phases cannot be predicted simply from the atomic Table 3.9. A sublattice model suggested for the main Laves phase types. Sublattice model MgCu2 WPs included: MgZn2 WPs included: MgNi2 WPs included: WP means Wyckoff Position.

(16-a)1

(12-a)2

8a 4f 4e 4f(1)

16d 2a 6 h 4f(2) 6g 6h

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dimensions; a comparison of the shape of the phase fields of several ternary Laves phases evidenced the role played by electronic factors. In conclusion to this paragraph we quote a paper by Yan et al. (2006), in which, by means of several experimental and theoretical techniques, a thorough study was performed on a ternary Laves phase alloy system and which is also a good example of the contemporary and complementary use of various investigation methods. The Ti(Fe1xAlx)2 Laves phase with the hP12-MgZn2 type structure was studied. X-ray and neutron diffraction were employed in order to establish the atom site distribution. The Rietveld refinement of the diffraction data revealed that Ti atoms occupy the 4f sites whilst Fe and Al atoms randomly share the 2a and 6 h sites. Ab-initio calculations for various compositions agree well with the experimentally defined site preferences and lattice parameters. Enthalpies of formation were obtained by a comparison of the heat effect obtained in an isoperibolic calorimeter by dropping samples of Al and of the alloys in a liquid bath of initially pure Al. The calculated enthalpy of formation and the magnetic phase diagram were in good agreement with experimental data. 3.9.3.2 Structures based on frameworks of fused polyhedra: Samson phases. In addition to the Frank–Kasper phases, other structures may be considered in which the same four types of coordination polyhedra prevail, although some regularity is lost. Many of these structures, and in particular the giant cell structures studied by Samson (1969) can be described as based on frameworks of fused polyhedra rather than on the fully interpenetrating polyhedra. Among the most important polyhedra, the truncated tetrahedron can be related to the CN 16 polyhedron (Friauf polyhedron). The two polyhedra can be transformed into each other by removing (adding) the 4 six-fold vertices of the CN 16 polyhedron, corresponding to positions out from the centre of each of the four hexagons of the truncated tetrahedron. Several other coordination polyhedra occur in giant cell structures in addition to the Frank–Kasper polyhedra and to the truncated tetrahedron. The most important are polyhedra corresponding to CN between 11 and 16. The following phases represent a few examples of structures to which the aforementioned considerations especially apply. cI58-α-Mn (a 891.4 pm) type structure (and its binary variants, cI58-Ti5Re24 or χ phase and cI58-γ-Mg17Al12), cF1124-Cu4Cd3 type (a 2587.1 pm); cF1192NaCd2 type (a 3056 pm); cF1832-Mg2Al3 (a 2823.9 pm), etc. In the giant cell structures partial disorder and/or partial occupancy in some atomic positions have generally been reported; for cF1124-Cu4Cd3, for instance, the structure was described as corresponding to the occupation, in several Wyckoff positions, of 388 atomic sites by Cd atoms, 528 by Cu atoms and of 208 by Cu and Cd atoms in substitutional disorder. For complex intermetallic structures and their description, see also the paragraphs (in Chapter 4) dedicated to clusters and cluster compounds.

Structural Characteristics of Intermetallic Phases

185

3.9.4 Recombination structures, intergrowth structure series Some of the previously reported relationships between structures may be included in the general term ‘recombination’ structures. Such a term (see Lima de Faria et al. 1990) can be considered when topologically simple parent structures are periodically divided into blocks, rods or slabs. It means that structure portions, which are finite or infinite in one or two dimensions, are recombined into derivative structures through one or more structure building operations. The most important operations are: unit cell twinning, intergrowth of blocks, rods or slabs of different structural types (for instance, intergrowth of cF24-MgCu2 type and hP6-CaCu5 type slabs to obtain the hP36-Ce2Ni7 type structure), periodic out of plane, anti-phase boundaries (AuCu(II), as an example), rotation of rods or blocks and crystallographic shear planes. For a definition and examples of crystallographic shear planes see § 7.6.4 and Fig. 7.54 where a number of TiO2 derivative structures are especially described. The frequency of structure building operators and, therefore, the size of undisturbed structure portions, can vary by well defined increments, so that many phases may occur as members of homologous series. A few considerations about possible schemes of relationships between inorganic crystal structures based on a systematic ‘construction’ of complex structural types by means of a few operations (symmetry operations, topological transformations) applied to some building units (point systems, clusters, rods, sheets), have been previously reported in § 3.9.1, following criteria suggested, for instance, by Hyde and Andersson (1989) and by Zvyagin (1993). Within the ‘recombination’ scheme, a very interesting method of describing, interpreting and interrelating complex structures is that based on the aforementioned ‘intergrowth’ concept (Kripyakevich et al. 1972, 1976, 1979, Grin’ et al. 1982, 1990, Parthé et al. 1985, Lima de Faria 1990, Pani and Fornasini 1990, Daams 1995). According to this concept, selected structure types can be considered as belonging to certain intergrowth structure series. The different structure types of an intergrowth series are described as being constructed from structure segments of more simple structures (the so-called parent structures). Said in another way, according to this approach the construction modules, instead of being defined on a mere geometrical basis, are selected with reference to specific crystallochemical criteria. To this end, groups (series) of similar complex structures are analysed in order to recognize ‘fragments’ which could be identified as structure segments of more simple structural types. The structure series are then classified according to the kind of fragments and the method of construction. On the basis of the kind of fragments the structure series is described as homogeneous or inhomogeneous: the homogeneous intergrowth structures consist of identical fragments; the inhomogeneous intergrowth structures consist of segments, differing in composition and/or coordination, belonging to

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different parent structures. According to the method of construction, the intergrowth structure series can be classified into 1D (linear), and 2D or 3D series. In a linear series we have 1D stacking (along one direction) of 2D, infinite segments (slabs) of the parent structures. The different structures of a 2D intergrowth series, on the other hand, are built up by aggregations of several 1D fragments (infinite rods, columns). Finally, the structures of a 3D intergrowth series are constructed from (zero-dimensional, finite) parent structure blocks stacked in three dimensions. It has been pointed out (Grin’ 1992) that slicing the parent structure into segments can be done in different ways. When predicting the composition and symmetry for the members of a particular structure series, the segment to be used in that series should fulfil a number of requirements. The segments should contain certain symmetry elements (in a linear series, for instance, all the segments used for the description usually contain some symmetry elements, mostly parallel to the stacking direction, which are retained in any stacking sequence, and represent the ‘minimal symmetry’ of the series). The segment interfaces necessarily pass through atom centres. The composition of the segment is proportional to the stoichiometry of the parent structure: by addition it is possible to obtain the compositions of all possible structures of the series. The segments, moreover, selected from different parent structures, must have, at least, one topologically equal interface in order to make the intergrowth possible. Additional requirements are necessary when the atomic arrangement on the interface permits more than one possibility of intergrowing and when more complex (2D, 3D) series are studied. Considering, for instance, the particular case of the ‘linear intergrowth structure series’, many binary and ternary intermetallic phases can be considered members of those series, both homogeneous and inhomogeneous. A representative of a structure belonging to a linear inhomogeneous series is shown in Fig. 3.40. In this case, the parent structures are the oS8-CrB and oS12UPt2 types. The intergrowth structure presented is the oS28-W3CoB3 (or Y3Co3Ga) type. Its unit cell contains a segment arrangement corresponding to two repetitions of a sequence containing a UPt2 fragment followed by two CrB-type fragments. A simple code of this structure may be (2CrB1UPt2)2. Other members of the series have been described; for instance: 1CrB1UPt2 (corresponding to the oI10-W2CoB2 type); 3CrB1UPt2 (corresponding to the mS18-Y4Co4Ga type); (4CrB1UPt2)2 (corresponding to the oS44-Y5Co5Ga type). It is interesting to observe that many real representatives of this series may be found in the Y–Co–Ga system. This is considered an example of the fact that, often, several members of a certain intergrowth series have representatives in the

Structural Characteristics of Intermetallic Phases

b

187

b a

c x=0

x=0 Cr x = 0.5

x = 0.5

z=0

z=0 Pt

B

U z = 0.5

z = 0.5

c b

x=0 W x = 0.5 x=0 Co x = 0.5 x=0 B x = 0.5

Figure 3.40. The oS28-W3CoB3 type structure as resulting from the intergrowth of the oS8-CrB and oS12-UPt2 types. Projections of two cells of each structure are shown: the values of the third coordinate (along the direction perpendicular to the drawing plane) are indicated. Typical blocks of the parent structures are marked in the resulting structure. The unit cell of this one contains twice a sequence formed by an UPt2 fragment together with two CrB-type fragments (2CrB1UPt2)2.

same binary and ternary alloy system. In the same system, or in chemically analogous systems, representatives of the parent structures may also be found. In the example reported, for instance, YCo has the CrB-type structure. The interest of a crystallochemical description based on the intergrowth concept is thus evident.

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As a further simple example, we may mention the structure of the oS16NdNiGa2 type belonging to the series BaAl4-AlB2. Its unit cell contains indeed two BaAl4-type segments and two AlB2-type segments. The previously considered simple code will be (1BaAl4 1AlB2)2. Notice, however, that in a more complex and detailed notation, superscripted indexes may be added to the formulae of the segments in order to specify, for instance, their symmetry (Grin’ et al. 1982, Parthé et al. 1985). General compositional formulae are often used for representing a series (Grin’ 1992). MemnX5m3nY2n, for instance, may be the overall formula of a series consisting of intergrown CaCu5- and CeCo3B2-type slabs. (For the hP6-CaCu5 type and its ordered variant hP6-CeCo3B2 type structures, see § 3.8.5.) Members of this series are the following structure types: hP12-CeCo4B (corresponding, in the aforementioned formula, to m 1, n 1), hP18-Ce3Co11B4 (m 1, n 2), hP24Ce2Co7B3 (m 1, n 3), hP18-Nd3Ni13B2 (m 2, n 1) and hP30-Lu5Ni19B6 (m 2, n 3). We may notice, in this case too, the close chemical analogy among the alloy systems (rare earth, nickel or cobalt, borides) forming structures corresponding to the different members of a given series. Within the intergrowth concept several ternary compounds can be considered as the result of a chemical or structural ‘interaction’ between the binary compounds. This could be reflected also in some regularity in the characteristics of the equilibria and phase diagrams (trends of the tie-lines, for instance). An analysis of some formal aspects of the isothermal sections of several R–T–X systems (R rare earth metal, T transition metal, X Si,Ge) has been carried out by Morozkin and Seropegin (1996). A number of stoichiometries have been evidenced (such as RT2X2, RTX3, RTX2, RTX, R2TX3) frequently found in those systems. These compounds define the ‘main’ equilibria line on which they lay and which generally connect two binary compounds or one binary compound with the third component. In many cases this seems to be in agreement with the types of ‘interactions’ (recombination of structure fragments) deduced by crystallographic analyses and comparisons. More comments and examples on these points are reported in Chapter 7. Relevant comments on the concept of intergrowth and the underlying principles have been presented by Nesper (1991) in a review about bonding patterns in intermetallic compounds. It has been observed that this type of structure formation can be considered as an extension to one or two dimensions of structures with isolated clusters. Notice that this author, following the analysis and the treatment performed by Andersson (1983), names these arrangements ‘chemical twinning’. As a consequence, it is suggested that the building of complex structures could be described theoretically with two approximations. One of these must define the chemical bonding in the interior of the partial structure, while the other should consider the chemical bonding at the surfaces. An improvement of these concepts could be the

Structural Characteristics of Intermetallic Phases

189

use of the ‘Atomic environments’ (see § 3.7.5) in the descriptions of the slabs because it would show more directly the relations between the combining slabs and the structures in the series (Daams 1995). 3.10. GROUP–SUBGROUP RELATIONS BETWEEN SPACE GROUPS FOR THE REPRESENTATION OF CRYSTAL–CHEMICAL RELATIONSHIPS

According to the presentation given by Bärnighausen (1980), if two structures are topologically equivalent, their interrelation can be conveniently expressed by group–subgroup relations between their space groups. Graphic representation of these relations leads to hierarchic ordering resembling a family tree. At the top of the tree there is the so-called aristotype (a highly symmetrical structure). From the aristotype the other structures of the tree may be derived along specific routes of symmetry reduction. In order to obtain a well-defined description, the symmetry reduction is presented in terms of minimal steps, that is, a given structure is followed by another whose space group is a so-called maximal subgroup (M) of the space group (G) of the former structure (see Hahn 2002). The minimal steps of symmetry reduction can be classified according to the following terms: Lattice equivalent (‘translationengleich’, abbreviation: t). M contains all the translations of G, the crystal class of M is of lower symmetry than that of G. Class equivalent (‘klassengleich’, abbreviation: k). M and G have the same crystal class but belong to different space-group types: M has lost translational symmetry, that is, the primitive cell corresponding to M is larger than that of G. Crystallographically equivalent (abbreviation: e). G and M belong to the same space group type, that is, as in the previous case, M has lost translational symmetry. The abbreviations t, k, e are generally accompanied by a number related to the symmetry reduction in the transformation. The structural relationship between diamond and sphalerite types (see § 7.4.2.3), for instance, may be described as– lattice equivalent, t, in the form: Diamond type (space group Fd3m, N. 227) : t2 : sphalerite type (space group – F4 3m, N. 216). Several examples concerning the inorganic crystallochemistry have been described by Bärnighausen (1980); among intermetallic phases, the structural relationship between NiAs and MnP types, between Rh5Ge3 and Ca5Sb3 and the order–disorder transition of MoNi4 are highlighted. As a further example of application of the Bärnighausen formalism, a number of ternary fluorite related phases in the systems Li–Pt–Sn (and Li–Pd–Sn) have been analysed and discussed by Hoffmann et al. (2003) on the basis of a group–subgroup

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scheme. The cF16-Li2PtSn compound may be related to the binary BiF3 type (a filled CaF2 type), where Bi forms an face-centred cubic arrangement, and the two different fluorine sites occupy the tetrahedral and octahedral voids on 4b and 8c in – the space group Fm3m, respectively. In comparison with CaF2, the two Li atoms replace 4/8 of the fluorine positions in an ordered manner, with a consequent symmetry reduction. The structure becomes non-centro-symmetric in the space group – – F4 3m, a translationengleich subgroup of index 2 of the group Fm3m. A number of other ternary Li–Pt–Sn compounds adopt superstructures of the CaF2 type with the doubling of the three axes of the subcell. In the chemically similar system Li–Pd–In, the compound LiPdIn2 has a structure which is a ternary ordered variant of the BiF3 type.

3.11. QUASI-PERIODIC CRYSTALS

According to Yamamoto (1996) quasi-periodic structures belong to the following structure kinds: ●

●

●

Modulated structures, corresponding to substances in which there is an average structure with a three-dimensional periodicity showing modulated perturbations. Composite crystals, in which the structure can be described as resulting from two or more substructures (related to two or more sets of three dimensional lattices) having different periodicity along at least one direction (chimney-ladder structures, vernier structures, misfit-layer structures, etc.). See the scheme presented in Fig. 3.42. Quasicrystals, the diffraction patterns of which show non-crystallographic symmetry.

3.11.1 Modulated structures These structures are represented by substances in which some atomic parameter and/or the partial occupancy of some sites of the average structure vary periodically through the structure. The periodicity may or may not be commensurate with the unit cell of the basic structure; that is, the ratio between the repetition length of this parameter and the lattice constant may or may not correspond to the ratio between two integer numbers (commensurate and incommensurate modulated structures). Generally, the diffraction patterns of such substances present a group of prominent, strong reflections (main reflections), related to the 3D basic structure, accompanied by weak satellite reflections related to the weak perturbation from the average structure.

191

Structural Characteristics of Intermetallic Phases

Different kinds of modulations can be considered: the displacive modulation is related to the shift of the atom position from the average structure; the occupational (or substitutional) modulation is related to the changes of the atomic occupation probability depending on the position. Generally, in alloys, displacive modulation is small but not negligible (Yamamoto 1996) whereas substitutional modulation often occurs. Several non-stoichiometric compounds present such modulations among which various binary and complex sulphides and tellurides, FeSx, Yb3–xS4, etc. Various modulated structures have also been considered, for instance, for the NiAs-type structure (see Chapter 7). An interesting case of magnetic modulated structure is that reported for EuCo2P2 (Reehuis et al. 1992). The positional structure of the atoms (of the atomic nuclei, nuclear structure) corresponds to the tI10-ThCr2Si2 type. A magnetic structure has also been determined, which is related to the ordering of the magnetic moments of the Eu atoms. These moments are oriented perpendicular to the c-axis and form an incommensurate spiral with the turning axis parallel to the c-axis. The magnetic moments lie in the basal planes and they order parallel within these planes. Along the c-axis, from one basal plane to the next one, there is a periodic rotation of the moments. The ratio, along the c-axis, of the characteristic lengths of the magnetic and nuclear structures is slightly dependent on temperature. At 64 K it is close to 5/6 (that is: there are 5 translation lengths of the magnetic cell for 6 translation lengths of the nuclear structures). At 15 K the ratio was found to be close to 6/7. If this magnetic structure is maintained at still lower temperatures, it may correspond to the exact 6/7 value. The ground state may then be called a commensurate structure with this ratio. A special case of long-period structure to be considered is the oI40-AuCu(II) type structure which has 1D substitutional and displacive modulations (Fig. 3.41). We must first mention that ordering of the Au–Cu face-centred cubic (cF4-Cu type) solid solution, having a 50–50 atomic composition, re-distributes Cu and Au atoms

c at b

Figure 3.41. The oI40-AuCu(II) structure. This superstructure contains 10, slightly distorted, tP4-AuCu( I) pseudo-cells. The long-period ordering corresponds to a periodic shift of the structure (every five cells along the orthorhombic b-axis) by 1⁄2 (at c) in the at, c plane. The anti-phase domain contains 5 AuCu(I) pseudo-cells.

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alternatively on two layers, resulting in a tetragonal structure, tP2-AuCu(I) with the c-axis perpendicular to the layers (see Chapter 7). The more complex structure, oP40-AuCu(II) type, is obtained by a long-period ordering which results in an orthorhombic cell containing 10 slightly distorted AuCu(I) pseudo-cells. This ordering corresponds to a periodic shift (every five cells along the orthorhombic baxis) of the structure by: 1⁄2(at c) in the at, c plane. That is, by shifting a group of five cells along the direction of the diagonal, by a half diagonal step. This out-of-step shift corresponds to a so-called anti-phase boundary. An anti-phase domain may correspondingly be defined; in this case it contains five AuCu(I) type pseudo-cells. This structure, therefore, is an example of a commensurate modulated structure with a 1D modulation. Several examples of 1D long-period structures found in 1:1 and 1:3 alloys and of 2D long-period structures (characterized by two different domain periods and two-step shifts) found in 1:3 alloys have been presented by Pearson (1972); the role of the valence electron concentration in defining the superstructure period has also been discussed. A general presentation of several antiphase boundaries, not only planar, but also cylindrical, and related structure groups may be found in the book by Hyde and Andersson (1989). Long-period structures in A3B alloys (like TiAl3, Ag3Mg, PdCu3) have been studied by Selke (1989) and compared with the Axial Next Nearest Neighbour Ising (ANNNI) model. Anti-phase domain boundaries play an important role in phase changes and microstructural stability of ordered alloys and intermetallics also affecting mechanical behaviour. The origin of anti-phase domain boundaries has been examined and discussed by Morris (1992). Emphasis has been given to the differences between a sharp boundary, as produced by crystal shear, and a relaxed fault structure. The kinetics of relaxation of a shear produced fault have been examined and it was shown by Morris (1992) that fast relaxation may affect the movement of dislocations by creating locking stresses as well as affecting cross slip behaviour which in turn has a significant effect on mechanical properties. An important point in this study, as far as the origin of the anti-phase domain boundaries are concerned, is the principle that a disordered crystal exists initially, which subsequently becomes ordered. According to Cahn (1987), the observation of grown-in domain network is proof that the material existed, even if momentarily, in a disordered crystalline state before becoming ordered. In agreement with this, domain networks are commonly observed in weakly ordered alloys, for example AuCu3, FeNi3 and sometimes FeAl, but not in strongly ordered intermetallics such as Ni3Al and TiAl. A review on the interactions of ordering and recrystallization has been published by Cahn (1990), and a more specific study on the morphology of the anti-phase domains during recrystallization of heavily rolled AuCu3 by Yang et al. (1996). Aspects of recovery and recrystallization in the L12 (Co0.78V0.22)3V ordered alloy have been reported by Gialanella and Cahn (1993).

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Structural Characteristics of Intermetallic Phases 1

1+2

2

Figure 3.42. Schematic representation of a double layer composite structure. Two substructures (1 and 2) are sketched. The composite structure (1 2) resulting from the mutual intermingling of the two substructures has a period corresponding to six subcells 1 commensurate to seven subcells 2.

3.11.2 Composite crystals A group of crystals show diffraction patterns in which two or more 3D lattices having periods commensurate or incommensurate to each other may be recognized. In other words, the crystal consists of two or more interpenetrating substructures (two or more different atom sets) with different periods at least along one direction (see Fig. 3.42). Names such as composite crystals, vernier structures, misfit-layer structures, and chimney-ladder structures have been used for this group of structures. 3.11.2.1 Nowotny phases, chimney-ladder structures. The Nowotny chimneyladder phases are an example in alloy field chemistry of composite structures. They are a series of intermetallic TnXm compounds formed by transition metals T from the 4th to 9th groups with p-block elements X from the 13th to the 15th groups. In these phases, the unit cell (superstructure cell, super-cell) contains along the c-axis n pseudo-cells of T atoms and m interpenetrating pseudo-cells of X atoms. These phases (Nowotny phases) have been called chimney-ladder phases because they contain rows of atoms X (the ‘ladder’), with variable interatomic spacing from one compound to another, which are inserted into channels (‘chimneys’) in the T array. The T metals in all of the superstructures form a β-Sn-like array (see Chapter 7) with the number of T metal atoms in the formula of the compound corresponding to the number of β-Sn-like pseudo-cells stacked in the c direction of the super-cell. The arrangement of the atoms in these phases can be compared to that found in the structure of TiSi2. The following is a list of some chimney-ladder phases (more complex phases containing as many as 600 atoms in the unit cell have been described). – tP20 Ru2Sn3 (space group P4 c2, a 617.2 pm, c 991.5 pm, c/(2a2) 0.568). The Ru atoms form a β-Sn-like array with two pseudo-cells along the c direction of the super-cell.

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– tP32-Ir3Ga5 (space group P4 n2, a 582.3 pm, c 1420 pm, c/(3a2) 0.575) – tP36-Ir4Ge5 (space group P4 c2, a 561.5 pm, c 1831 pm, c/(4a2) 0.576) – tP120-Mn11Si19 (space group P4n2, a 552.0 pm, c 4820 pm, c/(11a2) 0.561 – tI156-Rh17Ge22 (space group I4 2d, a 560.4 pm, c 7845 pm , c/(17a2) 0.587 – tP192-V17Ge31 (space group, P4n2, a 591 pm, c 8365 pm, c/(17a2) 0.589). In V17Ge31, for instance, there are 17 β -Sn like pseudo-cells of V atoms and 31 Ge pseudo-cells stacked along the c-axis. Examples of the atomic arrangements in a few chimney-ladder phases are shown in Fig. 3.43 and compared with that found in TiSi2. This compound has an orthorhombic cell oF24-TiSi2 type with a0 826.7 pm, b0 480.0 pm, c0 855.1 pm. It can, however, be approximately described in terms of a smaller bodycentred tetragonal pseudo-cell, shown in Fig. 3.43 (a) having: a⬘ a0/2 c0/2; c⬘ b0 and c /a0 0.58, close to the ‘ideal’ value 1/3 0.577… More recently the structural characteristics of this family of compounds have been thoroughly analysed and discussed by Hoffmann and co-workers (Fredrickson et al. 2004a, b). In a number of papers a brilliant presentation of the Nowotny structures is given beginning with figures such as that shown in Fig. 3.44 which is also used to underline ‘the intriguing and beautiful structural features of these phases’ characterized by ‘a helix within a helix’. It may indeed be noticed that the transition metals form four-fold helices (in the shape of chimneys), inside of which the X metals form separate helices: see the three-fold helix of the X atoms in the Ru2Sn3-type structure, as an example. Two empirical rules, moreover, have been enunciated. The first rule concerns the number of valence electrons: for the Nowotny, TnXm, phases formed by the late transition metals, it is that the total number of valence electrons per T atom is 14. With reference to previously cited phases we have, for instance: Valence electron number per T atom (2 8 3 4)/2 14 Ru2Sn3 (4 9 5 4)/4 14 Ir4Ge5 (10 9 17 3)/10 14.1 Rh10Ga17 (11 7 19 4)/11 13.9 Mn11Si19 (17 9 22 4)/17 14.2 Rh17Ge22 (1 8 2 3)/1 14 OsGa2 The fact that the electron concentration appears to play some role in the control of this family of structures was noted by Nowotny (Schwomma et al. 1964a, b, Jeitschko and Parthé 1967, Flieher et al. 1968a, b, Parthé 1969) and reported by Pearson (1972). The second rule, discernible in the electron diffraction of the TnXm Nowotny chimney-ladder phases, is the appearance, along the c-axis of a

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Structural Characteristics of Intermetallic Phases

(a) TiSi2

(b) Ru2Sn3

(c) Mn11Si19

(d) Rh17Ge22

Figure 3.43. Examples of chimney-ladder structures (b)–(d) and the reference oF24-TiSi2 type structure (a) presented in terms of a tetragonal pseudo-cell (12 atoms in the pseudo-cell). Notice that the metal atoms (black circles) form sequences of βSn like cells.

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c cn

cm

Figure 3.44. Views, according to Fredrickson et al. (2004a, b), of the Ru2Sn3 structure type, an example of the chimney-ladder Nowotny phases. On the left, a lateral view of the Ru helix (black balls) and of the Sn helix (white balls). The periods of the two helices (cn and cm) are given together with the lattice parameter c.

pseudo-periodicity with a spacing cps which is directly related to the stoichiometry and to the lattice parameter c by the relation: c (2n m)cps In short the TnXm Nowotny chimney-ladder phases are viewed as twinned structures consisting of building blocks of the ‘RuGa2’ type of thickness cps/2 with the successive layers rotated relative to each other by 90°. To complete this description, at the interfaces between layers the deletion of sterically encumbered X atoms was considered. The creation of more interfaces reduces therefore the ratio of the X to T atoms in the different Nowotny phases. According to Fredrickson et al. (2004a, b) this is controlled by the 14 electron rule. A theoretical explanation for these rules was also given in the mentioned papers and the connection discussed with electron number rules of organo-metallic complexes. A description of the Nowotny chimney-ladder phases in terms of slab stacking had been proposed by different authors. Grin (1986) showed that structures and space group symmetries of the phases of this family may be accounted for, considering, along c, linear combinations of T2X2, T2X4 and T3X4 layers.

Structural Characteristics of Intermetallic Phases

197

In the book by Hyde and Andersson (1989), the Nowotny phases are presented as a special case of a group of ‘1D, columnar misfit structures’ which also include compounds such as Bam(Fe2S4)n and other complex sulphides. Layer misfit structures, such as those of some oxide-fluorides, arseno-sulphides, etc., are also presented and classified with reference to a concept of structure commensurability based on the recognition that (along one or more axes) the ratios between the different repeat units of various interpenetrating substructures can (or cannot) be represented as ratios between integer numbers. 3.11.2.2 Combination of commensurate and incommensurate periodic ‘substructures’. An example of non-periodic sequence is obtained by superimposing two periodic 1D sequences having incommensurate periods; for instance, following Giacovazzo et al. (1992), a sequence A, having period a, and the sequence T, having period aτ/2, where τ is defined as τ (1 5)/2 1.6180339… (τ, an irrational number, is the solution of the equation τ 1 1/τ; τ 1 is the ‘golden’ section of the unit. The number τ is also associated with the geometries of pentagon and icosahedron: It is: τ 2 cos(π/5)). The resulting (A T) sequence is perfectly ordered (its diffraction pattern would be built by ‘peaks’) but it is not periodic (the two periods a and aτ/2 are incommensurate) (See Fig. 3.45). Approximations to this composite structure may be built considering the representation of τ through a continuous infinite fraction: τ = 1+

1 1+

1 1+

1 1+

1 1+ ----------

According to this formula, successive approximations of τ are: τ0 1, τ1 2, τ2 3/2, τ3 5/3, τ4 8/5, etc. (In these different fractions, in the numerator and in the denominator, we have the subsequent ‘Fibonacci numbers F’ defined as 1, 1, 2, 3, 5, 8, 13, 21, … Fn Fn1 Fn2. We have: Lim (n : ) Fn/Fn1 τ.) By substituting in the sequence T (having period aτ/2) the values: τ0, τ1, τ2, etc., we obtain the periodic structures T0 (period a/2), T1 (period a), T2(period a3/4), T3 (period a5/6), T4 (period a8/10), etc. These structures superimposed to (combined with) structure A give rise to a series of (periodic, commensurate) approximants of

198

Intermetallic Chemistry A + T0 A + T1 A + T2 A + T3

A + T∞

A

T

Figure 3.45. A Ti composite structures. The period of A is ‘a’ and that of Ti is ‘t’. The t/a is approximated by 1⁄2 for A T0, 1 for A T1, 3⁄4 for A T2, 5⁄6 for A T3 and is τ/2 (0.809017.....) for A T. The ‘structures’ A T0, A T1, A T2, … etc., are approximants of the quasiperiodic structure A T.

the non-periodic incommensurate A T structure (see Fig. 3.45); notice that better periodic approximations of a periodic structure may be obtained by higherorder approximants. By using slightly different words, approximants are translationally normal crystal compounds generally with large unit cells that contain condensed, highly symmetric building blocks such as dodecahedra and icosahedra and have compositions close to those of related quasicrystals. 3.11.3 Quasicrystals In a famous paper by Shechtman et al. (1984) electron diffraction patterns were shown of rapidly quenched and solidified aluminium-manganese alloys. Sharp diffraction peaks, suggesting long-range translational order, were observed with the presence however of five-fold symmetry (that is of a non-crystallographic symmetry see § 3.6.1.1). By different orientation of the specimen five-fold axes (in 6 directions), three-fold axes (in 10 directions) and two-fold axes (in 15 directions) were identified; with the subsequent observation of the existence also of an—inversion centre the assignment of this phase to the icosahedral point group, m35, was defined.

Structural Characteristics of Intermetallic Phases

199

Figure 3.46. A non-crystallographic sphere packing with five-fold symmetry.

Later, in several alloy systems, a large number of phases showing noncrystallographic symmetries were discovered. Besides the icosahedral ones, phases have been observed with diffraction symmetries 8/mmm (octagonal phases), 10/mmm (decagonal phases) and 12/mmm (dodecagonal phases). Compare with the definitions given in § 3.6.1.1 and notice that the same criteria are used to build these symmetry symbols. As for a general classification of all crystalline and noncrystalline 2D and 3D point groups see Hahn (2002). According to some comments included in a systematic structural description by Wells (1970) (one of the forerunners), an interesting example of a sphere packing with five-fold symmetry is shown in Fig. 3.46. This may be the model of a 3D packing possessing a unique five-fold axis. This can be described as obtained by the superimposition (with their five-fold axes coincident) of layers, of an indefinite bi-dimensional extension, formed by concentric pentagons alternatively having even or odd numbers of spheres along their sides. This packing is periodic only in one dimension, in the direction coincident with the five-fold axis. Its density is only slightly lower than that of the closest packing: the space-filling parameter is 0.7236 in comparison with the value 0.7405 of the close-packed structure (see § 4.3.2.5). 2D examples of quasi-periodic structures are shown in Figs 3.47 and 3.48. They are based on two kinds of rhombi with equal sides which have to be fitted together according to a ‘matching rule’. The first is a representation of a ‘Penrose tiling’ built up by rhombi having angles of 72° (360°/5) and 108°, and respectively of

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Figure 3.47. Example of Penrose tiling. A few years before the discovery of quasicrystals the mathematician R. Penrose showed that if two shapes of tiles are allowed, tiling can be made which is nearly periodic and shows almost five-fold symmetry. This example is based on two kinds of rhombi with equal sides (with angles of 72° and 108° and respectively 36° and 144°) which have to be fitted together according to a ‘matching rule’: the arrows indicated on the edges of the single rhomb when fitting the rhombi together must be of the same kind (single or double) and in the same direction.

36° and 144°. The second figure is a tiling model of an octagonal phase. It is constructed by rhombi having angles of 45° (360°/8) and 135° and squares. In concluding this section in which some properties of modulated structures and of quasicrystals have been considered, we underline that the characteristics of these two types of structures do not coincide. Incommensurately modulated structures show main and satellite diffractions, an ‘average structure’ and crystallographic point symmetry. The quasicrystals have no average structure, non-crystallographic point symmetry, and give one kind of diffraction only. 3.11.3.1 Notes on the crystallography of quasi-periodic structures. A general way to face the problems related to the interpretation of quasi-periodic structures (modulated structures, quasicrystals) is based on the introduction and application of higher-dimensional crystallography (de Wolff 1974, 1977, Janner and Janssen 1980, Yamamoto 1982, 1996, Steurer 1995).

Structural Characteristics of Intermetallic Phases

201

Figure 3.48. Example of a bi-dimensional quasicrystal lattice obtained from squares and rhombi (with angles of 45° and 135°).

A modulated crystal does not have a 3D lattice periodicity: its Euclidean symmetry is not represented by a 3D space group. It is possible, however, to obtain a space-group symmetry by building a periodic structure in a higher-dimensional space, (3 d)D, such that a 3D section of it may correspond to the crystal under consideration (Janner and Janssen 1980). The higher-dimensional space is the superspace and its periodic structure is the supercrystal. The additional d dimensions define the so-called internal space (generally indeed they correspond to internal degrees of freedom as the phase of the modulation). The 3D subspace is called position space or external space (the positions in the modulated crystal are defined in this space). The (3 d)D space groups coherent with the role of the position space (admitted groups) are called the superspace groups. The relation between a higher-dimensional periodic structure and a lower-dimensional non-periodic structure can be illustrated by an example of projection from a higher-dimensional space. Fig. 3.49 shows the projection from a 2D square lattice to obtain a 1D nonperiodic structure. A number of commensurate and incommensurate modulated structures have been analysed in terms of 4D crystallography, starting with Van Aalst et al. (1976). The structures of the commensurate composite crystals BaxFe2S4 (x 10/9 and 9/8) have also been refined by using a 4D formalism (Onoda and Kato 1991) by using single-crystal diffraction data. Similarly the anti-phase domain structure of AuCu II (previously described, see § 3.11.1 and Fig. 3.41) has been analysed (Yamamoto 1982) on the basis of a 4D space group, regarding the structure as having a 1D (density and displacive) modulation. The same approach was followed in

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Intermetallic Chemistry W

XII

X⊥

Figure 3.49. Projection from a 2D periodic square lattice to obtain (on XII) a 1D non-periodic crystal. The projection space XII is inclined with an irrational slope (1/τ) to the square lattice axes. The window W (the strip) parallel to XII is chosen so that a structure with a physically reasonable density is obtained (Kelton 1995). The points contained in the ‘window’ are projected.

the analysis of polytypes of SiC and ZnS, regarded as modulated structures, the symmetry of which was described by a space group in 4D space (a 4D space group was considered including, as a subgroup, the 3D space group of the polytype under consideration). A more complex example may be represented by TaSe2: its modification called 2H-TaSe2 is hexagonal (space group P63/mmc, with two formula units in the unit cell). This layered compound shows a displacive 2D modulation (defined by two vectors); its symmetry may be therefore described in terms of a supergroup in a 5D superspace (Janner and Janssen 1980). A general point is therefore denoted by the 5 parameters x, y, z, t, u, and a position vector by the five components xa yb zc td ue of the superspace, with a, b, c basis in the ‘position space’ and d and e in the ‘internal subspace’. As far as quasicrystals are concerned, an important and numerous group of these substances is represented by those quasi-periodically ordered in two dimensions forming layers periodically stacked in the 3rd direction. According to their diffraction symmetries, octagonal, decagonal and dodecagonal quasicrystals have been described. In these cases too, the embedding of their structures in higher-dimensional space resulted in a more compact and ‘economical’ description. The structure solution in 5D space (3 2 order parameters) of the decagonal Co6.7Ni22.7 Al70.6 has been reported by Cervellino and Steurer (2002). It has been found that the atoms fill the space forming recurrent structure motifs, the spatial arrangement of

Structural Characteristics of Intermetallic Phases

203

which is perfectly quasi-periodic. A summary has also been given of the different Al-rich Co–Ni–Al phases and a comparative analysis of the different structural models proposed for the decagonal phase by different authors. Several icosahedral quasicrystals have been described: the indexing of their diffraction patterns is conveniently done, in a 6D representation, in terms of six unit vectors, which can be defined in terms of the three unit vectors of the external space, and three of the internal space. A list of relevant space super groups with highest symmetries has been reported by Yamamoto (1996) for 5D and 6D spaces. For the 5D space, the octagonal (primitive, P, and body centred, I), the decagonal (only primitive lattice exists) and the dodecagonal (only primitive) space groups are shown (examples are P8/mmm, I8/mmm, P10/mmm, P12/mmm). For the 6D space, the icosahedral space groups are reported which are subdivided among three lattice types (primitive, P, body centred, I, and face centred, F): typical examples may be P235, I235, F235. In the same paper (Yamamoto 1996) an authoritative description is given of several interrelated topics such as: super-space group determination, structure determination, indexing of diffraction patterns of quasicrystals, polygonal tiling, icosahedral tiling, structure factor calculation, description of quasicrystal structures, cluster models of quasicrystals. 3.11.3.2 Types of quasicrystals and examples of alloy systems showing their formation. A short description of the main types of quasicrystals and of their occurrence is given here below (Kelton 1995, Steurer 1996). Decagonal quasicrystals. Their structures can generally be described in terms of columnar clusters quasi-periodically packed. The clusters are periodic along the ten-fold axis with a translation period of 400 pm (or a multiple up to 3600 pm) and a layered structure corresponding to the stacking of flat or puckered atomic layers having a thickness of 200 pm. According to Steurer (1996) three principal decagonal types may be considered: deca Al–Co–Cu, deca Al–Mn and deca Al– Fe–Pd types. Deca Al–Co–Cu type, found in the stable phases Co15Cu20Al65, Rh15Ni15Al70, Co15Ni15Al70, etc. has a two layer structure with a translation period (c) of about 400 pm (In the space group P105/mmc for d-Co15Ni15Al70 c 408.1 pm and, for d-Co15Cu20Al65 c 414.8 pm). A related crystal (approximant) structure is that of the monoclinic mS93-Co4Al13. Deca Al–Mn type, found in the metastable phase Mn22Al78, in the Pd-stabilized Mn16.5Pd13Al70.5, and in Cu20Cr7Fe8Al65 has a translational period along the 10-fold axis in the order of 1200 pm (for d-Mn16.5Pd13Al70.5, space group P105/mmc, c 1240 pm). Approximant structures are those of MnAl3 and of μ –MnAl4.12

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Intermetallic Chemistry

(MnAl3 oP160-MnAl3 type is orthorhombic, space group Pnma, a 1480 pm, b 1240 pm, c 1260 pm). Deca Al-Fe-Pd type has been observed in the stable phases T10Pd10Al80 (T Fe,Ru,Os). It shows a translational periodicity along the 10-fold axis of 1600 pm; the crystalline approximant structure is the Fe4Al13 type. Dodecagonal quasicrystals. Dodecagonal, generally metastable phases have been observed in Cr71Ni29, V3Ni2 alloys and similar systems. The translational period along the 12-fold axis is in the order of 450 pm. These structures are closely related to that of the tP30–σCrFe phase. Icosahedral quasicrystals. Many icosahedral phases (both stable and metastable) have been identified in several systems, mainly Al-based but also Mgbased, Ti-based, etc. According to Steurer (1996) two main groups of icosahedral quasicrystals can be considered. Icosahedral Al–Mn type with a quasi-lattice constant of about 460 pm and a concentration of free electrons of about 1.75 electrons per atom. Phases pertaining to this type are, for instance, Cr15Al85, Mn14Al86, Cr19Al62Si19, Cr15Cu20Al65. As further examples, we may mention Mn21Al73Si6 (described with a primitive hypercu–– bic cell, in the 6D super-space group Pm35 with ar 460 pm) and Fe15Cu20 Al65 (with a face-centred hypercubic unit cell, ar 445 pm, in the super-space–– group Fm35). Icosahedral Al–Mg–Zn type with a quasi-lattice constant of about 520 pm and a concentration of free electrons of about 2.1 electrons per atom. Examples are –– represented by Li3CuAl6 (ar 504 pm, super-space-group Pm35), Li3AuAl6, Pd13Mg44Al43, CuMg4Al6, Mg32Zn52Ga16, Y–Mg–Zn and Y–Zr–Mg–Zn alloys, etc. 3.11.3.3 Structural relations between quasicrystals and other intermetallic phases. As discussed in several sections of the review published by Kelton (1995) on quasicrystals and related structures, numerous studies and observations indicate structural similarities between non-periodic quasicrystal phases with crystalline phases and also, on the other hand, with amorphous, glassy and liquid phases. Crystal approximants. Several crystalline phases contain more or less closely packed atomic assemblies (polyhedra, clusters) which have been considered fundamental constituents of several quasicrystals, metal glasses and liquids. Such crystalline phases (crystal approximants), as reported in the previous paragraph, are often observed in the same (or similar) systems, as those corresponding to the formation of quasicrystals and under similar preparation conditions. Crystalline phases closely related to the quasicrystals (containing similar building blocks) have generally complex structures; as approximants to the ico-quasicrystals we may, for instance, mention the Frank–Kasper phases (previously described in § 3.9.3.1).

Structural Characteristics of Intermetallic Phases

205

These are typically found in transition metal alloys with smaller atoms generally in icosahedral sites and the larger ones in non-icosahedral coordination. Among the polyhedral clusters found in related structures a fundamental one is the so-called Mackay cluster formed by 54 atoms, and consisting (in ico-Al–Mn quasicrystals) of an inner icosahedron of 12 Al atoms, with a vacant centre, surrounded by a double-sized icosahedron with Mn in the 12 vertices and 30 Al atoms located slightly out of the middle of the Mn icosahedron edges. The mentioned considerations have been more recently underlined by Lin and Corbett (2003). They observed that to date there is still no general set of rules for predicting which alloys, and which compositions, are prone to form quasicrystals. They observed, however, that in the search for new icosahedral quasicrystals a sound reference is found in the known quasicrystals plus their presumed approximants. These are generally normal crystalline compounds with large unit cells containing highly symmetric building blocks (icosahedral, dodecahedral) having compositions close to those of quasicrystals and useful for modelling the quasicrystal structure. They, moreover, underline, that, for instance, alkaline metal compounds with Ga, In, Tl contain several examples of building blocks related to icosahedra (isolated, centred, interbridged, fused) and may represent another route to the exploration for new quasicrystals, also considering substitution by better network-forming cations such as Mg, Ca, Zn, Cd, etc. (considered among the so-called ‘icosogen metals’). An interesting example of such relations is found in the binary ytterbiumcadmium system, where the first stable binary quasicrystal was identified (Tsai et al. 2000). As a reference point, the phase diagram of these alloys is shown in Fig. 3.50. This was determined by Palenzona (1971). Several compounds exist in this system, especially in the Cd-rich region; among them a congruently melting phase with an approximate formula YbCd5.7 (that is about 85.1 at.% Cd) was identified; its crystal structure was not determined, only an indication was obtained of a complex structure with a large unit cell. In this system the Cd-richest phase is YbCd6 (that is a phase with the composition of 85.71 at.% Cd very close to the previous one). This one to six stoichiometry is observed in nearly all the alloy systems of Cd with the rare earth metals (R). Even higher Cd/R atomic ratios however are present in the compounds of the light lanthanides such as LaCd11, La2Cd17, CeCd11, etc. A complex structure was described for the RCd6 phases and reported as YCd6-cI184(168) or YbCd6-cI176(168). In a reassessment of the isostructural compound CeCd6, the composition Ce6Cd37 (86.05 at.% Cd) was proposed and a structure Ce6Cd37cP188(172) type suggested (Armbrüster and Lidin 2000). All these types correspond to similar descriptions of the structure which cannot be easily represented in terms of isolated polyhedra, but is better described in terms of successive polyhedral shells. It was therefore realized (Tsai et al. 2000) that YbCd6 could be what in the jargon of quasi-crystallography is called an approximant and (considering also

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Intermetallic Chemistry

the various stable quasicrystals found in R–Mg–Cd systems) that the very close YbCd5.7 was an excellent candidate for a quasicrystal. A preparation of samples of these alloys and their examination (electron microscopy, X-ray diffraction) confirmed that this stable congruently melting phase is a quasicrystal with 3D icosahedral symmetry. Structural relations with liquid and glasses. Several observations suggest the existence of a structural similarity between liquid and glasses and quasicrystals especially the icosahedral ones (Kelton 1995). The so-called total and partial radial distribution functions, describing the atomic pair correlations in the structure, constructed for metallic glasses (see § 3.12.1) and icosahedral phases show common characteristics. It has been underlined that, in certain alloy systems, depending on the cooling rate from the liquid, different phases may be obtained. For a low cooling rate it is possible to have crystallization, that is to have a 3D ordered periodic array, even giving rise to complex crystalline phases (Frank–Kasper phases for instance). If the cooling rate is too rapid, the various atomic substructures may become entangled and produce a glass. If the cooling is at an intermediate rate, it is possible to maintain, from the under-cooled liquid, a long-range icosahedral order, without obtaining the crystalline order. 3.12. AMORPHOUS ALLOYS, METALLIC GLASSES

Among the different solid phases which may be observed in metallic systems, an interesting group is represented by the amorphous alloys or glassy alloys. 819

796

800

703

462 400

Yb

20

40

60 at.% Cd

80

∼YbCd6

200

Yb3Cd8 Yb14Cd51 YbCd5.7

321 αYbCd2

Temperature (°C)

655 636 600

Cd

Figure 3.50. The Yb–Cd binary phase diagram. The congruently melting compound YbCd57 is the first stable binary quasicrystal identified.

Structural Characteristics of Intermetallic Phases

207

Authoritative reviews on this subject have been published by Buschow (1984) and Cahn and Greer (1996). These alloys can be defined as solids lacking long-range 3D atomic periodicity. When subjected to diffraction experiments (X-ray, neutron or electron diffraction) these alloys generally show a small number of diffuse holes with the absence of sharp peaks. The thermodynamic formation functions (Δf H, Δf G) of amorphous alloys are less negative than those of the crystalline alloys of the same composition; they are metastable and tend to transform into the stable crystal phases, either directly or via metastable crystalline phases. The crystallization kinetics, however, is often very sluggish, so several metastable alloys may be kept for an indefinite time even at temperatures substantially higher than room temperature. An indication of this behaviour can be obtained from the TTT (time–temperature–transformation) diagrams such as that shown in Fig. 3.51. In this figure a complete TTT diagram (described by Löffler 2003) is shown for a bulk metallic glass (Pd40Ni10Cu30P20). The typical ‘C’ shape of the diagram is due to the fact that the thermodynamic driving force for crystallization increases with increasing under-cooling, while the atomic mobility in the liquid decreases. Basically, indeed, a glass (either metallic or of a different nature) may be considered a ‘frozen’ liquid. In order to obtain a glass, crystallization must be avoided on cooling. This may be achieved by quenching.

Temperature (°C)

550 460

Tliq = 550°C

440 420 N

400 380 360 340

Tg = 310°C

320 300 0

50

100

150

200

250

300

Time (s)

Figure 3.51. TTT diagram of the bulk metallic glass Pd40Ni10Cu30P20 (adapted from Löffler 2003). Tliq: melting temperature; Tg: glass temperature. Crystallization of the alloy will occur if, during the cooling from Tliq, the T/t curve passes through the shaded area. The position of the ‘nose’ (N) in the diagram determines the ‘critical cooling rate’ to be used in order to obtain the glass (to avoid crystallization).

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The so-called glass transition temperature, Tg, must be considered: below this temperature the liquid configuration is frozen in a structure corresponding to equilibrium at Tg. Around Tg a rather abrupt change is observed of several properties as a function of temperature (viscosity, diffusion, molar volume). Above Tg, for instance, viscosity shows a strong temperature dependence; below Tg only a rather weak temperature dependence is observed, approximately similar to that of crystal. Notice that Tg is not a thermodynamically defined temperature: its value is determined by kinetic considerations; it also depends on the quenching rate. Several rapid or very rapid quenching techniques have been devised: an outline of several methods of liquid quenching and of other related techniques (vapour quenching, solid-state amorphization processes, etc.) is given in Chapter 6. Starting from the first experiments made by Duwez and co-workers (Klements et al. 1960) by using a variety of methods and investigating several types of alloys, new glassforming compositions have been found that have small critical cooling rates (less than 100 K/s) and can be obtained in the glassy state in dimensions of several centimetres (see Fig. 3.52). These ‘bulk metallic glasses’ are also of increasing importance for technological applications: the relevant mechanical properties of these materials (high-strength materials) are promising for applications as are those based on the superior magnetic properties of magnetic glasses.

Critical casting thickness (cm)

102 101

9 5

8

1

6 7 4

3

10−1 10−2

10

2

1

10−3 1960

1970

1980

1990

2000

2010

Year

Figure 3.52. Historical development of metallic glasses and of their maximum preparation thickness (adapted from Löffler 2003). 1: Au–Si, 2: Pd–Cu–Si, 3: Fe–Pd–P, 4: Au–Pb–Sb, 5: Ni–Pd–P, 6: La–Ni–Al, 7: Y–Cu–Mg, 8:Zr–Ni–Cu–Al, 9: Zr–Ti–Ni–Cu–Be, 10: Ni–Pd–Cu–P.

Structural Characteristics of Intermetallic Phases

209

3.12.1 Structure of metallic glasses In amorphous solids there is a considerable disorder and it is impossible to give a description of their structure comparable to that applicable to crystals. In a crystal indeed the identification of all the atoms in the unit cell, at least in principle, is possible with a precise determination of their coordinates. For a glass, only a statistical description may be obtained: to this end different experimental techniques are useful and often complementary to each other. Especially important are the methods based on diffraction experiments: only these will be briefly mentioned here. The diffraction pattern of an amorphous alloy does not show sharp diffraction peaks as for crystalline materials but only a few broadened peaks. Much more limited information can thus be extracted and only a ‘statistical’ description of the structure may be obtained. The so-called radial distribution function is defined as: RDF(r) 4πr2ρ(r) where ρ(r) is the number of atoms in a spherical shell of radius r and thickness dr. Often the reduced radial distribution function G(r) is deduced which is given by: G(r) 4πr[ρ(r)–ρ0] where ρ0 is the number of atoms per unit volume of the sample. The radial distribution function which may be obtained from a given diffraction pattern is the total one in which the different types of atoms are not distinguished. For a binary alloy, containing the elements X and Y, it is also important to obtain the partial radial distribution functions: 4πr2ρxx(r), 4πr2ρyy(r) and 4πr2ρxy(r). The first two functions describe the correlations between similar atoms, the third one the correlation between different atoms. To obtain the three partial functions, at least three different scattering experiments must be performed in such conditions that, in each experiment, sufficiently different atomic scattering factors are shown by X and Y. Different methods are, in principle, available in order to change the relative scattering powers of X and Y. It is possible to use different radiations (performing X-ray, neutron and electron diffraction experiments) or, for instance, to make isotopic substitution. This leaves the glass structure unaltered but may change the neutron scattering factor. From the partial functions it is possible to determine the nearest-neighbour coordination numbers and the nearest-neighbour distances. A few typical data are listed in Table 3.10 for a few easy glass-forming systems and compared with the values obtained for crystalline phases of similar compositions.

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Table 3.10. Examples of coordination and interatomic average distances in crystalline and amorphous alloys (Buschow 1984). System

Crystalline phase

Gd–Fe

GdFe2 cF24-Cu2Mg type

Y–Ni

YNi2 cF24-Cu2Mg type

Atoms involved Fe–Fe Gd–Fe

6 12

261 306

Gd–Gd Ni–Ni

4 6

320 254

Y–Ni

12

298

Y–Y

4

311

4.8 2.4 6 12

245 249 287 318

Co–Co Gd–Co

a b

GdCo5 hP6-CaCu5 type

NNNa Distance (pm)

Gd–Co Gd–Gd

Amorphous phase (am)Gd0.36Fe0.64

(am)Y0.33Ni0.67

Atoms CNb Distance involved (pm) Fe–Fe Gd–Fe

6.5 6.5

2.54 3.04

Gd–Gd Ni–Ni

6 2 4 9 3

3.47 2.40 2.55 2.71 3.05

Y–Ni

Ni–Y Y–Y Co–Co (am)Gd0.18Co0.82

4.5 2.71 1.5 3.05 4 3.40 7.2 247

Gd–Co

12

297

Gd–Gd

3

340

NNN: nearest neighbour number. CN: coordination number.

Thermodynamic approach to evaluation of amorphization tendency. In a paper by Zaitsev and Zaitseva (2005), it is observed that the search for new glass-forming systems is generally performed on the basis of a certain number of criteria. Three groups of criteria are generally considered: thermodynamic (enthalpy of formation, coordinates of deepest eutectics, etc.), kinetic (nucleation regularity, crystal phase growth, etc.) and structural (liquid and glass structures, atomic dimensions, etc.). A fundamental criterion, of course, is also based on the chemical properties of the substances involved and the nature of the chemical interactions. Special attention was dedicated in this paper to thermodynamic considerations: on this basis it was stated that key properties that control the capacity of molten metallic alloys for transition into an amorphous state are the excess entropy and heat capacity of the liquid. Chemical short-range order in liquids exhibiting various tendencies to glass formation was analysed in terms of the associated solution theory; an interrelation was established between association and characteristics (viscosity, crystallization) that determine the amorphization possibility and glass state stability.

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Structural Characteristics of Intermetallic Phases

1405 1400 β Al11La3

875

918 865

800 640

0 Al

10

20

30

AlLa3

200

400 AILa

400

530 520 Al2La

660 600

α Al11La3 Al3La

Temperature (°C)

1000

Alx La

1240 1200

40

50 at.% La

60

70

80

90

100 La

Figure 3.53. The La–Al phase diagram. The composition ranges corresponding to easy glass formation are marked.

3.12.2 Examples of metallic systems with glass-forming capability Several groups of binary and complex systems have been identified in which amorphous alloys may be obtained. The formation of amorphous alloys by vapour quenching may generally be obtained in a large composition range, possibly with the exception, in a binary system, of the two extreme composition regions. The preparation of amorphous alloys, usually by liquid quenching is possible in more restricted ranges of composition (the so-called ‘easy glass-forming ranges’).Very often these regions correspond to alloys forming ‘deep’ eutectics, both binary and complex. See an example in Fig. 3.53. In a number of cases more than one glassforming region may be observed in a given system. Besides the quenching rate and the preparation methods, a number of factors have been considered as governing the glass formation; among these, favourable factors are the atomic radius ‘mismatch’ between the components (a critical radius mismatch of 15% is generally considered), and a negative deviation of the volume of the liquid with respect to the ideal volume of mixing. A detailed discussion of the different factors and the construction of ‘glass-forming ability’ maps have been presented by Cahn and Greer (1996).

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As for the types of glass-forming alloys, according to Cahn and Greer (1996), the following examples of representatives groups of alloys can be considered: Metal-nonmetal alloys: Ti80–85Si20–15; W80N20; Re65Si35 Fe75–88B25–12; Ni18B82 Ni59–69B41–31; Pd78–86Si22–14; Pt64–66Sb36–34 (and alloys pertaining to ternary systems such as Fe–Ni–B; Fe–Ni–B–P; Fe–Co– Si–B; Fe–P–C; etc.) Fe-, Co-, Ni-based alloys of this group are also commercially important for their soft-magnetic properties. The Ni–Pd–Cu–P family of alloys shows among the metallic systems the highest glass-forming ability known to date (Inoue et al. 1997, Löffler 2003). Early transition metal–late transition metal: Zr9Fe91; Zr75Fe25; Zr10Ni90; Zr33–80Ni67–20 Zr25–60Cu75–40; Nb30–60Ni70–40; Ta30–60Ni70–40 Alkaline earth-based alloys: Mg68–75Zn32–25; Ca52–88Al48–12; Y10Cu25Mg65 Aluminium-based alloys: Ni15Al70Si15; V10Cu15Al70; Zr5Ni10Al85, La5Fe10Al85 The Al alloys, mainly with a lanthanide and a late transition metal, generally exhibit good mechanical properties. Lanthanide- and actinide-based alloys: Gd50–68Fe50–32; La66–72Al34–18; La78–83Ge22–17; La74–82Au26–18; La55Ni20Al25; U60–74Co40–26 The ternary alloys of a lanthanide with Al and a late transition metal have very high glass-forming ability and low critical cooling rate: bulk samples may be cast. REFERENCES

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Chapter 4

Intermetallic Reactivity Trends in the Periodic Table

4.1. INTRODUCTION

Just as it is effective in the other fields of inorganic descriptive chemistry, the Periodic Table is an essential reference point in intermetallic chemistry too. The general alloying characteristics of the different metals, their reactivity towards the other metals, the variety of their intermetallic derivatives usually are very complex and cannot be easily explained and rationalized on the basis of a few concepts and data. Nevertheless a sound first criterion for a description and classification of the intermetallic behaviour of the various metals lies in their position in the Periodic Table. On the basis of the Periodic Table, topics of intermetallic systematics will be presented in the next chapter. In the present chapter the Periodic Table will be revisited and its structure and subdivisions summarized. In relation also to some concepts previously presented, such as electronegativity, Mendeleev number, etc. described in Chapter 2, typical property trends along the Table will be shown. Strictly related concepts, such as Periodic Table group number, average group number and valence-electron number will be considered and used in the description and classification of intermetallic phase families.

4.2. THE PERIODIC TABLE AND ITS STRUCTURE

4.2.1 The Periodic Table and the electron configurations of the elements The Periodic Table of the elements is shown in Fig. 4.1, in one of its most popular versions. Special names for families of elements are indicated in Fig. 4.2. In particular, notice that the elements having atomic numbers from 58 to 71 together with La (atomic number 57) pertain to the lanthanide family, and those from Z 90 to Z 103, together with Ac, Z 89, to the actinide family. In the Periodic Table of Fig.4.1, which is commonly used, the elements La and Ac, together with Sc and Y, are placed in their proper positions of the 3rd column (3rd group) of the Table. The other lanthanides and actinides are reported separately at the bottom of the figure. 219

220

Intermetallic Chemistry 1

18 1

1

H

2

Li

2

2 3

11

13 4

19

K 37

5 Rb 55

6 Cs 87

7

Fr

5

Be

B

12

3 Na Mg 4

13

3

20

Ca

21

Sc

38

Sr

39

Y

56

Ba

57

La

5

4 22

23

V

Ti 40

Zr

41

72

73

Ta

Lanthanides

Ce

Actinides

Th

88

6 24

Cr 42

Nb Mo

Hf

Ra

14

74

W

7 25

Mn 43

Tc 75

Re

8 26

Fe 44

Ru 76

Os

9

10

27

Co

28

Ni

45

Rh

46

Pd

77

Ir

78

Pt

11 29

Cu

30

Zn

47

Ag

31

6

C

48

49

In

80

81

Hg

Tl

7

33

17

Cl

34

Se

51

35

Br

52

Sb

82

9

F

16

S

As

50

Pb

8

15

Te

83

84

Bi

He

17

O

P

32

Sn

16

N

14

Si

Ga Ge

Cd

79

Au

Al

12

15

Po

53

I

10

Ne 18

Ar 36

Kr 54

Xe 85

At

86

Rn

89

Ac 58

90

59

Pr 91

Pa

60

61

62

63

Nd Pm Sm Eu 92

U

93

Np

94

95

64

Gd

65

Tb

96

66

Dy

97

Pu Am Cm Bk

98

Cf

67

Ho 99

Es

68

Er

69

70

Tm Yb

100

101

102

Fm Md No

71

Lu 103

Lr

Noble gases

Halogens

Chalcogens

Transition metals

Pnicogens

Y

Triels

Sc

Tetrels

Alkali metals

Alkaline earths

Figure 4.1. The Periodic Table of the elements, in which symbols and atomic numbers of the different elements are reported. On the left the progressive numbers of the rows (of the periods) and on the top the numbers of the columns (the groups) are indicated.

La Ac Lanthanides Actinides

Figure 4.2. The Periodic Table: special collective names. The informal symbols of these families of elements are: A alkali metals, Ae alcaline earth metals, Ln lanthanides; R rare earth metals Sc Y lanthanides, An actinides, Hal halogens, Chal chalcogens, Pn pnicogens, Tr triels, Tt tetrels.

221

Intermetallic Reactivity Trends in the Periodic Table

A survey of the trends of some atomic and physical properties of the different elements against their atomic number is summarized in Figs. 4.3–4.5. In Fig. 4.3 the energies of 1st and 2nd ionization are reported. The first stage ionization energy of the element M is the energy required to remove the least tightly bound electron from the neutral atom in the gas phase, that is, to perform the following reaction: Mgas : Mgas e Notice in the corresponding graph the maxima for the inert noble gases and the minima for the alkali metals. The second stage ionization energy corresponds to the reaction Mgas : M gas e , that is to a reaction involving an atom deprived of one electron, and therefore isoelectronic with the neutral atom of the previous element. Notice the resulting shift of one place in this graph (in comparison with the previous one) of the positions of the minima and maxima and the similar shapes of the two graphs underlining the similar electron configuration for a given number of electrons. 8000 Li

First ionization energy Second ionization energy

Ionization energy (kJ/mol)

7000 6000 5000

Na

4000 K

3000

Rb He

2000

Cs

Ne Ar

Kr

Xe

1000 0 0

20

40

60

80

100

Atomic number

Figure 4.3. Ionization energies of the elements. The values of the energies (in kJ/mol of atoms) of 1st and 2nd ionization are shown. Notice the ‘periodic’ character of these values as a function of the atomic number. Notice the similar trends of the two graphs when the same number of electrons are considered: the maxima, for instance, are observed for the 1st ionization of He and the 2nd ionization of Li, for 1st and 2nd ionization of Ne and Na, respectively (having both 10 electrons), etc.

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Intermetallic Chemistry

Melting temperature (°C)

4000

C W

3000

Mo V

2000

Th

Si Ge

1000

0 −273 0

20

40

60

80

100

Atomic number

Figure 4.4. Melting temperatures (ºC) of the elements plotted against the atomic number. Notice, within the different periods of the Periodic Table, the similar trends of the values. Those elements have been indicated for which a very high melting point and a clear maximum have been observed.

300

Fr

Cs Rb K

Atomic radius CN 12 (pm)

250 Na

200 Li 150 100 50 0 0

20

40

60

80

100

Atomic number

Figure 4.5. Atomic radius (pm, CN 12) of the elements ordered according to their atomic number. Notice the high values corresponding to the alkali metals, the progressive decrease along each period, and the abrupt increase at the beginning of the next period. Notice also the progressive lengthening of the different periods due to the occurrence of the transition elements in the periods starting from K, Rb, Cs and of the lanthanides in the Cs period. In the Cs period, within the lanthanides, observe the peaks of Eu and Yb with the high values of their radii, corresponding to a divalent metal state.

Intermetallic Reactivity Trends in the Periodic Table

223

Similar shifts and trends may be noticed considering the much higher values, and their trends of the energies of the 3rd, 4th, etc. ionizations. Figs 4.4 and 4.5 show the trends of the melting temperature and of the atomic radius of the elements vs. their atomic number. The ‘rhythmic’ (periodic) aspect of the graphs is apparent and corresponds to the ‘rhythmic’ variations of the ground valence-electron configurations along the Periodic Table. It is well known, indeed, that the structure of the Periodic Table and the positioning of the different elements in it, are strictly related to the electronic structure of the atoms of the elements themselves and to the changes in this structure from one element to the next one. These arguments are fully and systematically treated in the books of general chemistry, inorganic chemistry, physical chemistry, etc. Only a few notes will be reported here mainly to remind the reader of the different nomenclature and symbols generally used. As for the properties of the different elements, and especially those relevant to their alloying behaviour, a selection is reported in the specific paragraphs of Chapter 5. 4.2.1.1 Remarks about the structure of the Periodic Table. The elements, written in sequence of their atomic number, are arranged in the Table in horizontal rows (periods) and vertical columns (groups). Notice that two rows, the lanthanide and the actinide series, are placed in a special position outside the main body of the Table. This arrangement, which is related to the electronic structure of the atoms, illustrates and reflects the occurrence among the elements of similarities in the properties and analogies in their behaviour. In general, elements in the same column display similar chemical properties, possibly smoothly changing along the column, while along a period there is a progressive variation in the chemical behaviour, with an abrupt change at the borders. As a consequence it is possible to recognize natural subdivisions into several ‘families’ of the different elements. These points are briefly discussed in the subsequent paragraphs and related figures. The history of the Periodic Table, its layout and interpretation is well known, starting with Mendeleev and his precursors (de Chancourtois, Newlands, Odling, Hinrichs, Meyer) up to the insertion of the lanthanides, actinides, and transuranium elements and heavy and super-heavy elements. This history is closely related to fundamental stages in the development of chemistry (for instance, the identification and preparation of new elements, the discovery and application of a number of rules and concepts in descriptive inorganic chemistry) and physics, by the work of Bohr, Moseley, Schrödinger, etc. up to the final clarification of the Periodic Table through quantum mechanics. Broad reference to the above-mentioned topics may be found in a book containing the proceedings of an international conference with the contributions of several authors, edited by Rouvray and King (2004).

224

Intermetallic Chemistry

4.2.1.2 The electronic structure of the atoms. The electronic structure of the atoms of the different elements and their relation to the characteristics of the Periodic Table are based on a number of experimental data and theoretical models which are fully discussed in many elementary and advanced texts of inorganic chemistry such as Cotton et al. (1999), Greenwood and Earnshaw (1997), Huheey et al. (1997), Wells (1984). Only a few relevant points about the atomic structures are summarized in the following. Table 4.1 collects basic data about the fundamental physical constants of the atomic constituents. Neutrons (10n) and protons (11p), tightly bound in the nucleus, have nearly equal masses. The number of protons, that is the atomic number (Z), defines the electric charge of the nucleus. The number of neutrons (N), together with that of protons (A N Z) represents the atomic mass number of the species (of the nuclide). An element consists of all the atoms having the same value of Z, that is, the same position in the Periodic Table (Moseley 1913). The different isotopes of an element have the same value of Z but differ in the number of neutrons in their nuclei and therefore in their atomic masses. In a neutral atom the electronic envelope contains Z electrons. The charge of an electron (e) is equal in size but of opposite sign to that of a proton (the mass ratio, me/mp) is about 1/1836.1527). Elementary charge, e 1.60217653(14) 1019 C The unified atomic mass unit (u), previously symbolized as AMU or amu, is defined to be 1/12 of the mass of one atom of isotope 12 of carbon. Therefore, 1 u 1.66053886(28) 1027 kg A concept strictly related to the Avogadro Number (NA) is that of ‘mole’. It is the amount unit of a substance and it is defined as an NA of entities (to be specified, if not clearly implied). A mole of atoms of 12C, for instance, corresponds by definition, to NA atoms of 12C that is to 12 g of 12C. Similarly a mole of atoms of oxygen (15.9994 g) corresponds to NA atoms of oxygen and a mole of molecules of oxygen (31.9988 g of oxygen) corresponds to NA molecules O2 and as a final example, Table 4.1. Fundamental physical constants (adapted from Nist Codata, Mohr and Taylor (2005)). Mass (kg)

Mass (atomic mass unit, u)

Charge (e)

Electron

9.1093826(16) 1031

5.4857990945 (24) 104

1

Proton

1.67262171 (29) 1027

1.00727646688 (13)

1

27

1.00866491560 (55)

0

Neutron

1.67492728 (29) 10

Symbol 0 1e 1 1p 1 0n

Intermetallic Reactivity Trends in the Periodic Table

225

a mole of sodium chloride is an NA of formula NaCl which corresponds to 58.4425 g of sodium chloride. The recommended value for Avogadro’s number is: NA 6.0221415(10) 1023 mol1 1 u 1/(NA) g 1/(1000 NA) kg The arrangement of the electrons in an atom, that is the electron configuration of an element in the ground state of its free neutral atom, is in direct and simple correspondence to the form of the Periodic Table and the position in it of the element under consideration. The so-called quantum approach to the Periodic Table is based on the following principles (Ostrovsky 2004): The quantum numbers n and . Multi-electron atoms can be characterized by a set of principal and orbital quantum numbers {n, } which labels one-electron wave functions (orbitals). The Pauli Exclusion Principle. No two electrons in an atom may have the same four quantum numbers n, , m, ms where m and ms are respectively the magnetic and spin quantum numbers. The Aufbau (building up) Principle. One-electron orbitals are filled (occupied) by electrons sequentially, in the order of increasing energy. With reference to the previously reported statements a summary of the role of the quantum numbers is in the following. The principal quantum number n may be considered the principal determinant of an electron energy level. Electrons corresponding in an atom to the subsequent possible values n 1, 2, 3, 4, etc. are also referred to as pertaining to the ‘shells’ K, L, M, N, etc.; the orbital quantum number defines the shape and the symmetry of the electron charge distribution and its orbital angular momentum. For atoms, or ions, containing more than one electron, the energy also depends to some extent on . The number of possible values for depends for a given electron on the value of n, its principal quantum number; n different values are possible from 0 up to n 1. Orbitals (electrons) with 0, 1, 2, 3, etc. are designated, respectively, as s, p, d, f, … orbitals. Notice that, in an atom, the sequence of increasing energy levels is in the order of increasing n values (between 2 electrons with the same n value, the one with a smaller value of n is more tightly bound). This rule (Madelung 1936) has been especially noted by Ostrovsky (2004) who underlined that it is not only a mnemonic device but has deep roots in quantum theory and links together many subjects. The ordering of one-electron levels (the definition of their energy sequence) is crucial for the application of the Aufbau principle.

226

Intermetallic Chemistry

The general filling order, therefore, is: 1s : 2s : 2p : 3s : 3p : 4s : 3d : 4p : 5s : 4d : 5p : 6s : 4f : 5d : 6p : etc. This means that 3d (for which n 3 2 5) is filled after 4s (n 4 0 4), 4d (n 4 2 6) after 5s (n 5 0 5), 4f (n 4 3 7) after 6s (n 6 0 6), 5d (n 5 2 7) after 4f (n 4 3 7), etc. As for the third and fourth quantum numbers, in agreement with what is generally mentioned in textbooks on chemistry, such as, for instance, Greenwood and Earnshaw (1997) we may say that: The magnetic quantum number m is related to the fact that only in an applied magnetic field it is possible to define a direction within the atom with respect to which the orbital can be directed. In general for a value of the orbital quantum number we have 2 1 possible values of the magnetic quantum number (which are 0, 1, 2, … up to ). To an s orbital, for instance, for which 0 and is spherically symmetrical, only one value corresponds for the magnetic quantum number (m 0). For p orbitals ( 1) we have three possibilities (m 1, 0, 1) corresponding to three orientations (generally assumed as the x, y, z directions in Cartesian coordinates). Similarly we have five possibilities for d orbitals ( 2) (that is m 2, 1, 0, 1, 2), seven for f orbitals ( 3), etc. The spin (angular momentum) quantum number ms. In their interpretation of many features of atomic spectra Uhlenbeck and Goudsmit (1925) proposed for the electron a new property called spin angular momentum (or simply spin) and assumed that only two states of spin were possible. In relativistic (four-dimensional) quantum mechanics this quantum number is related to the symmetry properties of the wave function and may have one of the two values designated as 1⁄2. However, while one-electron quantum numbers n and might be ascribed to an atom even in an approximate sense, the two other numbers m and ms generally cannot be associated with an atomic state in any valid approximation. They however are quite often used not as physical quantities but as mere counters. All electrons in atoms can be described by means of these four quantum numbers and, as first enunciated in 1926 by Pauli in his Exclusion Principle, each electron in an atom must have a unique set of the four quantum numbers. A summary of the electron ‘shells’ and of the corresponding maximum numbers of orbitals, and electrons, is shown in Table 4.2 where each shell is defined by the value of the principal quantum number (K 1, L 2, etc. according to X-ray spectroscopy nomenclature). This description of the electronic structure can be related to the form of the Periodic Table. Hydrogen with a nucleus having a charge 1 and only one electron

227

Intermetallic Reactivity Trends in the Periodic Table Table 4.2. Numbers of orbitals and maximum numbers of electrons in the electron shells. Shell

Quantum numbers

K L

n 1 2

M

3

N

4

m 0 0 0 0 1 1, 0,1 0 0 1 1, 0,1 2 2,1, 0, 1,2 0 0 1 1, 0,1 2 2,1, 0, 1,2 3 3,2,–1, 0,1,2,3

No. of orbital

1 1 3 1 3 5 1 3 5 7

Type of orbital

s s p s p d s p d f

Maximum number of e in the group of orbitals 2 2 6 2 6 10 2 6 10 14

Maximum number of e in the shell

2 8 18

32

is the first element and, in the ground state (the lowest-energy state), has the electronic configuration represented by 1s1 (that is n 1 and 0 with zero orbital angular momentum). Helium (Z 2, two electrons in the neutral atom) has the configuration 1s2: this completes the first period; no other value combination exists for n 1, 0 (m 0, ms 1⁄2). With the next element, lithium, Z 3, the least tightly bound electron has the configuration 2s1 (the complete Li electron configuration is 1s22s1, which in a way corresponds to the ‘addition’ of a third electron to a He type configuration, that is [He]2s1) and this corresponds to the beginning of the second period. Notice that in all the reported configurations we have symbols of the type nx y, where n is the principal quantum number, x is the letter (s, p, d or f ) corresponding to the different values of the orbital quantum number () and the exponent y is the number of electrons in the given orbital (or group of orbitals). The maximum value of y is defined by the number of alternative permitted combinations of different m and ms values. It corresponds, in the different cases, to s2, p6, d10 or f 14. For a few elements following lithium, the electron configurations corresponding to the progressive attribution of electrons to the different orbitals according to the energy increase are: Be (Z 4): 1s22s2; B (Z 5): 1s22s22p1; C (Z 6): 1s22s22p2; N (Z 7): 1s22s22p3; O (Z 8): 1s22s22p4; F (Z 9): 1s22s22p5; Ne (Z 10): 1s22s22p6; Na (Z 11): 1s22s22p63s1; etc.

228

Intermetallic Chemistry

With Na, the electron configuration of which may also be described as [Ne]3s1, the third period begins. A similar situation is found for each of the other periods in the Table: the number of the period is the principal quantum number of the least tightly bound electron of the first element (an alkali metal) of the period. A few more details of these questions and the characteristics of special points in the Periodic Table are discussed in following paragraphs. The electron configurations of all the elements are given in Chapter 5. 4.2.2 Blocks and subdivisions of the Periodic Table Different regions in the Periodic Table, that is, different grouping of elements, can be identified, having some analogies in the elemental properties and behaviour, useful as reference framework in a systematic description of the different chemistry fields. 4.2.2.1 ‘Blocks’ of the Periodic Table. On the basis of the nature of the orbitals to which the valence electrons are assigned in the different elements (in their ground states), a subdivision into ‘blocks’ of the Periodic Table is commonly made (see Fig. 4.6). The block s, on the left of the Table, contains the alkali and alkaline earth metals. Each atom of these metals possesses an inert gas core and one or two electrons in the s orbital of the valence shell, that is, an ‘external’ electron configuration ns1 or ns2 where n is the value of the principal quantum number, and also the period number in the Periodic Table. Notice however that He, owing to its general chemical inertness and to the behaviour similarity with the other noble gasses is generally placed at the far right of the Table. The p block contains elements corresponding to electron

s

p

s d

f

Figure 4.6. Blocks of the Periodic Table. The names (symbols) of the so-called blocks are indicated. In the p block two types of elements can be considered, roughly separated by the Zintl line: semi-metals in the left-hand part and non-metals in the right-hand part.

Intermetallic Reactivity Trends in the Periodic Table

229

configurations from ns2 np1 to ns2np6. These elements may be considered as semimetals (in the bottom left-hand part of the block) or non-metals (in the top right-hand part): the separation, in this block, between semi-metals and non-metals is roughly indicated in the Table by a ‘diagonal’ line (the so-called Zintl line or Zintl border). Inserted within the s and p blocks, there are the d block elements (metals) having valence-electron configurations (n 1)d x ns0,1,2 corresponding to a number of electrons included between 1 and 10 in d orbitals and 1 or 2 (or no) electrons in the external s orbital (see in Chapter 5 the detailed description of the electron configurations of all the elements). The d block metals are also called transition metals. The 1st transition series is made up of the elements from Sc to Zn, the 2nd of the elements from Y to Cd, the 3rd of the elements from La to Hg. The 3rd transition series however is longer, and in it another set of elements is included: an inner transition series, corresponding to the metals of the f block from Ce to Lu, for which there is a progressive occupation of the 4f orbitals by the valence electrons. A similar description could be made for the subsequent row (7th period) containing the heaviest metals of the s block known (francium, Fr, and radium, Ra) and for another transition series, which starts from actinium (Ac) and includes the metals of the f block involved in the occupation of the 5f orbitals. Compare with Fig. 4.1 and, for an alternative nomenclature of the various families of elements, with Fig. 4.2. 4.2.2.2 Comments on some trends and on the ‘Divides’ in the Periodic Table. It is clear that, on the basis also of the atomic structure of the different elements, the subdivision of the Periodic Table in blocks and the consideration of its groups and periods are fundamental reference tools in the description and classification of the properties and behaviour of the elements and in the definition of typical trends in such characteristics. Well-known chemical examples are the valence-electron numbers, the oxidation states, the general reactivity, etc. As far as the intermetallic reactivity is concerned, these aspects will be examined in detail in the various paragraphs of Chapter 5 where, for the different groups of metals, the alloying behaviour, its trend and periodicity will be discussed. A few more particular trends and classification criteria, which are especially relevant in specific positions of the Periodic Table, will be summarized here. Lanthanide contraction. This effect, which is the progressive decrease of the atomic dimensions of the LnIII ions, is due (as discussed in § 5.5.2) to the imperfect shielding from the nuclear charge of 4f n electrons. A similar overall reduction is observed in the metal radii with the exceptions of Eu and Yb (containing larger LnII) and of Ce (containing slightly smaller atoms in an oxidation state a little higher than 3). An important effect of this trend is observed in the post-lanthanide elements: we have indeed a dimension reduction of the atomic structures also in

230

Intermetallic Chemistry

the next metals of the 3rd transition series (Hf, Ta, W, …) and this results in very similar sizes and properties with the corresponding metals of the 2nd transition series (Zr, Nb, Mo respectively). This means that, for instance, the hafnium chemistry will follow very closely that of zirconium. d block contraction. This effect, similar in principle to the lanthanide contraction, is due to the fact that, for instance after the end of the 1st transition series, differently from Al, we have the insertion of the 3d10 electrons in the atomic structure of Ga. The 10d electrons do not completely shield the corresponding extra positive charge of the nucleus. This results in a higher ‘effective’ nuclear charge which causes an increase in the attraction for the whole electron cloud, with a relative size contraction and an increase of the ionization energy. In the 13th group of the Periodic Table for the sequence B, Al, Ga, In and Tl, we have therefore an apparently irregular trend of several properties due to the influence of the 3d electrons (Ga), and then of the 4f electrons (Tl). Relativity: heavy transition metal species. Relativistic effects and their impact on the Periodic Table have been recently summarized by Balasubramanian (2004). Emphasis has been especially placed on gold. Au has the atomic number 79, so the inner 1s electron is subjected to the field generated by the 79 charge of the nucleus. In order to have equilibrium the electron has to move faster: it has been estimated that its speed is about 60% of the speed of light. As a consequence the relativistic mass of the electron, given by m m0/ (1 (2/c2) (where m0 is the stationary mass of the electron, its average speed and c the speed of light), is about 25% larger than m0. This results in an increase of the electron (kinetic) energy and in a consequent contraction of the orbital extension. This contraction is relevant for the core electrons, but it is also not negligible for the valence electrons. A relativistic contraction of the 6s orbital follows, with an increase of its stability (an increase of the energy needed to remove it). A comparison of the ionization potential of the elements of the 11th group Cu, Ag and Au does not show a monotonic decrease, as could be expected since the outermost electron is further from the nucleus. A decrease is only observed on passing from copper to silver; gold can be considered an anomaly since its ionization potential is higher than both silver and copper. The relativistic stabilization of the 6s orbital is also observed for other 6th row elements. Several peculiar properties (in the 12th group) of mercury in comparison with Zn and Cd have been related to this fact. The gradual decrease of the atomic radii from La to Lu (the lanthanide contraction), mainly attributed as previously mentioned to an incomplete screening of the 4f shells, has been shown to be partially due to relativistic effects. See the detailed discussion reported by Balasubramanian (2004).

231

Intermetallic Reactivity Trends in the Periodic Table

Diagonal relationships. A number of analogies exist between element pairs, generally light elements in the upper left region of the Table, which in the Periodic Table are placed in a relative diagonal position; that is, there is a certain similarity between an element and the one to its lower right. A typical example is represented by Li and Mg, for which the similarity of the size of their ions Li (r 76 pm) and Mg2 (r 72 pm) may be relevant. Similarity in charge density of the ions has also been considered related to a resemblance in chemical behaviour: charge density (Rayner-Canham 2004) is defined as the ion charge (number of charge units times the proton charge in coulomb) per unit ion volume (in cubic millimetres). Other element pairs for which this kind of relationship has been underlined are: Be and Al, B and Si, N and S. ‘Divides’ in the Periodic Table. A particular scheme of subdivision of the Periodic Table has been presented by Stone (1979) and applied to the classification of alloying tendencies: it is summarized in Fig. 4.7. In this figure, a number of vertical lines, termed ‘divides’, have been drawn in particular positions of the Table. These are so placed that any element near a divide, and on one side of it, will form a compound or compounds with a counterpart element at the other side of that divide or, in other words, will form compounds with a specific bonding mechanism. The ‘ionic divide’, at group 18, separates elements at its immediate right, which easily form positive ions (cations), from those (halogens, chalcogens) which easily form negative ions (anions). Group number 4

Ti

5

6

V

Cr

7

8

10

11

12

13

14

15

16

17

18

1

2

H

He

Li

Be

Na Mg

B

C

N

O

F

Ne

Al

Si

P

S

Cl

Ar

K

Ca

Mn Fe

Co

Ni

Cu

Zn

Ga Ge

As

Se

Br

Kr

Rb

Sr

Rh Pd

Ag

Cd

In

Sb

Te

I

Xe

Cs

Ba

Zr

Nb Mo

Tc

Hf

Ta

Re Os

W

9

Transition metal divide

Ru

Ir

Pt

Sn

Au Composite divide

Covalent divide

Ionic divide

Figure 4.7. The metallurgist’s Periodic Table showing the four ‘divides’ proposed by Stone (1979). Notice that the position of the different groups has been shifted, in comparison with the conventional presentation of the Table, in order to give special emphasis to the ionic divide.

232

Intermetallic Chemistry

He

H Be

B

C

N

O

F

Ne

Na Mg

Al

Si

P

S

Cl

Ar

Li

Cr

Mn

Fe

Co

Ni

Cu

Zn

Ga Ge

As

Se

Br

Kr

Zr

Nb Mo

Tc

Ru

Rh

Pd

Ag

Cd

In

Sn

Sb

Te

I

Xe

Hf

Ta

W Re

Os

Ir

Pt

Au

Hg

Tl

Pb

Bi

Po

At

Rn

K

Ca

Sc

Ti

Rb

Sr

Y

Cs

Ba

La

Fr

Ra

Ac

V

Transition metal divide

Composite divide

Ionic divide

Tb

Dy

Ho

Er

Tm Yb

Lu

Pu Am Cm Bk

Cf

Es

Fm Md No

Lr

Ce

Pr

Nd Pm Sm Eu

Th

Pa

U

Np

Covalent divide

Gd

Figure 4.8. The metallurgist’s Periodic Table shown in the conventional layout. In comparison with Fig. 4.7, some of the divides have been slightly modified in their lower parts in order to better account for the properties of the heavier metals (Stone 1979, King 2004b).

As underlined by King (2004a), in addition to the noble gas divide, that is the ‘ionic divide’, at group 18, the ‘covalent divide’ at group 14 (C, Si, Ge, Sn, Pb) is also familiar in conventional chemistry: it separates ‘hyperelectronic’ elements like nitrogen, forming molecules with lone pairs from ‘hypoelectronic’ elements like boron, giving molecules with multi-centre bonding. The remaining two divides: the so-called transition metal divide at group 6 (Cr, Mo, W) and the composite divide at group 12 (Zn, Cd, Hg) were introduced by Stone on the basis of the alloying behaviour of the metals close to the divides themselves. For these divides too, the compound formation capability was related to the same rule. According to Stone, moreover, if two metals are near to, but on the same side of, such divides, no compounds are formed and some different phase diagram types, from solid solubility to liquid immiscibility, are observed. So, for instance iron, which is on the right of the transition metal divide, forms compounds with metals on the left of the same divide. On the other hand, considering the composite divide, metals close to it or to its right (such as Cu, Ag, Cd, Hg, In, Tl, Pb, Bi) do not form any compound with a metal, such as Fe, on the left of the same divide (compare with Fig. 5.25). In a more conventional representation of the Periodic Table, the Stone subdivision is shown in Fig. 4.8. However, in this figure, according to the so-called s–d shear

233

Intermetallic Reactivity Trends in the Periodic Table He

H Be

B

C

N

O

F

Ne

Na Mg

Al

Si

P

S

Cl

Ar

Li

Cr

Mn

Fe

Co

Ni

Cu

Zn

Ga Ge

As

Se

Br

Kr

Zr

Nb Mo

Tc

Ru

Rh

Pd

Ag

Cd

In

Sn

Sb

Te

I

Xe

Hf

Ta

Re

Os

Ir

Pt

Au

Hg

Tl

Pb

Bi

Po

At

Rn

K

Ca

Sc

Ti

Rb

Sr

Y

Cs

Ba

La

Fr

Ra

Ac

V

W

True metals

Meta-metals

Nonmetals

Tb

Dy

Ho

Er

Tm Yb

Lu

Pu Am Cm Bk

Cf

Es

Fm Md No

Lr

Ce

Pr

Nd Pm Sm Eu

Th

Pa

U

Np

Semimetals

Gd

Figure 4.9. The Periodic Table division suggested by Klemm (1950).

hypothesis proposed by Stone, slight deviations from vertical lines were introduced. This arrangement of the composite and of the transition metal divides is in better agreement with the general alloying behaviour of the metal families involved, and may be discussed in terms of their atomic and ionic electronic configurations. As we are considering this kind of subdivision of the Table, we turn our attention to the classification depicted in Fig. 4.9, introduced by Klemm (1950), and based on the tetra-partition of the elements into metals (true metals), meta-metals, semimetals and non-metals. According to King (2004b), typical properties of the four types of elements are the following: True metals: alkali, alkaline earth metals, Al, Cu, Ag, Au, etc., having a high specific electrical conductivity (Ohm1 cm1): κ 105–106 and crystal structures of high symmetry and coordination numbers (CN 8–12). Meta-metals: Be, Zn, Cd, Hg, In, Tl, Pb, etc., κ 104–105, crystal structures with small deviations from high symmetry (and CN 6 6, 8 4). Semi-metals: Si, Ge, Sn, As, Sb, Te, etc., κ 102–106, CN 2–4. Non-metals: N, O, S, Se, Halogens, etc., κ 106, low coordination numbers, molecular structures. 4.2.2.3 ‘Geochemical’ subdivision of the Periodic Table. The Goldschmidt’s geochemical classification of the elements in the Periodic Table is presented in Fig. 4.10

234

Intermetallic Chemistry He

H Be

B

C

N

O

F

Ne

Na Mg

Al

Si

P

S

Cl

Ar

Li

Cr

Mn

Fe

Co

Ni

Cu

Zn

Ga Ge

As

Se

Br

Kr

Zr

Nb Mo

Tc

Ru

Rh

Pd

Ag

Cd

In

Sn

Sb

Te

I

Xe

Hf

Ta

W

Re

Os

Ir

Pt

Au

Hg

Tl

Pb

Bi

Po

At

Rn

Ce

Pr

Nd Pm Sm Eu

Gd

Tb

Dy

Ho

Er

Tm Yb

Lu

Th

Pa

U

K

Ca

Sc

Ti

Rb

Sr

Y

Cs

Ba

La

V

Lithophile

Siderophile

Chalcophile

Atmophile

Figure 4.10. Geochemical classification of the elements in the Periodic Table, after Faure (1991). For a few elements (Tc, Pm, Pa) not indicated in the Table, no relevant data are available.

(Goldschmidt 1954, Faure 1991). The element subdivision siderophile (iron-loving), lithophile (rock-loving), chalcophile (copper-loving, implying however coppersulphide-loving, that is, sulphur-loving) and atmophile (atmosphere-loving) was proposed by Goldschmidt on the basis of systematic analyses of meteorite materials and sulphide ore smelting products. An interpretation of this classification scheme may be obtained by making reference to a complex system in which three melts (molten Fe–Ni alloy, sulphide and silica magma) are in equilibrium. It may be expected that a lithophile element (such as K) will be enriched in the silica magma, and therefore in the Earth’s crust, whereas a siderophile element (such as Pt, Au) will be especially enriched in the Fe–Ni melt, and therefore in the Earth’s core. The clustering in the Periodic Table of elements having similar behaviour is evident. Notice, however, the approximate character of this subdivision in which, for instance, no consideration has been given to the elemental valences. A typical example is the element chromium, which in a reducing ambient, that is as Cr3, is clearly a chalcophile, whereas in oxidizing conditions, as (CrO4)2, is a lithophile. This classification may of course be useful as a reference, when considering the occurrence in nature of the various elements and/or their preparation methods.

Intermetallic Reactivity Trends in the Periodic Table

235

Figure 4.11. Superconducting elements in the Periodic Table (adapted from Cheetham and Day (1992)).

4.2.2.4 Superconducting elements in the Periodic Table. A further example of the applications of the Table is shown in Fig. 4.11, where for the different elements an indication is given of their superconductivity behaviour. A correlation exists between this behaviour and the position in the Periodic Table. 4.2.2.5 ‘Technological’ subdivision of the Periodic Table. As a concluding remark, we identify in the Table some classes of the most commercially important metals for which widespread common names are used. As an example, the following groups of important technological metals can be evidenced on the basis of their properties and applications (see Fig. 4.12). Notice also their clustering in the Table. Light metals (Densities are given in g cm): Be (1.845), Mg (1.738), Al (2.699), Ti (4.50). Alkali metals, especially Li (0.534), Na (0.97) may be considered as additional alloying metals to light alloys. Refractory metals (Melting point, in °C, are given): Zr (1855), Hf (2231), V (1910), Nb (2469), Ta (3020), Mo (2623), W (3422), Re (3186).

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L

L

L

L

L L

R F

R R

F R

F

F

R F

R

F R F

R

F

C

P

P

P

P

P

P

P C P C

S S

S

S

S

S

Figure 4.12. The position in the Periodic Table of a few classes of commercially important metals. L: Light metals, R: Refractory metals, F: Ferro alloy metals, P: Precious metals, C: Coinage metals and S: Soft solder metals.

Precious metals Ag, Au, and the Pt group metals. Indicative prices (in euro g1), as listed in July 2006, are: Au: 10.68, Ag: 0.19, Pd: 5.24, Pt: 22.2, Rh: 38.7. Coinage metals Cu, Ag and Au Soft solder metals (Melting point, in °C, are given): Ga (29.8), In (156.6), Sn (231.9), Pb (327.5), Sb (630.7), Bi (271.4). Ferro alloy metals Cr, Fe, Mn, Mo, Nb, V, Ti, W. Notice however that, in the different categories, the use of some metals (for instance, Be, Pb) has been discouraged or banned for their high toxicity. 4.3. TRENDS IN THE PERIODIC TABLE: THE ROLE OF THE ATOMIC DIMENSIONS AS A FACTOR CONTROLLING THE STRUCTURE OF INTERMETALLIC PHASES

4.3.1 Introduction A systematic description of bond characteristics in intermetallic phases involves several different approaches. A bond characterization in intermetallics, as related to thermodynamic properties and considerations concerning the stability of intermetallic phases, has been reported by Ellner and Predel (1995). On this subject we observe the peculiar properties of alloys of extraordinary stability formed by

Intermetallic Reactivity Trends in the Periodic Table

237

elements such as Al, Ti, Zr, Hf and the rare earth metals with the transition metals Re, Ru, Os, Rh, Ir, Pd, Pt, characterized by very high formation heats and discussed by Brewer (1973, 1990) as examples of generalized Lewis acid–base interactions in metallic systems. A general presentation and discussion of the origin of structure of crystalline solids and of the structural stability of compounds and solid solutions was given by Villars (1995) and Pettifor (1995). For an introduction to the electronic structure of extended systems, see Hoffmann (1987, 1988). In this chapter a brief sampling of some useful semi-empirical correlations and, respectively, of methods of classifying (predicting) phase and structure formation will be summarized. The search for regularities and criteria for the synthesis of new representatives of particular structure types has been carried out by many authors. Several factors have been recognized to be important in controlling the structural stability, and some of these were used as coordinates for the preparation of ‘classification and prediction maps’ in which various compounds can be plotted and separated into different structure domains. Intermetallic phases could be classified following the most important factor which controls their crystal structure (Pearson 1972, Girgis 1983, Hafner 1989, Westbrook and Fleischer 1995, Cahn and Haasen 1996). As a recapitulation of these points we may again refer to Pearson (1972), who underlined the role of the following factors in the classification of intermetallic phases: ● ● ● ●

Geometrical factor, Size factor. Chemical bond factor. Electrochemical factor (electronegativity difference). Energy band factor (electron concentration).

Some aspects of the mentioned relationships have been presented in previous chapters while discussing special characteristics of the alloying behaviour. The reader is especially directed to Chapter 2 for the role played by some factors in the definition of phase equilibria aspects, such as compound formation capability, solid solution formation and their relationships with the Mendeleev Number and Pettifor and Villars maps. Stability and enthalpy of formation of alloys and Miedema’s model and parameters have also been briefly commented on. In Chapter 3, mainly dedicated to the structural characteristics of the intermetallic phases, a number of comments have been reported about the effects of different factors, such as geometrical factor, atomic dimension factor, etc. on these characteristics. In the following paragraphs a few more remarks will be made on this matter. Emphasis, however, will be especially given to those aspects which are more directly related to the positions in the Periodic Table of the metals involved, and reference will be made to this in the presentation of systematic alloying behaviour schemes.

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4.3.2 Atomic dimensions, interatomic distances in the intermetallic phases 4.3.2.1 Atomic radii and volumes. (Pauling’s rule, Vegard’s and Biltz-Zen’s formulae) With reference also to the previous paragraphs, some comments about the atomic dimension concept will help to present some characteristic parameters and diagrams, such as space-filling parameters, reduced strain parameters, nearneighbours diagrams, etc. As an introduction to this subject, it is necessary to mention the fundamental contribution by Viktor M. Goldschmidt (Goldschmidt 1928): mineralogist, geochemist and one of the founders of crystal chemistry. By considering the data concerning the crystal structures of several metals, the distance of closest approach of the atoms was assumed equal to twice the radius of hypothetical tangent spheres. In a body centred cubic cI2-type structure this distance is a3/2; in a cF4-type structure it is a2/2, where a is the unit cell edge, etc. Such direct comparison was made for a number of elements, in their stable crystalline forms, and completed with an analysis made by extrapolation of the interatomic distances found in alloys, in order to deduce the interatomic distances for unstable crystalline forms. As a result, Goldschmidt found for a given metallic element that in general the interatomic distance is about 3% less when the CN is 8 than when it is 12, it is 4% less when CN is 5 than when it is 12, and 12% less when it is 4 than when it is 12. Twice the radius for coordination 12, determined directly or deduced by extrapolation, is called the Goldschmidt atomic diameter. We underline these results and the implied concepts quoting from a comprehensive review on this subject (Simon 1983). We remember indeed that, ever since it was experimentally possible to determine atomic distances in molecules and crystals, efforts have been made to draw conclusions about the nature of the chemical bonding, and to compare interatomic distances (dimensions) in the compounds with those in the chemical elements. Distances between atoms in an element can be measured with high precision. As such, however, they cannot be simply used in predicting interatomic distances in the compounds. In a rational procedure, reference values (atomic radii) have to be ‘extracted’ from the individual (interatomic distances) measured values. Various functions have been suggested for this purpose. In the specific case of the metals it has been pointed out that interatomic distances depend primarily on the number of ligands and on the number of valence electrons of the atoms (Pearson 1972). Pauling has found empirically that there was a simple logarithmic relationship between the bond length R and the bond order Θ, namely: RΘ R1 A log10Θ

(4.1)

where A is a constant that depends on the particular element. For example, as well known, the single, double and triple carbon–carbon bond length decreases from

Intermetallic Reactivity Trends in the Periodic Table

239

151 to 134 to 120 pm as the bond order increases from 1 to 2 to 3. In order to account for fractional bonds that arise due to resonance in carbon systems or metals, Pauling defined the resonant bond order by Θ N/z where N is the number of valence electrons per atom available for forming resonating electron-pair bonds between the z neighbours. Pauling showed that the above logarithmic relationship was valid not only for organic systems but also for transition metals, where A took the value of 0.6 Å, provided N was suitably chosen across the transition metal series. The quantifications of the valence-bond concept, of the bond order within the molecular-orbital framework, and a theoretical recovery of the empirical logarithmic relationship were discussed by Pettifor (2000). Pauling’s rule (Pauling 1947): Rn R1 30 log10 n (pm)

(4.2)

it relates the radius for bond order (bond strength) n (number of valence electron per ligand) to that of strength 1. It gives a mean of correcting radii for coordination and/or for effective valence. It has been shown (Pearson 1972, Simon 1983) that, no matter what the limitations may be of any particular set of metallic radii (or valences) that is adopted, Pauling’s relation appears to be reliable, giving a basis for comparing interatomic distances in metals. According to Simon (1983) slightly better results could be obtained by changing Pauling’s formula to: Rn R1(1 A log10 n)

(4.3)

where A is not a constant, but can be represented as a function of the element valence. The next point is to select a set of atomic radii which can be used when discussing interatomic distances. The radii given by Teatum et al. (1968), and reported in the different paragraphs of the Chapter 5 dedicated to the specific metals together with the assumed ‘valences’, are probably the most useful for discussing metallic alloys. These radii have been reported for a CN of 12; they were taken from the observed interatomic distances in the f.c. cubic cF4-Cu type structure and in the hexagonal close-packed hP2-Mg type structure (averaging the distances of the first two groups of six neighbours, if the axial ratio does not have the ideal (8/3) 1.633 … value) or from the b.c. cI2-W type. Since the coordination is 8 in the cI2-W type structure, for the elements having this structure the observed radii were converted to coordination 12 by using a correction given by the formula: RCN 12 1.0316 RCN 8 0.532 (pm)

(4.4)

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Intermetallic Chemistry

which was empirically obtained from the properties of elements having at least two allotropic modifications, cI2-W type and either cF4-Cu type or hP2-Mg type. The radii in the two structures, calculated at the same temperature by means of the known expansion coefficients, were compared and used to construct the reported equation. For the other metals, that is for the more general problem of the radius conversion from any coordination to CN 12, a percentage correction was applied by using a curve which ranges from about 3% for the conversion from CN 8 to CN 12 to about 20% for the conversion from CN 3 to CN 12, as suggested by Laves (1956) in a detailed paper dealing with several aspects of crystal structure and atomic sizes (see Fig. 4.13). As for covalent-ionic bonding, we mention a formula reported by Shomaker and Stevenson (1941) which gives the shortening of covalent bond length with increasing ionic bonding character according to: dA–B RA RB 0.09 |Δη|

(4.5)

where Δη is the electronegativity difference.

18 16

Percent correction

14 12 10 8 6 4 2 0 2

4

6

8

10

12

14

Coordination number

Figure 4.13. Atomic radii of metals and their dependence on the CN. In order to obtain the value corresponding to coordination 12, the given percent correction has to be added to the radius observed for a given CN.

241

Intermetallic Reactivity Trends in the Periodic Table

For an indication of the values of the atomic radii of the different elements and of their trend along the Periodic Table, see Figs 4.5 and 4.14. Notice the variations along each period (each horizontal sequence in Fig. 4.14) and the smaller values (and their small changes) for the metals in the middle of the transition block. Notice also in the lanthanide sequence the greater dimensions of the ‘divalent’ Eu and Yb. While dealing with atomic dimension concepts, atomic volumes may also be considered. A value of the volume per atom, Vat in a structure can be obtained from the room temperature lattice parameter data by calculating the volume of the unit cell and dividing by the number of atoms within the unit cell. An equivalent atomic radius could be obtained by computing, on the basis of the space-filling factor of the structure involved, the corresponding volume of a ‘spherical atom’, and then using the relationship Vsph 4πR3/3 (see the space-filling concepts in § 4.3.2.5). In the cP2-W type (CN 8) structure Vsph is 0.68 Vat (only a portion of the available space is occupied by the atomic ‘sphere’). In the cF4-Cu type and in the ‘ideal’ hP2-Mg type (CN 12) structures, Vsph is 0.74 Vat. Considering now the previously reported relationship between RCN 12 and RCN 8, we may compute for a given element very little volume (Vat) change in the allotropic transformation from a form with CN 12 to the form with CN 8, because the radius variation is nearly

Group number 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Figure 4.14. Atomic dimensions of the elements. In this scheme each element, represented in its position of the Periodic Table, is indicated by a circle the diameter of which is roughly proportional to the atomic radius for coordination 12 (Teatum et al. 1968).

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Intermetallic Chemistry

counterbalanced by the change in the space-filling. This is generally in agreement with the experimental observations (Pearson 1972). We will see that on the basis of the atomic dimensions of the metals involved, expressed, for instance, as RX–RY or RX/RY, many characteristic structural properties of an XnYm phase may be conveniently discussed and/or predicted (size factor effect). As a comment to the atomic dimensions concept, two ‘rules’, Vegard’s and BiltzZen’s rules, formulated for solid solutions, and to a certain extent for ordered compounds can be mentioned here. These rules, mutually incompatible, are very seldom obeyed; they may however be useful either as approximations or for defining reference behaviours. The first one, Vegard’s rule (1921), corresponds to an additivity rule for interatomic distances (or lattice parameters or ‘average’ atomic diameters). For a solid solution AxB1x (x atomic fraction) between two components of similar structure it takes the form (dAB interatomic distance, dA and dB atomic diameters): dAB xdA (1 x)dB

(4.6)

The Biltz (1934) or Zen (1956) rule has been formulated as a volume additivity rule: VAB xVA (1 x)VB

(4.7)

These rules are only roughly verified in the general case. For the evaluation of interatomic distances weighted according to the composition and for a discussion on the calculation and prediction of the deviations from Vegard’s rule, see Pearson (1972) and Simon (1983). According to Goldschmidt (1928) the two ‘rules’ may be represented by only one more general expression: dABn xdAn (1 x)dBn

(4.8)

where n (1 or 3 in the two mentioned hypotheses) has to be determined in the different cases. As contributions to the general issue of predicting the variation of the average atomic volume in alloying a few different approaches can be mentioned. Miedema and Niessen (1982) calculated atomic volumes and volume contractions on the basis of the same model and parameters used for the evaluation of the formation enthalpy of the alloy (see § 2.2.1.3). In a simple model proposed by Hafner (1985) no difference of electronegativity and no charge transfer were considered. Volume and energy changes in the alloy formation were essentially related to elastic effects. Good results have been obtained for alloys formed between s and p block-elements. An empirical approach has been suggested by Merlo (1988). Deviations from the

Intermetallic Reactivity Trends in the Periodic Table

243

Biltz–Zen trend have been discussed and represented as a function of a ‘charge transfer atomic parameter’ which correlates with Pauling’s electronegativity. This approach has been successfully employed for groups of binary alloys formed by the alkaline earths and the divalent rare earth elements. In a review on this subject (Fornasini and Merlo 2006), the binary phases MeXn formed by Me Ca, Sr, Ba, Eu and Yb with Li, Be and with the elements from the groups 7th to 15th (X) were considered. For some details on these alloys see § 5.4.4.3. For several series of this group of alloys, the experimental trend vs. composition of the average atomic volume (Vexp) was compared with the reference linear trend of the alloy volume (Vcal) additively calculated. Generally a volume contraction (ΔV Vcal Vexp) was observed. Fornasini and Merlo studied the so-called ‘integral volume effect’ represented in the V vs. x diagram by the area contained between the calculated and experimental lines and given by: 1

ΔVint

∫

(Vcal Vexp )dx

(4.9)

0

For the group of alloys considered, the trend of this quantity vs. the position in the Periodic Table of the partner element X was discussed. High values were observed for the alloys of Ni, Pd, Pt, Hg and a roughly regular trend was noticed from a minimum within the region of the Cu, Ag, Zn, Cd alloys to a maximum for the As, Sb and Bi compounds. For a given X element, the highest ΔVint values were generally shown by the Sr and Ba alloys, while lower (and comparable) values were observed for the Ca, Eu and Yb phases. Empirical correlations for the prediction of the ΔVint values were discussed and possible relations examined between volume changes and heats of formation. As previously remarked, negative experimental deviations from additive rules and values of the volume contractions have sometimes been considered as an approximate indication of the formation of strong bonds and related to more or less negative enthalpies of formation. Kubaschewski (1967), for instance, discussed several ideas on the relationships between volume changes (and coordination changes) and heats of formation. However, the indication obtained is only very poor in the general case. For selected groups of alloys, the existence of a correlation between the formation volume and (ΔformV and ΔformH) has been pointed out, even if only as an evaluation of relative trends. 4.3.2.2 Relationship between ΔformV and ΔformH for selected groups of alloys. Gschneidner’s formulae. With reference to the previous considerations, for particular groups of alloys relationships between ΔformV and phase stability may be suggested. This is the case of the rare earth (R) alloys. As noticed by Gschneidner

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(1969), considering the trivalent members of the lanthanide series, we may compare the decreasing atomic volume observed in the metals (R) (lanthanide contraction) with the decreasing of the average atomic volume measured in a series of RMeX compounds with a metal Me. If this diminution is more (less) severe in the compounds than in the R metal series, this is considered an indication that the bonding strength in the RMeX compounds increases (decreases) as we proceed along the series from La to Lu; the heats of formation are expected to increase (decrease) in the same order. To make this comparison, the unit cell volumes of the compounds are divided by the atomic volumes of the pure metals. The volume ratios for the series of compounds are then divided by that corresponding to a selected rare earth, giving a relative scale. If the resultant values increase with the atomic number of the rare earth, then the lanthanide contraction is less severe in the compounds in comparison to the rare earth element, and a decrease of the heat of formation is expected. Conversely, if the relative volume ratio decreases, an increase of the heat of formation (more negative enthalpy of formation) is expected. Examples of this correspondence are examined in Fig. 4.15. 4.3.2.3 Atomic dimensions and an example of stability multi-diagrams. The role of atomic dimensions in defining the alloying behaviour can be highlighted considering characteristic ‘families’ of metals and alloys, such as, for instance, a selected group of alloys of the rare earths. The rare earth metals (R metals), that is, Sc, Y and the lanthanides, and especially the so-called ‘trivalent’ ones, that is with the exception of the ‘divalent’ europium and ytterbium, form a characteristic group of elements within which several properties change according to systematic well-defined patterns. A few details on this point are given in Chapter 5, in the paragraphs dedicated to this family of metals. This behaviour is reflected in a number of regularities that can be noticed when examining the alloy systems formed by the different rare earth metals with a given element, and when considering the progressive change of the constitutional properties of these alloys on passing from one lanthanide to the next one. The binary (R–Mg) and ternary (R –R–Mg) magnesium alloys with one or two different rare earth metals form a group of systems which may be particularly illustrative as an example of a special alloying behaviour and also as an application of a method (the multi-diagrams) which can be convenient for a compact and systematic presentation of the general alloying behaviour of alloy families. A multidiagram is just an assembly of different phase diagrams arranged according to certain rules, conveniently summarizing the behaviour of several alloys systems. In a number of favourable cases, this may give an indication of factors on which the alloy stability depends. Figs. 4.16 and 4.17 show a summary of the alloying behaviour of Mg with the different rare earths through a selection of the various binary diagrams. As far as the trivalent rare earths are concerned, on passing from one rare

245

Intermetallic Reactivity Trends in the Periodic Table

Volume ratio relative to Cerium

ΔHf (kJ/mol of atoms)

(a) −30

RIn3

RTl3

−40 −50 −60 (b) 1.1 1.0 0.9 (c)

Reduced melting temperatures

1.3 1.1 0.9 0.7 0.5

Ce Nd Sm Gd Dy La

Pr

Pm Eu

Tb

Er

Yb

Ho Tm

Lu

Ce Nd Sm Gd Dy La

Pr

Pm Eu

Tb

Er

Yb

Ho Tm

Lu

Figure 4.15. Gschneidner’s plot for two groups of rare earth alloys (RIn3 and RTl3 compounds). The following data are reported as a function of R atomic number: (a) formation enthalpy; (b) volume ratio relative to cerium; (c) reduced melting temperature TR. This is the ratio (K/K) of the melting point of the phase and of the melting point of the involved metal (( ) experimental values and (䊊) hypothetical values (reference values) of TR computed for compounds assumed to have a constant melting point). The difference between the experimental and computed slopes of the TR curves is considered to be an indication of the thermal stability variation of the phases along the series. In these cases, all the diagrams show, for the two groups of alloys, decreasing phase stability for an increase of the atomic number.

•

earth to the next we have a progressive change in the shape of the equilibrium curves and a more or less gradual change in the stoichiometries of the compounds. These changes may be compared with the progressive change of the melting point of the lanthanide which becomes higher and higher on moving from the first to the last one. The similarity between the Y–Mg system diagram and those given by the first heavy earths is remarkable. This may be related to the similar atomic dimension of Y and Dy or Ho. On the other hand, the different behaviour of the divalent

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Intermetallic Chemistry

1500

1500

1000

1000

500

500

La

Mg

Pr

1500

1500

1000

1000

500

500

Gd

Mg

Dy

1500

1500

1000

1000

500

500

Er 0

50

Mg

Mg

Y

100

0

Mg

Mg 50

100

Figure 4.16. Rare earth–magnesium binary systems. A few selected diagrams of ‘trivalent’ lanthanides are shown. Notice the progressive regular changes on passing from the ‘light’ to the ‘heavy’ lanthanides. Notice also the similarity of the Y–Mg diagram with those of the heavy lanthanides.

lanthanides and their analogy with another divalent metal, such as the alkaline earth calcium, can be noticed when comparing the Yb–Mg and Ca–Mg diagrams. As for the trivalent lanthanides (and Y) their compounds with Mg correspond to the following formulae and structure types: RMg12 (oI338-CeMg12 type, R La and Ce and tI26-ThMn12 type for Ce and Pr); R2Mg17 (hP38-Th2Ni17, R La, Ce); R5Mg41 (tI92-Ce5Mg41, R La, Ce, Pr, Nd, Sm);

247

Intermetallic Reactivity Trends in the Periodic Table 1500

1500

1000

1000

500

500

Yb 0

50

Mg

Ca

100

0

Mg 50

100

at.% Mg

Figure 4.17. The binary phase diagrams of the magnesium alloy systems with the divalent metals ytterbium and calcium (Ca is a typical alkaline earth metal and Yb one of the divalent lanthanides). Notice, for this pair of metals, the close similarity of their alloy systems with Mg. The compounds YbMg2 and CaMg2 are isostructural, hexagonal hP12-MgZn2 type.

RMg5 χ1 (cF448-GdMg5 type, R Sm, Gd, Tb); R5Mg24 χ2 (cI58 αMn, Ti5Re24 type, R Y, Tb, Dy, Ho, Er, Tm, Lu) having a composition very close to that of previous χ1; RMg3 (cF16-BiF3 type, R La, Ce, Pr, Nd, Sm, Gd, Tb, Dy); RMg2 (cF24-Cu2Mg type R La, Ce, Pr, Nd, Sm, Gd stable only at high temperature for La, Ce, Pr, Nd, or hP12-MgZn2 type R Y, Tb, Dy, Ho, Er, Tm, Lu); RMg (cP2-CsCl type R Y, La to Lu); R2Mg (high temperature phase, cI2-W type R Ho, Er, Tm). These data are summarized and collected in the multi-diagram of Fig. 4.18, prepared as a collection of isothermal sections of the different R–Mg phase diagrams. In Fig. 4.18 the La–Mg, Ce–Mg, Pr–Mg, etc. segments representing these sections have been placed side by side in a triangle with the Mg vertices in common. The points corresponding to the different R have been placed on the opposite side of the triangle in positions corresponding to their atomic dimensions. The values of the ionic radii (R3) resulted in a convenient measure of these dimensions. The intermediate phases formed in the various binary systems have been represented, in a first approximation, as point compounds. The points, which in the different binaries correspond to phases having the same composition and structure, have then been connected, defining multi-component ternary stability fields (in this case, line fields). On each horizontal line of this multi-diagram triangle the same overall composition is found (the same Mg content and the same total

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Intermetallic Chemistry Mg R2Mg17

χ1

80

χ2

RMg12 R5Mg41 ~RMg5 RMg3

Mg

HT

c

h

RMg2

at.

%

60

RMg 40 HT

~R2Mg

20

103.2

101

99 98.3

97

95.8 94.7 93.8 92.8

La

Ce

Pr Nd Pm Sm

Gd Tb

Eu(3 +)

91.2 90.1

Dy

89

88 86.8 86.1

Ho Er Tm Y

Lu

Yb(3+)

Figure 4.18. Multi-diagram of the Mg alloys of the trivalent rare earths. Isothermal sections of the different R-Mg diagrams (La–Mg, Ce–Mg, Pr–Mg, etc.) are arranged in a triangle with Mg placed at the common vertex. On the multi-element side of the triangle, the trivalent lanthanides (and yttrium) have been placed according to their atomic dimensions, which, in this case, are appropriately represented by the radii of the trivalent ions. The values, in pm, of the radii are shown. The horizontal segments inside the triangle connect the isostructural phases of the different binary systems. Notice nearly on the same line the two separate, but overlapping, fields of the χ1 and χ2 phases. In the case of Tb both structures have been observed. The symbol HT on the RMg2 and R2Mg lines represents phases stable only at high temperature; c and h indicate the cubic and the hexagonal Laves phases RMg2.

content of rare earth metal). Notice, for instance, the formation of the RMg phases (cP2-CsCl type) with all the rare earths. The stability regions of these structures include the complete range of the atomic dimensions depicted. For the Laves type RMg2 compounds, the cubic type is given by the light R (for the first ones, only as high-temperature stable phases); the hexagonal Laves type, on the other hand, is formed with the heavy R. For different composition values notice also the intersecting stability fields of χ1 and χ2 formed for an R/Mg ratio close to 1/5.

Intermetallic Reactivity Trends in the Periodic Table

249

In the limits of an alloying behaviour almost solely dependent on the atomic dimension parameter, it should not be relevant how a certain value of the atomic dimension is obtained, that is, either as the characteristic elemental value of a pure metal (a pure lanthanide) or as the resulting averaged value of a mixture of various metals (two different lanthanides). In the specific case of the lanthanides, this behaviour may be related to the concept of pseudo-lanthanides introduced by Gschneidner (1980). A pseudo-lanthanide is defined as a material which contains in a given ratio two rare earth metals (except Sc and the divalent ones Eu and Yb) and which may be expected to display physical (constitutional) properties similar to those of the specific true lanthanide which is being simulated. A typical pseudo-lanthanide may be prepared, for instance, by alloying La and Lu. Alloys containing increasing quantities of Lu will progressively simulate the behaviour of Ce, Pr, Nd, etc. The sequence of crystal structures observed in these pseudo-lanthanides, their polymorphic transformations and melting temperatures are generally in agreement with those of the true rare earth metals. It must be noted, however, that certain physical properties which depend directly on the 4f electrons, such as the optical properties, cannot be duplicated in the pseudo-lanthanides. The behaviour, moreover, of the ‘divalent’ rare earths, Eu and Yb, which is different from that of the other ‘normal’ rare earths, cannot be simulated by a mixture of trivalent lanthanides. The multi-element side of the triangle shown in Fig. 4.18 can therefore represent (simulate) not only the pure trivalent lanthanides, but also all their mixtures. A mixture for instance of La and Gd, the representative point of which is placed somewhere between the La and Gd points, may be considered a ‘simulation’ of Pr or Sm (or even of another mixture for example of Pr and Nd) depending on its composition and on the corresponding average atomic radius. These considerations can be extended to the entire triangle of Fig. 4.18, the internal points and regions of which may be considered simulations of specific, more complex, ternary alloys and systems prepared by combination of Mg with a mixture of two lanthanides. An application of these concepts is shown in Fig.4.19 where a simulation of the diagram Y–Pr–Mg (Giovannini et al. 1995a) is obtained from the multi-diagram and compared with the experimental diagram of the same system. In the two cases (the portion of the multi-diagrams included between Pr and Y and the experimental Y–Pr–Mg diagram) we have on the Y–Pr base side a similar sequence of atomic dimensions; in the first case this corresponds to the decreasing radius of the intermediate lanthanides; in the other case to the decreasing average radius of the various Y–Pr mixtures. On the basis of the predominant role played in this case by the atomic dimensions, which defines the alloying behaviour of the lanthanide with Mg, each of the two diagrams may be considered a ‘simulation’ of the other. Notice indeed that a similar arrangement of the various single-phase fields may be observed in the two triangles.

250

Intermetallic Chemistry Mg

Mg

RMg12

PrMg12

R5Mg41

10 Pr5Mg41 Pr

χ1

at.

%

20

c

h

∗

40

RMg

Y5Mg24

∗

80

∗

PrMg3 30

RMg2

τ

Mg

RMg3

∗

90

∗

70 YMg2

∗

λ∗

60

PrMg

99 98.3

95.8

93.8 92.8 91.2 90.1

Pr Nd

Sm

Gd Tb

Dy

%

χ2

∗

a t.

~RMg5

∗

YMg 10

20

30

40

at.% Y

Y

Figure 4.19. The Y–Pr–Mg region, as ‘extracted’ from the multi-diagram of Fig. 4.18, is shown on the left. The experimentally determined isothermal section of the ternary system Y–Pr–Mg is shown on the right. (The significant regions corresponding to a Mg content higher then 50 at.% are displayed). Notice the qualitatively similar arrangement of the different phases in the two diagrams. With an increasing Mg content the following phases are observed in the two diagrams: CsCl-type phase (corresponding to the PrMg–YMg continuous solid solution); Laves phases (c and h and, in the experimental diagram, the λ phase, cubic and the hexagonal YMg2-based solid solution); RMg3 (PrMg3-based solid solution in the experimental diagram) partially extending into the ternary field; the χ1 and χ2 phases and, in the experimental diagram, the corresponding GdMg5-type ternary phase (τ) and the Y5Mg24-based solid solution and, in the Mg-richest region, the R5Mg41 and RMg12 phases partially extending in the ternary field.

Especially noteworthy is the behaviour of the χ1-phase, ideally corresponding to the cF448-GdMg5 type, which seems to be stable only for an intermediate value of the lanthanide radius. In the binary systems it is indeed observed only with Sm, Gd and Tb, but neither with Pr nor with Y. This behaviour is observed however for ternary Mg alloys with both Pr and Y, a mixture of which, with its value of the average atomic radius, simulates a lanthanide having an intermediate value of the atomic radius. Similar results have also been obtained in the investigation of a number of other Mg ternary systems with two different lanthanides: Y–La–Mg (Giovannini et al. 1995b), Y–Ce–Mg (Flandorfer et al. 1997), Y–Gd–Mg (Giovannini et al. 1997). The schemes described are useful for collecting experimental data, preparing crucial experimental work and giving some ‘predictions’, at least for selected groups of

Intermetallic Reactivity Trends in the Periodic Table

251

alloys and phases; even though not always valid and subject to experimental verification. As ‘prediction maps’ (see § 4.4.7.1), the mentioned diagrams can provide additional guidelines for planning the preparation of complex alloys and for designing their characteristics and composition. A description of other groups of alloys performed with similar maps, even if based on different parameters, is given in § 4.4.6. 4.3.2.4 Partial molar (atomic) volume. Another useful and general way of discussing the actual trend in an alloy system of the average molar dimensions, as represented for instance by the molar (average) volumes, is through the definition and use of the partial molar (atomic) volume. The partial molar quantity of a molar quantity Q, related to the component A, is – generally written as QA and is defined by: ⎛ ∂Q ⎞⎟ ⎟⎟ QA ⎜⎜⎜ ⎜⎝ ∂nA ⎟⎠ T , P,n ,n i

(4.10) A

The following rules generally apply to the partial molar quantities: Σi xi Qi Q

(4.11)

(where xi is the molar fraction of species i) and, on differentiation, Σi xi dQi 0

(4.12)

In a binary A–B system, from the graph of the integral quantity vs. composition, the partial values may be obtained, for each composition z, from the intercepts on the A and B axes of the tangent, at the composition z, to the integral curve. The construction is very simple in the special case that, in a certain range of compositions, the curve of the integral quantity is close to a straight line. As an example for the specific case of vanadium alloys with palladium, the trend of the average atomic volume of the alloys is shown in Fig. 4.20 and compared with the phase diagram. These data were obtained by Ellner (2004) who studied the solid solutions of several metals (Ti, V, Cr, Mn, Fe, Co and Ni) in palladium. The alloys were heat treated at 800°C and water-quenched. From the unit cell parameters measured by X-ray diffraction methods, the average atomic volume was obtained Vat a3/4 (see Table 4.3). These data together with those of the literature were reported in a graph, – and the partial molar (atomic) value of the vanadium volume in Pd solid solution (Vv)

252

Intermetallic Chemistry (a)

Temperature (°C)

1910

1600 1555

1200 (Pd)

(V)

Pd

10

20

PdV3

Pd2V

Pd3V

800

30

40

50

60

70

80

90

V

at.% V

Average atomic volume (V/pm3 × 106)

(b) 14.5 14.0

Vat,V

13.5 VV

13.0 12.5

Pd

10

20

30

40

50

60

70

80

90

V

at.% V

Figure 4.20. Palladium–vanadium system. In (a) the phase diagram is shown: the phase sequence at 800°C is indicated. The corresponding trend of the average atomic volume is shown in (b). For – pure vanadium the value of the partial atomic volume in Pd solution is indicated (Vv, as obtained by extrapolation from the Pd-rich alloys) and, as a reference, the elemental atomic volume (Vat,V) of the pure metal.

was obtained by extrapolation (see Fig. 4.20). This value is reported in Fig. 4.21 together with those similarly obtained for other metals. The partial atomic volumes are compared, in the same figure, with the atomic volumes of the pure non-alloyed metals. Notice that for Sc, Ti, V and Cu, Zn, Ga there is a ‘lattice compression’ in alloying – (VMe VMe), whereas for Cr, Mn, Fe, Co, Ni there is an expansion. The relation between this trend and the values of the partial molar enthalpy of formation (measured or computed) for the metal Me dissolved in Pd has also been discussed. Generally

253

Intermetallic Reactivity Trends in the Periodic Table Table 4.3. Unit cell parameters and average atomic volumes for palladium and Pd(V) solid solution (adapted from Ellner (2004)). Composition (at.%)

Unit cell parameter (face centred cubic cF4) (a/pm)

Average atomic volume (Vat /pm3 106 Vcell/4)

Average molar volume (NA Vat /cm3 mol1)

Pd Pd98V2 Pd96V4 Pd94V6 Pd92V8 Pd90V10 Pd85V15 Pd80V20

389.11 (1) 389.09(2) 388.46(2) 388.14(2) 387.84(1) 387.51(2) 386.95(1) 386.50(1)

14.728 14.726 14.655 14.619 14.585 14.548 14.484 14.434

8.869 8.868 8.825 8.804 8.783 8.761 8.772 8.692

24

Atomic volume (Å3 )

22 20 18 16 14 12 Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Cu

Zn

Ga

Figure 4.21. Solid solutions of transition metals (Me) in palladium. The elemental atomic volumes of the pure metals (VMe, open circles) and their partial atomic volumes in Pd solid – solution (VMe, filled circles) are shown (adapted from Ellner (2004)).

– increasing values of ΔHMe have been observed for an increasing value of the ‘lattice deformation’ (compression or expansion). The methodology for obtaining the partial atomic volume and its application as a ‘realistic’ measure of atomic size in metals and alloys has been discussed by Bhatia and Cahn (2005): they illustrated its use as a powerful tool in understanding the behaviour of solid solutions in both ordered and disordered states.

254

Intermetallic Chemistry

4.3.2.5 Geometrical considerations about intermetallic crystal structures. When discussing the factors which control the structures of the metallic elements, Laves (1956) proposed three interrelated principles that are mainly geometric in character and also related to the atomic dimensional characteristics: (i) The principle of highest symmetry (symmetry principle). (ii) The principle of the greatest number of connections (connection principle). (iii) The principle of efficient (economical) use of space (space-filling principle). These principles may be considered to be valid to a certain extent for the intermetallic phase structures and not only for the metallic elements. (See also some comments on this point as a result of the atomic environment analysis of the structure types summarized in § 3.7.5.) 4.3.2.5.1 The principle of highest symmetry (symmetry principle). According to Laves, a tendency to build configurations with high symmetry is evident. This tendency is particularly clear in metallic structures, especially in the simple ones. However, according to Hyde and Andersson (1989), for instance, the validity extension of this principle is difficult to evaluate. As time passes, crystallographers are able to solve more and more complex crystal structures, and these tend to have low symmetry. The symmetry principle could be restated by observing that a crystal structure has the highest symmetry compatible with the efficient use of space and the specific requirements of chemical bonding between nearest neighbours. For a discussion on the ‘symmetry principle’, its alternative formulations and the history of its development, papers by Brunner (1977) and by Bärninghausen (1980) may be consulted. In these papers a number of statements are reported which may be considered equivalent. When considering close sphere packings, the following statements are especially worthy of mention. (a) A tendency to form arrangements of high symmetry is observable. (b) Points are disposed around each point in the same way as around every other. (c) Atoms of the same type tend to be in equivalent positions. 4.3.2.5.2 The principle of the greatest number of connections (connection principle). To understand the meaning of this principle it may first be necessary to define the concept of connection. To this end we consider a certain crystal structure and imagine connecting each atom with the other atoms present in the structure by straight lines. There will be a shortest segment between any two atoms. We will

Intermetallic Reactivity Trends in the Periodic Table

255

then delete all links except the shortest ones. After this procedure, the atoms that are still connected constitute a ‘connection’. The connection is homogeneous if it consists of structurally equivalent atoms; otherwise it is a heterogeneous connection. Such connections may be finite or 1, 2, 3 dimensionally infinite and are respectively called islands, chains, nets or lattices. Symbols corresponding to the letters I, C, N, L (homogeneous connections) or i, c, n, l (heterogeneous connections) have been proposed. (See also the dimensionality indexes reported in § 3.7.3.) As pointed out by Laves (for instance, Laves 1967) metallic elements and intermetallic phases show a tendency to form multidimensional, possibly homogeneous, connections (connection principle). 4.3.2.5.3 Space-filling principle. The tendency to use space economically (to form structures with the best space-filling), which is especially exemplified by the closest packing of spheres, is considered to be the result of a specific principle which operates in metal structures (and also in ionic and, to a lesser degree, in Van der Waals structures). This principle is less applicable to covalent crystals because, for these crystals, the characteristic inter-bond angles are not necessarily compatible with an efficient use of space. Among the metallic elements, 58 metals possess a close-packed arrangement (either cubic or hexagonal) which, in the assumption that the metal atoms are non-deformable spheres having fixed diameters, corresponds to the best space-filling; 23 of the remaining metals crystallize in another highly symmetric structure, the body centred cubic, which corresponds to a slightly less efficient space-filling. The space-filling concept has been analysed and discussed by several authors, among which Laves (1956), Parthé (1961) and Pearson (1972). A short summary of this discussion will be reported in the following, together with some considerations on the atomic dimension concept itself. 4.3.2.5.4 Space-filling parameter (and curves). The space-filling parameter introduced by Laves (1956) and by Parthé (1961) is an index which may be useful in studying the relationships between atomic dimensions and structure. For a compound it is defined by the ratio between the volume of atoms, assumed as spheres of well-defined radii in a unit cell, and the volume of the unit cell itself. ϕ (4π/3) ΣiniRi3/Vcell

(4.13)

(ni, Ri are number and radius of type i atoms). To calculate the space-filling value for a specific compound, one has to know the radii of the atoms and the lattice constant. Neither of these is needed for the construction of a space-filling curve of a crystal structure type: it is sufficient to know the point positions of the atoms and the axial ratios. The curve is based on a hard sphere

256

Intermetallic Chemistry

model of the atoms: the cell edges are expressed as functions of the atomic radii (RX and RY for a binary system) for the special cases of X–X, X–Y and Y–Y contacts. The parameter can then be given (and plotted) as a function of the RX/RY ratio. Considering, for instance, the cF8-ZnS-sphalerite type structure (containing 4 Zn 4 S in the unit cell) the space-filling (Parthé 1964) can be given by: ϕ [4π/3(4R 3X 4R 3Y)]/a3

(4.14)

where a is the cubic cell edge and RX and RY are the radii of the atoms in the (a) and (c) positions in the unit cell (4 Zn in 0,0,0;0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0; and 4 S in 1⁄4, 1⁄4, 1⁄4; 1⁄4, 3⁄4, 3⁄4; 3⁄4, 3⁄4, 1⁄4; 3⁄4, 1⁄4, 3⁄4; respectively). See the structure description in Chapter 7. In the case that the two atoms (or, more accurately, the hard spheres) occupying the Zn and S sites are touching each other, then the sum of the two radii must be equal to one-quarter of the cubic cell diagonal: RX RY a 3/4

(4.15)

By expressing the unit cell volume as a function of the sum of the radii: ϕ (4π/3)(4R X3 4 R Y3)/[(43/33)(R X R Y)3]

(4.16)

Introducing the radius ratio ε RX/RY: ϕ (–3π/4) (ε3 1)/(ε 1)3

(4.17)

This equation describes the middle section (0.225 ε 4.44) of the space-filling curve for the sphalerite type structure plotted (with log scales) in Fig. 4.22. The other sections, 0 ε 0.225 and 4.44 ε l correspond to the cases in which Y–Y atoms or X–X atoms are touching. In the ϕ vs. ε diagram every structure type is generally characterized by its own individually shaped space-filling curve. The space-filling curves, however, of all binary structures belonging to one homeotect structure set coincide with one curve (see § 3.9.2). By assuming appropriate values for the radii RX and RY it is possible to compare the points representing the actual compound with the specific curve of a given structure. Generally a good agreement is found for ionic structures (and/or compounds) while it is often observed that the ϕ vs. ε points for particular metallic phases lie above the space-filling curves, indicating a denser packing and emphasizing the lack of unique radii associated with X–X, X–Y, etc. contacts (compressible

Intermetallic Reactivity Trends in the Periodic Table

257

0.9 0.8 0.7 0.6

CsCI

j

NaCI

0.5

0.4 NaTI 0.225

0.3 0.2

ZnS 0.414

0.3 0.4

0.731

1.365

0.6 0.8 1.0

2.42

2.0

4.44

3.0 4.0 5.0

ε = Rx /Ry

Figure 4.22. Space-filling curves for compounds having the NaCl, CsCl, NaTl or ZnS type structures. For the different structures, the ratio ϕ between the volume of atoms (assumed as spheres of well-defined radii) contained in the unit cell and the volume of the unit cell itself is shown as a function of the ratio between the radii of the two atom types. (Notice the log scales.)

atom model) (Pearson 1972). In the specific case of unary structures (element structures), providing that there are no variable atomic positional parameters or axial ratios, there is a unique space-filling parameter (independent of atomic size for every structure type). For the cF4-Cu type structure, for instance. ϕ (4π/3)(4R3/a3)

(4.18)

Assuming the atoms to be hard spheres a 22 R, then ϕ π/(32 ) 0.740 (which is the highest value for an infinite collection of close-packed hard spheres of the same radius). Typical space-filling parameters of elemental structures are the following: cF4-Cu type ϕ 0.740 hP2-Mg type ϕ 0.740 (for the ‘ideal’ value, c/a 1.633.., of the axial ratio, ϕ 0.65 in the case, for instance, of Zn, for which c/a 1.86) cI2-W type ϕ 0.680 tI4-β Sn type ϕ 0.535 (for c/a 0.5456) cP1-Po type ϕ 0.524 cF8-Diamond ϕ 0.340

258

Intermetallic Chemistry

Several other considerations and applications of the space-filling concept can be found in Parthé (1961), for instance: space-filling diagrams of ternary structures, applications of space-filling concept for discussing and predicting possible pressure structures, etc. Volumetric Index A treatment similar to that previously described has been made by Liu and Bassett (1986) defining a special ‘volumetric index’ α, considering that the molar volume V of a crystal must be a linear function of the cube of the nearest neighbour interatomic distance dmin 3 V αd min

(4.19)

where α is a function of the axial ratio, axial angle(s) and positional parameters of a crystal structure. Within a group of isostructural substances, small variations are therefore generally observed in the α-value. If dmin is given in nm and V in cm3/mol (moles of atoms or moles of formulae), the following α-values may be mentioned. 425.9 (cF4-Cu); 425.9 to 485.0 (hP2-Mg for 1.633 c/a 1.86); 463.6 (cI2-W); 589.7 (tI4-βSn, c/a 0.5456); 602.2 (cP1-Po); 927.2 (cF8-diamond); 927.1 (cP2CsCl); 1204.4 (cF8-NaCl); 1843 (hP4-C graphite); etc. The α-values are the slopes in the plots of molar volume vs. the cube of interatomic distances for given types of structures such as those illustrated in Fig. 4.23. These indexes (as the space-filling parameters) may be useful for instance in a systematic description of the effect of pressure on the phase transformations which may be observed for a given compound. In a discussion of high-pressure phases of elements, oxides and silicates, with implications for the Earth’s interior, Liu and Bassett (1986) presented data relevant to several families of compounds in a number of graphs such as those of Fig. 4.23. The transformations at increasing pressure from C graphite to diamond, from Si and Ge diamond type to βSn type, the modifications of a number of 1:1 compounds from NaCl to CsCl type structure and also for elements, such as Cd and Zn, the preservation of the same structure, but with c/a approaching the ‘ideal’ 1.633 value, can all be effectively summarized in this graph type. More complex considerations, however, are necessary when a change in the ‘valence’ of specific atoms and significant changes in their own volume occur as a function of pressure. Reduced dimensional parameters (strain parameters and near-neighbours diagrams) By comparing the space-filling theoretical curves and the actual values of intermetallic phases it has been observed that an incompressible sphere model of the atom gives only a rough description when discussing metallic structures.

259

Intermetallic Reactivity Trends in the Periodic Table

3

3′ z

4 5 ′′

5′

5

-C s P2

8 -N aC I an

dc

cF

hp4 -C

d) on

40

20 4-

cF

Po =1 1/a cP g c M 2.63 hP =1 /a c -W Mg cI2 2hP d an

Cu

0.05 3

d min

n

βS 4-

t1 .86

ia m (d

2

60 C

y

cF 8-

Molar volume

1

Molar volume (cm3/mol)

80 x

CI

(b) (gra phit e)

(a)

0.10

3

d min (nm3)

Figure 4.23. Molar volumes, VM, of selected groups of phases as a function of nearest neighbours interatomic distances (dmin). On the left a schematic trend is shown for hypothetical X, Y, Z, structural types. Generally a single straight line corresponds to each structure. The range of values assigned to Y could represent a structure for which, for instance, owing to different c/a axial ratios, different values of VM may correspond to the same dmin. The arrows 1 : 2, 2 : 3 or 2 : 3 , etc. represent different structure transformations observed by increasing pressure. On the right, the trends calculated for a group of common crystal structure types are shown.

Pearson (1972) suggested the use of a model which allows the atoms of a binary X–Y alloy to be compressed until, according to the structure geometry, X–X, X–Y are Y–Y contacts are established. The contacts are considered to occur when the X–X, X–Y and Y–Y interatomic distances in the compound structure, dX, dXY and dY are equal to 2 RX (DX), RX RY and 2 RY (DY) (RX, RY, DX, DY are the atomic radii and diameters, respectively). According to Pearson, the metallic radii chosen are those appropriate for the coordination of the atoms. The distances between all the close atoms in the structure may be expressed in terms of the cell (and atomic site) parameters. As an example, see the phases XY3, AuCu3 type, described in §3.7.7 and in Figs. 3.27 through 3.29. In these phases around each X atom there are 6X atoms at a distance equal to the unit cell edge dX a. Around the X atoms there are 12Y atoms at a distance dXY a2/2, and around the Y atoms 8Y and 4X atoms at the same distance dY a2/2. All these distances may then be expressed as a function of one of them, selected as a reference. In the case of the AuCu3 type phase, for instance: dXY dX 2/2,

dY dX 2/2

(4.20)

260

Intermetallic Chemistry

A reduced strain parameter is then defined with reference to an arbitrarily selected set of contacts. With reference to the dX distances the strain parameter may be defined as: S (DX dX)/DY. This parameter gives an indication of the atomic dimension compression. It is computed, as a function of the ratio ε DX/DY RX/RY, for the different kinds of interatomic contact. In the aforementioned AuCu3-type phases, we have three cases corresponding to X–X, X–Y and Y–Y contacts. If X–X atoms are touching dX DX, then the strain parameter SXX will be (DX dX)/DY 0

(4.21)

– for all the ε values. If X–Y atoms are considered to be in contact, dXY dX2/2 will be equal to 1⁄2(DX DY) so we will have: SX–Y DX/DY dX/DY DX/DY dXY2/DY DX/D Y (1⁄22Dx 1⁄22Dy)/DY

(4.22)

If, on the other hand, the Y–Y atoms are those which are considered to be in contact we will have: dY dX2/2 DY; dX DY2

(4.23)

SYY DX/DY 2Dy/DY DX/DY 2

(4.24)

and:

The values of the strain parameters are then plotted, according to Pearson (1972), as a function of ε RX/RY. Several straight lines are obtained (see Fig. 4.24). The lines corresponding to the reference contacts are horizontal and set at zero. What matters is only the relative position of the different straight lines (which does not change by taking another contact as the reference one: a rotation will only be obtained of the whole diagram). The diagram is called near-neighbour diagram. In the diagram, points may also be plotted which represent actual phases. To this end the experimental dX, dXY, etc., values will be used. According to Pearson (1972), when a point representing a specific phase has a larger value of the strain parameter than that of a particular contact line, then the contacts corresponding to that line are to be considered compressed, on the basis of the DX and DY assumed for the components. If, on the other hand, the experimental points lie below a line then those contacts have not been established. Fig. 4.24(a)–(c) represent the data and the trends for a few structure types. For compounds having the cF8-ZnS sphalerite structure it can be seen that the X–Y (Zn–S)

261

Intermetallic Reactivity Trends in the Periodic Table (a) XY3 (AuCu3 type)

8

Y Y− X−X

Strain parameter

0

6

−0.2

X−Y

12−4

−0.4

−0.6 0.6

0.8

1.0

1.2

1.4

1.6

e = Rx /Ry (b)

(c) XY2 (Cu2Mg type)

XY (ZnS type) 12

Y–

Y

0.4

0.6

0.2

Y–

Y X– 12–6 0.2

X–X

0

Strain parameter

Strain parameter

6 Y

0.4

X–X

0

12

−0.2 −0.4

4–4

4 −0.6

1.0

1.2

1.4

e = Rx /Ry

1.6

X–Y

0.6

0.8

1.0

1.2

1.4

1.6

e = Rx /Ry

Figure 4.24. Near-neighbour diagrams for binary phases calculated according to Pearson (1972) for a few structural types. The lines calculated for the different interatomic contacts are shown. The numbers of contacts X–Y, Y–X, X–X, etc. are indicated. The experimental values determined for the various compounds are contained, for each structure type, within the hatched fields. (a) XY3 compounds belonging to the cP4-AuCu3 structural type; (b) XY2 Laves phases of the cF24-Cu2Mg type; (c) XY compounds of the cF8-ZnS structural type. Notice the importance of the high coordination contacts in the more metallic phases, whereas in the ZnS-type compounds the role of the chemical bond factor is clearly relevant.

262

Intermetallic Chemistry

bonds, corresponding to a tetrahedral coordination, are the most important in controlling the structural characteristics. The different experimental points, representing actual compounds, are very close indeed, for a wide range of diameter ratios and of electronegativity differences, to the line corresponding to the X–Y contacts (the X–X and Y–Y contacts are not formed). The structure can, therefore, be considered as formed by a skeleton of presumably covalent X–Y bonds (directional in character). An X–Y chemical bond can similarly be recognized as important in several compounds having cF12-CaF2 type (or antitype), cF16-Li3Bi, hP3-CdI2, hP8-Na3As, etc., type structures. The different behaviours of more ‘metallic’ phases can be seen in Fig. 4.24(a) and (b). The AuCu3 type near-neighbour diagram (Fig. 4.24(a)) shows the importance of contacts corresponding to high coordinations. A similar trend can be observed for the XY2 Cu2Mg-type Laves phases (see Fig. 4.24(b)) for which, moreover, a certain compression of the X–X contacts generally results. The X–X curve is, for ε 1.25, far below the data points. Many near-neighbour diagrams have been presented by Pearson (1972) and systematically discussed for several structure types in order to show the importance of parameters such as geometrical or chemical bond factors in controlling the occurrence and structural characteristics of different phases. For an analysis of the meaning and the applications of these diagrams, see also Simon (1983). A representation of structure families for alloy phases with given XYn compositions has been presented, in generalized near-neighbour diagrams, and discussed. 4.4. REMARKS ON THE CHEMICAL BOND FACTOR AND VALENCE-ELECTRON COUNTING RULES

… …the name is BOND, Chemical bond… …. (Paraphrase of Fleming’s 007 saga)

4.4.1 Introduction A chemical bond factor can be considered to control the structure when interatomic distances, and as a consequence unit cell dimensions, can be said to be determined by a particular set of chemical bonds. Two extreme situations can be taken into consideration (these are especially well defined when small atomic groups are involved): (i) Bonds having high ionic characteristics: these are largely non-directional; the larger anions tend to form symmetrical coordination polyhedra subjected to limitations related to the anion/cation atomic size ratio and the stoichiometry of the compounds is controlled by the balance of the ionic electric charges.

Intermetallic Reactivity Trends in the Periodic Table

263

(ii) Bonds having covalent character: the localized covalent bond has generally a short range of action (where generally there is a strong bond) extending only from one atom to the next one. The directional and ‘saturation’ characteristics related to this bonding mechanism tend to determine the structural and stoichiometric arrangements in the phase. 4.4.2 Normal valence compound rule To an increasing weight of the chemical bond factor (ionic and/or covalent bonding) will correspond, as an extreme case, the formation of valence compounds. According to Parthé (1980), a compound CmAn can be called a normal valence compound if the number of valence electrons of cations (eC) and anions (eA) correspond to the relation meC n(8 – eA) (normal valence compound rule, octet rule)

(4.25)

If we consider only the s and p block elements without the noble gases, the number of valence electrons of the elements is included between 1 and 7. In this case, considering that no anions are formed from the elements of groups 1, 2 and 3, the following formulae can be deduced for the normal valence compounds, formed in binary systems with large electronegativity difference between elements: – 144 – 224 – 3443 – 135 – 2352 – 35 – 4354 – 126 – 26 – 3263 – 462 – 5265 – 17 – 272 – 373 – 474 – 575 – 676 In these formulae each element is indicated by a number corresponding to its number of valence electrons; for instance: 17 indicates NaCl or KCl, KBr; 3263 indicates Al2O3, etc. In the more general case where some electrons are also considered to be used for bonds between cations or between anions we have: m(eC eCC) n(8 – eA – eAA) (general valence compound rule)

(4.26 a)

In this formula, which can only be applied if all bonds are two-electron bonds and additional electrons remain inactive in non-bonding orbitals (or, in other words, if the compound is semiconductor and has non-metallic properties), eCC is the average number of valence electrons per cation which remain with the cation either in nonbonding orbitals or (in polycationic valence compounds) in cation9cation bonds; similarly eAA can be assumed to be the average number of anion9anion electron-pair bonds per anion (in polyanionic valence compounds).

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Notice, moreover, that the last equation may be rewritten in the form: m(eC – eCC – eip) n(8 – eA – eAA) (general valence compound rule) (4.26b) if we wish to explicitly indicate the number of not available electrons, eip, such as the inert pair 6s2 in Tl. When one component in a binary alloy is very electropositive relative to the other, there is a strong tendency to form compounds of high stability in which valence rules are satisfied (Pearson 1972). Such alloys are considered to show a strong electrochemical factor. 4.4.2.1 ‘Tetrahedral structures’. In a more limited field than that of the previously considered general octet rule, it may be useful to mention the ‘tetrahedral structures’ which form a subset of the general valence compounds. According to Parthé (1963, 1964, 1991), if each atom in a structure is surrounded by four nearest neighbours at the corner of a tetrahedron, the structure is called ‘normal tetrahedral structure’. In accordance with Parthé (1964), a few more details about these structures are introduced. In a normal tetrahedral structure every atom has 4 near neighbours at the vertices of a surrounding tetrahedron. The shape of such a tetrahedron will determine regular and distorted tetrahedral structures. In a defect tetrahedral structure not all the four vertices are occupied by an atom. A filled tetrahedral structure contains extra-atoms inserted in a normal tetrahedral structure. The bonding mechanism, however, may be different from that of the other tetrahedral structures and, generally, less simple relations are observed between the number of valence electrons and structure. The general formula of the normal tetrahedral structure, for the compound CmAn, is: (meC neA) 4(m n)

(4.27)

that may be considered a formulation of the so-called Grimm and Sommerfeld Rule (1926). For the same elements previously mentioned the possible combinations are: 4X4Y (all compositions, for instance, C, Ge, SiC) 35 (BP, AlSb, etc.), 26 (BeO, MgTe, ZnS), 17 (CuBr, AgI), 326, 337, 252 (ZnP2, ZnAs2), 2372, 153 and 1263.

Intermetallic Reactivity Trends in the Periodic Table

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For instance, for a compound 2372 we have, according to the formula reported (3 2 2 7) 4 (3 2) Ternary or more complex combinations may be obtained by a convenient addition of different binary formulae; for instance: 14253 (153 44): for instance CuGe2P3 1362 (1263 326)/2: CuAlS2, CuInTe2, etc. 122464 (1263 26 4): for instance Cu2FeSnS4 (FeII), etc. The aforementioned rule may be extended to include the ‘defect tetrahedral structures’ where some atoms have less than four neighbours: (meC neA) 4(m n) NNBO(m n) (general tetrahedral structure) (4.28) In this formula NNBO is the average number of non-bonding orbitals per atom. By adding the symbol 0 (zero) to the described notation, vacant tetrahedral sites can be represented. Examples of formulae of defect tetrahedral structures are: 40374 (SiI4, SnI4); 4062 (GeS2); 3605463 (Ga6As4Se3), 1252064 (CuSbS2); etc. Notice that the aforementioned compositional scheme is a necessary condition for building the tetrahedral structures, but not every compound that fulfils this condition is a tetrahedral compound. The influence of other parameters, such as the electronegativity difference, has been pointed out. By means of diagrams, such as that reported by Mooser and Pearson (1959) (average principal quantum number vs. electronegativity difference) the separation of tetrahedral structures from other structures can be evidenced. 4.4.2.2 Valence compounds: notes for a classification (VEC and partial VEC). In several compounds, the so-called Valence-Electron Concentration (VEC) proved to be a parameter relevant to their composition, structure and stability. For a compound CmAn the VEC parameter is defined by: VEC

meC neA mn

(average valence -electron numb ber per atom) (4.29)

where m and n are the composition indexes in the formula and eC and eA the numbers of valence electrons of the elements C and A.

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Notice that for the alkali and alkaline earth metals and all the elements to the right of the 10th group the valence-electron numbers are 1, 2 and, respectively assumed to be given by the group number minus 10. For the transition elements, various assumptions have been used in some cases. For certain families of compounds it may be convenient to separate the VEC into partial VEC values. It is possible to define the following partial VEC values (Parthé 1969) relative to the ‘cationic’ and ‘anionic’ components: VECC

meC neA m

(4.30a)

VEC A

meC neA n

(4.30b)

and

According to the conventional simple chemical definition, the valence compounds are those in which individual atoms are assumed to reach a ‘filled valence shell’ by accepting, donating or sharing electrons. This definition was first applied to the compounds (normal valence compounds) where the cations may donate the exact number of electrons to complete the valence shells (particularly the octet shells) of every anion. In this case we have: VECA (VECanion) 8

(normal valence compound)

(4.31)

This concept was then extended to include compounds having anion9anion or cation9cation bonds, that is, the so-called polyanionic or polycationic valence compounds, assuming: VECanion 8

(polyanionic valence compounds)

(4.32a)

VECanion 8

(polycationic valence compounds)

(4.32b)

and

Intermetallic Reactivity Trends in the Periodic Table

267

These relations may be included in the following general formula (Parthé 1969, compare with (4.25)): VECanion 8

m e eAA n CC

(4.33)

in which eCC is the average number of cation9cation bonds per cation (the average number of electrons per cation not involved in cation9anion bonds) and eAA is the average number of anion9anion bonds per anion. This equation can be applied if all bonds are two–electron bonds and additional electrons are inactive in non-bonding orbitals of cations and anions. These compounds are therefore semiconductors; the equation is not applicable to compounds of metallic character. Similar classification criteria may be made by using the total valence–electron concentration previously defined (see equation 4.27) and defining, according to Parthé (1995) the tetrahedral structure equation: meC neA VEC 4 N NBO mn

(4.34)

According to Parthé (1995) a convenient description and classification of several structures of several tetrahedral compounds may be performed as in the following: VEC 4: a tetrahedral structure cannot be formed. VEC 4: a normal tetrahedral structure is formed with NNBO 0. VEC 4: a compound with a defect tetrahedral structure may be obtained with NNBO 0. 4.4.3 Polyanionic compounds 4.4.3.1 Zintl phases: an introduction. The Zintl phases are a large number of substances which in a way may represent a bridge, a transition, between the ionic and the intermetallic compounds. The expression ‘Zintl Phases’ was introduced by Laves (1941) in recognition of the work carried out by E. Zintl. In papers describing new compounds of this family, Jiang et al. (2005), Jiang and Kanzlarich (2006) reminded that Zintl phases are valence-specific compounds formed between electropositive elements, such as alkali metals, alkaline earth metals, or rare earth elements, and the main group elements. There are a significant number of Zintl compounds of the alkali or alkaline earth metals with the elements of the 13th through 16th groups. Although less is known about the rare earth compounds, Jiang et al. (2005) underlined a recent flurry of research on them because of their promising thermoelectric properties. Superconductivity has been discovered in

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several Zintl compounds. Moreover unique magnetic, electronic, magneto-resistive properties have been observed in several new compounds. A comprehensive book on chemistry, structure and bonding of Zintl compounds has been edited by Kauzlarich (1996); in this book several aspects of Zintl phases such as structural patterns, molecular transition complexes of Zintl ions, transition metal Zintl compounds are deeply discussed. A traditional example of a Zintl phase is represented by NaTl which may be considered as a prototype of the Zintl rules. The structure of this compound (face centred cubic, cF16, a 747.3 pm) can be described (see also § 7.4.2.2.) as resulting from two interpenetrating diamond type lattices corresponding to the arrangements of the Na and Tl atoms respectively (Zintl and Dullenkopf 1932). Each Tl atom therefore is coordinated to other four Tl at a distance a3/4 747.33/4 323.6 pm which is shorter than that observed in elemental thallium (d 341–346 pm in αTl, hP2-Mg type, CN 6 6) and d 336 pm in β Tl, (cI2-W type, CN 8). NaTl was described by Zintl as NaTl with Tl corresponding to a diamondlike framework 3 [Tl4/4] isostructural and isoelectronic with diamond 3 [C4/4]. The Na ions, owing to their small dimensions (r 97 pm) can be considered isolated and inserted in the holes of the Tl framework. The electron transfer from the alkali metal to the other element, which assumes a partial structure similar to that of the electron-richer elements of the next group, has also been assumed for other compounds (Klemm and Busmann 1963). It is now defined as Zintl–Klemm concept the assumption of the formation of negatively charged ions (anions) resulting in partial structures which are identical to those of the (neutral) main group elements having the same number of valence electrons. In NaSi, for instance, the structure (monoclinic, side-centred mS32) contains regular tetrahedra of Si atoms between which the Na atoms are situated. Accordingly we have the overall composition NaSi in which, however, the silicon ions have a discrete (molecular like) tetrahedral structure Si44similar and isoelectronic to the typical molecules P4 or As4 present in white phosphorus or yellow arsenic. The distances Si9Si in a tetrahedron are 240–249 pm; the Na–Si distance is about 292 pm and the Na9Na distance about 322 pm. The NaSi structure may also be compared with that of NaGe (mP32) in which tetrahedra of Ge atoms are contained (and Na in the intervening space) even if there is a somewhat different arrangement of the tetrahedra. As another example, CaSi2 (hR18), which could be considered as Ca2 Si2 2 , may be examined. The structure can be regarded as a filled-up As-like arrangement. The silicon atoms, described as having an average charge Si, form rumpled double layers (again as found in the next group elements black phosphorous and grey arsenic). These Si layers form 63 nets which are arranged in the sequence abc and are interleaved with 36 nets of Ca atoms. Typical interatomic distances in this structure are: Si9Si: 251–252 pm, Ca9Si: 298–311 pm, and Ca9Ca: 389 pm.

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269

More complex examples of Zintl phases are given by ternary compounds in which the anionic part of the structure may be compared for instance to molecular halides. This point is illustrated by Ba4SiAs4 which can be described as (Ba2)4(SiAs4)8 in which the (SiAs4)8 group is isostructural to the tetrahedral molecule SiBr4. A similar description may be used for Ba3AlSb3 considered as (Ba2)6(Al2Sb6)12 in which the (Al2Sb6)12group is isostructural to the dimer molecule Al2Cl6 formed by two Al-centred Cl tetrahedra having a common edge (2Cl atoms). See Fig. 4.25. As an indication, however, of the limits of the Zintl interpretation and with reference to the prototypal NaTl structure, notice that the description of the filled tetrahedral structures given by Zintl cannot be considered valid generally (with all the elements). An example is the occurrence of this structure in compounds such as LiZn or LiCd in which the diamond-like framework of Zn and Cd atoms cannot obtain the four electrons necessary to give sp3 hybrids. 4.4.3.2 Zintl phases: remarks on their definition. We have seen that the Zintl phases may be considered as a group of compounds formed by an electropositive (cationic) component (alkali, alkaline earth metal, lanthanide) and an anionic component (for instance a main group element of moderate electronegativity). The anionic part of the structure may be described in terms of normal valence combination. In a review, Van der Lugt (1996) observed that a number of liquid alloys (K–Pb, Rb–Pb, Cs–Pb, K–Sn, Rb–Sn, Cs–Sn, K–Te) behave as if all the anions were in the form of perfect simple Zintl anions like tetrahedra and dumbbells: this being suggested by the behaviour of many physical properties (resistivity, thermodynamic properties, etc.) as a composition function. In this context a simple Zintl ion was defined as a polyanion that assumes the same configuration as a neutral isoelectronic element. A similar definition was reported by Van der Lugt and Verkerk

Al

Sb

Figure 4.25. Structure of the (Al2Sb6)12 ion (isostructural with the Al2Cl6 molecule) identified in the Zintl compound Ba3AlSb3. Another important compound having this structure, consisting of two-centred tetrahedra with a common edge, is the simple di-borane (B2H6).

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(2002): Zintl ions are polyanions formed by anion clustering in ionic alloys. Two categories were considered: those that fit the so-called Zintl–Klemm concept and those that are electron-deficient. In a more detailed description and according to Nesper (1990), the criteria for defining the Zintl phases may be summarized in the following points: (i) The Zintl phases can be described within the group of normal valence compounds and a well-defined relationship can be assumed within their electronic and chemical structures. (ii) Zintl phases should be semiconductors (energy gaps less than 2 eV) or, at least, they show increasing electrical conductivity with increasing temperature. (iii) Zintl phases are mostly diamagnetic, but they can be paramagnetic. However they should not show temperature independent (Pauli) paramagnetism as observed for normal metals. As underlined by Miller et al. (2002) in a comprehensive review about structure and bonding around the Zintl border of the Periodic Table, the Nesper criteria imply that Zintl phases (as valence compounds) are generally point compounds and may have a semi-metallic behaviour. A review about the Zintl phases has been published by Sevov (2002); from the introduction of this publication we quote a few remarks. It was preliminary observed that the number of Zintl phases has increased many-fold since Zintl’s time and that the definition of a ‘Zintl phase’ has never been very exact: often compounds that include non-metals have been considered in this family. The paper by Sevov is mainly dedicated to clearly intermetallic Zintl phases (that is phases containing main group metals, semi-metals or semiconductors only). Attention has therefore been dedicated to compounds of alkali metals with the elements of the 13th, 14th and 15th groups (without B, Al, C, N and P). To this end the following definitions and statements have been considered. Zintl phases are compounds that: (i) contain an alkali (or alkaline earth) metal and a p block element (a metal, semi-metal or small-gap semiconductor), (ii) are closed-shell compounds (electronically balanced, that is the number of electrons given by the constituents is that needed for covalent bonding in the structure), (iii) are point compounds, (iv) are brittle, (v) are semiconductors (or poor conductors), (vi) are diamagnetic or display very weak, temperature independent, paramagnetism.

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271

According to these definitions, making full reference to his own vast investigation, Sevov presented typical groups of Zintl phases. These are: (i) Zintl phases with delocalized bonding: corresponding to isolated clusters, mainly of the elements of the 13th and 14th groups such as Cs4Ge9 where the clusters Ge94 are monocapped square anti-prismatic, nido deltahedra, or, as another example, the substituted , hetero-atomic, 11-atom clusters of group 13 represented by [In10Hg]8, [Tl9Au2]9, [Tl8Cd3]10. (ii) Zintl phases with interconnected (homo- and hetero-atomic) clusters mainly given by alkali metals and 13th group elements. Generally in these compounds two types of bonding are combined: delocalized within the clusters (endo-bonds) and localized (2c,2e exo-bonds) between them. Several Ga compounds have been described. (iii) Zintl phases with localized bonding. Compounds containing only 2c,2e (two centres–two electrons) bonds between the p-elements (generally at least two different p-elements). In the introduction to this group of phases attention has been especially given to compounds containing tetrahedral units often formed by one of the p-elements and centred by the other. Examples may be: isolated Sn-centred Sb tetrahedra in Na8SnSb4, corner and edge shared Ga- (or In) centred As tetrahedra in K3Ga3As4, K3In2As3, etc. 4.4.4 ‘Cluster’ compounds 4.4.4.1 Cluster compounds: introductory remarks. The word ‘cluster’ was introduced by F.A. Cotton in the early 1960s to describe compounds containing metal– metal bonds. However its meaning has progressively changed to include other substances containing element9element bonds, such as main group polyhedra, and any molecule containing metal9metal bonds. For a detailed historical account, see Cotton and Walton (1982). Clusters have become progressively important in a variety of fields which include inorganic chemistry, organo-metallic and bio-inorganic chemistry, and several subjects of solid state and of intermetallic chemistry. Quoting from ‘Highlights in inorganic chemistry over the last 100 years’ by McCleverty (2004), significant landmarks in the history of the chemistry of cluster compounds are mentioned in the following. The chemistry of small metal atoms cluster compounds grew naturally out of metal carbonyl chemistry (Lewis, Johnson 1970s onward), but the discovery that high nuclearity metal carbonyl clusters could be isolated caused an explosion in the field. Possibly key discoveries in this area were made by the Chini group (late 1970s) with the noble metals (especially Rh, Pt). The rationale synthesis of these complexes, using simple techniques and readily available starting materials, is a beautiful example of creative inorganic chemistry at its best (see

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for instance Longoni and Chini 1976). Further noteworthy developments in the chemistry of all the metals of the 8th, 9th, 10th groups were supported by the theories of cluster bonding (Wade, Mingos) and by the application of the isolobal principle (Hoffmann 1982). This principle states that two molecular fragments are isolobal if the number, symmetry properties and approximate energies of their frontier orbitals are the same; they may or may not also be isoelectronic. It was also observed that in the development of the chemistry of various types of cluster compounds, including for instance the Chevrel phases, the role of the X-ray crystallography cannot be underestimated. Considering now the authoritative treatise by Cotton and Wilkinson (1988), the following assertions can be stated: ●

●

The formation of polyhedral cages and clusters is a widespread phenomenon; examples can be found in nearly all parts of the Periodic Table. A cluster may be considered, in a sense, the antithesis of a complex even if there are many similarities between the two groups of compounds due to common symmetry properties. In both cases a set of atoms defines the vertices of a polyhedron; in the complex, however, these atoms may be considered as bound to another, central, atom and not to each other. In the cluster, on the other hand, there is not necessarily a central atom and the atoms at the vertices can be described as directly connected to each other.

As underlined by Mingos and Wales (1990), according to Cotton and Walton (1982) the following statement can be considered as a first-approach working definition: a metal cluster compound may be defined as a group of two or more metal atoms where ‘direct and substantial’ metal9metal bonding is present. The presence of such metal9metal bonding could be deduced by a comparison between the metal9metal bond lengths with the sum of the covalent radii which should not be exceeded by, say, more than 15%. Examples may be given by the following series of compounds for which the metal9metal distance (d) is reported together with the sum of the metal radii (Σ): [Mo6Cl8]4 (d 2.62, Σ 2.80), [Co(C5H5)(μ2PR2)]2 (d 2.56, Σ 2.50). This concept, however, may be ambiguous and problematic especially when the metal atoms are connected to bridging ligand atoms and also because variations in the metal9metal bond length may be observed between different compounds having a similar bonding scheme. Nevertheless a formal metal9metal bond designation may be assumed in order to underline a relation with the simple bonding schemes based on the inert gas rules (‘octet’ rule). It has been noticed moreover that in metal cluster chemistry a difference in quality is observed when the sizes of the clusters being progressively characterized are

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273

sufficiently large to make meaningful comparison of properties with either bulk metals or metal surfaces. A point worth indeed to be underlined is that clusters can be considered intermediate in character and structure between molecules and solids. The shapes of many clusters are based on polyhedra such as the tetrahedron and octahedron. These polyhedra have triangular faces: a feature also common in the structures of metals. The close packing in many metals leads to the occurrence of tetrahedra and octahedra. Having particularly in view intermetallic substances (crystals, quasicrystals) a critical discussion by Steurer (2005) on several questions concerning clusters (definition, stability, etc.) is especially interesting (see also § 4.4.4.8). Two books to which the present authors are greatly indebted and which represent a comprehensive introduction to different aspects of the chemistry of clusters and their applications are Introduction to Cluster Chemistry by D.M.P.M. Mingos and D.J. Wales (1990) (presenting several theoretical and experimental aspects and a classification of different types of clusters) and Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry by R.B. King (1993) in which the mathematical background, principles from topology, graph and group theories, atomic orbitals and their hybridization are presented with their applications to cluster chemistry. 4.4.4.2 Cluster compounds and remarks on the ‘2e, 2c bonding scheme’. A formal metal–metal bond designation may be introduced having as reference the simple bonding schemes based on the inert gas rules (‘octet’ rule). A reference picture for the bonding between atoms is indeed related to the electrons which are needed for an atom to obtain the electron configuration of the next noble gas in the Periodic Table. In the specific case of a pair of electrons shared by two atoms, each atom gains one electron in its valence shell. The energy decrease of the shared electron pair ‘links’ the two atoms (the two centres) and we speak of a ‘two electron-two centre bond’ (2e, 2c bond). According to Müller (1994), a cluster may be defined as an accumulation of three or more atoms of the same element (or of similar elements) directly linked with each other. If there is a sufficient number of electrons in the cluster to have an electron pair for every connection between two adjacent atoms, then to each of these connections a 2e, 2c bond can be assigned, as in a normal valence-bond compound. Assuming moreover that, through the formation of such bonds, the atoms at the vertices of the (ring or polyhedron) cluster achieve an ‘inert gas configuration’ (8 valence electrons for a main group element and 18 for a transition element), we will have a kind of reference cluster structure with limiting values of the bond and electron numbers.

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In this case the total number of valence electrons (Σe) in the cluster will be given by: Σe 8n 2B (main group elements) or by Σe 18n 2B (transition elements) where n is the total number of atom (vertices) in the metal cluster (Mn) and B the number of 2-electron bonds (number of edges in the cluster skeleton). In a ring cluster (a ring molecule) the number of edges is equal to the number of vertices (atoms) B n, so we have: Σe 8n 2n 6n

(main group element ring)

or Σe 18n 2n 16n

(transition metal ring)

For triangular clusters, for instance, this means 18 or 48 electrons. A classic example may be the Os3 triangular group in the carbonyl compound Os3(CO)12 in which 4 CO are connected to each Os (to each triangle vertex). Each Os atom contributes 8 valence electrons whereas the CO group acts as a 2-electron donor so: Σe 3 8 2 12 48 in agreement with the result obtained from the previously reported formula. More complex cluster structures may correspond to a higher number of bonds (edges) converging on each vertex: the symbol nx may be defined indicating the number of vertices (of degree x) at which x edges (metal–metal bonds) meet. The previously reported formulae can be rewritten:

or:

Σe 6n2 (2e, 2c bound main group element ring) Σe 16n2 (2e, 2c bound transition metal ring)

More generally: Σe 7n1 6n2 5n3 4n4 (2e, 2c bound main group element cluster) or: Σe 17n1 16n2 15n3 14n4 (2e, 2c bound transition metal cluster) (nx for x 4 are not indicated, because vertices of higher degrees have generally never been observed in such clusters).

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275

For a tetrahedron, for instance, there are 4 vertices in each of which 3 edges meet: it is an example of three-connected cluster. Therefore:

or:

Σe 5n3 5 4 20 (2e, 2c bound main group element tetrahedral cluster) Σe 15n3 15 4 60 (2e, 2c bound transition metal tetrahedral cluster)

Examples may be: Ir4(CO)12 (3 CO attached to each Ir vertex). The electron count based on 9 electrons for Ir atom and 2 electrons for CO group, corresponds to Σe 4 9 12 2 60, in agreement with the computation made on the basis of the mentioned tetrahedral structure. K4Ge4, can be described as a polyanionic compound (as a Zintl phase also) containing the ion Ge44. This tetrahedral ion can be considered a naked (that is without any ligands bounded to the vertices) tetrahedral cluster formed by a main group element (that is Σe 5n3 5 4 20). The electron count, on the basis of the Ge valence electrons and of the ion charge results in Σe 4 4 4 20. Molecules such as P4, As4, Sb4 may also be considered in this context and described according to this formalism. Notice however that the reported formulae are valid only in the limiting case of clusters having all the edges corresponding to 2e, 2c bonds; cluster compounds having other (higher or lower) numbers of electrons are frequent, and, as a consequence, various different classes of clusters may be defined. 4.4.4.3 Wade electron counting rules: borane-like cluster nomenclature. On initially studying compounds such as boranes (boron hydrides) and carboranes (or carbaboranes boron9carbon hydrides), Wade (1976) proposed a number of rules which have then been extended to several compounds and which relate the number of skeletal electrons with the structure of deltahedral clusters. A polyhedron which has only Δ-shaped, that is triangular, faces is also called a deltahedron. The following nomenclature is generally used: Closo-cluster: (a cage) a complete deltahedral group. Nido-cluster: (a nest) a deltahedral structure with one missing vertex. Arachno-cluster: (a spider-web) a deltahedral structure with two missing vertices. Hypho-cluster: (a net) a deltahedral structure with three missing vertices. The following optimum electron numbers have been defined on the basis of the so-called ‘Polyhedral Skeletal Electron-Pair Theory (PSEPT)’. Closo, nido, arachno, hypho deltahedral clusters based on n main group vertex atoms are characterized by 4n 2, 4n 4, 4n 6 and 4n 8 total valence electrons respectively. The corresponding optimum VEC for closo and nido deltahedra

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Valence electron concentration

5

15

4.8

14.8

nido

4.6

14.6

4.4

14.4

closo

4.2

14.2

4

14 0

5

10

15

20

25

30

35

n (number of vertices)

Figure 4.26. Optimum values, in accordance with Wade’s rules and as summarized by Miller et al. (2002), of the valence electron concentration VEC (total number of electrons divided by the cluster atom number) as a function of the number of cluster atoms for closo and nido deltahedra. On the left the values computed for the main group elements and on the right those relevant to the transition metals.

is shown, according to Miller et al. (2002), in Fig. 4.26. For the analogous clusters based on n transition metal atoms the valence-electron numbers are 14n 2, 14n 4, 14n 6 and 14n 8 respectively. Examples of the application of the mentioned rules to a few naked metal clusters according to Mingos and Wales (1990) are reported in Table 4.4. For each species the valence electron (s and p) count is made both on the basis of the component valences by adding/subtracting one electron for each negative/positive charge, and on the basis of the geometry and the number of vertices. In addition to the rules reported, a relation between the total electron count (TEC) and the number of ‘skeletal’ electrons (SE) may be mentioned. This may be summarized as follows (Wade 1976): TEC 4n 2/14n 2 : SE 2n 2 TEC 4n 4/14n 4 : SE 2n 4 TEC 4n 6/14n 6 : SE 2n 6 TEC 5n/15n : SE 3n

closo nido arachno

277

Intermetallic Reactivity Trends in the Periodic Table Table 4.4. Electron count for some typical naked clusters. Cluster

∑e

Structure of the cluster

Electron count Total (TEC)

Skeletal (SEC)

P4, As4, Sb4

4 5 20

Tetrahedral, three-connected

Bi42

4 5 2 22

Square planar

arachno 4n 6 4 4 6 22

2n 6 14

Ge52, Pb52

5 4 2 22

Trigonal bipyramid

closo

4n 2 4 5 2 22

2n 2 12

Sn94, Pb94

9 4 4 40

Capped square antiprism

nido

4n 4 4 9 4 40

2n 4 22

TlSn93

3 9 4 3 42 Bicapped square closo antiprism

4n 2 4 10 2 42

2n 2 22

Se42

4 6 2 22

Square planar

arachno 4n 6 4 4 6 22

2n 6 14

Bi53

5 5 3 22

Trigonal bipyramid

closo

4n 2 4 5 2 22

2n 2 12

Bi82

8 5 2 38

Square antiprism

arachno 4n 6 4 8 6 38

2n 6 22

5n 5 4 20

3n 12

These two groups of rules are an example of a description of the cluster structure (of a complex cluster structure as in a polyanionic compound) as consisting of two parts: an interior, for which a certain number of skeletal electrons are required, and an exterior which interacts with its surroundings via exo-bonds, generally twoelectron two-centre bonds. A lone electron pair may be assigned to an exo-orbital of a cluster atom having no exterior linkage. Different types of skeletal bonding are found in various clusters: according to King (1993) the two extreme types of skeletal chemical bonding in molecules formed by polygonal or polyhedral clusters of atoms, including planar aromatic hydrocarbons and polyhedral boranes and metal clusters, can be defined as edge-localized or globally delocalized respectively. In an edge-localized polyhedron, or polygon, along each edge there is a two-electron two-centre bond. In the other extreme type of cluster, a multi-centre bond involves all the vertex atoms resulting in a fully aromatic system, such as the polygonal, bidimensional benzene or a three-dimensional deltahedral borane anion. A classic example of the application of the above-mentioned rules is given by the borane series B6H62 (octahedron, closo), B5H9 (square pyramid, nido) and B4H10 (butterfly, that is two triangles joined by sharing an edge, arachno). The total electron counts (TEC) result in the three clusters 26, 24 and 22 whereas the skeletal electron

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count (SEC) gives for all these species the same value 14 (2 6 2, 2 5 4 and 2 4 6 respectively). The nido and the arachno species may be described as generated by successive removal of B9H vertices from the parent, octahedral, structure. The same rules may be applied to the Zintl anion B62 observed in compounds such as CaB6 and corresponding to a framework of corner-sharing boron octahedra as described in the following § 4.4.4.7. 4.4.4.4 Electron-precise, electron-deficient and electron-rich clusters. A cluster classification often adopted in several books, and related to the rules previously presented, corresponds to a subdivision into three categories: electron-precise, electron-deficient and electron-rich types. The electron-precise clusters may be considered as reference structures. Electron-precise clusters are defined according to the following requirements (Mingos and Wales 1990): ●

● ● ●

A simple localized 2c, 2e bond treatment is adequate: there are sufficient electrons for all the connections to be made by electron pairs. Each cluster atom obeys the octet rule. Each cluster atom has a lone pair or it is bonded to an exocyclic group. Each vertex is three coordinate.

The implication of these rules is that: An electron-precise n-atom cluster will have 5n (15n) electrons, of which 3n are used to bond the cluster (to form 3n/2 skeleton electron pairs). Notice that the total number of electrons in a cluster is given by the sum of the electrons on cluster vertex atoms plus the electrons, on vertex atoms, from covalent bonds with exocyclic groups. A simple, previously mentioned example may be represented by the tetrahedral molecule P4. In this structure there are 4 vertex atoms (n 4) and there are no exocyclic groups. On the other hand, P has 5 valence electrons, so the number of cluster electrons is 4 5 20 electrons. This number (20) is therefore related to the number of vertices by the condition 20 5n. The cluster is electron-precise. According to McGrady (2004), however, a ‘continuum view’ of the different types of clusters may be considered as illustrated in Fig. 4.27, which shows the relations between vertex count and electron count in main group clusters. 4.4.4.5 Interstitial atoms in clusters. As the size of clusters increases (and also that of their central cavity) the insertion of atoms becomes easier and easier. In particular for 12-atom clusters having a cubo-octahedral structure, the insertion of an atom having the same radius as that of the peripheral atoms is possible. Notice that this arrangement can be compared with those of the metallic cubic and hexagonal, close-packed structures.

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38 36 4n 8

Valence electron number

34

4n 6

32

4n 4

o

ph

30

hy

ido

n

28

Electron-rich 5n Electron-precise

Electron-deficient

4n 2 4n

26 o

hn

24

c ara

Hypoelectronic o

s clo

22 20

4

6 5 Vertex number

Figure 4.27. Valence electron count and vertex count in main group clusters. Notice, according to McGrady (2004), that the different classes of clusters (electron-rich, electron-precise, etc.) simply occupy different domains in a continuum defined by the two variables (electron and vertex counts).

Typical examples are: carbon interstitial carbonyl clusters such as the octahedral Co6C(CO)132, the trigonal prismatic Co6C(CO)152 and its isoelectronic (mononegative) nitrogen interstitial Co6N(CO)15 or the icosahedral cluster Ni12Ge(CO)222 with the interstitial atom (Ge or Sn) in the centre of a Ni icosahedron. 4.4.4.6 Condensed and high nuclearity cluster compounds. In different fields of inorganic chemistry, from organo-metallic to intermetallic chemistry, a huge variety of compounds are known, the complex (or very complex) structures of which may be described as derived from some of the cluster types previously presented. Several derivation mechanisms could be considered, and some concepts underlined when studying typical relations between groups and families of structures such as ‘modular’ and ‘intergrowth’ structures (see § 3.9), which may possibly be applied and also extended to cluster chemistry. An important mechanism consists of joining clusters to form large building blocks, which are to form condensed clusters. Relevant contributions to this field have been carried out especially by Simon (see, for instance, Simon 1981, 1988, 1995) and Corbett (Corbett 2000, Liu and Corbett 2004). Among the condensed clusters those obtained by linking octahedra are an interesting example. Fig. 4.28 shows

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(b)

(c)

Figure 4.28. Schemes of octahedral cluster condensation. (a) Vertex-sharing, (b) edge-sharing and (c) face-sharing. In these examples octahedra centred by interstitial atoms are shown.

possible condensation schemes between octahedra (centred octahedra in these examples) having one common vertex or two adjacent vertices (an edge) or three (a common face). More complex structures can be obtained by repeated condensation processes: chains, for instance, may result by merging opposite vertices (or edges) of an octahedra sequence. Some general comments on the solid-state chemistry (‘From a molecular view on solids to molecules in solids’) have been reported by Simon (1995); emphasis was especially placed on the structural chemistry of metal-rich compounds formed by the metals in groups 1 to 6 and it was underlined that it is largely based on discrete and condensed clusters. In the chemistry of metals in low oxidation states, the residual valence electrons can be used for metal9metal bonding. Metal-rich compounds lie between normal valence compounds and the elemental metals themselves, with respect to their compositions, and often also with respect to their structures: fragments of usual metal structures (close-packed, b.c.c., etc.) are often component units in the structures of metal-rich compounds. As for the electron count in a condensed cluster, a ‘condensation principle’ has been enunciated (Mingos and Wales 1990). It can be summarized in the following sentences: the TEC of a condensed cluster is given by the sum of the electron counts for the parent clusters minus the electron count characteristic of the atoms, pair of atoms or face of atoms common to both polyhedra. In the transition metal

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chemistry, these characteristic electron counts are 18 for a shared metal vertex, 34 for a common edge (a shared pair of atoms), 48 for a common triangular face and 62 for a common square face. In the (less common) main group condensed polyhedra, the corresponding numbers are 4 for a shared vertex, 12 for a shared edge and 18 for a shared triangular face. An example of vertex-sharing condensed cluster which obeys the mentioned rules is given by Os5(CO)19, the structure of which corresponds to two triangles with a common vertex. Reference may be made to the cluster Os3(CO)12 for which we have an electron count of 3 8 12 2 48. For the resulting vertexcondensed cluster we calculate 2 48 18 78, and the electron count for Os5(CO)19 is 5 8 19 2 78. An example of an edge-sharing cluster is [Ru10C2(CO)24]2 (condensation of two octahedral clusters of the type [Ru6(CO)18]2); another example may be the structure of the ion [Re4(CO)16]2 which can be described as the edge-sharing condensation of two triangular structures of the neutral cluster type Os3(CO)12. Several examples of complex clusters are reported in the literature, not all of them however conforming to the reported rules. 4.4.4.7 From clusters towards solid state intermetallics. In the preceding paragraphs a few types of complex inorganic compounds, mainly molecular however, have been reported, and some rules concerning their composition and structure exemplified. It is interesting to underline the ‘continuity’ between several topics of general inorganic chemistry and intermetallic chemistry, so a look will be given, albeit with few details, to some connections between cluster chemistry and solidstate chemistry. The scheme of cluster condensation or cluster fragment condensation leads eventually to structures observed in bulk metals. Particularly through extensive condensation of tetrahedral and octahedral clusters, arrangements closely related to the hexagonal and cubic close-packed structures can be obtained. Condensation also of icosahedral five-fold symmetrical clusters may be related to crystalline and quasicrystalline metallic structures. The variety, the richness, the beauty of the countless collection of known solid state intermetallic structures must be declared even if, unfortunately, only a few examples of the above-mentioned concepts can be covered here. Notice moreover that, on passing from cluster compounds to intermetallics, we may possibly consider several steps with more or less sharp sequential changes in the properties (changes in the interatomic distances and in the presence of different groups of interatomic distances, in the bonding characteristics, etc.). In this paragraph, through a few examples, attention will be especially given to structural and geometric characteristics. In a way, the reader may compare this approach with that previously adopted in the presentation of modular aspects

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of crystal structures, in the analysis of their characteristic fragments and in the description of recombination structures and intergrowth structure series (see § 3.9.1 to 3.9.4). However notice that, on passing from a mere, more or less convenient, geometric description of a certain atomic arrangement to considerations about the physical meaning of such a description, ambiguities and problems may arise. A few remarks about some aspects related to the relations between clusters and complex intermetallic structures will be included in the following § 4.4.4.8. 4.4.4.7.1 Calcium hexaboride. An introductory example is represented by the calcium boride (CaB6) in which, however, boron octahedra are not condensed with each other but connected via normal (2e, 2c) bonds. A scheme of the structure is – shown in Fig. 4.29. It is cubic, space group, Pm 3m, N.221 with: 1 Ca in (a) 0, 0, 0; – 1⁄2, 1⁄2; 1⁄2, x, 1⁄2; 1⁄2, x, – 1⁄2; 1⁄2, 1⁄2, x; 1⁄2, 1⁄2, x– 6 B in (f) x, 1⁄2, 1⁄2; x, (a 414.5 pm and xB 0.207).

Figure 4.29. CaB6 structure. The B6 octahedra and their interconnections are outlined. Eight unit cells with a common (Ca) vertex are partially shown. Notice that the Ca atom is placed at the origin of the conventional cubic cell (position 0, 0, 0) and the centres of the boron octahedra are in the positions 1⁄2, 1⁄2, 1⁄2 (and equivalent).

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Environment data: Ca (a) CNE 24: 241.0.0.0.0.2 B (f) CNE 5: 42.114.0 From a geometrical point of view only, this structure could be compared with that of CsCl, with 1 Ca in place of Cs, and the centre of a 6 B octahedron in place of the Cl atom (in the centre of the cell with its axes parallel to the cell axes). Ca is surrounded by 24 B in a regular truncated cube (octahedra and truncated cubes fill space). A number of hexaborides (of Ca, Sr, Ba, Y and several lanthanides and Th, Np, Pu, Am) have been described as pertaining to this structural type. CaB6 can be described in terms of the Wade rules. In this compound the B6 octahedra are linked with each other via 2e, 2c bonds; six electrons per octahedron are required for these bonds, together with the 2n 2 (14) electrons for the octahedron skeleton. This adds up to a total of 20 valence electrons. The boron atoms give 3 6 18 of these and calcium the remaining two. 4.4.4.7.2 Chevrel Phases. These phases were first synthesized by Chevrel et al. (1971) and are of great interest owing also to their noteworthy superconducting properties discovered by Matthias et al. (1972). The Chevrel phases are represented by a series of ternary molybdenum chalcogenide compounds and have the general formula Mo6MxX8 with M alkaline, alkaline earths, lanthanides, actinides or a metal such as: Ag, Cd, In, Sn, Pb, and X S, Se, Te. Most of these compounds crystallize in a rhombohedral structure with αrh 90° and space – group R3 (and related to the Mo6PbS8, hR45 type). The building blocks of the Chevrel-phases crystal structure are M element atoms and Mo6X8 clusters; each Mo6X8 unit is a slightly deformed cube with the X atoms at the corners and the Mo atoms at the face centres. Their comparatively simple crystal structures may be described as a primitive packing of quasi-molecular units, and, in a way, they represent the border line between molecular and infinitely extended units in a solid (Cheetham and Day 1992). The Mo6 type core is completely surrounded by X atoms and inter-cluster bonding essentially occurs through the Mo–X interactions. The Mo9Mo bonding between clusters is very weak. – 4.4.4.7.3 Mo6PbS8. It is rhombohedral (hR45), space group R 3, N.148, with the following atomic positions (45 atoms in the triple primitive hexagonal cell): (0, 0, 0; 1⁄3, 2⁄3, 2⁄3; 2⁄3, 1⁄3, 1⁄3) 3 Pb in (a) 0, 0, 0 (with a 0.92 occupancy) 6 S in (c) 0, 0, z; 0, 0, –z;

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18 S in (f) 18 Mo in (f)

Intermetallic Chemistry

– z; x, – –y, –z; y, y x, –z; x y, x, –z; x, y, z; –y, x y, z; y x, x, – – – –y, –z; y, y x, –z; x y, x, –z; x, y, z; y, x y, z; y x, x, z; x,

with the following values of the positional free parameters: zS(c) 0.2436 xS(f) 0.9662, yS(f) 0.6747, zS(f) 0.4168 xMo(f) 0.8255, yMo(f) 0.8398, zMo(f) 0.4018 The constants of the triple primitive hexagonal cell are: a 921.3 pm, c 1144.0 pm, c/a 1.2417. The constants of the corresponding simple, primitive, cell in rhombohedral setting are aR 654.5 pm, α 89.47°, corresponding therefore to a nearly cubic shaped cell. (Notice that this can be an exercise for the application of the hexagonal–rhombohedral transformation formulae presented in the § 3.6.1.3.2). The equivalent sets of atomic positions (15 atoms) in this rhombohedral cell are: 1 Pb in (a) 0, 0, 0 (with a 0.92 occupancy) 2 S in (c) x, x, x; –x, –x, –x; 6 S in (f) x, y, z; z, x, y; y, z, x; –x, –y, –z; –z, –x, –y; –y, –z, –x; 6 Mo in (f) x, y, z; z, x, y; y, z, x; –x, –y, –z; –z, –x, –y; –y, –z, –x; with the following values of the positional free parameters (related to this rhombohedral unit cell): zS(c) 0.2436 xS(f) 0.3830, yS(f) 0.1253, zS(f) 0.7421 xMo(f) 0.2273, yMo(f) 0.4162, zMo(f) 0.5620 The nearly cubic, rhombohedral unit cell of Mo6PbS8 is shown in Fig. 4.30. The bonding between different clusters in the crystal structure of the Chevrel phase Mo6PbS8 is indicated in Fig. 4.31. 4.4.4.7.4 Cu4Mo6Se8. The triclinic structure of these compounds has been described by McGuire et al. (2006). It contains nearly regular Mo6 clusters; the Cu atoms fully occupy four sites between faces of two adjacent Mo6Se8 clusters. This compound is a member of a series of MexMo6X8 Chevrel phases. Preparation and properties have been discussed. A Cu intercalation apparatus was built for

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285

Figure 4.30. The, nearly cubic, rhombohedral unit cell of Mo6PbS8 is shown. with the Pb atoms (black) at the origin. The Mo6S8 cluster consisting of a Mo6 octahedron inscribed in a S8 cube is in evidence. Compare with Fig. 4.31 where the spatial arrangement of the clusters is shown.

Figure 4.31. Crystal structure of the Chevrel phase Mo6PbS8. Portions of four rhombohedral unit cells with one common Pb atom (black) are shown. The bonding between different clusters is suggested by the Mo9S inter-cluster links.

adding Cu to a Chevrel phase Cu2Mo6Se8 which was prepared by synthesis from the elements. 4.4.4.7.5 Mo6S8 and Mo6Se8 clusters. These clusters have been identified in several ternary Mo chalcogenides often together with other structural units, for instance, with Mo12S14 in Tl2Mo9S11, that is Tl4(Mo6S8)(Mo12S14), Potel et al. (1980). Mo9Se11

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Intermetallic Chemistry

building blocks together with Mo6Se8 have been identified in In3Mo15Se19 (Grüttner et al. 1979). The binary Mo chalcogenides Mo3S4 and Mo3Se4 (hR42-Mo3Se4 type) contain the same structural blocks present in the Chevrel phases. Their main crystal structural data, in the hexagonal and in the rhombohedral settings, are the following: Mo3S4: a 920.0 pm, c 1088.0 pm, c/a 1.183 (aR 643.2 α 91.32°) Mo3Se4: a 954.5 pm, c 1121.1 pm, c/a 1.175 (aR 665.8 α 91.57°) – The space group is R3, N.148 with 42 atoms in the (triple primitive) hexagonal cell (14 atoms in the equivalent, primitive, rhombohedral cell). The atomic positions, in the hexagonal cell of the prototype Mo3Se4, are: (0, 0, 0; 1⁄3, 2⁄3, 2⁄3; 2⁄3, 1⁄3, 1⁄3) 6 Se in (c) 0, 0, z; 0, 0, –z; 18 Se in (f ) x, y, z; –y, x y, z; y x, –x , z; –x, –y, –z; y, y x, –z; x y, x, –z; 18 Mo in (f ) x, y, z; –y, x y, z; y x, –x, z; –x, –y, –z; y, y x, –z; x y, x, –z; with the following values: zSe(c) 0.2137 xSe(f ) 0.9621, ySe(f) 0.6724, zSe(f) 0.4171 xMo(f ) 0.8290, yMo(f) 0.8479, zMo(f) 0.3940 It can be easily checked that these atomic positions are nearly identical to those of S and Mo in Mo6PbS8: Pb is not present, but we have the same structure for the groups Mo6X8. Preparation of the compounds Mo6 X8 . According to McGuire et al. (2006), Mo6Te8 can be prepared by direct reaction of the elements while Mo6S8 and Mo6Se8 cannot. It is therefore common to prepare partially Cu-filled Chevrel phases CuxMo6X8 and then to remove Cu to obtain the unfilled Mo6X8. The compound CuxMo6X8 (x 2) is synthesized from the powder of the elements, sealed in evacuated silica tubes and slowly heated up to 1000–1100°C. As for the removal of Cu from the ternary compound one way in which this may be done is through reaction with iodine dissolved in acetonitrile. The phase reacts with the I2 in solution and forms CuI, which is soluble in acetonitrile. 4.4.4.7.6 Mo and W halides. Structures similar to those previously presented are found in several other compounds; for instance in the halides of Mo and W in the formal oxidation state 2 of these metals. The key structural unit is an octahedron of metal atoms surrounded by a cubic array of halogen atoms: it is shown in Fig. 4.32. A formula such as [Mo6Cl8]4 applies to this unit, which may be observed in the

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287

structures of MoCl2. See Fig. 4.33, where a layer formed by the linking of Mo6Cl8 clusters via extra Cl atoms is shown. The ion [Mo6Cl14]2 is shown in Fig. 4.34. The related structure of M6X12 groups, such as found in [Nb6Cl12]2 or in [Ta6Cl12]2 clusters, is shown in Fig. 4.35.

Figure 4.32. The key structural unit [Mo6Cl8]4 is shown (Cl atom black), which is found in molybdenum (and similarly in tungsten) halides. The edges of the Cl8 cube (around the Mo6 octahedron) have not been indicated: emphasis has been given to the interatomic connections.

Figure 4.33. Layer formed by the linking of Mo6Cl8 clusters via extra Cl atoms (4 links per cluster). Each of these Cl atoms is shared between two clusters so, on average, 4/2 2Cl are added to each Mo6 group. Considering also the two unshared Cl atoms linked to each Mo octahedron we have an overall stoichiometric ratio of 6 Mo to (8 2 2) Cl corresponding to the di-halide Mo6Cl12. An isolated group formed by the 6 Mo octahedron with all (14) the surrounding Cl is shown in the next figure.

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Figure 4.34. The cluster [Mo6Cl14]2 is shown. Numerous compounds are known which contain this group as a negative ionic cluster. Six Cl atoms were added to the six vertexes of the white octahedron shown in Fig. 4.32.

Figure 4.35. The structure of the [Nb6Cl12]2 and [Ta6Cl12]2 clusters.

4.4.4.7.7 Pentatitanium tetratelluride (vertex-sharing octahedra). The structure of Ti5Te4 (tI18, structural type) gives an example of cluster condensation. The reference cluster has a structure (and a formula, Me6X8) similar to that previously considered in the Chevrel phases. The body centred tetragonal structure of Ti5Te4 corresponds to the following data: Space group I4/m, N.87, with the following atomic positions: (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) 2 Ti in (a) 0, 0, 0; 8 Ti in (h) x, y, 0; –x, –y, 0; –y, x, 0; y, –x, 0; with x 0.3144 and y 0.3752 8 Te in (h) x, y, 0; –x, –y, 0; –y, x, 0; y, –x, 0; with x 0.0589 and y 0.2797

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289

(b)

Ti

Te

Figure 4.36. The body centred tetragonal structure of Ti5Te4. (a): perspective view of three superimposed unit cells. A Ti5Te4 chain passing through the centres of the cells is outlined. Inside see the clusters Ti6Te8. In every unit cluster, the Ti6 octahedron and the Te8 cube are shown. (b) projection on the x, y plane of the structure. The projections of parallel Ti5Te4 chains passing through the centre and the vertices of the cell may be noticed.

The constants of the b.c. tetragonal cell are: a 1016.4 pm, c 377.2 pm, c/a 0.371. Me5X4 compounds with this structure are known with Me Ti, V, Nb, Ta, Mo and X S, Se, Te, As, Sb. A perspective view of this structure and a projection of the unit cell are shown in Fig. 4.36. Notice the chain structure resulting from the condensation of Ti6Te8 clusters. Similar groups (such as Mo6S8) are found, as building units, in several compounds. According to a discussion reported by Müller (1994), it may now be underlined that joining clusters to form larger building blocks may relieve the existing deficiency of binding electrons. Among the condensed Me6X8 clusters, a substructure consisting of Me6 octahedra linked with each other may be noticed. When joining Ti6Te8 units via common vertices of the metal octahedra (that is, merging the vertex metal atoms with one another) it is necessary for some X atoms to merge too. In the condensation scheme shown in Fig. 4.36 merging of the opposite vertices of the octahedra results in an average number of 5 Ti atoms in each unit of the chain. On the other hand, the sharing of 4 Te atoms by two cubes results in an average content per cube of 4 Te, giving an overall composition ratio Ti5Te4. In the same book,

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Müller introduces and discusses examples of more complex compounds, in which extended condensation processes of Mo6X8 and Mo6X12 clusters are observed. 4.4.4.7.8 Edge-sharing and face-sharing poly-condensed clusters. Polyhedra interconnection and condensation constitute a basic mechanism for the description and interpretation of several complex structures. As suggested by the examples shown in Fig. 4.28, condensation and poly-condensation may correspond to the sharing of one or more vertices, edges or faces. Using as a reference a paper by Simon (Simon 1992), other examples of the Mo chemistry may be examined, and several derivatives of the molybdenum Mo6 octahedral group considered. Cluster condensation via opposite faces of the Mo6X8 type clusters have been examined, and oligomeric units describable as resulting from the decomposition of the parent cluster into Mo3X4 fragments with the insertion of Mo3X3 groups have been described. Several ternary molybdenum chalcogenides, containing such groups, have been discussed; among them: Cs2Mo12S14 (Mo3X4[Mo3X3]2Mo3X4)2, Rb4Mo18Se20 (Mo3X4[Mo3X3]4Mo3X4)4, Cs6Mo24Se26 (Mo3X4[Mo3X3]6Mo3X4)6; Cs8Mo30Se32 (Mo3X4[Mo3X3]8Mo3X4)8, up to Tl2Mo6Se6 containing the infinite ionic structure 1[Mo3X3]. As an example of a structure derived from the union of different polyhedra, the structural motif resulting from the connection of two trigonal prisms (around a Co atom), and a distorted rectangular prism (around an Al atom) has been identified by Richter et al. (2005) in the monoclinic phase Co4Al7xSi2x; this motif is shown in Fig.4.37. 4.4.4.7.9 Concentric polyhedral clusters. Among the various contributions made by Corbett and co-workers to the different aspects of cluster science, special attention may be given to the investigations (preparation, structural description, electronic classification, etc.) carried out on phases containing multi-hedral, concentric polyhedral, clusters. An interesting example is represented by the investigation of a phase, approximant to the icosahedral quasi-crystalline phase Sc3Cu2.1Zn15.9, and which is homogeneous in the region Sc3CuxZn18x(0 x 2.2) (Lin and Corbett 2004). It is – body centred cubic (space group Im3, a 1383.1–1375.3 pm, cI184(168)-type) basically isostructural with the RCd6 phases known for many rare earth metals. The structure is a body centred array of interpenetrating triacontahedra (30 faces, 72 vertices polyhedra) of Zn atoms. These large polyhedra contain successive concentric atomic shells around their centres (in the origin and in the 1⁄2, 1⁄2, 1⁄2 position of the cell) consisting of a disordered Zn tetrahedron followed by a pentagonal dodecahedron of Zn Cu atoms (20 atoms), an icosahedron of Sc atoms (12) that cap the pentagonal faces of the internal dodecahedron, and an icosidodecahedron of 30 Zn

Intermetallic Reactivity Trends in the Periodic Table

Co

AI

291

AI, Si

Figure 4.37. A view of the atomic arrangement in mS26-Co4Al7xSi2x according to Richter et al. (2005). Atomic clusters containing trigonal prisms centred by Co and distorted rectangular prisms centred by Al are evidenced.

atoms. It has been observed that, in the homogeneity composition range, to an increasing Cu quantity corresponds a reduction of the electron count per atom (to 2.04) and of the average atomic dimensions, until increasing quantities of Zn-poor quasicrystals separate along with the described crystalline approximant phase. Another contribution is represented by an investigation of a cubic thallium cluster phase of the Bergmann type Na13(TlxCd1–x)27 (0.24 x 0.33) (Li and Corbett – 2004). For this phase too the body centred cubic structure (space group Im 3, a 1587–1599 pm) may be described in terms of multiple endo-hedral concentric shells of atoms around the cell positions 0, 0, 0, and 1⁄2, 1⁄2, 1⁄2. The subsequent shells in every unit are an icosahedron (formed by mixed Cd–Tl atoms), a pentagonal dodecahedron (20 Na atoms), a larger icosahedron (12 Cd atoms); these are surrounded by a truncated icosahedron (60 mixed Cd–Tl atoms) and then by a 24 vertices Na polyhedron. Every atom in the last two shells is shared with those of like shells in adjacent units. A view of the unit cell is shown in Fig. 4.38. According to Li and Corbett (2004), it may be described as an electron-poor Zintl phase. A systematic description of condensed metal clusters was reported by Simon (1981). 4.4.4.8 Problems in the relations between complex intermetallic alloys and clusters. After the previous short survey of cluster structures and some comments

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Figure 4.38. The body centred cubic cell of Na13(TlxCd1x)27 (adapted from Li and Corbett (2004)). The large, interpenetrating, polyhedra contain concentric atomic shells and are centred around 0, 0, 0 and 1⁄2, 1⁄2, 1⁄2.

about their possible relevance to intermetallic structures, a few summarizing observations taken from a critical contribution by Steurer (2005) may now be considered. Steurer observed that, without doubt, the cluster approach has been a very successful and useful tool for describing and modelling the structure of quasicrystals. Open questions however are: how stable these clusters are, in what way they contribute to the stability of the quasicrystals and what physical properties they have. Several remarks have been made about the definition and the nature of clusters. In the introduction to the paper Steurer remarked that most models of quasi-periodic structures and their approximants are based on one or more structural units commonly referred to as clusters. The term ‘cluster’, however, may denote a purely geometrical pattern (a structure motif ), a structural building block, a quasi-unit cell, a complex coordination polyhedron, possibly with some chemical stability; finally, in terms of electronic stabilized entities, a cluster, with reference to the so-called jellium model, can be considered a kind of soft super-atom. These concepts have been further considered in a discussion edited by Henley et al. (2005). Different meanings often given to the word ‘cluster’ and consequent problems in an unambiguous definition of cluster were examined. In particular, considering

Intermetallic Reactivity Trends in the Periodic Table

293

definitions of clusters connected to binding or physical properties it was remarked that a distinction, by the degree of binding, between a cluster and the remaining parts of the system may be significant for covalently bonded structures but generally not for metals, including complex intermetallics and quasicrystals, where a sufficiently localized meaning cannot be ascribed to a binding concept. An energetic distinction between the inter-cluster and intra-cluster interactions and those between clusters and their environment will be especially problematic with structures for which a geometrical description in terms of interpenetrating overlapping clusters seems to be convenient. 4.4.4.9 Thermochemistry of cluster compounds. In this short summary of cluster structures and their bonding, a few remarks on their thermochemical behaviour are given, in view of a possible relationship with the intermetallic alloy properties. To this end we remember that for molecular compounds, as for several organic compounds, concepts such as bond energies and their relation to atomization energies and thermodynamic formation functions play an important role in the description of these compounds and their properties. A classical example is given by some binary hydrocarbon compounds. Before carrying out such an examination, however, it is necessary to underline that thermochemical quantities, even if in principle accurate and significant, in practice are affected by experimental errors, and often by inaccuracies, due to the need to obtain relatively small values as differences between large values. As a consequence, the reader may find in books and treatises differences in the values of the specific bond energies as large as 5% to 10%. Taking methane, CH4, as a reference compound, its standard enthalpy of formation is defined by the reaction: C(graphite) 2H2(g) : CH4(g) for which the value ΔfH 74.9 kJ mol1 has been reported. Considering now the sublimation enthalpy of graphite (evaluated for the sublimation to monoatomic C gas) and the dissociation energy of hydrogen: C(graphite) : C(g) H2(g) : 2H(g)

ΔH 0 713.4 kJ mol1 ΔH 0 436.3 kJ mol1

we have: C(g) 4H(g) : CH4(g) 74.9 (713.4 2 436.3) 1661 kJ mol1 corresponding to the so-called atomization energy.

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Intermetallic Chemistry

On the basis of the CH4 structure corresponding to four identical 4 C9H bonds, the C–H bond energy can be assumed to be 1660/4 415 kJ mol1. A similar calculation performed on the next hydrocarbon, C2H6, takes into account its formation enthalpy given by the reaction: 2C(graphite) 3H2(g) : C2H6(g) ΔHI0 85.0 kJ mol1 from which the atomization energy may be obtained by considering, as previously highlighted, the graphite sublimation energy and the hydrogen dissociation energy: 2C(g) 6H(g) : C2H6(g) ΔH 85.0 (2 713.4 3 436.3) 2821 kJ mol1 Considering the C2H6 structure schematically indicated as H3C9CH3, the C2H6 atomization energy corresponds to the breaking of six C9H bond and one C9C bond, that is to the sum of 6 C9H 1 C9C bond energies. Therefore, the C9C bond energy is 2821 6 415 331 kJ mol1. The interest of these calculations and of the determination of the bond energies lies for instance in the fact that with only the two values of C9C and C9H bond energies it is possible to compute the atomization energies, and consequently the formation enthalpies, of a high number of hydrocarbons, while also confirming their structures. This kind of calculation, by using convenient definitions, has also been satisfactorily extended to different kinds of covalent compounds containing various elements (oxygen, sulphur, halogens, etc.) and characterised not only by single bonds like C9C, but also by double and triple bonds or by ‘aromatic’ groups. Notice also that the formation of compounds such as the hydrocarbons cannot be obtained by a direct synthesis reaction. The formation enthalpy therefore must be determined through a reaction cycle, by comparison for instance with the combustion reactions of C (graphite), H2 and the compound itself. The procedure is exemplified below: C(graphite) O2(g) : CO2(g)

ΔH II0 394 kJ mol1

H2(g) 1⁄2O2(g) : H2O(l)

ΔH III0 286 kJ mol1

C2H6(g) 7/2O2(g) : 2CO2(g) 3H2O(l) ΔHIV0 1561 kJ mol1 2C(graphite) 3H2(g) : C2H6(g)

ΔHI0

ΔHI0 2ΔHII0 3ΔHIII0 ΔHIV0 ΔHI0 2(394) 3(286) (1561) 85.0 kJ mol1 Similar thermochemical aspects have been considered also in cluster compounds.

Intermetallic Reactivity Trends in the Periodic Table

295

Taking for instance a metal carbonyl cluster Mm(CO)n a ‘disruption’ enthalpy (ΔdH) can be defined (Connor 1977, 1981, Mingos and Wales 1990) according to the following reaction: Mm(CO)n (g, 298 K) : mM (g, 298 K) nCO (g, 298 K) which may be obtained from the following standard thermochemical data: ΔdH mΔf H°(M,g) nΔf H°(CO,g) Δf H°(Mm(CO)n,g) If, moreover, the cluster structure is described in terms of a number of localized bonds: metal9CO terminal bonds (T bonds), metal9CO bridging bonds (B bonds) and metal9metal bonds (M bonds) and the assumption is made that the bond – – – enthalpy contributions T, B and M are transferable, these may be estimated and aver– aged. As for the M value the data (kJ/mol) obtained from a number of carbonyls – – (MCO) are compared, in Table 4.5, with those ( Mmet) obtained considering the bulk – metal, its atomization energy ΔatH and its CN, according to Mmet 2ΔatH/CN. From the thermochemical data some general, albeit approximate, assertions have been obtained (Mingos and Wales 1990) and in particular: – – (i) A comparison between the bond enthalpies Mclu and Mmet in cluster and in metal, which follow a similar trend along the Periodic Table, seems to support the hypothesis of a similarity (in type and strength) of the metal–metal bonding in clusters and in bulk metals. (ii) As observed also by Schäfer and Schnering (1964), metal9metal bonding should be frequent with those metals which have the highest heat of sublimation. – Mmet approaches a maximum toward the centre of the transition series where the d and s bands are half filled. Table 4.5. Average values (kJ/mol) of the metal9metal bond – enthalpies estimated from metal carbonyls (MCO) and from – bulk metals (Mmet) (adapted from Mingos and Wales (1990)). M9M bond

– M CO

– M met

Mn9Mn Fe9Fe Ru9Ru Os9Os Co9Co Rh9Rh Ir9Ir

67 82 117 130 83 166 110

71 104 108 132 71 93 112

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Intermetallic Chemistry

This may be related (Simon 1992) to the very stable metal clusters formed with the elements placed in the middle of the Periodic Table (Nb, Ta, Mo, W, Re). – Notice that the cluster bond enthalpy contribution, Mclu, increases in a given column of the Periodic Table on passing from the light to the heavy elements.

4.4.5 ‘Hume–Rothery phases’ and VEC An important class of intermetallic phases (generally showing rather wide homogeneity ranges) are the Hume–Rothery phases, which are included within the so-called ‘electron compounds’. These are phases whose stable crystal structures may be supposed to be mainly controlled by the number of valence electrons per atom, that is, by the previously defined VEC. The Hume–Rothery phases constitute an interesting and ubiquitous group of binary and complex intermetallic substances; it was indeed Hume–Rothery who, already in the twenties, observed that one of the relevant parameters in rationalizing compositions and structures of a number of phases is the average number of valence electrons per atom (ne/nat). An illustration of this fact may be found in Table 4.6, where a number of the Hume–Rothery structure types have been collected, together with a few more major structure types relevant to transition metal alloys. For each phase the corresponding VEC has been reported as ne/nat ratio, both calculated on the basis of the s and p electrons and of s, p and d electrons. In a first hypothesis (s and p electrons, according to Hume–Rothery), the following valence-electron numbers have been assumed: Transition elements with non-filled d-shells 0; Cu, Ag, Au 1; Mg, Zn, Cd, Hg 2; Al, Ga, In 3; Si, Ge, Sn 4 and Sb 5. In the calculation based on s, p and d electrons the following values are considered: Mn 7; Fe 8; Cu, Ag, Au 11; Mg 2; Zn, Cd, Hg 12; Al, Ga, In 13. The Hume–Rothery types listed in Table 4.6 include structures of different complexity ranging from the simple close-packed (fcc and hcp) and bcc structures to the more complex Mn-type and γ-brass type structures. As for the hexagonal hcp structures, notice that for this type several variations are known: three branches of this structure are generally considered. The ζ-hcp corresponds to the true closest packing with the value of the axial ratio c/a close to the ideal one (8/3) 1.6329 ... (see § 3.7.4 and Fig. 3.16). The ε-hex corresponds to c/a ranging around 1.55 to 1.58 and the η phase to c/a values of about 1.77 to 1.88. As observed by Lee and Hoistad (1995), the various hexagonal types can be considered genuinely different. The types listed in Table 4.6 include several groups of isostructural phases, each group corresponding to a given value of the VEC. Particular emphasis has generally

297

Intermetallic Reactivity Trends in the Periodic Table

Table 4.6. Structure types and valence electron concentration. Examples of intermetallic phases Phase conventional name and symbol, Pearson symbol fcc

cF4

(*)

ζ hcp

hP2

Example and composition range (Okamoto 2000) Cu–Zn Cu–Al Cu–Sn Cu–Sb Au–Zn Au–Al Au–Sn Ag–Al Ag–Ga

Cu–Cu61.7Zn38.3 Cu–Cu80.3Al19.7 Cu–Cu90.9Sn9.1 Cu–Cu94.2Sb5.8 Au–Au66.5Zn33.5 Au–Au87Al13 Au–Au93.4Sn6.6 Ag–Ag79.6Al20.4 Ag–Ag82Ga18

Ag–Cd Ag–In Ag–Sn Ag–Sb Au–In Au–Sn

Ag50.5Cd49.5–Ag44Cd56 Ag75In25–Ag54.1In45.9 Ag88.2Sn11.8–Ag77.1Sn22.9 Ag91.5Sb8.5–Ag83.6Sb16.4 Au87.8In12.2–Au77.6In22.4 Au90.9Sn9.1–Au82.4Sn17.6

c/a axial ne/nat s,p ratio electrons (#) Villars et al. (1995) 1–1.38 1–1.39 1–1.27 1–1.23 1–1.335 1–1.26 1–1.20 1–1.41 1–1.36 1.615–1.609 1.62–1.58 1.633–1.607 1.634–1.617 1.648–1.640 1.646–1.633

ne/nat s,p,d electrons

-------------------------------------------

1.49–1.56 1.50–1.92 1.35–1.68 1.34–1.66 1.24–1.45 1.27–1.53

------------------------------------

bcc (β-phase)

cI2

Ag–Zn Ag–Cd Ag–Al Cu–Be Cu–Zn Cu–Al Cu–Si Cu–Sn Au–Al

Ag63.5Zn36.7 –Ag41.4Zn58.6 Ag60Cd40–Ag45Cd55 Ag79.5Al20.5–Ag70.2Al29.8 Cu77.5Be22.5–Cu56.7Be43.3 Cu63.9Zn36.1–Cu44.2Zn55.8 Cu82Al18–Cu69.5Al30.5 Cu85.8Si14.2–Cu82.8Si17.2 Cu86.9Sn13.1–Cu84.3Sn15.7 Au81.2Al18.8–Au80Al20

1.37–1.59 1.40–1.55 1.41–1.60 1.22–1.43 1.36–1.56 1.36–1.61 1.43–1.52 1.39–1.47 1.38–1.40

11.37–11.59 11.40–11.53 --------------11.36–11.56 --------------11.39–11.47 --------

βMn (μ-phase)

cP20

Ag–Al Al–Au

Ag79Al21–Ag76Al24 Au4Al

1.42–1.48 1.40

--------

c152 cF1124 cP52 cP52 cI52 cI52 cP52 cI52 cI52 cP52 cI52

Cu–Zn Cu–Cd Cu–Al Cu–Ga Ag–Zn Ag–Cd Ag–In Au–Zn Mn–Zn Co–Zn Pd–Zn

Cu43Zn57–Cu30Zn70 Cu55.9Cd44.1–Cu58.2Cd41.8 Cu62.5Al37.5–Cu68.5Al31.5 Cu70.5Ga29.5–Cu65.3Ga34.7 Ag42Zn58–Ag35.3Zn64.7 Ag43Cd57–Ag37.5Cd62.5 Ag68.9In31.1–Ag66.4In33.6 Au37.5Zn62.5Au24Zn76 Mn23Zn77–Mn15.2Zn84.8 Co31Zn69–Co14.6Zn85.4 Pd24Zn76–Pd14.5Zn85.5

1.57–1.70 1.44–1.42 1.75–1.63 1.59–1.69 1.58–1.65 1.57–1.62 1.62–1.67 1.62–1.76 ----------------------

11.57–11.70 11.44–11.42 11.75–11.63 11.59–11.69 11.58–11.65 11.57–11.62 11.62–11.67 11.62–11.76 10.85–11.24 11.07–11.56 11.52–11.71 (Continued)

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Intermetallic Chemistry

Table 4.6. (Continued) Phase conventional name and symbol, Pearson symbol

Example and composition range (Okamoto 2000)

c/a axial ne/nat s,p ratio electrons (#) Villars et al. (1995)

ne/nat s,p,d electrons

ε hcp

hP2

Cu–Zn Ag–Zn Au–Zn Ag–Cd Li–Cd

Cu22Zn78–Cu12Zn88 Ag34Zn66–Ag11Zn89 Au16Zn84–Au11Zn89 Ag35.5Cd64.5–Ag19Cd81 Li29Cd71–Li20Cd80

1.568–1.554 1.587–1.567 1.557–1.555 1.582–1.556 ~1.586

1.78–1.88 1.66–1.89 1.84–1.89 1.645–1.81 1.71–1.80

11.78–11.88 11.66–11.89 11.84–11.89 11.65–11.81 --------

η

hP2

Ag–Zn Au–Zn Ag–Cd Cu–Zn

Zn–Ag0.05Zn0.95 Zn–Au0.075Zn0.925 Cd–Ag0.07Cd0.93 Zn–Cu0.025Zn0.975

1.86–1.76 1.86–1.75 1.89–1.83 1.86–1.81

2–1.95 2–1.92 2–1.93 2–1.97

12–11.95 12–11.92 12–11.93 12–11.97

(*) χ σ

cI58 tP30

Ti–Re Ti5Re24 Al–Mg Al56.8Mg43.2–Al37.7Mg62.3 Cr–Fe Cr–Co Ir–W Os–Ta

Cr44.5Fe55.5–Cr50Fe50 Cr53.6Co46.4–Cr67Co33 Ir26W74–Ir22W78 Os46Ta56–Os22Ta78

6.49 2.57–2.38 ~0.518 ~0.512 ~0.518

7.11–7.0 7.39–6.99 6.78–6.66 6.48–5.66

(*) terminal solid solutions (#) c/a values general refer to a composition range smaller than (and included in) that given in the previous column

been given to three main categories of Hume–Rothery phases: those corresponding to VEC values (based on s and p electrons) of 3/2 (that is three valence electrons every two atoms), 21/13 and 7/4, respectively. ‘Ideal’ simple formulae, representative of these groups of Hume–Rothery phases are the following: VEC 3/2, body centred cubic, (cI2-W type): CuZn, Cu3Al, Cu5Sn, etc. VEC 3/2, complex cubic, (cP20-β Mn type): Cu5Si, Ag3Al, etc. VEC 21/13 (1.62), complex cubic, 52 atoms in the unit cell (or superstructures); cP52: Cu9Al4, Cu9Ga4, Ag9In4, Co5Zn21, etc.; cI52: Cu5Zn8, γbrass, Ag5Cd8, Ag5Zn8, Ru3Be10, etc.; cF408: Fe11Zn40, etc. VEC 7/4 (1.75), hexagonal close-packed, (hP2-Mg-type or superstructures): AgZn3, Ag5Al3, etc. The given ratios and compositions are short indications of solid solution ranges, which can even overlap. It has to be noted, moreover, that the number of electrons to be considered may be uncertain. The VEC values, therefore, indicate only a composition range where one of the aforementioned structure types may occur.

Intermetallic Reactivity Trends in the Periodic Table

299

According to Girgis (1983) the existence field of the electron phases may be especially related to the combinations of d elements with the elements of the Periodic Table columns from 11 to 14 (from the Cu to Si groups). It can also be observed that, for several alloy systems, the dependence of the structures (structure types) on the electron concentration (instead of on the composition) may be clearly illustrated by well-known diagrams such as those shown in Fig. 4.39. Notice, for instance, the similar shape of the β phase field: in all three systems the β phase is the cI2-W type structure. A review of different approaches to theoretical interpretations of these correlations may be found in Kauzlarich (1996). Cahn (2001), Lee and Hoistad (1995) described how a modified tight-binding method, based on second moment scaling of the electronic density of states, can be used to rationalize both crystal structure and electron counting rules. Several electron counting rules were considered including the Hume–Rothery rules for metals and alloys (Fig. 4.40). A number of papers on the ‘evolution’ of the Hume–Rothery rules and concepts may be found in the proceedings (edited by Turchi et al. 2000) of a symposium held in St. Louis (USA) in 2000. The following titles may be mentioned: ‘Hume–Rothery Rules Revisited’ (by T.B. Massalski), ’From Hume–Rothery 8-N Rule to Valence Electron Rules for Zintl Phases and their Extensions’ (by E. Parthé), ‘The Hume–Rothery Parameters and Bonding in the Hume–Rothery and Transition-Metal Alloys’ (by R.E. Watson, M. Weinert, L.H. Bennett), ‘Controversial Concepts in Alloy Theory Re-visited’ (by D.G. Pettifor).

4.4.6 VEC and stability multi-diagrams. Brewer diagrams For certain well-defined groups of metals a compact presentation of the ‘stability regions’ of structural types in the phases of their alloys was proposed by Brewer (1965) as a function of VEC. Special attention was dedicated by Brewer to the transition metal alloys; for most of these elements the atomic sizes are reasonably close to each other, making extended solid solubility ranges possible. The VEC (valenceelectron number per atom) can often be replaced by the (averaged) group number (column number of the Periodic Table) of the components of the alloys. Brewer type diagrams for transition metals of the 6th period (6th row, 3rd transition series metals) are shown, as an example, in Fig. 4.41. The elements Ta (of the 5th group), W (6th group), Re (7th group), Os (8th group), Ir (9th group) and Pt (10th group) have been considered and their alloys with Cr, Mo and W are shown. In this figure, three composite diagrams (Brewer multi-diagrams) have been represented. To this end, isothermal sections of the diagrams of the alloys of Cr, Mo and W, with Ta, W, Re, Os, Ir and Pt, have been combined in three schemes. In the specific case of the Mo alloys, the construction of the Brewer multi-diagram is illustrated. As an example,

Temperature (°C)

1

e /a 1.5

2

1

1200

1200

1000

1000

800

b

e /a 3

1

1.5

2

3

4

1200 g0

b

1000

800

800 g1

g

600

e /a 2

1.5

b

e

600

600

400

400

400

200

200

200

g e

e

Cu

40 at.%Zn

80

Zn

Cu

20

40

60

at.%Al

80

AI

Cu

20

40

60

80

Sn

at.%Sn

Figure 4.39. The phase diagrams of the binary Cu systems with Zn, Al and Sn are shown. In order to highlight their similarities the phase equilibria have been plotted with different scales of the atomic composition in order to have the same extension for a scale based on the average v.e.c. in the alloys (number e/a of electrons per atom). Notice the consequent change of length of the at.% scale. The values 1, 2, 3, 4 have been assumed for the valence electron numbers of the metals Cu, Zn, Al and Sn.

301

Intermetallic Reactivity Trends in the Periodic Table Theoretical fcc z -hcp bcc b -Mn g -brass z ,e -hcp h -hcp

Theoretical s -phase c -phase hcp

Experimental

fcc Experimental bcc s -phase c -phase hcp fcc 7

8

9 e/a

10

11

fcc z -hcp bcc b -Mn g -brass z ,e -hcp h -hcp 11.0

11.4 e/a

11.8

Figure 4.40. Valence electron (s, p, d) concentration ranges for different types of phases as reported by Lee and Hoistad (1995). Experimental average values are compared with those computed. (For the conventional names of the phases, compare with Table 4.6.) On the left transition metal binary alloys, on the right the Hume–Rothery electron phases are shown.

the binary Mo–Pt and Mo–Os diagrams and their isothermal sections are shown in Fig. 4.41; these sections consist of horizontal lines from Mo to the other metal and contain a sequence of single and two-phase regions. The sections are reported in the multi-diagram, where they are arranged according to the positions, in the Periodic Table, of the second metals, that is, according to their ‘Group Numbers’ (from 5 for Ta to 10 for Pt). Notice that in order to have a higher coherency among the different systems, we selected the temperatures of the different isothermal sections not on the basis of absolute values but as ‘reduced’ values of the ‘average’ melting temperatures (even if the reduction was made in a rather arbitrary way) defining, for a Me–X alloy: Tred 0.7(Tmelt,Me Tmelt,X)/2 (in K)

(4.35)

In the diagrams obtained in this way, the composition limits of each phase have been connected from one binary system to the next. A number of single-phase fields (shaded regions) have thus been obtained. These correspond to well-defined structure types, which are listed in the figure.

302

Intermetallic Chemistry Pt

W G

Ir

W E

Os

W

T (°C)

C Re

W A W

W

W

Ta

2623 2200 1800

at.%

1455

1769.0

1400 1000

Mo

H

F Mo

Mo

Ir D

Os C

Mo

B

at.%

3033

2623

W

1800

Ta

1400

1898

Mo Cr Cr

at.%

Pt

Pt D

Ir E

Cr

Os C

Cr

Re

A Cr Cr

Pt

3000

2200

A

Mo

Re

at.%

T (°C)

E

Mo

Mo

Pt G

W at.%

A: cI2-W (A2) B: cI58-a Mn, c phase (A12) C: tP30-s (Cr−Fe) (D8b) D: cF8-Cr3 Si (A15) E: hP2-Mg (A3) F: hP8-Ni3 Sn (D019) G: cF4-Cu (A1) H: oI6-MoPt2

Ta

Figure 4.41. Brewer type multi-component diagrams for 6th period transition metals. Isothermal sections of the diagrams of the alloys of Cr, Mo and W, with Ta, W, Re, Os, Ir and Pt, are combined in three composite diagrams. The hatched fields are the single-phase stability regions, corresponding to the structure types listed. The binary diagrams reported on the right-hand side (Mo–Pt and Mo–Os) show the way the composite diagrams are built. In the Mo–Os system, for instance, along the selected isotherm (see the text), the following single-phase fields (segments) may be identified: Mo solid solution (cI2-W type, 0–13 at.%Os), Mo3Os (Cr3Si-type, 24.5–25.5 at.%Os), σ-phase (30–39at.%Os) and Os solid solution (hP2-Mg type, 54.5–100 at.%Os). These single-phase segments are marked on the Mo–Os horizontal line of the Mo composite diagram (in the fields labelled (A), (D), (C) and (E) respectively).

Intermetallic Reactivity Trends in the Periodic Table

303

Notice, moreover, that the multi-element lateral axis of each multi-diagram may be considered as corresponding to the sequence of sections of the inter-transition metal binary systems: Ta–W, then W–Re, Re–Os, etc. The role played also for this group of alloys by the electron number (or better by the average group number) may be noticed by the fact that on the same axis we find, not only a schematic representation of the binary systems formed by two adjacent metals, but also of those given by non-adjacent elements (see Fig. 4.42). In this figure, indeed, the phase sequences formed for instance in the isothermal sections of the W–Re, Re–Os, as well as in the W–Os system, are in agreement with the reported ‘multidiagram’. Therefore every point in the lateral axis represents all the binary mixtures corresponding to the same average group number. A point for instance halfway between W and Re should ideally correspond to a mixture of 50 at.% W and 50 at.% Re, but also to a mixture of 25 at.% Os with 75 at.% W and, say, to a mixture of 12.5 at.% Pt and 87.5 at.% W, etc. All these mixtures correspond indeed to an average group number 6.5 (that is 6 0.5 7 0.5; 6 0.75 8 0.25; 6 0.875 10 0.125). Similar considerations could be extended from the right-hand axis to the entire diagram, the internal points of which will represent ternary mixtures formed, in the example shown in Fig. 4.42, by Mo with various combinations of two of the other metals.

Pt

Mo F

H

G Ir

Mo D

E Os

Mo C

Mo

B

Re

A Mo

W

Mo

Ta

Figure 4.42. Mo alloys multi-diagram. Notice that along the vertical axis, from Ta to Pt, the sequence of the isothermal sections Ta–W, W–Re, Re–Os, etc. is shown. In the same axis an approximate representation is also suggested for the other binary combinations (Ta–Re; Ta–Os, Ta–Ir, etc., W–Os, W–Ir, etc.). A confirmation of the (even partial) validity of this representation is given by the phase sequences observed in the W–Re and Re–Os systems in comparison with that of the W–Os system. (For the symbols see Fig.4.41).

304

Intermetallic Chemistry Mo

6

7

8

9 Pt 10 9 8.5

Mo

Ir

9

8 7.5 Mo

Mo

Mo

7 6.5

Os 8

Re 7

6

W 6 5.5

Mo

Ta 5

Figure 4.43. Trends of the isoelectronic curves in the different Mo–Me systems and in their combinations (curves of constant average group number of the atoms involved). The values of the average electron number per atom are indicated.

Fig. 4.43 shows for all such combinations the curves corresponding to a constant ‘average group number’ (in a way, ‘isoelectronic’ lines). Notice that their shapes are, more or less, similar to that of the boundary lines, shown in the previous figures for the various phase stability regions. A different version of these diagrams is presented, according to Ferro and Cacciamani (2002), in Fig. 4.44, where sections of the binary and ternary systems formed by Mo are collected in a triangle with Mo at one vertex. The construction criterion is similar to that adopted in § 4.3.2.3 for the rare earth-magnesium multi-diagrams. The triangle is built by connecting to this vertex the different segments representing the sections of the various binary Mo–Me diagrams. As in the previous example, the different transition metals are arranged on the third side according to their group number. Notice that in this representation the isoelectronic curves (not reported in figure) would be straight lines parallel to each other and to the segment Mo–W which corresponds to six electrons per atom. Notice now that, on the assumption that the alloying behaviour is essentially dependent on the value of the electron concentration, the multi-diagram may be considered to contain a representation (and a ‘simulation’ and a ‘prediction’) not only of the binary diagrams but also of the ternary ones.

305

Intermetallic Reactivity Trends in the Periodic Table (a)

(b)

Pt

Pt

Ir

Ir

G H

Os

Os E

F

Re

E D C

B

Re C

W

D

W

A

A Ta

Mo Os

(c)

Mo

Ta

(d)

E Os E

C

D

C

W

D A Mo

A W

Mo

Figure 4.44. Isothermal multi-diagram, at the reduced temperature Tred (see text), of the Mo–Me and Mo–Me1–Me2 systems formed by Mo with a number of transition metals (T ) of the 6th row. Single-phase fields are represented by the hatched regions. For the phase symbols see Fig.4.41. (a) The sections of the different Mo binary systems are reported along the Mo–Me1 segments with the common Mo point at one vertex of the triangle. In this representation, the isoelectronic curves (not shown) are straight lines parallel to each other (and to the segment Mo–W which corresponds to six electrons per atom). (b) The simulation of the Mo–W–Os system is shown as it is contained in the multi-diagram. Notice that in this ‘simulation’ the Re point simply represents a composition (a mixture) having an average number of seven electrons per atom. (c) The experimental isothermal (1600°C) section of the Mo–W–Os diagram (Villars et al. 1995). (d) The same experimental Mo–W–Os diagram is presented with a convenient reduction (compression) of the W–Os axis in order to make the comparison with the simulated diagram of (b) easier.

In Fig. 4.44, as a specific example, the simulation of a ternary Mo diagram (in this case the Mo–W–Os diagram) ‘extracted’ from the multi-diagram is compared with the experimental version of the same system. A general agreement may be noticed; this may highlight the relevance, and the limits, of the role played by the average valence-electron number per atom

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(or average group number) in the stabilization of a phase with a well-defined structure and composition. The advantages of a compact representation such as that of the multi-diagrams are clear. In this case, it highlights the role of the VEC, whereas in the previously reported (§ 4.3.2.3) example of the magnesium alloys of the rare earths, the role of the (average) atomic dimensions was singled out. Similar criteria have been successfully applied to the description of several groups of alloys; Engel (1969) for instance presented Brewer type diagrams also for the combinations of the fourth and fifth column transition metals (Ti, Zr, Hf, and V, Nb, Ta) with B, C, N, O. 4.4.7 New developments in electronic counting in intermetallic compounds It has been recently underlined (Grin 2006) that the understanding the nature of intermetallic compounds is still not complete, mainly due to the strong bias imposed by applications research and to insufficient comprehension about their chemical bonding. Grin even remarked that some questions cannot be definitely answered, for instance: why some intermetallic compounds form only at distinct compositions, why others give homogeneity ranges, why some structural motifs are stable and can be often found among intermetallics, while others appear very rarely. Moreover it must be realized that attempts to find causal links between properties and chemical bonding in this class of inorganic substances are often frustrated by the lack of reliable information on bonding and properties and therefore on their relationship. He remarked that the ‘chemical bonding in intermetallic compounds is a rather open question : the local environment of atoms in the crystal structures of intermetallic compounds is difficult to describe by means of traditional molecular orbital pictures as well as by means of the free electron gas model. The atomic coordination is usually more complex as in other inorganic compounds and not necessarily may be derived from the closest sphere packing motifs characteristic or instance for structure of elemental metals’. (See also Kohout et al. 2002, Kohout 2004; Alekseeva et al. 2006, Ormeci et al. 2006a). The bonding analysis in real space is a promising way to reach a clearer comprehension of the subject. A number of quantum chemical functions are being considered and developed as tools for the analysis of the electron density and for the examination of bonding problems in the chemical compounds in the direct space. The ‘electron localization function’ has been especially considered: this function, originally defined in the framework of Hartree–Fock theory (Becke and Edgecombe 1990), and later developed for ‘density functional theory’ (Savin et al. 1992), belongs to the so-called bonding indicators in the real space (position space). The electron localization function (an approximation of the more general function ‘electron localization indicator’, Kohout 2004) represents a charge distribution of electron pairs,

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and thus is a suitable tool for the analysis of chemical bonding in terms of the Lewis theory, in which the pair formation has a central role. An application of the electron localization function together with electron density gives a way of electron counting for a large group of intermetallic compounds. Full references and computation details have been reported. Crystal structure refinement and chemical bonding description in a number of substances have been obtained such as in LaMe2Ge2 (Kohout et al. 2002), diamond, elemental metals (Ormeci et al. 2006b), Eu5Ga9. For MgB2 (Grin 2006), which is not a Zintl phase, a bond order of 1.25 was derived in the graphite-like boron nets of Mg0.96B2, slightly smaller compared to 1.33 in Al0.9B2 (which is in agreement with the Zintl count). The crystal structure of the ternary boride Mg8Rh4B (Alekseeva et al. 2006) was identified as a boron stabilized, filled variant of the cF96-Ti2Ni-type structure, and was described in terms of covalently bonded [Rh4B]3 anions embedded in a cationic magnesium matrix. 4.4.7.1 Stability maps and correlation diagrams. As a concluding remark to some topics considered in this chapter and a recapitulation of procedures often employed in the description and classification of intermetallic systems, a little additional information about ‘correlation diagrams’ is included here. Several authors indeed have tried to classify and order the numerous data concerning the different intermetallic substances by using two (or three) dimensional structure maps (stability, existence diagrams). General comments on several correlation diagrams, maps and functions and their ‘predictive’ applications and use as a tool for data-driven material design have been reported in literature (See a systematic description for instance in the ‘Pauling File’ (Villars et al. 2004)). Maps and correlation diagrams have been prepared by selecting coordinates based on those parameters (generally properties of the component elements) which were considered to be determining factors of the structural stability and phase formation control. These concepts have been previously introduced (especially in § 2.2.1.3 and in the following paragraphs). A few more remarks will be reported here; particular reference will again be made to the Pettifor’s chemical scale and structure maps. 4.4.7.1.1 Pettifor’s structure maps: additional remarks. We have seen that in a phenomenological approach to the systematics of the crystal structures (and of other phase properties) several types of coordinates, derived from physical atomic properties, have been used for the preparation of (two-, three-dimensional) stability maps. Differences, sums, ratios of properties such as electronegativities, atomic radii and valence-electron numbers have been used. These variables, however, as stressed, for instance, by Villars et al. (1989) do not always clearly differentiate between chemically different atoms.

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As already mentioned, Pettifor (1984–1986) created a chemical scale (χ) which orders the elements along a single axis. This scale, and the progressive order number of the elements in this scale, the so-called Mendeleev number M, starts with the least electronegativity element and ends with the most electronegative one (see Table 2.2). We have seen that for binary X–Y alloys, two-dimensional χX, χY (or MX , MY ) maps may be prepared which are useful for instance in the classification of compound-forming (or non-forming) systems. Similar MX , MY maps may be prepared for binary compounds XnYm (with a given n:m ratio). It has been proved that by using this ordering of the elements, an excellent separation may be obtained between the different structure types of the binary compounds of various stoichiometries (n:m 1:1, 1:2, 1:3, 1:4, ...., 1:13, 2:3, 2:5, ..., 2:17, 3:4, ..., etc.) (Pettifor 1986). See also Villars et al. (1989) who have updated the Pettifor maps for several stoichiometries. An extension of the application of these maps to the systematic description of certain groups of ternary alloys has been presented also by Pettifor (1988a, b). Composition averaged Mendeleev numbers can be used, for instance, in the description of pseudo-binary, ternary or quaternary alloys. All these maps show well-defined domains of structural stability for a given stoichiometry, thus making the search easier for new ternary or quaternary alloys with a particular structure type (and which, as a consequence, may have the potential of interesting properties and applications (Pettifor 1988a, b)). 4.4.7.1.2 Savitskii–Gribulya–Kiselova method (cybernetic computer-learning prediction system). A powerful formulation and planning of a rational description of intermetallic and, more generally, inorganic chemistry was suggested by Savitskii et al. (1980). Cybernetic computer-learning methods were proposed for predicting the existence of intermetallic phases with a given structure and/or with certain properties. The computer learning, in this case, is a process of collecting experimental evidence on the presence (or absence) of a property of interest in various physicochemical systems (defined by means of a convenient selection of the properties of the components). As a result of machine learning a model is produced of the characteristic exhibition of a property (for instance, the formation of a particular type of chemical compound) which corresponds to a distribution ‘pattern’ of this property in the multidimensional representative space of the properties of the elements. The subsequent pattern recognition corresponds to a criterion for the classification of the known compounds and for the prediction of those still unknown. Examples of this approach reported by Savitskii are the prediction of the formation of Laves phases, of CaCu5 type phases, of compounds XY2Z 4 (X, Y any of the elements, Z O, S, Se, Te), etc. (Data on the electronic structures of the components were selected as

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input.) The main principles and applications for the cybernetic prediction of inorganic substances which would have pre-defined properties have been summarized and discussed by Kiselyova (1993). 4.4.7.1.3 Analysis of the dependence of the behaviour of alloy systems on the properties of the component elements. In an examination of the binary structure types containing more than five representatives, Villars and Girgis (1982) observed that 85% exhibited the following regularities: (a) linear dependence of interatomic distances on concentration weighted radii; (b) narrow ranges of the space-filling parameter and of the unit cell edge ratio c/a (and b/a) for the representatives of a given structure type; (c) dependence between the position of the elements in the Periodic Table (in the s, p, d and f blocks) and their equipoint occupation in the structure; (d) narrow grouping of the phases pertaining to a given structure type, in isostoichiometric diagrams based on the positions of the components in the Periodic Table. These relationships have been used to predict the existence and/or the structure type (and the unit cell characteristics) of binary intermetallic compounds. By using a systematic procedure to find the relevant element properties representing the alloying behaviour of binary systems, Villars (1983, 1985) defined three expressions for atomic properties which enable systems that form compounds to be separated from those that do not. A similar procedure was also used by Villars to find atomic property expressions which could be used to distinguish the crystal structures of intermetallic compounds; 182 sets of tabulated physical properties and calculated atomic properties were considered. These were combined, for binary phases, according to the modulus sums, differences and ratios. The best separations were obtained by using threedimensional maps, which, for a binary AxBy, x y compound, were based on the following variables (Villars and Hulliger 1987, Villars et al. 1989). ΣVE, averaged sum of the valence electrons of the elements A and B, defined by ΣVE (xVEA yVEB)/(x y),

(4.36)

ΔX, electronegativity difference, according to the Martynov and Batsanov (1980) scale defined by ΔX [2x/(x y)] (XA XB)

(4.37)

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Δ(rs rp)Z, difference of Zunger’s pseudo-potential radii sum (Zunger (1981), defined by Δ(rs rp)Z [2 x/(x y)][(rs rp) Z,A (rs rp)Z,B]

(4.38)

Several structural types, corresponding to about 5500 binary compounds and alloys, were considered; 147 structure types were classified as 97 coordination types. The applications of these maps, which, in the most favourable cases make it possible to predict not only the CN and polyhedron but also the structure type or a limited number of possibilities, were discussed. The possible extension to ternary and quaternary phases was also considered. As an example of an investigation on a selected group of ternary alloys, a paper by Hovestreydt (1988) can be mentioned. In analogy with the work of Villars, a three-dimensional structure stability diagram was constructed. For the equiatomic RETX compounds formed by the rare earth metal (RE) with transition metal (T) and Ga, Si or Ge (X) the variables considered were: the difference in atomic radii rX rRE, the Martynov–Batsanov electronegativity of the T metal and the expression GT GX PX, related to the position in the Periodic Table of the T and X elements, where G is the group and P the period number. A good separation was obtained for the 8 structural types considered (corresponding to 202 compounds). Special, modified, structure stability diagrams have been used for the elements by Villars and Daams (1993). Maps were built by using the variables, valenceelectron number and Zunger pseudo-potential radius and reporting the atomic environment types (see § 3.7.5) found in the element structures. A simple separation into different stability domains was observed. By including the high-temperature, highpressure crystal structure data, a prediction was made of the atomic environment modifications, hitherto unknown for several elements, to be found under highpressure, high-temperature conditions. An empirical relation between band gap and Zunger’s orbital electronegativity in sp-bonded compounds has been determined by Makino (1994a) using a formula derived from the bond orbital model. Based on the bond orbital model and Zunger’s orbital electronegativity, new structural maps of AB, AB2 and AB3 compounds between transition metals have been successfully constructed (Makino 1994b). The relevant data concerning the different elements have been reported in the specific paragraphs of Chapter 5. 4.4.7.1.4 Prediction of the properties of selected families of alloys: Gschneidner’s relations as an example. Stability maps and/or correlation diagrams

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may be especially simple and easy to handle for selected groups of similar alloys; for instance, alloys of the elements of the same group of the Periodic Table. The alloys of the rare earth metals, especially the ‘trivalent ones’, are a good example. It is well known that, within this family of elements, several properties change according to well-recognized and systematic patterns. The atomic number itself can be used in this case as a simple and convenient chemical parameter. In several instances it has been pointed out that a systematic consideration of the crystal structures and of the phase diagrams of alloys formed by analogous elements (such as those of the trivalent rare earth family) enables a number of empirical regularities to be deduced and theoretical statements to be made. See a general discussion on this subject by Gschneidner (1969) Gschneidner and Mc Masters (1971), the comments by Yatsenko et al. (1979, 1983), Colinet et al. (1984a, b) on alloy thermodynamics, the papers by Massalski (1989) on the applications of this behaviour to phase diagram assessment, by Parthé and Chabot (1984), Rogl (1984) and by Iandelli and Palenzona (1979) for a systematic crystal-chemical description. See Sereni (1984) for examples and a discussion of the properties of the rare earth metals themselves. See also some comments on this point in § 4.3.2.2. Criteria based on the mentioned characteristics have been used in assessment procedures and in the prediction of phase diagrams and of phase and structure type formation. Fig. 4.15 may be considered as an example of such typical trends and of their correlations. Special applications (prediction of Pm-alloys) have been described by Saccone et al. (1990). The applicability of similar criteria to the assessment and prediction of phase equilibria in selected groups of ternary rare earth alloys, containing two different rare earth metals, has been exemplified by Giovannini et al. (1995a, b) in the description of complex Mg–R alloy systems. Considering other families of similar compounds, the contributions given by Guillermet and Frisk (1992), Guillermet and Grimvall (1991) (cohesive and thermodynamic properties, atomic average volumes, etc. of nitrides, borides, etc. of transition metals) are other examples of systematic descriptions of selected groups of phases and of the use of special interpolation and extrapolation procedures to predict specific properties. 4.4.7.1.5 Miedema’s theory and structural information. The Miedema model for energy effects in alloys, presented in § 2.2.1.3 has been very useful in an evaluation, albeit approximate, of the formation enthalpies and in the ‘prediction’ of compound formation capability. For an example of the application and limits of this model, see the comments on the thermochemistry of the Laves phases reported in § 3.9.3. However notice that the general usefulness of the Miedema approaches has diminished with time, both for its inherent approximation and for

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the increasing number of experimentally determined and available values of the formation enthalpy. In any case, just for the sake of completeness we remind here that the two main Miedema parameters, ΔΦ* and ΔnWS1/3, have also been used (Zunger 1981, Rajasekharan and Girgis 1983) as variables for the construction of structural plots of intermetallic phases (stability maps, correlation diagrams). REFERENCES

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Parthé, E. (1964) Crystal Chemistry of Tetrahedral Structures (Gordon and Breach, New York). Parthé, E. (1969) The Concept of a partial electron concentration value and its application to problems in crystal chemistry. In: Developments in the Structural Chemistry of Alloy Phases, ed. Giessen, B.C. (Plenum Press, New York), p. 49. Parthé, E. (1980) Valence and Tetrahedral Structure Compounds, ed. Parthé, E. (Summer School on Inorganic Crystal Chemistry, Geneva). Parthé, E. (1995) Wurtzite and Zinc-Blende Structures. In Intermetallic Compounds Principles and Practice, eds. Westbrook, J.H. and Fleischer, R.L. (John Wiley & Sons Ltd., Chichester), Vol. 1, pp. 343–362. Parthé, E. and Chabot, B. (1984) Crystal structures and crystal chemistry of ternary rare earth-transition metal borides, silicides and homologues. In: Handbook on the Physics and Chemistry of Rare Earths, ed. Gschneidner Jr., K.A. and Eyring, L. (North–Holland, Amsterdam), Vol. 6, p. 113. Pauling, L. (1947) J. Amer. Chem. Soc., 69, 542. Pauling, L. (1960) The Nature of the Chemical Bond (Cornell University, Ithaca, New York). Pearson, W.B. (1972) The Crystal Chemistry and Physics of Metals and Alloys (WileyInterscience, New York). Pettifor, D.G. (1984) Solid State Commun., 51, 31. Pettifor, D.G. (1985) J. Less Common Met., 114, 7. Pettifor, D.G. (1986) J. Phys. C: Solid State Phys., 19, 285. Pettifor, D.G. (1988a) Physica B, 149, 3. Pettifor, D.G. (1988b) Mat. Sci. Technol., 4, 675. Pettifor, D.G.(1995) Structure mapping. In: Intermetallic Compounds-Principles and Practice, eds. Westbrook, J.H. and Fleischer, R.L. (John Wiley & Sons Ltd., Chichester), Vol. 1, pp. 419–438. Pettifor, D.G. (2000) Controversial concepts in alloy theory revisited. In: The Science of Alloys for the 21st Century, eds. Turchi, E.A., Shull, R.D., Gonis, A. (TMA, The Minerals, Metals and Materials Society, Warrendale, Pennsylvania), p. 121. Potel, M., Chevrel, R. and Sergent, M. (1980) Acta Crystallog., B36, 1319. Rayner-Canham, G.W. (2004) The richness of periodic patterns. In: The Periodic Table: Into the 21st Century, eds. Rouvray, D.H. and King, R.B. (Research Studies Press Ltd., Baldock, Hertfordshire), p. 161. Rajasekharan, T. and Girgis, K. (1983) Phys. Rev. B, 27, 910. Richter, K.W., Prots, Y. and Grin, Y. (2005) Inorg. Chem., 44, 4576. Rogl, P. (1984) Phase equilibria in ternary and higher order systems with rare earth elements and boron. In: Handbook on the Physics and Chemistry of Rare Earths, eds. Gschneidner Jr., K.A. and Eyring, L. (North-Holland, Amsterdam), Vol. 6, p. 335. Rouvray, D.H. and King, R.B. eds. (2004) The Periodic Table into the 21st Century (Research Studies Press Ltd., Baldock, Hertfordshire, UK). Saccone, A., Delfino, S. and Ferro, R. (1990) CALPHAD, 14, 151. Savin, A., Flad, H.J., Flad, J., Preuss, H. and von Schnering, H.G. (1992) Angew. Chem. Int. Ed. Engl., 31, 187. Savitskii, E.M., Gribulya, V.B. and Kiselyova, N.N. (1980) J. Less Common Met., 72, 307.

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Schäfer, H. and Schnering, H.G. (1964) Angew. Chem., 76, 833. Schomaker, V. and Stevenson, D.P. (1941) J. Am. Chem. Soc., 63, 37. Sereni, J.G. (1984) J. Phys. Chem. Solids, 45, 1219. Sevov, S.C. (2002) Zintl phases. In: Intermetallic Compounds, eds. Westbrook, J.H. and Fleischer, R.L, (John Wiley & Sons Ltd, Chichester, England), Vol. 3, Chapter 6, p 113. Simon, A. (1981) Angew. Chem. Int. Ed Engl., 20, 1. Simon, A. (1983) Angew. Chem. Int. Ed. Engl., 22, 95. Simon, A. (1988) Angew. Chem. Int. Ed Engl., 27, 159. Simon, A. (1992) Metal-rich compounds. In: Solid State Chemistry (Compounds), eds. Cheetham, A.K. and Day, P. (Clarendon Press, Oxford, England). Simon, A. (1995) J. Alloys Comp., 229, 158. Steurer, W.(2005) Stable clusters in quasicrystals – fact or fiction? Proceedings of the 9th International Conference on Quasicrystals, Ames, 22–26 May, http://www.icq9.ameslab.gov Stone, H.E. (1979) Acta Met., 27, 259. Teatum, E.T., Gschneidner Jr., K.A. and Waber, J.T. (1968) Compilation of Calculated Data Useful in Predicting Metallurgical Behavior of the Elements in Binary Alloy Systems, Report LA-4003, UC-25, Metals, Ceramics and Materials, TID-4500, Los Alamos Scientific Laboratory. Turchi, E.A., Shull, R.D. and Gonis, A. eds. (2000) The science of alloys for the 21st century: A Hume–Rothery symposium celebration, Proceedings of a Symposium Held During the Fall Meeting St. Louis, October 2000 (TMS). Uhlenbeck, G.E. and Goudsmit, S. (1925) Naturwiss., 13, 925. Van der Lugt, W. (1996) Polyanions in liquid ionic alloys. In: Chemistry, Structure and Bonding of Zintl Phases and Ions, ed. Kauzlarich, S.M. (VCH Publisher, New York), p. 183. Van der Lugt, W. and Verkerk, P. (2002) Molten Zintl alloys. In: Inorganic Chemistry Highlights eds. Meyer, G., Naumann, D. and Wesemann, L. (Wiley, VCH, Weinheim), p. 1. Vegard, L. (1921) Z. Physik, 5, 17. Villars, P. (1983) J. Less Common Met., 92, 215. Villars, P. (1985) J. Less Common Met., 109, 93. Villars, P. (1995) Factors governing crystal structures. In: Intermetallic Compounds Principles and Practice, eds. Westbrook, J.H. and Fleischer, R.L. (John Wiley & Sons Ltd., Chichester), p. 227. Villars, P. and Daams, J.L.C. (1993) J.Alloys Compd., 197, 177. Villars, P. and Girgis, K. (1982) Z. Metallkd., 73, 455. Villars, P. and Hulliger, F. (1987) J. Less Common Met., 132, 289. Villars, P. Mathis, K. and Hulliger, F. (1989) The Structures of Binary Compounds. Cohesion and Structure, eds. Boer, F.R. and Pettifor, D.G. (North-Holland, Amsterdam), Vol. 2, p. 1. Villars, P., Prince, A. and Okamoto, H. ed. (1995) Handbook of Ternary Alloy Phase Diagrams (ASM International, Materials Park, OH), Vol.1–10. Villars, P., Berndt, M., Brandeburg, K., Cenzual, K., Daams, J., Hulliger, F., Massalski, T., Okamoto, H., Osaki, K., Prince, A., Putz, H. and Iwata, S. (2004) J. Alloys Comp., 367, 297.

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Wade, K. (1976) Adv. Inorg. Chem. Radiochem., 18, 1. Wells, A.F. (1984) Structural Inorganic Chemistry, 5th Edition (Clarendon Press, Oxford). Westbrook, J.H. (1977) Metall. Trans., 8A, 1327. Westbrook, J.H. and Fleischer, R.L. eds. (1995) Intermetallic Compounds. Principles and Practice (John Wiley & Sons Ltd., Chichester). Yatsenko, S.P., Semyannikov, A.A., Semenov, B.G. and Chuntonov, K.A. (1979) J. Less Common Met., 64, 185. Yatsenko, S.P., Semyannikov, A.A., Shakarov, H.O. and Fedorova, E.G. (1983) J. Less Common Met., 90, 95. Zen, E.-An. (1956) Amer. Min., 41, 523. Zintl, E. and Dullenkopf, W. (1932) Z. Phys. Chem., B16, 195. Zunger, A. (1981) Structure and Bonding in Crystals, eds. O’Keeffe, M. and Navrotski, A. (Academic Press, New York), Vol. 1, p. 73.

Chapter 5

Elements of Alloying Behaviour Systematics

5.1. INTRODUCTORY NOTES

This chapter describes typical aspects of the alloying behaviour of the different metals, with reference to the general topics previously discussed. The metals will be considered according to their order in the Periodic Table and to their reactivity towards the other elements. The Pettifor scale and the so-called Mendeleev number have been used in previous chapters as an introduction to some aspects of the alloying systematics. Owing to the considerable amount of available information relevant to the numerous intermetallic phases and simple and complex alloy systems studied, only a selection of these data is presented here. Although our treatment is by no means exhaustive and not all the alloy systems or intermetallic systems will be dealt with, the main aim is to give examples of the systematic alloying behaviour of the metals and of the typical aspects of intermetallic chemistry. Close attention is devoted to the crystal chemistry of the intermediate phases and to the mutual reactivity of different metal pairs as depicted by their phase diagrams. Analogies among various alloys are drawn, and the trend of their properties along the Periodic Table is particularly highlighted. The uses and applications of some common metals and of their alloys are briefly discussed. Binary systems and intermetallic phases are considered. For a few metals, however, examples of complex alloys are described in order to present some aspects of general interest and/or on the basis of the variety of compounds and applications known. Generally, each paragraph of this chapter is dedicated to a group (or column) of the Periodic Table. The introduction and the initial part of each paragraph describe the metals of the group and provide general information and reference data, such as their reference electron configurations, their occurrence and preparation, a few of their atomic and physical properties and their general chemical properties and reactivity. Numerical values for some properties of the elements and, in some cases, of the compounds are reported. Selected atomic and physical properties like atomic radii, melting and boiling temperatures of the elements and the related transformation enthalpies are considered. Solid-state data of the elements are also given including the structures of the different allotropic forms, their temperature (and pressure) stability ranges, the corresponding lattice parameters, as well as the relevant values of the average atomic volume in the solid (as obtained 319

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from the cell volume divided by the number of atoms in the cell), the corresponding molar volume (atomic volume multiplied by the Avogadro number) and the calculated density (instead of the experimental density which often depends on the particular mechanical treatments to which the metal has been subjected). Concerning the ionization energies, in order to avoid very long lists, only two or three values, from the first to the last, relevant to the valence electrons and the lowest value of the core electrons are given. For the above-mentioned data, we are indebted to a number of fundamental treatises and publications of inorganic chemistry to which the interested reader may refer for a thorough examination of the subject. These data will play a significant role in defining and discussing the alloying behaviour of the metals involved. With regard to the values reported in the tables, we are more concerned with the general order of magnitude rather than with the precise values. In literature, slightly different values appear, owing to the variety of preparation and measurement techniques or often, for a given phase, to the existence of not so well-defined homogeneity ranges. The tables are therefore intended to provide a general idea of the behaviour of the elements, and particularly of the compounds, as well as of the trends of quantities such as melting and transformation temperatures, enthalpies, lattice parameter data, etc. However, accurate and more recently assessed individual values of such parameters and quantities should be found in the original literature. 5.1.1 Symbols and nomenclature Besides the crystallographic and chemical symbols and nomenclature previously introduced, a few special symbols have been used in this chapter. Generally, for nearly all the metals (Me), a summary is given of their reactivity with the other elements. This is outlined in the text and in figures representing the Periodic Table. In some cases, more than one table is provided for each element. The different binary systems Me–X are identified by the position in the Table of the element X, and their characteristics are briefly described by one of the following symbols inserted in the corresponding box: : This indicates the element being described. : Some intermediate phases formed either from the liquid or, for instance, by ordering in the solid state, have been identified in the system considered. See several examples shown in Figs 2.18 and 2.19 as well as that in Fig. 2.20 where a continuous solid solution is formed, but ordered phases (intermediate compounds) at different temperatures may also be observed. Notice, however, that in many cases, compounds have been identified by preparative and crystallographic studies only, even without being defined by a phase diagram investigation.

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Contradictions and disagreements may therefore be found in the literature. In the tables included in this chapter, intended to describe the reference stable behaviour, attention has been especially dedicated to the results of phase diagram studies. : The formation of intermediate phases has been suggested but not confirmed. : The system has been studied and no intermediate phases have been found. The phase diagram resulted, for instance, in a simple peritectic or eutectic type or in an extended monotectic type. The only solid phases existing in the system are the terminal phases. See the examples of Ag–Cu, Au–Si, Ga–Bi in Figs 2.10, 2.11 and 2.16, respectively. : No reliable information on the phase diagram and/or any intermediate phases. The formation of at least one solid solution phase extending from one component to the other has been identified in some Me–X phase diagrams. This phase may either be stable in the complete temperature range or only in a limited temperature interval. (See the V–Mo and Ni–Au diagrams in Figs. 2.1 and 2.9, the Ta–V diagram in Fig. 2.19 and the Au–Cu system in Fig. 2.20.) Elements X, forming diagrams characterized by extensive solid solutions with a given metal Me, are generally close to each other in the Periodic Table and to the metal Me. Further tables show such cases. A similar layout has been generally adopted in the preparation of the various tables and schemes relevant to the different groups of elements. However, from one group to another a few changes may be noticed: this may be due to the more or less complete availability of the relevant data or to some peculiar characteristics of the element properties (and/or of their trends). Typical examples are: the description of the alloying behaviour of a group of ‘divalent’ metals (Ca, Sr, Ba together with Eu and Yb) as discussed in the introductions of § 5.4 and 5.12), the presentation of the lanthanides and actinides (§ 5.5), and the description of the metals of the 8th, 9th, and 10th groups (‘iron family’ and ‘platinum family’ metals and alloys in § 5.10). Commercial alloys: composition, nomenclature. A simple and general way of identification of a commercial alloy (or of a group of similar alloys) consists of a ‘label’ which gives (as rounded values) the mass% contents of the main components indicated by their chemical symbols. The alloy, for instance, Ti–6Al–4V, is a titanium-based alloy typically containing 6 mass% aluminium and 4 mass% vanadium. Notice however that for several common metal alloys (Mg, Al, Fe, etc.) special designation codes are used. As an example of the standard ASTM designation system, the codes used for the commercial magnesium alloys are shown in § 5.12.4.5.

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A complete reference to this subject may be found in the ASM Handbook Series published by ASM International (USA). Alloy crystal and thermal data symbols. A number of tables show, for selected alloys, the highest melting points observed in the systems considered, as well as the mechanism of formation (p peritectic melting, syn synthetic reaction, s.s.r. solid-state reaction, est. estimated melting point, etc.), the value of the Raynor Index (1, 1 or 1). The question mark means that no reliable data are available. A selection of the crystal data is generally given in tables where examples of the most frequent structural types found in the alloys of the concerned metals are listed. The Pearson symbols and the coordination environmental symbols are given. The accompanying texts underline some characteristics of the structure types observed in the alloys of the given group of metals. However, for the crystallography and general characteristics of each structure (coordination, relations with other structure types, occurrence, etc.), reference should be made to Chapter 7 where a number of common structural types have been collected and described. In several cases, without attempting to give an exhaustive description, an indication is given of the homogeneity ranges for various solid solution phases. At a given stoichiometry, several intermediate compounds may exist as different polymorphs depending on temperature; this means that different crystal structures may be listed in the tables for the same stoichiometry. For simplicity, the different polymorphs are reported in the tables without the indication of their respective temperature ranges of existence. Additional information on this subject may be found in Chapter 7 and in the collections of phase diagrams and crystal structure data in the literature sources reported below. Alloys of the p-block elements. In this chapter a look is given at the alloys and compounds of nearly all the elements from the metals of the 1st group up to the semimetals and non-metals of the 16th group. This is especially to show the gradual change in properties and behaviour on passing through the full extension of the Periodic Table. However, since particular attention is given to the intermetallic systems, a much more reduced description is presented for the elements of the last groups. Sources of the specific data given in the tables were from the following authors: Barin and Knacke (1973); Chase (1998); Freeman and Keller (1991); Gschneidner and Calderwood (1982); Massalski et al. (1990); Okamoto (2000); Shannon (1976); Teatum et al. (1968); Villars and Calvert (1991); Villars et al. (1995).

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Elements of Alloying Behaviour Systematics 5.2 ALLOYS OF HYDROGEN

Hydrogen, H

5.2.1 Introduction Hydrogen: (H, 1s1), name and symbol from the Greek υδωρ ´ -γενναω ´ (water forming). First identified as an element by Henry Cavendish (1766). Odourless, colourless gas, flammable and explosive. Hydrogen atomic number 1, atomic relative mass 1.00794. Occurrence. Hydrogen is the most abundant element of the universe. It is the tenth abundant element (in mass%) of the earth’s crust, after O, Si, Al, Fe, Ca, Na, K, Mg, Ti. Isotopes of hydrogen. Three isotopes of hydrogen are known 1H, 2H (deuterium or D), 3H (tritium or T). Isotope effects are greater for hydrogen than for any other elements (and this may by a justification for the different names), but practically the chemical properties of H, D and T are nearly identical except in matters such as rates and equilibrium constants of reactions (see Tables 5.1a and 5.1b). Molecular H2 and D2 have two forms, ortho and para forms in which the nuclear spins are aligned or opposed, respectively. This results in very slight differences in bulk physical properties: the two forms can be separated by gas chromatography. Deuterium. Naturally occurring hydrogen contains 0.0156 at.% D. Deuterium as D2O is separated from H2O by fractional distillation or electrolytic enrichment of normal water. Table 5.1a. Atomic properties of hydrogen and its isotopes. Property

H

D

T

Relative atomic mass Nuclear spin quantic number Radioactive stability 1st ionization energy/kJ/mol

1.007825 1/2 Stable 1312.0

2.014102 1 Stable

3.016049 1/2 βt1/2 12.35y

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Intermetallic Chemistry Table 5.1b. Physical properties of hydrogen and its isotopes. Property

H2

D2

T2

Melting point/K Boiling point/K ΔHmelting/kJ/mol ΔHboiling/kJ/mol Critical temperature/K Critical pressure/MPa

13.957 20.39 0.117 0.904 33.19 1.315

18.73 23.67 0.197 1.226 38.35 1.665

20.62 25.04 0.250 1.393 40.6 1.83

Tritium. In natural hydrogen it occurs in amounts of 1 in 1017–1018. It is continuously formed in nuclear reactions induced by cosmic rays, and it is radioactive. It may be made, from lithium, in nuclear reactors by the thermal neutron reaction 6 Li(n,α)3H. Preparation. Many reactions and processes are available for the preparation of hydrogen. Among the large-scale processes, the catalytic steam hydrocarbon reforming process can be mentioned. After de-sulphurization, natural gas (or oil-refinery feedstock) is mixed with steam and, at 700–1000°C, passed over a nickel-based catalyst. The irreversible reaction occurs: CnH2n2 nH2O : nCO (2n 1)H2 together with reversible reactions corresponding to the equilibria: CO H2O N CO2 H2 CO 3H2 N CH4 H2O Further treatments of the gases mainly involve cooling, conversion of CO into CO2 and H2, absorption of CO2, etc. Generally such processes are carried out in integrated plants where hydrogen is used for instance for ammonia synthesis, petrochemical work, etc. Hydrogen is also obtained as a by-product of brine electrolysis for the production of chlorine and sodium hydroxide. Small electrolytic plants (hydrogen generators) are often used for in situ applications when small quantities of hydrogen are required at remote locations. For the purification of hydrogen, and its separation from mixed gases, its interaction with palladium may be used. A large quantity of hydrogen may be absorbed by metallic palladium; it is first chemisorbed at the surface of the metal but at

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increased pressure it enters the metal lattice forming the so-called α and β hydrides: hydrogen has a high mobility within the lattice and diffuses rapidly through the metal. This behaviour is highly specific to hydrogen (and deuterium), palladium being impervious to all other gases (even to helium). Both laboratory and large industrial installations operate on this basis. In these operations the formation of the H-richer β-hydride must be avoided since it results in distortions and hardening, and possibly splitting, of the palladium diffusion membrane. This may be obtained either maintaining the temperature above 300°C or, possibly better, using palladium alloyed with about 20% Ag which, moreover, results in an increase of the permeability to hydrogen. The gas mixture containing hydrogen is passed through a diffuser separator composed of a large number of small diameter thinwalled Pd–Ag tubes packed in a stainless steel case. The emerging hydrogen is pure and dry. Atomic hydrogen. Di-hydrogen has the strongest element–element single bond. It is therefore difficult to obtain atomic hydrogen thermally. At ambient pressure at 2000°C there is 1% of atomic hydrogen in hydrogen gas and at 3000°C about 10%. The dissociation of H2 into radicals is so difficult to achieve that a very intense energy source (light arc) is necessary: recombination of H to give H2 releases a very large amount of energy that can generate temperatures up to 6000°C.

5.2.2 Intermetallic chemistry of hydrogen 5.2.2.1 Remarks on the systematics of hydrogen reactivity with the elements. The binary combinations of hydrogen with the various elements (and, more so, ternary and more complex combinations) correspond to several types, various structures and bonding mechanisms and form a vast number of compounds having a variety of quite different stability and reactivity characteristics. A number of broad sections of chemistry (inorganic chemistry, organic chemistry, etc.) could be included in this topic. As an introduction to this subject and in the prospect of giving special attention to metallic (metal-like) combinations, Fig. 5.1 may be considered. In this figure an indication of the reactivity of hydrogen with the different elements and of the characteristics of the hydrides formed is given. According to the scheme shown in this figure we can subdivide (even with some uncertainties) all the elements in a few categories defined by the reactivity with hydrogen. A short description of these different hydride categories will be given here below. However, before going any further, it may be useful to quote from Greenwood and Earnshaw (1997) a few remarks which may be relevant also when considering the description and the classification of other families of compounds. Greenwood and Earnshaw underlined that one criterion usually adopted for grouping the binary

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hydrides of the elements into various classes is the presumed nature of their bonding: ionic, metallic, covalent, polymeric and ‘borderline’ (intermediate). They pointed out that this is unsatisfactory because the nature of bonding is but poorly understood in many cases and the subdivision in different classes may obscure the relevant point that there is an almost continuous gradation in properties (and in bonding mechanism) between the members of the different classes. Moreover the various bond types cannot be considered mutually exclusive. They finally observed that this behaviour is not unique to hydrides but it is also well known for several other binary compounds such as oxides, sulphides, halides, etc. A summary of the various ‘families’ of hydrides is reported in the following. A first group of hydrides (ionic hydrides) is formed with the more electropositive elements of the s-block of the Periodic Table. This group of hydrides includes the salt-like MeH (MeH) NaCl-type compounds of the alkali metals and the di-hydrides (Co2Si-type) formed by the divalent metals Ca, Sr, Ba and also by Eu and Yb. The thermal stability of these hydrides decreases from Li to Cs and from Ca to Ba; the chemical reactivity on the contrary increases from Li to Cs and from Ca to Ba. While the reaction of NaH with water is very violent, the reaction of LiH or CaH2 can be used for a portable source of hydrogen. With the metals of the following groups (d-block, f-block metals), in a number of cases, phases of variable composition (solid solutions) are formed. Typically in the hydrogen systems with the lanthanides and actinides, besides more or less extended solid solutions of hydrogen in the different crystal forms of the metals, solid solution phases, generally homogeneous for composition ranges around 60– 70 at.% H or around 75 at.% H, have been identified. The crystal structures of these phases correspond to the CaF2-type (identified in the hydrides of Sc, Y, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Lu, Np, Pu), or to the Co2Si-type (as previously remarked for the divalent Eu and Yb), or ThH2 , and, for higher H contents for hydrides having about 75 at.% H, to the HoH3 type (for Y, Sm and heavier lanthanides) and Na3As-type (Dy, Np, Pu). Phases identified in these systems and corresponding to other structures and compositions are for instance those defined by the following approximate stoichiometries: Pr3H7, Th4H15, etc. These hydrides have a more or less clear metallic character especially for compositions around 1:2; with increasing H content, a decrease of the electric conductivity is observed. Uranium hydrides (of composition 1:3), which when finely powdered are very reactive, may be used as a starting product for the preparation of uranium compounds. With the metals of the 4th group (Ti, Zr, Hf), solid solution phases are observed which, for the limiting composition 1:2, have the CaF2-type structure and (through solid state reactions) the tI6-ThH2-type. The systems of hydrogen with the 5th group elements (V, Nb, Ta) are very complex and show several phases generally stable at not high temperatures and with variable H contents up to the 1:2 composition.

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With the following elements up to the metals of the 12th group, only a few intermediate phases are observed with Cr (NiAs and CaF2 types), with Mn (wide solid solution NiAs-type) or, in a number of cases (with Fe, Co, Ni, Cu) appreciable solid solutions in the different crystal forms of the metal. A special behaviour is shown by Pd with which, at T 300°C, hydrogen forms a large solid solution field (0 to 50 at.% H) that decomposes on cooling in two phases (see the phase diagram in Fig. 3.37). The crystal structure of the solid solution, with the progressive increase of the H content, can be described as passing from the Cu-type (Pd) to a more or less ordered and deficient NaCl-type. Moving towards the other groups of the Periodic Table, after a gap in the hydrogen compound formation capability, a new class of hydrides is encountered. In the right part of the Table hydrides having covalent characteristics are observed. For the elements of the last groups several covalent hydrogen compounds are known: numerous compounds are given by B, C, Si, Ge, N, P, O, S, Se. In the usual ambient conditions, as it is well-known, the carbon chemistry is especially rich of hydrides (that is of several series of hydrocarbons). In this class of compounds more or less complex molecules and structures are found: the catenation (chainforming) tendency is a characteristic shown by several elements in this portion of the Periodic Table. The following is a short collection of examples of such hydrides: Chalcogens: H2O, H2O2, H2S, H2S2, H2Sn, H2Se, H2Te, (H2Po). Compounds such as H2Sn (sulphanes, containing chains!S!S!) are thermodynamically unstable with respect to the reaction: H2Sn (liq.) : H2S (gas) (n 1)S (sol.) (which however is generally slow). The di-hydrides H2X may be obtained from the chalcogenides with dilute acids; their thermal stability and bond strength decrease down the group. H2Se is stable up to about 280°C, H2Te and H2Po are thermodynamically unstable with respect to the elements. Pnicogens: NH3, N2H4, PH3, AsH3, SbH3, BiH3. The stability of these compounds falls down the group. SbH3 and BiH3 are thermally very unstable, AsH3 readily decomposes to As and H2. Ammonia (boiling point 239.7 K), the important synthesis equilibrium of which is well-known, resembles in the liquid state water, in its physical behaviour. Carbon, tetrels. The unusual stability of the catenated carbon compounds must be underlined. This may be related to the intrinsic strength of the C!C bond and, as regards stability towards oxidation, to the relative strengths of C!C and C!O bonds. As a reference, the following average values (kJ/mol) of some bond energies may be considered: C!C 331; C!O 360, C!H 415; Si!Si 222; Si!O 452; Si!H 318. Catenation is a special characteristic of the 14th group elements, but in Si (and Ge, etc.) it is not as extensive as in carbon. SiH4, Si2H6 are indefinitely stable at ambient temperature, higher silanes decompose. Germanes (GeH4, Ge2H6,

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Ge3H8) less flammable than silanes, are rapidly oxidized in air. Stannane (SnH4) decomposes rapidly even at 0°C; plumbane (PbH4) has a doubtful existence. Boron, triels. Boranes are molecular compounds of low thermal stability. They are generally endothermic and their free energy of formation is also positive: their thermodynamic instability may be related, rather than to the weakness of the B–H bond, to the very strong interatomic bonds in elemental boron and hydrogen. The simplest borane B2H6 provides the prototypal example of three-centre two-electron (3c, 2e) bonds. It consists indeed of two BH2 groups connected by two hydrogen bridges (corresponding to two 3c, 2e B!H!B bonds), this structure is the same as that of Al2Cl6 shown in Fig. 4.25. Boranes are generally very reactive and flammable in air; several preparative methods are now known. Borane chemistry started in 1912 with the classic work by Alfred Stock (1933): he prepared several hydrides by the action of acid on magnesium boride, MgB2, obtaining a mixture of volatile compounds. In order to handle, separate, etc. these compounds, he developed special vacuum techniques based on the use of vacuum manifold glass lines. This chemistry now represents an important chapter in various Inorganic Chemistry books to which the reader is referred. The complexity and richness of the borane chemistry resulted also in the creation of a special nomenclature which was also applied to several families of compounds (neutral and ionic clusters, etc.). Five main series of boranes (neutral, anionic, corresponding to deltahedral, triangular-faced polyhedra) can be considered: (i) Closo-boranes (name derived form Greek κλωβóς, clovos, a cage) have complete closed polyhedral clusters of boron atoms. (ii) Nido-boranes (form Latin nidus, nest) have non-closed structures in which the nB atoms of the Bn cluster occupy n vertices of a (n 1) vertices polyhedron (that is polyhedra that lack one vertex). (iii) Arachno-boranes (from Greek αρ ´ αχνη, ´ aracne, spider’s web) have structures corresponding to polyhedra from which two adjacent vertices are missing. (iv) Hypho-boranes (from Greek υϕ ´ η, ´ hyphe, a net) have a more open structure corresponding to a polyhedral fragment obtained by removing three contiguous vertices. (v) Conjuncto-boranes (from Latin coniungo, to join together) have structures in which two or more fragments of the preceding types are linked. Several subtypes may be defined according to the connection scheme (for instance: by sharing a B atom, by sharing 2B in a common edge, by sharing 3B as a common face of the interconnected clusters, etc.).

Elements of Alloying Behaviour Systematics

329

Wade rules. A set of semi-empirical rules relating structure and composition of boranes of formula BnHmx, (m n, x 0) have been presented by Wade (1976). These can be summarized as follows: ●

●

●

●

For a BnHnx borane, the preferred structure is a closo structure with a preferred charge of 2 (there are (n 1) pairs of skeleton electrons). For a BnHn4 borane, a nido structure is preferred (with nB at n vertices of an (n 1) vertices polyhedron) when in the corresponding anion BnHn4 there are (n 2) pairs of framework electrons. For a BnHm borane based on an anion BnHn6, an arachno-structure is preferred with B at n vertices of an (n 2) vertices polyhedron; (n 3) pairs of framework bonding electrons are required. For a BnHm borane based on an anion BnHn8, a hypho-structure is preferred. B is at n vertices of an (n 3) vertices polyhedron requiring (n 4) pairs of framework bonding electrons.

These rules can be extended to isoelectronic anions, carbaboranes, metalloboranes, etc. (see also § 4.4.4 ff). The following notes conclude this description for the remaining elements: AlH3 has several crystalline and amorphous forms; it appears as a non-volatile solid instable above 150°C. In α-AlH3, aluminium is octahedrally surrounded by 6 hydrogen atoms. (GaH3)n has been described as a viscous liquid that decomposes at room temperature. Formulae such as InH and InH2 have been reported for the questionable indium hydrides. BeH2, an amorphous white solid, has been described which evolves hydrogen at 250°C; no compound, however, is contained in the proposed Be–H phase diagram. As a conclusion to this point, and in order to illustrate the variety of behaviour in the reactions of the different elements with hydrogen, a few phase diagrams of binary hydrogen systems can be considered. 5.2.2.2 Examples of phase diagrams of metal–hydrogen systems. The scheme shown in Fig. 5.1 gives an indication of the general characteristics of the phase diagrams and of the different phase types formed in the binary combinations of hydrogen with the various elements. In order to give a look at this subject, a selection of characteristic diagrams is shown in Figs 5.2–5.5 which have generally been re-drawn according to Okamoto (2000).

330

Intermetallic Chemistry 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17

Ionic hydrides

Intermediate hydrides

No hydrides

Metallic hydrides

Covalent hydrides

Unknown

Figure 5.1. Hydrogen combinations of the different elements. An approximate scheme of the complex reactivity behaviour of hydrogen is shown. Notice that in most cases, especially at the right part of the Table, every box may correspond to a large variety of reactions and products, possibly with the formation of a large number of stable and/or metastable compounds.

Fig. 5.2 concerns an element (Sr) at the left in the Periodic Table: a temperature range higher than the ambient is shown. There is a small region of Sr-rich solid solution (γ phase) and the formation of a nearly stoichiometric compound, SrH2, the formula of which corresponds to the ionic valences of the two elements. The two subsequent figures, Figs 5.3 and 5.4, show parts of the phase diagrams formed by two transition metals. In the Mo–H system, for which only the high-temperature region is shown, the equilibria between hydrogen and elemental (solid and liquid) molybdenum may be noticed. In the Nb–H system, on the contrary, for which several multi-disciplinary investigations have been carried out at low and very low temperatures, a complex sequence of equilibria and solid-state transformations has been assessed (Smith 1983). An enlargement of the central region only of this system is shown in Fig. 5.4. A phase diagram formed by hydrogen with an element at the right side of the Periodic Table is shown in Fig. 5.5. This is the hydrogen–oxygen phase diagram and it is the only example of a low-temperature phase diagram with the right-hand side elements that we have found in literature. It is probable that similar diagram shapes and behaviour may be found in the low-temperature regions of systems of hydrogen with other elements (nitrogen, phosphorus, sulphur, etc.) with which it forms stable and/or metastable covalent compounds. Ammonia, NH3, is a well-known example of a species in thermodynamic equilibrium with the elements

331

Elements of Alloying Behaviour Systematics Mass% H 0.5

1.0

1.5

2.0 2.5

L

900

(β Sr)

700 600 500

γ

SrH2

Temperature (C)

800

400 300 200 (α Sr) 100 0

Sr

10

20

30

40

50

60

70

at.% H

Figure 5.2. The phase diagram of the Sr–H system. An intermediate phase, stable in a range of temperature and composition values (solid solution γ) is formed in the Sr-rich region. The other phase (practically a stoichiometric compound) corresponding to the formula SrH2 may be considered a representative of the ‘ionic’ hydrides. The low-temperature form of this compound has the oP12-Co2Si-type structure.

(H2 and N2). The complexity, however, of a diagram such as that of the system C–H, of its (stable and metastable) compound multitude and of its possible sequences of reactions can barely be guessed. 5.2.2.3 Comments on the crystal structures of typical hydrogen–metal phases. A few general remarks about a group of metal–hydrogen phases have been included in § 3.8.4.1 where interstitial hydrogen solutions in metallic structures have been described. However, as previously observed, a number of intermediate phases are also formed in several systems. A short summary of these is shown in Table 5.2 where their formulae very often have only an indicative character and several structure types correspond to more or less extended solid solution ranges. Notice that most of the indicated prototypes correspond to structures frequently found not only in intermetallic phases but also in ionic compounds. 5.2.2.4 Notes on the application of metal hydrides. The study of the hydride formation in metallic systems is important not only in view of the (often deleterious)

332

Intermetallic Chemistry Mass% H 1

2

5

10 20

4600

Temperature (C)

G 4200 3800 Mo(liq) + G 3400 3000 2600 (Mo) + G 10

20

30

40

Mo

50

60

70

80

90

at.% H

H

Figure 5.3. The high-temperature region of the Mo–H system is shown. In this temperature range the negligible solubility of hydrogen in solid and liquid molybdenum can be noticed. Mass% H 25

Temperature (C)

−25

0.75

0.80

0.85

0.90

0.95

1.00

1.05

β −39

−48

−75 λ −125

ν

ε

−175

? γ

−225

41

Nb

42

43

44

45

46

47

48

49

at.% H

Figure 5.4. The niobium–hydrogen system. A small part (from 40 to 50 at.% H) of the diagram is shown in the low- and very-low-temperature region. Notice the complex equilibria and the high number of intermediate solid solution phases. Other phases are formed in the composition ranges not shown in figure: the η (11 to 39 at.% H) and θ (21 to 41 at.% H) solid solutions in the Nb-richer part and the nearly stoichiometric δ phase (NbH2, cF12-CaF2-type).

333

Elements of Alloying Behaviour Systematics Mass% O 89

90

91

92

93

94

0

0

−20

HO

−30

L

H2 O

Temperature (C)

−10

−40

−50.2

?

H3O2

−50 −60 34

H

36

38

40

42

44

46

48

at.% O

Figure 5.5. The oxygen–hydrogen system as reported by Okamoto (2000). Notice in the phase diagram the formation of the well-known covalent hydrogen–oxygen compounds.

effects that H uptake and dissolution may have on the properties of metals and alloys, but also for the research and development of metal hydride systems suitable for hydrogen storage. This point, indeed, is an essential step for planning and increasing hydrogen-based energy production and distribution. Among various hydrogen storage materials, several metal–hydrogen systems appear attractive from the point of view of high volumetric density and safety. As summarized by Pande et al. (1994), the desired properties of hydrogen storage materials are: (1) high hydrogen retentive capacity, (2) low temperature (typically 100°C) of dissociation, (3) high rate of hydrogen uptake and discharge, (4) low heats of formation, (5) light weight, (6) stability towards oxygen and moisture and (7) low cost of the alloy. The preparation and experimental and theoretical properties of several alloys (Ni–Mg, Ti–Fe, Pd) and their behaviour with hydrogen are discussed in the mentioned paper. In this respect, Mg-based alloys are particularly interesting for their high capacity, light weight and low cost (De Negri et al. 2005), although up to now limitations exist due to the low sorption kinetics. On the other hand, La–Ni alloys are good candidates for increasing hydrogen capacity. The La–Ni–Mg alloys therefore are especially promising materials for the hydrogen-based energetic technologies. In the

334

Intermetallic Chemistry

Table 5.2. Structures of a few selected hydrogen–metal compounds. The formulae very often have only an indicative character. Solid solution ranges are frequently observed. Structure type cF16-BiF3

Examples of isostructural phases Composition ranges at.% H MeH3: Me La(60–80H), Tb, Yb

hP8-Na3As

MeH3: Me Dy, Np, Pu( 74H), Am, Bk

hP24-HoH3

MeH3: Me Y, Sm, Ho(73–75H), Tm, Lu

cF12-CaF2

MeH2: Me Sc, Y, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho(66–69H), Er, Tm, Lu, Ac, Np, Pu(63–73H), Am, Ti, Zr, Hf, V, Nb, Ta, Cr(55–67H)

oP12-Co2Si

MeH2: Me Ca, Sr, Ba, Eu, Yb

cF8-NaCl

MeH: Me Li, Na, K, Rb, Cs, Pd(0 50H)

hP4-NiAs

MeH: Me Cr(47–50H), Mn

mentioned paper, crystal structures and phase equilibria in the La–Ni–Mg system are studied. A number of questions concerning alloy hydriding and the formation of complex hydrides had been discussed by Van Mal et al. (1974) and Buschow et al. (1975). Special attention was dedicated to CaCu5-type compounds among which the behaviour of LaNi5, with its favourable absorption properties, was underlined. It absorbs hydrogen to a density of nearly twice that of liquid hydrogen (that is up to about 6.2 1022 atoms/cm3). Several related compounds were investigated (LnNi4Me, Me Cr, Fe, Co, Pd, Cu, Ag and La0.8R0.2Ni5, R Y, Nd, Gd, Er, Zr, Th). The equilibrium pressure was studied in the two-phase regions associated with the hydrogen absorption or desorption at a given temperature. This pressure can be considered as a measure of the stability of the hydride. It was observed that, for series of isostructural compounds, the stability of ternary hydrides can be related to the heat of formation of the parent compounds. It was observed that it may be generally expected that in the formation of ternary hydrides, the more stable the binary compound one commences with, the less stable the ternary hydride will be (rule of reversed stability). In the evaluation of the capacity of an intermetallic compound to absorb large quantities of hydrogen at room temperature it was also concluded that it is necessary that the compound contains a metal which forms a hydride which should be more stable than the intermetallic compound. Quantitative predictions about the heats of formation of hydrides of intermetallic compounds have been discussed by Shilov et al. (1989); they studied reversible and irreversible transformations in intermetallic compound-hydrogen systems and observed that four basic types of P/T diagrams exist for these systems.

Elements of Alloying Behaviour Systematics

335

5.3. ALLOYS OF THE ALKALI METALS (1ST GROUP METALS)

Lithium, Li; sodium, Na; potassium, K; rubidium, Rb; caesium, Cs; francium, Fr

5.3.1 Introduction Lithium (Li, [He]2s1), name and symbol from the Greek lithos (stone). Discovered (1817) by J. August Arfvedson, isolated (1818) by Sir H. Davy (1821) and by William T. Brande. Silvery, white, soft, easily cut, metal. Atomic number 3, atomic relative mass 6.941. For lithium, as for a few other elements (noble gases), modified isotopic compositions may be found in commercially available material because it has been subject to undisclosed isotopic fractionation: commercially available lithium specimens have atomic weights that range between 6.939 and 6.996: if a more accurate value is needed it must be determined for the specific material. Occurrence. Its most important minerals correspond to alumino-silicates: LiAlSi2O6 (spodumene), LiAlSi4O10 (petalite), lithium mica (lepidolite), LiAlSiO4 (as the rare eukryptite). Preparation. Li is currently produced by electrolysis of molten LiCl, the melting point of which (614°C) is lowered by addition of KCl. The salt mixtures used (not very different from the eutectic one) contain about 45–55 mass% LiCl: the electrolysis is carried out at 400–460°C. The cells commonly used resemble the cell used for the production of sodium (Downs cells). Main uses of lithium alloys. Li additions often change completely the properties of metals to which it is added, for instance hardness of Al and Pb (addition of Li to Pb results in the formation of Pb solid solution and a eutectic at 15.7 at.% Li with LiPb) and ductility of Mg. Al-alloys can be of great interest in aerospace industry: Li (as Be) simultaneously reduces the density of Al and increases its modulus of elasticity. Each 1 mass% Li up to the solubility limit (4.2 mass%) reduces density by about 3% and increases modulus by 5%. Precipitates homogeneously distributed of spherical LiAl3 in diluted Li-alloys during heat treatment may improve strength.

336

Intermetallic Chemistry

The designation of typical commercial Li–Al alloys are (approximate data in mass%): weldalite 049 (5Cu, 1.3Li, 0.4Ag, 0.4Mg: for propellant tanks in space launch systems), alloys 2090 and 2091 (2–2.7Cu, 2–2.2Li, 0.1Zr), alloy 8090 (2.5Li, 1.3Cu, 0.9Mg, 0.1Zr, low-density high-modulus damage tolerant medium-strength), alloy CP276 (2.7Cu, 2.2Li, 0.5Mg, 0.1Zr). Li addition can be used in metallurgy as a reducing agent, and de-oxidizing, de-sulphurizing agent for Co, Ni alloys. A rapidly growing application of lithium metal is in sacrificial anodes in batteries. Sodium (Na, [Ne]3s1), name from the English word soda, perhaps from the Latin word sodanum (glasswort), symbol from the Latin natrium (sodium carbonate). Identified and isolated (1807) by Sir Humphry Davy. Silvery white, soft metal. Atomic number 11, atomic relative mass 22.989768. Occurrence. It occurs as NaCl (as the main component of the sea water salts and as rock salt), Na2CO3 (trona), NaNO3 (Chile saltpetre), Na2SO4 (thenardite), Na2B4O7 (borax). Preparation. Sodium can be produced by electrolysis of a mixture of NaCl (40%) and calcium chloride, CaCl2 (60%), melting at about 580°C. The electrolysis is carried out as a melt in a ‘Downs cell’, producing also calcium metal as well, which is solidified in a collection pipe and returned back to the melt. Since 1950 a modified Downs cell has been used with an electrolyte consisting of a ternary mixture of NaCl, BaCl2 and CaCl2. Main uses of Na alloys. Hypoeutectic Al–Si alloys (from 5 mass% Si to the eutectic) through the so-called modification (structural modification of the normally occurring eutectic) achieve somewhat higher tensile properties and improved ductility. Modification is obtained by the addition of elements such as Na (or Sr, Ca, Sb) and results in a finer lamellar or fibrous eutectic. Phosphorus, which reacts with sodium, interferes with the modification mechanism. Sodium can be used as the reductant of several chlorides in the preparation of metals such as Ti (Hunter process), Zr, Hf, Nb, Ta. Na–K alloys are used in heat-exchange systems. Ternary alloy 10.1 at.% Na, 47.4 at.% K and 42.5 at.% Cs (L K (Cs) (K) (CsNa2, KNa2)) probably has the lowest known melting point (76°C) of all the metallic systems. Sodium amalgams, owing to their reducing properties, can be used in chemical synthesis processes. Potassium (K, [Ar]4s1), name from the English word potash (pot ashes), symbol from the Latin word kalium (alkali). Identified and isolated (1807) by Sir Humphry Davy. Silvery white, soft metal. Atomic number 19, relative atomic mass 39.0983.

Elements of Alloying Behaviour Systematics

337

Occurrence. Potash salt deposits were formed by evaporation of ancient lakes and sea beds. Main minerals are sylvite (KCl), carnallite (KMgCl3 6H2O), polyhalite (K2MgCa2[SO4]4 2H2O), langbeinite (K2Mg2[SO4]3), kainite (KMg[ClSO4])4 11H2O). Preparation. It is obtained by the reaction of metallic sodium with molten potassium chloride at 850°C: KCl Na N NaCl K The equilibrium is rapidly established, at high temperature, between Na, K, NaCl and KCl. The equilibrium shifts to the products when K is continuously removed by distillation through a packed column. During operation, KCl is melted and introduced through a trap to the column. Molten Na is fed to the bottom of the column (the lower portion of which acts as a reactor whereas the upper portion is a fractionator). K vapour is fractionated and condensed in an air-cooled condenser, with the reflux pumped back to the column. Waste NaCl is continuously removed from the bottom of the column. Other reactions such as: K2CO3 2C : 3CO 2K; 2KCl CaC2 : CaCl2 2C 2K; 2KN3 : 3N2 2K are used at laboratory scale. Main uses for K alloys. Intercalation compounds with graphite are powerful solid reducing agents. See Na for Na–K alloys. Rubidium (Rb, [Kr]5s1), name and symbol from the Latin rubidius (deep red, the colour of its main spectral lines). Discovered (1861) by Robert Bunsen and Gustav Kirchhoff. Atomic number 37, atomic relative mass 85.4678. Silvery white, soft metal. Occurrence. Unlike its homologues Li and Cs, Rb is not a major component of any mineral. It is found mainly in association with K (similarity of their ionic radii) and also with other alkali metals (with Li in lepidolite, with Cs in pollucite). Preparation. It is made by the reaction of metallic sodium with hot molten rubidium chloride. Na RbCl N Rb NaCl Under these conditions the rubidium is highly volatile and removed from the system.

338

Intermetallic Chemistry

Caesium (Cs, [Xe]6s1), name and symbol from the Latin caesius (sky blue, the colour of two bright lines in its spectrum). Discovered (1860) by Robert Bunsen and Gustav Kirchhoff. Soft, silvery gold metal, liquid around room temperature. Atomic number 55, atomic relative mass 132.90543. Occurrence. The most important mineral corresponds to an alumino-silicate, pollucite, (Cs4Al4Si9O26 H2O) typically containing about 20 mass% of caesium oxide. Preparation. As amalgam by electrolysing Cs concentrated salt solutions on Hg cathode. More important are the reduction of CsCl with Ca or Ba and the removal of Cs by vacuum distillation. Main uses. Caesium metal is used in the production of vacuum tubes as a scavenger to reduce residual gaseous impurities after the tubes have been sealed. Cs may be generated in situ by heating a pellet of caesium chromate mixed with a metal powder (Zr, Ca, Ba). Cs metal is used as the propellant in ion thrusters (employed in satellites for orientation control): it is ionized in a vacuum chamber, the Cs are then accelerated through a nozzle (high specific impulse because of high atomic mass). Francium (Fr, [Rn]7s1), name and symbol, after France, the country where it was prepared (Curie Institute in Paris). Discovered (1939) by Marguerite Perey. Very rare in nature, artificially prepared, highly radioactive. Atomic number 87, atomic relative mass 223.019731 (nuclidic mass of the longest half life isotope). Francium occurs as a result of the disintegration of actinium. Francium is found in uranium minerals, and can be made artificially by bombarding thorium with protons. It is the most unstable of the first 101 elements.

5.3.2 The alkali metals: a summary of their atomic and physical properties The main atomic and physical properties of the alkali metals are summarized in Tables 5.3 and 5.4. Their typical electron configurations correspond to the outermost ns1 electron. Consequently, the first ionization energy is relatively low, and the second stage ionization energy is very high (see Fig. 4.3). This explains the reactivity of these elements and their oxidation state never exceeding 1. The large values of the atomic radii, in comparison with the other elements of the same rows of the Periodic Table, may also be noticed and related to the low densities of these

339

Elements of Alloying Behaviour Systematics Table 5.3. Alkali metals: selected atomic and physical properties. Property

Li

Na

K

Rb

Cs

r/pm, metallic, CN 12 [‘Metallic valence’] r/pm, ionic, M+1, CN 6 1st ionization energy/kJ/mol 2nd ionization energy/kJ/mol Tmelting/°C Tboiling/°C ΔHmelting (at Tmelting)/kJ/mol ΔfH 0 of Me1 gas at 298.15 K/kJ/mol

156.2 [1] 76 520.2 7298.1 180.6 1342 3.0 159.3

191.1 [1] 102 495.8 4562.4 97.8 883 2.6 107.3

237.6 [1] 138 418.8 3052 63.71 759 2.3 89.0

254.6 [1] 152 403.0 2633 39.48 688 2.2 80.9

273.1 [1] 167 375.7 2234 28.39 671 2.1 76.5

Table 5.4. Alkali metals: crystal structures, lattice parameters of their allotropes, calculated densities. Element (allotrope) Temperature range/°C Pressure/GPa

Crystal structure

Lattice parameters/pm a

c

Atomic volume, Vat/106 pm3

Molar volume/ cm3/mol

Density/ g/cm3

αLi βLi

Lithium 193° 193° to 180.6°

hP2-Mg cI2-W

311.1 350.93

509.3

21.34 21.61

12.85 13.01

0.54 0.53

αNa βNa

Sodium 233° 233° to 97.8°

hP2-Mg cI2-W

376.7 429.06

615.4

37.81 39.49

22.77 23.78

1.01 0.97

K

Potassium 63.71°

cI2-W

532.1

75.38

45.36

0.86

αRb βRb γRb

Rubidium 39.48° 1.08 GPa 2.05 GPa

cI2-W

570.5

92.84

55.91

1.53

cI2-W cF4-Cu cF4-Cu

614.1 646.5 580.0

115.79

69.73

1.91

Caesium αCs 28.39° βCs 2.37 GPa β Cs 4.22 GPa γCs 4.27 GPa

metals (lithium has the lowest density of any solid at room temperature). These data, together with the low values of the melting and boiling temperatures and of the heats of sublimation and vapourization, may be considered an indication also of the weak bonding in the solid state of the single valence electron.

340

Intermetallic Chemistry

The alkali metals are soft and have a high lustre when freshly cut. Lithium is the least fusible and volatile, the least dense and soft. The values of these properties change regularly down the 1st column of the Periodic Table. Notice, however, the trend of the density. Their normal crystal structure, at ambient conditions, corresponds to the bodycentred cubic cI2-W-type structure. At very low temperatures, the close-packed hexagonal hP2-Mg-type structure has been observed for Li and Na, while for Rb and Cs the face-centred cubic close-packed cF4-Cu-type structure is known at high pressure. No polymorphic transformation has been reported for potassium. 5.3.3 The alkali metals: remarks about their general chemical properties and reactivity All the alkali metals are extremely reactive chemically. Both for safety reasons and for protection from heavy contamination they should be handled with care, under an inert atmosphere or protective media. The alkali metals are easily tarnished by air and combined with most elements. Lithium alone combines directly with nitrogen and is relatively inert towards oxygen and the halogens. The other metals of this group react with oxygen increasingly as the atomic number increases, forming oxides such as Na2O and Na2O2 (peroxide) and, in the case of the heavier metals, superoxides, such as KO2. They react violently with water giving the soluble hydroxides and hydrogen, which generally ignites. The reaction with the halogen, often with inflammation and explosion, results in the formation of the halides. With hydrogen, the alkali metals form the mono-hydrides MeH, having salt-like properties and a partially ionic, MeH, NaCl-type structure. They are colourless crystalline solids having a fairly negative ΔH of formation. The mono-hydrides react with water. They may be prepared from hydrogen and the metal (heated at 700–800°C for Li, 350–400°C for the others) or through the reaction of hydrogen with the alkali mono-oxide, nitride, etc. Interesting is the reaction of the alkali metals with ammonia; with gaseous NH3, when heated, they generally form the amide MeNH2, with liquid ammonia they give an electrically conductive often deep blue solution. The electric conductivity of a saturated Na solution in liquid NH3 is about half that of metallic mercury. These solutions react forming the amides; the time required for this reaction, however, is several days for Li and Na, about an hour for K and minutes for Rb and Cs. Several reactions with the alkali metal can be carried out using their ammonia solutions. The reaction, for instance, of K with metal oxides may result in the reduction to a lower valence state (for instance CuII to CuI, MoVI to MoIII) or in the precipitation of the metal or of its alloys with K. Reactions of the alkali–ammonia

341

Elements of Alloying Behaviour Systematics

solutions with S, Se, Te, P, As, Sb, Bi, Pb, Hg may result in the formation of several compounds such as: Li2S, Li2Sx, Na2S, Na2Sx, Na2Se, Na2Se2, Na2Se6, K2Te, K2Te3, K3As, Na3Sb5, Na3Bi, NaPb, NaPb2, NaHgx, etc. 5.3.4 Intermetallic chemistry of the alkali metals 5.3.4.1 Phase diagrams of alkali metal alloys. The pattern of the intermetallic reactivity of these metals is shown in Fig. 5.6, where the compound formation capability with the different elements is summarized. The overall reactivity pattern summarized in this figure fits well within the general alloying behaviour shown by the metals pertaining to the first columns of the Periodic Table, as confirmed in the following paragraphs 5.4 (alloys of the representative metals of the 2nd group), 5.5 (alloys of the metals of the 3rd group), etc. A few comments about Fig. 5.6 may be useful. According to their reactivity with the alkali metals all the elements X can be divided, even with a few uncertainties, into three principal categories: (i) The metals of the block s. These metals form with the alkali metals only a few compounds (Li with Ca (Li2Ca), Sr (Li23Sr6, Li2Sr3, LiSr3), Ba (Li4Ba), Na

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Li

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Na

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

K

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Rb

Cs

Compound-forming element

Phase diagram known; no intermediate phases formed

No information available

Questionable compound forming capability

Figure 5.6. Compound formation capability in the binary alloys of alkali metals. The different elements, the binary combinations of which with Li, Na, K, Rb, Cs are considered, are identified by their positions in the Periodic Table. No reliable data have been found about the stable equilibrium phases in the Na–P and Cs–As systems: compound formation is, however, probable.

342

Intermetallic Chemistry

with K (KNa2), with Cs (CsNa2) and Ba with Na (NaBa s.s., Na4Ba), K with Cs (CsK2) or continuous solid solution fields (Rb–K, Cs–K, Cs–Rb systems), even if only at high temperature with subsequent de-mixing or compound formation (Cs–K system) at lower temperature. In the inter-alkali alloys, eutectic equilibria have been observed in a number of systems: very low melting points have been determined for instance in the Rb–Na system (L N (Rb) (Na), at 82.5 at.% Rb and 4.5°C) and even lower melting temperatures have been observed in ternary systems. Binary sodium–potassium alloys, liquid at room temperature (at 25°C in a composition range of about 15–70 at.% Na, about 7–57 mass% Na), have a good thermal conductivity and a wide temperature range where they are liquid; they may be used in heat-exchange systems. Their extremely high chemical reactivity must of course be taken into account. (ii) The transition metals of the 3nd to 8th–10th groups. These metals are characterized by a very low reactivity with the alkali metals. No intermediate phases are formed (low electronegativity difference) and between the components there are very large, or complete, regions of immiscibility (great difference in the atomic dimensions). This type of phase diagram applies to the metals included between the 3rd up to the 7th (Li) or up to the 9th (Na) or to the 10th (K, Rb, Cs) groups. (iii) The last transition metals and the p-block elements. The diagrams of the alkali metals with this set of elements (last transition metals, semi-metals and nonmetals of the p-block) are generally characterized by the formation of a number of intermediate phases, both line and point compounds, very often showing a high thermal stability and high melting points. In a number of cases this tendency to form compounds may be compared also with the behaviour in the liquid state where the formation of ‘associates’ has been considered (see § 3.2). The strong electronegativity difference between these elements and the alkali metals may be therefore underlined. Solubility of metals in liquid alkali metals. During an investigation of the properties of low-melting metals, a specific aspect of the alloying behaviour of the alkali metals has been studied by Guminski (1989, 1990), who compiled and discussed the data concerning the solubility of the different elements in these metals. Solubility data at 600°C have been plotted and discussed as a function of the atomic number: curves showing periodic variations were obtained with trends very similar to each other. Elements showing, at 600°C, a low or very low solubility in liquid lithium, taking this metal as an example, are Ti, V, Cr, Fe, Co, Y, Zr, Nb, Mo, Hf, Ta, W, Re whereas a high solubility (which at 600°C may result in the existence

Elements of Alloying Behaviour Systematics

343

of a continuous liquid solution) is shown by Ca, Zn, Ga, Sr, Pd, Ag, Cd, In, Ba, Au, Hg, Tl, etc. A similar trend is shown for the solubility in liquid sodium. 5.3.4.2 Melting point trend in the binary alkali metal alloys. The intermetallic reactivity of the alkali metals and the stability of their alloys are further testified by the values of the melting points observed in the compound-forming systems of the alkali metals. To this end, Table 5.5 shows the sequence of systems with different metals along one row of the Periodic Table (the 5th in this example) through the different groups. For each alkali metal-M system, the formula and melting temperature of the highest melting compound is reported (p means peritectic melting, s.s is a short-hand indication that around the given formula there is a solid solution range). The indication is also given whether the Raynor Index (IR, see § 2.2.4.1) is higher or lower than 1. Nearly all the compounds listed show IR 1. The high melting points of the compounds of the noble metals may be noticed. With elements of the groups from Ag to Te, alkali metal compounds are formed

Table 5.5. Highest melting points in the alloys of alkali metals (A) with compound-forming elements of the 5th row of the Periodic Table. See the introduction for the meaning of the symbols. System

Li compounds

Na compounds

K compounds

A–Ru

LiRu3

Na–Ru no compounds

K–Ru no compounds

A–Rh

LiRh 1800°C est., IR 1

Na–Rh no compounds

K–Rh no compounds

A–Pd

LiPd7 1500°C est., IR 1

NaPd2 797°C, p, IR 1

K–Pd no compounds

A–Ag

βs.s. Li0.6Ag0.4 317°C, p, IR 1

NaAg2 322°C, p, IR 1

K–Ag no compounds

A–Cd

LiCd s.s 549°C, IR 1

NaCd2 384°C, IR 1

KCd13 487°C, IR 1

A–In

LiIn s.s 632°C, IR 1

Na5In8 441°C, IR 1

KIn2 s.s 478°C, IR 1

A–Sn

Li7Sn2 783°C, IR 1

NaSn 578°C, IR 1

K2Sn3 860°C, IR 1

A–Sb

Li3Sb 900°C, IR 1

Na3Sb 857°C, IR 1

K3Sb 813°C, IR 1

A–Te

Li2Te 1204°C, IR 1

Na2Te 953°C, IR 1.

K2Te 920°C, IR 1

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which have an increasing ionic covalent character of the bonding mechanism and increasing melting temperatures. 5.3.4.3 Remarks on the crystal chemistry of the alkali metal alloys. Several intermediate phases are formed in a number of binary systems of the alkali metals. It may be remarked that these phases cover a very large range of compositions from high alkali contents as in Li9Ag, Li6Hg, Li5Pt, Na6Tl, Na15Pb4, K3Sb up to very high contents of the partner as in LiCx (x 18, 36, 40, 72), LiPt7, NaZn13, NaSn6, KHg11, KCd13, etc. A selection of frequent stoichiometries and common structural types found within the binary intermetallic compounds of the alkali metals is given in Table 5.6. Several 1:1 compounds are formed, generally corresponding to simple symmetric structures: especially notice the CsCl and the NaTl types. Among the compounds given by the alkali metals with the chalcogens, the ionic-like CaF2-antitype structure may be mentioned for the ‘normal valence’ 2:1 compounds, whereas, within the pnictides, several 3:1 compounds are observed with the Na3As-type structure, in which the chemical bond factor has been underlined. Laves phase type structures are observed in a few inter-alkali phases and in a few compounds with some noble metals. Examples of phases corresponding to high stoichiometric ratios are some CaCu5-type compounds and the characteristic NaZn13-type compounds formed with Zn and Cd. Stoichiometries such as 1:11, 1:12, 1:13 generally correspond to the cP36-BaHg11, tI48-BaCd11, tI26-ThMn12, cF112-NaZn13 structure types characterized by high coordination numbers around an atom of large dimension (such as alkali, alkaline earth metals, etc.). See in § 7.5.1.9–7.5.1.11, under the descriptions of the BaHg11 and NaZn13 structural types, some general remarks on the characteristics of these ‘size factor’ controlled phases. 5.3.4.4 A glance through complex intermetallic compounds of the alkali metals. The formation of large (with hundreds of atoms) clusters has been observed in mass spectrometric studies of alkali metals in molecular beams (Mingos and Wales 1990). The atoms of such large clusters do not lie on a single spherical surface. The structure of such clusters may be described as multi-spherical; the geometries adopted may be related to close-packed arrangements or to shells with icosahedral symmetry. It has been observed that certain cluster nuclearities are formed in greater abundance, indicating the high relative stability of these fragments. In molecular beam experiments with sodium, for instance, the following atom numbers (magic numbers) have been especially observed: 8, 20, 34, 40, 58, 92. For the heavier alkali metals, cluster compounds mainly based on octahedra have been discovered especially due to the systematic work by Simon (for instance, Simon 1973, 1979, 1988). The sub-oxides, for instance, Rb9O2 and Cs11O3 contain groups formed by the connection (by sharing one or two faces, respectively) of centred

Elements of Alloying Behaviour Systematics

345

Table 5.6. A selection of formulae and structure types of intermediate phases in the alkali metal binary alloys (CNE coordination number around the A alkali metal). Structure type

CNE (A)

Examples of isostructural phases Li compounds

Na, K, Rb and Cs compounds

cF16-BiF3

14

Li3X: X Au

Cs3X: X Sb, Bi

hP8-Na3As

9–11

Li3X: X P, As, Sb

Na3X: X P, As, Sb, Bi K3X: X P, As, Sb, Bi Rb3X: X As, Sb, Bi

cF12-CaF2 (antitype)

10

Li2X: X O, S, Se, Te

Na2X: X O, S, Se, Te, Po K2X: X O, S, Se, Te Rb2X: X O, S, Se

Li2X: X Ca

hP12-MgZn2

12

oP12-Co2Si

13

cP2-CsCl

14

cF8-NaCl

6

Cs2X: X S, Se, Te LiX: X Pd(40–41Pd), Ag, Au, Hg(37–62Hg), Pb(50–53Pb), Tl

RbX: X Au CsX: X Au

LiX: X H

NaX: X H KX: X H RbX: X H CsX: X H NaX: X Sn, Pb KX: X Si, Ge, Sn, Pb RbX: X Si, Ge, Sn, Pb CsX: X Si, Ge, Sn, Pb

tI64-NaPb

11–12

cF16-NaTl

14

hP12-MgZn2

16

cF24-Cu2Mg

16

hP6-CaCu5

18

KX5: X Au RbX5: X Au CsX5: X Au

cF112-NaZn13

24

NaX13: X Zn KX13: X Zn, Cd RbX13: X Zn, Cd CsX13: X Zn

LiX: X Zn(50–54Zn), Cd, Al(45–55Al), Ga(43–50Ga), In(23–55In)

NaX: X In, Tl

KX2: X Na, Au, Pb CsX2: X Na, K LiX2: X Pt

NaX2: X Pt, Ag, Au(60–68Au) KX2: X Bi RbX2: X Bi CsX2: X Bi

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M6O octahedra (see Fig. 4.28). The solid-state structure results from the packing of such groups. The inter-cluster distances are similar to those found in the metals. According to Simon, these compounds could be described as ([Rb9O2]5, 5e) and ([Cs11O3]5, 5e) with the five electrons donated to a conduction band, both interand intra-cluster metal–metal bonding, in agreement with the metallic conductivity of these compounds. Another interesting group of alkali compounds contain, together with the alkali metal, more or less complex ‘substructures’ (clusters, etc.) formed by the atoms of the other components. In the compound (Na, K)10Tl13 (Cordier and Müller 1994) the alkali metals form a framework of truncated octahedra, whereas the 13 Tl atoms are arranged in Tl12+1 icosahedra (centred by Tl) and separated by each other by alkali metal atoms. Notice that the Tl13-centred icosahedra represent a structural feature characteristic of intermetallic phases, such as those pertaining to the NaZn13 (CaCu6.5Al6.5, etc.) type. In a review by Corbett (1996), many families of Zintl phases are described; especially those containing triels and tetrels, that is elements of the 13th group (Al family) and elements of the 14th group (Si family). Especially compounds of the alkali and alkaline earth metals have been considered, and a systematic description of the triel and tetrel atomic groups (clusters, networks, etc.) contained in such compounds was given. In the case of the triels derivatives starting from compounds such as LiAl, LiGa, LiIn, NaIn and NaTl, all having the NaTl-type structure, a sequence of more and more complex structures has been identified. A few examples are: Rb2In3 in which a network was identified formed by In octahedra interbridged at four equatorial vertices into square nets (2[In 4 6 ]), K3Ga13 containing closo-Ga12 and nido-Ga11 clusters interconnected by Ga atoms, the Ga alloy K3Ga13, etc. Considering more complicated structures and stoichiometries, we may directly quote Corbett: ‘We will close this section with an indium example that exhibits another step forward in complexity and, perhaps, beauty but a step backward in our ability to readily understand details of bonding and properties’. The example reported corresponds to ‘carbon-free indium fullerenes’. Interesting is a ternary Na–In compound containing a small quantity of Ni, that is: Na96In97Ni2 (Sevov and Corbett 1993, Corbett 1996). The basic (inter-bonded and condensed) structural components of this compound are multiple, onion-like, endo-hedral cluster constructions formed by In74 units containing Na39 polyhedra, which in turn contain a partially disordered In10 unit centred by a single Ni atom, corresponding to the symbolic description: Ni@In10@Na39@In74. In several cases, complex structural patterns such as, for instance, homo- and hetero-nuclear anions in Zintl phases are observed not only in the solid, but also in the liquid state. This can be related, for the liquid phase of several systems, to the

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347

particular trends of various properties as a function of the composition and to the consequent identification, at certain compositions, of a ‘peculiar behaviour’, leading to the definition of ‘liquid intermetallic compounds’. This point was discussed in § 3.2, reporting a number of examples concerning alkali metal alloys (with Tl, Sn, Pb, Bi). 5.4 ALLOYS OF THE ALKALINE EARTH METALS AND OF THE ‘DIVALENT’ RARE EARTH METALS

Calcium, Ca; strontium, Sr; barium, Ba; radium, Ra; europium, Eu; ytterbium, Yb

5.4.1 Introduction Calcium, strontium, barium and radium, the alkaline earth metals proper, are the typical elements of the 2nd column (the 2nd group) of the Periodic Table. In the first places of this column, however, two other metals are present, beryllium (Be) and magnesium (Mg), which, on the basis of their properties and alloying behaviour, will be presented in § 5.12, together with the metals of the 12th group (zinc, Zn, cadmium, Cd, and mercury, Hg). On the other hand it may be noticed that some aspects of the chemistry and alloying behaviour of Ca, Sr and Ba could be conveniently compared with those of the ‘divalent’ rare earth metals europium and ytterbium. In this chapter, therefore, together with Ca, Sr, Ba (and Ra) a short presentation will also be given of Eu and Yb. A few more details on the Eu and Yb chemistry are given in § 5.5 in comparison with the trivalent lanthanides. Calcium (Ca, [Ar]4s2), name and symbol from the Latin word calx (lime). Identified and isolated (1808) by H. Davy. Silvery white, soft metal. Atomic number 20, atomic relative mass 40.078. Occurrence. It is the fifth most abundant element in the earth’s crust. It is found in many naturally occurring minerals such as limestone (CaCO3), dolomite (MgCO3 CaCO3), gypsum (CaSO4 2H2O), anhydrite (CaSO4), fluorspar (CaF2), apatite (CaF2 3Ca3(PO4)2) as well as silicates.

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Intermetallic Chemistry

Preparation. Previously, electrolysis of fused CaCl2 was used; today the process used is the thermal reduction of lime with Al. The reactants, lime and Al powder, are briquetted and charged into a high-temperature alloy retort. The reaction vessel is evacuated to 0.1 Pa, or less, and then heated to 1200°C. Al reduces the lime producing Ca metal vapour: this is removed from the reaction chamber by condensation, thus allowing the reaction to continue. High purity Ca requires highly purified lime and Al and, generally, a further vacuum distillation step. Main uses. Calcium is important in steel production. It has a strong ability to alter the oxides and sulphides. Treatment with calcium modifies the melting points of inclusions which rapidly float out of the steel. Calcium is important in one method of producing a neodymium–iron alloy which is a neodymium ferro boron raw material (through, for instance, the reaction Nd2O3 Ca Fe : NdFe byproducts). Calcium is important also in the purification of Pb through the de-bismuthizing process. Calcium metal is used in the reduction of zirconium fluorides, thorium and uranium oxides to obtain the metals. Strontium (Sr, [Kr]5s2), name and symbol from Strontian, the town in Scotland where it was discovered by the Irish scientist A. Crawford (1790). Silvery yellowish metal. Atomic number 38, atomic relative mass 87.62. Occurrence. Strontianite (SrCO3) and celestite (SrSO4) are the only minerals of economic importance. Preparation. Strontium metal can be obtained by electrolysis of the fused chlorides or by reduction of the oxide by aluminium. Uses. Strontium master alloys are used in Al foundry practice. As an addictive to Al–Si alloys, it enhances mechanical properties and machining performance; it modifies the morphology of the eutectic from coarse acicular plates of Si to a fine interconnected fibrous morphology, resulting in higher tensile strength and greatly improved ductility. .. Barium (Ba, [Xe]6s2), name and symbol from the Greek βαρυ (heavy). The pure element was discovered (1808) by H. Davy. Atomic number 56, atomic relative mass 137.327.

Elements of Alloying Behaviour Systematics

349

Occurrence. Barium occurs mainly as witherite (BaCO3) and baryte or heavy spar (BaSO4). Preparation. On industrial scale Ba metal is produced in a vacuo by reduction of its oxide with Al or Si (higher temperature is required in this last case). The overall reactions are for instance: 4BaO 2Al : 3Ba BaAl2O4 3BaO Si : 2Ba BaSiO3 In the case of reduction by Al, the intermediate formation, however, of BaAl4 has been considered with a longer series of reactions. Uses. It is used as a getter: it has a relatively low vapour pressure and is very reactive towards H2, O2, N2, CO2, H2O, etc., even removing inert gases by inclusion. It is used as de-oxidizer for steel, etc. and also as modifying agent of Al–Si eutectic alloys (as Na and Sr). Radium (Ra, [Rn]7s2), name, and symbol, after Latin radius (ray). Discovered (1898) by Marie and Pierre Curie. Silvery white, soft metal, radioactive. Atomic number 88, atomic relative mass 226.025403 (nuclidic mass of the longest half life isotope). Occurrence. Radium is found naturally in uranium ores such as pitchblende (mostly UO2). One tonne of pitchblende might yield about 0.15 g of radium. Preparation. The element was isolated in 1911 by Mme. Curie and A. Debierne by the electrolysis of a solution of pure radium chloride, employing a mercury cathode. By distillation in hydrogen atmosphere this amalgam yielded the pure metal. Radium is currently prepared by reduction of the oxide by Al at 1200°C in vacuum. Uses. The main use of radium is the preparation of 227Ac, via neutron capture in a nuclear reactor. Europium (Eu, [Xe]4f 76s2), name and symbol after Europe. Discovered (1901) by E.A. Demarcay. Silvery white, metallic. Atomic number 63, atomic relative mass 151.964. Occurrence, preparation: see § 5.5.

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Intermetallic Chemistry

Table 5.7. Alkaline earth metals: selected physical properties. Property r/pm, metallic, CN 12 [‘metallic valence’] r/pm, ionic, M2 r/pm, ionic, M3, CN 6 1st ionization energy/kJ/mol 2nd ionization energy/kJ/mol 3rd ionization energy/kJ/mol Tmelting/°C Tboiling/°C ΔHmelting (at Tmelting)/kJ/mol ΔfH0 of Me1 gas at 298.15 K/ kJ/mol

Ca

Sr

Ba

197.4 [2]

215.1 [2] 223.6 [2]

100 CN 6

118 CN 6

135 CN 6

589.8 1145.4 4912.4 842 1484 8.5 177.8

549.5 1064.2 4140 769 1382 7.4 164.0

502.9 965.3 3600 727 1898 7.1 179.1

Ra

Eu

229.4 [2] 204.1 [2] 179.8 [3] 148 117 CN 8 CN 6 94.7 509.3 546.7 979.1 1085 – 2404 700 822 – 1597 – 9.2 – 175.3

Yb 193.9 [2] 174.1 [3] 102 CN 6 86.8 603.4 1176 2415 819 1194 7.7 152.1

Ytterbium (Yb, [Xe]4f 146s2), name and symbol after the village of Ytterby (Sweden). Discovered (1878) by J. de Marignac. Silvery white, metallic. Atomic number 70, atomic relative mass 173.04. Occurrence, preparation: see § 5.5. 5.4.2 The alkali earth metals and Eu and Yb: a summary of their atomic and physical properties Main atomic and physical properties of the alkali earth metals are summarized in Tables 5.7 and 5.8. Their typical electron configurations correspond to the outermost ns2 electrons. Alkali earth metals show relatively low 1st and 2nd ionization energies: this can be related to the fact that almost without exception both the external s electrons take part together in bond formation whether the bond is ionic or covalent. 5.4.3 The alkali earth metals and Eu and Yb: remarks about their general chemical properties and reactivity Calcium, strontium and barium are strongly chemically reactive. For safety reasons and for protection from contamination their handling must be carried out under dry inert conditions wearing goggles, shields, etc. The high radioactivity of radium requires special handling techniques and precautions. Its high radioactivity is far more important than any chemical toxicity but from a chemical point of view its hazards are similar to those of barium.

351

Elements of Alloying Behaviour Systematics Table 5.8. Alkaline earth metals: crystal structures, lattice parameters of their allotropes and calculated densities. When not differently indicated the allotropic transformations refer to room pressure. Element (allotrope) Temperature range/°C Pressure/GPa

αCa βCa αSr βSr β Sr αBa βBa γBa Ra Eu αYb βYb γYb

Calcium 443° 443° to 842° Strontium 547° 547° to 769° 3.5 GPa Barium 727° 5.33 GPa 23 GPa Radium 700° Europium 700° Ytterbium 3° 3° to 795° 795° to 819°

Crystal structure

Lattice parameters/pm a

Atomic volume, Vat/106 pm3

Molar volume/ cm3/mol

Density/ g/cm3

c

cF4-Cu cI2-W

558.84 448.0

43.63 44.96

26.28 27.07

1.52 1.48

cF4-Cu cI2-W cI2-W

608.4 487 443.7

56.30 57.75

33.90 34.78

2.58 2.52

cI2-W hP2-Mg

502.27 390.1

63.36

38.15

3.60

cI2-W

514.8

68.27

41.08

5.50

cI2-W

458.27

48.12

28.98

5.24

hP2-Mg cF4-Cu cI2-W

387.99 548.48 444

41.63 41.25 43.76

25.07 24.84 26.4

6.90 6.97

615.4

638.59

Europium and ytterbium are very readily oxidizable and react with O2, and especially with moist air. They rapidly dissolve in dilute mineral acids. Eu and Yb and the alkaline earth metals form, like the alkali metals, deep blue strongly reducing solutions in liquid ammonia. 5.4.4 Intermetallic chemistry of the alkaline earth metals and of Eu and Yb 5.4.4.1 Phase diagrams of the alkaline earth metals and of Eu and Yb. The general trend, along the Periodic Table, of the phase diagram types is similar for the three metals Ca, Sr and Ba. With the exception of the light elements of the first two groups (H, Li, Be, Mg and Na with Ba) no compound is formed with the metals of the groups from 1 to 8. A very similar pattern is shown by Eu and Yb (for which however the no-compound region includes only the metals of the groups up to the 6th). For all these elements no compounds are known with the metals of the

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Intermetallic Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Ba

Sr

Ca

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Eu

Compound-forming element

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Yb

Phase diagram known; no intermediate phases formed

No information available

Figure 5.7. Binary compound formation capability of Ca, Sr, Ba and of Eu and Yb. Those elements are marked for which compounds with the mentioned ‘divalent’ metals are known.

lanthanide and actinide series. A summary of the binary compound formation capability of these metals is given in Fig. 5.7 where a sharp subdivision of the Periodic Table is evident. Even clearer may be the subdivision of the elements between those forming and those not forming compounds with the alkaline earth metals when considered in the order of the Mendeleev Number as indicated in Fig. 2.22. A comparison between Figs 5.6 and 5.7 may be useful in order to underline a certain similarity in the alloying behaviour of the metals of the first two groups. 5.4.4.2 Melting point trend in the binary alkaline earth metal alloys. Table 5.9 reports the values of the melting points observed in the compound-forming systems of the alkaline earth metals, with the elements of one row of the Periodic Table. Reference is made to the 4th row elements, but only examples concerning the 5th row metals are given, due to the limited data available. For the different alkaline earth metals–Me systems formulae and melting temperatures of the highest melting compounds are shown (p means peritectic melting, s.s is a short-hand indication that around the given formula we have a solid solution range). The indication is also given if the corresponding values of the Raynor Index (IR, see § 2.2.4.1) are higher than 1. Notice that, generally, IR is higher than 1 in the systems with the elements (semi-metals, non-metals) of the right-hand part of the Periodic Table. The very high thermal stability of compounds with the elements representative of the 15th to 16th groups such as the antimonides, tellurides, etc. may be underlined.

353

Elements of Alloying Behaviour Systematics Table 5.9. Highest melting points (T (°C)) in the alloys of the ‘divalent’ metals (Me) with compound-forming elements of the 4th or of the 5th row of the Periodic Table. The 5th row elements are marked by an asterisk. See the introduction for the meaning of the symbols. System

Ca compounds

Sr compounds

Ba compounds

Me–Ni

CaNi5 SrNi no compounds 1230°, p, IR 1 860°, p, IR 1

Me–Cu

CaCu5 951°, IR 1

Eu compounds

Yb compounds

EuNi5 YbNi3 1440°, est. IR 1 1310°, IR 1

SrCu5 BaCu13 845°, p, IR 1 758°, p, IR 1

EuCu5 847°, IR 1

Yb2Cu9 937°, IR 1

Me–Ag* Ca2Ag7 725°, IR 1

SrAg5 783°, IR 1

BaAg2 770°, IR 1

s.s. EuAg2 792°, IR 1

Yb2Ag7 749°, IR 1

Me–Zn

CaZn11 724°, IR 1

SrZn13 830°, IR 1

BaZn13 885°, IR 1

EuZn2 750°, IR 1

YbZn11 755°, IR 1

Me–Ga

CaGa2 990°, IR 1

s.s. SrGa2 1045°, IR 1

BaGa4 1016°, IR 1

EuGa2 1030°, IR 1

YbGa2 1100°, IR 1

Me–Ge

Ca2Ge 1380°, IR 1

SrGe 1165°, IR 1

BaGe 1155°, IR 1

EuGe 1220°, IR 1

Yb3Ge5 1080°, IR 1

Me–Sb* Ca11Sb10 1123°, IR 1

SrSb 935°, IR 1

Me–Te*

SrTe 1490°, IR 1

Yb4Sb3 1500°, IR 1 BaTe 1470°, IR 1

s.s. EuTe 1526°, IR 1

YbTe 1730°, IR 1

s.s.: solid solution field close to the formula indicated.

These data may be compared with those typical of more electronegative elements of these groups (for instance, CaO 2600°C, BaO 2010°C, BaSe 1780°C, Eu2O3 2300°C, EuS 2200°C, Ca3N2 1450°C, Ba3P2 1340°C, CaC2 2200°C, CaSi 1325°C). A clear indication of the various intermediate phase stability may be obtained from the values of their ΔfH (ΔfG). The enthalpies of formation, in the liquid and in the solid state, of divalent metal alloys with Pb, as a typical element in the p-block, have been measured, and their trend discussed, by Sommer et al. (2006). The most exothermic values observed, for instance, in the Ca–Pb and Ba–Pb systems, correspond (for the solid compounds, in kJ/mol of atoms, at 300 K) to 62 2 (for Ca2Pb) and 73 2 (for BaPb). A relevant compound forming tendency was observed also for the liquid alloys, for which the association model (see § 3.2) was successfully applied confirming the existence of strong chemical short-range order. 5.4.4.3 Remarks on the crystal chemistry of the alloys of the alkaline earth metals and of Eu and Yb. A review of the binary MeXn intermetallic phases formed by Ca, Sr, Ba, Eu and Yb (Me) with Li, Be and 7th to 15th group elements (X) has

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been published by Fornasini and Merlo (2006): nearly 570 intermediate phases were considered, distributed over 50 compositions and 140 structure types. They observed that most compounds (52%) are localized over five compositions: MeX2 (105 phases, mainly distributed in the Laves-type structures, AlB2 type, or derivative types, etc.), MeX (81 phases), Me5X3 (40), MX3 (38) and Me2X (34). They especially studied atomic size and volume effects in alloying, as briefly reported in § 4.3.2.1. While examining the trends of the interatomic distances in families of isotypic compounds, they introduced also a set of new empirical atomic radii which, in comparison with the conventional ones, shown in Table 5.7 as obtained from the elemental structures, are 3–8% smaller. Table 5.10 summarizes the data relevant to a few selected compositions and more common structure types of the phases formed in the binary alloys of Ca, Sr, Ba, Eu and Yb. Considering the alloys given by the elements of the different groups, some remarks can be made on the following points: Alloys with the 1st and 2nd group elements. Li2Ca (MgZn2 type), Li23Sr6 (Th6Mn23 type) and MeBe13 (NaZn13 type) formed by all the divalent metals with Be, MeMg2 compounds having the MgZn2-type structure. Alloys with the 7th to 9th group elements. Several Laves phases are formed either as the hexagonal MgZn2 type (with Re, Fe, Ru, Os) or as the cubic Cu2Mg type (with Fe, Co, Rh, Ir). CsCl-type compounds are given mainly by Yb. Alloys with the 10th group elements. Typical compositions and structure types of the binary phases formed with Ni, Pd, Pt are 1:1 (CsCl type or FeB or CrB), 1:2 (Laves phases), 2:7 (Gd2Co7 or Ce2Ni7 type), 1:5 (CaCu5), etc. Alloys with the 11th group elements. The 1:1 compounds with Cu, Ag, Au pertain to several structure types, mainly FeB, CrB or stacking variants. The 1:2 compounds, mainly formed with Ag and Au, have generally the KHg2 (CeCu2) type structure. The CaCu5-type structure is characteristic for several 1:5 compounds. Alloys with the 12th group elements. MeCd and MeHg compounds (and some MeZn) have the CsCl-type structure. Various MeX2 are formed (with the structure MgZn2 or KHg2–CeCu2 or CeCd2 type). Typical are the MeZn5 compounds and those corresponding to the 1:11 or 1:13 stoichiometries with high coordination numbers around the large divalent atoms. Alloys with the 13th group elements. Phases pertaining to nearly 40 different structure types have been identified in these systems with significant changes on passing from the alloys with Al to those with Ga, In and Tl. The most frequently observed compositions are the following: Me2X (Co2Si type in In alloys), MeX (mainly with the CsCl-type structure), MeX2 (Laves phases and other structural types such as CaIn2), MeX3 (especially MeTl3 phases with the AuCu3 type or related structure types), MeX4 (as Al alloys with a BaAl4-type structure, Ga alloys with a BaAl4- or a CaGa4-type structure, and a few MeIn4 phases).

Table 5.10. A selection of intermediate phases in the divalent metal binary alloys (CNE coordination number, around Me divalent metal). Structure type

CNE (Me)

Examples of isostructural phases Ca, Sr and Ba compounds

Eu and Yb compounds

oP12-Co2Si (or PbCl2)

13

Ca2X: X In, Ga, Ge, Si, Sn, Pb Sr2X: X Ga, Si, Ge, Sn, Pb Ba2X: X Ga, Si, Ge, Sn, Pb

Eu2X: X Ga, In, Si, Sn, Pb Yb2X: X Au, Ga, In, Tl

cP2-CsCl

14

CaX: X Pd, Cd, Hg, In, Tl SrX: X Cd, Hg, Tl BaX: X Zn, Cd, Hg

EuX: X Zn, Cd, Hg, Tl YbX: X Ru, Rh, Ir, Pd (50–52Pd), Ag, Au(50-54Au) Zn, Cd, Hg, In, Tl

cF8-NaCl

6

CaX: X O, S, Se, Te, Po SrX: X O, S, Se, Te, Po BaX: X O, S, Se, Te, Po

EuX: X N, P, O, S, Se, Te, Po YbX: X N, P, O, S, Se, Te, Po

oI12-CeCu2

16

SrX2: X Ag, Au, Al BaX2: X In

EuX2: X Cu, Ag, Au YbX2: X Cu, Ag

cF24-Cu2Mg

16

CaX2: X Ni, Pd, Pt, Al SrX2: X Rh, Ir, Pt BaX2: X Pd, Pt

EuX2: X Rh, Pd, Ir, Pt YbX2: X Co, Ni, Rh, Ir, Al

hP12-MgZn2

16

CaX2: X Li, Mg, Cd BaX2: X Mg

EuX2: X Mg, Re, Fe, Al YbX2: X Re, Ru, Os, Mg

oP12-Co2Si

10

CaX2: X H SrX2: X H BaX2: X H

EuX2: X H YbX2: X H

cP4-AuCu3

12

CaX3: X Tl, Sn, Pb SrX3: X Bi

EuX3: X Tl, Sn, Pb YbX3: X Pd, Pt, Al, Tl, Sn, Pb

tI10-BaAl4

22

CaX4: X Al SrX4: X Al, Ga BaX4: X Al, Ga, In

EuX4: X Al, Ga

cF24-AuBe5

16

CaX5: X Au

hP6-CaCu5

18

CaX5: X Ni, Pd(84–87Pd), Pt, Cu, Zn SrX5: X Pd, Pt, Ag, Au, Zn BaX5: X Pd, Pt, Ag, Au

EuX5: X Ni, Cu, Ag, Au, Zn YbX5: X Ni, Cu

tI48-BaCd11

22

CaX11: X Zn SrX11: X Cd BaX11: X Cd

EuX11: X Zn, Cd YbX11: X Zn

cP36-BaHg11

20

CaX11: X Hg SrX11: X Hg BaX11: X Mn, Hg

cF112-NaZn13

24

CaX13: X Be, Zn SrX13: X Be, Zn BaX13: X Be, Cu, Zn

EuX13: X Be, Zn YbX13: X Be, Yb

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Alloys with the 14th group elements. Phases of 22 different compositions and distributed over 46 structure types have been identified in the binary alloys with Si, Ge, Sn, Pb. Typical compounds are Me2X, with Co2Si- or Ni2In-type structure, and several Me5X3 phases. Binary and related interstitial ternary compounds corresponding to the 5:3 stoichiometry are described and discussed in § 7.5.6.2. Various 1:1, 1:2 compounds and the closed-packed MeSn3 and MePb3 (1:3) are generally distributed over different structure types. Alloys with the 15th group elements. The main phases identified in the alloys with As, Sb, Bi correspond to the following compositions: Me2X (probably oxygen stabilized Me4X2O phases of the so-called La2Sb type), Me5X3 (and related hydrogen stabilized compounds), Me16X11 (Ca16Sb11 type), Me11X10 (tI84–Ho11Ge10 or Ba11Sb10), MeX2, MeX3. Compounds with the 16th group elements. Among the various phases formed with these non-metal elements, the ‘normal valence’ compounds, NaCl type, may be mentioned. Some of them have been described as ‘point compounds’ (for instance BaS, BaSe, BaTe); a few others as corresponding to a solid solution range (for instance, EuS: 43–50 at.% S, EuTe: 50–57 at.% Te). 5.5. ALLOYS OF THE METALS OF THE 3RD GROUP OF THE PERIODIC TABLE

Scandium, Sc; yttrium, Y; lanthanum, La; trivalent lanthanides, Ln; actinium, Ac; actinides, An

5.5.1 Introduction The 3rd group of the Periodic Table (the 1st column within the block of the transition elements) contains the metals scandium, yttrium, lanthanum, and actinium. Lanthanum (atomic number 57) may be considered the earliest member of the family of metals, called lanthanides (general symbol Ln), forming, inside the principal transition series, an inner transition series (up to atomic number 71). Scandium and yttrium together with the lanthanides are also called rare earth metals (general symbol R).

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Within the lanthanides the first ones from La to Eu are the so-called ‘light’ lanthanides, the other are the ‘heavy’ ones. Together with the heavy lanthanides it may be useful to consider also yttrium; the atomic dimensions of this element and some general characteristics of its alloying behaviour are indeed very similar to those of typical heavy lanthanides, such as Dy or Ho. An important subdivision within the lanthanides, or more generally within the rare earth metals, is that between the ‘divalent’ ones (europium and ytterbium which have been described together with other ‘divalent’ metals in § 5.4) and the ‘trivalent’ ones (all the others, scandium and yttrium included). Notice that by analogy with La and the lanthanides, similarly actinium (atomic number 89) and the following metals (up to atomic number 103) compose the family of actinides (general symbol An).

5.5.2 Lanthanide and actinide concept, lanthanide contraction The introduction of the lanthanide collective name and concept, may be justified considering that these elements are chemically characterized by having a relatively similar behaviour, especially in aqueous solution. All these metals tend to form trivalent ions and give analogous chemical compounds. Generally small differences only in their physical and chemical properties may be noticed between adjacent elements in the series. If placed in the main part of the Periodic Table according to similarities in chemical features, all the 14 elements following La would occupy the same single position fixed for La (the prototypal element of the family) at the atomic number 57. The approximate chemical similarity of the lanthanides results from the relatively small radial extension of the 4f valence orbitals which are buried beneath the spatially more extended 5d and 6s orbitals. The 4f orbitals therefore have little opportunity to be involved in chemical bonding. As a consequence, on passing from one element to the next, the addition of another f electron to the valence shell has a small effect on the overall reactivity and bonding characteristics of the element and all the lanthanides show the tendency to have a similar chemical behaviour. To a certain extent an analogous tendency towards a uniform chemical behaviour is exhibited by the elements of the actinide series, especially the heavy ones. Some analogies for instance can be observed between the chemistry of Pu and that of U and Np and it may be also underlined that the elements from americium onwards show a very similar behaviour. It was Seaborg who proposed the ‘actinide’ concept; it has become generally accepted practise to call the 15 elements beginning with Ac the actinide elements. However, we have to notice that, although immediately following lanthanum the 4f orbitals become more favourable than the 5d for the entrance of further electrons; in the following elements there is not (until later) a similar situation for the 5f–6d

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orbitals. Thus for the metals following Ac there may be electrons in the 5f or 6d orbitals, or both. Later on, however, after 6 (or more) electrons have been added to the Ac configuration, the 5f orbitals become the more stable. On the basis of the electronic structures of the different series of elements a few additional comments may be useful. In a d-block element the partially filled d orbitals project clearly out to the periphery of the atoms (or ions). The electrons occupying these orbitals are therefore strongly influenced by the surroundings of the atom and, on the other hand, may significantly influence this environment. Several properties of an atom with partly filled d orbitals are therefore significantly influenced by the number and arrangement of the d electrons. On passing through a series of the d-block (through a principal transition series) there is therefore a complex property trend and somewhat irregular variations of chemical properties. On the contrary, owing to the 4f orbitals being deeply buried, the f electrons in the lanthanides are largely screened from the surroundings: the change of their number has therefore very little chemical relevance and along the (internal transition) lanthanide series there is a clearly homologous behaviour. The actinide behaviour is included between that of a d series and that of the lanthanides: the 5f orbitals indeed are not as well shielded as are the 4f but not even so prominent as the d orbitals in the d-block metals. Lanthanide contraction. As noted in § 4.2.2.2 and remarked in the preceding paragraph, an important characteristic of the lanthanide metals is the existence of the so-called lanthanide contraction, that is a steady decrease in atomic and ionic dimensions with increasing atomic number. As seen before, this contraction occurs because, although each increase in nuclear charge is exactly balanced by a simultaneous increase in the electronic charge, the directional characteristics of the 4f orbitals cause the 4f n electrons to shield themselves and other electrons from the nuclear charge only imperfectly. As a consequence, each unit increase in the nuclear charge causes an increase in the attraction for the whole electron charge cloud and each ion ‘shrinks’ a little in comparison with the preceding ion. Similar effects occur also in the d series, where, however, there is a greater cumulative effect than in the f series, due to the fact that there are 14 lanthanides and the 4f electrons screen more poorly the outer electrons than the nd. It has also been observed that the lanthanide contraction is partly due to relativistic effects which influence the shielding properties of the electrons in the inner shell. According to Greenwood and Earnshaw (1997), the following consequences may be related to the lanthanide contraction: (i) The size reduction from one LnIII to the next makes their separation possible, by using convenient chemical/physical methods; the regularity and smallness of such reduction, however, makes the separation difficult.

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(ii) Going on through the lanthanide series, when dysprosium or holmium are reached, the Ln3 radius has been reduced so much to be nearly identical with that of Y3. This is the reason why the much lighter yttrium has a chemistry very similar to that of the heavy lanthanides and it is generally associated with them in their ores. (iii) The extent of the total lanthanide contraction is similar to the expansion observed in passing from the first to the second transition series, which could also be expected in passing from the second to the third transition series. The insertion of the lanthanide series practically compensates almost exactly for this expected expansion with the results that in each column of the d-block the members of the second and third series have very similar atomic dimensions and properties. Lanthanides properties and general references. For a systematic treatment and general references of the physical and chemical properties of the rare earths and their compounds and alloys mention can be made to a periodical publication in which several contributions to these subjects are being collected. See for instance Gschneidner and Eyring (1978) and Gschneidner et al. (2005). We would also like to quote a sentence, included in the prefaces of all these books, which hints at the complexity and richness of the rare earth behaviour and the ever-increasing interest in their properties and applications. The mentioned sentence is as follows: ‘These elements perplex us in our rearches [sic], baffle us in our speculations, and haunt us in our very dreams. They stretch like an unknown sea before us – mocking, mystifying, and murmuring strange revelations and possibilities (Sir William Crookes, February 16, 1887)’.

A similar publication has been edited for the actinides (Freeman and Lander 1984, Freeman and Keller 1991). 5.5.3 Rare earth metals Scandium (Sc, [Ar]3d14s2), name and symbol after the Latin Scandia (Scandinavia). Discovered (1879) by Lars F.Nilson (in Uppsala, Sweden). Silvery white, soft metal. Atomic number 21, atomic relative mass 44.955910. Yttrium (Y, [Kr]4d15s2), name and symbol after Ytterby, Sweden. Discovered (1789) by the Finnish chemist Johann Gadolin. Silvery white, soft metal. Atomic number 39, atomic relative mass 88.90585.

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Lanthanides Lanthanum (La, [Xe]5d16s2), name and symbol after the Greek name λανθα´ νειν (lanthanein, to lie hidden). Discovered (1839) by Carl Gustaf Mosander. Silvery white metal. Atomic number 57, atomic relative mass 138.9055. Cerium (Ce, [Xe]4f 15d16s2), name and symbol after the asteroid Ceres. Discovered (1803) by Jöns Jacob Berzelius and Wilhelm Hisinger and independently by Martin Klaproth. Silvery white metal. Atomic number 58, atomic relative mass 140.115. Praseodymium (Pr, [Xe]4f 36s2), name and symbol after the Greek words πρασι´ος διδυμος (prasios didymos, green twin). Discovered (1885) by Carl F. Auer von Welsbach. Silvery white, yellowish tinge, metal. Atomic number 59, atomic relative mass 140.90765. Neodymium (Nd, [Xe]4f 46s2), name and symbol after the Greek words ν´εος διδυμος (neos didymos, new twin). Discovered (1885) by Carl F. Auer von Welsbach. Silvery white, yellowish tinge, metal. Atomic number 60, atomic relative mass 144.24. Promethium (Pm, [Xe]4f 56s2), name and symbol after Prometheus who, in Greek mythology, stole fire from the gods. Discovered (1945) by J.A. Marinsky, L. Glendenin and C.D. Coryell by use of ion-exchange chromatography on residues in a nuclear reactor. Metallic, radioactive. Atomic number 61, atomic relative mass 144.912744 (nuclidic mass of the longest half life isotope). Samarium (Sm, [Xe]4f 66s2). Name and symbol after the mineral samarskite. Discovered (1879) by Paul Emile Lecoq de Boisbaudran. Silvery white metal. Atomic number 62, atomic relative mass 150.36. Europium (Eu, [Xe]4f 76s2). Atomic number 63, see § 5.4. Gadolinium (Gd, [Xe]4f 75d16s2), name and symbol after the Finnish chemist and mineralogist J. Gadolin. Discovered (1880) by Jean de Marignac. Silvery white metal. Atomic number 64, atomic relative mass 157.25.

Elements of Alloying Behaviour Systematics

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Terbium (Tb, [Xe]4f 96s2), name and symbol after the village Ytterby (Sweden). Discovered (1843) by C. Mosander. Silvery white metal. Atomic number 65, atomic relative mass 158.92534. Dysprosium (Dy, [Xe]4f 106s2), name and symbol after the the Greek word δυσπροσιτος (dysprositos, hard to obtain). Discovered (1886) by Paul Emile Lecoq de Boisbaudran. Silvery white metal. Atomic number 66, atomic relative mass 162.50. Holmium (Ho, [Xe]4f 116s2), name and symbol after the Latin word for the city of Stockolm, Holmia. Discovered (1879) by P.T. Cleve even though the holmium absorption spectrum was observed the year before by the Swiss chemists J.L. Soret and M. Delafontaine. Silvery white metal. Atomic number 67, atomic relative mass 164.93032. Erbium (Er, [Xe]4f 126s2), name and symbol after the village Ytterby (Sweden). Discovered (1843) by C.G. Mosander. Silvery white metal. Atomic number 68, atomic relative mass 167.26 Thulium (Tm, [Xe]4f 136s2), name and symbol after Thule, an ancient name for Scandinavia. Discovered (1879) by P.T. Cleve. Silvery white metal. Atomic number 69, atomic relative mass 168.93421. Ytterbium (Yb [Xe] 4f 146s2). Atomic number 70, see § 5.4. Lutetium (Lu, [Xe]4f 145d16s2), name and symbol after the Latin word Lutetia (Paris). Discovered (1907) by Georges Urbain and Carl Auer von Welsbach. Silvery white metal. Atomic number 71, atomic relative mass 174.967. 5.5.3.1 Rare earth metals: occurrence and preparation. The rare elements are lithophilic and therefore they are concentrated in carbonates, silicates, phosphates, etc. According to the mineralization process, rare earths occur in three different groups of minerals: (i) Minerals containing light rare earths, lanthanum, cerium, praseodymium, neodymium, samarium, europium, in which Ce and, in some cases, La or Nd are the main components (cerium earths). Typical minerals of this group are bastnaesite (Ce, La, Y)CO3F and monazite (Ce, La, Nd, Pr, Th, Y)PO4. (ii) minerals containing rare earth from gadolinium to lutetium and yttrium as main components

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(yttrium earths). Typical minerals are xenotime YPO4, gadolinite Y2FeBe2Si2O10. (iii) Complex minerals in which both yttrium earths and cerium earths are present, generally in ore containing Ti, Ta, Nb, U. Scandium is a very rare element; it occurs in minerals such as thortveitite (Sc2Si2O7). Despite their name, the lanthanides are not particularly rare: La, Ce, Pr and Nd are more common than Pb. Due to the great similarity of the chemical properties of the rare earth elements, their separation represented, especially in the past, one of the most difficult problems in metallic chemistry. Two principal types of process are available for the extraction of rare earth elements: (i) solid–liquid systems using fractional precipitation, crystallization or ion exchange; (ii) liquid–liquid systems using solvent extraction. The rare earth metals are produced by metallothermic reduction (high purity metals are obtained) and by molten electrolysis. The metallothermic reduction of the oxides by La produces the metals Sm, Eu, Tm, Yb, all having high vapour pressures. The reaction goes to completion due to the removal of the rare earths by volatilization from the reaction chamber (lanthanum has a low vapour pressure). The remaining rare earth metals (Sc, La, Ce, Pr, Nd, Y, Gd, Tb, Dy, Ho, Er, Lu) can be obtained by quantitative conversion of the oxides in fluorides, followed by reduction with Ca. The metallothermic reduction of the anhydrous rare earth chlorides could be also used to obtain La, Ce, Pr and Nd. The molten electrolysis can be applied to obtain only the first four lanthanide metals, La, Ce, Pr and Nd, because of the high reactivity of the materials that limits the operating temperatures to 1100°C or lower. According to Abell (1989), refinement methods of the rare earth metals include vacuum re-melting (Ce, La), zone refining (Ce, La, Pr, Nd, Gd, Tb, Y), solid-state electron transport in vacuum (Ce, La, Pr, Nd, Gd, Tb, Y, Lu), solid-state electron transport under inert gas (Nd, Gd, Tb, Y, Lu, Sc, Er, Ho, Dy), distillation (Gd, Tb, Y, Lu, Sc), sublimation (Er, Ho, Dy, Eu, Sm, Yb, Tm) and distillation to remove volatile impurities from high boiling rare earth metals. Several aspects of the preparation of high purity rare earth metals, and of the role that impurities may play in defining their properties have been reviewed and discussed by K. Gschneidner, with a special reference to the work carried out in the highly specialized Ames laboratory in the Iowa State University (USA). 5.5.4 Actinides Actinium (Ac, [Rn]6d17s2), name and symbol after the Greek ακτ´ιζ (actis, ray). Discovered (1899) by André Debierne and, independently, by Friedrich O. Giesel (1902). Silvery white, solid metal; it is so radioactive that glows, with a blue light, in the dark.

Elements of Alloying Behaviour Systematics

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Atomic number 89, atomic relative mass 227.027747 (nuclidic mass of the longest half life isotope). Thorium (Th, [Rn]6d27s2), name and symbol after Thor (the Norse God of thunder). Discovered (1828) by the Swedish chemist Jöns Jacob Berzelius. Silvery white, metal. Atomic number 90, atomic relative mass 232.0381. Protactinium (Pa, [Rn]5f 26d17s2), name and symbol after the Greek πρωτος (protos, first) and actinium (Protoactinium gives actinium when it decays). Discovered (1913) by K. Fajans and O.H. Göhring. Silvery metal. Atomic number 91, atomic relative mass 231.03588. Uranium (U, [Rn]5f 36d17s2), name and symbol after the planet Uranus. Discovered (1789) by Martin J. Klaproth, the metal was isolated (1841) by Eugène M. Peligot. Silvery metal. Atomic number 92, atomic relative mass 238.0289. Neptunium (Np, [Rn]5f 46d17s2), name and symbol after the planet Neptune. Discovered (1940, Berkeley) by Edwin M. McMillan and Philip H. Abelson. Silvery metal. Atomic number 93, atomic relative mass 237.048167 (nuclidic mass of the longest half life isotope). Plutonium (Pu, [Rn]5f 67s2), name and symbol after the planet Pluto. Discovered (1940, Berkeley) by Glenn T. Seaborg, J.W. Kennedy, A. Wahl. Silvery metal. Atomic number 94, atomic relative mass 244.064198 (nuclidic mass of the longest half life isotope). Americium (Am, [Rn]5f 77s2), named after the Americas. Identified (1944, Chicago) by Glenn T. Seaborg, Ralph A. James, Leon O. Morgan, Albert Ghiorso. Silvery metal, tarnishes slowly in dry air. Atomic number 95, atomic relative mass 243.061373 (nuclidic mass of the longest half life isotope). Curium (Cm, [Rn]5f 76d 17s2), named after the scientists Marie and Pierre Curie. Discovered (1944) by Glenn T. Seaborg, Ralph A. James, and Albert Ghiorso. Silvery white metal. Atomic number 96, atomic relative mass 247.070347 (nuclidic mass of the longest half life isotope).

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Berkelium (Bk, [Rn]5f 97s2), named after Berkeley, California. Obtained (1949) by Stanley G. Thompson, Albert Ghiorso and Glenn T. Seaborg. Silvery solid metal. Atomic number 97, atomic relative mass 247.07030 (nuclidic mass of the longest half life isotope). Californium (Cf, [Rn]5f 107s2), named after the state of California. Artificially produced (1950, Berkeley) by Stanley G. Thompson, Kenneth Street Jr., Albert Ghiorso and Glenn T. Seaborg. Silvery white metal. Atomic number 98, atomic relative mass 251.079580 (nuclidic mass of the longest half life isotope). Einsteinium (Es, [Rn]5f 117s2), named after the physicist Albert Einstein. Traces discovered (1952) by Albert Ghiorso and co-workers in the debris of the first test of the hydrogen bomb. Solid, unknown colour. Atomic number 99, atomic relative mass 252.082297 (nuclidic mass of the longest half life isotope). Fermium (Fm, [Rn]5f 127s2), named after the physicist Enrico Fermi. Traces discovered (1952) by Albert Ghiorso and co-workers in the debris of the first test of the hydrogen bomb. Solid, unknown colour. Atomic number 100, atomic relative mass 257.095099 (nuclidic mass of the longest half life isotope). Mendelevium (Md, [Rn]5f 137s2), named after the chemist Dimitri Mendeleev. Discovered (1955, Berkeley) by Gregory R. Choppin and co-workers. Solid, unknown colour. Atomic number 101, atomic relative mass 258.09842 (nuclidic mass of the longest half life isotope). Nobelium (No, [Rn]5f 147s2), named after the scientist Alfred Nobel. Identified (1958, Berkeley) by Albert Ghiorso and co-workers. Solid of unknown colour. Atomic number 102, atomic relative mass 259.10102 (nuclidic mass of the longest half life isotope). Lawrencium (Lr, [Rn]5f 146d17s2), named after the scientist Ernest O. Lawrence (the inventor of the cyclotron). Prepared (1961) by Albert Ghiorso, Almon E. Larsh and Robert M. Latimer. Solid of unknown colour.

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Atomic number 103, atomic relative mass 262.10969 (nuclidic mass of the longest half life isotope). 5.5.4.1 Actinides: occurrence and preparation. With the exception of U and Th, the availability of the actinides of the first half of the series ranges from the g to kg scale; that of the elements of the second half of the series from the mg scale for Cf to the sub-mg scale for Es. Isotopes of Np, Pu, Am, Cm can be available as byproducts of nuclear fuel processing; other elements such as Ac, Cf, Bk, Es can be obtained by irradiation of selected isotopes in high flux reactors, or by reprocessing large quantities of ore (Pa). Thorium is widely but rather sparsely distributed; its only commercial sources are monazite (together with the rare earths) and uranothorite (a mixed Th, U silicate). Uranium is surprisingly common and more abundant than mercury, silver or cadmium in the earth’s crust. It is widely distributed and it is found scattered in the faults of old igneous rocks. Concentration by leaching followed by re-precipitation has produced a number of oxide minerals of which the most important are uranite (also called pitchblende) U3O8 and carnotite, K2(UO2)2(VO4)23H2O. Preparation and handling of actinides are very difficult, because of their scarcity, radioactivity, toxicity and reactivity. The actinides isotopes are unstable and they transform spontaneously into other elements by α and β decay or by fission. The chemical toxicity of the actinides is similar to the toxicity of other heavy elements. The radio toxicity is extremely high giving radiation damage in cells. The safe handling of actinides samples needs hermetically closed containments (glove boxes) maintained under low pressure with respect to the laboratory to avoid the risk of dispersion and inhalation of the particles if a break of containment occurs. The actinides can be obtained by metallothermic reduction of the oxides, carbides or halides, generally fluorides. The reductant La can be used for Am, Cf and Es between 900°C and 1300°C; reduction by Th can be used to prepare Ac, Pu, Cm and Bk. A pelletized mixture of the actinide oxide and of the reductant metal is heated in vacuum (at a temperature typically between 900°C and 1300°C) allowing a rapid evaporation of the actinide metal, leaving behind the oxide and the excess of the reductant. The metallothermic reduction of the fluorides, by using calcium as reductant, is the widely used production technique for all the commercially available actinide metals. This method presents disadvantages in order to prepare actinide metals for solid-state physics investigations on the laboratory scale, such as irregular yield, difficulties in the recovery of the actinide metal from the crucible and slag, presence in the metal of all the impurities present in the reactant as well as the corrosion products of the crucible. For special crucible problems, see § 6.2.1.2. The transition elements Nb, Zr, Ti, Ta are able to reduce to metals the actinide carbides (these last obtained by carboreduction of their oxides in vacuum). The actinide

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metals are separated from the reaction products by evaporation in vacuum; the distilled metal is collected on a water-cooled condenser. The tantalothermic reduction of the carbides presents interesting advantages, such as the preparation of all the actinide metals via vapour phase with good yield and large rate and the obtainment of high purity material even starting from very impure materials, for instance waste. The Van Arkel process can also be used to prepare actinide metals if the starting compound reacts easily with the transporting agent (I2). The thorium and protactinium carbides react with I2 to give volatile iodides above 350°C; these are unstable above 1200°C and decompose into the actinide metals and iodine. Attempts to prepare other actinides, such as U and Pu, through the process were not successful, because from Th to Pu along the actinide series, the vapour pressure of the iodide decreases and the thermal stability increases. An interesting, peculiar laboratory preparative reaction may finally be mentioned. This is based on the very high stability of the intermetallic compounds of actinides (and lanthanides) with the platinum family metals. The combined reduction capability of Pt with H2 (coupled reduction, see § 6.7.2 ff) can be used to obtain, from its oxide, the ‘platinide’ of the actinide metal. The An–Pt intermetallic compound can then be decomposed by heating in vacuum and the actinide can be obtained by distillation. Different techniques are necessary to refine actinide metals, because their properties range from those typical of the transition elements (at the beginning of the series) to those typical of the rare earths. Among the different techniques mention can be made to: vacuum melting (the metal is melted in vacuum and the volatile impurities are evaporated), selective evaporation and condensation (the metal to be refined is evaporated at the lowest possible temperature leaving behind the less volatile impurities and it is simultaneously condensed at the highest possible temperature to re-evaporate the more volatile impurities), electrorefining (Th, U, Np, Pu metals are successfully refined by electrolysis in molten salts, such as LiCl–KCl or NaCl–KCl eutectics, in which the impure metal dissolves). Secondary refining processes (zone melting and solid-state electrotransport) can be also applied to reach purity levels very close to ideal, even though the ultra-refining process would be very expensive and time consuming. 5.5.5 The 3rd group metals: a summary of their atomic and physical properties 5.5.5.1 The rare earth metals. A summary of the main atomic and physical properties of the rare earth metals has been collected in Tables 5.11–5.13. To complete the information and the presentation of the entire series of lanthanides the data relevant to Eu and Yb have been included in these tables. However, the same data are reported also in Table 5.7 in comparison with those of the other typical ‘divalent’ metals (the alkaline earth metals). As for the properties of liquid rare earth metals and alloys see Van Zytveld (1989).

Table 5.11. Lanthanides selected physical properties. Element Metallic radius Ionic radius Tmelting/ CN 12/pm, M3, [Mn] °C [‘valence’] CN 6/pm Sc Y La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

164.1 177.3 187.7 184.6 167.2 182.8 182.2 180.9 180.2 204.1 179.8 180.1 178.3 177.5 176.7 175.8 174.7 193.9 174.1 173.5

[3] [3] [3] [3] [4] [3] [3] [3] [3] [2] [3] [3] [3] [3] [3] [3] [3] [2] [3] [3]

74.5 90.0 104.5 101.0 78 [4] 99.7 98.3 97 95.8 117 [2] 94.7 93.8 92.3 91.2 90.1 89.0 88.0 100 [+2] 86.8 86.1

Vapour pressure at Tmelting/Pa

Tboiling/ °C

ΔHmelting/ ΔHsublimation kJ/mol at 25°C/ kJ/mol

1541 1522 918 798

11 3 101 4 108 1 1010

2836 3345 3464 3443

14.1 11.4 6.20 5.46

931 1021 1042 1074 827

3 107 4 10 3 – 9 102 1.2 102

3520 3074 3000 est. 1794 1529

1313 1356 1412 1474 1529 1545 819

3 102 1 101 9 101 8 101 3 101 2.46 104 2.4 103

3273 3230 2567 2700 2868 1950 1196

10.0 10.79 11.06 17.0 est. 19.9 16.8 7.66

397.5 388.7 290.4 300.8 317.1 232.2 152.1

1663

1.0

3402

22 est.

427.6

6.89 7.14 7.7 est. 8.62 9.21

377.8 424.7 431.0 422.6 355.6 327.6 348 est. 206.7 175.3

est.: estimated values.

Table 5.12. Ionization energies of the rare earth metals. Element

1st ionization energy/kJ/mol

2nd ionization energy/kJ/mol

3rd ionization energy/kJ/mol

4th ionization energy/kJ/mol

Sc Y La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

631.0 616 538.1 527.4 523.1 529.6 536 543.3 546.7 592.6 563.7 572 580.6 588.6 596.7 603.4 523.5

1235 1181 1067 1047 1018 1035 1052 1068 1085 1166 1112 1126 1139 1151 1163 1176 1341

2389 1980 1850 1949 2086 2132 2152 2258 2404 1990 2114 2200 2204 2194 2285 2415 2022

7089 5963 4819 3547 3761 3899 3966 3994 4110 4245 3839 4001 4101 4115 4119 4220 4360

Table 5.13. Rare earth metals: crystal structures, lattice parameters of the allotropes and calculated densities. Element Temperature Stability range/°C Pressure/GPa

Crystal structure

Lattice parameters/pm a

b

c

T/°C

Atomic volume pm3/106

Molar volume/ cm3/mol

Density/ g/cm3

αSc βSc

1337° 1541° to 1337°

hP2-Mg cI2-W

330.88 373 est

526.80

24 1337

24.97 25.95

15.04 15.6

2.99 2.88

αY βY

1478° 1522° to 1478°

hP2-Mg cI2-W

364.82 (410)

573.18

24 1478

33.03 34.46

19.89 20.75

4.47 4.28

αLa βLa γLa β La αCe βCe γCe δCe α Ce

310° 865° to 310° 918° to 865° 2.0 GPa 177° 177° to 10° 10° to 726° 761° to 798° 5.4 GPa

hP4-αLa cF4-Cu cI2-W cF4-Cu cF4-Cu hP4-αLa cF4-Cu cI2-W oS4-αU

377.40 530.3 426 517 485 368.10 516.10 412 304.9

24 325 887

37.53 37.28 38.65

22.60 22.45 23.3

6.15 6.19 5.97

196 24 24 757

28.52 34.78 34.37 34.97

17.2 20.95 20.70 21.1

8.16 6.69 6.77 6.65

αPr βPr γPr

795° 795° to 931° 4.0 GPa

hP4-αLa cI2-W cF4-Cu

367.21 413 488

1183.26

24 821

34.55 35.22

20.80 21.2

6.77 6.64

αNd βNd γNd

863° 863° to 1021° 5.0 GPa

hP4-αLa cI2-W cF4-Cu

365.82 413 480

1179.66

24 883

34.18 35.22

20.58 21.2

7.01 6.80

αPm 890° βPm 890° to 1042°

hP4-αLa cI2-W

365 410 est.

1165

24 890

33.60 –

20.24 –

7.16 –

1217.1

1185.7

599.8

521.5

αSm βSm γSm δSm

734° 922° to 734° 1074° to 922° 4.0 GPa

hR9-αSm hP2-Mg cI2-W hP4-αLa

362.90 366.30 410 est. 361.8

cI2-W

458.27

αGd 1235° βGd 1235° to 1313° γGd 3.0 GPa

hP2-Mg cI2-W hR9-αSm

363.36 406 361

α Tb αTb βTb γTb

53° 53° to 1289° 1289° to 1356° 6.0 GPa

oS4-α Dy hP2-Mg cI2-W hR9-αSm

360.5 360.55 (407) 341

624.4

α Dy αDy βDy γDy

187° 187° to 1381° 1381° to 1412° 7.5 GPa

oS4-α Dy hP2-Mg cI2-W hR9-CdCl2

359.5 359.15 (403) 343.6

618.4

1474° 7.5 GPa

hP2-Mg hR9-αSm

357.78 334

Er

1529°

hP2-Mg

Tm

1545°

hP2-Mg

αYb βYb γYb

3° 3° to 795° 795° to 819°

Lu

1663°

Eu

αHo βHo

700°

2620.7 584.48 1166

24 450 922

33.21 33.96 –

20.00 20.45 –

7.52 7.35 –

24

48.12

28.98

5.24

24 1265

33.05 33.46 32.64

19.90 20.2

7.90 7.80

53 24 1289

32.11 32.07 33.71

19.34 19.31 20.3

8.22 8.23 7.82

187 24 1381

31.56 31.56 32.73

19.00 19.00 19.7

8.55 8.55 8.23

561.78 2450

24

31.14

18.75

8.795

355.92

558.50

24

30.64

18.45

9.07

353.75

555.40

24

30.09

18.12

9.32

hP2-Mg cF4-Cu cI2-W

387.99 548.48 444

638.59

23 24 763

41.63 41.25 43.76

25.07 24.84 26.4

6.90 6.97 6.57

hP2-Mg

350.52

554.94

24

29.52

17.78

9.84

578.10 2603 570.6 569.66 2450 567.8 565.01 2483

370

Intermetallic Chemistry

As a comment to this table we may especially remark the properties of cerium. Quoting Gschneidner and Pecharsky (1999), it can be observed that Ce is one of the most fascinating metals in the Periodic Table, exhibiting a variety of phenomena under various conditions of temperature and pressure: it is an anti-ferromagnet, a superconductor, a mixed valence system (a valence fluctuator), displays Kondo scattering and a solid-solid critical point. Gscheidner and Pecharsky observed that all this occurs because the energy of the inner 4f level is nearly the same as those of the outer valence 5d and 6s levels so that only small amounts of energy are required to change the relative occupancy of the levels producing variable electronic structures. This is especially evident in the polymorphic transformation between the two fcc structures γCe (ambient temperature and pressure phase) and αCe (low-temperature or high-pressure ‘collapsed’ phase) in which the valence changes from 3.06 (γCe) to 3.67 (αCe). On the basis also of previous experimental work (the β to γ transformation in cerium: a 20 year study by Gschneidner et al. 1996) it was also stated that the double close-packed hexagonal βCe slowly transforms to the face-centred cubic γCe near room temperature and ambient pressure, indicating that γCe is the stable modification at 298 K and 1 atm. 5.5.5.2 The actinides. A summary of selected physical properties of the actinide metals is shown in Tables 5.14 and 5.15. Crystal structure data are shown in Table 5.16: notice the complex nature of the polymorphic transformations of a number of these elements and especially of plutonium (compare with Fig. 5.11). The plutonium thermal expansion is very large: it goes through six solid-state structures before melting: in the transformation from α to δ plutonium there is a volume expansion in the order of 25% (the only other similar expansion, of about 20%, is observed in the isostructural transformation from fcc α to fcc γCe). The δ phase contracts as it is heated and Pu contracts as it melts. In Table 5.16 lattice parameters, volume and density data are generally referred to the temperature ranges indicated. The following values of the densities of each phase (g/cm3) have been listed by Boring and Smith (2000): α(19.86), β(17.70), γ(17.14), δ(15.92), δ (16.00), ε(16.51), liquid(16.65), and in the same paper the effects of these properties on the metallurgy of plutonium have been presented and discussed. 5.5.6 The 3rd group metals: remarks about their general chemical properties and reactivity 5.5.6.1 The rare earth metals. The rare earth metals are extremely reactive elements especially with respect to the normal atmospheric gases. The light trivalent lanthanides oxidize with air at room temperature: they should be stored (and handled) in vacuum or under He or Ar. Divalent Eu oxidizes much more readily than any of

371

Elements of Alloying Behaviour Systematics Table 5.14. Actinides selected physical properties. Element

Ac Th Pa U Np Pu Am Cm Bk Cf

Es Fm Md No Lr

Metallic radius/ pm [‘valence’] 187.8 179.8 162.6 154.3 152.8 164 159.2 173.0 174.3 170.4 203 169.4

[3] [4] [5] [6] [6] [4.8] [5] [4] [3] [3] [2] [3]

201.5 [2] 200 [2] 198.5 [2] 197 [2] 166 [3]

Ionic radius Mx, CN 6/pm Ac3 Th4 Pa5 U6 Np5 Pu4 Pu5 Am3 Cm3 Bk3 Cf 2 Cf 3 Cf4 Es2 Fm2 Md2 No2 Lr3

112 94 78 73 75.6 86 74 97.5 97 96 112.5 95 82.9 110.2 108.3 106.4 105.2 89.6

Tmelting/°C

Tboiling/°C

ΔHmelting at Tmelting/ kJ/mol

1051 1755 1572 1135 639 640

3200 4788 – 4134 – 3230

– 13.8 12.3 9.1 3.2 2.8

1176 1345 1050 900

– – – –

14.4 – – –

860 (1527) (827) (827) (1627)

– – – – –

– – – – –

Table 5.15. Ionization energies of the actinides. Element

1st ionization energy/kJ/mol

2nd ionization energy/kJ/mol

3rd ionization energy/kJ/mol

4th ionization energy/kJ/mol

Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr

499 587 568 598 605 585 578 581 601 608 620 627 635 642 444

1170 1110

1930

2780

2113 2152 2287 2267 2316 2422 2576 –

3657 3541 3666 3840 3888 4004 4091 –

1420

1061 1129 1148 1225 1177 1187 1196 –

372

Intermetallic Chemistry

Table 5.16. Actinides: crystal structures, lattice parameters of their allotropes, calculated densities. Element (allotrope) Temperature range/°C Pressure/GPa

Crystal structure

Lattice parameters/pm a

b

c (β)

Atomic volume/ pm3 106

Molar Density/ volume/ g/cm3 cm3/mol

Ac

1051°

cF4-Cu

531.1

37.45

22.55

10.07

αTh βTh

1360° 1360° to 1755°

cF4-Cu cI2-W

508.42 411

32.85 34.71

19.79 20.90

11.73 11.10

αPa β Pa

1170° 1170° to 1572°

tI2-αPa cI2-W

392.1 381

24.87 27.65

14.98 16.65

15.43 13.87

αU βU γU

668° 668° to 776° 776° to 1135°

oS4-αU tP30-βU cI2-W

20.75 21.82 21.88

12.49 13.14 13.18

19.05 18.11 18.06

αNp β Np γ Np

280° 280° to 576° 576° to 639°

oP8-αNp tP4-βNp cI2-W

666.3 488.3 352

19.22 20.20 21.81

11.58 12.17 13.13

20.48 19.48 18.05

αPu

125°

mP16-αPu

618.3

20.25

12.19

20.02*

βPu

125° to 215°

mS34-βPu

22.44

13.51

18.065

γPu δPu δ Pu εPu ζPu

215° to 320° 320° to 463° 463° to 483° 483° to 640° 40 GPa

oF8-γPu cF4-Cu tI2-In cI2-W hP8

482.2 1096.3 101.97° 928.4 1046.3 785.9 92.13° 315.87 576.82 1016.2 463.71 332.61 446.30 363.43 –

23.14 24.93 24.69 24.00

13.94 15.01 14.87 14.45

17.51 16.26 16.42 16.89

αAm βAm γAm δAm εAm

769° 769° to 1077° 1077° to 1176° 12.5 GPa 15 GPa

hP4-αLa cF4-Cu cI2-W mP4-δAm oS4-αU

346.81 1124.1 489.4 – – 306.3 596.8 516.9

29.27 29.30

17.63 17.65

13.79 13.77

323.5

285.37 586.95 495.48 1075.9 565.6 352.4 472.3

488.7 338.9

–

–

–

αCm 1277° βCm 1277° to 1345° γCm 43 GPa

hP4-αLa cF4-Cu oS4-αU

349.6 (438) –

1133.1

29.98

18.06

13.68

αBk βBk γBk

977° 977° to 1050° 25 GPa

hP4-αLa cF4-Cu oS4-αU

341.6 499.7

1106.9

27.96

16.84

14.67

αCf βCf γCf δCf

590° 590° to 900° 30 GPa 41 GPa

hP4-αLa cF4-Cu aP4-γCf oS4-αU

339 –

1101.5

27.41

16.50

15.21

αEs βEs

860° 860° to 927°

hP4-αLa cF4-Cu

– –

* Compare with the values reported in §5.5.5.2.

Elements of Alloying Behaviour Systematics

373

the trivalent rare earths. The heavy lanthanides and Sc and Y do not oxidize at room temperature (they form a protective oxide coating which prevents further oxidation), the divalent Yb also can be handled in air without particular difficulties. The oxidation rate of the different lanthanides, which is higher when its atomic number is lower, depends on several factors: it increases when there is a high level of impurities (especially C, Fe, Ca, etc.), when the relative humidity is high and the temperature is high. A more quantitative indication of the tendency of these elements to react with oxygen may be obtained from Fig. 6.9, where, for several metals, the standard free energies of formation of their oxides are shown. The large negative values relevant to these oxides may be noticed. Cerium metallic radius, and valence, in intermetallic compounds. As a reference to the question of the cerium atomic dimensions in its compounds and its trivalent and tetravalent radii, a paper by Sereni (1982) can be cited. A series of intermetallic compounds of cerium (Laves phases CeMe2 with various metals Me) was examined and the anomalous contraction that it undergoes was used to estimate its radius when joined to a given Me component. Isostructural compounds formed by the same Me components with the trivalent rare earths and the tetravalent metals Zr, Hf and Th were taken as the reference system. The value 184.6 pm of the trivalent metallic radius was confirmed and a value of 168.8 pm was attributed to the tetravalent metallic radius. In discussing the characteristics of the different compounds, in comparison also with other physical properties, it was observed that Ce may be considered in its pure trivalent state in CeMg2 (in which rCe 184.6 pm, V 3) and close to tetravalent (V 3.90, rCe 168.8 pm) in CeFe2 and CeCo2. Intermediate values were assigned to other compounds; for instance: CeAl2 (V 3.06, rCe 183.5 pm), CeOs2 (V 3.25, rCe 180.0 pm), CeNi2 (V 3.40, rCe 174.4 pm). Notice, however, that the terms trivalent or tetravalent, when applied to cerium very often should be considered only as an indication of a general behaviour and not necessarily an explicit sign of a specific bond mechanism. Europium and ytterbium di-valence. The oxidation state II for Eu and Yb has already been considered when discussing the properties of a number of divalent metals (Ca, Sr, Ba in § 5.4). This topic was put forward again here in order to give a more complete presentation of the lanthanide properties. The sum of the first three ionization enthalpies is relatively small: the lanthanide metals are highly electropositive elements. They generally and easily form in solid oxides, complexes, etc., Ln3 ions. Different ions may be formed by a few lanthanides such as Ce4, Sm2, Eu2, Yb2. According to Cotton and Wilkinson (1988) the existence of different oxidation states should be interpreted by considering the ionization

374

Intermetallic Chemistry

enthalpies, sublimation energies, lattice energies, etc. in Born–Haber cycles. The idea that the stability of the various species may be supported merely by the approach to a stable empty 4f 0 (Ce4), half-filled 4f 7 (Eu2) or completely filled 4f 14 (Yb2) f subshells should be considered dubious. Eu2, Yb2. Lattice parameter and heat of formation trends in compounds and alloys. It has been observed that Eu and Yb behave like divalent metal in several of their compounds, as can be deduced from magnetic data, lattice parameter values, etc. They can, however, also form compounds containing the metal in valence III. Typically in the sesqui-oxides and in the trihalides these metals are trivalent as it can be seen by the lattice parameter values of Eu2O3 and Yb2O3 which lie on the curve corresponding to the continuous smooth trend of the normal trivalent lanthanide sesqui-oxides Ln2O3 (Fig. 5.8). The trend of the formation heats of these compounds (showing a difference between the divalent and trivalent lanthanide compounds) may be explained (even if in a first approximation description) in terms of the different steps involved in the reaction of formation and shown in the insert of Fig. 5.8. In the cases of Eu2O3 and Yb2O3, the ΔpromH is involved: the two metals pass from the divalent state in their elementary forms to the trivalent state in their oxides. The promotion energy of Yb (and Eu) has been defined and evaluated by Johansson and Mårtensson (1987). The criteria for the calculation of the values ΔfHII, and ΔfHIII, that is the formation enthalpies in the two cases in which there is no valence change on passing from the metals to the compound, have been suggested by Miedema and co-workers (Niessen et al. 1983). In the case of the Yb–Pb compound a number of data suggest the existence of a quasi-divalent Yb in these alloys with a valence 2.15 according to Gschneidner and McMasters (1971), Percheron-Guegan et al. (1974) and Bauchspiess et al. (1981). For YbPb3 the presence of the metal in the divalent state (higher atomic dimensions) may be noticed from the trend of the lattice parameters shown in Fig. 5.8. As a consequence, we may observe that in all the LnPb3 phases the same valence as in the metals is maintained, that is: III in the general case and nearly II for Eu and Yb. From a thermochemical point of view this should correspond to the absence of the promotional term ΔpromH and, therefore for Yb, to a value Δf H closer to those relevant to the other LnPb3 phases. In conclusion the estimates made by Miedema and co-workers were also used to predict the relative stabilities of the two valence states in the alloys with different metals and to prepare a systematic description of the alloying behaviour (compound formation, miscibility gap formation, etc.) of Eu and Yb. An interesting aspect of this behaviour (see for instance Brutti et al. 2002) may be presented considering the alloys formed by ytterbium with the transition metals of the 8th, 9th and 10th groups. In the binary systems of Yb with Fe, Co, Ni, Ru, Rh, Os and Ir in the Yb-rich regions no compound is formed and a miscibility gap in the liquid state is generally observed. Owing to the variable valence state of this metal,

375

ΔformH ° (kJ/mol of atoms) Lattice parameter (pm)

Elements of Alloying Behaviour Systematics R2O3

RPb3

492 490

1140

488

1120

486 1100

484

1080

482

1060

480

1040

478 −60 −55

−340

−50

−350

−45

−360

−40

−370

−35 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

YbIII element

ΔpromH YbII element

ΔformH III

ΔformH II H

YbIII compound

YbII compound

Figure 5.8. Lanthanide Ln2O3 oxides (cubic cI80-Mn2O3 type, on the left side) and Pb alloys (LnPb3, cubic cP4-type, on the right). The trends of the lattice parameter and of the heat of formation are shown (see the text and notice the characteristic behaviour of Eu and Yb). A schematic representation of the energy difference between the divalent and trivalent states of an ytterbium compound is shown. ΔpromH represents the promotion energy from di- to trivalent Yb metal, ΔfHII, and Δf HIII are the formation enthalpies of a compound in the two cases in which there is no valence change on passing from the metal to the compound: the same valence state (II or III) is maintained.

divalent Yb is assumed to be present in the composition range 50 at.%Yb where intermediate phases are expected to be unstable; trivalent Yb on the contrary is assumed for the range 50 at.%Yb giving alloys more similar to those of the other lanthanides.

376

Intermetallic Chemistry

Lattice stabilities of Ca, Sr and Yb disilicides have been reported by Brutti et al. (2006). Structural stabilities of six different prototype lattices have been investigated and discussed. 5.5.6.2 The actinides. The actinides metals are electropositive and very reactive; they are pyrophoric in finely divided form. They tarnish rapidly in air forming an oxide protective coating in the case of Th, but more slowly for the other actinides. The metals react with most non-metals. With steam or boiling water, oxide is formed on the surface of the metal and H2 evolves; in this way hydrides are produced that react rapidly with water and facilitate further attack on the metals. The oxidation states observed in the chemistry of lanthanides and actinides are shown in Fig. 5.9. Notice the predominant oxidation state III for the lanthanides

La

Ce

Pr

Nd

Pm

2 3

Ac

3

3

3

3

4

4

4

Th

Pa

U

3

Np

Sm

Eu

2

2

3

3

Pu

Gd

3

Am

Cm

2

2

Tb

Dy

Ho

2

2

3

3

3

4

4

Bk

Cf

Tm

Yb

2

2

3

3

3

3

Es

Fm

Md

No

Lr

2

2

2

2

2

3

3

3

3

3

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

4

4

5

5

5

5

5

6

6

6

6

7

7

Er

Lu

3

Figure 5.9. Lanthanide and actinide chemical properties. A scheme is shown of the oxidation states they present in their various classes of compounds. A rough indication of a greater frequency and a higher relative stability of each state is given by the darker blackening of each box. Notice the overwhelming presence of oxidation state 3, in the lanthanides and heavy actinides, oxidation state 2 in Eu and Yb and of several higher oxidation states in U and nearby elements.

Elements of Alloying Behaviour Systematics

377

and for the heavy actinides, whereas a more complex chemical behaviour is characteristic for the actinides from Th and Cm.

5.5.7 Intermetallic chemistry of the 3rd group metals 5.5.7.1 Phase diagrams of the 3rd group metals. Owing to the high number of elements pertaining to this group it could be useful to subdivide the description of their alloys into two large families: for the lanthanides (Ln) it may be useful to consider the intra-lanthanides (Ln –Ln) alloys and then the Ln-Me combinations of the lanthanides with other elements. Similar considerations may be applied to the actinide family. 5.5.7.1.1 Ln–Ln alloys. A systematic investigation and description of the intrarare earth metal alloying behaviour has been performed (Gschneidner 1985, Gschneidner and Calderwood 1986). As a summary of this work a so-called generalized phase diagram for the trivalent intra-lanthanide (and yttrium–lanthanide) binary alloys was proposed. It is shown in Fig. 5.10. This diagram was constructed from the melting and transformation temperatures of the trivalent lanthanides (assuming Ce and Sm trivalent). In this diagram the data for Eu and Yb were evaluated for the hypothetical trivalent state. The different lanthanides are plotted in sequence according to their atomic number; as an easier reference, a so-called systematization number (SN) was defined which is shown on the top of the diagram. This number varies from zero (for La) to 14 (for Lu); it results equal to the total number of 4f electrons for the corresponding trivalent lanthanides: in a way however this coincidence should be considered fortuitous without any implication about the relation between these numbers. According to its general properties yttrium was assigned the value SN 9.5. It is well known that a number of physical properties of the lanthanides (such as lattice parameters of compounds and alloys, density, melting points, several thermodynamic properties) show smooth regular variations along the series. This is the basis of the systematics of the lanthanides which may result in reliable property evaluation by interpolation or extrapolation procedures. Examples of such methods have been presented in § 4.3.2.2/3. According to this principle, the diagram of Fig. 5.10 may be considered a summary of the entire combination of trivalent intra-lanthanide diagrams. In order, indeed, to estimate the position of a ‘special point’ (a critical composition, a phase boundary, etc.) in any intra-lanthanide alloy system (between the lanthanides Ln and Ln ) the following rule has been proposed: (1 xLn )SNLn xLnSNLn SNsp

378

Intermetallic Chemistry

0

1

2

3

4

Systematization number 5 6 7 8 9 10 11 12 13 14

1800

1600

1400

Temperature (°C)

1200 Liquid 1000

bcc

800

600 fcc

dhcp

hcp

400

200

Sm Y La Ce Pr Nd Pm Sm

Gd Tb Dy Ho Er Tm (Eu)

Lu (Yb)

Atomic number

Figure 5.10. The generalized phase diagram, at atmospheric pressure, for trivalent (not Eu and Yb) intra-lanthanide alloys. The so-called systematization number is shown according to Gschneidner and Calderwood (1986). Notice that, in principle, the same behaviour should be expected for every mixture of any two trivalent lanthanides as long as the same (averaged) systematization number is calculated (see the text).

where xLn and SNLn are the mole fraction and the systematization number of the lanthanide Ln, and SNsp is the systematization number corresponding to the position of the special point considered. The coordinates (the systematization number) of a few special points are listed in Table 5.17. Notice that for simplicity, in Fig 5.10 the phase boundaries are shown as narrow lines; however, according to Gschneidner and Calderwood (1986), in the actual

379

Elements of Alloying Behaviour Systematics

Table 5.17. ‘Systematization’ numbers of a few characteristic points in the generalized rare earth phase diagram (according to Gschneidner and Calderwood 1986) (see Fig. 5.10). Special point fcc – dhcp (Phase boundary) dhcp – δ (Sm) (Phase boundary) δ (Sm) Decomposition δ (Sm) – hcp (Phase boundary) bcc – hcp – liquid (Phase boundary)

Temperature/°C 400 25 Maximum 25 1400

Systematization number 1.2 4.4 5.0 5.6 9.8

phase diagrams the two-phase regions are generally between 2 and 10 at.% wide (compare with Fig. 5.11); for neighbouring diagrams they may be as wide as 20 at.%. The applications and the limits (for instance in the case of cerium and in some cases regarding the formation of the δ phase) of these concepts have been discussed by Gschneidner and Calderwood (1986) and high-pressure generalized phase diagrams have also been presented. A thermodynamic assessment of a number of inter-lanthanide systems (Ho–Tb, Ho–Dy, Ho–Er, Er–Tb, Er–Dy) has been carried out by Norgren (2000). The calculated diagrams confirm the hypothesis that solutions of two rare earth metals not more than two apart in atomic number can be approximated as ideal solutions, while, if the difference is more than two, weak interaction parameters are needed. As for the Ce–Y system it was previously suggested (Gschneidner and Calderwood 1982) the formation of a high-temperature continuous bcc solid solution (δCe–βY) and, at lower temperature, of another (βCe–αY) continuous solid solution, which on cooling gives rise through 2nd order transition to an intermediate Sm-type phase. However according to the experimental work by Flandorfer et al. (1997), this is a metastable phase and βCe and αY show only a partial mutual solubility. A thermodynamic assessment performed by Meng et al. (2006) agrees with these data. 5.5.7.1.2 An-An alloys. A summary of the phase diagrams for adjacent actinide metals is shown in the connected binary phase diagrams of Fig. 5.11. The structure of this diagram resembles that reported in Fig. 5.10 for the lanthanides: notice, however, that such a sequence of interconnected diagrams could be used as a generalized diagram in a more limited way only, possibly for the heavier actinides from americium onward. In comparison with the lanthanides, the actinides show a more complex dependence of several properties on the atomic number; an analysis, for instance, of the

380

Intermetallic Chemistry

Temperature (°C)

1500

bcc Liquid

1000 fcc

fcc Tetragonal

Pa

U

. tho Or linic nic c cli no no Mo Mo o. nal Orth

Th

Complex cubic

Ac

ago Tetr

Orthorhombic

500

Np

Pu

δ′ δ γ β α

dhcp

Am

Cm

Atomic number

Figure 5.11. Connected binary phase diagrams of the actinides. The binary phase diagrams (temperature vs. composition) for adjacent actinide metals are connected across the entire series (two-phase regions are in black, uncertain regions in grey). The transition from typical metallic behaviour at thorium to complex behaviour at plutonium and back to typical metallic behaviour past americium can be noticed (adapted from Hecker 2000).

trends of atomic volumes, melting temperatures, etc. shows that it is not possible to find a simple relation between the properties of the elements having the same position in the two rows. This may be related to the remarks made by Smith and Kmetko (1983) and Boring and Smith (2000) and summarized in Fig. 5.12. In this figure the Periodic Table is arranged in order to show only the d and f electron series: the f series are put on the top and squeezed together in order to fit as shown. A ‘diagonal dividing strip’ may be roughly evidenced. The d and f electron metals away from the diagonal (normal metals) may be subdivided into two categories. In one category (elements in the bottom-left part of Fig. 5.12) the d and f electrons are itinerant, fully bonding, and they tend to form a superconducting ground state at low temperature, in the other category the d and f electrons are fully localized usually forming local magnetic moments and ordering into a magnetic ground state at some low temperature. For the elements highlighted by the ‘diagonal strip’ there is an indication that the f and d electrons may be balanced between being localized and itinerant. According to Smith and Kmetko (1983), materials close to this localization– delocalization transition can have their properties modified appreciably by small

381

Elements of Alloying Behaviour Systematics Localized-Magnetism Empty shell La

Tb

Dy

Ho

Er

Tm

Full shell Yb Lu

Ce

Pr

Nd

Pm Sm Eu

Ac

Th

Pa

U

Np

Pu Am Cm Bk

Cf

Es

Fm

Md

No

Lr

Partially filled shell Gd

Ca

Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Cu

Zn

Sr

Y

Zr

Nb

Mo

Tc

Ru

Rh

Pd

Ag

Cd

Ba

La

Hf

Ta

W

Re

Os

Ir

Pt

Au

Hg

Itinerant-Bonding

Figure 5.12. A ‘revised’ Periodic Table of the f and d series. According to Smith and Kmetko (1983) this table of the d and f transition elements shows the cross-over between itinerant, fully bonding electrons and fully localized electrons usually forming local magnetic moments.

perturbations. As an example, the pure elements on the diagonal strip exhibit a large number of allotropic crystal structures which can be alternately stabilized by temperature and/or pressure variations. See Tables 5.13 and 5.16 where the structural data for Ln and An are collected and notice the special complex behaviour of Pu. A kind of summary of the similarities which, albeit with some uncertainties, may be evidenced between the single lanthanide and actinide metals is reported, according to Ferro et al. (2001a) in Fig. 5.13. According to this scheme the alloying behaviour of plutonium could be simulated by cerium whereas a set of similarities may especially be considered between the block of elements from praseodymium to samarium with those from americium to californium. 5.5.7.1.3 R–Me and An–Me alloys. A summary of the alloying behaviour of the 3rd group metals with special attention to the compound formation capability is shown in Fig. 5.14. For the lanthanides two examples are shown La and Gd, the behaviour of which may be considered to give a reasonable first approximation description of the general intermetallic reactivity pattern of the lanthanides. For the actinides the reactivity schemes are shown for Th, U and Pu; for the alloys of the other metals of this series, only a few data are available.

382

Intermetallic Chemistry La

Ce

Pr

Nd Pm Sm Eu

Ac

Th

Pa

U

Np

Gd

Tb

Dy

Ho

Er

Tm Yb

Lu

Pu Am Cm Bk

Cf

Es Fm Md No

Lr

Figure 5.13. Scheme of ‘correspondence’ between the different lanthanide and actinide elements which may be assumed on the basis of several similarities and analogies in their chemical and alloying behaviours. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Sc

Y

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

La

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Th

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Gd

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

U

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Pu

Compound-forming element

Phase diagram known; no intermediate phases formed

No information available

Questionable compound forming capability

Figure 5.14. Compound formation capability in the binary alloys of Sc, Y, light trivalent lanthanides (as exemplified by La), heavy trivalent lanthanides (exemplified by Gd) and of the actinides (exemplified by Th, U and Pu). The different partners of the 3rd group metals are identified by their position in the Periodic Table. Notice that a sharper subdivision between compound-forming and not forming metals will result from a shifting of Be and Mg from their position in the 2nd group towards the 12th group (see § 5.12.3). The behaviour of the divalent lanthanides Eu and Yb is shown in Fig. 5.7 where it is compared with that of the alkaline earth metals.

Elements of Alloying Behaviour Systematics

383

The alloying patterns shown in Fig. 5.14 are similar to those relevant to the metals of the surrounding groups. Very few compounds or no compounds are formed with the metals of the first groups (generally up to the 6th to 7th). With the following metals, semi-metals and non-metals, several, often very stable, compounds are formed. However, a different behaviour is shown by the first two metals of the 2nd group (beryllium and magnesium) which give several compounds with the 3rd group metals (see for instance in § 4.3.2.3 the description of a number of alloys of magnesium with the lanthanides). In this respect, therefore, Be and Mg, as discussed in the introduction to § 5.4, have a higher resemblance with the metals of the 12th group rather than with the typical ones of the 2nd group. 5.5.7.2 Remarks on the stability of the binary alloys of the 3rd group metals (melting point and formation enthalpy trends). In order to give an idea of the thermal stability of the various compounds of the 3rd group metals, a selection of them has been included in Table 5.18 together with their melting points. The compounds of yttrium, uranium and plutonium have been considered as representative examples. Notice, however, that for the series of lanthanide or actinide compounds the values reported in the table must be considered an ‘average indication’. Not for all the compounds reliable data are available, in any case some regularities can be underlined. Notice the high melting points of the noble metal compounds and then, at the right hand of the Periodic Table, from the 12th group on, the strongly increasing thermal stability of the intermediate phases. Examples of refractory compounds formed with the semi-metals and non-metals of the last groups (even if with approximate values of composition and melting points) are: oxides (Y2O3 m.p. 2400°C, ThO2 3390°C), sulphides (ScS s.s. 2280°C, CeS 2450°C, US 2480°C), nitrides (YN dec. 2670°C, UN dec. 2805°C, PuN s.s. 2830°C), phosphides (PrP 2850°C, ThP 2990°C), arsenides (LuAs 2500°C, UAs 2700°C), carbides (s.s. UC–UC2 2500°), etc. The data reported in Table 5.18 concerning the thermal stability, the melting points of a few typical compounds and their trends along the Periodic Table may be usefully compared with the values of the formation enthalpies, standard enthalpies of formation at 298 K (related to one mole of atoms of the compound), that is to the reaction: xR (1 x)Me : Rx Me1x According to Colinet and Pasturel (1994), Borzone et al. (1999) and Ferro et al. (2001b) a short summary of the formation thermodynamics of binary compounds of the rare earth metals may be given by the following indicative values (Δf H/kJ/molat),

Table 5.18. Highest melting points (°C) in the alloys of rare earth metals and actinides with compound-forming elements of the 4th and 6th rows of the Periodic Table. See the introduction for the meaning of symbols. Alloys with Mn

Yttrium compounds Y6Mn23 1150°, IR 1

Re

UMn2 1120°, IR 1

Os

Ni

YCu4 971°, IR 1

Cu Au Zn

Ga

UCu5 1052°, p, IR 1

Tl Ge

Pu4Cu17 954°, IR 1

U2Zn17 970°, IR 1

Y5Tl3 1470°, IR 1

Y5Ge3 1965°, IR 1

PuPt3 1620°, IR 1 PuAu3 1250°, IR 1

UAu2 1390°, IR 1

YHg 625°, p, IR 1 YGa 1385°, IR 1

s.s.PuNi5 1300°, IR 1 UPt3 1700°, IR 1

YPt3 2000°, IR 1 YAu 1600°, IR 1

Hg

PuCo2 1320°, IR 1

UNi5 1305°, IR 1

YZn 1105°, IR 1

PuOs2 1500°, IR 1

UIr3 2005°, IR 1

YIr2 2400°, IR 1

Pt

PuFe2 1240°, IR 1

s.s. UCo2 1185°, IR 1

YNi5 1430°, IR 1

PuRe2 2000°, p, IR 1

UOs2 2280°, IR 1

YOs2 2500, IR 1

Ir

ssPuMn2 1050°, IR 1

UFe2 1230°, IR 1

Y2Co17 1357º, IR 1

Co

Plutonium compounds

URe2 2200°, IR 1

YRe2 2520°, p, IR 1 Y2Fe17 1400º, IR 1

Fe

Uranium compounds

PuZn2 935°, IR 1 UHg 488°, p, IR 1

PuHg3 500° PuGa2 1264°, IR 1

UGa2 1355°, IR 1 U5Ge3 1670°, IR 1

Pb

Y5Pb3 1770°, IR 1

UPb 1280°, syn, IR 1

Pu5Pb4 1385°, IR 1

Bi

YBi 2020°, IR 1

UBi 1400°, syn, IR 1

PuBi 1300°, IR 1

As

Elements of Alloying Behaviour Systematics

385

averaged for the trivalent R, and reported in the order of the Periodic Table (see also Fig. 5.14): Group 1: No compounds are formed with the alkali metals: weak interactions are shown with these metals not only in the solid but also in the liquid state. Liquid immiscibility has been described for several trivalent R with alkali and also alkaline earth metals. Group 2: Only Be and Mg form intermediate phases with rare earth metals. For typical RBe13 compounds, the following data apply: YBe13 (16.2 to 20.3), LaBe13 (12.8), CeBe13 (8.0). For the various Gd–Mg phases values between 18 and 20 have been estimated. Groups 3–6: No compound formation. Group 7: No compound formation with La and Ce; small negative values (a few kJ/molat) may be attributed to the RMnx phases formed by the heavy R. Groups 8–10: From the very low exothermic values of the iron alloys increasingly negative Δf H are found moving towards the 9th and 10th groups (and down each group). Therefore the high stability of the alloys of the 3rd group metals with the noble metals can be highlighted. The corresponding formation enthalpies are among the highest observed within ‘true’ intermetallic compounds (that is leaving out for instance the compounds with the non-metals of the last groups). A similar behaviour is observed in the alloying of other metals of the first transition groups with those of the last transition groups. Very high negative enthalpies of formation are observed also in the alloys of the Pt-family metals with Zr, Hf, Th, etc. In a number of papers Leo Brewer and co-workers (see for instance, Brewer and Wengert 1973) systematically examined the thermodynamics of systems consisting of metals of the left half of the transition series (that have empty d orbitals) with metals of the right half of the transition series (which have internally paired d electrons not available for bonding). Brewer suggested that the alloying, for instance of Zr and Ru, could be considered as an example of a generalized Lewis acid–base reaction, which could be compared with the ‘classic’ example given by the addition of BF3 to NH3 (with an empty p boron orbital reacting with the non-bonding pair of electrons of NH3). Similarly, according to this scheme, the use of the empty orbitals of Hf or Ta by the non-bonding electrons of Os or Pt could optimize the involvement of available orbitals and achieve, in their alloys, a very strong bonding. The high stability of the compounds could thus be related to the strong interaction between a last transition metal (acting as an electron donor, Lewis base) and an early transition metal acceptor (Lewis acid). This stability prediction has been found in

386

Intermetallic Chemistry

agreement with the data obtained in several thermodynamic measurements; generally large negative enthalpies of formation have been observed for the aforementioned compounds. A few examples of these data will be quoted here from a broad review dedicated to this subject by Guo and Kleppa (2001). In this review, mainly the results obtained in their calorimetric measurements are reported and discussed. The experimental techniques employed were solution calorimetry, solute–solvent drop calorimetry and direct synthesis calorimetry. A selection of typical data is the following (ΔfH°, kJ/mol atoms, 298°C): ScPd: 89.3, YPd: 94.9, GdPd: 82.6, ScIr: 89.7, YIr: 65.9, ScPt: 104.8, YPt: 104.0, LaPt: 99.7, HoPt: 121.8, TiPt: 90.7, ZrPt: 104.1, HfPt: 113.7, ThRh: 120, URh3: 79, ThPt5: 93, UPt2: 128, PuPt2: 71, AmPt2: 138 Moving now to the far right of the Periodic Table the increase of the melting points and of the negative values of Δf H can be considered an indication of the strengthening of the R–Me interactions possibly related to a decreasing of the metallic character and an increasing of the ionicity. See Fig 5.15 where according

Metallic

Covalent

Percentage

80

60

40

20

Ionic

7

8

9

10

11

12

13

14

15

16

17

Group number

Figure 5.15. Binary rare earth compounds. According to a suggestion by Gschneidner and Daane (1988), the bonding character (percentage of metallic, covalent and ionic bonding) is shown for the R compounds with the elements of the various groups from the 7th (Mn group) to the 17th (halogens).

Elements of Alloying Behaviour Systematics

387

to Gschneidner and Daane (1988) a suggestion is given of the changes in the bonding mechanism. As a conclusive remark about this topic we underline that the trend of the intermetallic reactivity described for the 3rd group metals and the phase stability scheme shown may be considered an example of a systematic alloying behaviour generally presented by several metals of the first groups of the Periodic Table. The reader may indeed compare the patterns here reported in Fig. 5.14 with those previously presented for the 2nd group metals and with those shown in the next paragraphs for the metals of the 4th group. 5.5.7.3 Further remarks on the actinide alloys. Among the different alloys of the actinides especially those formed by Th, U and Pu are well known. The compound formation patterns of these metals are shown in Fig. 5.14 where a comparison is made with the behaviour of the other metals of the 3rd group, that is, the rare earth metals (Sc, Y, lanthanides). It is worth presenting here a few more details about the alloying behaviour of these actinides. Thorium. Solid intermediate compounds are formed with all the elements from the 7th group on. A few compounds, moreover, are formed with the light elements of the 1st and 2nd groups. Solid solution phases are observed in several systems; a continuous solid solution (corresponding to the complete composition range) is formed, generally at high temperature, with Zr and the trivalent rare earths. With La, two fields of complete mutual solubility are observed: the bcc, W type (stable at high temperature, between γ-La and β-Th) and, at intermediate temperature, the fcc, Cu-type (between β-La and α-Th). In the liquid state, generally a mutual complete solubility is observed with nearly all the elements: a partial miscibility gap is present in the systems with oxygen, europium, ytterbium and uranium. Uranium. The compound formation region includes a large portion of the Periodic Table from the 4th group on, even if with a gap in the 5th to 6th groups and a small gap in the 11th. However, within this part of the Periodic Table, the formation of intermediate phases showing a remarkable thermal stability is restricted to the alloy systems formed by metals included between the 7th and the 9th to 10th groups. A further group of very stable (refractory) compounds is formed (as noticed in the comments to Table 5.18) with the elements at the far right part of the Periodic Table. Within the general reactivity pattern of uranium (Fig. 5.14), the seemingly ‘irregular’ behaviour shown by the U–Ag system (2nd box in the 11th column) may

388

Intermetallic Chemistry

be a little more commented. This blank box is completely surrounded by black boxes (that is, completely surrounded by compound-forming systems). Notice that this box is not blank because of lack of information, but because it is well known that no compounds are formed in this system, which shows complete mutual insolubility in the solid state and nearly complete also in the liquid state. The reader knows that the various reactivity patterns are not the expressions of a simple ‘law’ but show preferential tendencies; therefore ‘irregularities’ and ‘deviations’ can be expected. In any case it may be useful to compare the lack of mutual reactivity in the U–Ag system with the tendency to give only a low, reduced, mutual reactivity shown in this part of the Periodic Table. The behaviour of U with the other metals of the 11th group is as follows: in the U–Cu system UCu5 forms through a peritectic reaction but together with a large region of immiscibility in the liquid state (with a monotectic extending up to U); similarly, in the U–Au system the compounds U14Au51 and UAu2 are formed, but, in the region between UAu2 and U, a large monotectic is observed. A certain tendency to de-mix or to form compounds of low stability may be observed also with the elements of the following group (12th). In the U-richer region of the U–Zn system, there are the peritectically formed compounds UZn12 and U2Zn17 and a large immiscibility region (a monotectic). In the U–Cd system, UCd11 is formed and a few compounds are formed in the U–Hg system: all these compounds are stable only up to not very high temperatures. Other uranium binary systems de-mixing in the liquid state are U–Pb and U–Bi and several uranium–lanthanides systems which are characterized by nearly complete immiscibility in the liquid and solid state. Complete solubility in the liquid and, at least at high temperature, in the solid state is observed in the systems with Ti, Zr, Hf and Nb. Plutonium. The compound formation pattern of this metal shows several analogies with that of uranium. Compound formation is systematically observed with the elements from the 7th group on and, with a few intermediate phases, in the systems with some elements of the very first groups. More or less extended miscibility gaps in the liquid state are shown by the alloys of Ag and Cd and by those with the lanthanides. Solid solutions corresponding to the complete composition range are observed as high-temperature phases (cI2-W type) in the systems with Sc, Zr, U and Np (in the U–Pu system this phase is stable in a very narrow temperature range). While considering the alloying behaviour of plutonium attention must be given to its various polymorph transformations. The addition of another element, indeed, to a metal having various crystal forms, generally exhibiting different properties, may strongly influence the stability of these forms, often resulting in

389

Elements of Alloying Behaviour Systematics (a)

(b) L

700 ε

600 Temperature (°C)

L ε

500 400 δ

δ

300 γ +δ 200

γ +δ

Pu3Ga

β +δ

δ + Pu3Ga

β +δ

100 α + Pu3Ga

α +δ 0

5

10 at.% Ga

15

0

5

10

15

at.% Ga

Figure 5.16. Two versions of the Pu–Ga phase diagram as reported, according to Hecker and Timofeeva (2000), by Peterson and Kassner (1988) and by Chebotarev et al. (1975). According to the first version the fcc δ-Pu phase is retained at room temperature for Ga concentrations included between approximately 2 at.% and 9 at.%. According to the second version the δ-Pu phase undergoes (below 100°C) a eutectoid decomposition to the α-Pu phase plus Pu3Ga. Both diagrams were extrapolations to equilibrium.

the formation of solid solution fields corresponding to more or less large ranges of composition and temperature. Another well-known example of such behaviour is given by the iron alloys for which some specific and general comments are given in § 5.10. A peculiar and illustrative example may be given by the plutonium– gallium alloy system. The question of the stabilization of delta plutonium and the related investigation of the phase diagram has been the subject of an intense research activity carried out, during the cold war, separately by two teams, the Anglo-American one and that from the Soviet Union, with the production of two different versions (see Fig. 5.16 (a) and (b), which only recently came to an agreement. The stability of the fcc δ-plutonium, which is malleable and easily shaped, is important because of its uses (in nuclear weapons, etc.). This phase may be retained, either in stable or metastable conditions, down to room temperature by the addition of gallium or aluminium. In a way, the two versions of the phase diagram may now be reconciled. The diagram in Fig 5.16 (a) is adequate for practical applications

390

Intermetallic Chemistry

representing the metastable conditions; the equilibrium diagram of Fig 5.16 (b) shows the eutectoidal decomposition which however, due to very slow diffusion processes, cannot be directly observed. It was only through long-term annealing treatments (several thousands of hours at 130°C, or at 150°C) with pre-treated (preconditioned) samples subjected to high pressure or compressive plastic deformation, that it was finally possible to deduce (to extrapolate from a slightly higher temperature) the equilibrium phase boundaries and confirm the diagram of Fig. 5.16 (b). As a final comment to this point we may remark that, as observed by Hecker and Timofeeva (2000), the situation in Pu alloys (especially Pu–Ga, Pu–Al) is similar to that in steel where for the Fe–C system two diagrams (stable with graphite and metastable with Fe3C) must be considered (see Fig. 5.29). General problems of phase stabilization in the light actinides, in their interactinide alloys and in the U-transition metal systems have been reviewed and discussed by Blank (2002). A definition and a quantification of the ‘phase stabilization’ concept were introduced. As an example the system U–Cr was considered. Its diagram is characterized by the terminal solid solutions of Cr in U (corresponding to the maximum solubility of 0.3 at.% Cr in α-U; 1.0 at.% Cr in β-U and 4 at.% in γ-U). The transformations α : β : γ correspond to two successive eutectoidal reactions (γ-U and, nearly pure, Cr form a eutectic). By dissolution of Cr in β-U, the α/β transition temperature is lowered (from 668°C for pure U to 630°C for the eutectoidal point at 0.9 at.% Cr) at an initial rate given by: σβ dT/dx (42 K/at.%). This means that the β field, extending towards lower temperatures, is stabilized at the expense of the α-U phase and the σβ value may be considered a significant parameter of the stabilization process. The solutes which stabilize the β-U field, which have a high value of σβ, are close to each other in the Periodic Table and are the following: Cr, Mn, Mo, Ru, Rh, Re, Os, Ir, Pt. Similar data were reported by Blank (2002) for the stabilization of the γ-U field. The data were discussed in terms of electronic structure. 5.5.7.4 Remarks on the crystal chemistry of the alloys of the 3rd group metals. A large number of intermediate phases have been identified in the binary alloys formed by the rare earth metals and actinides with several elements. A short illustrative list is shown in Tables 5.19 and 5.20. Compounds of a few selected rare earth metals and actinides have been considered in order to show some frequent stoichiometries and crystal structure types. The existence of a number of analogies among the different metals considered and the formation of some isostructural series of compounds may be noticed.

Elements of Alloying Behaviour Systematics

391

Table 5.19. A selection of intermediate phases in some rare earth binary alloys. Structure type

CNE (Me)

Examples of isostructural phases Sc compounds

Y and La compounds

cF408-Rh7Mg44

12–14

Sc44X7: X Os, Ir(11–14Ir)

cP140-Sc57Rh13

12–15

Sc57X13: X Ru, Rh, Ir(19–20Ir), Pt

cF120-Sc11Ir4

13

Sc11X4: X Ru, Os, Ir

cP4-AuCu3

12

La3X: X Ga, In, Tl

oP16-Fe3C

14–15

Y3X: X Ru, Os, Co, Rh, Ir, Ni, Pd, Pt La3X: X Ru, Os, Co, Ir, Ni

hP20-Th7Fe3

15

La7X3: X Rh, Ir, Ni, Pd, Pt

hP16-Mn5Si3

14–15

cI28-Th3P4 antitype

6

cP2-CsCl

14

ScX: X Mg(0–65Mg), Ru(40–50Ru), Co(52Co), Rh(45–53Rh), Ir(45–52Ir), Ni(46.5Ni), Pd(49–51Sc), Pt, Cu, Ag, Au, Zn, Cd(40–50Cd), Hg, Al, In

YX: X Mg(50–54Mg), Rh, Ir, Cu, Ag, Au, Zn, Cd, Hg, In, Tl LaX: X Ag, Cd, Hg, In, Mg, Tl, Zn

cF8-NaCl

6

ScX: X C, N, P, Sb, As, Bi, S, Se

YX: X N, P, As, Sb, Bi, S, Se, Te, Po LaX: X N, P, As(50As), Sb, Bi, S, Se, Te

oS8-CrB

17

ScX: X Ga, Si, Ge

YX: X Co, Al, Ga, Si, Ge LaX: X Rh, Ni, Pd, Pt, Au, Ga, Sn

cF24-Cu2Mg

16

ScX2: X Fe, Co(64–69Co), Ir(65–70Ir), Ni(64–72Ni), Al

YX2: X Mn, Fe, Co, Rh, Ir(65–68Ir), Ni, Os, Pt, Al, S LaX2: X Mg, Ru, Rh, Ir, Pt, Al

hP12-MgZn2

16

ScX2: X Tc, Re, Fe, Ru, Os

YX2: X Mg, Re, Ru, Tc

hP3-AlB2

20

cP4-AuCu3

12

hP6-CaCu5

18

Sc5X3: X Ga, Si, Ge, Sn, Pb

Y5X3: X Ir, Pt, Ga, In(38–45In), Tl, Si, Ge, Sn, Pb La5X3: X Bi, Ge, Sn, Pb La4X3: X Rh, As, Bi, Ge, Pb, Se(57–60Se)

YX2: X Hg, B, Si(62Si), Ge(60Ge) ScX3: X Rh(70–86Rh), Ir(77–86Ir), Pd, Pt, Al, Ga, In

YX3: X Pd, Pt, Al, In, Tl, Pb, Sn LaX3: X Pd, Tl, In, Sn, Pb YX5: X Rh, Co(83–86Co), Ni LaX5: X Ir, Co, Ni(16–18Ni), Cu

Table 5.20. A selection of intermediate phases in some actinides binary alloys. Structure type

CNE (Me)

tI28-U6Mn

13–15

hP20-Th7Fe3

15

cP4-AuCu3 tI32-W5Si3

12 14–15

tI12-CuAl2

15

cF8-NaCl

6

oS8-CrB

17

cP2-CsCl cI28-Th3P4

14

Examples of isostructural phases Th compounds

U and Pu compounds U6X: X Mn, Fe, Co, Ni Pu6X: X Fe

Th7X3: X Fe, Ru, Os, Co, Rh, Ir, Ni, Pt Pu3X: X Ga, In(23–28In), Sn, Pb Pu5X3: X Ru, Os, Ir, Ga(36–38Ga), Si, Pb Th2X: X Pd, Cu, Ag, Au, Hg, Zn, Al, Ga, In, Tl, Ge ThX: X C(large s.s.), Ge, N(~50N), P, As, Sb, S, Se

ThX: X Ru, Co, Rh, Ir, Pt, Au, Al ThX: X Bi, Se, Te Th3X4: X P, As, Sb, Bi, Se, Te

oP20-Sb2S3 tP6-Cu2Sb

9

hP3-AlB2

20

ThX2: X Ni, Cu, Ag, Au, Zn, Cd, Al

cF24-Cu2Mg

16

ThX2: X Mg, Ru, Os, Ir(64–69Ir)

cP4-AuCu3

12

ThX3: X Rh, Pd(79–81Pd), In, Tl, Sn, Pb

mP8-TiS3 hP65-Gd14Ag51 hP6-CaCu5

18

Th14X51: X Ag, Au ThX5: X Fe, Co, Ir, Ni(84–86Ni)

cF24-AuBe5 hP38-Th2Ni17 cP36-BaHg11

16 18–20 20

ThX11: X Cd

cF112-NaZn13

24

ThX13: X Be

UX: X C(47–66C), N(49–50N), P, As, Sb, Bi, S, Se, Te PuX: X C(44–48C), N(50N), P, As, Sb,Bi, S, Se, Te

U3X4: X P, As, Sb, Bi, Se, Te U3X4: X Se, Te(60–64Te) U2X3: X S, Se, Te UX2: X P, As, Sb, Bi, Te PuX2: X S, Se, Te UX2: X Au(derivative structure), Hg, B, Ga, Ge, Si(66.7Si), Si(62.5Si) PuX2: X B, Ga, Si(62.5Si), Ge(60Ge) UX2: X Mn, Fe, Os, Co, Ir, Al PuX2: X Mn(66–68Mn), Fe, Ru Co, Rh, Ir, Ni, Pt, Zn, Al UX3: X Ru, Rh, Ir, Pd, Al, Ga, In, Te, Si, Ge, Sn, Pb PuX3: X Rh, Pd, Pt, Al, In(72–75In), Ge, Sn, Pb UX3: X S, Se, Te U14X51: X Au

UX5: X Ni, Pt, Cu Pu2X17: X Co, Ni, Zn UX11: X Cd PuX11: X Pu UX13: X Be PuX13: X Be

Elements of Alloying Behaviour Systematics

393

5.6. ALLOYS OF THE METALS OF THE 4TH GROUP OF THE PERIODIC TABLE

Titanium, Ti; zirconium, Zr; hafnium, Hf

5.6.1 Introduction Titanium (Ti, [Ar]3d 24s2), name and symbol from the Titans of the Greek mythology. Discovered (1791) by the British Rev. William Gregor. Silvery metal. Atomic number 22, atomic relative mass 47.867. Occurrence. Ti is relatively abundant in the earth’s crust (6300 ppm). The more important ores are rutile (one of the various crystalline forms of TiO2) and ilmenite (FeTiO3). Preparation. The Kroll method is used on large scale and involves the reaction of chlorine and carbon upon ilmenite (TiFeO3) or rutile (TiO2). The resultant titanium tetrachloride, TiCl4, is separated from the iron trichloride, FeCl3, by fractional distillation. Eventually TiCl4 is reduced to metallic titanium with magnesium. Excess magnesium and magnesium dichloride are removed by treatment with water and hydrochloric acid to leave a titanium ‘sponge’. This can be melted under a helium or argon atmosphere to allow casting as ingots and bars. Ti reacts in the molten state with all the conventional crucible materials; melting is therefore possible in cooled metal crucibles of high thermal conductivity (copper). Melting can be performed by electric arc, plasma, electron beam or by induction (laboratory equipment). High purity Ti can be obtained by the Van Arkel iodide thermal decomposition (TiI4 is decomposed on an electrical heated W wire or better Ti fibre). Zirconium (Zr, [Kr]4d 25s2), name and symbol from the gemstone zircon (from the Persian zargun, gold like). The element was discovered (1789) by Martin H. Klaproth, the metal first prepared (1824) by Jöns Jacob Berzelius. Greyish-white metal. Atomic number 40, atomic relative mass 91.224. Occurrence. The more important minerals are zircon (ZrSiO4) and baddeleyite (a form of ZrO2). Preparation. It is made by the Kroll method that involves the reaction of chlorine and carbon upon baddeleyite (ZrO2). The resultant zirconium tetrachloride, ZrCl4,

394

Intermetallic Chemistry

is separated from the iron trichloride, FeCl3, by fractional distillation. Finally ZrCl4 is reduced to metallic zirconium by magnesium. Solid Zr is not hazardous but any high surface form of Zr metal (powder, dust, etc.) is hazardous because of its easy ignition in air and the exothermic (often explosive) reactions with many other elements and compounds. Hafnium (Hf, [Xe]4f 145d 26s2 ), name and symbol from the Latin name of Copenhagen (Hafnia). Discovered (1923) in Copenhagen by Dirk Coster (Danish) and Georg Karl von Hevesy (Hungarian). Silvery lustrous solid metal. Atomic number 72, atomic relative mass 178.49. Occurrence. The chemical similarity between Zr and Hf is reflected in their geochemistry: Hf is found in all the Zr minerals as a fraction of percentage of Zr. The separation of the two metals is generally difficult. Preparation. Many methods are available for separating Hf from Zr: ion exchange with dilute H2SO4 eluent (laboratory procedure), liquid–liquid extraction, fractional distillation of the mixed tetrachlorides above the triple point, extractive distillation; the degree of separation obtained from the different methods depends on the number of stages. Generally HfO2 is converted by carbochlorination into HfCl4 which is purified by sublimation and reduced by molten Mg. 5.6.2 The 4th group metals: a summary of their atomic and physical properties Titanium, zirconium and hafnium in normal conditions crystallize in the hexagonal close-packed structure (α modification) with a c/a slightly smaller than the ideal one: c/a 1.587 (Ti), 1.593 (Zr) and 1.581 (Hf). At high temperature they have the bcc W-type structure (β modification). High-pressure transformations are known (Tables 5.21–5.23). Table 5.21. Ti, Zr, Hf: selected physical properties. Property

Ti

Zr

Hf

r/pm, metallic, CN 12 [‘metallic valence’] Ionic radius/pm, M2, CN 6 Ionic radius/pm, M3, CN 6 Ionic radius/pm, M4, CN 6 Tmelting/°C Tboiling/°C ΔHmelting (at Tmelting)/kJ/mol ΔfH0 of Me1 gas at 298.15 K/kJ/mol

146.2 [4] 100 81 74.5 1670 3289 14.15 460

160.2 [4]

158.0 [4]

86 1855 4409 21.0 565

85 2231 4603 27.20 1279

395

Elements of Alloying Behaviour Systematics

5.6.3 The 4th group metals: remarks about their general chemical properties and reactivity The three metals are chemically similar. The especially close similarity between the Zr and Hf chemistries can be remarked. This may be mainly related to the effect of the lanthanide contraction having made their radii (both atomic and ionic) nearly identical. In comparison with Ti, the larger atomic dimensions of Zr and Hf result in more basic oxides and tendency to achieve higher coordination numbers, etc. Titanium. Resistant to corrosion. When heated, titanium burns in oxygen to form Ti2O3, in nitrogen to give the interstitial nitride TiN, in fluorine to form TiF4. It combines with C at high temperature to give TiC (see § 3.8.4.2 about interstitial compounds). Heated at high temperature and cooled in hydrogen it forms a hydride (up to TiH2). Titanium dissolves in hot HCl and H2SO4, while in HNO3 it forms Table 5.22. Ti, Zr, Hf: ionization energies. Element Ti Zr Hf

1st ionization energy/kJ/mol

2nd ionization energy/kJ/mol

3rd ionization energy/kJ/mol

4th ionization energy/kJ/mol

5th ionization energy/kJ/mol

658 660 654

1310 1267 1440

2653 2218 2250

4175 3313 3210

9573 7860 6596

Table 5.23. Ti, Zr, Hf: crystal structures, lattice parameters of their allotropes and calculated densities. Element (allotrope) Temperature range/°C Pressure/GPa Titanium 882° 882° to 1670° 2 GPa Zirconium αZr 863° βZr 863° to 1855° ωZr 2 GPa ω Zr 30 GPa Hafnium αHf 1743° βHf 1743° to 2231° ωHf 38 GPa ω Hf 71 GPa

αTi βTi ωTi

Crystal structure

Lattice parameters/ pm a

c

hP2-Mg cI2-W hP3-ωTi

295.06 330.65 462.5

468.35

hP2-Mg c I2-W hP3-ωTi cI2-W

323.16 360.90 503.6

hP2-Mg cI2-W hP3-ωTi cI2-W

319.46 361.0

Atomic volume/ pm3 106

Molar volume/ cm3/mol

Density/ g/cm3

17.66 18.07

10.63 10.88

4.50 4.40

23.28 23.50

14.02 14.15

6.51 6.44

22.32 23.52

13.44

13.28

281.3 514.75 310.9

505.10

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Intermetallic Chemistry

a rather insoluble hydrous oxide. The best solvent however is a solution of HF. Compounds are known in which Ti has an oxidation state II (for example, TiCl2, TiI2, etc. generally solid compounds readily oxidized by air) or an oxidation state III (simple compounds generally having a certain ionic character and complex ions containing TiIII). Numerous are the compounds containing TiIV (tetrahalides, several complex anions, adducts, peroxy compounds). Several organo-titanium compounds with the oxidation states IV, III, II, 0, I have been prepared. A starting point was the discovery by Ziegler et al. (1955), Ziegler (1963) and Natta et al. (1955) and Natta (1963) of the catalytic properties of TiCl3–Al–alkyl mixtures in hydrocarbons in reactions such as the ethylene and propylene polymerization. Zirconium. The solid metal is very resistant to corrosion. It reacts, when heated, with carbon, nitrogen, oxygen and the halogens. Finely divided may ignite spontaneously in air. It is attacked by HF and aqua regia. Hafnium. It is very similar to Zr. The best solvent is HF; the formation of anionic fluoro-complexes is, also in this case, determinant in the stabilization of the solution. 5.6.4 Intermetallic chemistry of the 4th group metals 5.6.4.1 Phase diagrams of the 4th group metals. A summary of the alloying behaviour and of the characteristics of their binary alloy systems is shown in Figs 5.17 and 5.18. The compound formation pattern of Fig. 5.17 is in agreement with the characteristic trend observed for the metals of the first groups of the Periodic Table (as previously observed in the paragraphs dedicated to the metals of the 1st, 2nd, and 3rd groups). In the region at the left of the Periodic Table (in this case up to the 4th, 5th groups) the metals do not form compounds with the elements under consideration. Besides H and Be, exceptions to this scheme are represented by a few phases formed with the actinides which however are stable only in small temperature ranges and, on heating, decompose in the solid state through peritectoidal reactions. These phases are: Np4Zr and Pu4Zr (solid solution ranges between 10 and 30 at.% Zr which decompose at 320°C and 345°C, respectively), NpZr2 (hexagonal phase, decomposition at 550ºC) and, in the Pu-rich region of the Pu–Hf system, the so-called θ phase (94 at.% Pu, decomposition at 340°C) and the ζ phase (97 at.% Pu, decomposition at 300°C). Notice, however, that for these systems different versions of the phase equilibria are reported in the literature, and the θ and ζ Hf–Pu phases could be not real binary compounds but oxygen–stabilized phases. In Fig. 5.18 on the other hand, binary systems of Ti, Zr, Hf are indicated in which complete mutual solubility in the solid state is observed (even if only in a limited range of temperature). Notice the peculiar behaviour of titanium which exhibits

397

Elements of Alloying Behaviour Systematics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Ti

Zr

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Hf

Compound-forming element

Phase diagram known; no intermediate phases formed

No information available

Questionable compound forming capability

Figure 5.17. Compound formation capability in the binary alloys of Ti, Zr, Hf. Notice the reactivity pattern similar to that shown by the metals of previous groups. No compound formation with metals of the first groups, except Be, lanthanides included.

Sc

V

Cr

Zr

Nb

Mo

Hf

Ta

W

Ti

Sc

Ti

Zr Hf

V

Cr

Ti

V

Cr

Nb

Mo

Zr

Nb

Mo

Ta

W

Ta

W

Hf

Figure 5.18. Ti, Zr, Hf binary alloys. Dashed boxes show selected metals which, at least at high temperature, form one field (and in some cases two, α and β, fields) of continuous solid solutions with the 4th group metals. Notice that these metals are in a small region of the Periodic Table close to the 4th group. In the systems marked by an asterisk intermediate compounds are formed (with or without a continuous solid solution).

complete solid solubility with all the metals of the three groups considered (4th, 5th and 6th) and with Sc. With particular attention to the titanium alloys, the characteristics of the Ti-rich regions may be of special interest due to the α/βtransformation; in view of the applications of these alloys, a few remarks are reported in the following. 5.6.4.1.1 / titanium alloys. The titanium products, in both commercially pure and alloy grades, may be classified into three categories according to the predominant phases in their structure: alpha (α), alpha–beta (α β) or beta (β). In pure Ti the α phase (hexagonal close packed) is stable from room temperature to 882°C and the β (body-centred cubic) from 882°C to the melting point (about 1670°C). The addition of alloying elements may have different effects on the stability of the Ti-based phases and on the α/β transformation temperature; this enables a wide range of physical and mechanical properties to be obtained.

398

Intermetallic Chemistry

According to their effects on Ti alloying, elements may be subdivided in the following categories which represent an example not only of a structural, but also of an application-oriented classification: (i) Alpha stabilizers. Interstitial elements (C, N, O), aluminium, tin raise the temperature at which the alloy will be completely transformed to the beta phase (beta transus temperature) or inhibit change in this phase transformation temperature. Alpha alloys generally have creep resistance higher than beta alloys; they are preferred for high-temperature applications. (ii) Alpha strengtheners. A few metals especially Zr and Sn have a small effect on the transformation temperature (neutral solutes) and act as strengtheners of the alpha phase. (iii) Beta stabilizers. Several metals (V, Nb, Ta, Cr, Mo, Mn, Fe, Cu) stabilize the beta phase lowering the α to β transformation temperature. These alloys have very good forgeability over a range of temperature wider than alpha. They have good hardenability and respond easily to heat treatments (for instance, solution treatment and aging at 450–650° which results in fine alpha particles dispersed in the retained beta). (iv) Alpha beta alloys. They contain a mixture of alpha and beta phases (10–50% beta). Compositions and properties can be controlled through heat treatments. The most common alpha beta alloy is Ti–6Al–4V. 5.6.4.2 Melting point trend in the binary alloys of the 4th group metals. An indication of the melting points of the binary alloys of the 4th group metals (Ti, Zr, Hf ) is shown in Table 5.24 which lists the compounds with the highest melting points, formed by two series of elements (along the 4th and 6th rows of the Periodic Table) from the 7th to the 15th groups with Ti, Zr and Hf. We notice the high thermal stability of the alloys with the metals (especially the heavy ones) of the groups 7th to 10th. A short series of relatively low melting alloys follows (11th to 12th groups); increasing values of the melting points are again found with the semi-metals and some non-metals of next groups. Selected refractory compounds formed with typical non-metals are: oxides TiO2 (one of the many compounds formed in the Ti-O system: 1870°C), ZrO2 (2710°C, dec.), HfO2 (2810°C), nitrides (generally corresponding to solid solution ranges) TiN (3290°C), ZrN (3410°C, dec.), HfN (3390°C), carbides (generally corresponding to solid solution ranges) TiC (3066°C), ZrC (3430°C), HfC (3950°C). Refractory compounds are formed also in the systems with sulphur, phosphorus, silicon, etc. The binary phase diagrams of the titanium oxides and sulphides are very complex with the formation of a very high number of intermediate phases (a similar behaviour is observed also for other intermediate transition metals such as vanadium). In the

Table 5.24. Highest melting points (°C) in the alloys of Ti, Zr and Hf with compound-forming elements of the 4th and 6th rows of the Periodic Table. See the introduction for the meaning of the symbols. Alloys with Mn

Titanium compounds

Zirconium compounds

s.s. TiMn2 1325°, IR 1 Ti5Re24 2750°, p, IR 1

Re Fe

s.s. ZrMn2 1450°, IR 1

Os Co

s.s. TiOs 2160°, IR 1 s.s. TiCo 1325°, IR 1

Ir Ni Pt Cu

TiPt3 1930°, IR 1

Au

Hg

s.s. Hf Os2 2700°, IR 1

ZrOs2 2660°, IR 1 s.s. HfCo2 1670°, IR 1

s.s. HfIr3 2470°, IR 1

s.s. ZrIr3 2280°, IR 1 Zr2Ni7 1440°, IR 1

HfNi 1530°, IR 1 s.s. ZrPt3 2154°, IR 1

s.s TiAu 1495°, IR 1 compds.

Ga

ZrCo2 1600°, IR 1

s.s. Hf Re2 3160°, IR 1 s.s. HfFe3 1820°, IR 1

Zr14Cu51 1115°, IR 1

s.s. TiCu 982°, IR 1

Zn

s.s. ZrRe2 2750°, IR 1

s.s. TiIr 2130°, IR 1 TiNi3 1380°, IR 1

s.s. HfMn2 1730°, IR 1

s.s. ZrFe2 1675°, IR 1

s.s. TiFe2 1427°, IR 1

Hafnium compounds

Hf2Cu 1310°, IR 1 ZrAu3 1572°, IR 1

s.s. HfAu 1750°, IR 1

Zr3Hg Dec., 560°

Hf2Hg Dec., 359°

ZrZn2 1180°, IR 1 compds.

Ti2Ga 1420°, p

Zr5Ga3 1580°, IR 1

Hf5Ga3 1750°, IR 1

Ti5Ge3 1980°, IR 1

Zr5Ge3 2330°, IR 1

Hf5Ge3 2200°, IR 1

Tl Ge Pb

Ti4Pb 1305°, p

Zr5Pb3 2000°, IR 1

Ti3Bi 1300°, p, IR 1

Zr3Bi2 1497°, IR 1

Ti4As

As Bi

HfBi2

400

Intermetallic Chemistry

oxide systems, for instance, the existence of several, very close to each other, stoichiometric phases is observed for certain composition ranges. In the Ti–O system, in the composition range around 60–66.7 at.% oxygen several oxides (Magnéli phases, reduced rutiles) are formed. A short description of their structure is given in § 7.6.4 in comparison with that of TiO2 (rutile). Taking Zr as an example, the trend of the melting temperature in the binary alloys of this group of metals is also outlined in Fig. 5.19. There are two sets of especially stable alloys: those formed, possibly via ionic and covalent bonding, with the elements at the right in the Periodic Table and those (more intermetallic in character) given by the metals in the middle of the Periodic Table. Between these two sets of compounds there are a few alloys (formed with the elements placed close to the 12th group) with a low thermal stability. This behaviour may be compared with that shown by the metals of the following groups, the reactivity patterns of which contain, close to this position in the Periodic Table, a gap in the compound formation capability. 5.6.4.3 Remarks on the alloy crystal chemistry of the 4th group metals. Selected groups of isostructural phases, pertaining to simple common structural types have been collected in Table 5.25. A number of them (for instance CsCl, AuCu types, Laves phases, AuCu3 type) correspond to more or less extended solid solution 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16

Zr

<1000

1000–2000

2000–3000

>3000

Temperature (°C)

Figure 5.19. Zr alloys. Trend of the highest melting points of the binary compounds with the different elements. Notice that the data concerning the Zr–S system are very uncertain.

Table 5.25. A selection of intermediate phases in the binary alloys of the 4th group metals (Me). Structure type

CNE (Me)

Examples of isostructural phases Ti compounds

Zr and Hf compounds

cP4-AuCu3

12

Zr3X: X Al

cP8-Cr3Si

14

Ti3X: X Ir, Pd, Pt(22–29Pt), Au, Hg, Sb

Zr3X: X Au, Hg, Sn(20Sn)

tI6-MoSi2

14

Ti2X: X Rh, Cu, Ag, Cd, Zn

Zr2X: X Pd, Cu, Ag, Au, Cd Hf2X: X Pd, Cu, Ag, Au, Zn, Cd, Hg

cP2-CsCl

14

TiX: X Tc, Os(38–51Os), Co(49–55Co), Rh(38–58Rh), Ni(50–57Ni), Pd(47–53Pd), Pt(46–54Pt), Ir(35–58Ir) Au(38–52Au), Zn, Al(29–41Al)

ZrX: X Ru(48–52Ru), Os, Co, Rh(50–62Rh), Pt, Ir(48–53Ir), Cu, Zn HfX: X Ru(47–51Ru) Os(47–51Os), Rh(48–62Rh), Co(49–51Co), Ir, Pt

tP4-AuCu

12

TiX: X Rh(38–58Rh), Ir(40–59Ir)

ZrX: X Hg

tP4-TiCu

14

TiX: X Cu(48–52Cu), Ag(48–50Ag), Au, Cd

ZrX: X Ag(49–51Ag), Cd HfX: X Ag, Au(49–51Au), Cd

hP4-NiAs

8

TiX: X As, Sb, S, Se, Po

ZrX: X P HfX: X Po

hP8-TiAs

7

TiX: X As

ZrX: X As HfX: X As

cF24-Cu2Mg

16

TiX2: X Be, Cr(63–65Cr), Co

ZrX2: X V, Cr(62–69Cr), Mo(60–67Mo), W, Fe(67–73Fe), Ru(66–68Ru), Co, Ir, Zn Hf X2: X V(64–66V), Cr(65–67Cr), Mo, W, Fe

hP12-MgZn2

16

TiX2: X Cr(64–66Cr), Mn(60–70Mn), Fe(65–73Fe), Zn

ZrX2: X Cr(66–68Cr), Mn(63–74Mn), Tc, Re, Ru, Os, Al Hf X2: X Cr(65–67Cr), Mn(62–75Mn), Tc, Re(62–67Re), Fe(67–76Fe), Os(64–68Os), Al

hP24-Ni2Mg

16

TiX2: X Cr(64–66Cr), Co (69–72Co)

ZrX2: X Cr(64–69Cr) HfX2: X Mo, Mn, Fe, Zn

tI6-MoSi2

14

TiX2: X Pd(65–67Pd), Au

ZrX2: X Pd, Au HfX2: X Pd, Au

cP4-AuCu3

12

TiX3: X Rh(73–78Rh), Co(75–80 Co), Ir(72–77Ir), Pd(78–85Pd), Zn, Pt(75–81Pt)

ZrX3: X Rh(78–81Rh), Ir(70–81Ir), Pt, Hg Hf X3: X Rh(72–80Rh), Ir(73–79Ir), Pt,(77–85Pt)

hP6-CaCu5

18

ZrX5: X Be

HfX5: X Be

hR57-Nb2Be17

19

Ti2X17: X Be

Zr2X17: X Be Hf2X17: X Be

hP38-Th2Ni17 cF112-NaZn13

18–20 24

Ti2X17: X Be

Hf2X17: X Be ZrX13: X Be HfX13: X Be

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Intermetallic Chemistry

ranges. Notice, for a few structural types, that they are observed both at the Merich and the Me-poor sides of the systems: the MoSi2 type, for instance, is found for Me2X and MeX2 compounds. In some cases, as in the Zr–Pd and in the Hf–Au alloys, the two formulae and compounds are observed in the same system. Several 1:1 compounds with CsCl, AuCu-type structures are formed especially with metals close to the end of the transition series and with semi-metals and nonmetals of the 15th and 16th groups. A high number of Laves phases are formed with several transition metals, and in some cases with Be, Zn, Al. Very often with the same metal different Laves polytypes are observed. Remarkably, Ti–Cr alloys form, in different ambient conditions, the three main polytypes. 5.6.4.4 Notes on the applications of the 4th group metals. Ti-based alloys are used in aerospace applications (Bhadeshia 2003). A typical example is a so-called ‘blisk’, made of the Ti–6Al–4V alloy, of an aero-engine turbine compressor. The blisk is a bladed disc obtained joining blades and disc in a single metallic component with no discontinuities. The joining procedure is an example of the ‘linear friction welding’. The blades are rubbed against the disc while a load is applied normal to the junction until the joint is obtained: oscillation amplitude of a few millimetres is maintained with a frequency of some tens of Hz. The heat generated by the friction softens the alloy at the weld interface. As for the specific nomenclature notice that blisks in which the blades are integral with a ring, that is with a disc with the centre missing, are called ‘blings’; assemblies of blings, in the form of a drum, are called ‘brums’. Titanium alloys generally show a combination of strength and biocompatibility which makes them suitable for medical devices (prosthesis, surgical instruments). The high strength Ti–6Al–7Nb alloy has several orthodontic applications. Only a limited number of alloys have the necessary combinations of properties needed for successful use in the human body. Titanium and its alloys, stainless steels and cobalt–chromium alloys are the workhorse alloys in the medical device industry. Zirconium is used for structural parts in the core of water moderated nuclear reactors; to this end Zr has several good properties and especially it has low thermal neutron cross-section. Hf, on the contrary, has a high thermal neutron absorption coefficient, so it is necessary to be able to prepare Hf-free zirconium. On the other hand, in some cases the Hf properties too may be useful in nuclear technology, in the control rods of submarine reactors. 5.6.4.4.1 Titanium and zirconium intermetallics. Various metals of practical relevance (Ti, and also Nb, Fe, Ni) form several fields of solid solutions with aluminium in presence, often, of rather complex phase equilibria. Several investigations and re-examinations of such systems, performed in the course of time, have been reviewed and assessed during the European Congress EUROMAT 2005

Elements of Alloying Behaviour Systematics

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(Morris et al. 2006). The data concerning the ternary system Al–Fe–Ti have been reviewed and discussed by Palm and Lacaze (2006); the assessments of the limiting binary systems (especially of Ti–Al and Fe–Al) have also been reported and commented. The Fe–Ni and Ti–Fe systems have been examined and discussed in papers dedicated to the assessment of Ti–Fe–Ni alloys (Cacciamani et al. 2006, Riani et al. 2006). Ti–Al intermetallics. Within the Ti (and Zr) alloys with Al, materials based on intermetallic compounds are among the most advanced of engineering materials and a variety of compositions have been developed to achieve specific performances. A few remarks on these compounds may be noteworthy. The Ti–Al phase diagram shows the formation of a number of intermediate phases. Of special interest are Ti3Al, TiAl (47–67 at.% Al, peritectic melting at 1476°C), and TiAl3 (75 at.% Al, peritectic melting at 1387°C). For the structures of these phases, see § 7.4.4.4 and Fig. 7.47. Ti3Al (also called Ti–Al α2 phase) has a close-packed hexagonal structure (hP8Ni3Sn-type D019). It has a specific modulus and stress rupture resistance comparable to that of super-alloys but (as with several other intermetallics) the complete absence of room-temperature plasticity poses severe mechanical–structural problems. Significant improvements have been obtained by the addition of Nb (typically in the range 10–12 at.%) or of Nb V Mo. TiAl (so-called γTiAl) has the tP4-AuCu-type structure (L10). It is a light-weight material with a good oxidation resistance; it maintains strength and resists creeps at high temperature and, over a wide temperature range, has a high stiffness. As other intermetallics, however, TiAl, without modifications lacks the ductility and toughness which are needed for structural applications. Several processing methods have been devised and additions of various elements considered. Generally this results in the industrial preparation of multi-phase alloys in which different microstructures and properties are obtained by controlling the additions and their stoichiometry. A review of alloy and process development of the TiAl alloy has been published by Wu (2006). The main conclusions are that TiAl development is now relatively mature; the major requirement is the promotion of low cost processing coupled with the supply of high-quality raw material; the future application of net shape powder process routes could be cost effective both for complex large components and for some small components. Special attention is dedicated in this review to alloys based on Ti–(45–46)Al–(5–8)Nb (at.%) and Ti–48Al–2Cr–2Nb (at.%). TiAl3 is a point compound which has the tI8-TiAl3-type structure (D022), a derivative type of the cP4-AuCu3 type (L12 type). This compound and similar phases formed with the metals of the 4th and 5th groups constitute a group of interesting high-temperature, light-weight structural materials. Several ternary and complex TiAl3-based alloys have been considered, resulting not only in the tI8-D022 type but

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also (depending on the additions and the preparation methods) in cubic (cP4AuCu3-L12 type) variants. Zr-Al intermetallics. Zr3Al is a point compound with a peritectic melting at about 1020°C. It has the cP4-AuCu3-type structure (L12). Notice that, on the other hand, ZrAl3 is another more complex superstructure based on close packing and corresponds to the type tI16-D023. As discussed by Schulson (1994), a nuclear reactor such as the CANDU (Canadian Deuterium Uranium) Power Reactor uses natural uranium as fuel and heavy water as moderator and coolant; it distributes the coolant among a large number of thin-walled, small diameter pressure tubes. It requires structural components (pressure tubes and fuel sheaths) which resist oxidation, corrosion, creep deformation, and are also relatively transparent to thermal neutrons. Owing to these requirements, Zr-based alloys have been generally used (for instance Zircaloy, etc.). 5.7. ALLOYS OF THE METALS OF THE 5TH GROUP OF THE PERIODIC TABLE

Vanadium, V; niobium, Nb; tantalum, Ta

5.7.1 Introduction Vanadium (V, [Ar]3d34s2), name and symbol after Vanadis, the Scandinavian Goddess of beauty, because of its many colourful compounds. Discovered (1801) by the Mexican chemist Andrés Manuel del Rio and re-discovered (1830) by the Swedish chemist Nils G. Sefström. Bright grey metal. Atomic number 23, atomic relative mass 50.9415. Occurrence. Important minerals are carnotite K(UO2)VO4 3/2 H2O, more important as a uranium ore, vanadinite Pb5(VO4)3Cl and some complex sulphides. It occurs also in certain crude oils and may be recovered from dusts after combustion. Preparation. Commercially it is prepared mainly as ferro-vanadium alloy. It can be obtained by aluminothermic reduction of the oxide. Pure V may be obtained through the de Boer–Van Arkel process by iodide thermal decomposition (vanadium iodide is decomposed on an electrical heated W wire).

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Main uses of the metal. It is especially used as an alloying element in the steel industry and in the preparation of non-ferrous alloys (V–Ti alloys, Ni-based superalloys, etc.). Niobium (Nb, [Kr]4d45s1), name and symbol after the Greek mythological heroine Niobe (Tantalus’ daughter). Discovered (1801) by Charles Hatchett. The name niobium is now used in place of the original name ‘columbium’. Greyish-white metal. Bluish after a long exposition to air at room temperature. Atomic number 41, atomic relative mass 92.90638. Occurrence. The most important minerals are pirochlore (NaCaNb2O6F) and those of the columbite–tantalite series (Fe/Mn)(Nb/Ta)2O6 with various metallic ratios. Preparation. Nb and Ta always occur together in columbite and tantalite and therefore they must be separated from each other by processes based on solvent extraction. Metallic niobium is generally produced by aluminothermic reduction of Nb2O5. Generally an excess of Al is used, producing a Nb–Al alloy to give Nb which may be melted in vacuum or by electron beam or arc furnace. The carbo-thermic process is also used; it is a two-stage reduction (at 1950°C) according to the reactions: Nb2O5 7C : 2NbC 5CO Nb2O5 5NbC : 7Nb 5CO The product must then be refined through high-temperature processes. Very pure Nb may be obtained by electrowinning from O2-free molten salt system (double fluorides or chlorides). Uses. Used in various superconductor applications and for cutting tools. Nb steels are very heat resistant. Niobium has a good resistance towards corrosive chemicals even at high temperature: it is used in the construction of chemical equipment even if it is not as resistant as tantalum. Nb has a low neutron capture cross-section and it is especially resistant towards liquid sodium corrosion; it finds applications in the nuclear industry. Nb is very malleable and easy to shape and may be used in special jewellery; this is also because it is possible to give it beautiful colours (thinfilm interference colours) by heating in air or, better, by controlled anodization. Tantalum (Ta, [Xe]4f145d36s2), name and symbol after the Greek mythological hero Tantalus. Discovered (1802) by Anders Gustav Ekeberg. Greyish-silvery solid metal. Atomic number 73, atomic relative mass 180.9479.

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Occurrence. The more important minerals are those of the columbite–tantalite series (Fe/Mn)(Nb/Ta)2O6 with various metallic ratios. Preparation. Metallic Ta is generally obtained by reduction of the potassium fluotantalate with the strongly exothermic reaction: K2TaF7 5Na : 2KF 5NaF Ta Ta powder is recovered by leaching the reaction product. The Ta powder purified may be compacted and then sintered by passing an electric current (at 2500°C) or by arc melting, and finally shaped by forging, rolling, extruding or wire drawing. Main uses of the metal. Applications of Ta in medicine (in prosthetic implants) are also well known because of its lack of toxicity and excellent compatibility with tissue. It is used for producing capacitors. Tantalum carbide is used in cutting tools. 5.7.2 The 5th group metals: a summary of their atomic and physical properties Vanadium, niobium and tantalum have only the bcc, W-type, structure: no hightemperature or high-pressure polymorphs are known. The metals are comparatively soft and ductile; impurities generally have hardening and embrittling effects. Notice, as a result of the lanthanide contraction, the nearly equal atomic volumes of Nb and Ta, and the consequent very different values of the densities. Atomic and physical properties of V, Nb and Ta are collected in Tables 5.26–5.28. 5.7.3 The 5th group metals: remarks about their general chemical properties and reactivity The elements of this group are in many aspects similar to those of group 4. They react, at high temperature, with most non-metals often forming nonstoichiometric and interstitial derivatives. They are generally resistant to corrosion mainly due to the formation of surface films of oxides. Vanadium. It is stable in air below 250°C. After long exposition it becomes bluish grey to brownish black; significant oxidation takes place at about 300°C. Vanadium reacts with hot concentrate mineral acids, especially HNO3 and HF. It has good corrosion resistance towards molten low melting metals, especially alkali metals. Niobium and tantalum. Their chemistries are similar although not as nearly identical as for Zr and Hf. However, this similarity can be highlighted and, in this case too, related to the effect of the lanthanide contraction. The only acid that attacks them is concentrated HF or better a mixture of HF and HNO3. The metals may be dissolved by fusion with an alkali hydroxide or hydrogen sulphate. They oxidize in air at high temperature.

407

Elements of Alloying Behaviour Systematics Table 5.26. V, Nb, Ta: selected physical properties. Property

V

Nb

Ta

r/pm, metallic, CN 12 [‘metallic valence’] Ionic radius (pm) M2, CN 6 Ionic radius (pm) M3, CN 6 Ionic radius (pm) M4, CN 6 Ionic radius (pm) M5, CN 6 Tmelting/°C Tboiling/°C ΔHmelting (at Tmelting)/kJ/mol Δf H 0 of Me1 gas at 298.15 K /kJ/mol

134.6 [5] 79 64 58 54 1910 3409 22.8 515

146.8 [5]

146.7 [5]

72 68 64 2469 4744 26.9 733

72 68 64 3020 5458 36.6 782

Table 5.27. V, Nb, Ta: ionization energies. Element

1st ionization energy/kJ/mol

2nd ionization energy/kJ/mol

3rd ionization energy/kJ/mol

5th ionization energy/kJ/mol

6th ionization energy/kJ/mol

V Nb Ta

650 664 761

1414 1382 1500

2828 2416 –

6299 4877 –

12362 9900 –

Table 5.28. V, Nb, Ta: crystal structures and lattice parameters of their allotropes and calculated densities. Element (allotrope) Temperature range/°C Pressure/GPa

Crystal structure

Lattice parameters/ pm

Atomic volume/ pm3 106

Molar volume/ cm3/mol

Density g/cm3

a Vanadium 1910° Niobium Nb 2469° Tantalum Ta 3020° V

cI2-W

302.40

13.83

8.33

6.12

cI2-W

330.04

17.975

10.82

8.58

cI2-W

330.30

18.02

10.85

16.68

5.7.4 Intermetallic chemistry of the 5th group metals 5.7.4.1 Phase diagrams of the 5th group metals. The compound formation patterns of V, Nb and Ta are shown in Fig 5.20. Several analogies between them may be remarked: (1) no compound formation is observed with the lanthanides and the actinides, (2) an extended region of no-compounds is represented by the metals of the first groups (up to about the 6th group; however check the vanadium pattern),

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

V

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Nb

Ta

Compound-forming element

Phase diagram known; no intermediate phases formed

No information available

Questionable compound forming capability

Figure 5.20. Compound formation capability in the binary alloys of V, Nb, Ta. Ti

Cr

Ti

Nb

Mo

Zr

*Hf Ta * *

W

Hf

Zr

V

V

Nb Ta

Cr

Ti

*Mo

Zr

W

Hf

V

Cr

* Nb *Mo Ta

W

Figure 5.21. V, Nb, Ta binary alloys. The dashed boxes show the metals which, at least at high temperature, form one continuous range of solid solutions with the 5th group elements. In the systems marked by an asterisk intermediate compounds are formed (with or without a continuous solid solution).

(3) a gap, moreover, in the compound formation capability may be noticed for the elements around the 11th and 12th groups showing certain analogies with the metals of the following groups; compare for instance with Fig. 5.22. As for the formation of extended solid solutions, Fig. 5.21 summarizes the metals in whose binary phase diagrams a continuous field of solid solutions with V, Nb and Ta can be observed. Notice that the same crystal structure (body-centred cubic cI2-W type) is exhibited by V, Nb, Ta, Cr, Mo, W and it is observed as a high-temperature form (β-form) of Ti, Zr, Hf. The trend of intermetallic reactivity and alloy stability of V, Nb and Ta with the different elements may be further discussed in terms of the melting points of the compounds as described in the following paragraphs. 5.7.4.2 Melting point trend in the binary alloys of the 5th group metals. An indication of the intermetallic reactivity, compound formation tendency and stability may be given also by the trend of the melting points of the alloys. A piece of information about this point is given in Table 5.29. In this table, for two series of elements (along the 4th and 6th rows of the Periodic Table), from the 5th to the 15th groups, the compounds

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409

with the highest melting points formed in their alloys with V, Nb or Ta have been considered. We notice the high thermal stability of the compounds given by the metals, especially the heavy ones, that is, those of the 6th row, pertaining to the groups 7th (Re) to 11th (Au). Notice, however, that with Cu (of the same 11th group) a small ‘island’ of no-compound formation starts. Then with the highly electronegative elements at the right-top corner of the Periodic Table, compounds with a high thermal stability are again observed. A short list of these compounds with the corresponding melting points (°C) follows. In this list a number of interstitial compounds formed within borides, carbides and nitrides are especially remarkable: V2O3 (1960°), Ta2O5 (1870°), VS (s.s. 1800°), V2N1x (s.s. 2410°, dec.), Nb2N (s.s. 2430°, dec.), Ta2N (s.s. 3000°), VC (s.s. 2660°), NbC (s.s. 3620°), TaC (3970°), V5Si3 (2010°), Ta5Si3 (2350°), VB2 (2750°), NbB2 (2950°), TaB (3090°). The phase diagram of the vanadium – oxygen system is very complex with a very high number of compounds, such as V2O3, α,βV3O5, V4O7, V5O9, V6O11, V7O13, V8O15, α,βVO2, V6O13, V3O7, V2O5, etc. Other systems behave in a similar way such as Ti–O, W–O, Mo–O. See a few comments about the Magnéli-type phases in § 7.6.4 concerning the TiO2 rutile derivative structures. In Ti–S system also, a high number of superstructure polytypes are observed. 5.7.4.3 Remarks on the alloy crystal chemistry of the 5th group metals. A selection of common structural types found in the alloys of V, Nb and Ta is shown in Table 5.30. Both nearly stoichiometric compounds and solid solution ranges have been observed. In the V (Nb, Ta) rich regions of the systems, compounds related to the 3:1 stoichiometry are found. We may underline the formation of cP8-Cr3Si phases (an example of tetrahedrally close-packed structure: see § 7.4.4.5). These phases are observed in several transition element alloys with the metals of the 3rd, 4th and 5th main groups. A number of these phases formed in the Nb alloys have superconducting properties. Several alloys having other structures pertaining to the tetrahedrally close-packed family are observed in the V, Nb, Ta systems. The σ phase (tP30-Cr, Fe type) formed with several metals is noteworthy as the μ phases (hR39-W6Fe7 type) given by similar combinations of metals. Very often these structures correspond to ranges of intermediate solid solutions. Several Laves-type phases are formed in the alloys of these metals: different Laves polytypes are often present in the same system (generally depending on the composition and temperature) for instance αNbCr2 (Cu2Mg-type stable within 32–40 at.% Nb and for T 1625°C) and βNbCr2 (MgZn2-type for 30–38 at.% Nb and 1585° T 1730°). As another example we may mention the Ta–Co system for which three Laves polytypes have been described; the MgZn2-type, high T phase (1130° T 1540°) corresponding to 37 at.%Ta, the Cu2Mg-type stable within 30–36 at.% Ta and T 1620°C and the Ni2Mg-type stable within 28–29 at.% Ta and T 1450°C.

Table 5.29. Highest melting points (°C) in the alloys of V, Nb and Ta with compound-forming elements of the 4th and 6th rows of the Periodic Table. Compare with Figs. 5.20 and 5.21. See the introduction for the meaning of the symbols. Alloys with V

Vanadium compounds –

Ta Cr

s.s. NbCr2 1730°, IR 1 Cont. s.s. (V,W)

Cont. s.s. (V,δ Mn) σ, s.s.r., 1050° Re

Fe

σ 2460°, p, IR 1

Cont. s.s. (V,α Fe) σ, s.s.r.,1252° Os σ 1420°, p, IR 1

Co Ir

Cont. s.s. (Ta,Nb)

TaV2 1310°, s.s.r., IR 1

W

– TaCr2 2020°, IR 1

Cont. s.s. (Nb,W) s.s.NbMn2 1500° NbFe2 1640°, IR 1

s.s. VOs 2300°, IR 1

χ, 2730, IR 1 χ (s.s. Nb40Os60) 2270°, p, IR 1

Cont. s.s. (Ta,W). TaMn2 1500° Ta7Fe6 1776°, IR 1

χ, 2800°, IR 1 σ, 2500°, p, IR 1

Ta2Co 1800°, IR 1

s.s. NbCo2 1475°, IR 1 s.s. VIr3 2100°, p, IR 1

Tantalum compounds TaV2, 1310° s.s.r., IR 1

Cont. s.s. (Nb,V)

Cont. s.s. (V,Cr)

Mn

Niobium compounds

s.s. NbIr3 2435°, IR 1

s.s. Ta3Ir 2480°, p, IR 1

σ 1280°, p, IR 1

Ni

s.s. V3Pt 1800°, IR 1

Pt Cu

NbNi3 1400°, IR 1

Simple V–Cu monotectic

Simple Nb–Cu eutectic

V4Zn5 670°, p, IR 1

Zn Hg Ga

σ, 2000° p, IR 1

Nb3Au 1560° s.s.r.

Compl. immisc.

Tl

s.s. Ta3Pt 2470°, p, IR 1 Simple Ta–Cu eutectic

NbZn 1120°, dec.

s.s.V3Ga 1300° s.s.r.

Ge

s.s. NbPt3, 2040°, IR 1

V3Au 1280°, s.s.r.

Au

Ta2Ni 1790°, p, IR 1

Several compds. Compl. immisc.

Nb5Ga3 1950°, IR 1 Compl. immisc.

Several compds. 1300° Compl. immisc.

Compl. immisc.

V5Ge3 1965°, IR 1

s.s. Nb5Ge3 2180°, IR 1

Several compds.

Several compds.

Several compds.

Ta5As4 1400°

Pb As Bi

Compl. immisc.

Simple Nb–Bi eutectic

Compl. immisc.

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Intermetallic Chemistry

Table 5.30. A selection of intermediate phases in the binary alloys of the 5th group metals (Me). Structure type CNE (Me)

Examples of isostructural phases V compounds V3X: X Os(45–50Os), Co, Rh(23–39Rh), Ir(25–39Ir), Ni(22Ni), Pd, Pt(18–34Pt), Au(19–24Au), Al(10–35Al), Ga(18–32Ga), Si(19–25Si), Ge, Sn(20Sn), As, Sb

Nb and Ta compounds Nb3X: X Os(25–29Os), Rh, Ir(21–29Ir), Pt(19–28Pt), Au(17–27Au), Al(18–25Al), Ga(20–25Ga), In(12–25In), Ge(18–23Ge), Sn(15–33Sn), Sb(24–27Sb) Ta3X: X Sn, Au(16–18Au)

cP8-Cr3Si

14

tP32-Ti3P

13–16

Nb3X: X Si Ta3X: X Ge, Si

tI12-CuAl2

15

Ta2X: X B(28–31B), Be, Co, Ni(30–33Ni), Si

cF24-Cu2Mg

12

V2X: X Zr(33–35Zr), Hf(33–35Hf), Ta(33–36Ta)

tI32-W5Si3

14–15

V5X3: X Si, Ge, As

cP2-CsCl

14

VX: X Mn(30–55Mn), Tc(35–61Tc), Ru(25–55Ru), Os(20–45Os)

cF8-NaCl

6

VX: X C(38–48C), N(38–50N)

NbX: X C(38–50C) TaX: X C(38–49C), N(40–50N)

hP4-NiAs

8

VX: X P, Sb(42Sb), S, Se(50Se), Te

NbX: X Sb(50–51Sb), S(47S), C(29–34C)

tP4-AuCu

12

VX: X Rh(52–60Rh), Ir(52–60Ir),

tP30-σ-CrFe

12–15

V–X: X Mn(70–80Mn), Fe(33–68Fe), Co(29–55Co), Ni(25–42Ni).

cI58-Mn

16

Ta–X: X Re(65–80?Re),Os (48–65Os)

hR39-W6Fe7

12–16

Nb–X: X Fe(52Fe), Co(47–50Co), Ni(45–50Ni), Zn(55–60Zn) Ta–X: X Fe(51), Co(44–56Co), Ni (46–50Ni)

Nb5X3: X Si(38-41Si) Ta5X3: X Ga, Ge, Si

Nb–X: Re(54Re), Os(27–46Os), Rh(28–40Rh), Ir(33–42Ir), Pt(31–38Pt), Al(30–42Al) Ta–X: Re(55Re), Os(22–44Os), Rh(20–40Rh), Ir(11–41Ir), Pd(21–29Pd), Au(22–35Au), Al(21–35Al)

(Continued)

Elements of Alloying Behaviour Systematics

413

Table 5.30. (Continued) Structure type CNE (Me)

Examples of isostructural phases V compounds VX2: X Be, Re(68–72Re)

Nb and Ta compounds NbX2: X Cr(62–70Cr), Mn(60–72Mn), Fe(63–66Fe), Co(64Co) TaX2: X Cr(62–70Cr), Mn, Fe(63–74Fe), Co(63Co)

hP12-MgZn2

16

cF24-Cu2Mg

16

V–X: X Sn(60–62Sn)

NbX2: X Be, Cr(60–68Cr), Co (67–73Co), Sn TaX2: X Be, Cr(64–67Cr), Co (64–70Co), Sn(60Sn)

cP4-AuCu3

12

VX3: X Rh(65–77Rh), Ir(61–78Ir), Zn

NbX3: X Ru(74–76Ru), Rh(71–79Rh), Ir(63–80Ir), Cd, Zn TaX3: X Rh(69–78Rh), Ir(66–76Ir)

tI8-TiAl3

12

VX3: X Ni(72–79Ni), Pd(74–78Pd), Pt(73–78Pt), Al

NbX3: X Al(75–76Al), Ga(77–79Ga) TaX3: X Pd, Al

The AuCu3-type structure and its derivative structure tI8-TiAl3 type are observed in several alloys generated by all the three metals of this group for stoichiometries close to MeX3. 5.8. ALLOYS OF THE METALS OF THE 6TH GROUP OF THE PERIODIC TABLE

Chromium, Cr; molybdenum, Mo; tungsten, W

5.8.1 Introduction Chromium (Cr, [Ar]3d54s1), name and symbol after the Greek χρωμα (chroma, colour). Discovered (1780) by Nicholas Louis Vauquelin. Blue-white hard metal. Atomic number 24, atomic relative mass 51.9961.

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Intermetallic Chemistry

Occurrence. The ore of Cr of higher commercial importance is chromite (FeCr2O4). Other minerals are crocoite PbCrO4 and ‘chrome ochre’ Cr2O3. About 2% Cr in emerald Be3Al2Si6O18 is the source of its green colour. Chromium is comparable in abundance in the earth’s crustal rocks with V and Cl. Preparation. Oxidation of the chromite ore by air in molten alkali gives sodium chromate, Na2CrO4 that is then converted to Cr2O3. The oxide is further reduced with aluminium or silicon to form chromium metal. Solutions suitable for electrolytic production of chromium (for plating) can be obtained from ore by oxidative roasting in alkali or by dissolution of chromite in H2SO4 and especially by dissolving ferro-chromium in sulphuric acid. Main uses of the metal. Chromium can serve as a protective coating of alloys to prevent oxidation. It is an important component of several ferrous alloys, mainly stainless steels. Molybdenum (Mo, [Kr]4d55s1), name and symbol after the Greek word μoλνβδο (lead). The element was discovered (1781) by the Swedish chemist Carl Welhelm Scheele. Silvery-white hard metal. Atomic number 42, atomic relative mass 95.94. Occurrence. The most important ore of Mo is molybdenite, the sulphide MoS2. Another mineral is wulfenite (PbMoO4). The recovery of Mo from spent petroleum catalysts is widely used. Preparation. The sulphide MoS2 is roasted to form the oxide MoO3 (often used directly for adding Mo to steel). The oxide MoO3 is dissolved in ammonium hydroxide to make ammonium molybdate, (NH4)2(MoO4), that is reduced with hydrogen gas to form the molybdenum metal (powder). The production of compact molybdenum metal can be performed by sintering (possibly in hydrogen atmosphere) and also by melting in vacuum arc furnace, electron-beam furnace, etc. Main uses of the metal. Areas of application of Mo and Mo alloys are in electronic industries (semiconductor base plates, klystrons, etc.), high-temperature furnaces (heating elements radiation shields), glass and ceramic industries (electrodes, crucibles, drawing dies), casting technology (forging, extrusion dies), coating nuclear technology. Mo is used as alloying component in cast iron, steels, super-alloys to increase hardenability, strength, corrosion resistance. Mo–Re alloys have high strength, ductility, good welding properties. Mo–W alloys are especially resistant to molten

Elements of Alloying Behaviour Systematics

415

Zn and used in the metallurgy of this metal. Pure Mo finds applications also as a catalyst in several petrochemical processes. Tungsten (W, [Xe]4f 145d 46s2), name after the Swedish tung sten (heavy stone), symbol after the name of mineral wolframite (from which it was originally isolated). The name wolfram is still used mainly in the German literature. Isolated (1783) by Spanish chemists Juan José and Fausto d’Elhuyar. Greyish-silvery solid metal. Atomic number 74, atomic relative mass 183.84. Occurrence. Important ores are several tungstates such as scheelite, CaWO4, wolframite, (Fe,Mn)WO4, etc. Preparation. Tungsten is recovered by roasting the tungstic acid (a hydrated oxide) to WO3, which gives the metal powder by hydrogen reduction. Compact metal is obtained by heat treatment of a compacted preform. A maximum sintering temperature (2800°C) and sintering time of several hours are required. The tungstic acid can be obtained by dissolving wolframite in fused NaOH, followed by leaching and acidification with HCl, or by directly converting scheelite to insoluble tungstic acid by treatment with HCl. The reduction of WO3 by carbon is used for the production of tungsten carbide (direct carburization). Main uses of the metal. An important group of applications is represented by the ‘hard metals’ (for cutting, drilling tools, abrasive materials, etc.) the special properties of which are achieved by binding carbides, nitrides, carbonitrides of Ti, Hf, Nb, Ta and especially of W (WC) with a ductile metallic phase (for example, Co alloys) which surrounds them. W additions are important also in several steel types (high-speed steels, high-temperature steels, tool steels). Tungsten and tungsten alloys have a variety of applications in high-temperature technology, electrical, lightning, radiation technologies, in chemical industries, armaments, and rocket and aircraft construction. 5.8.2 The 6th group metals: a summary of their atomic and physical properties These metals, especially Mo and W, are extremely refractory and have very high melting points. Their crystal structure, as that of the metals of the preceding group (5th group, V, Nb, Ta) is body-centred cubic, cI2-W type. As for their densities, especially remarkable is that of tungsten which is in line with the values of the metals close to W in the Periodic Table. The metals having small molar volumes, high

416

Intermetallic Chemistry Table 5.31. Cr, Mo, W: selected physical properties. Property

Cr

Mo

r/pm, metallic, CN 12 [‘metallic valence’] Ionic radius (pm) M2, CN 6 Ionic radius (pm) M3, CN 6 Ionic radius (pm) M4, CN 6 Ionic radius (pm) M5, CN 6 Ionic radius (pm) M6, CN 6 Tmelting (°C) Tboiling (°C) Hmelting (at Tmelting)/kJ/mol fH0 of Me1 gas at 298.15 K/kJ/mol

128.2 [6] 73–80 61.5 55 49 44 1863 2672 20.5 397

W

140.0 [6] – 69 65 61 59 2623 4639 36.0 659

140.8 [6] – – 66 62 60 3422 5555 35.4 851

Table 5.32. Cr, Mo, W: ionization energies. Element Cr Mo W

1st ionization energy/kJ/mol

2nd ionization energy/kJ/mol

3rd ionization energy/kJ/mol

653 685 770

1500 1558 –

2987 2620 –

6th ionization energy/kJ/mol

7th ionization energy/kJ/mol

8738 6600 –

15 540 12 230 –

… … …

Table 5.33. Cr, Mo, W: crystal structures, lattice parameters of their allotropes and calculated densities. Element (allotrope) Temperature Range/°C Pressure/GPa Chromium Cr 1863° α Cr HP Molybdenum Mo 2623° Tungsten W 3422°

Crystal structure

Lattice parameters/ pm

Atomic volume/ pm3 106

Molar volume/ cm3/mol

Density/ g/cm3

12.00

7.23

7.19

a

c

cI2-W tI2-α Cr

288.48 288.2

288.7

cI2-W

314.70

15.58

9.38

10.22

cI2-W

316.52

15.86

9.55

19.26

atomic mass and as a consequence density close to or higher than 19 g/cm3 (with the maximum value of about 22.6 g/cm3) are W, Re, Os, Ir, Pt, Au and in the actinide series U, Np and Pu. Atomic and physical properties of Cr, Mo and W are collected in Tables 5.31–5.33.

Elements of Alloying Behaviour Systematics

417

5.8.3 The 6th group metals: remarks about their general chemical properties and reactivity Chromium. It is extremely resistant to most corrosive agents (it is often used as an electroplated protective coating). It may be dissolved in non-oxidizing acids (HCl, H2SO4) but not (due to passivation) in nitric acid or aqua regia. Its reactivity, however, depends on its purity. At high temperatures it reacts and combines with halogens, oxygen, sulphur, nitrogen, carbon, silicon, boron. Molybdenum and tungsten. They are not readily attacked by acids. They may be dissolved (Mo more easily) by a mixture of HF and concentrated HNO3. They are attacked, and dissolved, by oxidizing alkaline melts (fused mixtures of KNO3 and NaOH or Na2O2). They react, when heated, with oxygen to give the tri-oxides, with halogens (with F2 at room temperature forming the hexa-fluorides), nitrogen, carbon, silicon, boron. Mo and W burn at 500–600°C with oxygen; the oxides sublime at 600–800°C and a rapid oxidation occurs. Tungsten is stable to molten glass and silica up to 1400°C. 5.8.4 Intermetallic chemistry of the 6th group metals 5.8.4.1 Phase diagrams of the 6th group metals. The intermetallic reactivity pattern of Cr, Mo and W is summarized in Figs 5.22 and 5.23. The general schemes of compound formation capability (Fig 5.22) are in agreement with the trends observed in this part of the Periodic Table (compare with the reactivity patterns of the 5th group metals in Fig. 5.20, and especially with that of vanadium). We have here four regions of no-compound formation which roughly correspond: (i) To the first three groups of the Periodic Table. (ii) To the metals of the 5th and 6th groups. (iii) To the elements of the 11th, 12th (and 13th) groups and to the heavy elements of the last groups. (iv) Lanthanides and actinides also do not form any compound with Cr, Mo and W, with the exception of UMo2 (tI6-MoSi2 type), stable at low temperature up to 650°C, where it transforms congruently into γ-U solid solution. Another aspect of the intermetallic reactivity of Cr, Mo and W is shown in Fig. 5.23 which corresponds to a small portion of the Periodic Table close to the 6th group and containing metals giving complete solid-state miscibility in Cr, Mo and W. 5.8.4.2 Remarks on the melting point trends in the binary alloys of the 6th group metals. To complete, with reference to Fig. 5.22, the schemes of the stability trend along the Periodic Table of the solid phases formed by the 6th group metals, the

418

Intermetallic Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Mo

Cr

Compound-forming element

W

Phase diagram known; no intermediate phases formed

No information available

Figure 5.22. Compound formation capability in the binary alloys of Cr, Mo,W.

Ti

V

*Zr Nb *Hf * Ta * *

Ti

V

Mo

Zr

Nb

W

*Hf *

Ta

Cr

Cr

Mo W

Ti

V

Cr

Zr

Nb

Mo

*Hf *

Ta

W

Figure 5.23. Cr, Mo, W binary alloys. The dashed boxes show the metals which at least at high temperature form one continuous solid solution with the 6th group elements. In the systems marked by an asterisk, intermediate compounds (with or without a continuous solid solution) can be observed.

melting points of selected intermetallic compounds of these metals are collected in Table 5.34. We notice a significant thermal stability in the alloys with the metals of the 7th to 10th groups and, of course, the high melting points of a number of W alloys. In addition to the data reported in the Table, a few significant values concern compounds formed with the first elements (metals or non-metals) of the other groups. Compounds with beryllium (CrBe2, 1840°, IR 1; WBe2, 2250°, IR 1), aluminium (Cr5Al8, 1350°, p, IR 1; WAl2, 1650°, p, IR 1), carbon (Cr3C2, 1810°, p, IR 1; s.s. WC, 2776°, p, IR 1); silicon (s.s. Cr3Si, 1780°, IR 1; s.s. W5Si3, 2320°, IR 1), nitrogen (s.s. Cr2N, 18–32 at.% N, 1800° IR 1; γ-W-N, 29–42 at.% N, 1874°, p, IR 1), phosphorus (Cr12P7, 1725°, IR 1) can be mentioned. 5.8.4.3 Notes on the alloy crystal chemistry of the 6th group metals. A selection of the intermetallic phases, and of their structures, formed by Cr, Mo and W is shown in Table 5.35. Attention has been given in this list to the presence of several tetrahedrally close-packed alloys, often corresponding to ranges of solid solutions.

Table 5.34. Highest melting points (°C) in the alloys of Cr and W with compound-forming elements of the 4th and 6th rows of the Periodic Table. See the introduction for the meaning of the symbols. Alloys with Sc

Chromium compounds Sc–Cr simple eutectic

La Ti Hf V

Cont.s.s. (βTi,Cr) TiCr2 1370° s.s.r.

Ta – W Mn Re Fe Os Co Ir Ni Pt Cu

σ, 73–78 at.% Cr 1312°, p, IR 1 Cont.s.s. (Cr,α -Fe) σ, s.s.r. σ, 33–46 at.% Co 1280°, s.s.r. (Cr)–(Ni) eutectic, γ , s.s.r. Simple Cr–Cu eutectic

Au Zn Hg Ga Tl Ge Pb As Bi

Simple eutectic Extended monotectic

Cont.s.s. (V,Cr)

Cr

Tungsten compounds

CrZn13, 568°, p Cr3Ga, 1620°, p, IR 1 Cr3Ge, 1564°, p, IR 1 Cr2As, 1250°

s.s. HfCr2, 1825°, IR 1 TaCr2, 2020°, IR 1

Extended monotectic Cont.s.s. (βTi,W) s.s.r Cont.s.s. (V,W)

s.s. HfW2, 1512°, p, IR 1 Cont.s.s. (Ta,W)

Cont.s.s. (W,Cr) s.s. de-mix

Cont.s.s. (W,Cr) s.s. de-mix

–

σ, 56–68 at.% Re 2360°, p, IR 1

σ, 43–71 at.% Re 3000°, p, IR 1

σ, 30–35 at.% Os 1843°, s.s.r. ε, 32–70 at.%Ir 2200°, p, IR 1 Cr3Pt, 1600°, IR 1

s.s. W6Fe7 1637°, p, IR 1 s.s. W6Co7 1690°, p, IR 1 W2Ni 1060°, p, s.s.r.

σ, 20–36 at.% Os 2945°, p, IR 1 σ, 22–26 at.% Ir 2540°, p, IR 1 Compds., s.s.r.

Immisc. monotectic

Simple peritectic, s.s.r.

Simple eutectic

Compl. immisc.

Compl. immisc.

Extended monotectic

W2Ge3, 750°, s.s.r.

Simple W–Pb eutectic

Compds. Extended monotectic

Compl. immisc

420

Intermetallic Chemistry

Table 5.35. A selection of intermediate phases in the binary alloys of the 6th group metals (Me). Structure type

CNE (Me)

Examples of isostructural phases Cr compounds

Mo and W compounds Mo3X: X Be, Tc(54–55Tc), Os(25Os), Ir(22–26Ir), Pt(18–19Pt), Al(21–27Al), Ga, Si, Ge, Sn

cP8-Cr3Si

14

Cr3X: X Ru, Os(23–29Os), Rh(22–23Rh), Ir(17–27Ir), Pt(17–23Pt), Ga(23Ga), Ge(21–25Ge), Si(22–28Si), As(21As)

hP12-MgZn2

12

Cr2X: X Ti(34–36Ti), Zr(32–34Zr), Hf(33–35Hf), Nb(31–38Nb), Ta(30–38Ta)

cF24-Cu2Mg

12

Cr2X: X Ti(35–37Ti), Zr(31–38Zr), Hf(33–35Hf), Nb(32–40Nb), Ta(33–36Ta)

Mo2X: X Zr(33–40Zr), Hf(33–35Hf) W2X: X Zr(33–34Zr), Hf(33–34Hf)

hP24-Ni2Mg

12

Cr2X: X Ti(34–36Ti), Zr(31–36Zr)

Mo2X: X Hf(33–35Hf)

tI32-W5Si3

14–15

tP30-σ-CrFe

12–15

Cr–X: X Mn(73–78Mn), Tc(60–75Tc), Re(56–68Re), Fe(50–55Fe), Co(33–46Co), Ru(32–36Ru), Os(30–35Os)

hP4-NiAs

8

CrX: X H(47–50H) As(46–50As), Sb(47–50Sb), S(50–59S), Se(50–60Se), Te(52–53Te)

oP4-AuCd

12

MoX: X Ir(50Ir), Pt(43–53Pt), Rh(50Rh)

cF8-NaCl

6

Mo–X: X C(37–43C) W–X: X C(38–40C), N(30–42N)

hR39-W6Fe7

12–16

Mo–X: X Fe(56–61Fe), Co(51–59Co) W–X: X Fe(55–60Fe), Co(51–57Co)

hP2-Mg (ε phase)

12

Mo-X: X Co(80–84Co), Rh(42–82Rh), Ir(37–61Ir), Pd(48–51Pd), Pt(31–54Pt)

Mo5X3: X Si(37–40Si) W5X3: X Si(38–40Si) Mo–X: X Mn(64–65Mn), Tc(65–75Tc), Re(53–70Re) Ru(37–38Ru), Os(30–39Os), Co(36–39Co), Ir(28Ir) W–X: X Tc(60–78Tc), Re(43–71Re), Ru(34–41Ru), Os(20–36Os), Ir(22–26Ir)

Elements of Alloying Behaviour Systematics

421

Table 5.35. (Continued) Structure type

CNE (Me)

Examples of isostructural phases Cr compounds

Mo and W compounds W–X: X Rh(42–81Rh) MoX2: X B(61–66B)

hP3-AlB2

20

CrX2: X B

hP12-MgZn2

16

CrX2: X Be

hP6-MoS2

12

MoX2: X S(66–70S) WX2: X S(66–67S), Te

tI6-MoSi2

14

MoX2: X Si, U(66–68U) WX2: X Si

hP8-Ni3Sn

12

MoX3: X Co, Ir(64–75Ir), Pt(32–45Pt) WX3: X Co, Ir(70–80Ir), Rh

tI26-ThMn12

20

CrX12: X Be

MoX2: X Be, Fe WX2: X Be(64–72Be), Fe (metastable)

MoX12: X Be WX12: X Be

Among these phases, characterized by high coordination numbers, typical representatives are Cr3Si-type phases, σ phases and μ phases, Laves phases. As for phases formed with semi-metals or non-metals we may point out the NiAs, NaCl, MoS2, MoSi2 types. 5.9. ALLOYS OF THE METALS OF THE 7TH GROUP OF THE PERIODIC TABLE

Manganese, Mn; technetium, Tc; rhenium, Re

5.9.1 Introduction Manganese (Mn, [Ar]3d54s2), name and symbol after the Latin magnesia nigra (black magnesia). Isolated (1774) by the Swedish chemist Johan Gottlieb Gahn. Silvery, hard, brittle metal. Atomic number 25, atomic relative mass 54.938045.

422

Intermetallic Chemistry

Occurrence. In order of abundance in the earth’s crustal rocks, it is the third within the transition elements (after Fe and Ti) and the 12th in the general order of all the elements. It occurs in several minerals such as primary deposits of silicates and as secondary deposits (commercially more important) of oxides and carbonates as: pyrolusite, MnO2, hausmannite, Mn3O4, rhodochrosite, MnCO3, etc. Large amounts of manganese are present in the deep sea nodules located over certain areas of the ocean floor. Preparation. Pure manganese (mainly used in aluminium and steel industries) is available through the electrolysis of manganese sulphate, MnSO4. The main production of manganese is through the reduction with carbon (as coke) of manganese dioxide MnO2 mixed with iron oxide, Fe2O3, in appropriate proportions in a blast furnace to obtain ferro-manganese alloys. Main uses of manganese. Used to form many important alloys. It is present in almost all types of steel and cast-iron. In steel, manganese improves the rolling and forging qualities, strength, toughness, stiffness, wear resistance, hardness and hardenability. With aluminium and antimony, especially with small amounts of copper, it forms highly ferromagnetic alloys. Manganese metal is ferromagnetic only after special treatments. Technetium (Tc, [Kr]4d 65s1), name and symbol after the Greek τεχνικο (technikos, artificial). Detected in Italy (1937) by Carlo Perrier and Emilio Segré in a sample of Mo which had been irradiated with deuterons at the E.O. Lawrence cyclotron in California. It was the first artificially produced element. Silvery-grey hard metal, radioactive. Atomic number 43, atomic relative mass 97.907216 (nuclidic mass of the longest half life isotope). Occurrence. The natural abundance of Tc is negligibly small. Technetium is a by-product of the nuclear industry and it is a product of the uranium decay. Preparation. It can be made by the irradiation of molybdenum targets with deuterium nuclei. Technetium metal may be easily prepared by reduction of NH4TcO4 (or TcO2) with hydrogen or by electrodeposition from an NH4TcO4 solution. Main uses of the metal. It is used as a medical tracer and for calibration of particle detectors.

Elements of Alloying Behaviour Systematics

423

Rhenium (Re, [Xe]4f 145d 56s2), name after the European river Rhine. Discovered (1925) by the German chemists W. Noddack, I. Noddack-Tacke and O.C. Berg in minute amounts in a sample of gadolinite (a basic silicate of Be, Fe and lanthanides). Silvery-white metal. Atomic number 75, atomic relative mass 186.207. Occurrence. The Re concentration is extremely low. It is found as minor component in the gadolinite and molybdenite ores. Preparation. Rhenium is extracted commonly as a by-product from molybdenum smelter flue dust. The volatile Re2O7 is collected, converted to NH4ReO7 which is reduced in a stream of hydrogen. Main uses. Re is used as an alloying component with the metals W and Mo which are difficult to work: ductility and strength are improved. Thermocouples made of Re–W are used for measuring temperatures up to 2200°C. Rhenium catalysts are exceptionally resistant to poisoning from nitrogen, sulphur and phosphorus, and are used for hydrogenation of fine chemicals, hydrocracking, reforming and the disproportionation of alkenes. 5.9.2. The 7th group metals: a summary of their atomic and physical properties Notice the nearly equal values of the molar volumes of Mn, Tc and Re and consequently the strong increase of their density on passing from Mn to Re. Rhenium has the second highest melting point of all metals. When annealed, it is very ductile, then it can be coiled, rolled, etc. Atomic and physical properties of Mn, Tc and Re are collected in Table 5.36–5.38. 5.9.3 The 7th group metals: remarks about their general chemical properties and reactivity Manganese is reactive when pure, it burns in O2; it dissolves in dilute acids. Roughly similar to iron in several physical and chemical properties, but harder, more brittle and less refractory. At elevated temperatures it reacts violently with several non-metals. The MnII is the most stable state, readily oxidized in alkaline solutions. The highest oxidation state is VII (corresponding to the total number of 3d and 4s electrons). Technetium and rhenium differ markedly from manganese, but they are very similar to each other. They have little cationic chemistry, few compounds in the oxidation state II, more extensive chemistry in the IV and V states. The metals resemble Pt in their appearance (usually, however, they are in the form of a grey powder); they tarnish slowly in moist air, do not react with water. Metal dust is a fire and explosion hazard.

424

Intermetallic Chemistry Table 5.36. Mn, Tc, Re: selected physical properties. Property r/pm, metallic, CN 12 [‘metallic valence’] Ionic radius/pm M2, CN 6 Ionic radius/pm M3, CN 6 Ionic radius/pm M4, CN 6 Ionic radius/pm M5, Ionic radius/pm M6, Ionic radius/pm M7, CN 6 Tmelting/°C Tboiling/°C ΔH melting (at Tmelting)/kJ/mol ΔfH0 of Me1 gas at 298.15 K/kJ/mol

Mn

Tc

Re

130.7 [5] 125.4 [7] 67–83 58–64.5 53 33 CN 4 25.5 CN 4 46 1246 2062 12.1 283

136.5 [7]

137.5 [7]

– – 64.5 60 CN 6 – 56 2155 4265 – –

0.63 0.58 CN 6 0.55 CN 6 0.53 3186 5596 – –

Table 5.37. Mn, Tc, Re: ionization energies. Element Mn Tc Re

1st ionization energy/kJ/mol 717 702 760

2nd ionization 3rd ionization energy/kJ/mol energy/kJ/mol 1509 1472 1260

3248 2850 2510

… … …

7th ionization energy/kJ/mol

8th ionization energy/kJ/mol

11508 – –

18900 – –

Table 5.38. Mn, Tc, Re: crystal structures, lattice parameters of their allotropes and calculated densities. Element (allotrope) Temperature Range/°C

Crystal structure

Lattice parameters/ pm a

αMn βMn γMn δMn Tc Re

Manganese 727° 727° to 1100° 1100° to 1138° 1138° to 1246° Technetium 2155° Rhenium 3186°

Atomic volume/ pm3 106

Molar volume/ cm3/mol

Density/ g/cm3

12.21 12.59 14.38 14.61

7.35 7.58 8.67 8.80

7.47 7.24 – –

c

cI58-αMn cP20-βMn cF4-Cu cI2-W

891.26 631.52 386.0 308.0

hP2-Mg

273.8

439.3

14.26

8.59

11.40

hP2-Mg

276.09

445.8

14.71

8.86

21.02

425

Elements of Alloying Behaviour Systematics

5.9.4 Intermetallic chemistry of the 7th group metals 5.9.4.1 Phase diagrams of the 7th group metals. A summary of the phase diagram types given with the different elements by Mn, Tc and Re with special reference to their compound formation capability is shown in Fig. 5.24. For Mn, we may notice a close similarity between its main pattern and those shown in the precedent groups by V and Cr (that is by a series of metals pertaining to the first row of the transition metals) and, in the following column, by Fe. Notice, however, unlike V and Cr, the appearance for Mn (and Fe) of compounds with the lanthanides and the actinides. Tc and Re form three families of compounds, with the early transition metals, with p-block elements and with f-block metals, respectively. An indication of the trend of the solid phase stability in the alloys of Mn and Re with the different elements of the 4th and 6th rows of the Periodic Table is contained in Table 5.39, where the melting points of selected compounds have been collected. In the Mn series alloys we may notice, here too, the ‘gaps’ in the pattern of the compound formation. In the case of Re alloys, very high melting points are observed in the compounds with other refractory metals (even if often IR 1). 5.9.4.2 Remarks on the alloy crystal chemistry of the 7th group metals. A short list of phases, and corresponding structural prototypes, formed in the alloys of Mn, Tc and Re is shown in Table 5.40. We may underline the formation in the terminal regions of the various systems of phases having high stoichiometric ratios, such as, for instance, in the Mn-rich region the ThMn12 and Th6Mn23 types and, at the other side, the MnAl6, ZrZn22 and Mn types.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Mn

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Tc

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Re

Compound-forming element

Phase diagram known; no intermediate phases formed

No information available

Questionable compound forming capability

Figure 5.24. Compound formation capability in the binary alloys of Mn, Tc, Re.

Table 5.39. Highest melting points (°C) in the alloys of Mn and Re with compound-forming elements of the 4th and 6th rows of the Periodic Table. Compare with Fig. 5.24. For the meaning of the symbols, see the introduction. Alloys with Sc

Manganese compounds

Rhenium compounds Sc5Re24, 2570°, p, IR 1

ScMn2 La

Immisc. monotectic s.s. TiMn2, 1325°, IR1

Ti

s.s. HfMn2, 62–76 at.% Mn 1730°, IR 1

Hf V

Cont.s.s. (V,δMn) σ, s.s.r. Ta

Cr

Compl. immisc. Ti5Re4 2760°, p, IR 1

TaMn2, 1600°

σ, 23–26 at.% V 2460°, p, IR 1

σ, 22–27 at.% Cr 1312°, p, IR 1

σ, 32–44 at.% Cr 2362°, p, IR 1

–

σ, 48–50 at.% Mn 2300°, p

W Mn

σ, 50–52 at.% Re 2300°, p

Re Fe

Cont.s.s. (γFe,γMn) Os

s.s. HfRe2, 3160°, IR 1 χ, 20–35 at.% Ta 2800°, IR 1 σ, 29–57 at.% W 3000°, p, IR 1

– ε 1600° Cont.s.s. (Re,Os)

σ, 49.5–50.5 at.% Co 745°, s.s.r.

Co Ir Ni

Continuous s.s. (Re,εCo) s.s. MnIr

Cont.s.s. (γMn,Ni) complex s.s.r.

(Re), (Ni) Simple peritectic β, 33–59 at.% Pt 1500°, IR1

Pt Cu

Cont.s.s. (γMn,Cu) Au β 30–50 at.% Zn 850°, p, IR1

Zn Hg

ε, 24–36 at.% Ga 990°, p, IR 1

Ga Tl

Immisc. monotectic

MnHg, 400°, p, IR 1

Re3Ge7, 1132°, IR 1 Compl. immisc.

Mn2As, 1029°, IR1 Bi

Compl. immisc Compl. immisc.

Compl. immisc.

Pb As

(Re), (Pt) Simple peritectic.

β, 31–67 at.% Au 1260°, IR 1.

Mn5Ge3, 966°, IR 1

Ge

(Re), (Ir) Simple peritectic

compds. MnBi, 446°, p, IR 1

Compl. immisc.

Table 5.40. A selection of intermediate phases in the binary alloys of the 7th group metals (Me). Structure type

CNE (Me)

tI26-ThMn12

12–14

cF116-Th6Mn23

8–13

cF24-Cu2Mg

12

hP12-MgZn2

12

hP2-Mg

12

tP30-σ-CrFe

12–15

cP2-CsCl

14

hP4-NiAs

8

tP4-AuCu

12

hP12-MgZn2 cI58-Mn

16 16

oS28-MnAl6

10

cF184-ZrZn22

Examples of isostructural phases Mn compounds Mn12X: X Y, LnIII (Gd–Tm), Th Mn23X6: X Y, LnIII (Nd–Lu), Th Mn2X: X Y, Ln(Gd–Ho), U, Np, Pu(33–35Pu) Mn2X: X LnIII(Nd–Lu), Th, Ti(30–40Ti), Zr(26–37Zr), Hf (25–38Hf), Nb, Ta

Mn–X: X Al(40–47Al), Ga(24–36Ga) Mn–X: X V, Cr(22–27Cr), Re(50–52Re), Co(50Co)

MnX: X Rh(35–55Rh), Ir, Ni(45–52Ni), Pd(39–66Pd), Au(31–67Au), Zn(50Zn), Hg (50Hg) MnX: X As, Sb(41–49Sb), Bi, Te (43–51Te) Mn–X: X Ir(40–55Ir), Ni(47–56Ni), Pd(47–68Pd), Pt(33–60Pt), Zn(71–75Zn), Ga(28–36Ga) (40–45Ga) (48–56Ga)

MnX6: X Al, Ga,

Tc and Re compounds

Tc2X: X Sc, Y, LnIII(Gd–Lu), Th, Zr, Hf(33Hf) Re2X: X Sc, Y, Ln(Nd–Lu,) Th, U, Np, Pu, Zr, Hf(33–38Hf), V(28–32V)

Tc–X: X Cr(25–40Cr), Mo(25–35Mo), W(22–40W), Fe(34–85Fe) Re–X: X Nb(46–47Nb), Cr(32–44Cr), Mo(30–47Mo), W(29–57W), Ta(45Ta), Mn(48–51Mn), Fe(60Fe) TcX: X Ti( 50Ti), Hf

ReX2: X Be(60–70Be) Tc–X: X Sc(13.5Sc), Zr(14Zr), Hf(13.5Hf), Nb(25Nb), Ta(17Ta) Re–X: X Sc(17Sc), Ti(17Ti), Zr(17Zr), Nb(13–39Nb), Ta(20–37Ta), Mo(21–25Mo), W(26–27W) TcX6: X Al ReX6: X Al TcX22: X Be ReX22: X Be

Elements of Alloying Behaviour Systematics

429

5.10. ALLOYS OF THE METALS OF THE 8TH, 9TH AND 10TH GROUPS OF THE PERIODIC TABLE

Iron, Fe; ruthenium, Ru; osmium, Os; cobalt, Co; rhodium, Rh; iridium, Ir; nickel, Ni; palladium, Pd; platinum, Pt

5.10.1 Introduction The elements pertaining to these different columns of the Periodic Table are the following: 8th group: iron, ruthenium and osmium 9th group: cobalt, rhodium and iridium 10th group: nickel, palladium and platinum On the basis of their behaviour and of their applications, however, it may be useful to describe these metals subdividing them into two ‘families’: iron family and platinum family. 5.10.1.1 Metals of the iron family. These metals pertain to the 1st transition row. Iron (Fe, [Ar]3d 64s2), name from the Anglo-Saxon iron, symbol from the Latin name ferrum (iron). The use of iron dates back to prehistoric times. Reddish grey, solid metal. Atomic number 26, atomic relative mass 55.847. Occurrence. Iron is highly abundant (about 5.5% of the earth’s crust); it is believed that the core of earth is mostly molten iron together with nickel. The most common ore is haematite (Fe2O3). Iron is found in other minerals such as magnetite, limonite, siderite, pyrite. Iron is found native in meteorites known as siderites. Preparation. See in the following. (§ 5.10.4.5) Cobalt (Co, [Ar]3d 74s2), name from the German word kobold (evil spirit). Isolated (1735) by the Swedish chemist Georg Brandt. Bluish silvery, solid, hard, brittle metal. Atomic number 27, atomic relative mass 58.93320.

430

Intermetallic Chemistry

Occurrence. There are a number of important ores containing cobalt. These include linnaeite, Co3S4, cobaltite, CoAsS, and smaltite, CoAs2. Preparation. Industrially, cobalt is normally produced as a by-product from the production of copper, nickel and lead. The ore is roasted to form a mixture of metals and metal oxides. Treatment with sulphuric acid leaves metallic copper as a residue and dissolves out iron, cobalt and nickel as the sulphates. Iron is separated by precipitation with lime (CaO) while cobalt is produced as the hydroxide by precipitation with sodium hypochlorite. The trihydroxide Co(OH)3 is heated to form the oxide and then reduced with carbon (as charcoal) to form cobalt metal. Nickel (Ni, [Ar]3d84s2), name after the German kupfernickel (false copper). Discovered (1751) by the Swedish chemist Axel F. Cronstedt. Silvery white metal. Atomic number 28, atomic relative mass 58.69. Occurrence. Important commercial ores of Ni are sulphides (such as pentlandite (Ni,Fe)9S8) generally associated with Cu, Co and precious metals and oxide/silicate ores (as (Ni,Mg)6Si4O10(OH)8 and (Fe,Ni)O(OH)nH2O). It is also found in combination with As and Sb (as NiAs or in deposits consisting of NiSb, NiAs2, etc.). It is also present as Fe alloys in several meteorites and probably in the core of the earth. Preparation. High purity nickel can be produced through electrolytic process or by the carbonyl process. In the latter case carbon monoxide reacts at 50°C with impure Ni (or nickel–copper matte) to give the volatile tetracarbonyl from which the metal (99.9–99.99% purity) is obtained by decomposition at 200–230°C through the reaction: Ni 4 CO N Ni(CO)4 5.10.1.2 Metals of the platinum family. These metals pertain to the 2nd and 3rd transition rows. They represent, together with silver and gold, the metals also known with the common name of noble metals. Ruthenium (Ru, [Kr]4d 75s1), name and symbol from the Latin word Ruthenia (Russia). Discovered (1844) by the Russian chemist Karl K. Klaus. Bluish silvery, solid, hard, brittle metal. Atomic number 44, atomic relative mass 101.07. Occurrence. In Pt ores. Osmium (Os, [Xe 4f 14]5d 66s2), name from the Greek o´σμη´ (osme, smell). Powdered Os slowly gives off OsO4 toxic and with a strong smell. Discovered with

Elements of Alloying Behaviour Systematics

431

iridium (1803) by the English chemist Smithson Tennant in the residue left when crude Pt is dissolved by aqua regia. Bluish silvery, solid, hard, metal. Atomic number 76, atomic relative mass 190.2. Occurrence. In Pt-bearing river sands. Rhodium (Rh, [Kr]4d 85s1), name from the Greek ρo´δoν (rhodon: rose). Discovered (1803) by the English chemist William Hyde Wollaston. Silvery, solid metal. Atomic number 45, atomic relative mass 102.90550. Occurrence. Found in some deposits of Ni and Cu. Iridium (Ir, [Xe 4f 14]5d 9), name from the Latin word iris (rainbow: iridium compounds are highly coloured). Discovered (1803) by the English chemist Smithson Tennant. Silvery white, solid metal. Atomic number 77, atomic relative mass 192.22. Occurrence. In platinum ores as a by-product of Ni mining. Palladium (Pd, [Kr]4d10), name and symbol from the asteroid Pallas. Discovered (1803) by the English chemist William Hyde Wollaston. Silvery white, soft metal. Atomic number 46, atomic relative mass 106.42. Occurrence. Generally included in deposits of Pt, Ni, Cu, Ag, Au. Platinum (Pt, [Xe 4f 14]5d 96s1), name from the Spanish platina (silver). Known and used by the pre-Columbian South-American Indians since ancient times. Re-discovered and noticed by the Western scientists in 1735 (Antonio de Ulloa). Silvery, white solid, ductile and malleable metal. Atomic number 78, atomic relative mass 195.08. Occurrence. It occurs in its native form (Urals, Canada, Colombia, Peru) and can also be obtained as a by-product of Ni and Cu refining. 5.10.1.3 Platinum family metals preparation. The platinum metals (with gold and silver) are commonly found together, and a number of schemes are in current use for their separation. Platinum metals not only are extracted from ores but, due to their high value, are also recovered from a wide range of industrial residues such as Pt, Rh gauze catalysts, defective components from glass industries, etc. The first step in the preparation of Pt-group metals is the dissolution of the raw materials (primary deposits, ores, metal scraps, supported catalysts, etc.). According to the characteristics of their content in the different mixed noble metals, different dissolution methods are used. Typical processes are dissolution in

432

Intermetallic Chemistry

aqua regia, in HCl Cl2, or HCl Br2, or in molten salts (for instance KHSO4 or KOH KNO3). The subsequent treatment involves separation processes which are generally followed by purification stages. The separation process depends on the composition of the raw material and may change frequently, especially in the recovery of secondary metals. These processes make use of various combinations of precipitation, crystallization, solvent extraction and distillation. Several methods are employed for the purification of the single platinum metal salts, for instance re-crystallization of Na2[Pt(Cl)6] with oxidative hydrolysis of the impurities of Pd, Rh, Ir, etc. which together with base-heavy metals are removed as insoluble hydroxides. Generally the metals are obtained, initially as sponge or powder, by conversion of their salts through thermal decomposition or by reduction of aqueous solutions of the ammonium–chloro complexes. Os which has been oxidized to the volatile OsO4 and Ru have to be reduced by H2. 5.10.2 The metals of the 8th, 9th and 10th groups: a summary of their atomic and physical properties See Tables 5.41–5.45. 5.10.3 The metals of the 8th, 9th and 10th groups: remarks about their general chemical properties and reactivity Iron family metals Iron. Iron dissolves readily in dilute mineral acids giving, in absence of air and oxidizing agents, FeII. With air, or dilute HNO3, FeIII is formed. In the presence of air and water, iron rusts and gives hydrated FeIII oxides. Strongly oxidizing media (concentrated HNO3) passivate iron. Iron highest oxidation state is VI (FeO 42); it is rare and stable in strong alkali solution. Table 5.41. Fe, Co, Ni: selected physical properties. Property

Fe

Co

Ni

r/pm, metallic, CN 12 [‘metallic valence’] r/pm, ionic, M2, CN 6 r/pm, ionic, M3 CN 6 r/pm, ionic, M4 CN 6 r/pm, ionic, M6 CN 4 Tmelting/°C Tboiling/°C ΔHmelting (at Tmelting)/kJ/mol ΔfH0 of Me1 gas at 298.15 K/kJ/mol

127.4 [8] 61–78 64.5–55 585 25 1538 2862 13.8 415

125.2 [9] 65–74.5 54.5–61 53 – 1495 2928 16.2 427

124.6 [10] 69 56–60 48 – 1455 2914 17.15 430

433

Elements of Alloying Behaviour Systematics

Cobalt. Appreciably less reactive than Fe. It is stable, unless heated, to atmospheric oxygen. It is oxidized first to Co3O4 and then (above 900°C) to CoO. It dissolves slowly in diluted mineral acids (giving CoII), it reacts on heating with steam, the halogens and several non-metals (B, C, P, As, S). Nickel. It tarnishes when heated in air; finely divided Ni is pyrophoric. It reacts on heating with B, Si, P, S, the halogens and it is oxidized by steam. It may be dissolved in diluted mineral acid (rapidly in diluted HNO3; it is passivated however by Table 5.42. Fe, Co, Ni: crystal structures, lattice parameters of their allotropes and calculated densities. Element (allotrope) Temperature range/ºC Pressure GPa αFe γFe δFe εFe εCo αCo Ni

Iron 912° 912°C to 1394° 1394°C to 1538° HP 13 GPa Cobalt 422° 422° to 1495° Nickel 1455°

Crystal structure

Lattice parameters/ pm a

Atomic volume/ pm3 106

Molar volume/ cm3/mol

Density g/cm3

11.78 12.12 12.60

7.09 7.30 7.59

7.87 7.65 7.59

11.07 11.13

6.67 6.70

8.84 8.79

10.94

6.59

8.92

c

cI2-W cF4-Cu cI2-W hP2-Mg

286.65 364.67 293.15 246.8

hP2-Mg cF4-Cu

250.71 354.47

cF4-Cu

352.40

396 406.86

Table 5.43. Platinum family metals: selected physical properties. Property r/pm, metallic, CN 12 [‘metallic valence’] r/pm, ionic, M2, CN 6 r/pm, ionic, M3, CN 6 r/pm, ionic, M4, CN 6 r/pm, ionic, M5, CN 6 r/pm, ionic, M7 r/pm, ionic, M8 Tmelting/°C Tboiling/°C ΔHmelting(at Tmelting)/kJ/mol

Ru

Rh

Pd

133.9 [8]

134.5 [9]

68 62 56.5 38, CN 4 36, CN 4 2334 4150 25

66.5 60 55

137.6 [10] 86 76 61.5

1963 3697 21.5

1555 2964 17.6

Os

Ir

Pt

135.3 [8]

135.7 [9]

138.7 [10] 80

63 57.5 54.5 52.5, CN 6 39, CN 4 3033 5012 31.8

82 76.5 71

62.5 57

2447 4428 26.4

1769 3827 19.7

434

Intermetallic Chemistry

Table 5.44. Fe, Ru, Os, Co, Rh, Ir and Ni, Pd, Pt: ionization energies.

Iron Ruthenium Osmium

Cobalt Rhodium Iridium

Nickel Palladium Platinum

1st ionization energy/ kJ/mol

2nd ionization energy/ kJ/mol

3rd ionization energy/ kJ/mol

760 711 840

1561 1617 1600

2957 2747 –

1st ionization energy/ kJ/mol

2nd ionization energy/ kJ/mol

3rd ionization energy/ kJ/mol

758 720 880

1646 1744 –

3232 2997 –

1st ionization energy /kJ/mol

2nd ionization energy/ kJ/mol

3rd ionization energy/ kJ/mol

737 805 870

1753 1875 1790

3393 3177 –

… … …

… … …

… … …

8th ionization energy/ kJ/mol

9th ionization energy/ kJ/mol

14575 – –

22678 – –

9th ionization energy/ kJ/mol

10th ionization energy/ kJ/mol

17960 – –

26600 – –

10th ionization energy/ kJ/mol

11th ionization energy/ kJ/mol

21700 – –

– – –

concentrated HNO3). It is very resistant to the corrosion by aqueous caustic alkalis. It reacts with several non-metals such as B, C, P, As, Sb, S, Se, Te. Platinum family metals Ruthenium and osmium. The normal chemistry of Ru and Os shows little resemblance to that of iron (the first element in the same 8th column of the Periodic Table) except in some salt compounds, such as sulphides, phosphides, etc. High oxidation states (up to V, VI, VII, VIII) are much more easily obtained that for iron. Ru and Os are very corrosion resistant, are unaffected by non-oxidizing acids and also by aqua regia. Os is oxidized to the volatile OsO4 in air or oxygen above 200°C or converted to OsO4 by concentrated HNO3. Both ruthenium and osmium may be dissolved in molten alkali especially in oxidizing fluxes such as Na2O2 or KClO4. Ru is stable to atmospheric attack; very finely divided Os gives off the typical smell of the volatile OsO4. Rhodium and iridium. They react slowly (at red heat) with oxygen and halogens. Their high inertness to acids (even aqua regia) is characteristic. Dissolution of Rh

435

Elements of Alloying Behaviour Systematics

Table 5.45. Platinum family metals: crystal structures, lattice parameters and calculated densities. Element Temperature range/ºC Ruthenium 2334° Rhodium Rh 1963° Palladium Pd 1555° Osmium Os 3033° Iridium Ir 2447° Platinum Pt 1769°

Ru

Crystal structure

Lattice parameters pm

Atomic volume/ pm3 106

Molar volume/ cm3/mol

Density g/cm3

13.57

8.17

12.36

a

c

hP2-Mg

270.58

428.16

cF4-Cu

380.32

13.75

8.28

12.42

cF4-Cu

389.03

14.72

8.86

12.00

hP2-Mg

273.41

13.98

8.42

22.59

cF4-Cu

383.92

14.15

8.52

22.56

cF4-Cu

392.36

15.10

9.09

21.45

431.98

may be achieved by fusion with NaHSO4, of Ir by fusion with KOH KNO3 obtaining IrO2 to be treated with aqua regia. Both metals can be dissolved with a mixture of concentrated HCl with NaClO3 at about 150°C in sealed tubes. Palladium and platinum. These are resistant to chemical attack (Pt more than Pd). Both metals dissolve in fused alkali metal oxides and peroxides. Pt is attacked, at high temperature, by molten alkali and alkaline earth halogenides and by several compounds of B, Si, Pb, P, As, Sb, Bi. Pd dissolves slowly in oxidizing acids; Pt is dissolved by aqua regia.

5.10.4 Intermetallic chemistry of the metals of the 8th, 9th and 10th groups: general remarks In order to cast a glance over the intermetallic reactivity of the nine metals of the 8th, 9th and 10th groups, their schemes of compound formation capability have been collected together in Fig. 5.25. However, considering their high number and also their relevance, more details will be reported in the following paragraphs. On the basis of Fig. 5.25, anyhow, a few preliminary points may be remarked and a comparison made with the behaviour of the metals of the precedent column (Mn, Tc, Re). The lack of compounds may be noticed also here in the alloys formed with the s-block metals (of the 2nd and especially 1st groups) and in those given by a number

436

Intermetallic Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Fe

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Ru

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Os

Compound-forming element

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Co

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Rh

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Ir

Phase diagram known; no intermediate phases formed

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Ni

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Pd

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Pt

No information available

Figure 5.25. Compound formation capability in the binary alloys of Fe, Co, Ni and Pt-family metals.

of metals in the central region of the Periodic Table. A somewhat smooth change of the patterns may be noticed in Fig. 5.25, with an increasing number of compoundforming systems, moving right and downwards up to platinum. The iron pattern, however, is not in full agreement with this general scheme and shows a closer resemblance with that of preceding metals, such as Cr and Mn. To complete the general schemes of the stability trend of the solid phases formed by these metal families, Table 5.46 lists the melting points of selected alloys of the metals of these groups. The metals of the 9th group, Co, Rh and Ir, have been considered as representatives of an average behaviour of the 8th, 9th and 10th groups. The maximum melting points observed in their alloys with the various elements of two rows (the 4th row, that is the 1st long period and the 6th row) of the Periodic Table are reported in this Table.

Table 5.46. The highest melting points (°C) observed in the alloys of the central elements of the iron and platinum metals families (that is of Co, Rh, Ir) with compound-forming elements of the 4th and 6th rows of the Periodic Table. Alloys with Ca

Cobalt compounds Immiscibility

Ba

La s.s. TiCo 1325°, IR 1

Ti

LaCo13, 1275°, p, IR 1

s.s. HfCo2 1670°, IR 1

Hf σ, 45–71 at.% V 1422°, p, IR 1

V

Ta2Co 1800°, p, IR 1

Ta σ, 54–67 at.% Cr 1283°, s.s.r.

Cr W

σ, 50–51 at.% Cr 545° s.s.r.

Mn Re

Iridium compounds

Compds No compds.

s.s. ScCo2, 1520°, IR1

Sc

Rhodium compounds

s.s. W6Co7 1690°, p, IR 1 Cont. s.s. (Re,εCo)

s.s. ScRh 47–56 at.% Sc, 1990°, IR 1 s.s. TiRh 42–62 at.% Ti, 1940°, IR 1

s.s. VRh3 22–35 at.% V, 1740°, p, IR 1

ε, 18–68 at.% Cr, 1700°, p, IR 1 β, 45–65 at.% Mn, 1200°

Compds. Compds. s.s. ScIr2 2150°, IR 1 Compds. 1600°

s.s. HfRh, 38–52 at.% Hf, 2180°, IR 1

s.s. TaRh3 22–31 at.% Ta, 2125°, IR 1 ε, 19–58 at.% W, 2250°, IR 1 No compds. Simple peritectic

LaIr2, 2520°, IR 1 s.s. TiIr, 43–65 at.% Ti, 2130°, IR 1

s.s. HfIr3 2470°, IR 1

s.s. VIr3, 23–39 at.% V, 2100°, p, IR 1

s.s. Ta3Ir, 59–89 at.% Ta, 2480°, p, IR 1 ε, 30–68 at.% Cr, 2200°, p, IR 1 σ, 74–78 at.% W, 2540°, p, IR 1 Compds., s.s.r. No compds. Simple peritectic (Continued)

Table 5.46. (Continued) Alloys with Fe Os

Cobalt compounds Cont. s.s. (γFe,αCo) Compd. s.s.r. Cont. s.s. (Os,ε Co)

Co

Rhodium compounds Cont. s.s. (γFe,Rh), Ordering s.s.r.

Cont. s.s. (γFe,Ir) Ordering s.s.r. No compds. Simple peritectic

Cont. s.s. (Rh,α Co) Ir

Ni

Cont. s.s. (α Co,Ir) De-mix. s.s. Cont. s.s. (αCo,Ni)

Pt Cu Au Zn Hg Ga Tl Ge Pb As Bi

Cont s.s. (Rh,Ir) De-mix. s.s.

Cont. s.s. (αCo,Pt) Ordering.s.s.r.

β, 48–51 at.% Zn, 966°, p, IR 1 Complete immisc. β, 29–64, at.%Ga, 1210°, p, IR 1 No compds. s.s. Co5Ge3, 1210°, IR 1 Compl. sol. and liq. immisc CoAs, 1180°, IR 1 Complete immisc

– Cont. s.s. (Ni,Ir)

Cont. s.s. (Pt,Rh) De-mix. s.s. Cont. s.s. (Rh,Cu) De-mix. s.s.

No comps. Simple eutectic

No compds. Simple peritectic Cont. s.s. (αCo,Ir), De-mix s.s.

Cont. s.s. (Rh,Ni), De-mix. s.s.

No compds. Simple peritectic

Iridium compounds

Cont s.s. (Ir,Pt), De-mix. s.s. No compds. Simple peritectic

Monotectic

No compds. Liq. immisc.

Rh5Zn21 500°, IR 1 RhHg5, 560°, p

Complete immisc.

Compds.

Compds.

Rh2Ge, 1500°

Compds. RhPb4, 200°, p

Compds. s.s. RhBi, 52–55 at.% Bi, 997°, p, IR 1

IrPb IrAs3, 1000–1200°, p Ir2Bi 1440°, p, IR 1

Elements of Alloying Behaviour Systematics

439

As previously discussed in § 5.5.7.2, the compounds formed by the platinum family metals with the metals of the 3rd and 4th group exhibit relatively high thermal stability (high melting points in comparison with those of the metals themselves: IR 1). Typical melting points attributed to the alloys of the lanthanides and actinides are for instance YNi5: 1430°C, UNi5: 1305°C, PuNi5: 1300°C, YIr2: 2500°C, UIr3: 2000°C. 5.10.4.1 Phase diagrams of the iron family metals. Owing to the great relevance of its applications, several aspects of the iron alloying behaviour have been systematically and thoroughly studied. A first point to underline is that no stable carbides are formed in the carbon alloys of iron and of other metals of these groups. The stable and metastable Fe–C phase diagrams are shown in Fig. 5.29. The metastable Fe3C compound is known also with the current name cementite. Many other current names have been assigned to various (both single phase and complex) Fe–C alloys; a partial list of these names is given in § 5.10.4.5. Owing to the existence of different allotropic transformations of solid iron, a certain complexity may be noticed in the Fe-rich side of the diagram; the formation of C solid solutions takes place in the different forms of Fe. The transformation temperatures of the different iron forms may, of course, be changed also by the addition and dissolution of other elements. Fig. 5.26 schematically shows different aspects which may be observed in the Fe-rich region of various Fe–X diagrams and the relative extensions of the composition and temperature ranges of stability of the different terminal solid solutions. It may be especially useful, in view also of possible technological applications, to distinguish between elements which extend the stability ranges of the α or of the γ phases (alphaforming and gamma-forming elements). In Fig. 5.27 a summary of this kind of classification of the different elements is given with reference to their position in the Periodic Table. 5.10.4.2 Phase diagrams of the platinum family metals. Among the various alloys formed by the metals of these groups we may underline the particular behaviour shown by a number of inter-transition metal alloys. The role of the valence electron concentration (or of the ‘average group number’) has been evidenced in § 4.4.6, where, following Brewer, phase equilibria in binary and ternary systems (containing elements such as Cr, Mo, Ta, W, Re, Os, Ir, Pt) were summarized by using special multi-diagrams. The formation of several solid solution regions corresponding to χ, σ, etc. phases has been underlined. 5.10.4.3 Remarks on the alloys crystal chemistry of the metals of the 8th, 9th and 10th groups. A selection of intermediate phases formed in the alloys of the

440

Temperature (°C)

Intermetallic Chemistry

1538

1538

1538

1394

1394

1394

(γ Fe)

(γ Fe)

912

(γ Fe)

912

10

Fe at.% Ge

912

Fe

10

20

10

Fe

20

20

at .% Ru

at .% Cr

2447

2400

Temperature (°C)

40

2000

1538 1394

(γ Fe, Ir)

1200 912 800

400

(αFe)

Fe

10

20

30

40

50

at .% Ir

60

70

80

90

Ir

Figure 5.26. Iron binary alloys. Examples of the effects produced by the addition of different metals on the stability of the γFe (cF4-Cu type) field are shown. In the Fe–Ge and Fe–Cr systems the γ field forms a closed loop surrounded by the α–γ two-phase field and, around it, by the α field. Notice in the Fe–Cr diagram a minimum in the α–γ transformation temperature. The iron-rich region of the Fe–Ru diagram shows a different behaviour: the γ field is bounded by several, mutually intersecting, two (and three) phase equilibria. The Fe–Ir alloys are characterized, in certain temperature ranges, by the formation of a continuous fcc solid solution between Ir and γFe. Compare with Fig. 5.27 where an indication is given of the effects produced by the different elements of the Periodic Table on the stability and extension of the γFe field.

metals of the groups 8–10 and of their structure prototypes is shown in Tables 5.47 and 5.48a, 5.48b and 5.48c. On the basis of the general alloying behaviour of these metals and the belonging of their compounds to various families of prototypes, different tables have been prepared: in the first one (Table 5.47) the alloys of the Fe family metals (Fe, Co, Ni) are shown; in the following three Tables the alloys of the Pt-family metals are listed (Ru and Os in Table 5.48a, Rh and Ir in Table 5.48b and Pd and Pt in Table 5.48c).

441

Elements of Alloying Behaviour Systematics

H Li

He Be

B

C

N

O

F

Ne

Na Mg

Al

Si

P

S

Cl

Ar

K

Ca

Sc

Ti

Rb

Sr

Y

Cs

Ba

La

Fr

Ra

Ac

V

Cr

Mn

Fe

Co

Ni

Cu

Zn

Ga Ge

As

Se

Br

Kr

Zr

Nb Mo

Tc

Ru

Rh Pd

Ag

Cd

In

Sn

Sb

Te

I

Xe

Hf

Ta

W

Re

Os

Ir

Au

Hg

Tl

Pb

Bi

Po

At

Rn

Ce

Pr

Nd Pm Sm Eu

Gd

Tb

Dy

Ho

Er

Tm Yb

Lu

Th

Pa

U

Pu Am Cm Bk

Cf

Es

Fm Md No

Lr

Np

Pt

γ field continuous between Fe and the other metal γ field enclosed within the α region γ field bounded by a number of two-phase equilibria (appreciable solubility in γ ) γ field bounded by a number of two-phase equilibria (negligible solubility in γ )

Figure 5.27. Iron alloy binary systems. Position in the Periodic Table of the alpha-forming and gamma-forming elements in iron alloys.

Fe, Co and Ni alloys. In the selected lists of compounds there are several analogies (existence of isostructural phases) among these three metals. In the Fe-metal-rich regions mainly of the systems with lanthanides and actinides, several phases are formed with high stoichiometric ratios and high coordination numbers (corresponding to 2:17, 1:5, etc. formulae). The structure schemes shown in Fig. 5.28, according to Yamamoto et al. (1997), give additional information about these phases and the complex features of the terminal regions of the phase diagrams. All these structures, observed in the alloys of various metals of these groups (also of some Pt-family metals), may be described as recombination, in different compositional

Table 5.47. Alloys of the iron metal family: Fe, Co and Ni. Structure type

CNE (Me)

Examples of isostructural phases Fe compounds

Co compounds

Ni compounds

hP38-Th2Ni17

12–14

Fe17X2: X Y, LnIII (Ce, Sm–Tm), Yb, Lu(9–11Lu)

Co17X2: X Y(10–11Y), Ce, Gd, Tb, Ho, Er, Yb, Lu(8–12Lu), Pu

hR57-Th2Zn17

12–14

Fe17X2: X Y, LnIII(Ce–Sm), Tb, Th

Co17X2: X Y(10–11Y), Ce, Pr, Nd, Sm(10–13Sm), Gd, Tb, Dy, Ho, Th

hP6-CaCu5

12

Fe5X: X Th

Co5X: X Y, LnIII(La–Er), Th

Ni5X: X Ca, Sc, Y, La(16–18 La), Ln(Ce–Lu) ,Th, Pu

cF116-Th6Mn23 hP36-Ce2Ni7 hR54-Er2Co7

8–13 12 12

Fe23X6: X Y, Ln(Gd–Lu), Zr

Co7X2: X La, Th Co7X2: X LnIII(Sm–Tm), Lu, Th

Ni7X2: X Sc, La, LnIII(Pr–Dy), Th Ni7X2: X Ca, Y, La, Pr, Nd, Sm, LnIII(Tb–Er), Th

hR36-NbBe3 (or PuNi3)

12

Fe3X: X Y, LnIII(Sm–Lu), Th Co3X: X Y, LnIII(Ce–Tm), Yb, Lu, U, Pu

Ni3X: X Ca, Y, La, LnIII(Pr–Tm), Yb, Pu

cP4-AuCu3*

12

Fe3X: X Pt(16–33Pt)(*), Ga(26–29Ga) Ge(24–26Ge)

Ni3X: X Mn(15–29Mn), Fe(11– 37Fe), Pt(25Pt), Ga(23–30Ga), Si(23–25Si), Ge(22–25Ge)

cF24-Cu2Mg §

12

Fe2X: X Sc(36Sc), Y, LnIII (Ce, Sm–Lu), U, Np, Pu, Zr, Hf

hP12-MgZn2 §

12

Fe2X: X Sc, Eu, Mo, Nb(34–37Nb), Ti(28–35Ti), Hf(25–33Hf), Ta(26–37Ta)

oS8-CrB

17

tP30-σ-CrFe

12–15

Co2X: X Sc, Y, LnIII(Ce–Lu), Yb, U(27–33U), Np, Pu, Ti(33–34Ti), Zr(27–35Zr), Hf, Nb(27–33Nb), Ta(30–36Ta)

Ni17X2: X Y, Ln(Nd–Lu), Th, Pu

Ni2X: X Ca, Sc(28–36Sc),Y, LnIII(Ce–Lu), Yb, Np, Pu, Am

NiX: X LnIII(La–Tb), Pu, Zr, Hf, B Fe–X: X V(32–67V), Mo(43–57Mo), Tc(15–66Tc), Re(40Re)

Co–X: X V(45–71V), Mo(62–65Mo), Mn(49–51Mn)

Ni–X: X V(58–75V)

hR39-W6Fe7 (μ-phase)

12–16

Fe–X: X Nb(48Nb), Ta(51Ta), Co–X: X Nb(50–53Nb), Mo(39–44Mo), W(41–45W) Ta(44–56Ta), Mo(42–50Mo), W(43–49W)

Ni–X: X Nb(50–55Nb), Ta(50–54Ta)

hP4-NiAs

8

Fe–X: X Ge(34–41Ge), Sb(40–47Sb), S (50–55S), Se(50–58Se), Te (59–65Te)

Co–X: X Sn(37–42Sn), Sb (43–53Sb), Se(51Se), Te(55–65Te)

Ni–X: X Ga(35–41Ga), Ge(40–45Ge) (37–38Ge), Sn(39–43Sn), As(50–51As), Sb(43–52Sb), Bi(45–49Bi), S(50–53S), Se(51–57Se), Te(51–67Te)

cP2-CsCl

14

FeX: X Ti(50–53Ti, Rh (11–54Rh) Rh (48–55Rh), Al(23–55Al), Ga (32–48Ga), Si(10–22Si), Ge(10–22Ge)

CoX: X Be(46–75Be), Sc( 48Sc), Ti(45–51Ti), Zr, Hf(49–51Hf), Fe(29–75Fe), Al(20–54Al), Ga(29–64Ga)

NiX: X Be(48–75Be), Sc( 54Sc), Ti(43–51Ti), Mn(48–55Mn), Zn(47–58Zn), Al(31–58Al), Ga(30–58Ga), In(49–59In)

hP22-Ho4Co3 cP4-AuCu3*

8–9 12

oP16-Fe3C**

11

FeX3: X Ni(63–89Ni), Pd(62–85Pd), Pt(57–79Pt)

Co3X4: X Y, Gd, Ho, Tm, Lu

CoX3: X Y, La, LnIII (Pr–Er), Lu

NiX3: X Y, La, LnIII(Pr–Tm), Al

* Notice that the cP4-AuCu3-type structure is observed for the two phases having compositions close to Fe3Pt and FePt3, respectively. ** Co3B and Ni3B have the oP16-Fe3C type structure. § In the Fe–Be alloys the Laves structures are observed for Be-rich alloys: Cu2Mg type for the δ phase (82–93Be) and MgZn2 type for the ζ phase (63–89Be).

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Intermetallic Chemistry

Table 5.48a. A selection of intermediate phases in the binary alloys of the Ru and Os compounds. Structure type

CNE (Me)

Examples of isostructural phases Ru compounds

Os compounds

hP20-Th7Fe3* hP12-MgZn2 §

15 12

Ru7X3: X B(30–38B) Ru2X: X Sc(33–40Sc), Y, Ln(Gd–Lu), Np, Zr(32–34Zr)

Os2X: X Sc, La, LnIII(Nd–Lu), Yb, Np, Pu, Am, Zr, Hf(32–36Hf)

cF24-Cu2Mg

12

Ru2X: X LnIII(La–Gd), Th, Pu(33–34Pu), Ti(47–55Ti)

Os2X: X Y, Ce, Pr, Th, U(32–34U)

cP2-CsCl

14

RuX: X Sc(50–60Sc), Yb, Lu, Pu, Zr(48–52Zr), Hf(49–53Hf), V(45–75V), Nb(42–59Nb), Ta(38–75Ta), Al(50Al), Ga, Si(47–48Si)

OsX: X Ti(49–62Ti), Zr, Hf(49–53Hf), V(55–80V), Al(50Al)

tP30-σ-CrFe

12–15

Ru-X: X Cr(54–68Cr), Mo(62–63Mo), W(59–67W)

Os–X: X Nb(54–73Nb), Ta(56–78Ta), Cr(65–70Cr), Mo(61–70Mo), W(64–80W)

oP6-FeS2 (marcasite)

6

RuX2: X P, As, Sb, Te

OsX2: X P, As, Sb

cP12-FeS2 (pyrite)

6

RuX2: X S, Se, Te

OsX2: X S, Se, Te

hP20-Th7Fe3*

9

Ru3X7: X Ce(70Ce), Th

mS28-Pd5B2

6

Ru2X5: X Y, La, Ln (Pr–Lu)

cF120-Sc11Ir4

8–14

Ru4X11: X Sc

oP16-Fe3C

11

RuX3: X Y, Ln (La–Tm)

cP8-Cr3Si

12

Os3X7: X Th

III

Os4X11: X Sc III

OsX3: X Y, LnIII (La–Lu) Os–X: X V(50–55V), Nb(71–75Nb), Cr(71–77Cr), Mo(75Mo)

* The Th7Fe3-type structure is observed for a few alloys with the 7:3 and the 3:7 ratios. § The MgZn2-type structure is observed for the RuBe2 and OsBe2 compounds.

ratios, of Cu2Mg- and CaCu5-type fragments, forming an example of heterogeneous structural series in which slabs of one structure type are combined with those of another structure. In several Fe, Co, Ni alloy systems, phases having structures pertaining to the inter-related Laves type and σ and μ types are formed (often homogeneous in certain ranges of compositions). For compositions around 1:1, a number of solid solution phases with the CsCl-type structure and (with semi-metals) with the NiAstype are found.

445

Elements of Alloying Behaviour Systematics

Table 5.48b. A selection of intermediate phases in the binary alloys of the Rh and Ir compounds. Structure type

CNE (Me)

Examples of isostructural phases Rh compounds Rh5X: X Y, Gd, Tb, Dy, Ho, Er, Lu

Ir compounds Ir5X: X La, Pr, Nd, Th

hP6-CaCu5

12

hR36-NbBe3 (or PuNi3)

12

cP4-AuCu3

12

Rh3X: X Sc(15–30Sc), Ce, Th, Pa, U, Np, Am, Cm, Ti(22–27Ti), Zr(18–28Zr), Hf(20–28Hf), V(22–35V), Nb(21–29Nb) Ta(22–31Ta)

Ir3X: X Sc(14–23Sc), Pa, U, Ti(23–27Ti), Zr(19–30Zr), Hf(21–27Hf), V(23–39V), Nb(20–37Nb), Ta(24–34Ta), Mn(65–85Mn)

cF24-Cu2Mg

12

Rh2X: X Ca, Sr, Ba, Y, La, Ce, Pr, Nd(31–33Nd), Sm, Eu(29–35Eu), Gd(31–33Gd), Tb, Dy(32–34Dy), Ho(33–34Ho), Er(30–34Er), Tm, Yb, Lu(33–34Lu), Am

Ir2X: X Ca, Sc(30–35Sc), Y(32–36Y), La, Ce (30–37 Ce), Pr(32–35Pr), Nd(32–35 Nd), Sm, Eu, Gd(33Gd), Tb(32–35Tb), Dy(31–35 Dy), Ho(32–35Ho), Er(32–35Er), Tm(32–35Tm), Yb, Lu(32–34Lu), Th(31–36 Th), U, Np, Pu, Am, Cm

oP12-Co2Si ε hP2-Mg

13 12

Rh2X: X Ta, Si, Ge, Sn, As Rh-X: Rh–Cr(18–68Cr), Rh-W(19–58W)

Ir2X: X Si Ir–X: Ir–Fe(46–81Fe), Ir–W(22–66W), Ir–Cr (30–68Cr)

cP2-CsCl

14

RhX: X Be(50Be), Sc(47–56Sc), Y, LnIII (Sm–Lu), Yb, Ti(48–62Ti), Zr(38–50Zr), Hf(38–52Hf), Mn(45–65Mn), Fe(47–89Fe) (45–52Fe), Mg, Al(48–52Al), Ga, In

IrX: X Sc(48–55Sc), Y, Ho, Er, Tm, Yb, Lu, Ti (43–65Ti), Zr (47–52Zr), Hf (50Hf), Mn, Be (50Be), Al(48–52Al), Ga

hP4-NiAs

8

RhX: X B( 52B), Pb( 40Pb), Bi(52–55Bi), Se, Te

IrX: X Sn, Pb, Sb, Te

tP4-AuCu

12

RhX: X Ti(48–62Ti), V(41–48V)

IrX: X Ti( 40–60Ti), V(41–48V), Nb (47–48Nb), Mn (43–60Mn)

tP30-σ-CrFe

12–15 Rh–X: X Nb(60–71Nb), Ta(60–81Ta)

oP36-Sm5Ge4

9

Rh4X5: X La, Nd, Sm, Gd, Pu

tI140-Y3Rh2

9–11

Rh2X3: X Y, Tb, Dy, Er

Ir3X: X Y, La, Ce, Pr, Nd, Gd

Ir–X: X Nb(59–67Nb), Ta(59–89Ta), Mo( 72Mo), W(74–78W) Ir2X3: X Y, Gd, Tb, Dy, Ho, Er (Continued)

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Intermetallic Chemistry

Table 5.48b. (Continued) Structure type

CNE (Me)

Examples of isostructural phases Rh compounds

Ir compounds Ir3X5: X Y, LnIII(La–Tm), Yb Ir3X5: X Y(62–63Y), Tb, Dy, Ho, Er, Tm, Yb, Lu, Zr, Hf

tP32-Pu5Rh3

8–10

hP16-Mn5Si3

11

Rh3X5: X Gd (63–64Gd), Tb, Dy, Ho, Er, Tm, Lu

hP20-Th7Fe3 mS28-Pd5B2

9 6

Rh3X7: X Y, LnIII (La–Lu), Th

Ir3X7: X La, Ce, Pr, Th Ir2X5: X Y, LnIII(Pr–Lu)

oP16-Fe3C

11

RhX3: X Y, La, LnIII(Pr–Er), Eu,

IrX3: X Y, La, LnIII(Pr–Lu)

cP8-Cr3Si

12

RhX3: X V(61–77V), Nb, Cr(77–78Cr)

IrX3: X Ti(74Ti), V(61– 76V), Nb(71–79Nb), Cr(73–83Cr), Mo(74–78Mo) Ir7X44: X Mg, Sc

cF408-Rh7Mg44 12

Rh7X44: X Mg

Ru and Os alloys. A specimen of structure types observed in the alloys of these metals (very often as solid solution ranges) is shown in Table 5.48a. The formation of Laves-type phases, σ phases and several CsCl-type phases can be underlined. Notice the formation of marcasite and pyrite type compounds with the semimetals and non-metals of the 15th and 16th groups. Rh and Ir alloys. A choice of formulae, composition ranges and structure types observed in selected intermediate phases of the Rh and Ir alloys is shown in Table 5.48b. Notice in the Rh (Ir) regions of the systems, several CaCu5-, AuCu3-, Cu2Mg-type phases and, in the central parts of the diagrams, CsCl-type (and NiAsand AuCu-type) solid solutions phases. Pd and Pt alloys. Several phases, often corresponding to more or less wide composition ranges, belonging to 1:1 types are present. Representatives of the CsCl, AuCu, CrB, FeB, NiAs types are formed with various metals of the different groups; generally a close analogy between the Pd and the Pt compounds may be remarked. In the Pd (Pt) rich regions of the systems several compounds having the CaCu5-, AuCu3-, TiNi3- and Cu2Mg- type structures are formed. As a conclusion, notice for all the nine metals of these groups, the large diffusion of the CsCl-type-based (binary and complex) compounds and the solid solutions formed with metals of various groups. Among these, several aluminides can be of interest, possibly also as additional components in high temperature applications.

Table 5.48c. A selection of intermediate phases in the binary alloys of the Pd and Pt compounds. Structure type

CNE (Me)

Examples of isostructural phases Pd compounds

Pt compounds

hP6-CaCu5

12

Pd5X: X Ca(13–16Ca), Ba

Pt5X: X Ca, Sr, Ba, Ce, La, Nd, Pr, Pu, Am, Cm, Bk, Cf

oP16-Fe3C

14–15

Pd3X: X B, P, Si

Pt3X: X Si

hP16-TiNi3

12

Pd3X: X Np, Th(23–25Th), U(23–25U), Np, Ti, Zr (23–29Zr)

Pt3X: X Np, Hf

cP4-AuCu3*

12

Pd3X: X Sc, Y(21–25Y), La, Ce(24–25Ce), Pr(23–25Pr), Nd(23–35Nd), Sm(23–25Sm), Eu, Gd(21–25Gd), Tb(21–26Tb), Dy(21-25Dy), Ho(20-25Ho), Er(20-25Er), Tm(22–25Tm), Yb(21–25Yb), Lu(22–25Lu), Th(19–22Th), U(18–22U), Np, Pu, Am(21–27Am), Cm, Ti(15–23Ti), Zr, Cr(27–45Cr), Mn(32–36Mn), Fe(15–38Fe), Cu, Au(10–32Au), Sn(24–27Sn), Pb

Pt3X: X Mg(28Mg), Sc, Y, Tb, Dy, Ho, Er(24–25Er), Tm, Yb, Lu, Pu, Ti(19–25Ti), Zr(25–28Zr), Hf(15–23Hf), V, Cr(15–66Cr), Mn(15–37Mn), Fe(21–43Fe), Co, Zn(19–25Zn), Cd, Al (22–32Al), , Ga(24–33Ga), In(24–29In), Pb, Sn

Pd2X: X Ca, Ba

Pt2X: X Li(27–34Li), Na, Ca, Sr, Ba,Y, La, Ce(25–33Ce), Pr(25–33Pr), Nd(25–33Nd), Eu(27–35Eu), Sm(25–33Sm), Gd(24–33Gd), Tb, Dy, Ho, Er, Tm, Yb, Pu(32–34Pu), Am(26–33Am), Cm(25–33Cm)

cF24-Cu2Mg 12

Pt4X3: X LnIII(La–Lu), Yb

hR42-Pu3Pd4 12–14 cP2-CsCl

14

PdX: X Li(59–60Li), Be, PtX: X Be, Sc, Ti(46–54Ti), Zr, Mg(47–53Mg), Ca, Sc(49–51Sc), Hf, Al(44–48Al) Dy, Ho (50–51Ho), Er, Tm, Yb(48–50Yb), Lu, Ti(47–53Ti), Mn(34–61Mn), Cu(53–64Cu), Zn(30–65Zn), Cd(55–63Cd), Al(43–56Al), Ga(50–51Ga), In(39–55In)

tP4-AuCu

12

PdX: X Mg(45Mg), Cr(48–50Cr), Fe(40–52Fe), Mn(32–53Mn), Zn(37–56Zn), Cd(33–55Cd), Hg

Pt–X: X V, Cr(48–52Cr), Mn(40–67Mn), Fe(45–65), Co(26–59Co), Ni(50Ni), Cd(41–51Cd), Hg, Ga(33.3Ga), Zn(32–51Zn)

oS8-CrB

9–17

PdX: X Sr, Ba, La, Ce, Pr, Nd, Sm (50–51Sm), Eu, Gd (50–52Gd), Tb(49–50Tb), Cu

PtX: X La, Ce, Pr, Nd, Th, Pu, U, Np, Zr, Hf (Continued)

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Intermetallic Chemistry

Table 5.48c. (Continued) Structure type

CNE (Me)

Examples of isostructural phases Pd compounds

Pt compounds

oP8-FeB

9–17

PdX: X Tb(49–50Tb), Dy, Ho(50–51Ho), Yb, Th, Pu(50–51Pu), Sn

PtX: X Y, LnIII(Pr–Lu), Yb

hP4-NiAs

8

PdX: X Sn(32–38Sn), Pb(37–39Pb), Sb(50–51Sb), Te(50–54Te)

PtX: X In(39–42), Sn, Pb, Sb, Bi

oP36-Sm5Ge4 9

Pt4X5: X Sr, Y, Ln(Eu–Lu)

hP16-Mn5Si3

11

Pt3X5: X Y, Ln(Gd–Lu), Pu, Zr

cP12-FeS2 pyrite or oP6 marcasite

6

oP12-Co2Si § 10 tI6-MoSi2 14 hP20-Th7Fe3

9

PdX2: X Ti, Zr Hf(67Hf), Bi(65–67Bi) Pd3X7: X LnIII(La–Gd)

PtX2: X P(pyr), As(pyr), Sb(pyr), Bi(pyr), Bi(mar) PtX2: X Sc, Y, Ln(Gd–Lu), Pu

Pt3X7: X Y, LnIII(La–Gd), Th

Pd2X5: X Y, Ln (Tb–Lu) II

cF144-Dy5Pd2 oP16-Fe3C

PdX2: X As(pyr), Sb(pyr), Bi(mar)

11

PdX3: X Ca, Y, Yb

PtX3: X Y, LnIII(Gd–Lu)

* By solid-state ordering, the formation of PdAu3 (68–88Au) and of PdCu3 (78–92Cu) with the AuCu3-type structure is observed. § The oP12-Co2Si-type structure was described also for Pd2Al, Pd2In, Pt2Al and αPd2Tl.

5.10.4.4 Notes on the application of the metals of the 8th, 9th and 10th groups and their alloys. On the basis of their properties and also of their availability and cost, quite different applications have been considered for the two metal families we are describing. 5.10.4.4.1 Iron. Comments about the technological application of iron and its alloys are reported in § 5.10.4.5. 5.10.4.4.2 Platinum family metals and alloys. The platinum family (platinum group) metals (Ru, Os, Rh, Ir, Pd, Pt) belong (together with Au and possibly Ag and Re) to the class of precious metals. This characteristic together with their inertness to the environment (with regard to corrosion and oxidation) is the basis for a number of uses such as in the following. Jewellery, coinage and investment. In jewellery most of the Pt-alloys employed contain 95% platinum; the mechanically more stable alloys are Pt95–Cu5, Pt96–Pd4 and Pt90–Ir10 used for mounting precious stones.

Elements of Alloying Behaviour Systematics

RT3 hP24-CeNi3 (2H)

449

RT3 R2T7 R2T7 R5T19 R5T19 hR36-NbBe3 hP36-Ce2Ni7 hR54-Er2Co7 hP48-Sm5Ni19 hR72-Ce5Co19 (3R) (2H) (3R) (2H) (3R)

T R R2T4 cF24-Cu2Mg

RT5 hP6-CaCu5

Figure 5.28. Schematic representation of a family of inter-related structures (Haucke phases) composed by combinations of Cu2Mg- and CaCu5-type fragments. In the crystal structure of (3R)Ce5Co19, three block layers stack, along the c-axis with each block layer consisting of one unit layer of the LaNi5 type (CaCu5 type) and three unit layers of the LaNi2 type (Cu2Mg Laves type) (adapted from Yamamoto et al. 1997).

Laboratory apparatus represents an important application sector. Platinum crucibles, dishes, boats and electrodes for electrogravimetry have long been basic items in chemical laboratories. Today the more dimensionally stable alloys Pt97Ir3, Pt95-Au5, Pt99.7–Ir0.3 are mainly used. Platinum components are essential in fluorine chemistry. Chemical engineering equipments, glass industry, catalysts (heterogeneous catalysts, homogeneous catalysts, automobile exhaust catalysts).All platinum group metals have strong catalytic activity. The largest demand comes from the petroleum industry; the most important reactions are dehydrogenation, isomerization and cyclization, being

450

Intermetallic Chemistry

the resulting mixture gasoline with antiknock properties. The catalyst is generally Pt supported on γ-Al2O3, even though combination of Pt with other Pt-group metals, such as Pt–Ir, Pt–Re, Pt–Pd is also used. A large percentage of Pt (and Pd) consumption is related to their use in catalytic converters for emission control. Relevant applications are found also in particular technologies such as sensors, electronics, coatings, etc. Structural characteristics and applications of different classes of platinum metal intermetallic compounds have been recently reviewed by Wolff (2002). The following classes of compounds have been considered: CsCl-type (B2) alloys (important for high temperature structural and coating applications), materials containing the precious metals as a minor alloying addition, precipitation strengthened alloys (especially fcc L12 phases) analogous to the Ni-based super-alloys and a group of coloured intermetallics for ornamental applications. See in § 5.13.4.3 a similar gold alloy, the ‘purple glory’ Au6Al11. Coupled reduction with platinum group metals. Very pure metals of the alkaline earth, lanthanide and actinide series can be prepared from their oxides (or fluorides) by coupled reduction by pure hydrogen in presence of platinum group metals (see § 6.7.2.2). General references to these precious metals and their applications, prices, market, etc. are reported in the specialized publication Platinum Metal Review. 5.10.4.5 Iron and steel: Steel production, the Fe–C phase diagram, TTT diagrams, martensite. Owing to the widespread uses of a huge variety of steels and ferro-alloys, their processing often described through specific technical terms and a jargon developed in the historic course of metallurgy, a few notes on these points will be mentioned here. 5.10.4.5.1 Iron production Pure iron may be produced, on a small scale, by the reduction with hydrogen of pure oxide or by the carbonyl process according to which iron is heated with CO under pressure to produce Fe(CO)5 which, in turn, is decomposed (at about 250°C) to give the pure powdered metal. However, a very large quantity of iron is produced as a variety of steel types for a vast range of applications. Steel is created by alloying iron with a certain quantity of carbon (see Fig. 5.29); the addition of different impurities gives the steel different properties. A rough description only will be given here of the steel production routes. 5.10.4.5.2 Steel production Steelmaking can be performed according to two main routes, to which reference can be made as based on the basic oxygen converter and the electric steel process, respectively. The basic oxygen converter

451

Elements of Alloying Behaviour Systematics at.% C 5.0

1600 1538 (δFe)

10.0

15.0

20.0

1394

25.0

L C (graphite) 1252 1153

(γFe) Austenite

Fe3C Cementite

1147

1000 912 800

(αFe) 600

740 727

Pearlite

Temperature (°C)

1200

500 Cast iron

Steel

Fe

1

2

3 4 Mass% C

5

6

C

Figure 5.29. Fe-rich region of the Fe C phase diagram. Stable Fe-C (graphite) diagram: solid lines; metastable Fe-Fe3C diagram: dashed lines. The following current names are used: ferrite (solid solution in αFe), austenite (solid solution in γ Fe) and cementite (Fe3C compound). Pearlite is the name given to the two-phase microstructure which originates from the eutectoid reaction: γFe(C) : Fe3C αFe(C).

process requires a charge of molten iron which is produced in blast furnaces. Iron ore (usually haematite, Fe2O3 in lumps or pellets) is charged into the top of the blast furnace together with coke (see § 5.14.1), sinter and flux. ‘Sinter’ is a porous clinker obtained by heating, in a sinter plant, fine-sized ore mixed with coke and fluxes (limestone). Hot air (at about 900°C, or air with fuel oil) is blasted into the bottom of the furnace through special nozzles. Coke burns forming with the oxygen of air, carbon monoxide (CO) and generating intense heat (temperature approaching 2000°C may be reached near the basis of the furnace). The carbon monoxide flows up through the blast furnace and removes oxygen from the iron ores on their way down. The main reduction occurs near the top as the hot rising gases meet the descending charge. Reduction to the metal is completed at somewhat higher temperature after which fusion occurs and iron takes up C and Si and P (from the reduction of phosphates and silicates present in the ore, limestone, etc.). The resulting liquid iron is tapped at regular intervals by opening a hole in the

452

Intermetallic Chemistry

bottom of the furnace and allowing it to flow out (generally into the so-called torpedo-ladles, that is special railway containers which transport the liquid iron to the steel furnace). The fluxes, with the impurities of coke and ore form a molten slag which floats on the molten iron and is also removed at regular intervals. This process goes on continuously for 10 years or more (a campaign); on cooling, indeed, damage could be caused to the furnace-lining of refractory bricks (due to their contraction on cooling). The iron produced by the blast furnace (cast iron or pig iron) contains up to 4–4.5 mass% C with variable amounts of Si, Mn, P, S, etc. It is hard but brittle. Steelmaking refines iron mainly by reducing its carbon content and making a stronger and more malleable product. According to the basic oxygen converter process for making bulk steel (which supplanted the previously widely used and world dominating steelmaking Bessemer and open-hearth processes) the oxygen steelmaking vessel is first tilted to allow materials to be charged into it. Scrap steel is first charged followed by hot metal (liquid iron) from the blast furnace. A water-cooled lance is lowered into the vessel and through it very pure oxygen is blown at high pressure. Oxygen combines with carbon and several unwanted elements separating them from the metal leaving steel. Lime-based fluxes are charged which combine with the impurities forming slag. After having checked the composition of the steel, the vessel is again tilted to allow the molten metal to flow out (small additions of other metals and fluxes may be performed during this operations). The steel is tapped into a ladle in which secondary steelmaking may take place. This is a range of processes (stirring with argon, adding alloys, powder injection, vacuum-degassing, etc.) which make it possible to tune the chemical composition of the steel, to remove impurities and improve temperature homogeneity and control for subsequent casting. In the electric steel process the heating is obtained not by oxygen combustion of the additional elements present in the pig iron but from electric energy (by using an electric arc, an induction or a plasma furnace). In the arc-process, as a means of heating, an electric current is passed through the metal (direct-arc) or as an arc just above the metal (indirect-arc). It is used in the manufacture of alloy and highquality steel. This process is based on the use of scraps with small amounts of solid pig iron. The melting procedure includes the following stages: charging, melting, oxidization, decarburization with an increase of temperature, tapping. For general references to these topics see Habashi et al. (1997) and ASM Handbook Series published by ASM International (USA). 5.10.4.5.3 Stable and metastable iron–carbon phase diagram. The behaviour of iron and iron alloys depends on the existence of its different forms and on their transformations; technologically moreover the carbon content is crucial. These aspects are clearly shown in the iron–carbon phase diagram, especially in the low

Elements of Alloying Behaviour Systematics

453

carbon concentration region. The stable iron–graphite equilibria are shown in Fig. 5.29 where they are also compared with the reactions arising from the formation of metastable Fe3C (cementite). The current names often used in the designation of a number of phases and phase complexes in the iron–carbon system are listed in Table 5.49. A few questions related to phase transformation and the relevant heat treatments are briefly discussed in the following paragraphs.

Table 5.49. ‘Current names’ of iron alloys: Phases and Phase complexes in the iron–carbon system. Name

Description

Austenite

Solid solution of carbon in gamma iron (fcc), with up to about 8% of the available sites occupied by C atoms

Bainite

At temperatures below that of the pearlite reaction and above that (Ms) of the beginning of the martensitic transformation, austenite undergoes a transformation known as bainite reaction. The product bainite is not a single-phase material: it consists of fine particles of carbide embedded in laths of ferrite (generally combining high strength with higher ductility and showing considerable toughness). According to the temperature of formation (typically above or below about 350°C) two types of bainite (upper bainite or lower bainite) have been distinguished. The temperature below which bainite can form is denoted as Bs, whereas Bf is the temperature below which all the austenite is converted to bainite.

Cementite

The metastable, iron carbide Fe3C ideally corresponding to 6.69 mass% C.

Ferrite

Solid solution of carbon in alpha iron (bcc).

Ledeburite

The two-phase eutectic mixture of carbon saturated, austenite and cementite having the overall composition of 4.3 mass % C (17.3 at.%).

Martensite

A metastable transitional structure formed by a shear process during a phase transformation. In carbon steel it is a product of the conversion of austenite obtained by rapid cooling, it is a hard, metastable, super-saturated solid solution of carbon (9 at.% C) in a body-centred tetragonal arrangement of iron atoms. It is characterized by an acicular or needle-like structure. The crystal structure of martensite (tI4, space group I4/mmm) corresponds to the following unit cell edges, as obtained from the average trend of a graph, Okamoto (1993): a 285 pm, c 293 pm, c/a 1.028 (3 at.% C); a 285 pm, c 303 pm, c/a 1.063 (6 at.% C). Martensite range: the interval between the temperatures Ms (at which the martensite formation initiates) and Mf (at which the transformation is complete).

Pearlite

The two-phase structure (αFe,C Fe3C) originating from the eutectoidal decomposition of austenite (that is the C solid solution in γFe) and having the overall composition of 0.76 mass % C (3.46 at.%C). The stable Fe–graphite eutectoid has a composition of 2.97 at.% C.

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Intermetallic Chemistry

Table 5.50. ‘Current names’ of iron alloys: ‘technical irons’. Name

Description

Cast iron (pig iron)

Iron with a carbon content of 2–5%, containing more than 2.3% and usually 5–10 of foreign constituents. Its melting point lies between 1100°C and 1200°C, generally it casts well. Ordinary grey cast iron contains carbon chiefly as graphite. Slow cooling and high silicon content favours the decomposition of cementite into iron and free carbon. White cast iron is harder and more brittle; it contains carbon mainly as cementite.

Ferro-alloys

Master alloys containing a significant amount of iron and a few elements more or less soluble in molten iron which improve properties of iron and steels. As additives they give iron and steel better characteristics (increased tensile strength, wear resistance, corrosion resistance, etc.). For master alloy production carbothermic processes are used for large-scale ferro-silicon, ferro-chromium, ferro-tungsten, ferro-manganese, ferro-nickel and metallothermic processes (mainly alumino and silico-thermic) for ferro-titanium, ferro-vanadium, ferro-molybdenum, ferro-boron.

Malleable iron

It contains fewer impurities and has a lower C content (usually between 0.04% and 1.5%) and a higher melting point than cast iron. It can be forged and welded. It is prepared from white cast iron by annealing for several days (the iron carbide is decomposed into iron and nodules of graphite).

Soft iron

It contains 0.5% C at the most; tough and soft can be worked well.

Steel

It has a higher C content (usually 0.5–1%) and is harder than soft iron. An important property of steel is that it may be hardened. If heated to bright redness (to obtain an austenitic alloy) and suddenly cooled (quenched), by putting it in water, oil, etc, it becomes hard and brittle due to the formation of the very hard martensite. Brittleness can be removed by tempering (that is by a carefully heating for a short time at, say, 250–300°C) to release or diminish the internal strains resulted from quenching.

5.10.4.5.4 The TTT diagrams for steel. The temperature–time–transformation (TTT) diagrams are useful tools for showing the kinetics of a transformation and, with reference to a phase diagram, the evolution of structures related to various heat treatments. A simplified example of such a diagram was used in § 3.12 in a discussion about crystallization processes involving metal glasses. Fig. 5.30 schematically shows a TTT diagram applicable to steel (the prototype par excellence of the

Elements of Alloying Behaviour Systematics

455

diagrams of this sort). With reference to Fig. 5.29 (showing the Fe-rich region of the Fe–C phase diagram) we may underline that austenite is the high temperature fcc, γ phase, which at lower temperatures transforms to a bcc phase (α phase, ferrite) and to the orthorhombic compound Fe3C. The C-shaped curves of the TTT diagram indicate the start and finish of transformation experiments carried on (at a certain temperature) in isothermal conditions (IT diagram). The shape of these curves is a result of the ‘competition’ between the thermodynamic driving force and diffusion. At high temperature, diffusion is fast but the driving force (related to the difference ΔT from the equilibrium transformation temperature) is too low to trigger the transformation. At low temperature, on the contrary, the driving force is high, but diffusion is too slow for the transformation to proceed in a short time. If the γ phase is cooled quickly enough to avoid the C-curve (that is the T vs. t cooling curve lies at the left of the transformation diagram) and then it is held at a constant temperature (at 370°C in the example of the figure), then the transformation (γ : α Fe3C) will proceed according to the isothermal transformation curve. On the other hand, if the γ phase is so rapidly cooled to avoid touching the C-curve altogether, it will undergo another transformation, the martensitic transformation: the M s point indicates the temperature at which the transformation begins and M f the temperature below which no additional martensite forms. 5.10.4.5.5 Martensitic transformation. Several nucleation and growth transformations show temperature independent growth rate comparable with the sound velocity in the matrix. During this phase change, we have the transformation of a single-phase reactant into a single-phase product with a change of shape, but without any change in composition. These transformations are called martensitic transformations, and the product phase martensite. A detailed description and discussion of this topic and related subjects have been given by Jena and Chaturvedi (1992) and by Leslie and Hornbogen (1996). As a typical example, a Fe–C alloy may be considered, for instance, a 1.7 mass% C alloy which at, say, 1150°C is homogeneous, single-phase, fcc, austenite, and on quenching to ambient temperature gives, through a martensitic transformation, a body-centred tetragonal phase containing 1.7 mass% C. The Ms temperature, at which the diffusion-less martensitic transformation starts, depends on the alloy considered (its composition, etc.): it can be above or below room temperature. For the so-called austenitic steels Ms ambient temperature, whereas Ms ambient temperature for the martensitic steels. Notice that, in this context, diffusion-less means no random-walk mixing of atoms or atom-by-atom jumping across the interface during the structural change: the

456

Intermetallic Chemistry (a) 700 γ Temperature (°C)

600 α Fe3C

500 400

Ending Beginning

300 Ms Mf

200

(b) 100

0 Ending

50

50

Beginning 0 0.5

10

102

103

100 104

Austenite (%)

Transformation product (%)

100

Time (s)

Figure 5.30. Schematic drawing showing the construction of an isothermal transformation diagram from measurements of the progress of the transformation at various constant temperatures. This may be done, for instance, by metallographic examination of several specimens, quenched from the γ-field quickly enough to miss the nose of the C-curve and then isothermally annealed for various length of time. Notice that curves for the transformation of different samples may be shown on the same diagram and that more complex trends may be observed in real diagrams of specific alloys. In the example reported, Ms is the temperature at which the alloy will begin to show the martensitic transformation, Mf indicates the temperature below which no additional martensite forms.

product phase, as a consequence, has the same composition, atomic order and lattice defects of the parent phase. Martensitic transformations are dominated by the strain energy arising from shear-like displacements, and can be designated as displacive. This means that atoms move in an organized coordinated manner: these transformations are also called ‘military’ transformations because they correspond to a coordinated, regimented, motion of atoms. 5.10.4.5.6 Examples of martensitic transformation. This kind of transformation has been observed in a number of substances: elements, compounds, alloys, minerals, metallic and ceramic materials. A few examples of systems showing a

Elements of Alloying Behaviour Systematics

457

martensitic transformation are represented, according to Jena and Chaturvedi (1992), by the following materials: Alloys: Fe–C alloys: face-centred cubic to body-centred tetragonal structure change: (fcc : bct); Cu–Sn alloys: bcc : fcc; Au–Cd alloy (48% Cd): bcc : orthorhombic. Metals: Co: fcc : hcp; Hg: rhombohedral : body-centred tetragonal. Compounds: ZrO2: tetrag. : monoclinic; SiO2: rhomboh. : hex.; MnS: ZnS type : NaCl type. Another important group of alloys involved in martensitic transformation is represented by several plutonium alloys. The martensitic nature, for instance, of the δ to α transformation has been clearly established in Pu–Ga and Pu–Al alloys and a behaviour similar to that shown in Fig. 5.30 has been observed. For a systematic description of plutonium alloys, the stability of the different phases and their transformations see Hecker (2000). 5.11. ALLOYS OF THE METALS OF THE 11TH GROUP OF THE PERIODIC TABLE

Copper, Cu; silver, Ag; gold, Au

5.11.1 Introduction Copper (Cu, [Ar]3d104s1), name and symbol from Latin aes cyprium (later cuprum), from the island Cyprus, which was a source of this metal for the Romans. The use of copper dates back to prehistoric times. In mythology and alchemy copper was associated with the goddess Venus because of its lustrous reddish colour and one of its earliest applications, which is mirrors. Reddish, soft metal, good conductor of electricity and heat. Atomic number 29, atomic relative mass 63.546. Occurrence. Copper is a typical chalcophilic element; its principal minerals are sulphides, mostly chalcopyrite (CuFeS2), bornite (Cu5FeS4/Cu3FeS3) and chalcocite

458

Intermetallic Chemistry

(Cu2S). The processes for the recovery of the metal from scraps are becoming increasingly important (secondary copper). Preparation. Most copper production is based upon low-grade or poor sulphide ores, usually treated by pyrometallurgical procedures, several of which have been developed. After froth flotation to get a concentrate, the smelting of the concentrate produces two immiscible molten phases, the matte (heavier sulphide phase containing most of the copper) and the slag (oxide phase). The matte is converted by oxidation followed by reduction to crude copper. The resulting crude copper is then purified. The refining of copper may comprise three stages: pyrometallurgical refinement, electrolytic refinement and re-melting of cathodes. For extremely high purity copper, zone melting or repeated electrolysis of cathodes are used. Hydrometallurgical methods can be applied when low-grade oxidized (oxide) or mixed (oxidized and sulphidic) ores are available. These methods have advantages of high selectivity; disadvantages are the relative slowness of leaching and the large volume of solution per unit mass of copper. Silver (Ag, [Kr]4d105s1), name from Anglo-Saxon seolfor or siolfur (silver), symbol from the Latin argentum (from Greek αργο ´ ´, shiny). Known since ancient times. White lustre, solid. Very thin films are blue or green by transmitted light, thicker are yellow to brown. Ductile, slightly less than gold. Silver presents the highest electrical conductivity and the highest thermal conductivity of all metals. Atomic number 47, atomic relative mass 107.8682. Occurrence. Nearly all the silver ores are compounds of silver with sulphur and the neighbours in the Periodic Table arsenic, antimony and bismuth (argentite Ag2S, the most common silver compound, pyrargyrite Ag3SbS3, proustite Ag3AsS3). Other silver minerals include the halides. Silver is found sometimes as the free metal. Secondary silver (from catalysts, scraps, photographic films, etc.) is an important source. Preparation. Industrially, silver is usually a by-product of processes of extraction of other metals such as copper, lead, zinc. The so-called ‘anode slimes’ from the electrolytic purification of copper contain silver and the involved process is often finished by an electrolysis of a nitrate solution containing silver. From the silver ores a first extraction stage generally included process methods such as amalgamation, cyanidation, tiosulphate leaching. The importance of these methods, however, is now decreasing, especially amalgamation due to the toxicity of the reagents, and also because the largest proportion of Ag is contained in Cu, Zn, Pb ores.

Elements of Alloying Behaviour Systematics

459

Gold (Au, [Xe]4f145d106s1), name from Anglo-Saxon geolo (yellow), symbol from Latin aurum. Known since ancient times. Soft, shiny yellow metal (it can appear purple, ruby or black when finely divided). Atomic number 79, atomic relative mass 196.96657. Occurrence. Gold occurs in nature almost exclusively as free element, often associated with quartz, pyrite and other minerals. Preparation. In the past, in the traditional ‘gold rush’, gold was obtained from river sands by ‘panning’, taking advantage of the large density difference between gold (19.3 g/cm3) and sand ( 2.5 g/cm3). In recent time the production is based on the mining of gold-containing rocks. After crushing and after gravity concentration, gold can be isolated by amalgamation with Hg or by extraction through the cyanide process; the filtrate is then treated with zinc chips that precipitate the gold metal from the cyanide solution. Ecological problems are raised by the presence of mercury and sodium cyanide in the wastewater, even though, when exposed to air and sunlight, the cyanide is converted to cyanate and subsequently to carbonate. In closing this paragraph on gold recovery, we may quote a mythical tale from Greenwood and Earnshaw (1997). In ancient times gold-bearing river sands were washed over a sheep fleece which trapped the gold. It seems likely that this was the origin of the Golden Fleece in the Greek mythology. 5.11.2 The 11th group metals: a summary of their atomic and physical properties See Tables 5.51 and 5.52. Table 5.51. Cu, Ag, Au: selected atomic and physical properties. Property

Cu

Ag

Au

r/pm, metallic, CN 12 [‘metallic valence’] r/pm, ionic, M1, CN 6 r/pm, ionic, M2, CN 6 r/pm, ionic, M3, CN 6 r/pm, ionic, M5, CN 6 1st ionization energy/kJ/mol 2nd ionization energy/kJ/mol 3rd ionization energy/kJ/mol Tmelting (°C) Tboiling (°C) ΔHmelting (at Tmelting)/kJ/mol ΔfH0 of Me1 gas at 298.15 K/kJ/mol

127.8 [1] 77 73 54 – 746 1958 3554 1084.87 2563 13.14 338

144.5 [1] 115 94 75 – 731 2074 3361 961.93 2163 11.30 –

144.2 [1] 137 – 85 57 890 1980 – 1064.43 2857 12.55 –

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Intermetallic Chemistry

Table 5.52. Cu, Ag, Au metals: crystal structures, lattice parameters of their allotropes and calculated densities. Element (allotrope) Temperature range/°C Pressure/GPa Cu Ag Au

Copper 1084.87° Silver 961.93° Gold 1064.43°

Crystal structure

Lattice parameters/ pm

Atomic volume/ 106 pm3

Molar volume/ cm3/mol

Density/ g/cm3

a cF4-Cu

361.46

11.81

7.11

8.94

cF4-Cu

408.57

17.05

10.27

10.50

cF4-Cu

407.82

16.96

10.21

19.29

5.11.3 The 11th group metals: remarks about their general chemical properties and reactivity These elements, also called coinage metals, have some properties resembling those of the alkali metals. Such similarities however are confined almost entirely to the stoichiometries of the compounds of the 1 oxidation state. Since a filled d shell is far less effective than a filled p shell in shielding an outer s electron, the first ionization energies of the coinage metals are much higher, and their ionic radii smaller, than those of the corresponding alkali metals. Of consequence, they have higher melting points, are harder, denser, less reactive than the alkali metals. They are able to adopt oxidation states higher than 1 (2; 3). They also readily form coordination complexes. In other words, the coinage metals behave as transition metals. The reactivity of Cu, Ag and Au decreases down the group; all these metals are stable in pure dry air at room temperature, but Cu forms Cu2O at red heat. Copper reacts with sulphur, giving Cu2S, and it dissolves in HNO3 and H2SO4 in the presence of O2. Silver dissolves in oxidizing acids. Gold is generally unreactive, but reacts readily with halogens or with solutions generating chlorine, such as aqua regia. 5.11.4 Intermetallic chemistry of the 11th group metals 5.11.4.1 Phase diagrams of the 11th group metals. The intermetallic reactivity patterns of Cu, Ag and Au are similar, with no compound formation in the middle of the Periodic Table (groups 5–9 for Cu and Ag, about 6–9 for Au). The general reactivity pattern of the 11th group metals shown in Fig. 5.31 may be compared with that of the previous metals (of the 8th, 9th and 10th groups) summarized in Fig. 5.25. All these metals form compounds with the lanthanides and several

461

Elements of Alloying Behaviour Systematics 1 2 3 4 5 6 7 8 9 10111213141516

1 2 3 4 5 6 7 8 9 10111213141516

Cu

Ag

1 2 3 4 5 6 7 8 9 10111213141516

Au

Compound-forming element

Phase diagram known; no intermediate phases formed

No information available

Questionable compound forming capability

Figure 5.31. Compound-formation capability in the binary alloys of Cu, Ag, Au.

actinides. A no-compound zone can be identified in the middle of the Periodic Table. A certain broad analogy may be found between the alloying pattern of the 11th group metals and that of Zn, Cd, Hg, of the following 12th group, as shown in the last line of Fig. 5.33, as well as a certain gradual trend in the compound formation capability. A few more details about the intermetallic reactivity of the 11th group metals may be obtained from Table 5.53, where some information about the melting behaviour of their alloys is summarized. The higher values of the melting points generally observed in the gold alloys may be underlined. Notice also the relatively high thermal stability presented by the alloys of these metals with those of the 3rd and 4th groups. On the basis of the data reported by Ferro et al. (2003) on gold alloys, this behaviour may be compared with the trend of the formation enthalpy. The stability of the gold alloys with the elements of the first groups of the Periodic Table is evidenced by the strongly negative values of Δf H, with minima in the 3rd (70, 85 kJ/mol at.) and 4th (40 60 kJ/mol at.) groups. The high reactivity of Au may also be underlined considering the behaviour with the alkali metals: these, indeed, form no compounds with Cu, a few compounds (apparently only Li and Na) with Ag, and several compounds with Au. The gold alloys are characterized by strong interactions not only in the solid, but also in the liquid state (these systems generally show a complete liquid miscibility). The Cs–Au system can be considered an extreme case among these alloys. Liquid Cs–Au alloys possess unusual physical and chemical properties: at 50 at.% Cs liquid AuCs behaves as an ionic liquid and may be described as a molten salt consisting of Cs and Au ions (Pelton 1987). In the solid state two compounds are formed CsAu, CsCl-type and CsAu5, CaCu5-type. On moving towards the right part of the Periodic Table at first weak interactions of gold with the different elements (no solid compounds, and

Table 5.53. Highest melting points (°C) in the alloys of Cu, Ag and Au with compound-forming elements of the 4th and 6th rows of the Periodic Table. See the introduction for the meaning of the symbols. Alloys with K

Copper compounds –

No compds.

Cs Ca Ba Sc La Ti Hf V

Compl. Immisc. Ca2Ag7, 725°, IR 1

BaCu13, 758°, p, IR 1 ScCu, 1125°, IR 1 LaCu6, 920°, IR 1 s.s. TiCu, 48–52 at.% Ti 982°, IR 1 Hf2Cu, 1310°, IR 1

BaAg2, 770°, IR 1 ScAg, 1230°, IR 1 La14Ag51, 1005°, IR 1 s.s. TiAg 1020°, p, IR 1 Compds.

No compds., monotectic

No compds., monotectic No compds. Simple eutectic

Simple eutectic W

Mn Re

No compds., monotectic

Os

Compds. ScAu, 1700°, IR 1

LaAu, 1325°, IR 1 s.s. TiAu, 48–62 at.% Ti 1495°, IR 1 s.s.HfAu, 1750°, IR 1 σ, 65–78 at.% Ta 2000°, p, IR 1

α , 12–23 at.%Cr 350° s.s.r. No compds., immisc.

No compds., monotectic

Simple eutectic β, 33–69 at.%Mn 1260°, IR 1

No compds. Compl. sol. and liq. immisc.

No compds. Simple eutectic

s.s. KAu5 16–20 at.% K 1050°, IR 1 CsAu5, 1050°, IR 1 Ca10Au9, 1015°, IR 1

s.s. V3Au, 1280°, s.s.r.

No compds. Monotectic

No compds. Simple peritectic

Gold compounds

No compds. No compds. Monotectic

Cont. s.s. (γMn,Cu)

Fe

No compds.

CaCu5, 951°, IR 1

Ta Cr

Silver compounds

No compds. No compds. Simple peritectic

Compl. sol. and liq. immisc.

No compds.

Co

No compds. Simple peritectic Ir

Ni

Complete sol. and liq immisc. No compds. Simple peritectic

Cont. s.s. (Ni,Cu) De-mix s.s. Pt

Compl. sol. and liq. immisc. Extended monotectic

Cont. s.s. (Ni,Au) De-mix s.s. Ag15Pt17 s.s.r., 803°

Cont. s.s. (Pt,Cu) Ordering s.s.r.

Cu

Simple eutectic Au

Cont. s.s. (Au,Cu) Ordering s.s.r.

Zn

β 36–56 at.% Zn 902°, p, IR 1

Cu7Hg6 128°, p

Tl

β, 19–27 at.% Ga 915°, p, IR 1 No compds., monotectic ζ 11–18 at.% Ge 824°, p, IR 1

Ge Pb As Bi

Cont. s.s. (Pt,Au) De-mix. s.s. Cont. s.s. (Au,Cu) Ordering s.s.r.

Cont. s.s. (Ag,Au)

Hg Ga

No compds. Simple eutectic

ζ 43–46 at.% Hg 276°, p, IR 1

β 37–59 at.% Zn 710°, p, IR 1

α 16–23 at.% Hg 419°, p, IR 1

ζ, 22–34 at.% Ga 612°, IR 1 Simple eutectic

AuGa2 491°, IR 1 Simple eutectic

Simple eutectic

No compds., monotectic γ, 25–28 at.% As 827°, IR 1

Simple eutectic.

Simple eutectic

Simple eutectic

β 38–57 at.% Zn 751°, IR 1

ζ, 9–11 at.% As 582°, p, IR 1

Simple eutectic Au2Pb, 434°, p, IR 1 Simple eutectic Au2Bi, 371°, p, IR 1

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Intermetallic Chemistry

with Ru and Rh, a miscibility gap in the liquid state) can be observed followed by compound formation and stronger interactions (in the Al system, for instance, Al2Au has a melting point of 1060°C and Δf H 40 kJ/mol at.). Several alloy systems and the corresponding phase diagrams of the three metals of this group are important both in view of their applications and on the basis of their reference structures. The family of intermetallics corresponding to the ‘Hume-Rothery Phases’ and the role played by the ‘valence electron concentration’ have been described in § 4.4.5, where typical phase diagrams (Cu–Zn, Cu–Al, Cu–Sn) have been shown both with the compositions given in at.% and as the average number of valence electrons per atom. Characteristic sequences of solid solution phases may be noticed in these diagrams generally forming ‘cascades’ of peritectic reactions. 5.11.4.2 Remarks on the alloy crystal chemistry of the 11th group metals. A selection of the phases formed in the binary alloys of Cu, Ag and Au and of their crystal structures is shown in Tables 5.54a and 5.54b. For a number of these phases, more details (and a classification in terms of ‘Hume-Rothery Phases’) are given in § 4.4.5 and in Table 4.5 (structure types, valence electron concentration, etc.). Table 5.54a and 5.54b show the formation of several phases having a high content

Table 5.54a. A selection of intermediate phases in the binary alloys of Cu. Structure type

CNE (Cu)

Examples of isostructural phases

12–14 12 12–16 8–13 12 10 12–13 12–13

Cu6X: X LnIII(La–Gd), Th, Pu Cu5X: X Ca, Sr, Ln(La–Yb) Cu5X: X Gd(16–17Gd), LnIII(Tb–Lu), U Cu23X6: X Tb, Dy, Yb, Lu Cu3X: X Pd(8–22Pd), Pt(9–24Pt), Au(19–33Au) Cu2X: X Ln(Ce–Lu), Pu Cu–X: X Zn(57–70Zn), Cd(52–66Cd), Al(31–37Al) Cu–X: X Al(31–37Al), Ga(30–35Ga) Cu–X: X Al(18–30Al) CuX: X Be(45–50Be), Sc, Y, LnIII(Sm–Lu), Zr, Pd(36–47Pd), Zn(45–50Zn) CuX: X La, Ce, Pr, Nd, Eu, Yb CuX: X Al(39–45Al), In(33–38In), Sn(43–46Sn) CuX2: X Ti, Zr, Hf

oP28-CeCu6 hP6-CaCu5 cF24-AuBe5 cF116-Th6Mn23 cP4-AuCu3* oI12-CeCu2 cI52-Cu5Zn8 cP52-Cu9Al4 cI2-W 14 cP2-CsCl

14

oP8-FeB hP4-NiAs tI6-MoSi2

17 8 14

Cu compounds

* The same cP4-AuCu3-type structure is observed for Au3Cu and AuCu3 (ordering Au–Cu) and for Au3Pd and AuPd3.

Table 5.54b. A selection of intermediate phases in the binary alloys of Ag and Au. Structure type

CNE (Me)

hP6-CaCu5

12

tI10-MoNi4

12

Examples of isostructural phases Ag compounds

Au compounds

Ag5X: X Sr(15–17Sr), Ba, Eu

Au5X: X K(16–20K), Rb, Cs, Sr, Ba(14–22Ba), Eu Au4X: X Sc, Ho, Er, Tm, Yb, Lu, Ti(18–21Ti), Hf(14–17Hf), V(15–26V) Cr (12–23Cr), Mn(17–20Mn)

Ag51X14: X Y, LnIII (La–Tm), Th

hP65-Gd14Ag51

Au51X14: X LnIII(La–Ho), Th, U Au3X: X Sc, Y, LnIII(Sm–Lu), Yb, Zr, Hf, In (24–25In)

oP8-β-TiCu3

12

cP4-AuCu3

12

Ag3X: X Mg(19–27Mg), Tm, In

Au3X: X Cu(5–39Cu), Pd(12–32Pd)

oI12-CeCu2

10

Ag2X: X Ca, Sr, Ba, Eu(34–38Eu), La, Ce, Pr, Nd, Yb

Au2X: X Sr, Ce, Pr

tI6-MoSi2

14

Ag2X: X Sc, Y, Gd, Tb, Dy(33–34Dy), Ho, Er, Tm, Lu

Au2X: X Al(33–35Al), Be, Sc, Y, Ln(Gd-Lu), Ti, Zr, Hf(30–34Hf), Mn

hP3-AlB2

9

Ag2X: X Nd, Pr, Th

cI52-Cu5Zn8

12–13

Ag–X: X Zn(58–65Zn), Cd(57–63Cd)

Au–X: X Zn(63–76Zn), Cd(61–68Cd)

cP52-Cu9Al4

12–13

Ag–X: X In(31–34In)

Au–X: X In(29–31In)

cI2-W

14

Ag3X: X Zn(37–59Zn), Cd(40–55Cd), Al(21–30Al), Ga(50Ga), In(25–29In),

Au3X: X Al(19–20Al)

cP2-CsCl

14

AgX: X Li(50–77Li), Mg(36–65Mg), Sc, Y, La, Ce, LnIII(Pr–Lu), Yb, Zn

AuX: Au Li(55–56Li), Rb, Cs, Cd(43–57Cd), Sc, Y, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Tm, Er, Yb(46–50Yb), Lu, Ti(48–62Ti), Mn(33–69Mn) Mg(33–58Mg), Zn(48–57Zn)

oS8-CrB

9

AuX: X Ca, La, Ce, Dy, Ho, Er, Pr, Nd, Sm, Gd, Tb, Tm, Th

oP8-FeB

9

AuX: X La, Ce, Pr, Eu, Nd, Yb

tI6-MoSi2

14

cF12-CaF2

8

AuX2: X Al(66–67Al), Ga, In

oP12-Co2Si (or PbCl2)

10

AuX2: X Sc, LnIII(La–Lu), Yb

hP2-Mg

12

AgX2: X Ti, Zr, Hf

Ag–X: X Zn(66–89Zn), Cd(65–81Cd), Hg(43–46Hg), Al(23–42Al), Ga(22–34Ga) Sn(12–23Sn), As(10–11As), Sb(9–16Sb)

AuX2: X Hf, Mn, Zr

Au–X: X Hg(20–26Hg), In(12–22In), Sn(9–18Sn)

466

Intermetallic Chemistry

of the 11th group metals; typical structures correspond to the types oP28-CeCu6, hP6-CaCu5 and cF24-AuBe5, tI10-MoNi4, cF116-Th6Mn23, hP65-Gd14Ag51, cP4AuCu3, oP6-TiCu3, etc. Several phases having a structure related to the tI6-MoSi2 type are formed, either with the Me2X or the MeX2 stoichiometry: an example may be given by the Hf–Au system where both phases (Hf2Au and HfAu2) have been observed. Many 1:1 compounds have been identified, several of which having the cP2CsCl or the oP8-FeB (or oS8-CrB) type structures. Among the phases having a lower content of the 11th group metal, a number of oP12-Co2Si-type compounds may be mentioned. 5.11.4.3 Notes on the applications of the alloys of the 11th group metals. The major application of copper is as an electric conductor, it is widely used as the traditional brass, bronze and in coinage alloys. Silver is used in jewellery and silverware, for mirror silvering, for soldering, in electronics.

Au Gold -yellow 22 Ct 20

Green-yellow

80 18 Ct

60 14 Ct

%

Yellowish

Au

Pale greenish yellow

ss

Ma

40

Ma

ss%

Ag

Yellow

10 Ct

60

40 8 Ct

80 Red

20

Whitish Reddish

Ag

20

40

60

80

Cu

Mass% Cu

Figure 5.32. In the composition triangle (mass%) of ternary Au–Ag–Cu alloys, colours are indicated. Constant mass% values of Au are identified by dotted lines; for instance 22 carats 91.7 mass% Au, etc.).

Elements of Alloying Behaviour Systematics

467

Gold is generally alloyed with other metals in order to make it harder and cheaper. The proportion of gold is expressed in ‘carats’, being this the 24th part by mass of the metals. Pure gold is therefore 24 carats, and an 18 carat gold is an alloy containing 75 mass% Au (see Fig. 5.32). Notice that the word ‘carat’ has also another meaning: in the case of precious stones it is a mass unit (not the indication of the composition and purity). In this instance one carat corresponds to 200 mg. Besides the manufacture of jewellery, gold is used in electronics, dentistry, brazing alloys, the aerospace industry, etc. For several applications gold is alloyed with other metals in order to improve its mechanical properties. 5.12. ALLOYS OF BERYLLIUM, MAGNESIUM, ZINC, CADMIUM AND MERCURY

Beryllium, Be; magnesium, Mg; zinc, Zn; cadmium, Cd; mercury, Hg

5.12.1 Introduction Owing to some similarities among their properties and alloying behaviour, beryllium and magnesium, metals of the 2nd group, will be presented in this chapter together with the last transition metals zinc, cadmium and mercury (see a few more remarks in § 5.4). Beryllium (Be, [He]2s2), named from the mineral beryl. Also called, in the past, .. in the French speaking countries, glucinium, from the Greek γλυ´ κν´ (sweet). Discovered (1798) by N.L. Vauquelin. Grey, whitish, solid metal. Both finely divided metal and the compounds have serious toxic effects. Atomic number 4, atomic relative mass 9.012182. Occurrence. Beryllium is a rare element (2 ppm in the earth’s crust). The most commercially important minerals are beryl (3BeO Al2O3 6SiO2) and bertrandite 4BeO SiO2 H2O). Chrysoberil (BeO Al2O3) and the varieties of beryl, emerald (that contains about 2% Cr, the source of its green colour) and aquamarine are highly prized gemstones.

468

Intermetallic Chemistry

Preparation. The ores are converted to an acid-soluble form by fusion; chemical processes to obtain beryllium hydroxide or oxide and then beryllium chloride or fluoride are then applied, followed by electrolysis in the melt. Magnesium (Mg, [Ne]3s2), name, and symbol, from the Greek word Magnesia a city of Thessaly. Recognized as an element (1755) by Joseph Black, isolated (1808) by Humphry Davy. Solid, silvery white metal. Atomic number 12, atomic relative mass 24.3050. Occurrence. There are many minerals containing magnesium including magnesite (MgCO3), dolomite (CaCO3 MgCO3), brucite (Mg(OH)2), all used as prime raw material source, spinel (MgAl2O4), magnesium silicates such as olivine (Mg,Fe)2SiO4, not used for magnesium extraction. Sea water also contains magnesium. Preparation. Magnesium is obtained by electrolysis of magnesium chloride melts or by metallothermic reduction of magnesium oxide. A new production technique fully cost competitive with current processes could be the reduction of magnesium oxide by carbon to produce magnesium metal as a vapour and carbon monoxide gas: this technique, according to Brooks et al. (2006), will involve rapid quenching of the Mg vapour through a nozzle at supersonic velocity to avoid Mg reversion to magnesium oxide. Zinc (Zn, [Ar]3d104s2), name, and symbol, from the German zink (tin). First isolated in India (13th century) then (1746, Germany) by A.S. Margraaf. Bluish white, solid metal. Atomic number 30, atomic relative mass 65.39 (a value of 65.409 is recommended by the IUPAC Atomic Weights Commission, 2005). Occurrence. The principal mineral is sphalerite (ZnS), the most important impurity of which is FeS; sphalerite commonly occurs with galena (PbS). Other minerals are wurtzite (the hexagonal modification of ZnS) and smithsonite or calamina (ZnCO3). Preparation. Sulphides are readily converted to oxide by roasting in air, that remove all sulphur as SO2; this pre-treatment is followed by pyrometallurgical process by heating with carbon, or electrolytic process to obtain zinc. It is also possible by controlled oxidation to convert ZnS to the water soluble ZnSO4, which can be extracted and electrolyzed to produce zinc. Crude zinc obtained by pyrometallurgical process can be refined by distillation taking into account the comparatively low boiling temperature of zinc.

469

Elements of Alloying Behaviour Systematics

Cadmium (Cd, [Kr]4d105s2), name and symbol from the Latin word cadmia and Greek word καδμεσ´ια, both with the same meaning, calamine (ZnCO3). Discovered (1817, Germany) by F. Stromeyer. Silvery metal: it may be cut with a knife. Atomic number 48, atomic relative mass 112.411. Occurrence. Cd minerals are scarce: it generally occurs in almost all Zn ores by replacement of Zn due to the general chemical similarity. Preparation. Usually it is a by-product in the Zn metallurgy: it may be separated from Zn by distillation or by precipitation from sulphate solutions followed by reduction with Zn dust. Mercury (Hg, [Xe 4f 14]5d106s2), named after the planet Mercury (dedicated to the Roman God Mercurius), the symbol came from the Latin name hydrargyrum (liquid silver). Known since ancient times. Silvery, liquid at room temperature, metal. Atomic number 80, atomic relative mass 200.59. Occurrence. It is primarily found in cinnabar (HgS) ore. Preparation. This is roasted forming the oxide which decomposes (at 500°C) giving the Hg vapour. The metals of the 12th group have a relatively low abundance in nature: they, however, are easily obtained from their ores, mainly consisting of sulphides. 5.12.2 Be, Mg, Zn, Cd and Hg: a summary of their atomic and physical properties See Tables 5.55 and 5.56. Table 5.55. Be, Mg, Zn, Cd, Hg: selected atomic and physical properties Property

Be

Mg

Zn

Cd

Hg

r/pm, metallic, CN 12 [‘metallic valence’] r/pm, ionic, M1, CN 6 r/pm, ionic, M2, CN 6 1st ionization energy/kJ/mol 2nd ionization energy/kJ/mol 3nd ionization energy/kJ/mol Tmelting/°C Tboiling/°C ΔH melting (at Tmelting)/kJ/mol ΔH0 of Me1 gas at 298.15 K/kJ/mol

112.8 [2]

160.2 [2]

139.4 [2]

156.8 [2]

45 900 1757 14849 1289 2472 7.89 324

72 738 1451 7733 650 1090 8.48 147

74 906 1733 3833 419.58 907 7.32 130

95 868 1631 3616 321.108 767 6.20

159.4 [2] 119 102 1007 1810 3300 38.836 357 2.30 61.4

470

Intermetallic Chemistry

Table 5.56. Be, Mg, Zn, Cd, Hg: crystal structures, lattice parameters of their allotropes and calculated densities. Element (allotrope) Temperature range/°C Pressure/Gpa Beryllium αBe 1270° βBe 1270 to 1289° γBe 28.3 GPa Magnesium αMg 650° βMg 50 GPa Zinc Zn 419.58° Cadmium Cd 321.108° Mercury αHg 38.836° βHg

3.7 GPa

Crystal structure

Lattice parameters/ pm

Atomic volume/ 10 6 pm3

Molar volume/ cm3/mol

Density/ g/cm3

8.11 8.30

4.88 5.00

1.84 1.80

a

c

hP2-Mg cI2-W hP8

228.59 255.15 432.8

358.45

hP2-Mg cI2-W

320.94

521.07

23.24

13.99

1.74

hP2-Mg

266.50

494.70

15.21

9.16

7.14

hP2-Mg

297.93

561.96

21.60

13.00

8.64

hR3-αHg

346.99

671.93

23.35

14.06

tI2-αPa

399.5

282.5

–

–

14.27* sol. (38°C) –

341.6

* Density of liquid Hg at 0°C: 13.596 g/cm3.

5.12.3 Be, Mg, Zn, Cd and Hg: remarks about their general chemical properties and reactivity Metals of the 2nd group Beryllium and magnesium belong to the 2nd group of the Periodic Table together with calcium, strontium, barium and radium. Characteristic differences, however, may be noticed between the chemistry of Be and Mg and that of the alkaline earth’s proper. Be has a unique chemical behaviour with a predominantly covalent character. The heavier elements (Ca, Sr, Ba, Ra) have a predominant ionic behaviour in their compounds. Mg has a chemistry in a way intermediate but closer to that of Be. Analogies between the Mg and Zn chemistries may also be underlined. Beryllium. Be metal is relatively unreactive at room temperature; it does not react with water and steam even at red heat and it does not oxidize in air below 600°C. Powdered beryllium burns in air brilliantly on ignition forming BeO and Be3N2. It reacts with the halogens and dissolves easily in dilute aqueous acid solutions. It is passivated by cold concentrate HNO3. The Be compounds, especially as dusts or smokes, are extremely toxic (possibly due to the ability of BeII to displace MgII from Mg-activated enzymes).

Elements of Alloying Behaviour Systematics

471

Magnesium. Mg is more electropositive than amphoteric beryllium and reacts more readily with most of the non-metals of the 14th, 15th, and 16th groups. It ignites with the halogens, especially moist, and, nearly 500°C, burns with dazzling brilliance with air (forming MgO and Mg3N2). It reacts with H2 at about 570°C and high pressure, forming MgH2; it is readily soluble in acids. In ambient conditions it is not attacked by water (unless amalgamated) despite the favourable potential, because it is generally protected by a surface oxide film. Metals of the 12th group Zinc, cadmium and mercury are at the end of the transition series and have electron configurations nd10(n 1)s2 with filled d shells. They do not form any compound in which the d shell is other than full (unlike the metals Cu, Ag and Au of the preceding group): these metals therefore do not show the variable valence which is one of the characteristics of the transition metals. In this respect these metals are regarded as non-transition elements. They show, however, some resemblance to the d-metals for instance in their ability to form complexes (with NH3, amines, cyanide, halide ions, etc.). Zn and Cd chemistry is very similar, differing considerably from that of Hg. The general chemical behaviour of these metals resembles that of Mg and Be (compare the values of the ionization potentials of these elements).

5.12.4 Intermetallic chemistry of Be, Mg, Zn, Cd and Hg 5.12.4.1 Phase diagrams of the Be, Mg, Zn, Cd and Hg alloys. The systematics of the compound formation of these metals in their binary alloys with the different elements is summarized in Fig. 5.33. On the overall they give a rather complex picture; even so a number of relationships and similarities between various pairs of metals may be singled out. To go into this point in more detail, in the same figure a comparison has also been made with the compound formation patterns of Ca and Al which are described in § 5.4 and 5.13 but are close in the Periodic Table to the metals here considered. The similarity between the Be and Zn patterns may be underlined, as also that between Be and Al, being an example of the so-called ‘diagonal relationships’ presented in § 4.2.2.2. Obvious analogies between Mg and the elements of the 2nd group (notably with Ca) exist. Notice, however, the different behaviour shown in the alloys with the lanthanides and actinides: no compound formation is observed with Ca (and Sr, Ba, Eu and Yb) whereas there are several compounds in the alloys with Mg (and Be, Zn, Cd and Hg). As for the patterns given by Zn, Cd, Hg notice the smooth changes along the Periodic Table of the regions where there is, or there is not, compound formation: the trend observed in the (sub) group Zn, Cd, Hg is not very different

472

Intermetallic Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Be

AI

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Mg

Ca

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Zn

Cd

Hg

Compound-forming element

Phase diagram known; no intermediate phases formed

No information available

Questionable compound forming capability

Figure 5.33. Compound formation capability in the binary alloys of Be, Mg, Zn, Cd, Hg. For a comparison Al and Ca patterns are also shown.

from those displayed (in the following groups) by the series Ga, In, Tl and Ge, Sn, Pb (compare with the patterns shown in Figs 5.34 and 5.38). Amalgams. Considering the peculiar properties of mercury, a few special remarks on its alloys (the amalgams) may be noteworthy. Particular contributions (Galus et al. 1986 Guminski 1989, 1990, 2002) to the description of the alloying behaviour of mercury have been based on the solubility of the different metals in Hg and on their capability to give mercury compounds. Guminski observed that the different elements may by subdivided into four groups: (i) Elements forming with Hg stable intermetallics and showing high solubility in Hg: alkali metals, alkaline earth metals (not Be), lanthanides. (ii) Elements forming intermetallics but poorly soluble in Hg: Be, Sc, Y, Th, U, Pu, Am, the metals of the 4th group, Rh, the metals of the 10th group, Se and Te. (iii) Elements showing high solubility in Hg but non-forming intermetallics (Al, Ga, Bi) or forming intermetallics stable only at low temperature (Mn, Cu, Ag, Au, Zn, Cd, In, Tl, Sn, Pb).

Elements of Alloying Behaviour Systematics

473

(iv) Elements poorly soluble in Hg and non-forming intermetallics: V, Nb, Ta, Cr, Mo, W, Re, Fe, Ru, Os, Co, Ir, B, C, Si, Ge (and possibly As, Sb). 5.12.4.2 Remarks on the melting point trends in the binary alloys of Be, Mg and of the 12th group metals. The intermetallic reactivity of these metals and the stability of their compounds are also highlighted by the trends of the melting points of their alloys. A selection of these data has been collected in Tables 5.57 and 5.58 where compounds of Be and Mg and of Zn and Hg are listed. For several systems, information only on the existence of intermediate phases with no indication about their melting temperature is reported. 5.12.4.3 Remarks on the crystal structures of selected alloys of Be, Mg and of the 12th group metals. A number of analogies may be observed between the metals of the 12th group (Zn, Cd, Hg) and the first two metals of the 2nd group (Be, Mg) concerning the systematics of binary phase diagrams and, to a certain extent, also the crystal chemistry of their intermetallic phases. An abridged list of the most frequent structural types observed in the alloys of these metals is shown in Tables 5.59a and 5.59b. Some comments about a few of them (their stoichiometry and coordination) may be noteworthy. Within the alloys having a stoichiometry close to 1:1, several phases with structures related to the cP2-CsCl type (and more or less fully ordered) may be picked out. The β phase in the Cu–Zn system (homogeneous between 45 and 50 at.% Zn) is a characteristic example of a CsCl-type phase which at higher temperature (454– 468°C) undergoes the order–disorder transformation into the disordered bodycentred cI2-W type (the β phase, homogeneous between 36 and 56 at.% Zn, considered a ‘model’ representative of the Hume-Rothery phases, as described in § 4.4.5). The same structure is observed in several series of compounds of the metals of these groups (see, for instance, several Be phases, various compounds of Mg, Zn, Cd, etc.). However, among the 1:1 compounds, representatives of other structural types are known: with semi-metals or non-metals, phases have been identified having a more covalent–ionic character and structures belonging to one (or more) polytypes of the tetrahedral structures ‘family’ (cF8-ZnS, hP4-ZnS). Laves phases form in several of the most metallic systems listed (especially alloys of Be, Mg, Zn), whereas for many 3:1 compounds the presence of geometrically closepacked structures (such as the cP4-AuCu3 and the hP8-Ni3Sn types) is characteristic. Finally, a number of structures are characterized by high stoichiometric ratios and high coordination numbers, peculiar to these systems. Examples are the following types: hP38-Th2Ni17, hR57-Th2Zn17, tI48-BaCd11, cP36-BaHg11, tI26-ThMn12, cF112-NaZn13. In these structures the size factor (atomic radius ratio) is an important controlling factor. A short description of the characteristics of these structure types and of their interrelations is presented in § 7.5.

Table 5.57. Highest melting points (°C) in the alloys of Be and Mg with compound-forming elements of the 4th and 6th rows of the Periodic Table. Compare with Fig. 5.58. Alloys with

Beryllium compounds CaBe13, 1583°, p, IR 1

Ca Ba Sc

Magnesium compounds

BaBe13,1810°, IR 1

Compds. La

Ti Hf V Ta Cr

Ti2Be17, 1660°, IR 1 VBe2, 1800°, IR 1 CrBe2, 1840°, IR 1

LaBe13 Hf2Be17, 1760°, IR 1 Compds. 2000°

Fe Os Co Ir Ni Pt Cu

ζ, 21–37 at.%Fe 1463°, IR 1 β, 25–54 at.%Co 1420°, IR 1 β, 25–52 at.%Ni 1605°, IR 1 δ,18–36 at.%Cu 1220°, IR 1

Au Zn

Compds. Compds. BePt 1400°

Hg2Be

Co2Mg, 970°, p, IR 1 Ni2Mg, 1147°, IR1 Cu2Mg, 797°, IR 1

MgZn2, 600°, IR 1 Mg5Ga2, 470°, IR1

Monotectic

Mg2Ge, 1117°, IR 1 Immisc.

Compds. Bi

Immisc.

Monotectic Pb

As

Immisc.

Fe–Mg eutectic

Tl Ge

Compl. immisc. Extended monotectic

Mn–Mg simple peritectic

Extended monotectic

Ga

s.s. LaMg3, 798°, IR 1

Extended monotectic

s.s. ReBe2 30–40 at.%Re

s.s. AuBe5 850°, IR 1

Hg

Ba2Mg17, 707°, IR 1

Extended monotectic

Compds. Re

γ, 35–50 at.% Sc 520° s.s.r.

s.s. WBe2, 28–36 at.%W 2250° IR 1

W Mn

CaMg2, 711°, IR 1

Complete immisc.

Mg3As2, 1200°, IR 1

Mg3Ir, 1200° Compds. s.s. MgAu, 33–58 at.%Mg 1150°, IR 1 MgHg, 627°, IR 1 Mg5Tl2, 413°, IR 1 Mg2Pb, 550°, IR 1 Mg3Bi2, 823° IR 1

Table 5.58. Highest melting points (°C) in the alloys of Zn and Hg with compound-forming elements of the 4th and 6th rows of the Periodic Table. Alloys with K Cs Ca Ba Sc

Zinc compounds KZn13, 592°, (2liq) IR 1

KHg2, 270°, IR 1

CaZn13, 724°, IR 1

CaHg, 961°, IR 1

ScZn, 1230°, IR 1

La Ti

Mercury compounds

BaZn13, 885°, IR 1 La2Zn17, 974°, IR 1

Compds. Hf

Compl. immisc. Compds.

CrZn17, 568°, p W

Mn Re Fe Os Co Ir Ni Pt Cu

β 50–70 at.%Mn 850°, p, IR 1 Γ1, 17–31 at.%Fe 782°, p, IR 1 β, 49–52 at.%Co 966°, p, IR 1 β, 42–53 at.%Ni 1040°, p, IR 1 β, 44–64 at.% Cu 902°, IR 1

Au Zn

Ga

Immisc.

As Bi

Compl. immisc.

No compds.

Compl. immisc. No compds.

No compds.

Compl. immisc. NiHg4, 225°, p

Compds.

Compds. Cu7Hg6, 128°, p

β , 43–62 at.%Au 751°, IR1

γ, 70–77 at.%Zn 43°, IR 1 Extended monotectic

Extended monotectic Zn–Ge simple eutectic

Pb

Zn3As2, 1015°, IR 1

Compl. immisc.

Compl. immisc.

Zn–Ga simple eutectic

Ge

MnHg, 400°, p, IR 1

Immisc.

γ, 70–77 at.%Zn 43°, IR 1

Tl

Compl. immisc. Compl. immisc.

– Hg

LaHg, 1074°, IR 1 Hf2Hg, 368° p

Compds.

Ta Cr

BaHg, 822°, IR 1

Compds.

V4Zn5, 670°, p

V

Compds.

CsHg2, 208°, IR 1

Compl. immisc. Extended monotectic

β , 77–84 at.% Au 419°, p, IR 1

γ, 20–34 at.%Tl 15°, IR 1 s.s. Pb2Hg, 145°, IR 1

Hg3As2 Extended monotectic

Bi–Hg simple eutectic

476

Intermetallic Chemistry

Table 5.59a. A selection of intermediate phases in the binary alloys of Be. Structure type

CNE (Be)

Examples of isostructural phases Be compounds

cF112-NaZn13

10–12

Be13X: X Mg, Ca, Sr, Ba, Sc, Y, Ln(La–Lu), Th, Pa, U, Np, Pu, Am, Cm, Zr, Hf, Sb

tI26-ThMn12

12–14

Be12X: X Ti, V, Nb, Ta, Cr, Mo, W, Mn, Fe, Co, Pd, Pt, Ag, Au

hR57-Nb2Be17

12–14

Be17X2: X Ti, Zr, Hf, Nb, Ta

cF24-AuBe5

12–16

Be5X: X Pd, Au(14–18Au)

hP6-CaCu5

12

Be5X: X Sc, Zr, Hf

hR36-NbBe3

12

Be3X: X Ti, Nb, Ta

hP12-MgZn2

12

Be2X: X V, Cr, Mo, W(28–36W), Mn, Re(30–40Re), Fe(21–37Fe), Ru, Os

cF24-Cu2Mg

12

Be2X: X Ti, Nb, Ta, Mn(7.1–25Mn), Fe(7–18Fe), Cu(19–36Cu), Ag(27Ag)

cP2-CsCl

14

BeX: X Ti, Co(26–54Co), Rh, Ir, Ni(25–52Ni), Pd, Pt, Cu(50–55Cu)

cF8-ZnS

4

BeX: X S, Se, Te, Po

cI2-W

14

Be–X: X Cu(57–78Cu)

5.12.4.4 Notes on the application of Be, Mg, Zn, Cd, and Hg alloys. Beryllium and magnesium, together with aluminium and titanium, belong to the group of the so-called Light metals (density, g/cm3, Be: 1.85, Mg: 1.74, Al: 2.70 and Ti: 4.50). Beryllium. Beryllium alloys and beryllides could be potentially useful as hightemperature structural materials, owing to their high melting temperatures and thermodynamic stability, even if their low toughness and brittleness represent (especially for the high stoichiometry phases) heavy drawbacks. Possibly NiBe, and its alloys with NiAl, could be raw materials for the development of interesting structural products (Jacobson et al. 2002). A problem in the use and applications of beryllium is related to the high toxicity it has for some percentage of the human population, and bad understanding of the factors determining this toxicity. Magnesium. Magnesium and its alloys are used in a wide variety of structural and non-structural applications; structural applications include automotive and aerospace industry, industrial machinery, materials-handling and commercial equipments. Mg is also used as an alloying element in Al, Zn, Pb, etc. alloys. It is used as an oxygen scavenger and de-sulphurizer (in iron and steel industry) and as a reducing agent in the production of Be, Ti, Zr, Hf, U, etc.

Elements of Alloying Behaviour Systematics

477

Table 5.59b. A selection of intermediate phases in the binary alloys of Mg, Zn, Cd, Hg. Structure type

CNE (Me)

Examples of isostructural phases Mg compounds

Zn, Cd, Hg compounds Zn13X: X K, Rb, Ca, Sr, Ba, La, Eu Cd13X: X K, Rb, Cs

cF112-NaZn13 10–12 tI26-ThMn12

12–14

Zn12X: X Sc, Y, LnIII(Sm–Lu)

tI48-BaCd11

10–14

Zn11X: X Ca, La, Ce, Nd, Eu, Yb Cd11X: X Ln(La–Sm), Th, U, Np, Pu Hg11X: X Ca, Sr, Ba

hP38-Th17Ni2

18–20 Mg17X2: X Sr, La, Eu

Zn17X2: X Y, LnIII(Ce–Lu), Th, U

tI92-Ce5Mg41

8–15

cI184-YCd6

–

Cd6X: X Ca, Sr, Y, Ln(Ce–Lu), Pu

hP6-CaCu5

12

Zn5X: X Ca, Sr, Y, Ln(La–Gd), Dy, Er, Th,

cF448Sm11Cd45

12–16

Cd45X11: X Y, LnIII(Pr–Lu)

hP142Gd13Zn58

–

Zn58X13: X LnIII(Pr–Lu), Yb Cd58X13: X Y, Ln(La–Gd) Hg58X13: X La, Sr

oP16-YZn3

10–12

Zn3X: X Y, LnIII(Ce–Lu)

cP4-AuCu3

12

Mg3X: X In(26–38.5In)

cF16-BiF3

14

Mg3X: X LnIII(La–Dy)

hP8-Ni3Sn

12

Mg3X: X Cd(18–37 Cd), In

hP8-Na3As

9–11

Mg3X: X Ir, Pd, Pt, Au, Hg

hP3-CeCd2

14

Cd2X: X Y, LnIII(La–Ho), Tm, Lu Hg2X: X Ca, La, Ln(Nd–Ho), Yb

oI12-CeCu2

10

Zn2X: X Ca, Sr, Ba, Ln(La–Lu)

cF24-Cu2Mg

12

Mg2X: X Ln(La–Gd), Th, Sn, Ge

Zn2X: X Zr, Hf, Pu

hP12-MgZn2

12

Mg2X: X Ca, Sr, Ba, Y, Ln(Eu–Lu), Zn

Zn2X: X Mg, Ti

hP3-AlB2

9

Hg2X: X Na, Sr, Y, La, Ce, Ho, Er, U

cI52-Cu5Zn8

11–13

Zn8X5: X Ag(35.3–42Ag), Cu(30–43Cu), Fe(17–31Fe), Ni(15–30), Pd(14.5–24) (Continued)

Mg41X5: X Ln(La–Sm)

Zn3X: X Ti, V, Nb, Mn Hg3X: X Zr, Tl Cd3X: X Mg, Sc,Gd, Tb, Th Hg3X: X Li, Ca, Sr, Sc, Y, Ln(La Lu), Th

478

Intermetallic Chemistry

Table 5.59b. (Continued) Structure type

CNE (Me)

Examples of isostructural phases Mg compounds MgX: X Sr, Sc, Y, Ln(La– Tm), Lu, Ag(34.5–64.5Ag), Au(42–67Au), Rh, Pd, Hg, Tl

Zn, Cd, Hg compounds ZnX: X Ba, Sc, Y, Ln(La–Lu), Mn, Ni, Cu, Ag, Au, Pd(35–70Pd) CdX: X Ca, Sr, Ba, Sc, Y, Ln(La–Lu), Au(43–57Au), Pd(37–45Pd) HgX: X Li, Mg, Ca, Sr, Ba, Sc, Y, Ln(La–Lu), Mn, Tl

cP2-ClCs

14

cF8-ZnS

4

ZnX: X Ni, S, Se, Po CdX: X Se, Te, Po HgX: X S, Se, Te

hP4-ZnS

4

ZnX: X S, Se CdX: X S, Se, Te

cF8-NaCl

8

CdX: X S, Se, Te HgX: X S, Se, Te, Po

tP4-AuCu

12

HgX: X Ti, Zr, Ni, Pd, Pt, Pb(65–73Pb)

tI6-MoSi2

14

HgX2: X Ba, Hf, Cd, Hg2Mg

hP8-Ni3Sn

12

MgX3: X Cd(68–75Cd)

cP4-AuCu3

12

MgX3: X Ag(73–81Ag), In(69.5–75.5In), Pt

ZnX3: X Zn HgX3: X Ti

The ‘red mercury’ tale. The so-called red mercury has been the subject of an age-old somewhat mysterious and fabulous story possibly connected with nuclear contraband and trafficking. According to Guminski, who systematically reviewed phase diagrams and properties of mercury alloys, this material could be the reddish powder of a plutonium (and possibly uranium) amalgam (Guminski 2005). Because Hg captures neutrons any transportation or handling of this alloy is easier and safer than that for the pure actinide and, on the other hand, this may be recovered from the red powder by evaporation of mercury at high temperature. 5.12.4.5 Magnesium alloys: standard ASTM alloy designation. From a commercial and industrial point of view, standard systems of alloy (and temper) designation have been adopted and are generally used in different countries. As an illustration of such a practice, Table 5.60 summarizes the designation symbols used in the commercial Mg alloys according to the standard ASTM coding system. As an example of a specific magnesium alloy code we may mention the alloy designated by AZ91E-T6. It contains Al and Zn as principal alloying components. The

Elements of Alloying Behaviour Systematics

479

Table 5.60. Magnesium alloys: standard ASTM system of alloy (and temper) designation. An example of commercial alloy coding system. The ASTM designation code of the Mg alloys consists of a string of characters composed by four subsequent parts having the following meanings: First part Consists of two code letters representing the two main alloying elements arranged in order of decreasing percentage according to the following symbols: A: aluminium; B: bismuth; C: copper; D: cadmium; E: rare earth; F: iron; G: magnesium; H: thorium; K: zirconium; L: lithium; M: manganese; N: nickel; P: lead; Q: silver; R: chromium; S: silicon; T: tin; W: yttrium; Y: antimony; Z: zinc Second part Indicates the amounts of the two principal alloying elements by two digits corresponding to rounded-off mass percentages of these elements. Third part Distinguishes between different alloys with the same percentages of the two principal alloying elements and consists of a letter sequentially assigned as compositions become standard. Fourth part Indicates temper conditions according to the following symbols: F: as fabricated; O: annealed; H10 and H11: slightly strain hardened; H23, H24 and H26: strain hardened and partially annealed; T4: solution heat treated; T5: artificially aged only; T6: solution heat treated and artificially aged; T8: solution heat treated, cold worked and artificially aged.

rounded-off percentages of these elements are 9 and 1, respectively. The letter E specifies that this is the 5th alloy standardized with 9% Al and 1% Zn as principal additions. The T6 symbol indicates that this is solution heat treated and artificially aged. 5.13. ALLOYS OF THE ELEMENTS OF THE 13TH GROUP OF THE PERIODIC TABLE

Boron, B; aluminium, Al; gallium, Ga; indium, In; thallium, Tl

5.13.1 Introduction As can be inferred from their position in the Periodic Table, these elements pertain to the p-block. The first of them (boron) is just above the Zintl line; the others

480

Intermetallic Chemistry

are clearly more metallic in character. All these elements are at the left of the covalent divide and they have fewer than four valence electrons. The elements of the 13th group with 3 valence electrons as the elements of the 12th group (Zn, Cd, Hg) with 2 valence electrons may be called hypoelectronic elements, that is elements having fewer than 4 valence electrons in the four orbital sp3 manifold. These elements may acquire a noble-gas electronic configuration forming multi-centre bonds that is giving electron-deficient compounds in which an electron pair is not available for each pair of atomic orbitals to form only two-centre – two-electron bonds. Boron (B, [He]2s22p1), name and symbol from the Persian word burah and the Arabic word buraq (borax). The suffix-on was added because of the similarity to carbon. Discovered (1808) by J.-L. Gay-Lussac and L.J. Thenard in France and Humphry Davy in England. Semi-metal; impure (amorphous) boron is a brown powder; the pure element is shiny, silver grey. Atomic number 5, atomic relative mass 10.811. Occurrence. It is found as borates or as orthoboric acid in some volcanic spring waters. Important sources are borax (Na2B4O7 10H2O), kernite (Na2B4O7 4H2O), colemanite (Ca2B6O11 5H2O). Preparation. It is difficult to prepare very pure boron. The element can be obtained by magnesium reduction of the oxide, B2O3. The oxide is made by melting boric acid which in turn is obtained from borax. Amounts of very pure boron must be prepared through the thermal reduction of boron trihalides with hydrogen gas or by decomposition of BI3 using a heated tantalum wire. Uses. Amorphous boron is used as an addictive in pyrotechnic mixtures, solid rockets propellants, explosives, etc. Refractory metal borides are used as addictives to cemented carbides. High purity boron is used in electronics as a dopant to Ge or Si. Aluminium (Al, [Ne]3s23p1), name after the Latin word alumen (alum, K2Al6(OH)12(SO4)4, used in ancient times as an astringent). Discovered (1825) in Denmark by Hans Christian Oersted. Silvery white metal. Atomic number 13, atomic relative mass 26.981539.

Elements of Alloying Behaviour Systematics

481

Occurrence. It is the commonest metallic element in the earth’s crust. Aluminium occurs in many silicates such as micas and feldspars, hydroxo oxide (bauxite), cryolite (Na3AlF6). Preparation. Aluminium is mined on vast scale as bauxite (AlOx(OH)32x 0 x 1). Bauxite is purified to remove impurities such as Fe2O3, SiO2 and other oxides by treatment with sodium hydroxide solution. Al(OH)3 is precipitated, filtered off, washed, and heated to 1200°C to form pure alumina, Al2O3. Aluminium is obtained by an electrolytic method from the pure Al2O3 dissolved in cryolite at 800–1000°C. For the production of high pure aluminium in the electrolytic refinement cells, a segregation sump is added for the removal of the impurities. Fractional crystallization (possibly in subsequent different steps) is used to refine aluminium. For economic reasons, due to the high cost of the primary production, great efforts are being made to collect and recycle scrap of aluminium, for instance beverage cans. Uses. Aluminium is extensively used in thousands of industrial applications where a strong, light, easily constructed material is needed (modern aircrafts, rockets, etc.). It is used in electrical transmission lines because of its light weight although its electrical conductivity is only about 60% that of copper. Aluminium, evaporated in a vacuum, forms a highly reflective coating for both visible light and radiant heat. These coatings soon form a thin layer of the protective oxide and do not deteriorate as do silver coatings. They are used to coat telescope mirrors and to make decorative paper, packages, toys. Gallium (Ga, [Ar]3d104s24p1), name and symbol after the Latin word Gallia (France). Discovered (1875) by Paul-Emile Lecoq de Boisbaudran. Silvery white metal. Atomic number 31, atomic relative mass 69.723. Occurrence. Gallium ores are rare. It occurs in aluminium and zinc ores, for instance bauxite and zinc blende. Preparation. Gallium is extracted from the circulating liquors of the Al2O3 process, by fractional precipitation, electrolytic process or extraction with chelating agents. Uses. The main uses of gallium is in the manufacture of semiconductors which are generally obtained by the combination of Ga with P and As. Gallium arsenide is capable of converting electricity directly into coherent light (production of light-emitting diodes). Indium (In, [Kr]4d105s25p1), name and symbol after the indigo line in its atomic spectrum. Discovered (1863) by Ferdinand Reich and Hieronymus Theodor Richter. Silvery lustrous grey, very soft metal. Atomic number 49, atomic relative mass 114.82.

482

Intermetallic Chemistry

Occurrence. Indium is widely spread in nature, generally in very low concentrations (0.1 ppm, earth’s crust). Indium is present as a trace element in many minerals, such as sphalerite. Preparation. Indium is recovered by electrolysis or chemical reduction from residues, flues dusts, slags from zinc or lead or tin productions. Uses. Indium finds application in making low melting alloys; the eutectic alloy indium–gallium (14.2 at.% In, 21.4 mass% In) melts at 15.3°C. In is used as an additive to solder alloys to improve malleability at low temperature and corrosion resistance; it is also used in dental alloys, in the preparation of semiconductors, etc. Thallium (Tl, [Xe]4f 145d106s26p1), name and symbol after the bright green line of this spectrum (Greek word θαλλο meaning green twig or green shoot). Discovered (1861) by W. Crookes and C.A. Lamy. Silvery white soft metal. Atomic number 81, atomic relative mass 204.3833. Occurrence. Thallium can be associated to heavy metals that occur in sulphidic ores (chalcophilic element behaviour) or to alkali metals in minerals such as carnallite, sylvite, mica (the Tl1 ion behaves as an alkali metal ion), or in true, but very rare, thallium minerals such as lorandite (TlAsS2), chalcothallite (Cu3TlS2). Preparation. Thallium is recovered as by-product of zinc and lead processes. Uses. The unalloyed metal cannot be directly used owing to its bad mechanical properties and its high oxidability. Several thallium alloys are used as semiconductors or ceramic compounds; it may be used as additive to gold, silver or copper contacts in the electronic industries. Thallium is dangerously toxic. 5.13.2 B, Al, Ga, In, Tl: a summary of their atomic and physical properties Two allotropes of boron are known: the α rhombohedral boron that consists of nearly regular B12 icosahedra covalently linked by B–B bonds to form an infinite lattice (slightly deformed cubic close-packed structure) and the more complex β rhombohedral boron (hR315) consisting of an infinite lattice of B84 units, connected through B10 units. The B84 unit can be conveniently described in terms of covalently bonded sub-units (B12)(B12)(B60). Because of the five-fold rotation symmetry at the individual B atoms, the B12 icosahedra pack rather inefficiently (the percentage of space occupied by atoms in the α boron is only 37%). The covalent lattices of both allotropes are extremely rigid, making crystalline boron very hard and with a high melting point. Atomic and physical properties of B, Al, Ga, In and Tl are collected in Tables 5.61–5.63.

Table 5.61. B, Al, Ga, In, Tl: selected atomic and physical properties. Property

B

r/pm, metallic, CN 12 [‘metallic valence’] r/pm, ionic, M1, CN 6 r/pm, ionic, M3, CN 6 Tmelting/°C Tboiling/°C ΔHmelting (at Tmelting)/kJ/mol ΔfH0 of Me1 gas at 298.15 K/kJ/mol

Al

Ga

In

Tl

92.0 [3]

143.2 [3]

135.3 [3]

166.6 [3]

27 2092 4002 50.2 560

53.5 660.452 2520 10.7 330

62 29.7741 2205 5.6 272

80 156.634 2073 3.28 –

171.6 [3] 150 88.5 304 1473 4.14 –

Table 5.62. B, Al, Ga, In, Tl: ionization energies. Element

1st ionization energy kJ/mol

2nd ionization energy kJ/mol

3rd ionization energy kJ/mol

4th ionization energy kJ/mol

B Al Ga In Tl

801 578 579 558 589

2427 1817 1979 1821 1971

3660 2744 2960 2705 2878

25026 11577 6200 5210 –

Table 5.63. B, Al, Ga, In, Tl: crystal structures, lattice parameters of their allotropes and calculated densities. Element (allotrope) Temperature range/°C Pressure/GPa βB

Boron 2092°

Aluminium αAl 660.452° βAl 20.5 GPa Gallium αGa 29.7741° βGa 1.2 GPa γ Ga 3.0 GPa Indium In 156.634° Thallium αTl 230° βTl 230° to 304° γTl HP

Crystal structure

Lattice parameters pm a

hR315-βB

1093

cF4-Cu hP2-Mg oS-αGa tI2-In oS40-γGa

404.96 269.3

b

Atomic volume/ pm3106

Molar volume/ cm3/mol

Density/ g/cm3

c 2382

(7.82)

4.71

(2.29) dm 2.33

16.60

10.00

2.699

19.573

11.79

5.918

439.8

451.86 765.70 452.58 280.8 445.8 1059.3 1352.3 520.3

tI2-In

325.3

494.70

26.17

15.76

7.284

hP2-Mg cI2-W cF4-Cu

345.66 387.9

552.48

28.58 29.18

17.21 17.57

11.874 11.630

–

484

Intermetallic Chemistry

The α tetragonal form, firstly reported as a boron allotrope, has been reformulated as B50C2 or B50N2, depending on the preparative conditions; it never forms in absence of carbon or nitrogen.

5.13.3 The 13th group elements: remarks about their general chemical properties and reactivity Because the number of orbitals available for boron is higher than electrons (three electrons, four orbitals) boron is an electron-pair acceptor, a Lewis acid and it is prone to form multi-centre bonds. Boron is inert under normal conditions except for attack by fluorine. At high temperatures it reacts with most non-metals and most metals. The general chemical inertness of boron at lower temperatures is highlighted by the fact that it resists attack by boiling concentrated aqueous NaOH or by fused NaOH up to 500°C. Al, Ga, In and Tl differ sharply from boron. They have greater chemical reactivity at lower temperatures, well-defined cationic chemistry in aqueous solutions; they do not form numerous volatile hydrides and cluster compounds as boron. Aluminium readily oxidizes in air, but bulk samples of the metal form a coherent protective oxide film preventing appreciable reaction; aluminium dissolves in dilute mineral acids, but it is passivated by concentrated HNO3. It reacts with aqueous NaOH, while gallium, indium and thallium dissolve in most acids. Thallium. This metal has been considered the ornithorhynchus (duck-billed platypus) of the metals. The animal ornithorhynchus, indeed, shows a mixture of the characteristics of various different zoological species: it belongs to the unusual order of quasi-mammals or mammal-like reptiles. Chemistry of thallium often resembles that of metals of other groups than its own. This is especially true in the oxidation state I, which is quite stable: the radius of Tl can be compared with those of K, Rb and Ag, and similarities with the chemistries of these metals may be noticed. Tl metal tarnishes readily and reacts with steam or moist air to give TlOH which is very soluble and is a strong base, Tl2CO3 is also soluble and resembles the analogous Na and K compounds. The Tl behaviour similar to that of K may be related also to its capability to substitute for potassium in cell processes and possibly to its exceedingly high toxicity. Notice, along this row of the Periodic Table a sequence of highly toxic elements: Hg, Tl, Pb. On the other hand, a number of salts (halides, chromate, etc.) of Tl show properties well comparable with those of the analogous Ag compounds. Thallium may be described as a ‘relativistic alkali metal’: the downshift in energy of the 6s orbital, due to a combination of relativity and shell structure effect, favours the oxidation state I over III (see § 4.2.2.2). The stability of the oxidation state 1

485

Elements of Alloying Behaviour Systematics

in the 13th group increases in the sequence Al Ga In Tl. This may be considered also as an example of the occurrence of an oxidation state which is 2 less than the normal group valence and which is sometimes referred to as the ‘inert-pair effect’. There are indeed a number of cases among compounds of the heavier main group elements where one pair of valence shell electrons is confined to the valence shell s orbital where it is spherically distributed and plays no significant role in determining the bonding structure. Examples are InI, TlI, SnII, PbII, SbIII, BiIII, TeIV, PoIV. 5.13.4 Intermetallic chemistry of the 13th group elements 5.13.4.1 Phase diagrams of the 13th group elements. The reactivity patterns of the elements of the 13th group are shown in Fig. 5.34. A comparison between beryllium (Fig. 5.33) and aluminium and between boron and silicon shows several similarities between these pairs of elements and gives examples of the so-called ‘diagonal relationships’ presented in § 4.2.2.2. Considering the overall compound formation capability of the various elements of the 13th group we notice a certain number of analogies between them, such as the compound formation with the metals at the left side of the Periodic Table (with the exception of Al with the alkali metals), including lanthanides and actinides.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

B

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Ga

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Al

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

In

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Tl

Compound-forming element

Phase diagram known; no intermediate phases formed

No information available

Questionable compound forming capability

Figure 5.34. Compound formation capability in the binary alloys of B, Al, Ga, In, Tl.

486

Intermetallic Chemistry

Moving from one element to the other down the group we notice a decrease in the compound formation elements according to a scheme similar to those observed in the 12th, 14th and 15th groups. Owing to their numerous actual and potential applications, several ternary and complex systems of these metals, especially of aluminium, have been investigated; a few examples of the systematics of Al–Me–X alloys are presented in § 5.18 and in Fig. 5.41. Recent contributions to this subject have been given with the study of the systems R–Al–Cu (Riani et al. 2005, and references there in). These rare earth alloys, characterized by the formation of several intermediate phases, are interesting also as raw materials for the preparation of amorphous alloys. Regularities in the trends of their properties have been underlined. The experimental and calculated data relevant to the binary systems Al–Fe, Al–Ni and Fe–Ni have been examined and discussed in a paper concerning the assessment of the ternary Al–Fe–Ni system (Eleno et al. 2006). A specific aspect of the alloying behaviour of Ga and In was studied by Guminski (1989, 1990), who compiled and discussed the data concerning the solubility of metals in liquid low melting metals. Solubility data at 600°C have been plotted and discussed as a function of the atomic number; curves showing periodic variations were obtained with trends very similar to each other and to those prepared for Hg, Sn, Pb and Bi. Elements showing low or very low solubility (at 600°C) in liquid Ga or In are for instance: Ti, V, Cr, Fe, Co, Zr, Nb, Mo. Ru, Hf, Ta, W, Re, Os (with deep minima for V, Nb, W). High solubility (often resulting in the formation of a continuous liquid solution stable at intermediate temperatures) is shown by Mg, Zn, Cd, In, Hg, Tl and Bi. The intermetallic reactivity of Al and In and the stability of their compounds are also highlighted by the trends of the melting points of their alloys. A selection of these data are reported in Table 5.64. 5.13.4.2 Remarks on the crystal chemistry of the triel elements (Al, Ga, In, Tl). Tables 5.65a, 5.65b and 5.65c summarizes the crystal data of typical phases pertaining to the alloys of the 13th group. A few specific comments are in the following. Borides. A systematic contribution to the chemistry and crystallography of metal borides and their classification has been given by Rogl (1992). The crystal structures of metal borides can be classified with respect to the boron aggregation as a function of the metal to boron ratio. The boron-centred triangular prism is one of the dominating structural building elements. From a geometrical point of view, triangular prismatic coordination M6X may be produced by direct stacking of closepacked triangular layers 36 of atoms M on top of each other, and inserting a second set of layers 36 of atoms X between each two layers of M. With this arrangement half of the triangular prisms are centred and the trigonal prism M6X is the only

Table 5.64. Highest melting points (°C) in the alloys of aluminium and indium with compound-forming elements of the 4th and 6th rows of the Periodic Table. Alloys with K

Aluminium compounds

Indium compounds

Extended monotectic Cs

Ca Ba Sc La Ti Hf V Ta Cr W Mn Re Fe Os Co Ir Ni Pt Cu Au Zn

CaAl2, 1079°, IR 1 ScAl2, 1400°, IR 1 s.s. TiAl, 1476°, p, IR 1 V5Al8, 1670°, p, IR 1 Cr5Al8, 1350°, p, IR 1 ε, 53.2 to 60 1250, p, IR 1 s.s Fe2Al5, 1169°, IR 1 s.s. CoAl, 1640°C, IR 1 s.s. NiAl, 1638°, IR 1 β, 69.5 to 82 1049°, IR 1

Extended monotectic BaAl4, 1104°, IR 1 LaAl2, 1405°, IR 1 HfAl, 1800°, IR 1 Ta2Al, 2061°, p, IR 1 WAl2, 1650°, p, IR 1 Re2Al, 2002, p, IR 1

IrAl, 2000°, IR 1 s.s. Pt3Al, 1556°, IR 1 AuAl2, 1060°, IR 1

Eutectic Hg

Ga

s.s. Ti3In, IR 1

Pb

s.s. La3In5, 1185°, IR 1 Compds. Immisc.

Mn3In, 910°, p, IR 1 Extended monotectic CoIn2, 550°, p, IR1 ξ , 58–68.8 at.% Ni 950°, IR1 γ , 68.7–72.3 at.% Cu 684°, IR 1

Simple In–Ga eutectic Simple In–Ge eutectic

Monotectic

BaIn2, 965°, IR 1

Compds.

Extended monotectic AlAs, 1780°, IR 1

Cs2In3, synt 570°, IR 1

Extended monotectic

Immisc. Simple Al–Ge eutectic

Bi

Sc2In, 1400°, IR 1

Simple Zn–In eutectic

Simple Ga–Al eutectic

As

CaIn, 895°, IR 1

Simple Hg–Al eutectic

Tl Ge

s.s. KIn2, 478°, IR 1

InAs, 938°, IR 1

Compds. Pt2In3, 1064°, IR 1 ξ, 77.6–87.8 at.% Au, 641°, IR 1 ε, 6.1–22 at.% Hg, 108°, p, IR 1 α, 16–58 at.%Tl α, 13–28 at.%Pb 172°, IR 1 InBi, 110°, IR 1

Table 5.65a. Selected structural types of binary borides. Structure type

CNE (B)

Examples of binary borides

cF52-UB12

5

MeB12: Me Sc, Y, Yb, LnIII(Gd–Lu), Zr, Hf

cP7-CaB6

5

MeB6: Me K, Ca, Sr, Ba, Y, Eu, Yb, LnIII Th, Np, Pu, Am

tP20-ThB4

3–5

hP3-AlB2

9

MeB4: Me Y, Yb, LnIII(La–Lu), Th, U, Np, Pu MeB2 (or derivative structures): Me Ln(Gd–Lu), Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, Mn

oS8-CrB

9

MeB: Me V, Nb, Ta, Cr, Mo, W, Mn, Ni

oP8-FeB

9

MeB: Me Ti, Mn, Fe, Co

coordination polyhedron. Another form of triangular prismatic coordination is obtained from alternate stacking of 63 and 36 layers which results in a crystal structure AlB2-type with all triangular prisms centred. According to Rogl (1992) the triangular prismatic coordination M6B is the predominant structural building block in an intermediate composition range (between a B/M atomic ratio included between 1/8 and 4/1). Less frequent are the M6B octahedral and the M8B square anti-prismatic coordinations. As for the B substructures and atom aggregations in the metal borides, an indication is given by the scheme shown in Fig. 5.35. Notice for low B concentrations the presence of isolated B atoms, typically found in octahedral interstices of intermetallic host structures in which they may act as ‘stabilizers’ of ternary solid solutions or compounds (resulting in structures such as cF96-Ti2Ni type, β-Mn type, hP16Mn5Si3type, cP5-CaTiO3 (perovskite) type, etc.). With high B content, on the other hand, B substructures corresponding to polyhedra (octahedra, icosahedra, cubooctahedra) containing the M atoms in convenient interstices inside the rigid B framework are observed. For a number of boride structures and their inter-relations see § 7.2.2. Notes on cluster phases in triel alloys. Li and Corbett (2004) have shortly reviewed the systematic and extensive experimental and theoretical work carried out by Corbett and co-workers (see for instance Corbett 1996). Considering alkali metal–triel alloys, they underlined, particularly for Ga, In and Tl, the richness of their chemistry (see also § 5.3.4.4). Gallium forms many anionic network structures (and only a few phases containing isolated cluster units), indium gives several examples of both network and discrete cluster structures, thallium forms especially 7 discrete clusters (Tl48, Tl57, Tl66, Tl99, Tl11 , Tl10 13 ). An interesting related feature shown by several alloys of the more basic metals (alkali, alkaline earths) with many p-block (13th, 14th, 15th groups) elements, and,

Table 5.65b. A selection of intermediate phases in the binary alloys of Al and Ga elements. Structure type

CNE (Me)

Examples of isostructural phases Al compounds

cI26-WAl12 tP14-PuGa6 tI10-BaAl4 oI20-UAl4 hP8-Ni3Sn tI8-TiAl3

11 9–11 9–12 11–13 12 12

Al12X: X Mo, W, Mn, Re, Tc

tP4-AuCu3

12

Al3X: X Sc, Y, Pr, Dy, Tm, Yb, Lu, U, Np, Pu, Zr

tP16-CoGa3

12–14

hR48-PuGa3 cF24-Cu2Mg

12 12

hP3-AlB2

9

oP32-Tm3Ga5

10–12

hP5-Ni2Al3

11–12

cF8-ZnS cP2-CsCl

4 14

oS8-CrB

17

tP4-AuCu

12

oP16-DyAl tP20-Gd3Al2 tP20-Zr3Al2 oI12-CeCu2 hP16-Mn5Si3

10–12 10 10 10 11

tI32-Cr5B3

9–10

tI32-W5Si3

10

oP12-Co2Si tI6-MoSi2 cP4-AuCu3

10 14 12

AlX2: X Y, LnIII(Pr–Er), Pd, Pt AlX2: X Cr, Tc, Re, Os, Au AlX3: X La, Ce, Pr, Sm, Tb, Ni, Zr

hP8-Ni3Sn

12

AlX3: X Ce, La, Nd, Pr

Al4X: X Ca, Sr, Ba, Ln(La–Eu) Al4X: X Sm, Gd, Tb, U, Np, Pu Al3X: X Y, LnIII(La–Gd), Th Al3X: X Dy, Ti, Hf, V, Nb, Ta

Al2X: X Ca, Sr, Ba, Y, Sc, Ln(La–Lu), Th, Np, Pu

Ga compounds Ga6X: X Y, Ln(La–Yb), Pu Ga4X: X Na, Sr, Ba, Eu, Yb Ga3X: X Ti, Hf, Nb(21–23Nb) Ga3X: X Sc, LnIII (Dy–Lu), Np Ga3X: X Re, Ru, Os, Co, Rh, Ir Ga3X: X Dy, Pu Ga2X: X Ca, Sr, Ba, Y, Ln(La–Er), Th, U, Np, Pu Ga5X3: X Sc, Y, LnIII(Tb–Lu)

Al3X2: X Ru, Ni, Pd(38–42Pd), Pt, Cu(59.3–61.9Cu) AlX: X P, As, Sb AlX: X Sc, Y, Ce, Pr, Sm, Gd, Dy, Re, Fe, Ru, Os, Co, Rh, Ir, Ni, Pd, Pt

GaX: X P, As, Sb GaX: X Co, Rh, Ir, Ru, Ni GaX: X Ca, Y, Sc, Ln(La–Lu) Ga–X: X Mn(44.5–52Mn), Mn(55–60Mn), Ti, Yb, Pt

AlX: X LnIII(Pr–Lu) Al2X3: X Y, LnIII(Gd–Er) Al2X3: X Dy, Er, Tm, Lu, Zr, Hf

GaX2: X Sc, Tm, Lu, Cu Ga3X5: X Sc, Y, LnIII(Ho–Lu), Ti, Zr, Hf, V, Nb, Ta Ga3X5: X Ca, La, Nd, Sm, Gd, Dy, Tb, Ta Ga3X5: X Ce, Pr, Pu, Ti, Nb, Ta GaX3: X La, Ce, Pr, Nd, Sm, Pu, Fe(70.8–73.8Fe), Pt(67–76Pt) GaX3: X Fe(71–74Fe)

490

Intermetallic Chemistry

Table 5.65c. A selection of intermediate phases in the binary alloys of In and Tl elements. Structure type

CNE (Me)

Examples of isostructural phases In compounds

cP4-AuCu3

12

In3X: X Mg(24.5–30.5Mg), Sc, Y, LnIII(La–Lu), Yb, Th, U, Pu(25–27Pu)

tP16-CoGa3

12–14

In3X: X Co, Rh, Ir

oS32-Pu3Pd5

10–11

In5X3: X Ln(La–Tm)

hP6-CaIn2 tI12-CuAl2

10 15

In2X: X Ca, Sr, Eu, Yb

Tl compounds Tl3X: X Ca, Ln(La–Lu), Th, U

Tl5X3: X Y, LnIII(La–Er), Th Tl2X: X Pd, Pt

oI12-CeCu2

10

In2X: X Ba, La, Ce

cP2-CsCl

14

InX: X Ca, Y, Ln(La–Yb), Rh, Ni, Pd(45–61.5Pd)

TlX: X Li, Mg, Ca, Sr, Y, Ln(La–Yb)

tP4-AuCu

12

In–X: X Mg(41–61Mg), Pu(48–52Pu), Zr(66.7Zr)

TlX: X Sm, Er, Sn

cF8-ZnS (sphalerite)

4

InX: X P, As, Sb, Te(59.5–60.1Te)

cF8-NaCl

6

InX: X P, As, Sb Te

hP16-Mn5Si3

11

In3X5: X Y, LnIII(Er–Lu)

Tl3X5: X Y, LnIII (Gd–Lu), Th

hP6-NiIn2

11–14

InX2: X Sc, Y, LnIII(La–Lu), Ni, Cu, Bi

TlX2: X LnIII(Pr–Dy)

cP52-Cu9Al4

11

In–X: X Ag(66.4–68.9Ag), Au(68.6–71.2Au)

hP8-Ni3Sn

12

InX3: X Mg, Sc, Ti, Ru, Ni

cP4-AuCu3

12

InX3: X Mg(61.5–74Mg), Sc, Ln(La–Sm), Pu, Zr, Ni, Pt(71–76Pt), Ag

TlX3: X Ln(La–Nd), Np

as an important example with the triels, is the formation of liquid compounds (intermetallic, often complex structures, in the liquid state). A few notes and references on this point are shown in § 3.2 ff. Hetero-atomic clusters, moreover, may be derived from the binary structures mainly through the introduction of late transition or earlier post-transition elements. Examples of ternary alloys containing such structures are the alkali metal salts of centred clusters In10Me10 (Me Ni, Pd, Pt), Tl12 Me12 (Me Mg, Zn, Cd, Hg), etc. The crystal structure of the phase Na13(TlxCd1x)27 (0.24 x 0.33)

Elements of Alloying Behaviour Systematics

491

was also studied. Its bcc structure was described in terms of multiply endohedral concentric shells of atoms and considered as having a Bergman-type structure (see § 4.4.4.7 and Fig. 4.38). According to Li and Corbett (2004), it may be described as an electron-poor Zintl phase. Mg also was found able to form part of anionic clusters sharing atom sites with In. Li and Corbett (2006a) prepared K3Mg20In14 which was described as a stuffed variant of the cP36-BaHg11 type. Its network structure contains K-centred 22-vertex polyhedra K@Mg12In10 and cuboctahedral fillers In@Mg12. In comparison with the cP36-BaHg11-type structure (see § 7.5.1.9), in cP37-K3Mg20In14, K occupies the Ba positions, Mg and In the four Hg positions, and an extra In atom is present. New K–In–Me (Me Au, Zn, Mg) network compounds have been studied by Li and Corbett (2006b). The compounds K34In96.2Au8.8, K34In89.9Zn13.1 and K34In91.1Mg13.9 were synthesized by high-temperature means and characterized by single-crystal diffraction methods. All these compounds may be considered analogues of earlier products related to a hypothetical lattice K34In105. They consist of complex three-dimensional anionic networks built of In12 icosahedra and X28 triply fused icosahedra (X In or In/Me). The K atoms bridge between cluster faces or edges and form K136 clathrate networks. Two neighbouring X28 units are interconnected via an X atom, forming a sandwich complex. It was observed that in all the three compounds phase stabilization through electronic tuning was obtained via substitution of the electron-poorer metals for indium. The effect of the size of the substituted element was also considered. 5.13.4.3 Notes on the applications of aluminium alloys. Commercial aluminium alloys are discussed in next section. Curiosity on Al alloys. The congruent melting (1060°C) compound AuAl2 (facecentred cubic cF12-CaF2 type) has gone down in history. It was probably one of the first intermetallic compounds identified (Roberts-Austen 1892) and it has long fascinated metallurgists for its intense purple colour. This colour has been interpreted in terms of electronic band structure; its reflectivity falls off in the middle of the visible spectrum and rises towards the violet end (Saeger and Rodies 1977). The compound PtAl2 has similar properties, its yellow colour change to orange-pink on copper addition. The compound AuAl2 was the source of the ‘purple plague’ resulting from the formation of this brittle phase (with a consequent mechanical collapse) in the Au–Al bonding frequently made in the early method of connecting electrical leads to integrated circuits. In recent time the use in jewellery of ‘gems’ prepared with the AuAl2 compound has been proposed (Mintek). Details on the properties of this compound and suggestion about its application may be found in an interesting review by Cahn (1998).

492

Intermetallic Chemistry B

MB66 MB12 MB6 MB4 Boron framework

at. %

B

Boron net Boron net chain formation Boron chains Chain fragments boron pairs and isolated borons

Isolated boron atoms

Metal framework structures

M′

MB2 M2B3 MB

M2B M3B M4B M6B M12B M″

Figure 5.35. Schematic indication of the boron atomic arrangements inside the structures of binary and ternary M -M–B borides as a function of the overall B content (adapted from Rogl 1992).

5.13.4.4 Remarks on some commercial aluminium alloys. Al metal and Al alloys find several applications: this is also reflected in the variety of treatments and processing techniques to which they may be subjected. A recent example may be the semi-solid processing (thixoforming) of high-performance alloys. Just as a kind of introduction to the field of commercial aluminium alloys and to give in a broad outline an indication of their applications, the codes of typical Al alloys are reported here as taken from ASM Handbook, Vol. 2 (Cayless 1990). Table 5.66 is a summary of some typical commercial aluminium alloy series. Notice that for the 2xxx to the 7xxx series the alloy group is determined by the element present in the mean greatest percentage (an exception is the 6xxx series in which the proportions of Mg and Si to form magnesium silicide, Mg2Si, are predominant). In the 2xxx to 8xxx series the 2nd digit 0 indicates an original alloy, 1 to 9 indicates a modification of a previously registered alloy or a new alloy (see also Table 5.67). For a discussion on thixoforming processing, mainly applied to alloys Al– Zn–Mg–Cu of the 7xxx series, see Maciel-Camacho et al. (2003) and § 6.2.2.3.

493

Elements of Alloying Behaviour Systematics Table 5.66. Wrought Al and Al alloys. Series codes

General characteristics

Remarks

1xxx

Commercially pure Al, 1% other elements.

Chemical equipments, heat exchangers, food handling.

2xxx

Cu alloys 5%

Excellent strength and machinability poor corrosion resistance. Used for components requiring high strength/weight ratio.

3xxx

Mn alloys (1.2%)

Moderate strength, high workability, cooking utensils, heat exchangers, tanks, storage equipments.

4xxx

Si alloys (12%)

Low melting point low expansion coefficient. Used as filler materials for brazing, etc., for casting, etc.

5xxx

Mg alloys (0.3–5%)

Good strength and weldability, very good corrosion resistance in marine atmosphere. Ships, boat, cryogenic vessels.

6xxx

Mg–Si alloys

Good formability, high corrosion distance, in buildings, bridges, transport, welded constructions and where strength, weldability and corrosion resistance are needed.

7xxx

Zn alloys (3–8%) Mg

Heat treated and aged show very high strength. Aircraft structures. Used for equipments requiring high strength/weight ratio

8xxx

Other elements

Table 5.67. Al and Al alloys in the form of castings or foundry ingots. Series codes and general characteristics of alloys grouped by major alloying element. 1xx.x 3xx.x 5xx.x 7xx.x 9xx.x

Al ( 99) Si (Cu and/or Mg) Mg Zn Other elements

2xx.x 4xx.x 6xx.x 8xx.x

Cu Si Unused Sn

Notice that the last digit, separated by the decimal point, indicates the product for castings Xxx.0 or ingot Xxx.1

494

Intermetallic Chemistry

5.14. ALLOYS OF THE ELEMENTS OF THE 14TH GROUP OF THE PERIODIC TABLE

Carbon, C; silicon, Si; germanium, Ge; tin, Sn; lead, Pb

5.14.1 Introduction Carbon (C, [He]2s22p2), name and symbol from the Latin word carbo, coal. Known since ancient times, but recognized as an element much later. Atomic number 6, atomic relative mass 12.0107. Non-metal. Occurrence. Carbon is distributed very widely in nature as calcium carbonate (limestone). Coal, petroleum and natural gas are chiefly hydrocarbons. Carbon is found as carbon dioxide in the atmosphere of the earth and dissolved in all natural waters. The atmosphere of Mars contains 96% CO2. It is plentiful in the sun, stars, comets and the atmospheres of most planets. Allotropy of carbon Diamond. In this structure (see Chapter 7) all the atoms are equivalent; each atom being surrounded by a perfect tetrahedron of four other carbons, forming with each one of them a localized two-electron bond. Diamond has a high density and refraction index and thermal conductivity and the highest melting point (4000°C) of any element. Besides the well-known cubic form, a hexagonal form (lonsdaleite) is found in meteorites, and it is also obtained synthetically. The relation between these two forms of carbon, similar to that between the two forms (cubic and hexagonal) of ZnS (sphalerite and wurtzite) is discussed in Chapter 7. Graphite. The normal form (hexagonal graphite) described in Chapter 7 has a large separation between the layers, and therefore slight forces between them: softness and lubricity of graphite may be related to the easy slippage of the layers over one another. Different forms of graphite are known, differing in the order of superposition of the

Elements of Alloying Behaviour Systematics

495

layers; a rhombohedral form present in naturally occurring graphite has a stacking order …abcabc… Often graphite forms are also found in which regions with a certain layer sequence (hexagonal or rhombohedral) are separated by regions having the other sequence ( in a one-dimensional disorder). Graphite intercalation compounds are formed with different substances: one group (in which the graphite electrical conductivity is lost) includes the graphite ‘oxides’ (obtained by a treatment with strong aqueous oxidants) and the ‘fluorides’ (such as C5F–C2F obtained under pressure in liquid HF). A second group of graphite intercalation compounds, lamellar compounds, in which a high electrical conductivity is maintained, are formed by the insertion of different atoms, ions, etc. Among these compounds, those given by the alkali metals: formulae such as LiC6, LiC12, LiC18, KC8, KC24, KC36, KC48, NaC64, etc., which may be generally obtained by direct reaction of graphite with alkali vapours. These compounds ignite in air and react explosively with water. Generally for any guest species we have a series of possible stoichiometries each corresponding to a so-called stage. A compound corresponding to a stage n is defined as the graphitic structure in which every nth layer contains guest species. The highest guest concentration occurs therefore in the first stage intercalate such as KC8. As an example we may shortly describe the structure of KC8. We have here the vertical packing of practically intact graphite layers stacked above each other in a sequence such as ….bbb… or ….ccc…, instead of …bcbc… as in pure graphite. The distance between these layers moreover is much larger than in graphite (540 pm instead of 335 pm) due to the intercalation of a K layer (it is 561 pm in RbC8 and 595 pm in CsC8). The alkali metal layer forms a hexagonal bi-dimensional lattice commensurate to the graphitic one, with a 2agr. Microcrystalline and amorphous carbon. Different forms of carbon are known, such as carbon black, soot, charcoal, pitcoal, coke, etc., which in principle are all graphite like, but with a low degree of ordering and can be microcrystalline or amorphous. Many species have several pores and a large inner surface in the range, for instance, of 300–2000 m2/g for the activated carbons, prepared by special activation processes either by chemical or gas activation: they may adsorb large quantities of other substances (act as a decolourizing agent, etc.) and can be used as a catalyst in several processes. Coke. Metallurgical coke is obtained by high-temperature carbonization of coal. It is a poorly graphitized form of carbon; it is mainly used in blast furnace for steel manufacture (see Iron, § 5.10). Carbon black (soot). It is obtained by the incomplete combustion of natural gas or liquid hydrocarbons. The particle size of carbon black is very small; its applications are mainly in rubber industry (to strengthen and reinforce rubber) and also as a pigment in the preparation of inks, etc.

496

Intermetallic Chemistry

Strong graphite fibres may be prepared by pyrolysis (at 1500°C or above) of oriented organic polymer fibres. Other graphite forms such as foams, foils, etc. can also be prepared. Fullerenes. These may be defined carbon modifications consisting of cage-like molecules. These may be obtained in electric discharge devices between graphite electrodes in a controlled atmosphere of helium, condensing the evaporated carbon and eventually re-crystallizing from benzene solution. The main representative of these products is the fullerene C60 (called buckminster-fullerene after the engineer R. Buckminster Fuller who invented the geodesic dome which has the same architectural principle as the C60 molecule). The C60 molecule consists of 12 pentagons and 20 benzene-like hexagons (see Fig. 5.36). In crystalline C60, the nearly spherical molecules are arranged in a face-centred cubic close-packed structure. The crystalline C60 is as soft as graphite and similarly to graphite (but obviously with a different structural arrangement). It may enclose, for instance, potassium atoms. In this case a compound K3C60 may be obtained in which all the cavities (the tetrahedral and octahedral holes) between the C60 balls are occupied by K atoms. The alkali metal doped fullerene C60 are good conductors and when cooled become superconductor (Cs2RbC60, for instance, has a superconducting transition temperature of 33 K). However notice that, because of its high symmetry, C60 is orientationally disordered in the solid state: at room temperature the C60 molecules rotate rapidly. It was possible to have orientational order (and consequently to make a complete Xray structural analysis of the ‘ball’) breaking the nearly spherical symmetry through the preparation of some derivative in which a reactive group is for instance connected to one of the C–C bonds of the molecule (Hawkins et al. 1991). It was observed, in the preparation of an osmium derivative, that the reaction (the connection of the new group) occurs selectively (regio-chemical process) on one of the more electron-rich bonds common to two six-membered rings. Cages having other sizes may also be produced; generally, however, they are less stable. Smaller cages have been obtained and also, with a good yield, C70 which contains in its molecule 12 pentagons and 25 hexagons. Another important group of fullerene-related compounds are the carbon nanotubes, the reference compounds of the carbon nano-science. They may be obtained by convenient variations of the preparation procedure mentioned. These are long tubular fullerenes with a concentric shell structure a few nanometres wide and often capped with C60-like hemisphere or faceted tips. They are mechanically very strong and either metallic conducting or semiconducting types have been obtained. As a conclusion, a fascinating behaviour of C60 which may be a typical symbol of the nano-technology and turned up to be on the threshold of the quantum and

Elements of Alloying Behaviour Systematics

497

Figure 5.36. Schematic representation of the fullerene C60 molecule. Notice its highly symmetric structure (truncated icosahedron) in which all carbon atoms are identical and are located at the connection between two hexagons and one pentagon. The bond lengths are 138.6 pm for the bonds common to two hexagons (having a double-bond resonant structure) and 143.4 pm for the hexagon–pentagon common bonds. The bonding therefore seems to be not completely delocalized as in graphite.

classical worlds may be highlighted. It is big enough to be observed under an electron microscope and small enough to be ‘used’ as a quantum object. This was evidenced by Arndt et al. (1999) who showed that C60 possess wave-like properties. A beam of C60 molecules was directed through a diffraction grating with a periodicity of 100 nm, and the resulting diffraction pattern was observed. The molecule C60 is the largest object for which the dual wave-particle behaviour was observed. Carbon phase diagram. This diagram (and especially the boundary lines of the diamond phase) is very interesting and important. The experimental investigation of this system is very difficult owing to the extremely high temperatures and pressures which are needed to melt diamond. Several researches by different authors have been carried out on this topic (see for instance Bundy 1980). A review of the experimental investigation and an ab initio calculation has been reported by Wang et al. (2005). The phase diagram they propose is shown in Fig. 5.37.

498

Intermetallic Chemistry 103

Pressure (GPa)

Shockwave 102

Diamond Catalytic HPHT

HPHT synthesis

Liquid

synthesis

101

Metastable Graphite diamond 2000

4000 6000 Temperature (K)

8000

Figure 5.37. Pressure/temperature phase diagram of carbon.

Silicon (Si, [Ne] 3s23p2), name and symbol after the Latin word silex (gen. silicis) meaning flint. Discovered (1824) by Jöns Jacob Berzelius. Dark grey with a bluish-tinge, semi-metal. Occurrence. Silicon is the second most abundant element in the earth’s crust, after oxygen (about 28% by weight). It occurs mainly in oxides (quartz, agate, opal, etc.) and a great variety of silicate minerals (feldspar, clay, mica, olivine, etc.). Atomic number 14, atomic relative mass 28.0855. Preparation. For the carbo-thermal production of silicon and ferro-silicon, arc furnaces are used. Another method starts with SiF4. After purification and fractional distillation SiF4 can be reduced to silicon with Na. Alternatively the following reaction can be used: SiF4 (g) NaAlH4 (s) : SiH4 (g) NaAlF4 (s) SiH4 is then thermal decomposed to generate elemental Si. For the production of pure semiconductor silicon, silicon compounds such as chlorides are purified by distillation, and then transformed back to Si by chemical

Elements of Alloying Behaviour Systematics

499

vapour deposition. Pure silicon can be also obtained as single crystal (Czochralski crystal growth, float-zone crystal growth, etc.). Germanium (Ge, [Ar]3d104s24p2), name and symbol from the Latin word Germania (Germany). Discovered (1886) by Clemens Winkler, although its existence was predicted (1871) by Mendeleev, naming it as eka-silicon. Greyish-white, semi-metal. Atomic number 32, atomic relative mass 72.64. Occurrence. Germanium is widely dispersed, but only a few minerals have been isolated. Germanite Cu3(Ge,Fe)S4 and renierite (Cu,Fe,Ge,Zn,As)S were in the past the principal sources of germanium. Actually germanium is recovered as by-product of the zinc production. Preparation. The overall production process to obtain germanium consists of two steps, the first being the production of germanium concentrate followed by the germanium production. Pyrometallurgical (based on the volatility of GeO or GeS), hydrometallurgical (based on precipitation of Ge sulphide or hydroxide) or solvent extraction processes are used, depending on the raw material processed. The second step starts with a transformation of Ge concentrate (mostly GeO2 or Ge scrap) to GeCl4, in concentrate HCl or Cl2 atmosphere. Elemental Ge is generally produced by H2 reduction. High purity semiconductor-grade germanium is obtained by zone refining under controlled atmosphere. Ultrapurification of Ge can be obtained in single crystal grown in the most aseptic dust-free environment. Tin (Sn, [Kr]4d105s25p2), name from the Anglo-Saxon word tin, symbol Sn from the Latin word stannum (tin). Tin is one of the oldest metals known by man. There are domestic utensils and arms made of bronze (copper with about 15% of tin), dating from 3500 BC. Silvery white metal. Atomic number 50, atomic relative mass 118.710. Occurrence. Its most important ore is cassiterite, SnO2. Preparation. Cassiterite, that contains also Fe as the most important impurity, is easily reduced by carbon to tin. Because of the presence of iron in the ores, which leads to a hard product, it is mandatory to reduce the mineral at an oxygen pressure

500

Intermetallic Chemistry

sufficiently high to prevent the extensive reduction to iron. Sn is refined electrolytically. Lead (Pb, [Xe]4f145d106s26p2), name from the Anglo-Saxon word lead, symbol Pb from the Latin word plumbum. Known since ancient times. Bluish white, soft metal. Atomic number 82, atomic relative mass 207.2. Occurrence. It is by far the most abundant of the heavy elements. The most important ore is galena PbS. Other minerals are anglesite PbSO4, cerrusite PbCO3. Preparation. Lead is obtained by roasting PbS to oxide followed by reduction with carbon. 5.14.2 The 14th group elements: a summary of their atomic and physical properties See Tables 5.68–5.70.

Table 5.68. C, Si, Ge, Sn, Pb: selected atomic and physical properties. Property

C

Si

Ge

Sn

Pb

r/pm, metallic, CN, 12 [‘metallic valence’] r/pm, ionic, M2, CN 6 r/pm, ionic, M4 Tmelting/°C Tboiling/°C ΔHmelting(at Tmelting)/kJ/mol ΔfH0 of Me1 gas at 298.15 K/kJ/mol

87.6 [4]

132.2 [4]

137.8 [4]

163.1 [2] 158.0 [4]

175.0 [4]

15, CN 4 3827

40 CN 6 1414 3267 50.2 450

73 53 CN 6 938.3 2834 36.9 –

117 717

69 CN 6 231.9681 2603 7.0 –

119 77.5 CN 6 327.502 1750 4.8 195

Table 5.69. C, Si, Ge, Sn, Pb: ionization energies. Element

1st ionization energy kJ/mol

2nd ionization energy kJ/mol

3rd ionization energy kJ/mol

4th ionization energy kJ/mol

5th ionization energy kJ/mol

Carbon Silicon Germanium Tin Lead

1086 787 762 709 716

2353 1577 1537 1412 1451

4621 3232 3302 2943 3082

6223 4356 4441 3930 4083

37 830 16 091 9020 7000 6640

501

Elements of Alloying Behaviour Systematics Table 5.70. C, Si, Ge, Sn, Pbl: crystal structures, lattice parameters of their allotropes and calculated densities. Element (allotrope) Temperature range/°C Pressure/GPa Carbon C (graphite) C (diamond) 60 GPa Silicon αSi 1414° βSi 9.5 GPa γSi 16.0 GPa δSi 16.0 GPa Germanium αGe 938.3° βGe 12 GPa γGe 12 GPa δGe 12 GPa Tin αSn 13º βSn13 to 231.968° γSn 9.0 GPa Lead αPb 327.502° βPb 10.3 GPa

Crystal structure

Lattice parameters/ Atomic pm volume pm3 106 a c

Molar volume/ cm3/mol

Density/ g /cm3

hP4-C graphite cF8-C diamond

246.12 356.69

670.9

8.80 5.67

5.30 3.42

2.267 3.516

cF8-C diamond tI4-βSn cI16-γSi hP4-αLa

543.06 468.6 663.6 380

258.5

20.02

12.06

2.330

cF8-C diamond tI4-βSn tP12-γGe cI16-γSi

565.74 488.4 593 692

269.2 698

22.63

13.63

5.327

cF8-C diamond tI4-β Sn tI2-γSn

648.92 583.18 370

318.18 337

34.16 27.05

20.57 16.29

5.771 7.286

cF4-Cu hP2-Mg

495.02 326.5

538.7

30.33

18.26

11.346

628

5.14.3 Intermetallic chemistry of the 14th group elements 5.14.3.1 Phase diagrams of the 14th group elements. The reactivity patterns of the 14th group elements are shown in Fig. 5.38. We notice a number of analogies among them, such as the compound formation capability with the metals at the left side of the Periodic Table, including lanthanides and actinides. Moving from one element to the other down the group, we notice a decrease in the compound formation capability, according to a scheme similar to those observed in the other p-block groups. The intermetallic reactivity of Si and Sn and the stability of their compounds are also indicated by the trends of the melting points of their alloys. A selection of these data has been collected in Table 5.71. During an investigation of the properties of low melting metals, a specific aspect of the alloying behaviour of Sn and Pb has been studied by Guminski (1989, 1990),

502

Intermetallic Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

C

Si

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Ge

Sn

Pb

Compound-forming element

Phase diagram known; no intermediate phases formed

No information available

Questionable compound-forming capability

Figure 5.38. Compound formation capability in the binary alloys of C, Si, Ge, Sn, Pb.

who compiled and discussed the data concerning the solubility of the different elements in these metals. Solubility data at 600°C have been plotted and discussed as a function of the atomic number; curves showing periodic variations were obtained with trends very similar to each other and to those prepared for Hg, Ga, In and Bi. Examples of elements exhibiting low or very low solubility (at 600°C) in liquid Sn or Pb are for instance: Cr, Nb, Mo, W (with deep minima for Nb, Mo, W). High solubility is shown by Zn, Cd, In, Hg, Tl, Sn, Pb, Bi. Several Sn or Pb systems with these metals give low melting eutectics and form continuous liquid solutions stable at moderate temperatures. 5.14.3.2 Remarks on the alloy crystal chemistry of the 14th group elements. Carbides. Among the elements of the 14th group, the chemical behaviour of carbon is peculiar. It may be useful to dedicate a few particular comments to its combinations with the metals. Mainly depending on the electronegativity difference (Δη) between carbon and the other element, the following classes of carbides may be considered (see for instance Ruschewitz 2003): ●

High Δη carbides with salt-like, ionic-like properties (carbides of alkali, alkalineearth metals).

Table 5.71. Highest melting points (°C) in the alloys of Si and Sn with compound-forming elements of the 4th and 6th rows of the Periodic Table. Alloys with K

Silicon compounds

Tin compounds K2Sn3, 860°, IR 1

Compds. Cs

Ca Ba Sc La Ti Hf V Ta Cr W Mn Re Fe Os Co Ir Ni Pt Cu

CaSi, 1324°, IR 1 Sc5Si3, 2028° IR 1 Ti5Si3, 2130°C, IR 1 V5Si3, 2010°, IR 1 Cr3Si, 1790°, IR 1 Mn5Si3, 1283°, IR 1 FeSi, 1410°, IR 1 CoSi, 1460°, IR 1 θ, 59 to 66.6 at.% Ni 1306°, IR 1 η, 75.1 to 77.6 at.%, Cu 859°, IR 1

Au

BaSi2, 1180, IR 1 La5Si4, 1575°, IR 1 Hf3Si2, 2480°, IR 1 Ta5Si3, 2550°, IR 1 W5Si3, 2320°, IR 1 ReSi1.8, 1940°, IR 1 Os2Si3, 1840°, IR 1 Ir3Si5, 1402, p, IR 1 PtSi, 1238°, IR 1

Hg Simple Ga–Si eutectic Tl Ge Pb Bi

Sc5Sn3, 1800°, IR 1 Ti3Sn, 1670°C, IR 1 V3Sn, p, 1600°C, IR 1

SiAs, 1113°, IR 1

Cs2Sn3, 930°, IR 1 Compds. La5Sn4, 1575°, IR 1 Hf5Sn3, 1900°, IR 1 –

Partial liquid immisc. Mn3Sn, 984°, p, IR 1 Fe5Sn3, 910°, p, IR 1 Co3Sn2, 1200°, IR 1 Ni3Sn2, 1264°, IR 1 β, 84.3 to 86.9 at.% Cu 798°, p, IR 1

Simple Ga–Sn eutectic Extended monotectic

Compl. s.s. (Ge,Si)

As

Ca2Sn, 1135°, IR 1

Simple Au–Si eutectic Simple Zn–Si eutectic –

Zn Ga

Compds.

– Compl. immisc. – – PtSn, 1276°, IR 1 δ, 49.5 to 50 at.% Au, 419°, IR 1 eutectic β, 1.5 to 4.5 at.% Hg, 224°, p, IR 1 γ, 55 to 90 at.%Tl 273°, p, IR 1

Simple Ge–Sn eutectic Extended monotectic Extended monotectic

SnAs, 595°, IR 1

Simple Pb–Sn eutectic Simple Sn–Bi eutectic

504 ●

●

Intermetallic Chemistry

Intermediate Δη carbides with metallic properties (carbides of several transition metals). Small or negligible Δη carbides with more or less well-defined covalent bonding (compounds with some non-metals).

According to Ruschewitz (2003), moreover, on the basis of the coordination around C, different families of salt-like carbides may be described: methanides, where an anion C4 may be envisaged (even if only in a formal description) and a coordination 4 (tetrahedral) around C is observed (for instance Be2C (cF12-antiCaF2 structural type), Al4C3, etc.), acetylides, formally connected to an anion C2 2 and containing C2 dumbbells as for instance Na2C2 or CaC2 (see Fig. 3.7 and § 7.4.3.4 for the room temperature form, CaC2(I), of this phase); in these compounds the C–C distance (around 120 pm) corresponds to the value expected for a C-C triple bond. Another family of salt-like carbides corresponds to the allylenides, that is to compounds containing C 4 3 linear groups (such as Li4C3, Mg2C3). Within the transition metal carbides, the following classes of compounds could be considered: lanthanide and actinide carbides (LaC2, ThC2, Pu2C3) containing the C2 dumbbells, interstitial carbides (see § 3.8.4.2 and 3.8.4.3) containing C atoms inserted in the (octahedral) holes of a close-packed arrangement of metal atoms having large dimensions (typically RMe 130 pm), and a group of carbides (generally of metals with RMe 130 pm) characterized by more complex structures (Mn5C2, Fe3C, etc.). In the same paper (Ruschewitz 2003) a number of ternary alkali metal carbides have been described (the tP4-KAgC2 and hP4-LiAgC2 types which are characterized by Ag—C—C—Ag— chains running parallel to the principal structure axis, the hP5-Na2PdC2-type acetylides containing similar —Pd— C—C—Pd— parallel linear chains separated by the alkali metal ions). Groups of ternary alkaline earth metal carbides have also been described, for instance cP5MgNi3C which has the CaTiO3-type structure (with Mg in 0, 0, 0; C in 1⁄2, 1⁄2, 1⁄2; and 3Ni in 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0), containing Ni6 octahedra centred by carbon atoms. An example of a more complex structure is given by Ca4Ni3C5, which contains onedimensionally infinite polyanions Ni3C58. A summary of Zintl phases found in alkali–tin alloys has been reported by Fässler and Hoffmann (2003) together with the description of a new Na–Sn compound. It is Na7Sn12 which was synthesized by quenching stoichiometric amounts of the elements (700°C) in a sealed Nb ampoule and further thermal treatment at 270°C for 40 days. It was described as a Zintl phase suggesting that, on the basis of its structure, its formula can be rewritten as (Na)7[(2b)Sn2]1[(3b)Sn]5 [(4b)Sn0]6 (where 2b, 3b, etc. denote two-three-fold bonded atoms) resulting in a polyanion 2(Sn7– 12 ).

Elements of Alloying Behaviour Systematics

505

Notes on selected stannides and plumbides. In a review paper by Fässler and Hoffmann (1999) entitled ‘valence compounds at the border to intermetallics: alkali and alkaline earth metal stannides and plumbides’ emphasis was given to peculiar aspects of Sn and Pb chemistry. It was observed that Sn has the outstanding property that it appears in a metallic and in a semi-metallic modification, which posses almost the same stability. The consequent interplay between localized and delocalized bonding controls the structures of alkali and alkaline earth stannides and results in a large variety of structure types. Analogies with the Pb chemistry have been underlined: elemental Pb crystallizes in the typical metal fcc structure, but directed bonds between Pb atoms occur in compounds with electropositive metals. In their review Fässler and Hoffmann described several compounds, among which a number of Zintl phases. A short list of them is given here in the following with an indication of the structural units they contain: Na4Sn (isolated Sn4); NaLi5Sn4 4 (2[Sn0Sn3][Sn4 2 ]); KSn, RbSn, CsSn (Sn4 tetrahedra); NaPb, KPb, RbPb, CsPb 4 4 (Pb4 tetrahedra); K4Pb9, Cs4Pb9 (Pb9 nido type); Mg2Sn, Li2MgSn, CaMgSn, BaMgSn, etc. (Sn4 isolated); SrSn, BaSn (1[Sn2zig -zag]); Sr3Sn5, Ba3Sn5 (Sn6 5 arachno type); Mg2Pb, Li2MgPb, Sr2Pb, Ba2Pb (Pb4 isolated); Sr5Pb3, Ba5Pb3 (probably containing H, Pb4, Pb26); SrPb, BaPb (1[Pb2] zig-zag); Ba3Pb5 (Pb6 5 arachno type); etc. 5.14.3.3 Notes on some peculiar applications of diamond. Diamond has a very interesting and important range of material properties. It is the hardest and stiffest material known, it has a very high thermal conductivity and it is a very good electrical insulator. It is transparent to ultraviolet, visible and infrared light, and it is chemically inert to nearly all acids and bases. Large crystals may therefore find applications not only in jewellery; tiny diamonds are used in saw blades, in drill bits, etc. Electronic properties and colour of diamond depend on the impurities and their distribution within the crystal. Today, more than 100 tonnes of synthetic diamonds are produced annually worldwide (Yarnell 2004). Specifically in the company Gemesis diamonds are grown in high pressure high-temperature chambers. A tiny sliver of natural diamond is bathed in a molten solution of graphite and a proprietary metal-based catalyst at about 1500°C and 58 000 atm. Carbon precipitates onto the diamond seed crystal. According to Yarnell (2004), a gem quality rough yellow diamond grows up to 2.8 carat in just under 31⁄2 days. In the Apollo Diamond Company in Boston a low-pressure technique (a kind of ‘chemical vapour deposition’ technique) is used: in their reactor hydrogen gas and methane are flowed through a chamber containing a diamond seed crystal (natural or synthetic), the hydrogen is split by the action of a hot filament or a microwave generated plasma. Atomic hydrogen reacts with methane giving methyl radicals and H2, the radical species deposit carbon onto the

506

Intermetallic Chemistry

seed forming new diamond carbon–carbon bonds. Both single crystals and polycrystalline diamond may be prepared. In the paper by Yarnell thermodynamic and kinetic aspects of the diamond synthesis are also discussed. 5.14.3.4 Joining processes: tin-containing soft solders. 5.14.3.4.1 Soldering. Soldering is one of the metal joining processes which is obtained by melting a lower melting point alloy which will wet or alloy with the joint surface and then freeze in place. 5.14.3.4.2 Solders, tin alloys, the lead problem. A conventional definition of a (soft) solder is a joining material which melts below 427°C (800°F). In soldering joints are heated by torches, soldering irons, induction heaters, furnaces or by immersion in molten solders. Generally fluxes are used to support the soldering process (rosin soldering flux containing activating agents which promote wetting by the solder or, if stronger fluxes are needed, ammonium or zinc chloride). Alloys of tin and lead that melt below the melting point of tin were traditionally soft solders. Common solders usually contain 20–70 mass% Sn. Additions of metals such as Ag, Cd, As, Sb, Bi have been considered to improve strength, wetting properties, etc. and to obtain alloys having optimal melting ranges. The phase diagram of Pb (m.p. 327.50°C) and Sn (m.p. 231.97°C) shows the terminal solid solutions of Sn in Pb (up to 28.1 at.% 18.3 mass% Sn at 183°C) and of Pb in Sn (1.3 at.% 1.8 mass% Pb at 183°C) which form a eutectic of composition 73.9 at.% Sn (61.9 mass%) melting at 183°C. Lead, however, is now recognized as a heavy-metal poison: so the use of tetra-methyl and tetra-ethyl lead as anti-knock agents in petrol is now being phased out in favour of less polluting compounds and, similarly, according to a directive of the European Commission, lead alloys should be banned. Research is now playing an active part in the development of lead-free soldering. Most promising alloys under investigation are based on Sn being the primary or major constituent. The two other elements that are major constituents are In and Bi. Other alloying elements are Zn, Ag, Sb, Cu and Mg (Abtew and Selvaduray 2000, Tu et al. 2003). Improving in manifacturability and long-term reliability in many Pbfree alloys was found by their doping with trace amounts of rare earth elements (Wu and Wong 2007). 5.14.3.4.3 Brazing. This is a metal joining process similar to soldering but based on the use of filler materials of greater strength and higher melting temperature. Typically above 450°C, but below the melting temperature of the metals to be joined. According to the brazing design, the metals to be joined, etc., several filler materials can be used ranging from pure metals (Cu, Ag, Au) to complex alloys (of Co, Ni, Ag, Au, Mg, Al, etc.). There are several basic brazing processes: in torch brazing for

Elements of Alloying Behaviour Systematics

507

instance heat is applied by flame directly to the base metal; a mineral flux is generally used, the filler is pre-placed in the joint or face-fed into the joint itself. Other processes include resistance-brazing, furnace-brazing, dip-brazing, diffusion-brazing, etc. 5.14.3.4.4 Welding. This is a joining process of two, or more, metallic parts obtained by heating to a suitable temperature with, or without, the application of pressure and with, or without, the use of a filler metal. Generally industrial welding involves fusion: the edges to be welded are brought to the molten state: the liquid metal fills the gap between the parts and after removal of the heat source it solidifies joining the parts. According to the heat source several welding processes may be considered such as: arc welding, gas welding, resistance welding, electronbeam welding, laser welding, inertia welding (that is friction welding in which the heat produced at the rubbing surfaces is used to raise the temperature). Welding is the joining process widely used in the constructions of various components of titanium, tantalum, steel, nickel, copper, aluminium, lead and their alloys. 5.15. ALLOYS OF THE ELEMENTS OF THE 15TH GROUP OF THE PERIODIC TABLE

Nitrogen, N; phosphorus, P; arsenic, As; antimony, Sb; bismuth, Bi

5.15.1 Introduction Nitrogen (N, [He]2s22p3), symbol and name after the Greek words νιτρον γεινο− μαι (nitre forming) because it is a constituent of nitric acid and nitrates. Discovered (1772) by Daniel Rutherford. Gas at 273 K, colourless, non-metal. Atomic number 7, atomic relative mass 14.00674. Occurrence. Naturally occurring nitrogen (N2) makes up 78% (by volume) of the earth ‘atmosphere. Nitrogen is relatively unabundant in the crustal rocks. The major minerals are saltpetre (KNO3) and NaNO3 (Chile saltpetre). Preparation. The only important large-scale process is the fractional distillation of liquid air.

508

Intermetallic Chemistry

Phosphorus (P, [Ne]3s23p3), symbol and name from the Greek word φωζφορο (bringer of light). Discovered (1669) by the German alchimist Hennig Brand, who extracted phosphorus from urine. Non-metal, colour depending from the allotropic form. There are three main forms of phosphorus, white (soft, waxy solid at room temperature, highly reactive, toxic), red and black. Atomic number 15, atomic relative mass 30.973762. Occurrence. Widely distributed in many minerals (more than 200 minerals are known). Commercial sources of phosphorus are apatites (for instance fluoroapatite [3Ca3(PO4)2 Ca(F,Cl)2]). Preparation. The commercial route is by reduction of phosphate rock with silica and coke in an electric furnace at 1400/1500°C: 2Ca3(PO4)2 6SiO2 10C : 6CaSiO3 10CO P4 The element volatilizes and it is condensed under water as white phosphorus. Arsenic (As, [Ar]3d104s24p3), name and symbol from the Greek word αρσενικον and from the Persian word az-zarnikh (As2S3, yellow orpiment). Known since ancient times. Metallic grey, semi-metal. In addition to the metallic form there are other metastable modifications (yellow As, formed by sudden cooling of the vapour, and three amorphous forms: beta (black As), gamma and delta As). Atomic number 33, atomic relative mass 74.92159. Occurrence. Arsenic is associated with sulphide minerals (As4S4 realgar, As2S3 orpiment, FeAsS arsenopyrite, Cu3AsS4, enargite, etc.). Occasionally arsenic is found as free element, usually in ore containing cobalt, antimony, nickel. Preparation. Arsenic is obtained on large scale by thermolysis of FeAs2 or FeAsS at 650–700°C in the absence of air and condensing the sublimated element. Uses. In metallurgy for hardening copper and lead alloys; to prepare GaAs for electronic devices, doping agent in germanium and silicon solid state products, special solders. Antimony (Sb, [Kr]4d105s25p3), name and symbol from the Latin corruption of Arabic al-ithmı-d, which is derived from Latin stibium, coming from Greek στιβι (a cosmetic powder, Sb2S3). Known since ancient times. Silvery lustrous grey, semi-metal. Atomic number 51, atomic relative mass 121.75.

Elements of Alloying Behaviour Systematics

509

Occurrence. Antimony occurs chiefly as the sulphide, stibnite (Sb2S3). Preparation. Antimony metal is obtained by pyrometallurgical methods. The sulphide is converted into the oxide, which can be directly reduced by carbon. Uses. Large quantities of Sb metal have been used mainly in alloys with Pb (battery grids) and other metals. Alloys are the predominant use of antimony because its brittleness bars direct use. High purity antimony ( 99.999%) has a limited but important application in the manufacture of semiconductor devices. When alloyed with elements of 13th group (IIIA), the III-V compounds are formed; these have important applications as infrared devices, diodes and Hall effect devices. Also used for fireworks and thermoelectric piles. Bismuth (Bi, [Xe]4f 145d106s26p3), name and symbol from bisemutum, Latinized form of the German words Wiese Muten or perhaps Weisse Masse. Known since ancient times. Lustrous reddish white, metal. Atomic number 83, atomic relative mass 208.98037. Occurrence. Bismuth occurs in minerals such as bismite (Bi2O3), bismuthinite (Bi2S3), bismutite (BiO)2(CO3). Preparation. It is recovered as a by-product by Pb/Zn and Cu processes. Uses. Low melting solders, low melting alloys and metallurgical additives. Bismuth is a metal with some unusual properties; like Ge and Ga its volume increases in solidification. It is the most diamagnetic metal, its alloys show large thermoelectric effect; with the exception of Be has the lowest absorption cross-section for thermal neutrons.

5.15.2 The 15th group elements: a summary of their atomic and physical properties See Tables 5.72–5.74.

5.15.3 Intermetallic chemistry of the 15th group elements 5.15.3.1 Phase diagrams of the 15th group elements. Fig. 5.39 shows the compound formation pattern of the elements of the 15th group. Moving from one element to the other down the group we notice a decrease in the compound formation capability according to a scheme similar to those which may be observed in the other p-block groups. The intermetallic reactivity of Sb and Bi and the stability of their compounds are also indicated by the trends of the melting points of their alloys. A selection of these data has been collected in Tables 5.75.

510

Intermetallic Chemistry

Table 5.72. N, P, As, Sb, Bi: selected atomic and physical properties. Property

N

r/pm, metallic, CN 12 [‘metallic valence’] r/pm, ionic, M3, CN 4 r/pm, ionic, M3, CN 6 r/pm, ionic, M5, CN 6 Tmelting/°C

P

Tboiling/°C ΔHmelting(at Tmelting)/kJ/mol

82.5 [3] 146 16 13 – 210.0042 195.80 –

Δ fH 0 of Me1 gas at 298.15 K/kJ/mol

–

As

Sb

Bi

124.1 [1]

136.6 [5]

157.1 [5]

168.9 [5]

44 38 44.14 (P, white) 589.6 (TP, red) 277 0.66 (P, white) 18.8 (red, at 590°C) 313

58 46 614

76 60 630.755

103 76 271.442

– 24.4

1587 19.87

1564 11.30

–

–

–

Table 5.73. N, P, As, Sb, Bi ionization energies. Element

1st ionization energy kJ/mol

2nd ionization energy kJ/mol

3rd ionization energy kJ/mol

4th ionization energy kJ/mol

5th ionization energy kJ/mol

6th ionization energy kJ/mol

Nitrogen Phosphorus Arsenic Antimony Bismuth

1402 1012 945 834 703

2856 1905 1798 1595 1610

4578 2914 2735 2440 2466

7475 4960 4837 4260 4370

9445 6274 6043 5400 5400

53267 21270 12310 10400 8600

While investigating the properties of low melting metals, a specific aspect of the alloying behaviour of Bi has been studied by Guminski (1989, 1990) who compiled and discussed the data concerning the solubility of the different elements in this metal. Solubility data at 600°C have been plotted and discussed as a function of the atomic number; curves showing periodic variations were obtained with trends very similar to those obtained for Hg, Ga, In, Sn and Pb (with very deep minima, for instance, for the elements in positions close to Mo and W). 5.15.3.2 Notes on the crystal chemistry of selected alloys and compounds of the 15th group elements. Among the pnictides, several series of numerous isostructural compounds are found. The 1:1 compounds with Sc, Y, lanthanides and actinides, having the NaCl-type structure, generally correspond to very stable phases, strongly

511

Elements of Alloying Behaviour Systematics

Table 5.74. N, P, As, Sb, Bi: crystal structures, lattice parameters of their allotropes and calculated densities. Element (allotrope) Temperature range/°C Pressure/GPa Nitrogen 237.74º 210.004º 253º 3.3 GPa Phosphorus αP 44.14º (white) P(black) 589.6º (TP) Arsenic αAs 614° βAs 25GPa Antimony αSb 630.7° βSb 5 GPa γSb 7.5 GPa δSb 14 GPa

αN βN γN

Crystal structure

Lattice parameters pm a

b

Atomic volume pm3 106

Molar Density/ volume/ g /cm3 cm3/mol1

22.68 23.45

13.66 14.12

1.03 0.99

437.63 18.99

11.44

2.71

c

cP8-αN hP4-βN tP4-γN

566.1 405.0 395.7

c**P white

718

oS8Pblack

331.36

hR6-α As

375.94

1054.8 21.52

12.96

5.78

hR6-αAs cP1-αPo hP2-Mg mP3-

430.84 299.2 337.6 556

1127.4 30.21

18.19

6.69

hR6-α As mS4-β Bi

454.6 667.4

21.31

9.81

611.7

660.4 510.9

1047.8

534.1 422 β86.0°

αBi βBi

Bismuth 271.4º 2.6 GPa

γBi

3.0 GPa

mP4-

665

420

δBi ζBi

4.3 GPa 9.0 GPa

– cI2-W

– 380.0

–

1186.3 35.38 330.4 β110.3º 465 β85.33º

exothermic and with very high melting points. These are frequently stoichiometric phases or associated with very small homogeneity ranges. The cI28-Th3P4-type structure and the corresponding antitype are adopted by many phases in the same systems. Nitrides. Among the elements of the 15th group, the particular behaviour of nitrogen is notable. Several are the analogies with carbon in the formation, for instance, of interstitial compounds. A number of these phases, such as the refractory solid solution MeN1x phases, have been described in § 3.8.4 ff.

512

Intermetallic Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

N

P

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

As

Sb

Bi

Compound-forming element

Phase diagram known; no intermediate phases formed

No information available

Questionable compound-forming capability

Figure 5.39. Compound formation capability in the binary alloys of the 15th group elements.

Phosphides. The five elements of the 15th group are subdivided by the ‘diagonal’ Zintl line into two families with more or less metallic–non-metallic character. Arsenic shows intermediate properties, nitrogen and phosphorus are clearly nonmetallic, whereas metallic properties of antimony and bismuth are evident. In the context of our survey of intermetallic chemistry, therefore, the systematics of phosphorus chemistry may appear to be a marginal topic. A few notes and comments, however, about the phosphides may be of general interest. To this end a farreaching review by Von Schnering and Hönle (1988), especially dedicated to the polyphosphides, is a relevant reference source. According to this review, polyphosphides exhibit an unexpected wealth of composition and structures corresponding to a stepwise dismantling of group 15th element structures by the electron transfer of the electropositive components. The polyphosphides correlate the field of typical collective solids (as the NaCl-type compounds for which a clear separation into smaller units is impossible) with the fields of molecules. Due to their stoichiometries and structures, they cover a large range of physical properties and reveal new routines to the preparation of novel molecules, acting as precursors. Von Schnering and Hönle discussed several aspects of the polyphosphide chemistry (preparation methods, as here quoted in § 6.11.3, structure and bonding, thermochemistry, phase transitions, properties, chemical reactions, etc.) and enumerated a long list of compounds, among which: hP8-Na3As type (Li3P, Na3P, K3P: P3); cF8-NaCl type

Table 5.75. Highest melting points (°C) in the alloys of Sb and Bi with compound-forming elements of the 4th and 6th rows of the Periodic Table. Alloys with

Antimony compounds K3Sb, 813°C, IR 1

K Cs Ca

Ca11Sb10, 1123°, IR 1

Ba

Co3Sb, 725°, IR 1

La3Sb2, 1690°, IR 1

La Compds. Hf V Ta W Mn Re Fe Os Co

CrSb, 1113°, IR 1 Mn2Sb, 948°, IR 1 ε, 40–47 at.%Sb, 1025°, IR 1 β, 43.5–52.5 at.% Sb, 1220°, IR 1

Ir Pt Cu Au Zn Hg Ga

β, 69.2–20.6 683°, IR 1 ξ, 60–61 at.% Zn, 566°, IR 1 GaSb, 711.7°, IR 1

Ge

La4Bi3, 1670°, IR 1 Compds. Immisc.

Extended monotectic Immisc.

MnBi, 446°, p, IR 1

Immisc.

Immisc. Immisc.

Immisc. Compds.

Immisc. Extended monotectic BiNi, 654°, p, IR 1

PtSb2, 1225°, IR 1

Ir2Bi, 1440°, p, IR 1 Pt2Bi3, 685°, p, IR 1

Simple Cu–Bi eutectic AuSb2, 460°, p, IR 1

Au2Bi, 371°, p, IR 1 Monotectic

Compds.

Eutectic Monotectic Simple Ge–Bi eutectic

Simple Pb–Sb eutectic Compl. s.s. (As,Sb)

Bi

Ti3Bi, 1300°, p, IR 1

–

Simple Ge–Sb eutectic Pb

As

Ba3Bi2

Tl7Sb2, 187°, peritectoid, IR 1

Tl

Cs3Bi, 650°, IR 1

Immisc.

IrSb, 1645° Ni5Sb2, 71.2–74.8 at.% Ni 1161°, IR 1

Ni

Ca5Bi3, 1350°, IR 1

Compds. Compds.

Cr

K3Bi, 715°, IR 1

Compds.

Sc Ti

Bismuth compounds

Simple Bi–As eutectic Compl. s.s. (Bi,Sb)

α, 60 to 95 at.% Tl, 306°, IR 1 ε, 56.9 to 73.8 at.% Pb, 180°, IR 1

514

Intermetallic Chemistry

(LnP, AnP: P3); Na3P7, K3P7, Rb3P7 (different structure types containing P3 7 3 cages); Na3P11, K3P11, Cs3P11(different structure types containing P11 cages); 2 2 3 3 structures containing 1P 7 helical tubes, P10 linked tubes, P7 condensed cyclo P7 and cyclo P20, etc. Arsenides, antimonides and bismuthides. A number of salt-like related binary compounds formed with these semi-metals pertain to the following structure types NaCl, NiAs, ZnS, Na3As, FeS2, etc. Ternary antimonides and bismuthides. A number of families of characteristic compounds of Sb and Bi can be mentioned to underline the intermetallic behaviour of several combinations of these elements. Several 1:1:1 transition metal antimonides and bismuthides have been identified. The ternary compounds (with two transition elements and one main group element) TiFeSb, VFeSb, NbFeSb, TiCoSb, ZrCoSb, HfCoSb, VCoSb, NbCoSb, TaCoSb, TiNiSb, VNiSb, TiRuSb, ZrRuSb, HfRuSb, VRuSb, NbRuSb, TaRuSb, TiRhSb, ZrRhSb, HfRhSb, NbRhSb, ZrCoBi, ZrNiBi crystallize with the face-centred cF12-AgMgAs-type structure. For VFeSb and VNiSb the hexagonal, filled NiAs-type, structure was also found. Preparation, general properties, atom distribution on the structure sites have been discussed by Evers et al. (1997). 5.16. ALLOYS OF THE ELEMENTS OF THE 16TH GROUP OF THE PERIODIC TABLE

Oxygen, O; sulphur, S; selenium, Se; tellurium, Te; polonium, Po

5.16.1 Introduction Oxygen (O, [He]2s22p4), name and symbol after the Greek words οξυ´ (hard) γεινομαι (former), meaning acid former. Discovered (1774) independently by Joseph Priestley and Carl W. Scheele. Gas at 298 K, colourless as a gas, pale blue as a liquid, non-metal. Atomic number 8, atomic relative mass 15.9994. Occurrence. Oxygen is the most abundant element on the earth’s crust. It makes up 21% of the earth’s atmosphere and it occurs in combined form in water and as a constituent of most rocks.

Elements of Alloying Behaviour Systematics

515

Preparation. Oxygen is obtained on large-scale process by the fractional distillation of liquid air. Sulphur (S, [Ne]3s23p4), name and symbol from the Latin word sulphurium originated the Indo-European word suelphlos derived from swel (to burn slowly). Known since ancient times. Yellow, non-metal. Atomic number 16, atomic relative mass 32.066. Occurrence. Native sulphur occurs in deposits around volcanoes and hot springs. It occurs in numerous sulphides minerals, in sulphates, in crude oils, in coal and as H2S in natural gas. Preparation. Sulphur is obtained commercially from natural underground deposits by the Frasch process. Selenium (Se, [Ar]3d104s24p4), name and symbol after the Greek word σεληνη (moon). Discovered (1817) by Jöns Berzelius. Grey, metallic lustre, non-metal. Atomic number 34, atomic relative mass 78.96. Occurrence. Selenium is occasionally found as native. Minerals are rare and occur together with the sulphides of chalcophilic metals. Sometimes the minerals are partially oxidized (MSeO3 2H2O with M Ni, Cu, Pb). Preparation. Selenium is normally extracted as a by-product from electrolytic refining of copper. Uses. Selenium is used extensively in the manufacture and production of glass, pigments, rubber, metal alloys, textiles, petroleum and medical therapeutic agents. It is markedly photoconductive and widely used in photoelectric devices. Tellurium (Te, [Kr]4d105s25p4), name and symbol after the Latin word tellus (earth). Discovered (1782) by Franz Joseph Müller von Reichstein. Silvery lustrous grey, semi-metal. Atomic number 52, atomic relative mass 127.60. Occurrence. It is found in close association with sulphur and selenium. Tellurium is often found as gold telluride (calaverite), occasionally observed as free element. Production. Tellurium is obtained as a by-product of Pb, Cu, Bi, Pt-metal family processes and from sulphuric acid plants. Uses. Used in iron and steel production and in non-ferrous metals and alloys. It improves the creep strength of tin and the mechanical properties of lead. Used also in the vulcanization of rubber to reduce curing time and improve its characteristics.

516

Intermetallic Chemistry

Polonium (Po, [Xe] 4f145d106s26p4), name and symbol after Poland (native land of Marie Curie). Discovered (1898) by Marie Curie. Silvery, metallic, radioactive. Atomic number 84, atomic relative mass 208.98242 (nuclidic mass of the longest half life isotope). 5.16.2 The 16th group elements: a summary of their atomic and physical properties See Tables 5.76–5.78. 5.16.3 Intermetallic chemistry of the 16th group elements 5.16.3.1 Phase diagrams of the 16th group elements. Fig. 5.40 shows the compound formation pattern of the elements of the 16th group.

Table 5.76. O, S, Se, Te, Po: selected atomic and physical properties. Property

O

r/pm, metallic, CN 12 [‘metallic valence’] r/pm, ionic, M2, CN 6 r/pm, ionic, M2, CN 6 r/pm, ionic, M4, CN 6 Tmelting /°C Tboiling /°C ΔH melting (at Tmelting)/kJ/mol Δf H 0 of Me1 gas at 298.15 K/kJ/mol

89.7 [2] 140 218.789 182.97 –

S

Se

Te

Po

125.0 [2]

141.2 [6]

164.2 [6]

177.4 [6]

37 29 115.22 444.60 1.72 129 S2

50 42 221 685 6.69 –

97 56 449.57 988 17.49 –

94 67 254 – –

Table 5.77. O, S, Se, Te, Po ionization energies. Element

1st ionization energy kJ/mol

2nd ionization energy kJ/mol

3rd ionization energy kJ/mol

6th ionization energy kJ/mol

7th ionization energy kJ/mol

Oxygen Sulphur Selenium Tellurium

1314 1000 941 869

3388 2252 2045 1790

5300 3360 2974 2698

13326 8496 7880 6890

71335 27110 14990 13200

517

Elements of Alloying Behaviour Systematics

Table 5.78. O, S, Se, Te, Po: crystal structures, lattice parameters of their allotropes and calculated densities. Element Temperature Stability range Room pressure αO βO γO αS βS

Se αTe βTe γTe αPo βPo

Crystal structure a

Oxygen 249.28° mS4-αO 229.35° 218.70° Sulpur 95.5° 95.5° to 115.22° Selenium 221° Tellurium 449.57° 2.0 GPa 7.0 GPa Polonium 54° 54° to 931°

Lattice parameters pm

540.3

b 342.9

Atomic volume pm3 106

Molar Density/ volume/ g/cm3 cm3/mol

c 508.6 17.36 β 132.53° 1125.5 17.78 19.91

10.45

1.53

10.71 11.99

1.49 1.33

2448.6 1090 β 96.7°

24.60 20.43

14.81 12.30

2.16 2.61

hR6-βO cP16-γO

330.8 683

oF128-αS mP64-βS

1046.4 1102

hP3-γSe

436.59

495.37

27.26

16.41

4.81

hP3-γSe hR6-αAs hR3-βPo

445.66 420.7 470.85

592.64 1203.5 382.0

33.98

20.46

6.24

cP1-αPo hR3-βPo

336.6 509.4

495.3

38.14 37.11

22.97 22.35

9.10 9.35

1286.6 1096

The intermetallic reactivity of S and Te and the stability of their compounds are also indicated by the trends of the melting points of their alloys. A selection of these data has been collected in Table 5.79. Liquid alloys. In several binary diagrams of various elements with S, Se or Te the formation of miscibility gaps is noticed in the liquid state. This may be possibly related to the change, depending on composition, from one element to the other (from a metal to the non-metal) in the bonding characteristics. The miscibility gaps are generally located in a region of the diagram close to one component (mainly near the metal in the case of tellurium), in the diagrams of sulphur and selenium there are often two miscibility gaps separated in the central region of the systems by the existence of a miscibility field and the formation of solid compounds (see a few more details on these points in § 2.2.3). 5.16.3.2 A few notes about simple binary compounds of the 16th group elements. The reduced intermetallic character of these compounds is possibly reflected in

518

Intermetallic Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

O

S

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Se

Te

Po

Compound-forming element

Phase diagram known; no intermediate phases formed

No information available

Questionable compound-forming capability

Figure 5.40. Compound formation capability in the binary alloys of the 16th group

elements.

their not very high coordination numbers and in the covalent–ionic character of their structures. Sulphides. The partially ionic alkali metal sulphides Me2S have the anti-fluoritetype structure (each Me surrounded by a tetrahedron of S, and each S atom surrounded by a cube of Me). The NaCl-structure type (6/6 coordination) is adopted by several mono-sulphides (alkaline earth, rare earth metals), whereas for instance the cubic ZnS-type structure (coordination 4/4) is observed in BeS, ZnS, CdS, HgS, etc. The hexagonal NiAs-type structure, the characteristics of which are described in § 7.4.2.4.2, is observed in several mono-sulphides (and mono-selenides and tellurides) of the first-row transition metals; the related CdI2 (NiAs defectderivative) type is formed by various di-chalcogenides. Pyrite (cP12-FeS2 type: see in § 7.4.3.13 its description, and a comparison with the NaCl type) and marcasite oP6-FeS2 are structural types frequently observed in several sulphides containing the S2 unit. Selenides, tellurides and polonides. Se, Te and Po react easily with most metals and non-metals to form binary compounds (selenides and tellurides are common mineral forms of these elements). Non-stoichiometry is frequently observed in the compounds with the transition elements; many of these compounds may be described as metallic alloys. The compounds of the metals of the first two groups may be considered the ‘salts’ of the acids H2Se, H2Te, etc. The alkali metal selenides

Table 5.79. Highest melting points (°C) in the alloys of S and Te with compound-forming elements of the 4th and 6th rows of the Periodic Table. Alloys with

Sulphur compounds K2S, 948°, IR 1

K Cs Ca

Tellurium compounds

Cs2S, 600°, IR 1

Compds. Ba

Sc La Ti Hf V Ta Cr W Mn

s.s. ScS, 2277°, IR 1 Ti8S9, 2000°, IR 1 VS (50 at.%S), 1750°, IR 1

Compds. Compds. s.s. LaS, 2300°, IR 1

Re

Os Co Ir Ni

CoS, 1182°, IR 1 δ (47.5–50.2 at.% Ni) 995°, IR 1

WS2, 2400°, IR 1

Au Hg Ga Tl Ge Pb As Bi

Cr3Te4 (40.8–46.6 at.% Cr) 1283°, IR 1 MnTe, 1150, p, IR 1 β (51.5–53.5 at.%Fe) 914°, p, IR 1

Compds. Compds. Compds.

Cu2δS (digenite) 1130°, IR 1

Zn

ZnS, 1718°, IR 1 Ga2S3, 1100°, IR 1 GeS2, 850°, IR 1 AsS, 318°, IR 1

BaTe, 1470°, IR 1 LaTe, 1720°, IR 1 Compds.

Compds.

Pt Cu

Ti5Te4, 1500º, IR 1

Cs2Te, 831°, IR 1

Compds.

FeS, 1188°, IR 1

Fe

Compds.

Compds. Compds.

CrS, 1565°, IR 1 MnS, 1655°, IR 1

K2Te, 920°, IR 1

β (35–45 at.%Co) 1015, IR 1 β1 (56.7–63.2 at.%Ni) 1021°, IR 1 Cu2xTe, 1140°, IR 1

Tl2S, 470°, IR 1 PbS, 1100°, IR 1 Bi2S3, 775°, IR 1

β (48.5–57.2 at.% Re) ≈1000°, IR 1 Compds. Compds. PtTe2, 1147°, IR 1 AuTe2, 464°, IR 1

Immisc. HgS, 820°, IR 1

WTe2, 1020°, p, IR 1

S–Te eutectic GaTe, 835°, IR 1 β (49–50 at.% Ge) 724°, IR 1 As2Te3, 381°, IR 1

HgTe, 670°, IR 1 Tl5Te3, 470°, IR 1 PbTe, 924°, IR 1 Bi2Te3, 586°, IR 1

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Intermetallic Chemistry

and tellurides have the anti-fluorite structure and may be prepared by direct synthesis from the elements or in liquid ammonia solution. The NaCl-type structure is formed by the compounds with the alkaline earth and rare earth metals. Clusters. Even in a quick review of the compounds of the 16th group nonmetals and semi-metals, their clusters must be mentioned. With reference to Simon (1988), Mingos and Wales (1990), there is a wide range of clusters based upon octahedra of early transition metals, Me, with various numbers of halide or chalcogenide ligands, X, and different patterns of interconnection between the structural units. For structure descriptions, figures, etc. concerning this type of compounds and the related Chevrel phases, see § 4.4.4.7. Notice that an increasing degree of cluster linkage leads to increase electrical conductivity because the Me6 octahedra move closer together. The Chevrel phases (MeMo6X8, X S, Se, Te) generally exhibit relatively high critical temperatures. One-dimensional nanostructures of chalcogens and chalcogenides. An overview of solution-phase methods for generating one-dimensional nanostructures of chalcogens and chalcogenides has been presented by Mayers et al. (2004). Attention was especially focused on Se and Te because of their characteristic crystal structures and their catenation tendency. Basically, reactions were considered such as: H2SeO3 (aq) N2H4(aq) : Se(p) N2(q) 3H2O (and similarly from Te(OH)6(aq) to obtain Te or from a solution of a mixture of Se and Te acids to obtain Se/Te alloys). The precipitation of the chalcogen and its subsequent conversion from the colloidal to the nanocrystalline state was described. 5.17. GENERAL REMARKS ON THE SYSTEMATICS OF THE BINARY ALLOYS OF THE METALS

In a systematic analysis, Villars (1985a, b) defined a three-coordinate map that permits to separate compound-forming systems from the others. For a binary system containing the metals A and B, the three coordinates are: Z (i) Δ(rs rp)AB |(rs rp)AZ (rs rp) ZB| (the difference between the Zunger pseudo-potential radii sums, see Chapter 3) (ii) TA/TB (the ratio of the melting temperatures, TA TB) (iii) |ΔveAB| (the magnitude of the difference between the number of valence electrons)

A separation with accuracy of 96% was obtained. As a further step, Villars (1986) has shown that this kind of three-dimensional map may also be used to distinguish

Elements of Alloying Behaviour Systematics

521

between compound formation and absence of compounds in ternary systems. The coordinates were extended according to the following formulae: Z Z Z (i) 1⁄3 (|ΔrAB | |Δr AC | |Δr BC |) 1 (ii) ⁄3 (|ΔveAB | |ΔveAC| |ΔveBC|) (iii) 1⁄3 (TA/TB TA/TC TB/TC) (TA TB TC)

In terms of these coordinates the space of no-compound formation occurs around the origin and along the three axes of the diagram. In the conclusion of this chapter and on the basis of the data and schemes shown in the preceding paragraphs, we summarize some regularities observed in the description of the alloying behaviour shown by the different binary alloys. Giving special attention to the compound formation capability, the following points, even though qualitative, are underlined: (i) In the definition of the mutual reactivity of two elements a relevant role is played by their position in the Periodic Table. (ii) In the analysis of the progressive variations of the intermetallic reactivity along the Periodic Table, several peculiarities of the Table itself, besides the specific group characteristic trends, must be considered. Examples of such typical points are: the block subdivision, the ‘divide’ positions, the diagonal relationships, some similarity between elements of group n and those of group n 10, lanthanide and actinide concepts, etc. (iii) In each of the compound formation patterns of the different metals, arranged according to the Periodic Table, evident separation lines may be noticed between compound-forming and compound non-forming elements. According to their characteristic intermetallic reactivity ‘patterns’ a number of ‘families’ of metals may be identified and a somewhat smooth change in these patterns may be noticed on passing through the groups. The following ‘reactivity families’ may be defined: ●

●

First group metals. These show systematic compound formation with some late transition metals and with the p-block elements. Moreover, a few not very stable compounds are given with some metals of the s-block. Metals of the first groups (typically from the 2nd to the 4th). For these metals we have regions of no-compound-forming elements placed close to the left side of the Table, which include a number of adjacent groups. The widths of these regions decrease when passing from the metals of one group (2nd) to those of the next ones (3rd, 4th). Notice that in the conventional representation of the Table

522

●

●

●

●

●

●

Intermetallic Chemistry

reported in the various figures to show the reactivity patterns, clearer evidence could be given to the analogies of Be with the 12th group elements. Metals of the 5th, 6th, and 7th groups. A rough outline of the reactivity patterns of these metals shows several analogies. A first region of no-compound formation is observed with the first group elements, and a second region, more or less wide, originates in the central part of the Periodic Table. Notice, however, the characteristic behaviour of the 7th group metals, with which starts in the Table the formation of compounds with the 3rd group metals (lanthanides, actinides). Metals of the 8th, 9th, 10th (and 11th) groups. A close analogy may be observed between the ‘reactivity patterns’ of Fe, Co, Ni and those of the metals of the previous groups (especially Mn group). The ‘noble metals’ patterns show several similarities; they have no-compound formation regions at the far left and in the centre of the Table. Notice the systematic compound formation with lanthanides and actinides and, for Pt, the general reactivity with all the metals of the first transition row. A number of analogies may be observed between the general scheme of reactivity of typical metals of the 8th, 9th, 10th groups and that of the 11th group, especially Cu and Ag. Metals of the 12th group. Several analogies and similarities may be noticed between various elements in this part of the Periodic Table (Be with Zn, and also Be with Al, etc.). In the Zn, Cd, Hg group notice the shift (and the decrease) of the compound formation region on passing from Zn to Hg. Metals of the 13th group. The general pattern and the trend given by Ga, In and Tl show several analogies with those observed in the preceding group, with the metals from Zn to Hg. Slightly different is the behaviour of B and Al which may be compared better with Be. Elements of the 14th group. In this group too we notice a shift and a reduction of the compound formation region on passing from the light to the heavy elements. The no-compound formation region is generally placed near the right end part of the Table. Elements of the 15th and 16th groups. We notice, in comparison with the precedent groups, and especially for the light elements, a substantial increase of the compound formation regions which (for O to Te) practically cover the entire Periodic Table.

5.18. COMPLEX ALLOYS: A FEW NOTES AND REMARKS ABOUT THEIR SYSTEMATICS

In the preceding pages some indications have been given about the alloying behaviour in the binary systems, and a few trends and regularities have been underlined; this, of course, does not exhaust at all the problems of the alloy systematics. Taking

523

Elements of Alloying Behaviour Systematics

into account a few ‘numerical aspects’ only, notice that on the basis of 90 elements (metals, semi-metals), it is possible to define, along with 4005 binary systems, also 117480 ternary systems (and 2555190 quaternary, 43949268 quinary, etc.). To each of their corresponding stable phase diagrams, moreover, at least another one showing metastable features could be added. In so far as we want to remark some aspects of the ternary alloying behaviour only, we notice that the related systematics is obviously much more complicated than the binary one, both on the basis of the phase equilibria and on the phase structures, because a large variety of phase diagram types is formed. Considering for instance the formation of compounds, several variants may be observed due to the possible existence of binary (point or line) phases and/or of ternary, stoichiometric or solid solutions phases. Notice that ‘true’ ternary phases may be formed (that is phases corresponding to homogeneity regions placed inside the diagram and not connected with the components or any binary phases). However within the ternary composition fields, phases are observed which contain all the

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

AI−Fe−X

AI−Co−X

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

AI−Cu−X

AI−Mg−X

AI−Si−X

Compound-forming element

Phase diagram known; no intermediate phases formed

No information available

Questionable compound-forming capability

Figure 5.41. Schemes of ternary compound formation in ternary alloys. For a few metal

pairs (Al–Cu, Al–Fe, etc.) the third elements are indicated (defined by their position in the Periodic Table) with which ‘true’ ternary phases are formed; that is, phases are formed which are homogeneous in internal regions of the composition triangle not connected with the corners or edges. Compare these data with those shown for the formation of binary compounds in the figures relevant to the involved metals.

524

Intermetallic Chemistry

three components, but are connected through a continuous solid solution field with some phases of the boundary systems. In relation with this complex behaviour, knowledge of the ternary systems is only very partial (not to speak of the more complex ones, several alloys of which are of relevant commercial interest). In a large compilation such as that by Villars, data have been reported for about ten thousand systems (data ranging, according to the depth of the investigations carried out on the specific systems, from a nearly complete description of the phase diagram to a mere list of a few alloys studied). The formulation of some empirical rules underlying the formation of ternary (and complex) intermetallic compounds has been summarized through three-dimensional maps (Villars 1986). Just as an example about the ternary intermetallic reactivity, a few schemes of ternary compound formation for aluminium are given in Fig. 5.41, summarizing the formation capability of (true) ternary compounds. Data are generally available (although partial) about ternary aluminium alloys with selected metals (Fe, Mg, Si, etc.), owing to their relevant applications and commercial interest. With reference to the indicated metal pairs (Al–Fe, Al–Co, Al–Cu, etc.), the preferential formation of compounds with metals is evident. REFERENCES

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Ruschewitz, U. (2003) Coord. Chem. Rev., 244, 115. Saeger, K.E. and Rodies, J. (1977) Gold Bull., 10, 10. Schulson, E.M. (1994) A potential nuclear reactor structural material. In: Intermetallic Compounds: Principles and Practice, eds. Westbrook, J.H. and Fleischer, R.L. (J. Wiley & Sons Ltd, Chichester, England), Vol. 2, p. 133. Sereni, J.G. (1982) J. Less Common Metals, 84, 1. Sevov, S.C. and Corbett, J.D. (1993) Science, 262, 880. Shannon, R.D. (1976) Acta Crystallogr., A32, 751. Shilov, A.L., Kost, M.E. and Kuznetsov, N.T. (1989) J. Less Common Metal, 147, 185. Simon, A. (1973) Z. Anorg. Allg. Chem., 395, 301. Simon, A. (1979) Struct. Bonding, 36, 81. Simon, A. (1988) Angew. Chem. Int. Edingl., 27, 159. Smith, J.F. (1983) Bull. Alloy Phase Diagr., 4, 39. Smith, J.L. and Kmetko, E.A. (1983) J. Less Common Metal, 90, 83. Sommer, F., Borzone, G., Parodi, N. and Ferro, R. (2006) Intermetallics, 14, 287. Stock, A. (1933) Hydrides of Boron and Silicon (Cornell University Press, Ithaca, New York). Teatum, E.T., Gschneidner Jr., K.A. and Waber, J.T. (1968) Compilation of calculated data useful in predicting metallurgical behavior of the elements in binary alloy systems, Report LA-4003, UC-25, Metals, Ceramics and Materials, TID-4500 (Los Alamos Scientific Laboratory, Los Alamos, NM, USA). Tu, K.N., Gusak, A.M. and Li, M. (2003) J. Appl. Phys., 93, 1335. Van Mal, H.H., Buschow, K.H.J. and Miedema, A.R. (1974) J. Less Common Metal, 35, 65. Van Zytveld, J. (1989) Liquid metals and alloys. In: Handbook on the Physics and Chemistry of Rare Earths, eds. Gschneidner, Jr., K.A. and Eyring, L.R. (North-Holland, Amsterdam), Vol. 12, p. 357. Villars, P. (1985a) J. Less Common Metal, 109, 93. Villars, P. (1985b) J. Less Common Metal, 110, 11. Villars, P. (1986) J. Less Common Metal, 119, 175. Villars, P. and Calvert, L.D. (1991) Pearson’s Handbook of Crystallographic Data for Intermetallic Phases, 2nd Edition (American Society for Metals, Materials Park, OH) Vols. 1–4. Villars, P., Prince, A. and Okamoto, H. (eds.) (1995) Handbook of Ternary Alloy Phase Diagrams (ASM International), Vols.1–10. Von Schnering, H-G. and Hönle, W. (1988) Chem. Rev., 88, 243. Wade, K. (1976) Adv. Inorg. Chem. Radiochem., 18, 1. Wang, X., Scandolo, S. and Car, R. (2005) Phys. Rev. Lett., 95, 185701. Wolff, I.M. (2002) Precious metal compounds. In: Intermetallic Compounds, eds. Westbrook, J.H. and Fleischer, R.L., (John Wiley & Sons Ltd, Chichester, England), Vol. 3, Chapter 4, p. 53. Wu, X. (2006) Intermetallics, 14, 1114. Wu, C.M.L. and Wong, Y.W. (2007) J. Mat. Sci. Mat. Electron., 18, 77.

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Yamamoto, T., Inui, H., Yamaguchi, M., Sato, K., Fujitani, S., Yonezu, I. and Nishio, K. (1997) Acta Mater., 45, 5213. Yarnell, A. (2004) Chem. Eng. News, 82, 26. Ziegler, K. (1963) Consequence and development of an invention, Nobel Lecture, 12 December 1963. Ziegler, K., Holzkamp, E., Breil, H. and Martin, H. (1955) Polymerisation von Äthylen und anderen Olefinen, Angew. Chem., 67, 426.

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Double, double toil and trouble: Fire, burn; and, cauldron, bubble (Shakespeare, Macbeth, IV, 1)

Chapter 6

Laboratory Preparation of Intermetallic Phases

6.1. INTRODUCTION

In the following paragraphs an indication will be given of a few (mainly laboratory) methods which can be used in the preparation of intermetallic phases and compounds. Without any claim of being exhaustive, we will discuss a few characteristic manipulations and devices frequently employed in an intermetallic chemistry laboratory. This will also introduce general aspects of the intermetallic reactivity, while underlining some of its peculiarities. A number of the preparative methods employed in intermetallic chemistry are similar to those adopted in the preparation of other types of inorganic compounds; this, of course, is especially evident when considering techniques characteristic of solid-state chemistry and compounds on the border between true metallic and covalent (or ionic) behaviour. An example among many is represented by substances such as simple or complex sulphides, arsenides, silicides (polysulphides, polyarsenides, sulphoarsenides, sulpho or seleno antimonides, etc.). A number of specific techniques may of course be considered which are peculiar to the intermetallic laboratory. It is however worth paying some attention to the increasing relevance given in this field to methods of ‘soft chemistry’ (chimie douce), involving not very high temperatures, the use of solvents, etc. Before presenting a short list of preparation methods, some indication of a few general aspects and problems of these methods will be given. Questions concerning heat treatments and the effects of impurities will be discussed in some detail. 6.2. NOTES ABOUT PROCEDURES AND INSTRUMENTS FREQUENTLY USED IN AN INTERMETALLIC CHEMICAL LABORATORY

6.2.1 Heating, thermal treatments Heating, often up to high or very high temperatures, is a common procedure needed for melting or speeding up a reaction between solid or liquid components. 531

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It is also necessary for a number of heat treatments (annealing, quenching, etc.) which have possibly to be defined according to the aspect of the phase diagram of the materials involved. A variety of methods and instruments are used in order to achieve and control the selected temperatures. A selection of these will be presented in the following, either directly or through their applications. 6.2.1.1 Laboratory furnaces. Several types of furnaces are used in the laboratory; these are often available as commercial rigs, generally equipped with more or less sophisticated temperature measurement and control devices. As an alternative, a lab-made or commercial furnace and its temperature measuring devices may be connected to a multi-channel data acquisition/actuator/switch unit, to be programmed by a personal computer, in order to plan and carry out thermal treatments, to collect and retrieve measured thermal data, etc. A short list of the more common furnace types is presented in the following, with a few comments. 6.2.1.1.1 Electric resistor furnaces. Furnaces consisting of an electric resistance heating coil (wound on a suitable insulating tube, or in some cases, selfsupported) are generally available commercially and are useful, not only for preparative purposes, but also for long heat treatments (for instance annealing treatments, possibly followed by casting, quenching, etc.). Several types of resistor furnaces are commercially available; the most common of which are for temperatures up to 900°C, 1300°C, 1700°C. For the temperature range up to 1000–1100°C, Nichrome-wound resistance furnaces can be used; this is also the temperature limit at which heat treatments can be performed on samples enclosed in evacuated and sealed silica tubes. For higher temperatures up to 1400°C, ‘silit’ furnaces can be used (these are heated by silicon carbide rods placed about, and parallel to, the furnace tube). Platinum or platinum alloy wound furnaces can be used up to 1550–1650°C. Molybdenum or tungsten (strip or wire wound) furnaces may be used, but they must be operated in a reducing or neutral atmosphere (argon, mixture of hydrogen and nitrogen from ‘cracked’ ammonia gas, etc.). A Mo winding can be placed, for instance, on an alumina tube (up to about 1900°C) or embedded in zirconia (up to about 2200°C). Tungsten windings may be used in a similar way. A tungsten furnace for temperatures above 2500°C may be made, for instance, by a sheet formed as a self-standing split cylinder, surrounded by radiation shields of W and Mo, and fed by a high-intensity lowvoltage electric current. Carbon and graphite resistor furnaces of different types can be operated up to about 2200–2500°C. The sketch of a typical resistance furnace is shown in Fig. 6.1. It consists of an inner carbon furnace tube surrounded by packed granular carbon

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B

C D L

A

A

E F G

I

H

K J

Figure 6.1. High temperature Tammann type furnace and its application to differential thermal analysis. The supports A act also as connections to the electric supply (typically about 10 volts and several hundred amperes); B: upper lid and electric connection to the carbon tubular resistance C; the tube C is surrounded by packed granular carbon inside the ceramic insulating filling D; E: cooling water coil; F: lower electric connection; G: vacuum/argon connection. This scheme shows the use of the furnace for thermal analysis experiments. L: differential thermal analysis head; H: reference thermocouple joints; I: thermostatic water circulation; J: thermocouple wires; K: support of the thermal analysis apparatus.

inside an outer carbon tube. The furnace is enclosed and operated under inert atmosphere. The current is fed through water-cooled electrodes placed at the top and at the bottom. This type of furnace can be used up to about 2200°C. 6.2.1.1.2 Induction furnaces. These furnaces utilize the eddy currents flowing in a sample placed in a rapidly changing electro-magnetic field produced by a high-frequency current through a ‘coil’ (the inductor coil) which, in a way, becomes the primary of a transformer, while the sample becomes the secondary. The induction coils are generally made of copper tubing cooled by water circulation. Several coil designs have been proposed (frequently a multi-turn cylindrical or conical

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Water flow

Quartz tube

Figure 6.2. Sketch of the section of a high-frequency apparatus, in which, inside the primary induction coil (the inductor), another water-cooled copper tube, acting as a sample-container and as a ‘field concentrator’, is enclosed. In this copper tube, here shown in its transversal section, a hollow is made, obtaining a ‘cradle’ in which the sample is contained. The cool surface of this copper container generally is not attacked by the (albeit molten) alloy and promotes its fast solidification and cooling.

Molten metal

Copper tubes

Figure 6.3. Levitation of a molten metal in a radio-frequency field. The coil consists of water-cooled copper tubes. The counter winding above the sample stabilizes levitation. The same coils (and possibly additional ones) act as the induction heater. This technique has been applied to container-less melting and zone refining of metals and for drop calorimetry of liquid metals. It can be also used to decarburize and degas in ultrahigh vacuum mono-crystalline spheres of highly refractory metals (adapted from Brandt (1989)). The arrows indicate the instantaneous current flow directions in the inductors.

coil) in order to have the best distribution and/or concentration of the heat effects. Schemes of different arrangements are shown in Figs 6.2 and 6.3. 6.2.1.1.3 Arc furnaces (cold crucible technique). Small, commercial, laboratory arc-melting equipment generally includes a high-vacuum/argon atmosphere pumping

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system, with the related measuring instruments and a vacuum, gas-tight, chamber. It contains a water-cooled copper block, which acts as the positive electrode, with a few hollows in which samples are placed for melting. The other electrode, the anode, is generally a tungsten rod maintained in the vacuum chamber by a water-cooled manipulator operated from outside. The melting generator has leads carrying high current to the electrodes; it generally includes a high voltage (for instance 5 kV r.f.) ignition generator, which is switched off when the arc has been turned on. The current intensity of the arc may typically be adjusted up to 400–500 A. Before melting the samples, it may be useful to melt some pieces of, for instance, zirconium placed in one of the block cavities for gettering purposes, that is, to remove oxygen, etc. from the chamber atmosphere. The chamber is generally equipped with a sample manipulator which is used for turning, after melting and before re-melting, the alloy buttons without having to open the system. It consists of a vacuum-tight linear motion feed-through (equipped with a gripping device that can be operated from the outside) which, combined with flexible metal bellows, allows access to all crucibles (hollows). Melting and two or three times re-melting may be necessary in order to have a homogeneous specimen. 6.2.1.1.4 Vacuum plasma heating and spraying. Among several spraying techniques, the vacuum plasma has several applications especially in coating, possibly building up multiple layers of different materials. According to this technique, heatsoftened or molten particles (generally with dimensions from 10 to 100 μm) are accelerated by a plasma gas toward a substrate where they get squashed and solidify. The plasma, consisting of positive ions, free electrons and neutral atoms, is created by supplying a gas (generally argon) with the energy of an electric arc striking between the torch nozzle (the anode) and an internal tungsten cathode. Very high temperatures, in the order of several thousands of degrees, are reached. The powders of the material (ceramics, refractory metals) are injected into the plasma where they are heated, accelerated and directed towards a work surface. Different problems of the vacuum plasma technology (fundamentals, coating microstructure, diagnostic, applications) have been noted down in a short review by Azarmi (2005). Low temperature deposition with inductively coupled plasma has been considered by Lee et al. (2006). High-density plasma can be successfully used as an activation source for lowering the substrate temperature and enhancing the film quality. The mechanism of inductively coupled plasma generation is similar to the induction heating of conducting materials. Ion densities as high as 1011–1012 cm3 with a large number of high-energy electrons may be obtained. These densities are much higher than those obtained in a conventional plasma. Material depositions obtained are films of TiB2 (from TiCl4 BCl3 H2 Ar), TiN (from a precursor of TiCl4 N2 H2), SnO2 (by chemical vapour deposition from a gas mixture of SnCl4 H2 Ar O2) and TiO2 (by inductively coupled plasma assisted reactive sputtering).

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6.2.1.1.5 Electron-beam furnaces. The need to melt highly refractory metals such as tantalum and tungsten has led to the development of electron-beam melting already in 1907, by Von Pirani. The invention contained the ideas of selfand work-accelerated guns and of single and multiple gun furnaces. The commercialization of the process followed much later (Smith 1962). The combination of electron-beam heating and vacuum processing resulted in the transformation of many impossible tasks into an everyday basic laboratory and industrial materials processing technology. The main electron-beam melting (and metal-purifying) processes used at present can be subdivided into the ‘drip-melting’ and the ‘cold-hearth refining’ techniques. In drip-melting, the metal (Ta, Nb, Mo, and Ti, Zr and Pt metals) is drip-melted in a water-cooled mould. In this operation it is possible to remove dissolved gasses and other volatile impurities. In the cold-hearth refining technique, the molten metal flows along a water-cooled hearth entering then into a watercooled ingot. Purification of the metal is obtained by selective evaporation and impurity removal, owing to their lower density. The electron-beam guns may also be integral parts of several special pieces of equipment. Electron-beam evaporation and the related ‘directed vapour deposition’ technology are relevant examples. 6.2.1.1.6 Laser heating. Laser heating can be used especially for surface heat treatments (which can be easily followed by rapid or very rapid quenching), for welding and for several machining functions (cutting, drilling, etc.). Two types of lasers are generally used, namely the CO2 and the Nd:YAG. Both operate in the infrared region of the electromagnetic radiation spectrum. The Nd:YAG radiation is in the near infrared (it may be focussed by standard optics in spot sizes as small as 25 μm in diameter and it is absorbed quite well by conductive materials. The CO2 laser, which however can supply much higher power, has a wavelength in the far infrared, which requires special optics to focus the beam to a minimum spot size of 70–100 μm in diameter, and it has for most metals an initial reflectance of about 80–90%. (Nd:YAG is the symbol of a Nd-doped yttrium-aluminium garnet, see § 7.6.8.) Continuous laser melt quenching of hypoeutectic Ag–Cu alloys has been performed and discussed by Copley et al. (1995); nano-phase coupled growth structures (with spacing of 10 nm) have been observed in banded nano-structures. Nd:YAG and other types of lasers can be used in air to synthesize conductors and semiconductors as a second phase in SiC and AlN (Quick 1995). A short review on the development of laser heating in special applications under pressure has been published by Bassett (2001). A heating system to be used, with either ruby or YAG laser, under pressure in a diamond anvil cell has been described. Graphite to diamond and several silicate phase transformations have been studied.

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6.2.1.1.7 Optical furnaces. Mirrors or lenses to concentrate solar energy have been used for a long time now: they furnish a clean high-temperature heat source (see, for instance, Trombe and Foëx 1957). Temperatures up to 3200°C (possibly 3700°C) have been obtained. The temperature distribution obtained is generally uneven, but this may be used to advantage since the material to be melted may serve as its own crucible. Concentrated solar energy has been recently used by Sanchez-Bautista et al. (2006) as a novel method to process intermetallic coating. The main aim was to initiate an exothermic reaction in a mixture of powders (Ni and Al) and to obtain high-quality coatings (of NiAl) through a solar assisted, selfpropagating, high-temperature synthesis process. A vertical axis solar furnace with a power of 2 kW was used. The energy concentration system consists of a heliostat (a flat mirror) and a parabolic concentrator of 2 m in diameter. The heliostat reflects the radiation onto the parabolic mirror from which it is concentrated at the focus on an area of 15 mm in diameter (the focal distance is 85 cm). From a standard direct irradiation of 1000 W/m2 (Laboratory of Solar Energy, Odeillo, France) the power density at the focus is 1600 W/cm2. The sample is placed on a computer controlled two-ax table in a Pyrex glass chamber (transparent to the solar radiation). The main disadvantage of solar furnaces is, of course, that they depend on the availability of sunshine. The advantage of image heating may be maintained by using, instead of the sun, an artificial light source. Electric arcs have been proposed and (for lower temperatures) groups of incandescent projection lamps. A commercial apparatus has been produced by the Crystal Systems Corporation (CSC Japan): a high-temperature model (which can work up to 2200°C) is equipped with four air cooled halogen lamps (maximum 4 1550 W) each placed in an air cooled ellipsoidal mirror. The four lamps are symmetrically arranged, in a horizontal plane, around the vertical quartz tube containing the sample. This geometry gives a uniform horizontal temperature profile in the hot zone created by the focused radiation. In the travelling floating zone furnace the sample is a rod of the material to be studied: once a small section of the rod has been melted, the molten zone is translated along the sample length by moving the material with respect to the radiation focus. Crystal material is grown on the solidifying end of the float zone: large crystals of various materials can be grown by using this technique (Conder and Pomjakushina 2004). 6.2.1.1.8 Microwave heaters. Increasing interest is being shown towards applications in chemistry of microwave heating, both for solution and solid-state chemistry. Domestic ovens are so-called multi-mode instruments in which the microwaves are reflected by the walls of the cavity. This kind of equipment can irradiate several vessels in a cavity, whereas in a single-mode instrument there is one vessel at a fixed distance from the radiation source.

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Intermetallic Chemistry

Microwaves have been utilized as a tool for non-destructive testing of material defects (thickness measurement, etc.); increased usage is currently found also in many industrial heating applications. Advantages of microwave heating over conventional heating may be found in the higher heating efficiency with consequent reductions in time and energy cost. The disadvantages are mainly related to the fact that microwaves are inherently difficult to direct, can be used to heat only particular materials and can produce the so-called thermal runaway phenomenon (see in the following). Microwaves is the name for electromagnetic waves included in the frequency range from 1 to 300 GHz. Only some materials can be heated by microwaves: nonconducting materials are transparent to them; highly conducting materials reflect them. For other materials that absorb microwaves energy, the dielectric loss factor gives a measure of the fraction of the energy released as heat by the interaction with the electric field. Often an even dissipation of energy occurs in the specimen volume; in spite of this, a thermal gradient across the material volume can be created by the heat flow from inside towards the cooler environment. This is the opposite situation to what occurs in a conventional heating where the energy is conducted from the surface of the material towards its centre. A comparison of the temperature profiles in samples heated by microwaves or by a more traditional oil-bath method is schematically shown in Fig. 6.4. Another point relevant to the possibility of having a uniform heating is related to the temperature dependence of the loss factor. In some cases it decreases as the temperature increases; this helps in limiting and Temperature (°C)

500

450

400

350

Figure 6.4. A comparison of the temperature profiles in a sample heated by microwaves (left) or by an oil-bath method (right). Hotter zones are indicated by a darker hatching (Adapted from Marx (2004)).

Laboratory Preparation of Intermetallic Phases

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controlling the heating of the material and in obtaining an even distribution of temperature. A large number of materials however show an increase in their dielectric loss factor as a consequence of increased temperature. As a result, more energy will be absorbed by the hotter parts of the sample which will show a greater rate of heating while other parts will have increasingly low rates of heating. This behaviour is defined as the thermal runaway phenomenon. Questions and references about qualification of technical microwave systems and validation of microwave assisted reactions and processes have been raised and discussed by Ondruschka (2005). 6.2.1.2 Crucibles, refractory materials. In the high-temperature handling (melting, etc.) of the alloys, attention is obviously to be given to the properties of the materials employed for crucibles, containers, supports, etc. in order to avoid undesired side reactions. A short list of metallic and ceramic refractory materials is given in the following, together with a few comments about their reactivity and uses. Metals which have been used (generally in inert or reducing atmosphere) as container materials are: W (melting point 3422°C), Mo (2623°C), Pt (1769°C), Fe (1538°C), Ni (1455°C), Cu (1085°C), Au (1064°C), Ag (962°C). W and Mo do not react with many elements: they must be protected however from air oxidation. Pt and Au cannot be used, owing to their reactivity, for melting metallic materials; they are useful for other types of synthesis. Fe, of very high purity and with very low carbon content, could possibly be used for melting alkaline and alkaline earth metals and a number of their alloys. As for metallic materials, and for the refractory ones also (Mo, Ta), an illustration of a simple device which may be used to prepare and tightly close containers and crucibles is shown in Fig. 6.5. Materials of other types used for container, supports, high-temperature devices, etc. are glasses and ceramic materials. Among the different glasses along with the soft (‘window’) glasses (typically containing 75% SiO2, 12% CaO, 13% Na2O) hard glasses (Supremax, Pyrex, etc.) are very useful in chemistry (a characteristic composition could be 57% SiO2, 20% Al2O3, 9% B2O3, 8–9% MgO, 4% CaO, 1% K2O). Especially important is the silica glass (pure SiO2) which can be used up to about 1100°C. It is easy to work with, it can be welded air tight, and it has not a definite melting point but gets soft very slowly by increasing the temperature. A scheme for flame welding of silica tubes is shown in Fig. 6.6. Ceramic materials employed in high-temperature chemistry can be exemplified by the following: porcelain (based on starting compositions such as Al2(OH)4Si2O5 (50%) KAlSi3O8 (25%) SiO2 (25%), alumina (Al2O3: alsint, corundum, melting point 2052°C , max working temperature about 1900°C), stabilized zirconia (ZrO2 melting point 2710°C , max working temperature about 2200°C), boronitride (BN decomposition 2400°C, max working temperature about 1200°C in

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Intermetallic Chemistry −

Cooling water E F

W

A

D

C

C

L

S

B

Argon G

+

Figure 6.5. Scheme of the arc-welding apparatus for closing (tight sealing) small tubes, crucibles, etc. of Ta, Nb (Mo). A crucible (C) with the sample S inside and the lid L inserted, ready to be sealed is shown. Typical dimensions: crucible diameter 5–15 mm, thickness 0.1–0.2 mm. Notice the special arrangement which is given to the two pieces to be welded (crucible and lid): this is in order to achieve localized heating and welding, in the position W. A is a glass (or, better, silica) tube inside which vacuum can be made and then argon introduced. B is a brass block acting as a clamp and as a heat sink to avoid excessive heating of crucible (C) and sample. By means of the handle G, the sample can be revolved around its axis, in order to continuously weld the crucible along its rim. D is a rod-shaped tungsten electrode, the cooled end of which is handled by means of the flexible support E. F is a vacuum air valve.

oxidizing atmosphere and about 2200°C in reducing atmosphere), silicon carbide (melting point 2545°C, max working temperature about 1600°C in oxidizing atmosphere and about 2300°C in reducing atmosphere), tungsten carbide (WC melting point 2775°C, max working temperature about 1600°C in oxidizing atmosphere and

Laboratory Preparation of Intermetallic Phases

Vacuum

541

Vacuum

Figure 6.6. Schemes of flame welding of silica (or glass) tubes. The arrangements shown may be used when a sample prepared in a metallic crucible (Ta, Nb, etc.) must be annealed for a certain time at a moderately high temperature (for instance 800–900°C). The crucible must be protected from air oxidation. This may be achieved by using a silica container tightly closed by flame sealing. The simpler arrangement shown on the left may be more convenient when objects of small dimensions are handled; on the right it is shown that the insertion of a second tubular piece of silica may result in a safer, more solid and easier to handle equipment. In any case the silica tube must be conveniently connected to (and supported by) a vacuum/argon pumping device.

about 2000°C in reducing atmosphere), graphite (C max working temperature about 2500°C in reducing atmosphere). Crucibles, tubing and several objects of different ceramic materials (MgO, BeO, Al2O3, ZrO2) are commercially available. Materials such as BN and pyrolytic graphite can be easily machined in a laboratory. Materials based on amorphous silica fibres are of special interest; these are manufactured in a variety of textile forms (cloth, tape, rope, etc.) which can be used for several applications (thermal, electric insulation) for service temperatures generally up to about 1000°C. Typically they contain 93–96% SiO2 about 4% Al2O3 and small quantities of Ca or alkali oxides. Thorium oxide, has the highest melting point of the usual ceramic materials (3390°C). It is used to form ceramics, ThO2, as the so-called meta–ThO2, freshly prepared by low temperature decomposition of thorium oxalate; it is fairly soluble in acids and tends (especially in the presence of nitrate ions) to form colloidal solutions which can be dried to form stable gels that can be sintered to give highdensity ceramic bodies.

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A particular problem with crucibles for melting reactive materials arose during the Manhattan Project, and it was Leo Brewer, one of the founders of high-temperature chemistry, who had the task of predicting the high-temperature properties of the newly discovered plutonium, then available only in trace amounts, and of providing materials for crucibles that could contain molten Pu without contaminating it. Brewer studied the behaviour of all the elements at high temperature, and, dissatisfied with existing crucible materials, experimented with new sulphides of thorium and cerium which proved successful. Brewer’s new crucibles were ready when plutonium became available (Scheiber 2005). Crucible-less melting and processing (levitation techniques). An induction furnace scheme where, by means of a magnetic field, a sample is levitated and the melting may be achieved without using a container is shown in Fig. 6.3. This technique can be used both for preparative purposes and for other applications such as fast quenching, high- and very-high-temperature calorimetry (drop calorimetry). On this subject notice that, possibly combined with various heating methods, several physical effects may be considered which allow free flotation of solid and even liquid matter. Materials may be levitated for instance by a jet of gas, by intense sound waves or by beams of laser light. Conductors levitate in strong radiofrequency fields, charged particles in alternating electric fields, magnets above superconductors or vice versa. A review on levitation in physics with the description of several techniques and their principles and applications was made by Brandt (1989). Examples of reactions carried out in metallic welded tubes. According for instance to Park et al. (2003), containers made of Nb tubing (100 mm length, 10 mm o.d. and 0.2–0.5 mm thickness) with one end closed by welding in an Ar atmosphere were used. Before welding, the tubing was cleaned in a concentrated mixture of hydrofluoric, nitric and sulphuric acids (15:40:45 by volume). (Caution: this is an extremely corrosive mixture. Contact with skin is hazardous and may be fatal). After loading, the container was sealed by welding its open end in an argon atmosphere with active water cooling, so that the sample did not react due to heating during the welding. In order to protect the container from oxidation during heat treatment, it is put into quartz tubing flame sealed under vacuum. 6.2.2 Miscellaneous, special processing techniques and heat treatments In the preparation of intermetallic alloys, both in massive quantities for commercial purposes, or as small specimens for laboratory investigations, very often the alloys must be subjected to selected and well-defined heat treatments, in some cases in addition to mechanical treatments, in order to have their full characterization and/or optimal performance.

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Characteristics and implementation of the treatments depend on the expected results and on the properties of the material considered; a variety of processes are employed. In ferrous alloys, in steels, a eutectoid transformation plays a prominent role, and aspects described by time-temperature-transformation diagrams and martensite formation are of relevant interest. See a short presentation of these points in § 5.10.4.5. Titanium alloys are an example of the formation of structures in which two phases may be present in comparable quantities. A few remarks about α and β Ti alloys and the relevant heat treatments have been made in § 5.6.4.1.1. More generally, for the various metals, the existence of different crystal forms, their transformation temperatures, and the extension of solid-solution ranges with other metals are preliminary points in the definition of convenient heat treatments and of their effects. In the evaluation and planning of the treatments, due consideration must be given to the heating and/or cooling rate and to the diffusion processes (in pure metals and in alloys). During the history of metallurgy, by a combination of empirical trials and scientific analyses, several specific treatments have been developed and defined for particular groups of alloys. Owing to the relevance of this topic, in the multi-author book of ASM dedicated to heat treatments, detailed descriptions are given of the heat treating of steels, tool steels, stainless steels, cast irons and of a number of non-ferrous alloys (alloys of Al, Cu, Mg, Ni, Ti, Sn, Pb, U and precious metals). In the same book an extensive glossary of terms is included: a few definitions from this book, as well as from the basic book by Hume-Rothery et al. (1952), are reported in the following: Aging: A change in properties, and/or structure, that occurs in metals or alloys at ambient temperature (or not very high temperature) after a heat treatment or hot or cold working. Often the aging results from a phase change (precipitation). According to the composition and structure of the alloy considered, processes of age-hardening and age-softening have been described. Annealing: A process in which alloys are heated for some time at high temperature. Annealing treatments can be divided in two types: (i) homogenizing treatments (on ingots or compacts of powdered metals) in order to obtain a uniform composition throughout the sample and (ii) heat treatments of samples at a particular temperature in order to bring the sample to the equilibrium state at that temperature (often followed by quenching to retain the state obtained). The time needed to attain equilibrium strongly depends on the specific alloy and increases enormously as the temperature falls. Carburizing: One of several thermochemical treatments involving, by heating, carbon absorption from suitable material in contact with the surface layer, and diffusion into solid (ferrous) alloys. Surface hardening processes may then be

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carried out. Similar definitions may be applied to the boriding or nitriding treatments. Cementation: The introduction, by diffusion at high temperature, of elements in the outer portion of a metal piece. Hardening: A hardness increase obtained by a convenient treatment (often by heating and cooling). Homogenization: Holding at high temperature to eliminate (or reduce) by diffusion chemical segregation. Care should be taken in the definition of the temperature, possibly on the basis of the phase diagram. In an investigation work, after a preliminary homogenization treatment, the alloys should be quenched and, if sufficiently ductile, should be hammered or otherwise deformed so as to promote recrystallization on further annealing. Precipitation: Precipitation from a super-saturated solid solution of particles growing by long-range diffusion without recrystallization of the matrix (continuous precipitation) or of particles growing by short-range diffusion with recrystallization of the matrix (discontinuous precipitation). Precipitation hardening (age hardening, artificial aging) is the hardening caused by the precipitation of a constituent from a super-saturated solid solution. Quenching: (Rapid cooling): Several more specific and detailed terms may be used (water-quenching, oil-quenching, intense quenching, etc.). See the following paragraphs for a few remarks about special quenching treatments. Tempering: According to the more common meaning of the term it consists in reheating (in heat treatments) hardened steel or cast iron to a temperature below the eutectoid in order to decrease hardness and increase toughness. (For a few more terms especially relevant to the Fe alloys see Tables 5.49 and 5.50.)

6.2.2.1 Quenching (from the solid state). Metastable alloys have been very familiar to metallurgists for a long time now. Several alloys employed in everyday applications contain metastable phases. Typical examples are quenched steels and precipitation hardened aluminium alloys. Until the 1960s, metastable alloys were always obtained by quenching (rapid cooling) from the solid state. The traditional techniques for retaining a metastable phase in the solid alloy generally make use of the high-heat transfer from the hot solid to a fluid (a gas or a liquid). In the common procedure of quenching a solid piece in a liquid, heat removal is obtained according to three subsequent stages: in the first stage (vapour blanket cooling stage) soon after the immersion in the liquid, a vapour blanket forms around the quenched metal; this blanket inhibits cooling and can produce nonuniform heat transfer; the baths need therefore to be continuously stirred. In the subsequent stage (nucleate boiling stage) the vapour blanket collapses; the liquid

Laboratory Preparation of Intermetallic Phases

545

evaporates in contact with the metal surface and a rapid cooling takes place. The last stage (liquid cooling stage) begins when boiling stops and heat is further removed through convection and conduction. The sequence of quenching stages and the cooling rate are important in the control of the metal transformation and of the presence of unwanted residual stress and distortion. An important factor is the nature of the quenchant, for which a liquid medium is generally used. Water (possibly distilled or demineralized water) gives a high-cooling rate and is generally used for steels of low harden-ability. Brine (typically a 5–7% NaCl solution in water) and caustic solutions give faster cooling than water. For the alloys of several metals, oils may be convenient less extreme quenchants. Several polymer solutions provide convenient media for various quenching treatments of different alloys. 6.2.2.2 Super-Quenching (quenching from the liquid). Very high-cooling rates have been obtained by quenching from the liquid state. A basic principle adopted in this case consists in forcing a thin layer of liquid to solidify when suddenly placed in contact with a metallic surface having a high-thermal conductivity. Since the pioneer activity of P. Duwez (Duwez et al. 1960, 1963, Duwez 1967), great ingenuity has been dedicated to the design and construction of special instruments for fast liquid quenching. A short list of the principal experimental methods is contained in a systematic review of the subject prepared, a long time ago, by Giessen (1969), still giving valid indications about, for instance, the cooling rates achievable. ●

●

●

●

●

●

Wedge solidification technique: Molten metal is forced into a wedge-shaped metal mould by a vacuum (cooling rate is about 5 104 °C/s). Anvil and piston technique: A falling molten droplet is flattened between rapidly moving piston and anvil (cooling rate about 105–106 °C/s). Catapult technique: Molten metal is catapulted against a stationary substrate (cooling rates is about 5 104 °C/s to 105–106 °C/s). Splat cooling technique: Molten material is atomized by a shock wave (gun technique) against either a stationary substrate or a rapidly rotating cold hearth. The alloy either arc-melted or induction melted is propelled (for instance by an inert gas stream) against a cooling substrate (cooling rate up to about 108–109 °C/s). Plasma-jet spraying: Alloy powders are molten in a plasma jet and sprayquenched against a cold heat-conducting substrate (cooling rate about 109 °C/s). Vapour-quenching: Co-deposition, for instance, of the components in vacuum on a copper substrate (very high-cooling rates).

Copper and gold based alloys having giant magneto-resistance properties were produced by Das et al. (1995), by melt spinning from arc melted and cast rods. Typically a portion of a ternary alloy rod having a nominal composition Cu80Co15Fe5 was

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Intermetallic Chemistry

melted by induction heating in a silica crucible with a 500 μm orifice. The molten liquid at the proper temperature was ejected onto a rapidly rotating (surface velocity 36 m/s) polished Cu wheel in a He atmosphere. The ribbons obtained were approximately 30 μm thick and 1.5 mm wide. The results of several examinations and annealing treatments were described. Metastable phases and nano-crystalline forming ability of melt-quenched alloys. The formation by melt-quenching of metastable and nano-crystalline alloys in Ni-rich (Zr,Hf)-Ni alloys has been studied by Bakonyi (2006). The formation conditions of these phases have been discussed in terms also of the C-curves in a schematic TTT (time-temperature-transformation) diagram. (see § 5.10.4.5). By increasing the cooling speed, the formation (from the Ni-rich liquid or under-cooled liquid) of the following phases is considered: (i) equilibrium phases (fcc Ni ZrNi5 or Hf Ni5); (ii) a metastable bcc Ni(Zr,Hf) phase; (iii) nano-crystalline (Zr,Hf )Ni5; and (iv) a glassy amorphous alloy. Of particular interest is the possible formation of a single-phase nano-crystalline alloy by melt quenching in a one-step process. 6.2.2.3 Thixoforming, semi-solid processing. Semi-solid processing or thixoforming is the shaping of metal alloys in the semi-solid state. According to a review by Maciel Camacho et al. (2003), this is possible if the alloy structure consists of solid metal spheroids in a liquid matrix, that is, if the alloy is thixotropic. This means that if it is sheared, the viscosity falls and it flows like a liquid, but, if allowed to stand, it thickens again. A piece of alloy heated into the semi-solid state can be cut with a knife and spread like butter, provided the structure is non-dendritic. According to the thixoforming process, a slug of alloy is heated, (for instance in an induction heater) until it reaches the semi-solid state, and then forced into the die by a ram. The liquid fraction sensitivity is an important parameter for the determination of the semi-solid forming capability. It is defined as the rate of change of the liquid fraction in the alloy with temperature and is related to the relative slopes, in the phase diagram, of the liquidus and solidus curves. It may be determined by differential scanning calorimetry or predicted by thermodynamic modelling. Examples related to various Al alloys have been reported by Maciel Camacho et al. (2003), Dong (2003). See also several papers in Chiarmetta and Rosso (2000). 6.2.2.4 Temperature measurements. It is well-known that several generally commercially available instruments, based on different principles, may be used for temperature measurement and control. We will take a look at a few types, but a little more attention will be devoted to the thermocouple devices. 6.2.2.4.1 Radiance temperature measurements. In the high-temperature range, devices based on radiance measurement can be used. A differential thermal analysis

Laboratory Preparation of Intermetallic Phases

547

apparatus, for instance, to be used up to a temperature of 3400°C was already described by Wehner et al. (1977). In measurements carried out on test-specimens (Nb, Ta, ZrO2) the accuracy at 2300°C was estimated in 30°C. A frequently used instrument in the high-temperature range is the disappearing filament optical pyrometer. According to the National Institute of Standards and Technology, the uncertainty in the calibration of this instrument may range from 5°C to 10°C (at 2000°C) up to about 15°C to 30°C (at 3000–4000°C). The most important application of optical pyrometry is to measure the true temperature of the specimen. Notice however that when the pyrometer is aimed at the specimen the resultant temperature is the surface radiance temperature. To perform a meaningful conversion to the true temperature, the normal spectral emittance of the specimen at the wavelength of the measurement should be known. These data are not generally available and it is difficult to rely on the conditions of the specimen. The best approach to measuring the true temperature is to have a sample so prepared and shaped as to approximate blackbody conditions. 6.2.2.4.2 Resistance temperature detector. In the low-medium temperature range, thermometers based on resistometry are often used. A reference highaccuracy thermometer is the platinum resistance temperature detector which may be used as an interpolation standard in the temperature range from the triple point of hydrogen to the freezing point of silver. The platinum resistance may have the form of a coil supported on a crossed mica web or of a ‘bird-cage’ element, or of a bifilar wire wound on a ceramic bobbin or of a film deposited on a small ceramic substrate. The resistance can be measured using a bridge (Wheatstone bridge) or a four-wire ohmmeter (Hewlett® Packard 1997). For curve fitting of the data the following equation is frequently used: RT R0 R0α[T δ((T/100) 1)((T/100) β((T/100) 1)(T 3/100)]

RT: resistance at temperature T; R0: resistance at 0°C; α: temperature coefficient at 0°C, typically α 0.00392 (Ω/Ω)/°C: δ 1.49 typical value for 0.00392 Pt; β 0 (for T 0) 0.11 (for T 0). The coefficients α, δ and β may be determined by testing the detector at various well-known temperatures. For more accurate fitting, polynomials up to the 20th order may be used and implemented in computer controlled acquisition systems. Platinum is especially suitable for this application because even at high temperatures it has a good stability and a good resistance to contamination. However, different metals, all having a positive temperature coefficient, may be used, such as tungsten (for very high-temperature applications), nickel and nickel alloys and also (but rarely because of their low resistivity) gold and silver.

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Intermetallic Chemistry

Thermistors: These are resistance temperature detectors composed of semiconductor materials. Generally they have a negative temperature coefficient which may be as large as several percent per °C. They have large temperature sensitivity and may detect very small temperature changes. However they are non-linear devices: the thermistor response may be approximated (in a temperature range of say 100°C) by an equation such as: 1/T A B ln R C(ln R)3 (T temperature in Kelvin, R thermistor resistance, A, B and C fitting constants) Semiconductor based devices are the integrated circuit temperature transducers which, in a limited temperature range, may produce an easy-to-read output proportional to temperature and may also be used for thermocouple compensation. 6.2.2.4.3 Thermocouples. In several temperature ranges, the thermocouple is usually one of the most useful instruments for the accurate determination of temperature; it is probably the most versatile temperature transducer and, because of its small thermal capacity and ready response to changing temperatures, it is especially suitable for equilibrium diagram work (see also § 2.4.1). For this reason, and considering also the special conventional codes generally used to identify the various thermocouple types, a few more remarks will be reported here on this subject. The working principle of the thermocouple was discovered (1823) by Seebeck who observed that if wires of two different metals were joined to form a continuous circuit, a current flowed in the circuit when the two junctions were at different temperatures. In order to make a measurement, one junction (the reference junction) is maintained at a constant temperature (typically at 0°C) and the electromotive force produced when the other junction is at the test temperature is measured, or recorded, by a suitable instrument (or used as the input of a ‘controller’). In order to choose the right kind of thermocouple among the many types available, the temperature range to be studied must be considered, as well as several requirements regarding: sensitivity, calibration stability, chemical, thermal, mechanical inertia, etc. For the reader’s convenience, a short list of the more common thermocouple types, together with their commercial designations, is reported in Table 6.1. An indication of their temperature working ranges and of their sensitivities is given in Fig. 6.7. Other metallic thermocouples are the following. (The maximum temperature for continuous use is indicated together with the corresponding e.m.f against the cold junction at 0°C.) Iridium–Iridium 60 mass% rhodium (2000°C, 28.2 mV) Tungsten–Iridium (2100°C, 38.9 mV at 2000°C) Tungsten–Molybdenum ( 2300°C, 8.0 mV at 2500°C)

549

Laboratory Preparation of Intermetallic Phases Table 6.1. Characteristics of common thermocouples. ANSI Code

Positive leg

Negative leg

Temperature Typical values of range for the Seebeck continuous use (°C) coefficient (μV/°C)

J

Iron (magnetic)

Constantan* Cu 55 mass%, Ni 45

0–760

50.38 at 0°C

K

Chromel* Ni 90 mass%, Cr 10

Alumel (magnetic) Ni 95 mass%, Al 2, Mn 2, Si 1

0–1260

39.45 at 0°C

T

Copper

Constantan* Cu 55 mass%, Ni 45

184 to 371

38.75 at 0°C

E

Chromel* Ni 90 mass%, Cr 10

Constantan* Cu 55 mass%, Ni 45

0–861

58.67 at 0°C

`

S

Pt-10%Rh

Pt

540–1480

10.21 at 600°C

R

Pt-13%Rh

Pt

id

11.36 at 600°C

B

Pt-30%Rh

Pt-6%Rh

870–1700

5.96 at 600°C

N

Nicrosil

0–1250

25.93 at 0°C

C

W-5%Re

Nisil magnetic W-26%Re

0–2330

–

* Common approximate compositions

E 70 K

50 J

40

N

30 R S

1800

1600

1400

1200

1000

800

600

400

0

200

10

B 2200

T

20

2000

e.m.f. (mV)

60

Temperature (°C)

Figure 6.7. Characteristics of commonly used and commercially available thermocouples: e.m.f. data, with cold junction at 0°C (For the symbols of the various thermocouple types, see Table 6.1).

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Intermetallic Chemistry

Notice that the tungsten wires must be used in vacuum, hydrogen or inert gas atmosphere and that iridium embrittles in hydrogen. Common types of tungsten thermocouples contain Re alloys which are more malleable (W vs. W26%Re, W5%Re vs. W26%Re, etc.). Notice that two thermocouples can be differentially connected, for instance in a differential thermal analysis apparatus (see Fig. 2.39), in order to be able to measure at the same time the specimen temperature and the temperature difference in comparison to a reference sample. Several thermocouples, moreover, may be connected in series to form a thermopile, which is a device with an increased sensitivity relative to a simple couple. For the connection of a thermocouple to the measurement instrument, the best way is to use leads made of the same materials (extension leads); these avoid lead junction errors. For economic reasons, however, cheaper alloys having similar e.m.f. output, at least over a limited temperature range close to room temperature, are often used. These compensating leads are often supplied by the same producers of the thermocouple wires. Thermocouples: The reference junction. As previously mentioned, the resultant reading of a thermocouple depends on the temperature of the two junctions (the ‘measuring’ and the ‘reference’ junctions). A reference junction can be made up of an ice bath in which the wires are immersed. A simpler arrangement may be obtained by putting the reference junction (with its two identical copper connections to the voltmeter terminals) in an isothermal block. A thermistor, placed in the same block, measures the absolute temperature of the reference junction, and consequently allows correcting, either by software or hardware compensation, the voltage measured, that will be referenced to 0°C for the subsequent conversion. Thermocouples: Voltage to temperature conversion. For selected values of voltage, the conversion may be obtained by consulting tables or graphs. For a systematic conversion of data by a computer, power series polynomials may be used, such as exemplified by a nested 5th order polynomial: T c0 v(c1 v(c2 v(c3 v(c4 vc5)))) (T temperature, v thermocouple voltage, c0 to cn polynomial coefficients). To obtain a good fit, generally polynomials up to the 8th or 9th order are needed for a temperature range of a few hundred degrees. However a less-time consuming, faster acquisition and conversion procedure may be obtained if the entire voltage range is subdivided into a number of sections in each of which a simpler (for instance 3rd order) power series is used.

551

Laboratory Preparation of Intermetallic Phases

Thermocouples: The calibration. Several causes may result in an alteration and consequent ‘de-calibration’ of the thermocouple wires which will no longer conform to the certified polynomial. This may be caused by high-temperature diffusion of impurities into the metals, over-heating in welding a junction, cold working, annealing at high temperature, etc. A periodic check, a periodic re-calibration of the thermocouple may therefore be necessary. Notice that, when considering calibration problems especially in connection with thermal analysis or differential thermal analysis procedures, further questions should be considered. This point has been discussed by Tye and Gardner (1993) who underlined the need for ‘identical’ procedures in measuring and in calibrating, by using ‘standard’ samples, similar heating and cooling runs, similar crucibles, the same thermocouple position, etc. Importance was also given to the different precision that may be obtained in routine experiments, in comparison with the very accurate calibration procedures which can be carried out in a ‘standard’ laboratory. For a detailed description of thermocouple materials, their maintenance, insulation, welding, etc., see also Wang (1990). Thermocouples: Their protection. In the various, often hostile, environments suitable sheathing materials must be used to protect the thermocouple wires. The International Temperature Scale (ITS) revised in 1990 establishes fixed points and the corresponding temperatures. A few of them are reported in Table 6.2. 6.2.3 Laboratory equipment: a few additional remarks Several problems are met in the everyday running of an intermetallic laboratory, and suitable instrumentation is generally required: reliable temperature measurement, Table 6.2. A selection of temperature fixed points according to the (1990) Revision of the International Temperature Scale. Substance

Equilibrium type

Hydrogen Neon Oxygen Argon Mercury Water Gallium Indium Tin Zinc Aluminium Silver Gold

Triple point Triple point Triple point Triple point Triple point Triple point Melting point Freezing point Freezing point Freezing point Freezing point Freezing point Freezing point

T (K)

T (°C)

13.8033 24.5561 54.3584 83.8058 234.315 273.16 302.9146 429.7485 505.078 692.677 933.473 1234.93 1337.33

259.3467 248.5939 218.7916 189.3442 38.8344 0.01 29.7646 156.5985 231.928 419.527 660.323 961.78 1064.18

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Intermetallic Chemistry

control and recording, for instance, are possible only when a set of instruments of a good performance is available and periodically calibrated. Similar relevant problems are related to the adequate installation and working of small plants for vacuum production and control, gas purification and circulation and their connection to different pieces of equipment (and especially to a well-equipped glove-box). Particular techniques and instruments may, of course, be required for special purposes; for instance: the preparation of specimens for specific examination (for example, metallographic examination) and tests of their polishing, cutting, drawing, rolling, etc. Several instruments and devices are certainly commercially available; the need however for the availability of a precision mechanical workshop close to the laboratory must be underlined, since the construction of special apparatuses and components is often required, involving many machine tools (lathes, milling machines, presses, etc.), parts and different materials. See for instance remarks reported by Schnepf and Schnöckel (2002).

6.3. PURITY PROBLEMS, THE ROLE OF IMPURITIES

6.3.1 Introductory remarks Both in the preparation of intermetallics and in their handling, special problems are encountered due to impurities present in the materials involved or produced by unwanted side reactions, such as reactions with the atmosphere, the containers, etc. The purity control is especially important when working at high temperature. It is well-known that the fundamental law of high-temperature chemistry is that: … ‘everything reacts with everything!’ These problems have of course different weights for the different metals. The high reactivity of the elements on the left-side of the Periodic Table is well-known. On this subject, relevant examples based on rare earth metals and their alloys and compounds are given in a paper by Gschneidner (1993) ‘Metals, alloys and compounds: high purities do make a difference!’ The influence of impurity atoms, especially the interstitial elements, on some of the properties of pure rare earth metals and the stabilization of non-equilibrium structures of the metals are there discussed. The effects of impurities on intermetallic and non-metallic R compounds are also considered, including the composition and structure of line compounds, the nominal vs. true composition of a sample and/or of an intermediate phase, the stabilization of non-existent binary phases which correspond to real new ternary phases, etc. A few examples taken from the above-mentioned paper and reported here are especially relevant. They may be useful to highlight typical problems met in preparative intermetallic chemistry.

Laboratory Preparation of Intermetallic Phases

553

6.3.2 Formation of impurity-stabilized phases With reference to the R (rare earth) metals, the existence of various hypothetical polymorphs, that are now known not to exist in high purity R metals, was discussed at length in the past and is now only of historical interest (see a summary in Gschneidner 1993). These non-existent allotropes, which are impurity-stabilized phases, are: fcc Sc, fcc γ -Ce, the bcc Ho, Er, Tm and Lu and fcc phases of Nd, Sm, Gd and Dy, some of which have been described as formed at room temperature during mechanical milling. A number of fcc high-pressure polymorphs, for instance, are actually compounds, with a structure related to the NaCl-type, formed by reaction with O, N and/or H during mechanical milling (see also Alonso et al. 1992). Other typical examples of the stabilization of unstable rare-earth binary phases are the following: R3Al phases: The existence of these phases (cubic AuCu3 type) had been reported for R La, Ce, Pr, Nd and Sm. Subsequently, however, Buschow and van Vucht (1967) found that many of the R3 Al phases do not form, unless some carbon is present. C atoms occupy the body-centred site, which in the AuCu3 type structure is normally vacant, while the Au atoms occupy the corners, and the Cu atoms the face-centred positions. When the face-centred position is completely filled, the structure is known as the anti-perovskite structure. This occurs for R Nd, Sm, Gd, Tb, Dy Ho and Er. They also noted that neither N nor O would stabilize these compounds. Notice that Ce3Al and Pr3Al are truly binary compounds and C is not required for these two phases to form. Independently, Nowotny (1968) found that the anti-perovskite structure could be formed by C and N additions to R3M alloys, where M Al, Ga, In, Tl, Sn and Pb. La5 Sn3 phase: Kwon et al. (1990) state that the hexagonal modification, hP16Mn5Si3-type, reported several times for La5Sn3 is in reality an impurity stabilized La5Sn3Cx or La5Sn3Oy phase, and that the La5Sn3 binary compound is a phase which occurs only in the tetragonal tI32-W5Si3 type structure. 6.3.3 Examples of preparation of high-purity materials 6.3.3.1 Silicon. In a review on the role of materials science in microelectronics and its past, present and future, Mahajan (2004) described the methods, and their evolution, for the preparation of high-purity silicon. A first method was the zone refining, invented in the Bell Telephone Laboratories by W.G. Pfann in the early 1950s and at first applied to the preparation of extremely high-purity germanium. In principle, zone refining takes advantage of the fact that the solubility of an impurity is higher in the liquid than in the solid phases of the material being purified; it is therefore possible to segregate the impurity within the material. By passing a rod of the material

554

Intermetallic Chemistry

to be purified through a concentric ring heater, that is, by moving successive molten portions (zones) along the rod, a high-purity material can be obtained. This occurs because in every pass the concentration of impurities in the molten zone is higher than in the solid left-behind, and by successive passes the impurity can be concentrated into one end of the rod that can be cut away. Since zone refining is a slow and expensive method, it cannot be used for very large diameter Si crystals. Different techniques are currently used for the production of large scale electronic grade silicon. Metallurgical grade silicon powder at 300°C in the presence of a catalyst is reacted with anhydrous HCl: Si 3 HCl : SiHCl3 H2 SiHCl3 (boiling point 31.8°C) is subjected to fractional distillation and removed from Fe, B and Al halides. Finally pure SiHCl3 is converted into silicon by chemical vapour deposition according to the reaction: SiHCl3 H2 : Si 3 HCl carried out with high-purity hydrogen. Silicon is deposited on a thin high-purity silicon rod; this product is then used for the growth of bulk crystals (generally by the Czochralski method) which are used for electronic devices. 6.3.3.2 Rare Earth metals. As mentioned in § 6.3.1 rare earth metals and their alloys can be considered an especially representative example of the problems related to the preparation of high-purity samples, to the impurity role in defining the alloying behaviour, etc. These problems and several peculiar aspects of the rare earth metallurgy have been extensively underlined by Gschneidner (1980) who gave a description of several preparation and purification methods. These are briefly summarized below. 6.3.3.2.1 Preparation of the rare earth metals. Reduction of the fluoride: Generally, Ca with RF3 is heated up to 1450°C in a Ta crucible. After cooling, the slag and the reduced metal are easily separated. The metal obtained contains Ca, some fluoride and Ta, which can be removed by vacuum melting (for La, Ce, Pr, Nd) or by vacuum melting plus distillation (Gd, Tb, Dy, Ho, Er, Lu, Sc, Y). Especially pure Ca must be used, such as tripledistilled Ca further re-distilled under low He pressure and handled in He-filled glove boxes. Reduction of the chloride: The RCl3 compound is purified by distillation; the reductant used is lithium, which is distilled into the chamber containing the

Laboratory Preparation of Intermetallic Phases

555

distilled chloride; after the reduction, the same chamber, still sealed, is cooled at one end and heated at the other to remove LiCl from the metal, which remains as a solid. In order to avoid any contamination, all the distillation processes are very important. Reduction of the oxide: The oxide of a highly volatile rare earth metal (Sm, Eu, Tm, Yb) is mixed with La (or some other non-volatile metal such as Zr, Th) and heated; the volatile R distils out leaving behind the oxide of the other metal. Generally a re-distillation is then carried out. Electrowinning: Generally this method is limited to La, Ce, Pr and Nd because of their low-melting points. The rare earth salt (fluoride, chloride, etc.) mixed with an alkali or alkaline-earth salt is heated to 700–1100°C and then an electric dc current passed through the cell. If the bath temperature is above the melting point of the R, drops of the molten metal drip off of the cathode and are collected at the bottom of the cell. Generally, the electrowon metal is not as pure as that obtained by metallothermic reduction. 6.3.3.2.2 Purification of the rare earth metals. Vacuum melting: This is used to reduce the volatile impurities (such as H, CaF2, RF3) if present after the metallothermic reduction. Distillation, sublimation: This can be used to remove the metals from Ta (from crucibles, etc. dissolved by the molten R and re-precipitated). The volatile R (Sm, Eu, Dy, Ho, Er, Tm, Yb, Sc) are also purified from C, N, O (present as carbides, nitrides, oxides). Gschneidner (1980) underlined that, in order to obtain high purity, a very high vacuum (108–109 mmHg) and a slow sublimation rate must be maintained during the distillation process. Zone melting: A narrow molten zone is passed along a bar of the rare earth metal. The impurities more soluble in the liquid move in the direction of the moving zone, those less soluble will deposit on the solid left-behind the moving zone. By successively repeating the process, the impurities will segregate at the two ends of the bar (the interstitial H, O, N toward the starting end of the bar and the metallic elements and C toward the finishing end). The central portion of the bar is generally purer than the original material. However it is necessary that this process is carried out under a very pure atmosphere (He, vacuum). Electrotransport: In this process too a super-clean atmosphere is necessary. In electrotransport (a kind of solid-state electrolysis) a large dc current (typically 200 A cm2) is passed through a rod of the metal at a temperature 100–200°C below its melting point. In the rare earth metals the interstitial impurities slowly move towards the anode, while several metallic impurities move towards the cathode. In this case too, as in zone melting, the purest portion of the bar is its central part.

556

Intermetallic Chemistry

6.3.4 Effects of impurities on alloy properties and on the synthesis control Even without considering the formation of impurity-stabilized phases, it is obvious that impurities may have effects on the properties of the alloys. According to Gschneidner (1993) one of the major influences of the interstitial impurities is that these elements tie up some of the rare earth metal, which is not available for forming the desired alloy or compound, and thus the composition obtained is deficient in R. Typically in commercial metals such as the R, the impurities X may amount up to 5 at.% being mostly H, C, O and occasionally N, F. For point compounds (in a R–Me system) this will result in the presence of a second phase, the next Me-rich phase. Notice that the above-mentioned amount corresponds to about 0.5 mass% in the case of C and 0.05 mass% in the case of H. However, the amount of a second phase could be appreciable if the next X-rich phase is only a few (less than 10) atomic percent away from the composition of the desired phase, such as that found at the T-rich ends of the R–T systems (T Co, Ni, etc. R rare earth metal and also actinides, etc.). Some researchers compensate for this by alloying a slightly larger amount of R metal than calculated for the compound composition desired. But, since the interstitial content is not known, this also adds some uncertainty as to the final composition of the sample and to an unambiguous definition of its properties. As for solid-solution alloys, no second phase will be present, assuming that the interstitial compound, for example the oxide, slags off, unless the intended composition is at the non-rare earth metal terminus of the solid-solution region. The alloy true composition, however, will be at a concentration which is higher in the nonrare earth element content than intended. A specific case discussed by Gshneidner (1993) is the preparation of La3S4 (LaS1.333) using, for instance, a La stock containing 1 at.% O (about 0.1 mass%). Therefore: 3 (99La, 1 O) 4 (100 S) : La2O3 La295S400 (LaS1.356)

(6.1)

Thus a sample of composition LaS1.356 and not LaS1.333 will be obtained. In reaction equation (6.1) the La2O3 slag will float to the surface if the alloy is melted. If the alloy is not melted, but sintered, it will contain second phase La2O3 in addition to the matrix LaS1.356. Making the same calculation as in equation (6.1), assuming that the La metal has 600 ppm atomic O (which is toward the highest purity of samples prepared in the specialized Ames Laboratory) the actual composition would be LaS1.3346 instead of LaS1.333. In the case of La3S4–La2S3 alloys, several of the low temperature properties of these alloys have been studied by Westerholt et al. (1979, 1980a,b) using a commercial grade La and by Ikeda et al. (1982) using Ames Laboratory lanthanum. The reported superconducting transition temperatures vs. composition results are shown in Fig. 6.8 (a) and (b) where it is seen that there is a significant difference, that is a nearly constant shift in composition. If one assumes that the La used by Westerholt et al. contained 1 at.% O,

557

Laboratory Preparation of Intermetallic Phases (a) 10 Commercial La Ames laboratory La

4 2

Cubic

6 Tetragonal

Tc (K)

8

0 1.33 1.35

1.40

1.45

1.50

x (b) 10 Corrected for impurity Ames laboratory La

4 2

0 1.33 1.35

Cubic

6 Tetragonal

Tc (K)

8

1.40

1.45

1.50

x

Figure 6.8. An example of the impurity effects. (Adapted from Gschneidner (1993)). (a) An illustrative trend is shown of a property vs. composition: the superconducting transition temperature of La3S4–La2S3.solid solutions vs. x S/La atomic ratio is shown as reported by Westerholt et al. (1979, 1980) who used commercial (filled symbols) La and by Ikeda et al. (1982) who used high-purity lanthanum (open symbol). (b) Same data as in a): however the data by Westerholt were corrected assuming a content of 1 at.% O in the La they used. Notice now the good coincidence of the two sets of data.

and corrects their compositions accordingly, one finds that the results from the two studies essentially fall on top of each other. While discussing the role of the impurities in reactive metals, and continuing to use the R metals as typical examples, we have also to consider the effects due to the reactivity of the R and possible sources of contamination. As for the reactivity with hydrogen, the contamination of R thin films by RH2 is too important to be neglected. For instance, it is well-established that in thin rare earth films very often the

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Intermetallic Chemistry

metal and its hydrides coexist and that thinner film (10 40 nm thick) consists mainly of hydride. In this way, the highly powerful ‘getter’ effect of R for hydrogen may be emphasized as observed by Gasgnier (1995). On the other hand, problems due to this reactivity have been outlined by Corbett (2000) who stated that gross interference by hydrogen impurity might be responsible for the stabilization of phases or the existence of compounds formed by the rare earths (or by similar metals such as the divalent or alkaline-earth metals). A number of previously believed binary compounds probably originated with hydrogen impurities. For instance, some orthorhombic R5(Sb, Bi)3 compounds formerly suggested, are ternary hydrides, namely R5(Sb, Bi)3H. In order to obtain alloys without hydrogen impurities, Leon-Escamilla and Corbett (1994, 2001), suggested making the preparation in thin Ta (or Nb) weldable containers. Ta becomes permeable to H2 above 600°C. Heat treatment at 900 1100°C of the compounds sealed in tantalum crucibles for 2 hours in high vacuum was found to be sufficient to remove hydrogen impurities. Commercial alkaline-earth metals were often found important sources of hydrogen impurities and it has been noticed (Leon-Escamilla and Corbett 2001) that most active metals can become contaminated with careless handling: hydrogen is commonly retained during their reaction with adventitious water. Up to 5–20 at.% H in many reactive metals and alloys was fairly common in the past; recent products are better, although not clean (Corbett 2000). The reactivity towards oxygen (air, etc.) is, of course, very important. It is wellknown indeed, that rare earth metals may readily react with air. The high stability of rare earth oxides, as shown in Fig. 6.9, makes it evident that rare earth metals are unstable in the presence of oxygen. As one may expect, the rate of oxidization will depend on several variables: it will be higher when the level of the most common impurities, the relative humidity, the temperature are higher and when the atomic number of the lanthanide is lower. In relation to the high stability of rare earth oxides, the rare earth metals readily attack oxide crucible materials. The reactivity of liquid rare earths with Al2O3 crucibles has been discussed by Gschneidner and Beaudry (1991) (and for this, as well as for kinetic reasons, Ta, W, Mo, BN, BeO are used as better crucible materials). In this context we remember for some alloys the effect of melting in different oxide materials. It has been reported for instance by Gschneidner and Calderwood (1988) that melting of ErAl3 in a ZrO2 crucible instead of an Al2O3 crucible changed this compound from cubic AuCu3 type to rhombohedral HoAl3 type. The presence of oxygen may also cause other relevant effects as exemplified by an endothermic reaction, as given by platinum, and which may result in a chemical vapour phase transport: Ptsolid. O2 M PtO2 gas. At a temperature around 1200°C,

Laboratory Preparation of Intermetallic Phases 1000

0

2000 Na2O

559

3000 Fe2O3

PbO2

−0.2 Fe3O4

MgO SiO2 B2O3

−0.4

ΔG fφ, MJ/mole O2

MnO CaO

−0.6

Yb2O3 Sm2O3-B EuO

−0.8 Pr6O11 TiO2

−1.0 CeO2 Eu2O3-C

CaO

Al2O3

R′2O3 R2O3

−1.2

1000 2000 Temperature (K)

3000

Figure 6.9. Standard free energies of formation of selected metal oxides (adapted from Gschneidner (1990). R2O3 and R 2O3 give the ranges of values corresponding to the light and heavy lanthanides respectively. The high-chemical reactivity towards oxygen of metals such as Ca, R, etc. and the high stability of their oxides is clearly evidenced by the large negative free energy of formation of these compounds.

or higher, the gaseous PtO2 may be formed from Pt solid. It then diffuses to a lower temperature where it deposits Pt metal. In furnaces containing heating elements or thermocouple wires of Pt, and not having a well controlled inert atmosphere, it is common to find Pt micro-crystals deposited on the cooler parts. Intentional impurities, doping: After the comments previously reported on impurity effects and on the path towards higher and higher purity, a few remarks may be noteworthy on intentional addition of ‘Impurities’. To underline this point we quote

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Intermetallic Chemistry

from a book by Robert Cahn (2001): ‘… a willing acceptance of intentional impurity is one of the hallmarks of modern materials science. However, all things go in cycles: once germanium and silicon began to be used as semiconductors, levels of purity never previously approached became indispensable, and before germanium and silicon could be usefully doped to make junctions and transistors, these elements had first to be ultra-purified. Purity necessarily precedes doping, or if you prefer, impurity comes before purity which leads to renewed impurity. That is today’s orthodoxy’. 6.3.5 Effects of interstitial impurities on phase equilibria Examples of the effects of impurities on phase equilibria in alloys of Th, Zr, V, Nb have been considered and discussed by Carlson and Smith (1987). Phase stabilization and also phase de-stabilization (carbon effect on Zr4Sn) processes have been described. For the niobium–copper system different phase diagrams of the simple eutectic type (with the eutectic point very close to Cu) have been proposed, either with an S-shaped near horizontal liquidus line or with a monotectic equilibrium. It was stated that the presence of about 0.3 at.% O can induce the monotectic reaction to occur, whereas if a lesser amount of oxygen is present no immiscibility gap is observed in the liquid. A similar behaviour has been suggested for the vanadium–copper system. Examples of shifts of solid-solution boundaries due to small amounts of interstitial impurities have also been discussed with special reference to the Y–Th and Th–Zr alloy systems. The purities in mass%, declared by worldwide commercial suppliers, range from 99.9% for alkaline-earth metals and rare earths metals, to 99.999% for Al, Cr, Mn, Fe …, to 99.9999 for Au, Ag, Pt. In certain cases, these values can be misleading since they refer to the metal contents, disregarding the non-metallic impurities contents (interstitial H, C, N, O, etc.). Moreover, the concentration is expressed in mass% and, for low atomic mass impurities, such as H or O, this can result in a much lower at.% purity value. The elements for special use, such as for spectrography, may require very high purities, which can be attained only by specialized laboratories. 6.4. DIRECT SYNTHESIS OF THE INTERMETALLIC PHASES

6.4.1 Introduction A number of intermetallic phases may be prepared directly starting from the pure components suitably mixed together. The synthesis reaction may then be performed

Laboratory Preparation of Intermetallic Phases

561

by a variety of methods depending on the properties of the component metals, on their mutual and general reactivity, and also, especially if the main goal is the preparation of stable compounds, on the characteristics of the corresponding phase diagram (melting behaviour, number of intermediate phases, formation of solid solutions, etc.). According to the aggregation state of the component elements and the method selected for starting and performing their reaction, several preparative procedures can be considered, such as: melting (direct reaction in the liquid state), solid-state synthesis (mechanical alloying), combustion synthesis, etc. A short description of these procedures will be presented in the following paragraphs.

6.4.2 Melting (reaction in the liquid state) This is a traditional, often used, method of synthesizing the intermetallic compound; it consists in melting together the component metals and then cooling the molten mixture in order to crystallize the intermediate phase. The shape, the slope, of the liquidus line (or liquidus surface) is obviously an important point which has to be considered. Different situations however are possible which either simplify or complicate the preparation and the attainment of a compound of high purity. A few points may be discussed with reference to the phase diagram which summarizes the crystallization behaviour of the different alloys and the formation mechanisms of the compounds in their cooling from the liquid. Fig. 6.10 shows an example of a hypothetical binary system giving a diagram characterized by the formation of a few compounds. As for the congruently melting ABm compound for instance, it may be precipitated from the liquid either in region 3 or 4 of the diagram. A large range of crystallization temperatures (a large ΔT between the liquidus and the solidus) may be noticed in region 3: large crystals of ABm can possibly be obtained during the cooling from the liquidus down to the eutectic temperature. If the eutectic temperature is sufficiently low and the other properties of the alloy adequate, it will be possible, at an intermediate temperature, to separate the crystals from the liquid/ solid mixture by using a filtration or centrifugation technique. In the composition range corresponding to region 3, after complete solidification, the ABm crystals will be mixed with those of ABn, while in region 4 they will be mixed with an excess of the (B) phase (see § 6.4.4.7). As for the A-richer compound of the same A–B system, that is ABn, it may be directly crystallized from the liquid in the region 2, while, on cooling from the liquid in region 1, it must form through the peritectic reaction. Frequently it happens that only a partial progress is observed for a peritectic reaction, especially if the alloy is rapidly cooled; it is possible

562

Intermetallic Chemistry

Temperature

1

4 3 2

A

ABn

ABm

B

Figure 6.10. A generic binary phase diagram is shown for an A–B system in which two compounds, ABn and ABm, are formed. Different parts of the liquidus line are indicated. 1 is the line of primary crystallization of the terminal solid-solution based on the component A (which, on cooling, will be followed by the peritectic formation of ABn); 2 is the line of primary crystallization of the compound ABn (to be followed by the eutectic crystallization of ABn ABm); 3 and 4 are lines of primary crystallization of ABm (to be followed, respectively, by the crystallization of the eutectic ABn ABm or of the eutectic ABm B-based solid solution).

therefore to obtain alloys not in equilibrium, for which a subsequent annealing treatment may be useful in order to improve homogeneity. This is especially true when several peritectic reactions are encountered (a cascading series of peritectics occurs). See for instance in Fig. 2.21 diagrams such as those of the Er–Ge or Mn–Ga systems. In these cases serious problems are found for obtaining chemical homogeneity in the ingot. Some alloys may be difficult or impossible to prepare by fusion processes because the melting temperature of one component is greater than the boiling point of the other. This, according to Fenn et al. (2004) may be summarized in a diagram such as that shown in Fig. 6.11, where the different metals are indicated along the two axes of a diagram according to their approximate boiling and melting temperatures. Notice that the characteristic points of the different metals are reported only as approximate temperature ranges for groups of metals. In some cases the problem may be circumvented for instance by working under pressure in closed vessels. An extreme case of diagram with high-melting temperatures is represented by the system of Al (m.p. 660.5°C, b.p. 2520°C) with Re (m.p. 3186°C, b.p. 5596°C). Okamoto (2002) reviewed the literature concerning this system and underlined that the differences between two recently determined diagrams (from an evaluation of the thermodynamic properties and, respectively, by using several experimental

563

Laboratory Preparation of Intermetallic Phases Tb,y (°C)

0

00

6000

2

T m,x

T b,y

Ta, Os, Re, W

5000 B, Ru, Hf Ir, Nb, Mo

0

00

1 x

,

T m T b,y

4000

,x

T m T b,y

La, Ti, Pt, V

3000 Ga, AI, Ge, Ni, Fe Au, Cu, Mn, Co, Cr

0

00

1

T m,x

T b,y

2000 Bi, Pb, Sb Mg, Eu

1000 Hg, Cs, Cd K, Na, Zn

Tm,x (°C) 1000 Cs, Ga Bi, Pb Sb, Mg AI, Eu La, Ge

2000 Au, Cu Mn, Ni Co, Fe Ti, Pt Cr, V

3000 B, Ru Hf, Ir Nb, Mo

4000 Ta, Os Re, W C

Figure 6.11. A number of binary combinations of metals are shown in this map in order of the increasing boiling point temperature of one component (component y along the vertical axis) and of the melting point of the other (component x along the horizontal axis). For the combinations characterized by a high difference between these two temperatures, such as those included in the bottom-right part of the diagram, it may be very difficult to carry out a satisfactory fusion process without using special procedures and precautions, or relying for instance on the easy formation of a stable compound.

techniques) were significant and that some prominent unlikely features were present. Certain descriptions of the diagram reported earlier were so contradictory that no justifiable conclusion was derived. All this is mainly due to the difficulty in preparing equilibrium alloys because of the large difference in the melting points of the two metals. 6.4.2.1 Examples of reactions and synthesis by melting. In order to give an indication of the precautions which should be taken in the preparation of alloys by melting together the component metals and of different procedures adopted, a few examples are presented in the following. Y–Cu alloys (Fries et al. 1994): Samples were prepared in the course of an investigation (by DTA) of the phase diagram. In this case no special difficulty is related to the differences between the melting and boiling points of the two elements: these are Cu: m.p. 1084.87°C, b.p. 2563°C, Y: m.p. 1522°C, b.p. 3338°C. The DTA

564

Intermetallic Chemistry

examination was performed using pyrolytic boron nitride crucibles (6 mm length, 4 mm inner diameter, 1⁄2 mm thick wall and 1⁄2 mm thick flat lid). The sample mass was 180 mg and the starting materials were Cu rod (99.999 mass% pure) and Y chips (99.9 mass% pure). The Cu pieces were freshly cleaned in a 10% HCl solution to remove the surface oxide, washed in methanol, rinsed in acetone and dried. The Cu and Y were weighed and placed into a boron nitride crucible longer than the DTA crucible. The melting crucible was placed into a silica tube; the lid and a silica spacer were placed on top, and a small amount of Ti-getter was added. After repeatedly evacuating the sample to 104 bar and flushing with argon, the silica tube was sealed and the Ti-getter heated with a torch for several minutes to remove all the remaining oxygen. The sample was then isolated from the getter by sealing the silica tube, pre-melted at 1100°C for 1⁄2 hour, water quenched and finally annealed for 12 hours at 850°C. The samples could easily be removed from the melting crucibles, their small amount of surface discoloration was removed with fine SiC paper and they were then placed in the DTA crucibles. Mg–Pd alloys: Melting points Mg 650°C, Pd 1555°C; Boiling points: Mg 1090°C, Pd 2964°C. According to Ferro (1959) Pd–Mg (and Rh–Mg, Ir–Mg) alloys were prepared by enclosing the metals in very pure (low C content) heavy-walled iron bombs, closed under argon by electric welding, heated to 1000–1200°C for Mg-rich alloys and slowly cooled. Especially in the case of the Ir–Mg alloys, owing to the large density difference between Mg and the different phases, the precipitation of the compounds through the Mg-rich liquid during the slow cooling may result in a complete clear segregation of the phases at different heights of the ingot; in order to avoid this and to obtain a more uniform structure, a device was used which allowed the iron containers to be continuously stirred. Hlukhyy and Pöttgen (2004) prepared Pd–Mg compounds (Pd2Mg5) and Ir–Mg–In alloys. Pd2Mg5 was synthesized from cold pressed pellets prepared from Pd powder and Mg small pieces. The pellets were sealed under an argon pressure of 800 mbar in niobium tubes. The niobium tubes placed in the water-cooled sample chamber of an induction furnace were first heated at about 1000 K for half a minute and then cooled down to 700 K within 30 minutes and quenched by switching off the furnace. The samples could easily be separated from the niobium tubes, and no reaction with the crucible material was observed. Zr–Hf–Ir Alloys: An example of very high-temperature materials may be given by Ir-based (Ir melting temperature: 2447°C) alloys, the mechanical properties of which can be improved by the addition of Zr and Hf. A number of Ir-rich alloys containing up to 10–15% of Zr and Hf have been prepared by Sha et al. (2006) and

Laboratory Preparation of Intermetallic Phases

565

their microstructure, hardness, compressive strength, etc. studied. Button specimens were prepared by arc melting in a vacuum for five or six times to homogenize compositions throughout the ingots, which were finally annealed at 2000°C for 24 hours. Synthesis of ternary Sb phases: The ternary phases Na2M3Sb4 (M Sr, Ba) were prepared, and described as containing Sb4 2 units, by Chi and Corbett (2001). The preparation was carried out by direct fusion of elements at 750°C, followed by slow cooling to, and annealing at, 300°C. The alkaline-earth metals were first heated in sealed Ta tubes under high vacuum at 100–200°C below their melting points for 8–24 hours, to remove any pervasive hydrogen impurities after the surfaces of all the metals had first been cut clean with a scalpel. Reactions were run (about 0.2 g scale) in welded 9 mm o.d. Ta tubing. The charge was inserted under a glove-box in cleaned Ta tubing already welded at one end; the other end was tightly crimped in the glove-box and then welded shut under argon. For the subsequent heat treatment (heating, quenching) the container, in turn, was protected from the atmosphere within a fused silica ampoule sealed under high vacuum. Protection of the molten metals from air and moisture: The protection of the molten metals has always been an essential point. Fusion under vacuum or an inert atmosphere (pure He or Ar, possibly gettered) is systematically used. In the past, also for small scale laboratory preparations, fusion under a protective layer of molten non-reactive salts was often used. Low density salt mixtures having lowmelting point and high-boiling point were generally employed (for instance eutectic mixtures of anhydrous stable alkali halides). 6.4.3 High-temperature liquid intermetallic solution growth of single crystals and quasicrystals A review of several examples of single crystals (or quasicrystals) grown from metallic solutions has been reported by Canfield and Fisher (2001). Both congruently and incongruently melting phases can be prepared. A fundamental requirement for growth is that there is an exposed primary solidification surface in the appropriate equilibrium alloy phase diagram. For a number of alloys, a sealed Ta crucible with a built-in strainer was used. A simple version of such a crucible is referred to as a ‘three-cap crucible’. It is made from a piece of Ta tubing and three caps made of Ta sheet which can just fit inside the tube. The first cap is arc-welded into the tube closing it and creating a crucible, inside which the material is placed. The second cap, with holes drilled through it, is inserted inside the crucible just above the level of the solid material. Finally the third cap is arc welded, sealing the crucible. The crucible, possibly enclosed in a sealed quartz tube is heated in a vertical furnace and then slowly cooled down to a convenient decanting temperature

566

Intermetallic Chemistry

at which the crucible is inverted and the excess liquid decanted. Single crystals of rare earth alloys (RFe2, RAl3, RIn3, RSb2, RBi2) and icosahedral R–Mg–Zn quasicrystals have been prepared in a similar manner. The preparation of RCu2Ge2 (and RNi2Ge2) single crystals and icosahedral MnPdAl and decagonal CoNiAl quasicrystals have also been described, as well as the use of special Al2O3 crucibles. 6.4.4 Solid-state synthesis An old, simple and still widely used method to perform a solid-state reaction is to mix together the powdered reactants, possibly press them into a pellet and then, generally under a controlled atmosphere, heat it in a furnace for prolonged periods. In a number of cases, especially if fine, well mixed, and compacted component powders are used, this treatment will be sufficient to obtain a complete reaction. In other cases more complex treatments will be necessary (for instance to pulverize the partially reacted pellet and to mix, compact and heat it again). Intermetallic compound formation may be observed as the result from the diffusion across an interface between the two solids. The transient formation of a liquid phase may aid the synthesis and densification processes. A further aid to the reaction speed and completeness may come from the non-negligible volatility of the component(s). An important factor influencing the feasibility of the reactions between mixed powders is represented by the heat of formation of the desired alloy: the reaction will be easier if it is more exothermic. Heat must generally be supplied to start the reaction but then an exothermic reaction can become selfsustaining. Such reactions are also known as combustion synthesis, reactive synthesis, self-propagating high-temperature synthesis. Some examples of reactions between solid-state components and of their different uses and applications are reported in a few paragraphs in the following. 6.4.4.1 Direct synthesis from component powders. Ae4 Pn3, compounds of the alkaline earth metals with the pnicogen elements: The compounds Sr4Bi3, Ba4Bi3, Ba4As3x (anti tI28 Th3P4-type) were synthesized from stoichiometric mixtures of the pure elements. All operations were carried out in a N2 filled glove-box with the moisture level below 1 ppm. Mixtures were loaded in niobium containers that were sealed by arc welding under argon, and then enclosed in fused silica ampoules that were in turn evacuated and flame sealed. The samples were heated to 700°C, then to 1050°C, quenched and finally annealed at 800°C. The compounds are dark, brittle and air sensitive. These kinds of reactions are very exothermic and may result in an explosion. Notice that in the synthesis of these compounds, and of similar phases, a relevant role is certainly played by the high volatility of the pnicogen component.

Laboratory Preparation of Intermetallic Phases

567

Synthesis of sulfo-selenide Chevrel phases: Phases of M1Mo6S8xSex composition (M Cr, Mn) were prepared by the reaction of stoichiometric mixtures of MoS2 and MoSe2 binary powders with Mo and Cr, or Mn, metallic powders (Mançour–Billah and Chevrel 2004). The mixtures were pressed into pellets and then (inside an alumina crucible) sealed in evacuated silica tubes. After heating to 800°C and then to 1000°C for 24 hours, two further grinding and annealing (at 1000°C) treatments were performed. Powder X-ray diffraction methods were used to study the solid solutions, the trend of the lattice parameters, etc. Single crystals of the phases were obtained by melting, in a graphite resistor furnace, materials having the compositions CrMo6S2Se6 and MnMo6S5Se3; the pure Cr selenide CrMo6Se8, has an incongruent melting point of about 1710°C; the pure Mn selenide MnMo6Se8, a congruent melting point of about 1700°C. Direct formation of β-FeSi2: A preparation method for β-FeSi2 was proposed by Oikawa and Ozaki (2002) to activate the interfacial reaction between Fe and Si powders through a heat process in a sealed ampoule. The mechanism of the reaction process was investigated by using sputtered Fe films on Si substrate (and on sapphire substrates). It was found that Si vapour reacts, in sealed ampoules, with solid Fe, and it is saturated to form ε-FeSi. Reaction of FeSi with solid Si then takes place to form FeSi2. It was suggested that this process has a potential interest in the activation of reactions with Si of other refractory metals. 6.4.4.2 Direct synthesis from the solid components by ‘mechanical alloying’. Several methods (among which non-equilibrium processing of alloys) correspond to popular techniques to synthesize and develop novel alloys with improved properties. These techniques, among others include rapid solidification processing, laser processing, plasma processing, ion mixing and ‘mechanical alloying’. According to this technique, a powder charge is placed into a container together with a grinding medium (generally balls of a hard material) inserted in a mill (vibratory mill, vertical mill or horizontal, industrial, ball mill). Mechanical alloying, involving repeated cold welding, fracturing and re-welding of powder particles in the high-energy ball mill produces a variety of non-equilibrium phases such as super-saturated solid solutions, metastable intermediate phases, nano-structures, amorphous alloys. The alloying of difficult-to-alloy elements and the inducement of chemical reactions at low temperature are possible. A review of mechanical alloying processes has been published by Froes et al. (1995). Extended homogeneity ranges of intermetallic phases have been studied by Singh et al. (2003) in the Mg–Al system. Powders of the two metals (325 mesh size) were mixed and the mechanical alloying performed using a hardened steel vial and

568

Intermetallic Chemistry

hardened steel balls. The ball-to-powder weight ratio was maintained at 10 to 1. Typically the powders were milled for 15 hours and the results checked by X-ray diffraction. The loading and unloading of the powders was made in a glove box under an argon atmosphere to ensure minimum powder contamination. Stearic acid (about 1 mass%) was used as a process control agent to avoid excessive cold working and the formation of large agglomerates. The homogeneity ranges of the β (Mg2Al3) and γ (Mg17Al12) phases were significantly extended to lower Al contents. The increased Mg contents of the γ phase resulted in a lower density alloy, possibly with higher specific strength. Phase sequence during mechanical alloying: In a short synthesis of the preparation history of metallic glassy alloys, Sherif El-Eskandarany et al. (2003) underlined that the unique achievement of Klement et al. (1960), when they obtained Au–Si glass by applying very high-cooling rates to the metallic liquid, has led to subsequent studies for the preparation of a variety of glassy and amorphous materials at slower rates of cooling and also at room temperature by mechanical alloying. Glassy alloys have attracted wide interest due to their desirable physical, chemical and mechanical properties which make them important materials for several industrial applications. Sherif El-Eskandarany et al. (2003) described the preparation of the Zr70Pd20Ni10 glassy phase, and its subsequent de-vitrification, by mechanically alloying the elemental powders. Pure elemental powders of Zr (50 μm in diameter), Pd and Ni (10 μm) were employed and handled under pure Ar. In a ball-to-powder weight ratio of 14:1, the mixed powders were sealed into a tempered chromium steel vial together with the chromium steel balls. The experiments were carried out in a planetary ball mill. The milling was periodically interrupted and resumed in order to avoid increasing the temperature. Solid solution forcing by high-energy ball milling: Hahn et al. (2004) remarked that over the last three decades, powder processing by high-energy milling has gained wide practical interest as it offers a simple yet powerful way to synthesize non-equilibrium phases and microstructures, from nano-grain materials to extended solid solutions, amorphous phases, chemically disordered compounds and nanocomposites. In particular this technique can lead to forced mixing of elements which are immiscible at equilibrium. In particular they studied the effect of ambienttemperature ball milling of elemental powders of Cr and Mo in different compositions. The equilibrium phase diagram of the Mo–Cr system, of the type shown in Fig. 2.9 (d), is characterized by a high-temperature continuous solid solution which at lower temperatures, under about 880°C, has a miscibility gap and decomposes into the two terminal solid solutions. At 500°C the equilibrium solubility is 10 at.% Cr in Mo and 5 at.% Mo in Cr. The ambient milling leads to the complete mixing of the two metals into a body-centred cubic solution. The lattice parameter

Laboratory Preparation of Intermetallic Phases

569

of the solution displays a positive deviation from Vegard’s law, similar but somewhat larger than that observed in the solution formed by high-temperature annealing and quenching. The forced mixing obtained in this system is similar to the one reported for other systems with moderately positive heats of mixing, such as for instance Ag–Cu which, however, is based on the face-centred cubic close-packed structure. The synthesis of the compound MnFe2Ge was performed by Zhang et al. (2003). To avoid preferential evaporation of volatile components, mechanical alloying was used. Amorphous alloy powder was prepared by planetary ball milling elemental starting materials. The amorphous to crystalline transition was studied by means of differential scanning calorimetry. A cubic D03 type phase is formed by crystallization at about 300°C, and a transformation to a hexagonal D019 type at about 530°C. Mechanical alloying as a preliminary step in the synthesis of new intermetallics: The compound W3Mg, not observed in the stable phase diagram, has been prepared by Tang et al. (2003) by mechanical alloying and high-pressure techniques. Mechanical alloying of elemental powders of W and Mg resulted in an amorphous mixture. This was annealed in the cell of a cubic anvil press at high temperature (1200°C) and high pressure (4.5 GPa). A crystalline, tetragonal, W3Mg phase was obtained. 6.4.4.3 Combustion Synthesis. Besides solid-state reactions requiring heating even for several days at high temperatures to be completed, fast reactions are also known which give their products in minutes or seconds. Several nearly equivalent names are used for these reactions such as: solid-state combustion, combustion synthesis, self-propagating (self-sustained) high-temperature synthesis. Solid state direct combinations and solid-state metathesis have been described. In these cases starting materials are considered which react together with a highly exothermic reaction and with a fast and strong heat generation. Once the reaction is started a very high temperature may, at least locally, be attained and a rapid propagation of the process occurs. The combustion synthesis may involve both a selfpropagating high-temperature synthesis mode and an explosion mode. In the former, part of the reactant mixture is heated with an igniter (generally at a highheating rate); once started, the combustion wave will self-propagate through the sample. In the other mode the sample is heated (generally at a low-heating rate) within a furnace; as the ignition temperature is reached, the reaction becomes spontaneous and the complete sample is involved. Fan et al. (2001) studied the mononickel aluminide in the synthesis; in particular they studied the high-temperature synthesis of NiAl; measurements of temperature/time profile and wave rate were performed. For the temperature/time measurement some of the powders (hand mixed with the addition of a small amount of ethanol) were packed into a steel die

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Intermetallic Chemistry

Temperature (K)

2500 2000 1500 1000 500 0

5

10

15

20

Time (s)

Figure 6.12. Self-propagating high-temperature synthesis of NiAl (Fan et al. 2001). The temperature- time profile observed during the passage of a combustion wave is shown.

and dried at 350 K for 1 hour. The powders were compressed to form a compact 14 mm in diameter and 18 mm in length, with a relative density of about 60%. A small hole (2 mm diameter, 8 mm depth) was drilled in the bottom of the compact and a W/Re thermocouple inserted. The compact, in the reaction chamber, was ignited in 2–3 seconds by an incandescent graphite flat placed 2 mm above its top surface. A combustion wave then self-propagated through the compact. In a given point of the compact the temperature/time profile obtained during the passage of the combustion wave is shown in Fig. 6.12. Fast reactions between pure metal powders (Al Ni, Al Ti and Al Ni Ti) have been studied by Javel et al. (1997) by using time-resolved X-ray diffraction with the help of synchrotron radiation. The sample (20 10 2 to 3 mm3 was prepared under purified argon by cold pressing the metal powders mixed in the required proportion. It was then placed in a reaction chamber kept under He gas. A mylar window allows the incident and diffracted X-ray beams to pass in and out. Two small heating devices (tungsten coils on alumina supports) were included. The first one was used to keep the sample at a uniform temperature before ignition and the second one to start the self-propagating reaction at one end of the sample. X-rays irradiated the centre of the specimen. Specimens of different stoichiometries were prepared, in some cases with the addition of 20 mass% alumina powder introduced as heat sink to reduce the reaction violence. For the 1:1 NiAl alloy a record for a total time of 4.3 seconds was reported. Diffraction lines of Ni (111, 200) and Al (111) were detected at the beginning; then, when the reaction front penetrated the irradiated zone, Al melted and its line disappeared; Ni was wetted (and the intensities of its lines decreased) and the temperature jumped from 660°C to about 1400°C, as shown by the shift of the diffraction lines toward lower angles, with the appearance of the NiAl diffraction lines and subsequent cooling.

571

Laboratory Preparation of Intermetallic Phases (a)

(b)

(c)

(e)

(e)

(d)

Figure 6.13. Experimental arrangement of the ‘hot-explosive compaction’ method for the preparation of consolidated Ni–Al alloys (after Kecskes et al. 2004). (a) Precursor powder sample inside a steel-tube container placed in, (b) an asbestos thermal insulation sheet; (c) a concentric card-box filled with the powdered explosive (80% NH4NO3 20% TNT); (d) threaded steel plugs serving as contacts for the preliminary heating and to be lifted off just before detonating the explosive; (e) detonating cords.

For a better consolidation of the alloy, a hot-explosive compaction technique was employed by Kecskes et al. (2004) in the preparation of aluminium-nickelide composites. Two series of nickel-coated aluminium powder compositions were consolidated to full or near-full density by a hot-explosive compaction technique (Kecskes et al. 2004). Mixtures of 78Al-22Ni at.% or 39Al-61Ni at.% were placed in cylindrical containers preheated to a range of temperatures from ambient to 1000°C and once at a uniform temperature explosively compacted into a 150 mm long and 15 mm diameter rod billet) by using a cylindrical detonation arrangement (see the scheme shown in Fig. 6.13). Strict safety measures must be taken and possibly legal official authorization obtained. The precursor, nickel-coated aluminium powder, was prepared in an autoclave that was filled with Ni sulphate in an aqueous ammonium hydroxide solution and a catalyst. After a flush with nitrogen gas the autoclave was filled with hydrogen and continuously stirred when heated. After cooling, the coated powder was separated from the liquid, washed and dried in a flow of hydrogen. The ingots were examined by using several techniques, and it was observed that depending on the preheating temperature and the initial composition several Ni–Al intermetallics were obtained. Effects of particle size and pressure on the reactive sintering were studied by Gobran et al. (2004). The synthesis of RuAl was described; it was observed that reactive systems containing low-melting constituents such as aluminium are assisted in densification by the formation of a transient liquid phase. Reactive sintering using

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powder mixtures with small particle size of ruthenium was effective in synthesizing single-phase RuAl. The exothermic reaction between Ru and Al during sintering starts at T 625°C, and it is completed in the presence of a liquid phase. Maximum density obtained by reactive sintering was about 80% of the theoretical one. By reactive hot pressing, a multiphase alloy was generally obtained: this may be converted into a single-phase structure by extended homogenization. A maximum relative density of about 94% was thus obtained. Self-propagating reduction reactions: Several oxide reduction solid-state reactions have been known for a long time. Starting materials are considered which react together highly exothermically. Once the reaction is initiated, enough heat is produced for very high temperature to be attained, and complete reaction occurs rapidly. The so-called thermite process corresponds to the reactions: Fe2O3 2 Al : 2Fe Al2O3 or 3Fe3O4 8 Al : 9Fe 4 Al2O3 in which the ‘fuel’ Al and the oxidant Fe2O3 combine generating temperatures higher than 2000°C. It is used for welding railroad tracks. According to reports from Los Alamos National Laboratory (Son 2005) nanoaluminium powders with particle size as small as eight nanometres can be combined with metal oxides to make highly energetic explosives. Called super-thermite, the combined powders are said to increase the chemical reaction speed by a factor of a thousand because of its much larger surface area. Recently the mechano-chemical reduction of Cu2O with Al, induced by ball milling, has been studied and discussed by Bakhshai et al. (2002). If the mass of the reactant powder mixture was large enough, ignition took place within a few seconds after starting the mill. The following reaction was considered: 3Cu2O 2Al M Al2O3 6Cu The formation of CuAl alloys, however, was also observed. Preparation of rare earth metals and alloys by mechanical alloying: The refining of rare earth metals by direct solid-state reduction of their chlorides during mechanical alloying has been studied by McCormick et al. (1992). Rare earth chloride powders of Nd (or Sm, Gd, Er) having a purity of 99.9% and a particle size of 325 mesh, were mixed with calcium (99.9% pure, particle size 1–3 mm) and loaded in a sealed hardened steel vial with 10 mm diameter steel balls (with a ballto-powder mass ratio of 10:1). After milling for 24 hours a complete reduction of GdCl3 (or ErCl3) Ca to the rare earth metal was observed. The reaction with

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SmCl3 resulted in the reduction only to SmCl2. From NdCl3 Ca with the addition of Fe powder, the alloy Nd2Fe17 was obtained. In a discussion of the results it was observed that the products obtained at ambient temperature by mechanical alloying are the same which result from the conventional metallothermic reduction of the rare earth halides. However, the metallothermic reduction requires a temperature of 800–1000°C for the reduction of the chlorides and 1400–1600°C for the fluorides. The products of the mechanical process, on the other hand, are fine, amorphous or microcrystalline, highly reactive metal powders mixed with CaCl2. 6.4.4.4 Field-activated, self-propagating, high-temperature synthesis. It has been underlined by Munir (1997) that the use of self-propagating chemical reactions for the synthesis and processing of materials has focused attention on ways to enhance and extend the applications of this process. It has been shown that this kind of reaction can be activated through the application of a voltage perpendicular to the direction of the combustion wave. According to Munir (1997) this kind of activation initiates and propagates self-sustaining reactions with a wave velocity nearly proportional to the applied field. Several examples of the application of the method to various materials have been discussed (reaction of Al with Ti, synthesis of tungsten silicides and of AlN SiC composites, etc.). 6.4.4.5 Co-reduction of mixed oxides. A two-stage preparation of an alloy through the synthesis of a suitable precursor may be exemplified by the chemical route used by Jena et al. (2004) in the preparation of a copper–nickel alloy. The alloy was prepared from an aqueous solution of the nitrates of copper and nickel dissolved in a minimum amount of water and allowed to dehydrate and decompose to their oxides at a temperature around 350°C for an hour. Samples of the mixed oxide powders thus formed were subjected to reduction by pure hydrogen. The reduced powder (apparently containing partially alloyed metals) was sintered at 1000°C. The effect of temperature (250–450°C) on the reduction of the co-formed oxides was studied. 6.4.4.6 Fast, solid state, microwave-assisted, synthesis. A short history of reactions carried out in the solid state under the influence of microwaves was reported by Kniep (1993) who presented this technique as characteristic of a ‘fast solid-state chemistry’ and described the preparation of CuInS2 by using a method first developed by Whittaker and Mingos (1992) and extended by Landry and Barron (1993). Copper, indium and sulphur (all powders between 100 and 300 mesh) in a molar ratio 1:1:2 were thoroughly mixed and loaded into a silica ampoule. This, sealed under vacuum, was placed in a domestic microwave oven and irradiated at 400 W and 2450 MHz.

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After 5–10 seconds, blue flashes caused by the formation of sulphur plasma were observed. After the fading of the light (that is after another 40–50 seconds) the ampoule was removed from the oven and shaken to homogenize the powder. This procedure was performed three times. Crystalline CuInS2 (chalcopyrite structure) was obtained together with a small amount of an amorphous phase. Emphasis was given in this paper to the reaction speed and to the high, at least localized, temperatures (possibly greater than 1000°C) which were reached. A few more examples of microwave-assisted syntheses are reported here below. The synthesis of compounds such as MPS3 (M Mn, Cd) was performed (Villanueva et al. 2004) in a device consisting of a silica ampoule divided into a Dewar zone (hot zone) and a non-insulated part (cold zone) which can be operated inside domestic microwave ovens. This has been described as a rapid method which involves a heat concentration within the Dewar zone that allows the required temperature for the reaction to be reached. In the specific case a mixture of S, P, and the metal gives MPS3 compounds. The temperature gradient assures the vapour phase transport to the cold zone; MPS3 crystals are deposited within a few minutes in this zone. Synthetic reactions carried out in the liquid phase and using metal powders under microwave irradiation have been described and discussed by Whittaker and Mingos (2002). Preparation (and characterization) of Cu2SnSe4 nano-particles using a microwaveassisted polyol method was described by Grisaru et al. (2004). Microwave-assisted reactions were conducted in a domestic microwave oven (2.5.109 Hz working frequency, total power 900 W, heating regime, cyclic, 21 seconds on and 9 seconds off) which had been modified with a refluxing system. CuCl (or CuCl2 2H2O) was dissolved in polyethylene glycol by gentle heating in the microwave oven for 1 minute stoichiometric amounts of Sn and Se powders were then added, the system was purged with nitrogen and the reactor turned on (for about 2 hours). The product was centrifuged and then washed a few times with ethanol and dried under vacuum. A fast synthesis for Zintl phase compounds Na3SbTe3, NaSbTe2, K3SbTe3 by microwave irradiation has been described by Zhou et al. (2004). 6.4.4.7 ‘Extraction’ of a phase from a mixture. In several cases it is not easy to prepare a single-phase sample. Different preparation methods described in this chapter may result in a heterogeneous mixture containing, together with the wanted species, other compounds and phases. A classic example is the synthesis and crystallization from the liquid of a compound such as ABn in a system of the type shown in Fig. 6.10. In such a case it may be interesting to ‘extract’ crystals of ABn from a complex alloy, especially if cooling conditions have been controlled so as to permit substantial growth of the crystals. A compound having a low solubility for

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the components (see for instance Fig. 6.18) can be grown from a melt having a composition far removed from the stoichiometric value. In a number of cases the separation may be performed by mechanical means and, if part of the sample is liquid, by filtration, by using a centrifuge, or by distillation to remove volatile components. Chemical separation may be considered (acid treatment, leaching) when the parts to be removed are more reactive than the compound to be isolated and can be dissolved and washed away. A special case may be the electrolytic extraction when, in a solidified sample, there is sufficient electrochemical difference between the various phases; an example is the extraction from Al-rich ingots of compounds such as CrAl7 and MnAl6 (Raynor and Wakeman 1947). All the points mentioned have been discussed, in their systematic description, by Brown and Westbrook (1967) who underlined the utility of these methods but observed that they must be regarded with suspicion if a high purity of the compound is necessary; the reagent attack may not be very specific, excess of other phases or impurities may remain, etc. 6.5. SYNTHESIS IN SOLVENTS (UNDER FLUXES)

A number of reactions between metals (or metals and semi-metals) may be carried out by dissolving the elements in a suitable ‘solvent’, technically also termed a ‘flux’. The solvent may also act as a reactant and be involved in the formation of the compound (reactive solvent, reactive flux). Several fluxes, ranging from simple metallic elements up to complex substances have been used. An authoritative review entitled ‘The metal flux: a preparative tool for the exploration of intermetallic compounds’ has been published by Kanatzidis et al. (2005). In this paper, containing a long list of references, several general and experimental aspects of this technique are discussed. The paper is enriched also by beautiful photographs of intermetallic single crystals, for instance a dodecahedral Ho–Mg–Zn quasicrystal grown from an Mg and Zn-rich flux. Special attention was dedicated to the use of molten metals as media (metallic fluxes) for the synthesis of different materials, and a number of key characteristics were underlined which the metal must possess in order to be a suitable flux. The following points were noticed: – The metal should melt at an appropriate low temperature. – The metal should have a large difference between its melting and boiling temperatures. – It should be possible to separate the metal from the products by chemical dissolution, or filtration or centrifugation in the liquid state, or mechanical removal.

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– The possible formation of stable compounds of the metal with the reactants must be checked. With special attention to the use of metals as ‘reactive solvents’ (reactive fluxes), Kanatzidis et al. (2005) thoroughly discussed the relevance of a good knowledge of the phase diagrams formed by the flux and the reactants, for instance to define the optimum operation temperature and the excess of solvent to be used. The formation of intermediate compounds and their characteristics (congruent melting or peritectic melting) are also important points. Another relevant point may be the solubility of the reactant metals in the flux. A not too low solubility seems to be useful to avoid very long growth times. The flux may act as a transport medium dissolving the components in one place and growing the product in another place of the reaction container. The experimental solubility of several metals in low-melting potential metallic fluxes (Hg, Ga, In, Sn, Pb, Bi) have been compiled by Guminski (1990). Selected data have been reported in specific paragraphs of Chapter 5. In a paper by Fisk and Remeika (1989) several points concerning the growth of single crystals from metal fluxes have been discussed. Attention has been dedicated to various aspects of the problem of separating crystal and flux, for which two main approaches, chemical and mechanical, may be considered. The following examples drawn from the preparative chemistry of the rare earth alloys were described. Growth of rare earth rhodium stannides from excess Sn: The crystals can be leached with dilute HCl. As long as the crystals are in contact with the Sn flux, they remain shiny and metallic. Crystals separated from Sn, however, quickly form a black tarnish containing an amorphous mixture of Rh and Sn. The removal of the crystals from the leaching solution as soon as they are free of Sn flux is therefore necessary. Growth of CeCu2Si2 from molten Cu: It was assumed that growing CeCu2Si2 from pure Cu would provide for this material the limiting stoichiometry (relevant to its superconducting properties). Crystals were slowly extracted using a mixture of acetic acid and hydrogen peroxide: the process lasting approximately 1 month. Electrochemical removal of the flux: By suspending the melt anode in the bath, the crystals can fall free as the etching proceeds and, if not attacked by the electrolyte, they can be easily recovered. Dissolution of the flux by another metal: In the growth of CeIn3 crystals, the In excess may be removed by dissolution in Hg; the Hg film remaining on the crystals may be eliminated by gentle heating in a vacuum system. Other separation methods mentioned by Fisk and Remeika (1989) include centrifuging off low-melting fluxes, evaporation of a high-vapour pressure metal, cutting crystals from the melt, etc. In the conclusion of their review, Fisk and Remeika

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(1989) presented a short list of representative intermetallic compounds grown from various solvents. The metal solvents considered were: Al (for the preparation of several borides), Bi (platinum group alloys), Cu (borides, silicides, iridium alloys), Fe (BP, ZnS), Ga (Si, Ge, GaSb), In (Si, Ge, indium alloys), Pb (Pt alloys of the lanthanides), Sb (complex silicides and phosphides), Sn (binary and complex Sn alloys), Zn (GaSb, InAs, InSb, Si). In the following paragraphs a few examples of the preparation of intermetallic phases in various metallic and non-metallic solvents are reported.

6.5.1 Synthesis of intermetallic phases in liquid sodium The formation in liquid sodium of the intermediate phases of the system Th–Cu in the temperature range 200°–700°C was studied by Berlin (1972). The synthesis was performed inside sealed cylindrical stainless steel capsules, which were continuously shaken. After the reaction, excess sodium was removed by distillation. Similar reactions have been performed on Th–Ag, Th–Au and Ce–Si mixtures. According to Park et al. (2003), strontium and gallium nitrides (Sr3GaN3 and Sr6GaN5 containing isolated GaN36– anions) were obtained as single crystals by reaction of (NaN3 Sr Ga) in molten sodium; the preparation was performed inside Nb tubing. At the end of the reaction, Na was separated from the product by sublimation under dynamic vacuum. Conditions for seeded growth of GaN crystals by the Na flux method (850°C, 2 MPa of N2 for 200 hours) have been discussed by Aoki et al. (2002). For the solubility of metals in liquid Li and Na see § 5.3.4.1.

6.5.2 Synthesis in mercury solution The basic idea of the method consists of the preparation of binary Me –Me amalgams, that is, mercury-rich alloys of the ternary system Me –Me–Hg. A subsequent heating process results in Me –Me alloys. This method has been used by Lihl (1955) for the investigation of alloys of Me Fe, Co, Ni, Cu and Me Mn, Zn, Sn. These metals, when combined with Hg, give mixtures from which Hg can be distilled off at temperatures not far above its boiling point (356.6°C at atmospheric pressure). After Hg is removed, often the residue consists of the phases which are in equilibrium at 200–400°C. According to Kirchmayr (1965) the conditions which must be fulfilled in order to have a satisfactory application of the method are: (i) both Me and Me or at least one of them, must be soluble in Hg or form Hg compounds; (ii) the reaction between Me and Me must take place in liquid Hg, and the removal of Hg must be possible at a temperature close to its boiling point. Modifications of the method and the preparation of rare earth alloys by

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using similar techniques has been discussed by Kirchmayr (1965), where the synthesis of rare earth–manganese compounds was especially described. As a conclusion to this paragraph we have to remark that, in order to evaluate the feasibility of this method and its possible applications, it is necessary to have above all reliable data about the solubility of the different elements in liquid mercury. This is the same as saying that the binary, and possibly also the ternary mercury phase diagrams with the various elements must be available. A large contribution to the assessment of these diagrams has been given by Guminsky (1990); extensive compilations may be found in Massalski (1990), Okamoto (2000), etc. See a few remarks in § 5.12.4.1. Notice that, of course, analogous considerations may be applied to the reactions carried out in other metallic solvents, the phase diagrams of which will be an important reference point. 6.5.3 Synthesis in liquid aluminium 6.5.3.1 Al as solvent: the synthesis of beryllides as an example. According to Jacobson et al. (2002), several beryllides, such as UBe13, can be easily prepared by using molten aluminium as a solvent. U and Be in the stoichiometric ratio are dissolved in Al (typically in a UBe13/Al ratio of about 1:10–1:12). An outgassed BeO crucible heated to 1200°C and slowly cooled down to the melting point of Al is used. Aluminium is then dissolved in a concentrated NaOH solution obtaining faceted single crystals. The effects of the initial composition and of the cooling rate on the crystal quality and purity have been discussed. 6.5.3.2 Synthesis in liquid Al: Al as a reactive solvent. Several intermetallic aluminides have been prepared from liquid aluminium; very often the separation of the compounds may be achieved through the dissolution of Al which dissolves readily in several non-oxidizing acids (for instance HCl). For a review on the reactions carried out in liquid aluminium and on several compounds prepared, see Kanatzidis et al. (2005); binary compounds are listed (Re–Al, Co–Al, Ir–Al) as well as ternary phases (lanthanide and actinide-transition metal aluminides). Examples of quaternary compounds (alumino–silicides, alumino–germanides of lanthanides and transition metals) have also been described. As an example, a few preparative details of specific compounds are reported in the following. Gd–Pt–Al compounds have been prepared by reacting Gd and Pt in the proper atomic ratio with a 10 fold excess of Al (Latturner and Kanatzidis 2002). The mixture, placed in a silica tube sealed under vacuum was slowly heated to 1000°C, held at this temperature for several hours and slowly (over a few days) cooled to room temperature. The aluminium flux was removed by soaking the crucible in 5 M NaOH for 1 day. Gd1.33Pt3Al8, Gd0.67Pt2Al5 (and also compounds with Si) have been prepared; the main product, however, in all the syntheses was GdAl3.

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M3Au6xAl26Ti (M Ca, Sr, Yb), a stuffed variant of the BaHg11 type, has been prepared in Al solution (Latturner and Kanatzidis 2004). Molten Al reduces the multinary oxide reactant, such as perowskite SrTiO3, and, with the addition of gold, gives the intermetallic compound. It was also observed that the flux synthesis method has the additional advantage of being general in scope and of producing wellformed large crystals. 6.5.4 Synthesis in liquid gallium (reactive solvent) R–(Ni,Co)–Ga–Ge compounds: Quaternary alloys R3Ni3Ga8Ge3, RCoGa3Ge and RNiGa3Ge (R rare earth elements) have been synthesized in liquid gallium. Powders of the different elements, in a quantity of about 0.7 mmols, were loaded together with about 11 mmols of Ga into alumina crucibles under inert atmosphere. The crucibles were placed in silica tubes and evacuated. The samples were then slowly heated up to 1000°C, kept at this temperature for a few hours, slowly cooled down to 850°C , kept at this temperature for a few days and finally cooled down to 250°C. Most of the excess flux was removed by centrifuging through a silica filter with a coarse frit at 250°C. The residual Ga flux was then removed by overnight soaking in a 3–5 M solution of iodine in dimethylformamide, dissolving the residual Ga by converting it to GaI3. The resulting crystalline product was finally rinsed with dimethylformamide and hot water and dried by washing with acetone and ether (Zhuravlev et al. 2003). 6.5.5 Synthesis in liquid indium Molten aluminium and gallium fluxes have shown themselves to be excellent routes to complex ternary and quaternary intermetallic phases such as R–T–Al and R–T–Al–Si, R–T–Al–Ge (when Al is used as solvent) or R–T–Ga, R–T–Si, R–T–Ga–Si, R–Ga–Ge (when Ga is used as solvent), where R rare earth metal, T transition metal. Indium also has many of the characteristics that make Al and Ga very useful for such applications. Particularly important is its capacity to dissolve Si, Ge and several lanthanide and transition metals, producing highly reactive forms of the elements. Moreover In does not form binaries with Si and Ge and has a low-melting point. RNiGe2 compounds, for instance, were prepared from stoichiometric quantities of the components in fine powder mixed with a 10 fold quantity of In in alumina tubes. These, flame sealed in fused silica tubes, were slowly heated to 1000°C, held at this temperature for a few hours, ramped down to 850°C , held for an additional 4 days and finally cooled down to room temperature over the course of another 4 days. Compound isolation from the In excess was performed by centrifugation at 300°C through a coarse frit. Further purification was carried out by a 15-minute submersion and sonication in 6 M aqueous HCl (Salvador et al. 2004).

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An example of reaction in which indium is both a reactant and the flux is represented by the preparation of the Zintl compound Eu3InP3. Needle shaped single crystals were obtained from the reaction of elemental Eu/P/In in a ratio of about 1.5/1/50 (Jiang et al. 2005). All the products were handled under nitrogen atmosphere. Eu in small pieces and grains of red phosphorous were packed into an alumina crucible between layers of In metal. A second crucible, containing quartz wool, was inverted over the reaction crucible, and the entire reaction vessel was sealed in a fused silica jacket which was back-filled with argon. The reaction sequence involved heating to 500°C (1 hour), then to 1100°C (6 hours), slow cooling to 850°C, holding at this temperature for 19 hours and centrifuging at the same temperature. A different preparation route of In alloys was adopted in an investigation of the Pt–In–Sb phase diagram (determination of the isothermal sections at 400°C and 700°C and of the ternary reaction scheme). In this study by Patrone et al. (2006) the preparation of several alloys has been described. Antimony lumps, indium rods and platinum foil and wire were initially melted and annealed at 1000°C for 1 day. After quenching, the reguli were powdered and pressed into pellets for better homogenization. The pressed powder pellets were then sealed into evacuated silica ampoules and annealed at 400°C (or 700°C for compositions of more than 33.3 at.% Pt) for 5 weeks. Samples prepared without the high-temperature annealing after melting often did not reach the thermodynamic equilibrium. 6.5.6 Synthesis in tin flux A number of binary phosphides and polyphosphides (compounds containing P—P bonds), for instance those of Mn, Tc, Re, Fe, Ru, Os can be prepared, often in well crystallized form, by the tin-flux technique. The mixture generally containing an excess of P (red P) and a high excess of tin is heated, possibly at a slow rate, to the required temperature (600°–1000°C) and maintained at that temperature for several days and then slowly cooled. In several cases the products may be recovered by dissolving the tin-rich residue in hydrochloric acid. The preparation of several ternary phosphides and of arsenides and antimonides has also been described (see § 6.11.3). 6.5.7 Synthesis in lead flux According to Kanatzidis et al. (2005), good crystal growth has often been obtained in the preparation of ternary phosphides and arsenides (Ca2Ir12P7, Ca5Rh19P12, Eu6Rh30As19, CaIr2P2, etc.). The metals with an excess of Pb (typically 60 Pb for one formula unit) are heated up to 1000°–1100°C in an alumina crucible sealed in a silica tube. After the reaction, the flux may be dissolved using a mixture of concentrated acetic acid and 30% H2O2. Silicides of Mn and rare earth metals (RMn2Si2) have been also prepared by using this method.

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6.5.8 Single-crystal preparation and growth by NaCl/KCl flux reaction Single crystals of BaCuZn3As3 have been grown by NaCl/KCl flux reaction (reduction and synthesis) by Ozawa and Kauzlarich (2003). A charge was prepared by heating BaO, Cu, Zn and As. This, in a mass ratio 1:4 with the equimolar flux mixture, placed in an Al2O3 boat inside a fused silica tube, was heated at 860°C and slowly cooled. Single-crystal products from the flux reaction were washed with deionized water and ethanol, and then analysed. 6.5.9 Synthesis in alkali chalcogenide reactive flux Quaternary bismuth sulphides (such as RbSiBiS4, RbGeBiS4, CsSiBiS4) have been synthesized by using Rb2S3 or Cs2S3, prepared by stoichiometric reactions of the elements in liquid NH3, as reactive fluxes. The flux with the required quantities of the other elements was loaded into silica tubes under an argon atmosphere, in a glove-box. The samples were slowly heated to about 600°C, kept at that temperature for a few days and cooled down to room temperature, over a few days. After the reaction products cooled down, the silica ampoules were opened in an inert atmosphere glove-box and the solid product was soaked in N,N-dimethylformamide for a few hours in order to dissolve and wash away any remaining flux and to loosen the product crystals. 6.5.10 Synthesis in alkali poly-chalcogenide flux The synthesis of chalcogenides such as those of the rare earth elements has traditionally been performed through the reaction of rare earth metals or oxides with a molten or vaporous chalcogen source in a high-temperature environment. Soft synthetic methods utilizing lower temperature conditions, such as hydrothermal or flux syntheses, can allow access also to thermodynamically metastable phases. Flux syntheses of R chalcogenides via an alkali poly-chalcogenide flux have been shown to be extremely versatile for the preparation of many new structures, some of which cannot be obtained by direct synthesis from the elements. (K,Rb,Cs) SmGeSe4 and similar compounds have been prepared using K2Se2, Rb2Se3, Cs2Se2 fluxes. These were prepared from the stoichiometric combination of the elements in liquid ammonia (Martin and Dorhout 2004). Synthesis, structure and selected physical properties of quaternary chalcogenides have been studied by Mitchell et al. (2004). Compounds such as CsLnMnSe3, RbYbZnSe3, RbYbZnTe3 have been prepared, generally as single crystals. The reactive fluxes employed in the syntheses (Rb2Se3, Rb2Te3, Cs2S3, etc.) were previously prepared by the stoichiometric reaction of the elements in liquid NH3. The reaction mixtures, for instance Cs2Se3 Ln Mn Se or Cs2S3 Yb Zn S, or Se CsI, used to aid crystal growth, were loaded into carbon-coated fused silica tubes, inside an Ar filled glove box. The tubes, after sealing, were placed in a computer

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controlled furnace, typically heated to 900–1000°C in 48 hours, kept at this temperature for 50–100 hours and cooled in 100–150 hours. The reaction mixtures were washed with water and then with N,N-dimethylformamide, and finally dried with acetone. 6.5.11 Synthesis in liquid NH3 Ammonia (melting point 77.6°C, boiling point 33.3°C, density at 34°C 0.683 g/cm3, dielectric constant 22 at 34°C) which in the liquid state is probably the best known non-aqueous ionizing solvent, is a good solvent for several types of compounds. Much of the chemistry in liquid ammonia can be classified by analogy with similar reactions in aqueous solutions (metathesis reactions, acid-base reactions, solvolysis, redox reactions, etc.). However, peculiar properties of liquid ammonia are related to its ability to dissolve metals (especially alkali metals, see § 5.3.3, and Ca, Sr, Ba, Eu, Yb) forming highly coloured, conducting solutions containing solvated electrons. The alkali metal solutions are powerful and selective reducing agents. This type of solution may also be used for the synthesis of several compounds, including intermetallic phases. A forerunner of the application of this technique was Eduard Zintl who used the solubility of alkali and alkaline-earth metals in liquid NH3 for the preparation of compounds of these metals with other elements. As an example, the solution of Na is able to dissolve Pb metal, especially if it is finely divided. An interesting procedure includes the reduction, with the Na solution, of a dissolved salt of an electronegative element. For instance ZnI2, Hg(CN)2, PbI2, As2S3 are reduced to the finely divided metal, which reacts in the same solvent to give the intermetallic compound. 6.6. REACTIONS WITH THE GAS PHASE

Synthesis of intermetallics can be performed from their constituents involving the gas phase by using various methods. Notice that the presence of the gas phase may be relevant in several kinds of synthesis. A special role, however, is played by the gas phase in some groups of interrelated methods, which are generally defined as physical vapour deposition, chemical vapour deposition, vapour phase transport.

6.6.1 Physical vapour deposition It corresponds to the condensation of a gaseous species onto a suitable substrate. In this process, the molten metal is evaporated from single or multiple bath co-deposition and allowed to condense on a substrate (possibly a rotating collector). Heat sources which have been used include electron-beam and induction techniques.

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This technique has been described by Froes et al. (1995) in the general framework of ‘far from equilibrium processing’. Especially mechanical alloying and physical vapour deposition were considered, and their ability to develop novel structures compared. A number of light metal alloys have been described which cannot be prepared by more conventional techniques and have been obtained by physical vapour deposition. These are: high strength Al alloys containing the normally insoluble Fe, alloys of Cr, Mg with high-corrosion resistance containing Ti or Mn and alloys of Ti with Mg or Ca (the boiling point of Mg is below the melting point of Ti, so alloying with more conventional techniques is difficult). Preparation of Al2S3 : Aluminium and sulphur react slowly even at 800°C because liquid Al becomes coated with a skin of sulphide which acts as a barrier to further reaction. With the addition of I2 and a temperature gradient of 100°C, the aluminium sulphide separates as large colourless crystals at the cool end (700°C) of the reaction tube. This is because the transport of Al2S3 occurs via the following reactions and the formation of gaseous AlI3: 2Al 3S : Al2S3; Al2S3 3I2 M 2AlI3 3⁄2 S2 Preparation of Nb5Si3: Metallic niobium and silicon dioxide do not react if heated (for instance at 1100°C) under vacuum. In the presence of traces of H2 or I2 the formation of transporting compounds (SiO or NbI4) is observed, followed by their migration and reaction according to the following schemes: SiO2 H2 M SiO(gas) H2O; 3SiO 8Nb : Nb5Si3 3NbO Nb 2I2 M NbI4(gas); 11NbI4 3SiO2 : Nb5Si3 22I2 6NbO 6.6.2 Chemical vapour deposition This method is very important in the preparation of high-purity thin films and coatings: it consists in the decomposition of gaseous species (the precursor molecules) and the consequent deposition of the products on a suitable object. The decomposition in the gas phase may be induced by heat or, for instance, by irradiation. The precursor may be a simple molecule, as in the deposition of an element (for instance Si or Ge) from their hydrides, or a mixture of different molecules (Cr from CrCl2 H2; SiO2 from Si(CH2CH3)4 O2 of air; GaAs as described in § 6.12). An interesting application of this method is the preparation of diamond films which may be obtained from a precursor such as CH4, C2H2 and H2 activated by heating, microwaves, etc. typically at 600–1000°C at a reduced pressure. The direct deposition from the gas to the surface results in the formation of metastable diamond whereas, according to the phase diagram (see Fig. 5.37), the production of stable bulk diamond requires very high pressure and temperature. Kinetically, the

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diamond surface growing is promoted by the gradual attachment of hydrogen species and subsequent reorganization of the atoms in a tetrahedral rather than in a graphitic structure. The following reactions may be considered starting from the outermost surface of diamond crystallites containing9C9H bonds and involving ‘radical’ activated species such as atomic activated hydrogen (H ): 䊉

9C9H H : 9C H2; 9C CH4 : 9C9C9H2 H2 䊉

䊉

䊉

䊉

Diamond coatings as bulk diamonds may have important applications due to the unique properties of this substance (high hardness, low thermal expansion, highthermal conductivity). 6.6.3 Vapour phase transport Vapour phase transport consists in the formation of a volatile, instable, intermediate species which contains at least one of the components of the final product. Schematically, in its simplest version, the reactant X (to be transported) is placed at the end of a vacuum sealed tube together with a small quantity of the transporting agent Z. Inside the tube a temperature gradient must be maintained. The transport depends on the existence of a reversible reaction such as: X(sol.) Z(gas) M XZ(gas) The related formation equilibrium constant should have a small value: if it is zero no XZ would form; if, on the other hand, it is very large the stable XZ would not re-decompose and no X re-deposition could be obtained. Notice that if the synthesis of XZ is endothermic, the equilibrium will be displaced to the right with increasing temperature (the opposite is true if the reaction corresponds to an exothermic formation of XZ). Therefore, in order to have the transport of X, (synthesis of the intermediate at one end of the tube and re-decomposition with deposition of X at the other end) this must be placed at the hot end if the formation of XZ is endothermic (or the cold end, if exothermic). A classical example of this process is given by the ‘van Arkel method’ for the preparation (purification) of several metals. If impure Cr, for instance, is contained together with a small quantity of iodine in a vacuum tube maintained at a temperature at which chromium iodide volatilizes, and a hot zone is created by means of, say, a W filament heated by an electric current, the following reaction will be observed: Cr I2 M CrI2(gas) The formation of the iodide is exothermic and chromium is deposited on the filament (I2 is automatically re-cycled). Similar reactions may be used for the purification of

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5

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3

8

9

7 10

1

2 4

Figure 6.14. Scheme of the experimental apparatus for gravimetric measurements described by Zavrazhnov et al. (2003) in their investigation of the phase composition control in chemical transport reactions. (1) quartz ampoule, (2) thermocouples, (3) two-zone furnace, (4) quartz rods, (5) wire for suspending the ampoule, (6) support, (7) weighing beam of the analytical balance, (8) annealed sample, (9) products of minor transfer, (10) the heterophase Ga source (or getter) usually GaSe Ga.

Ti, Hf, Th,V, Nb, Ta, Fe, etc. starting from materials contaminated by carbides, nitrides, oxides. 6.6.4 Chemical transport reactions as a new variant of the phase composition control The composition of low-volatility two-component compounds in the Ga–Se system as controlled using chemical transport reactions has been studied (Zavrazhnov et al. 2003). For long-term heat treatment of a low-volatility phase in the presence of a transport agent, the annealed phase composition was found to be determined only by the temperature and the nature of the sample. In the case of a two-temperature anneal of gallium selenides with added iodine, the sample composition ranges are presented as a function of the cold and hot zones temperatures. A scheme of their experimental arrangement is shown in Fig. 6.14. 6.6.5 Single-crystal preparation by means of chemical transport reactions. (Ni–Sn–S compounds as an example) Single crystals of metal rich sulphides (Ni6SnS2, Ni9Sn2S2) have been prepared by chemical transport reactions (Baranov et al. 2003). The stoichiometric mixtures of the elements were previously annealed in evacuated silica ampoules at 540°C for

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8 days. The products, ground in an agate mortar, pressed into pellets, were further re-annealed several times (2–6 times) under the same conditions. The greyish powders obtained contained, according to the composition, one of the mentioned compounds. Single crystals were prepared from the powders by means of chemical transport reaction with I2 in a silica ampoule (10 100 mm) placed in a horizontal two-temperature furnace (600°C charge end and 570°C empty end). After heating for 2 weeks silvery crystals were observed in the cold part of the ampoule. 6.6.6 Synthesis of metastable Al and Ga monohalide solutions and subsequent preparation of large Al and Ga clusters A method for the synthesis of Al and Ga clusters has been described by Schnepf and Schnöckel (2002) which is based on the preparation of the gaseous monohalides subsequently isolated in metastable solutions at 78°C. The halogen atoms are substituted by bulky groups and, in a parallel disproportionation reaction, large Al (or Ga) clusters are formed. The monohalides were prepared on the basis of equilibria such as: 2Al(liq.) AlCl3(gas) M 3AlCl(gas) The reaction was carried out (at 1000°C and 102 mbar) under a flow of H2 HCl in a special co-condensation apparatus, a scheme of which is shown in Fig. 6.15. After exiting the reactor, the gaseous AlCl condenses on the cooled outer walls of the stainless steel vacuum vessel at 196°C. To prevent aggregation of the AlCl molecules and their disproportionation because of the previously shown reversing of the reaction, an excess of a suitable solvent (generally based on toluene) must be co-condensed with the monohalide. From the metastable solutions, the elements ultimately precipitate by means of a disproportion reaction at room temperature. On the way to the elemental forms, molecular Al and Ga cluster compounds are obtained by selection of suitable ligands (protecting groups). The largest clusters of this type prepared contained 77 Al or 84 Ga atoms. In their presentation of the method and of the apparatus, Schnepf and Schnöckel (2002) underlined the need for the availability and capabilities of a precision mechanical workshop, since the construction of high-vacuum apparatuses in stainless steel is often required, involving many parts and high and low temperature components. 6.7. SYNTHESIS OF INTERMETALLIC PHASES BY EXCHANGE REACTIONS (METATHESIS REACTIONS)

In many cases the reaction (the reduction) of a ‘precursor’ can be conveniently used to prepare intermetallic compounds. A few examples will be reported here, even

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1

2 5

3

AIX

4

LM/D(g)

HX

7 6

HV

Figure 6.15. The apparatus of Schnepf and Schnöckel (2002) for the preparation and co-condensation of Al (or Ga) mono-halide. 1: stainless steel vessel, 30l; 2: solvent input LM/D; 3: drainage channel; 4: Al in the graphite cell with resistance heating; 5: cooling shield; 6: Dewar with dry ice (78°C); 7: cooling water. HX: hydrogen halide gas; HV: high vacuum.

though a sharp division between the methods reported here and those described in previous paragraphs can be difficult to establish in some cases. 6.7.1 Metathesis (exchange) reactions 6.7.1.1 Solid-state metathesis reactions. For a number of compounds, solid-state metathesis (exchange) reactions have the advantages of a rapid high-yield method that starts from room-temperature solids and needs little equipment. The principle behind these reactions is to use the exothermicity of formation of a salt to rapidly produce a compound. We may say that for instance a metal halide is combined with an alkali (or alkaline earth) compound of a p-block element to produce the wanted product together with a salt which is then washed away with water or alcohol. Metathesis reactions have been used successfully in the preparation of several crystalline refractory materials such as borides, chalcogenides, nitrides. The synthesis of AlN described by Janes et al. (2003) may be mentioned as an example. The applications of this compound, mainly as a management material for silicon-based electronics, have been summarized together with its relevant properties (low coefficient of thermal expansion, close to that of Si, high thermal conductivity, high resistivity and low dielectric constant). Different preparation methods, often involving complex instruments, have been mentioned: ion beam evaporation,

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1800 1600 Temperature (°C)

(b) 1400

(c)

1200

(d)

1000 800 600 400 200 0

0

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10

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20 Time (s)

25

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Figure 6.16. Metathesis synthesis of AlN. Temperature trends in the self-propagating reactions (Janes et al. 2003). (a) AlCl3 0.5Ca3N2 ( in an insulating ceramic cap); (b) AlCl3 0.5Ca3N2 (in a steel vessel); (c) AlCl3 Li3N; (d) 0.5Al2S3 Li3N.

DC arc plasma which forces Al ingots to react with ammonia or nitrogen gas, carbothermal reduction of Al2O3 and C in N2 or NH3 atmosphere at high temperature ( 1400°C), and finally self-propagating high-temperature synthesis from Al powder with N2 or NaN3 at high pressure ( 1000 atm up to 1700°C). The following metathesis reactions have been studied: AlCl3 Li3N : AlN 3LiCl Al2S3 2Li3N : 2AlN 3Li2S 2AlCl3 Ca3N2 : 2AlN 3CaCl2 The synthesis of AlN was performed in a He-filled glove-box. Stoichiometric amounts of the reactants (adjusted to produce about 0.2 g of AlN) were ground together in an agate mortar, transferred into a stainless steel cup enclosed in a reaction vessel (similar to a bomb-calorimeter and equipped with a thermocouple). The reaction is initiated by using a resistively heated nickel–chrome wire and is completed in less than 1 second (Fig. 6.16). These solid-state metathesis reactions are highly exothermic and can start as the reagents are ground together. Extreme care has to be used when scaling up reactions. At the reaction scale of 0.2 g AlN a temperature of 1400°C was observed in the reaction of AlCl3 with Ca3N2 (carried out in a steel vessel) and of 1750°C (in an insulating cap) in comparison with a calculated

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adiabatic temperature of 1935°C. The products, removed from the dry box are washed in 0.5 M HCl (or H3PO4) and vacuum filtered. 6.7.1.2 Metathesis reactions in solution. Several examples of preparation of intermetallics by using metathesis reactions in solution have been reported by O’Connor et al. (1996) with special reference to Zintl phases. It was indeed remarked that intermetallic compounds may be prepared from Zintl phase reagents because of the electronegativity difference between the components of the precursor Zintl phase materials. This gives rise to a certain deal of ionic character in the Zintl phase which may be sufficient to allow the dissolution of ions in polar solvents. Series of compounds have thus been prepared by precipitation from aqueous solutions of metal (Me) chlorides or bromides with Zintl phases such as: K3GaTe3, K5InTe4, K4SnTe4 and K3SbTe3. The following example of a reaction scheme has been presented with divalent metal bromides of transition metals (Me Mn, Cr, Fe, Co, Ni): 5MeBr2 2K5InTe4 : Me5(InTe4)2 10 KBr Generally the materials resulting from this precipitation are amorphous (formed as very fine black powders).

6.7.2 Coupled reductions 6.7.2.1 Oxide coupled reduction with a metal and hydrogen. Interesting examples of this type of reaction are given by the combined reduction with H2 and a ‘noble’ metal (Pd, Pt, etc.) of the oxides of metals such as the lanthanides and the actinides. Such oxides are very stable and cannot be reduced by H2 alone: the simultaneous formation, however, of an intermetallic (such as a ‘platinide’) having a strongly negative ΔG of formation makes it possible to carry out reactions such as the following ones: Gd2O3 6Pd 3H2 : 2GdPd3 3H2O Am2O3 6Pt 3H2 : 2AmPt3 3H2O The preparation of PaPt3, PaPt5, NpPt3, NpPt5, AmPt3, CmPt5, NpPd3, AmPd3, of alloys of Ti, Zr and Hf with Rh, Ir, Pd, Pt, and of some rare earth and U alloys with Rh and Pd was described and discussed by Erdmann and Keller (1971, 1973). Mixtures of the oxides with very fine powders of the platinum group metals were heated in a high-temperature furnace (1200–1600°C). The reduction took place only under a flux of ultra pure hydrogen with an extremely low residual partial pressure of

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oxygen and water vapour. In a number of cases the intermetallic formed may be used as a precursor for the preparation of the other metal. By heating, the decomposition of the compound and the sublimation of the metal may be observed. 6.7.2.2 Preparation of ‘base’ metals by coupled reduction with platinum group metals. Very pure metals of the alkaline- earth, lanthanide and actinide series can be prepared from their oxides (or fluorides) through coupled reduction by pure hydrogen in presence of platinum group metals. According to a precursory paper on this subject (Berndt et al. 1974), the preparation scheme of Li, Ca, Sr, Ba, Am and Cf was described. As an example, Ca can be obtained by synthesis of a Pt compound, followed by its vacuum decomposition and recovery by distillation of the more volatile base metal: CaO 5Pt H2 : CaPt5 H2O (T 1200°C) or:

CaF2 5Pt H2 : CaPt5 2HF (T 1200°C) CaPt5 : Ptsol. Cagas (high vacuum, 1400°C) Cagas : Casolid (condensation) Pt can be re-cycled, by addition to a new Ca compound. In a way, Pt acts as a catalyst. The preparation of other metals, such as the lanthanides, and the use of Rh, Pd, or Ir instead of Pt were also described. Generally the stoichiometries of the compounds prepared were 1:5, as in the example reported or 1:3 or even 1:2. Generally all these compounds are characterized by highly negative values of the ΔH and ΔG of formation. 6.7.2.3 Oxide coupled reduction with boron and sulphur. A metathectical sulfidation method has been developed for the preparation of nano-particles of NdS2 (Wu et al. 2003). Nd2O3 powder was placed in a short silica tube. Excess amounts of amorphous boron and sulphur powders mixed (in the ratio 1:4) were placed in a separate similar silica tube. The two tubes (with that of Nd2O3 on top of the other) were then enclosed in a larger silica container which was evacuated and flame sealed. The container was gradually heated to 450°C and kept at this temperature for 1 day, and then cooled down to room temperature. The Nd2O3 was completely converted into an X-ray pure NdS2 product. According to the authors the formation of boron sulphides was implied in the process. The overall reaction was described as follows: Nd2O3 2B 4S : 2NdS2 B2O3

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Un-reacted sulphur, boron sulphides and the by-product B2O3 were washed away by using CS2 and de-ionized water. 6.8. ELECTRODEPOSITION AND ELECTROLYTIC REDUCTION (ELECTROWINNING)

6.8.1 Electrochemical reduction It consists in a deposition of ions from an electrolyte onto the cathode in an electrolytic cell, under the influence of an applied potential. Usually the process is accompanied by material dissolution from the anode. The electrowinning from aqueous solutions is an important commercial method for the production (and/or refinement) of many metals, including, for instance, chromium, nickel, copper, zinc. As for the electrodeposition from non-aqueous solutions, the primary production of aluminium, electrodeposited from a solution of Al2O3 in molten cryolite, is a typical example. Other metals which may be regularly reduced in a similar way are: Li, Na, K, Mg, Ca, Nb, Ta, etc. Electrodeposition of alloys: Electrolysis has also been used in order to obtain several metal compounds and alloys via the simultaneous co-deposition, from aqueous solutions or fused salts of the metal components. Electrolytic reduction of compounds: In electrolytic cells the reduction of an element to low oxidation states may be performed, and compounds such as sulphides, phosphides, antimonides, etc. may be prepared. 6.8.2 Electrodeposition of alloys. Ag–Bi alloys as an example of electro co-deposition The Ag–Bi system is a simple eutectic type (xBi 0.95, T 262.5°C) diagram. The solid solubility of Ag in Bi is negligible, that of Bi in Ag is 0.99 at the eutectic temperature, and it reaches a maximum value of 2.8 at.% Bi at 550°C. According to Ferro et al. (1976), metastable alloys were prepared by electrodeposition and by splat quenching. Ag-rich alloys were obtained by electrodeposition on a revolving cylindrical steel cathode; the cylindrical anode was 99.99% Ag. The solutions had compositions similar to those used by Raub and Engel (1950) and contained (g/103cm3) Ag: 25, Bi: 25, KCN: 22, K tartrate: 35, KOH: 10–30. The electrolysis was performed at 25°C with constant current density. An extension of the terminal solid solution up to 2–2.2 at.% Bi was obtained. In the preparation of Ag–Bi metastable alloys by liquid quenching this value was significantly exceeded and it was also possible to obtain (at xBi 0.12–0.16) a metastable phase (Mg-type, Hume-Rothery ζ-type), isostructural with the stable Ag–Sb ζ-phase (xSb 0.08–0.16). The splat quenching was performed by using a variant of the gun technique: the liquid alloy (at 1200°C) was ejected by means of high-pressure argon against a copper disc revolving at 8000–10000 r.p.m.

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(peripheral speed 450 km/h): the resulting cooling speed was of the order of 106 °C/s. The same hexagonal ζ-phase was prepared by high-cooling rate also by Predel and Bankstahl (1976). 6.8.3 Preparation of amalgams: electrochemical reduction on an Hg cathode According to Guminski (2002), the electrochemical reduction of metallic ions on an Hg cathode from aqueous or non-aqueous solvents (as well as from molten salts) allows the introduction of both soluble and insoluble metals into the Hg phase. n Some amalgams may be prepared by simultaneous reduction of Hg2 2 and Me from their solutions. On the other side, noble metal (Pd, Pt, Ag, Au) amalgams may by obtained by reduction of Hg2 2 on noble metal electrodes. 6.8.4 Preparation of transition metal compounds with non-metals by electrolytic reduction of fused salts The fused salt electrolysis technique was successfully applied to the preparation, also as single crystals, of several transition metal compounds. A review on this subject was published by Wold and Bellavance (1972). A systematic treatment of several reactions and processes, was presented possibly somewhat obsolete now and with a drawback due to the presence of several impurities in the synthesis products. The preparation of the following compounds was especially discussed. Sulphides. MoS2 was prepared by electrolysis at 1000°C of a melt consisting of sodium tetraborate, sodium fluoride, sodium carbonate in which molybdenum (VI) oxide and sulphur were dissolved. The electrolysis was carried out at 1000°C with the melt contained in a graphite crucible also acting as anode. After electrolysis, the excess electrolyte was dissolved in water to obtain crystalline MoS2, containing however up to 2% carbon. A similar method was used for WS2; carbon was the principal impurity in the sulphides. Phosphides: Several phosphides (Cr, Mo, W, Mn, Fe, Co, Ni) claimed to have been prepared were listed. As an example single crystals of FeP were grown from a melt composed by FeF3 and NaPO3 by electrolysis at 925°C. Arsenides and Antimonides: By electrolysis at 500–700°C of melts containing KAsO3 NaCl FeCl3, arsenides FeAs–FeAs2 were prepared. Mo and W arsenides and antimonides were also prepared. Carbides: It was observed that the synthesis of carbides by using this technique is difficult; however a few carbides (Mo, W, Fe) have been prepared by electrolysis (at about 800°C) of melts containing NaBO2 Na2CO3 LiF to which the metal oxide had been added.

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Silicides and Germanides: The electrolysis of melts containing Na2SiF6 (or Na2Ge2O5) and transition metal (Cr, Mn, Fe, Ni, etc.) oxides or fluorides often resulted in the synthesis of the silicides (or germanides). Borides: The electrolysis (at 950–1100°C) of a mixture of a borate and a transition metal fluoride (or alkaline-earth fluoride with the transition metal oxide) resulted in the synthesis of several borides (Ca, Sr, Y, Th, Ti, V, etc.).

6.9. SPECIAL TECHNIQUES

6.9.1 Sono-chemical techniques In a paper by Suslick et al. (1991) the interest and the applications of the amorphous metals and metallic alloys was underlined and the difficulties in the production of metallic glasses were remarked, in connection with the extremely rapid cooling from the melt which is necessary to prevent crystallization (typically, cooling rates of about 105–108 Ks–1 may be required). The authors remarked that acoustic cavitation was known to induce extreme local heating in otherwise cold liquids and to provide very rapid cooling rates. The effects of ultrasound were then considered. These were described as deriving from hot spots formed during acoustic cavitation: that is formation, growth and collapse of bubbles in a liquid. Suslick et al. (1991) observed that this process dramatically concentrates the low energy density of a sound field with the consequence that very high temperatures (5000–25000 K) may be locally obtained. Since the bubble collapse occurs in less than a nanosecond, very high-cooling rates (in excess of 1011 Ks–1) are probably obtained. They finally described the results of the ultrasonic irradiation (at 0°C) of iron pentacarbonyl (either pure or in decane solution). They obtained 10–20 nm size amorphous iron nano-particles. Bi compounds nanorods and lamellae: The preparation by sonochemical synthesis of one-dimensional BiPO4 nanorods and two-dimensional BiOCl lamellae has been described by Geng et al. (2005). They observed that in recent years sonochemical techniques have been extensively used in the synthesis of nano-structured materials; they remarked too that during the acoustic cavitation process, very high temperatures ( 5000 K), pressure ( 20 MPa) and cooling rates ( 1010 Ks–1) can be locally achieved upon the collapse of the bubbles. This provides a unique platform for the growth of novel nano-structures. In a typical preparation of BiPO4, dilute solutions of Bi(NO3)3 5H2O and Na3PO4 12H2O were mixed and the pH adjusted with HNO3 to 0.5–1. Ultrasonic irradiation was performed with a highintensity probe (0.6 cm diameter, 20 kHz, 60 W/cm2) immersed in the reaction solution. The reaction time (without cooling) was about 30 minutes. At the end a temperature of about 60°C was reached. The white precipitate was centrifuged and

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washed with water and absolute C2H5OH. For the preparation of BiOCl a similar procedure was used, adjusting however the pH value with HCl instead of HNO3. A review on using sonochemistry for the fabrication of nano-materials has been published by Gedanken (2004). It has been remarked that, in almost all the sonochemical reactions leading to inorganic products, nano-materials were obtained and it was observed that, in the field of materials science, among the methods developed to prepare nano-particles, the sonochemical techniques are superior to the other methods in the following aspects: Preparation of amorphous products: The preparation of metals (Fe, Co, Ni, Pd, Au), alloys (Au–Pd, Fe–Co, etc.), oxides, chalcogenides, etc. has been reported. The synthesis of sulphides, for instance, has been obtained in solutions (in water, ethanol, etc.) of the metal chloride or acetate using thioacetamide or thiourea as sulphur precursor. Insertion of nano-materials into mesoporous materials: Ultrasonic radiation has been used for the insertion of amorphous nano-sized catalysts into the mesopores. Deposition of nano-particles on ceramic or polymeric surfaces: According to the review by Gedanken (2004), sonochemistry has been used to deposit different nanomaterials (metals, oxides, semiconductors) on the surfaces of ceramic and polymeric materials. Stibnite nanorods: Regular stibnite (Sb2S3) nanorods (20–40 nm diameter, 220–350 nm length) have been synthesized by a sonochemical method under ambient air from an ethanolic solution containing SbCl3 and thioacetamide. In about 2 hours the solution self-heated up to about 60°C. The reaction product was separated by centrifuging and washing, in sequence, with absolute ethanol, water, acetone. 6.9.2 Shock-induced and shock-assisted reactions in powder mixtures Chemical reactions occurring in Mo2Si powder mixtures during a high pressure ‘shock-induced state’ and a ‘shock-assisted’ state, due to bulk temperature increases following unloading, were investigated (Vandersall and Thadhani 2003) using shock recovery experiments performed under a range of loading conditions. Cylindrical implosion geometry experiments showed fully reacted eutectic MoSi2 and Mo5Si3 microstructure in the axial region, while planar pressure geometry experiments generally showed a single-phase MoSi2 structure in the entire compact. Different types of explosives, especially ammonium nitrate fuel oil, were employed. 6.9.3 Sputtering Schematically the apparatus used for sputtering consists of a bell jar maintained at a reduced pressure of an inert gas such as argon. The gas is subjected to a potential difference of several kilovolts, producing a glow discharge from which positive ions are accelerated towards the target (the cathode). These high-energy ions remove

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material (eject atoms or ions) from the cathode, which then condenses for instance on a substrate to be coated which is placed in a convenient position in front of the cathode. This method can be considered a variant of the physical vapour deposition. Single metals or compounds may be used as the sputter targets and co-sputtering may be done from several elemental targets. Sputtering, which in a way may be considered as quenching from high-energy vapour onto a substrate, can be used to produce disordered structures (amorphous NiAl3 for instance). 6.9.4 Pulsed laser ablation deposition technique (PLAD technique) According to this technique, laser induces extraction (ablation) from a target of material which is used for depositing a variety of thin coatings, from superconductor to dielectric materials. General characteristics of the method and the deposition (onto Ti–6Al–4V substrates) of TiB2/TiN nano-laminate have been described and discussed by Roman et al. (1997). A sketch of the experimental apparatus is shown in Fig. 6.17. It includes a high-vacuum cryostat system, the pulsed laser system and the cylindrical stainless steel reactor. A raster scanned mirror system located outside the reactor allows each laser pulse to intercept a pristine portion of the target (TiB2/TiN). The reactor was evacuated to 107 mmHg, and then filled with high-purity N2 to the operating pressure of 105 mmHg. The Ti–6Al–4V substrates were prepared via standard metallographic procedures. Hard, smooth, well adhered coatings without cracks or de-laminations were generally obtained onto the substrates. Laser ablation of TiC targets was studied by De Maria et al. (1997). TiC films were realized on oriented [111] silicon. During ablation the chamber was kept under a dynamic vacuum (1.5 104 Pa); the laser fluence was varied in the range 0–15 J/cm2. Different ablation mechanisms, corresponding to different film characteristics, were observed related to the laser fluence values. At low fluence values (0–3 J/cm2), a film of composition TiC2 was obtained. Films obtained at 3–8 J/cm2 showed a composition close to TiC: they had the best characteristics of composition, crystallinity and compactness. 6.10. SYNTHESIS OF NANO-STRUCTURED METALS AND ALLOYS

There’s Plenty of Room at the Bottom Talk given by Richard P. Feynman, Nobel Prize in Physics 1965 at the annual meeting of the American Physical Society at Caltech on December 29th 1959 The famous talk by Feynman was first published in the February 1960 issue of Caltech’s Engineering and Science and has been made available on the web

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1

10

2

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9 4

7

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Figure 6.17. Scheme, according to Roman et al. (1997), of the deposition of nano-laminate coatings via the pulsed laser ablation technique. 1: Vacuum, chamber, 2: Ti–6Al–4V substrate holder and heater, 3: deposit (nanometer range), 4: laser-induced plasma, 5: target (TiB2/TiN), 6: laser focus, 7: quartz window and lens, 8: mirror (oscillating or raster scanned), 9: laser pulses, 10: Nd:YAG pulsed laser, 11: laser power density diagnostic, 12: cryostat, vacuum pump system, exhaust.

(http:// www.zyvex.com/nanotech/feynman.html). It was a masterly and provocative talk in which the problem of manipulating and controlling things on a small scale was discussed to its extreme limits. Points considered, several of which contained sound predictions, included: information on a small scale, comparisons with the biological systems, miniaturization by evaporation, making small machines, arranging the atoms one by one the way we want. It was also observed that when we will get the very, very small world (that is: assembly of a few atoms) we will have several new things representing new opportunities: atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanics. In a review by Gonsalves et al. (2000), techniques for the fabrication of nanostructured materials are outlined. Synthesis from corresponding organo-metal precursors of nano-structured metals (Fe, Co, Ni) and alloys (Fe–Co, Pt–Pd, and special steels) are discussed and various methods considered such as: thermal decomposition, ultrasonic irradiation, chemical vapour deposition, laser pyrolysis and reduction. Ultra fine micro structures having an average phase or grain size of the order of nanometres may be classified as nano-structured materials. In general terms, any material containing grains or clusters (or layers or filaments) below 100 nm may be included in such a classification. The small size of the building blocks and the high

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surface-to-volume ratio of these materials result in peculiar mechanical, optical, magnetic, electronic properties. The role and the relevance of nano-structured materials, which bridge the gap between the molecular level and the solid state, and their unique physical–chemical properties, have been underlined. The following micro-structural features are considered to be the main factors on which the properties of the nano-structured materials depend: (i) (ii) (iii) (iv)

Fine grain size and size distribution (100 nm). Chemical composition of the constituent phases. Presence of interfaces (grain boundaries, heterophase interfaces, free surface). Interactions between constituent domains.

More generally it may be said (Cahn 1990) that in nano-scale materials a variety of size-related effects may be included by controlling the size of the constituent components. The scheme adopted in the review by Gonsalves et al. (2000) to describe the techniques of preparation of nano-structures will be summarized in the following paragraphs in order to give a broad outline of different methods. 6.10.1 Synthesis of nano-structured alloys by the inert gas evaporation technique A precursor material, either a single metal or a compound, is evaporated at low temperature, producing atom clusters through homogeneous condensation via collisions with gas atoms in the proximity of a cold collection surface. To avoid cluster coalescence, the clusters are removed from the deposition region by natural gas convection or forced gas flow. A similar technique is sputtering (ejection of atoms or clusters by an accelerated focused beam of an inert gas, see § 6.9.3). 6.10.2 Synthesis of nano-structured alloys via mechanical deformation According to this method, nano-structured materials (even in commercial quantities) are produced by structural degradation of coarser-grained structures by the application of high-mechanical energy. 6.10.3 ‘Precursor’ preparation by solution chemistry This is used to prepare the precursor which is subsequently converted to nanoparticles by non-liquid phase chemical reactions (precipitation of a solid from a solution may be a general technique for the preparation of very small particles). More generally Gonsalves et al. (2000) underlined the role played by chemistry in developing new materials with interesting properties. One of the main advantages given by chemical processes over other methods is related to the good chemical homogeneity which may be obtained by mixing at the molecular level.

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6.10.4 Synthesis of nano-structured alloys by chemical vapour deposition and chemical vapour condensation This technique has been used in the preparation of metal alloys ceramics and composite materials. To this end a chemical precursor converted to the gas phase is decomposed at either low or atmospheric pressure to produce the nano-structured particles which, transported in a carrier gas, are collected on a cold substrate. 6.10.5 Synthesis of nano-structured alloys from organometallics According to Gonsalves et al. (2000), nano-structured metals and metal alloys can be prepared from organometallics following two principal methods: thermal or ultrasonic decomposition of organometallic precursors and reduction of the precursors. As a typical example of preparation of nano-structured metals from organometallics, the thermal decomposition of iron pentacarbonyl, Fe(CO)5, carried out in a high-boiling solvent (such as decalin), was described. 6.10.6 ‘Nanowires’ For a few remarks about a particular group of nano-structured materials we quote some comments and suggestions from a Forum published in an issue of Inorganic Chemistry, dedicated to nanowires and prefaced by Yang and Poeppelmeier (2006). They underlined the significant effort worldwide in nano-science especially in the preparation of nano-structures with planned size, shape and/or composition, where inorganic chemistry is continuing to play a pivotal role. The variety of methods developed for synthesizing colloidal nano-particles from several materials were emphasized and the special name (quantum dots) was mentioned, which is often used to refer to the colloidal nano-crystals exhibiting quantum size effects. The special class of nano-materials called nanowires corresponds to anisotropic nanocrystals with large length/diameter ratio. Generally they have diameters of 1–200 nm and lengths up to several tens of μm. They are very interesting both from a basic point of view and because of their potential applications in several technological fields (about 3000 papers have been published on this subject in 2005). In the above-mentioned Forum the following articles have been included: Solution–Liquid–Solid (SLS) growth of semiconductor nanowires by Wang et al. (2006). The synthesis proceeds by a solution-based catalysed growth mechanism in which nanometer-scale metallic droplets catalyse the decomposition of metalloorganic precursors and crystalline nanowire growth. Solution-based synthetic strategies for one-dimessional nano-structures by Wang and Li (2006). Recent progress in the solution–based routes to prepare onedimensional nano-structures are reviewed. The role of crystal structure in the determination of the growth behaviour of the nano-crystals is underlined.

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Solution-grown zinc oxide nanowires by Greene et al. (2006). Strategies for growing ZnO nanowires from zinc salts in aqueous and organic solvents are reviewed. One-dimensional colloidal gold and silver nano-structures by Murphy et al. (2006). Recent advances in the synthesis of metallic nanorods and nanowires are reviewed. The increasing relevance of the bottom-up chemical synthesis is underlined. Physical properties and potential applications are described with emphasis on silver and gold. Template-grown metal nanowires by Kline et al. (2006). The growth of metal nanowires using membranes as hard templates is reviewed. The method gives access to arrays of single-crystal metal nanowires and to quasi-one-dimensional metal structures with controlled compositional change along their length. Recent applications are discussed.

6.10.7 ‘Nano-structures’: comments on an example of extreme microstructure In a chapter entitled ‘Materials in Extreme States’, Cahn (2001) dedicated several comments to the extreme microstructures and summed up principles and technology of nano-structured materials. Historical remarks were cited starting from the early recognition that working at the nano-scale is truly different from traditional material science. The chemical behaviour and electronic structure change when dimensions are comparable to the length scale of electronic wave functions. Quantum effects do become important at this scale, as predicted by Lifshitz and Kosevich (1953). As for their nomenclature, notice that a piece of semiconductor which is very small in one, two- or three-dimensions, that is a confined structure, is called a quantum well, a quantum wire or a quantum dot, respectively. Finally, quoting a lecture by Madia (2006) two themes raised by Feynman (1959) deserve particular attention; that is, the possibility of creating small machines that can do a variety of things (microsurgery inside small blood vessels, etc.) and of producing materials with remarkable new properties through their precise structuring with self-assembling of atoms and/or arranging atoms as we want, and exploiting quantum effects to make useful structures with small number of atoms. The fraction of atoms at or near the surface becomes much larger as we move to smaller structures, so surface atoms begin to define bulk properties. Comments have been presented by Madia (2006) about synthesis and fabrication (a major challenge), technological applications, commercial interest, research training, etc. It has been pointed out however that further innovative steps are needed before single nano-tubes devices with adequate reproducibility can be made. A paper by Zhang et al. (2006) indicates parallel research lines intended to develop the various complementary aspects of nano-sciences and their applications. They observed that metallic and semi-conducting carbon nano-tubes generally coexist in as grown

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materials. A gas-phase plasma hydrocarbon reaction was then presented to selectively etch and gasify metallic nano-tubes, retaining the semi-conducting nano-tubes in near-pristine form. 100% of purely semi-conducting nano-tubes were obtained and connected in parallel for high-current transistors.

6.11. EXAMPLES OF PREPARATION ROUTES OF GROUPS OF COMPOUNDS WITH NON-METALS

6.11.1 Borides A paper by Motta-Chad et al. (2006) may be a good introduction to preparation methods of metal borides and as a first description of their characteristic properties. This paper was dedicated to an evaluation of the invariant reactions in the Ta-rich region of the Ta–B diagram, while reviewing previous work carried out on the system and discussing the different data. Ta–B alloys (3 g) were prepared by arc melting pure Ta and B under argon atmosphere in a water-cooled copper hearth, with a non-consumable tungsten electrode and titanium getter. Five melting steps were carried out for each alloy to produce chemically homogeneous samples. The mass losses associated with the melting steps were less than 0.5%. To define the stability of the compound Ta3B2, pellets were prepared from pure Ta and TaB powder mixture by cold pressing. Temperatures were measured with a W–Re thermocouple placed close to the samples as well as with a calibrated infrared pyrometer. The samples were examined through scanning electron microscopy, back scattered electron image and X-ray diffractometry. On the basis also of previous experimental investigations the following phases and equilibria were indicated for the revised phase diagram: TaB2 (s.s. congruently melting at 3037 20°C), Ta3B4 (s.s. peritectic melting at 3030 30°C), TaB (s.s. congruently melting at 3090 15°C), Ta3B2 (formation through solid-state reaction around 1950°C) and, under-stoichiometric, Ta2B (peritectic melting and decomposing through a euctectoidal reaction). MgB2: Magnesium di-boride is hexagonal hP3-AlB2-type (see § 7.4.3.14), and it is probably the most widely investigated superconducting material in recent years. Its superconductivity below 39 K was reported by Akimitsu (2001). Several papers have been devoted to the study of its chemical and physical properties and to the preparation techniques. In a paper by Brutti et al. (2006) a short summary is given of some of the reported preparation techniques with particular reference to the following: (i) Pulsed laser deposition of Mg/MgB2 on Al2O3 at 250°C, in situ annealing at 630°C. (ii) Pulsed laser deposition of Mg on electron-beam deposited B films, annealing at 900°C.

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(iii) Annealing of Mg B mixtures at 630°C in H2/Ar. (iv) Chemical vapour deposition in two-steps (B film and Mg incorporation). (v) Molecular beam epitaxy with the simultaneous deposition of Mg and B from the vapour target at 320°C. (vi) Powders in tube, wire deposition at 900°C. (vii) Mechanical alloying of the pure elements and vacuum hot pressing at 700°C. Brutti et al. (2006) also examined thermodynamic and kinetic aspects of decomposition of MgB2 in vacuo and discussed the implications for the optimization of its synthesis conditions. Bianconi et al. (2001) studied the variation of superconducting critical temperature as a function of charge density and lattice parameters in Mg1x AlxB2 superconducting samples. The spacing between boron layers (intercalated by Mg, Al layers playing the role of spacers) and their charge density are controlled by chemical substitution of Mg by Al atoms. The powder Mg1xAlxB2 samples have been synthesized by direct reaction of the elements. The starting materials were Mg and Al (rod, 99.9 mass% nominal purity) and boron (99.5% pure, mesh powder). The elements in stoichiometric ratio were enclosed in Ta crucibles sealed by arc welding under argon atmosphere. The Ta crucibles were then sealed in heavy iron cylinders and heated at 800°C (for 1 hour) and 950°C (for two hours). Mg8Rh4B: The synthesis of this compound is an example of an accurate and complex preparation method. As described by Alekseeva et al. (2006), Mg8Rh4B was obtained first by a direct reaction of magnesium, rhodium powders and amorphous boron in tantalum containers sealed in argon atmosphere at 1000°C for 5 days. However the samples contained about 5% MgRh and 2–3% MgO impurities. Amorphous boron was found to act as the source of oxygen. The oxygen content determined by the carrier gas hot extraction method, was found to be lower than the detection limit (0.04 wt.%) in crystalline boron and 4 wt.% in amorphous boron. Crystalline boron was therefore chosen as more convenient for preparing single-phase samples in spite of its lower reactivity. The difficulty of directly reacting the initial materials is reflected by the difference in their melting points (Mg: 650°C, Rh: 1963°C, B: 2092°C). In order to overcome this point a rhodium boride (m.p. 1150°C) was prepared as a precursor by arc-melting in argon atmosphere the powders of the two elements. Rhodium boride was ground in a tungsten carbide mortar and mixed with the powders of magnesium and rhodium, pressed into pellets and sealed in tantalum containers. All operations were carried out in a glove box under purified argon. The Ta containers were sealed in evacuated silica ampoules and annealed at 850–1000°C for 3–7 days with an intermediate re-grinding under argon atmosphere.

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6.11.1.1 Borothermic reduction of oxides enhanced by electron-beam bombardment. Light lanthanide borides have been prepared from the oxides according to a reaction such as the following one (Latini et al. 2002): Pr6O11(sol.) 47B(sol.) : 6PrB6(sol.) 11BO(gas) Crystalline boron pieces were ground in a stainless steel mortar, mixed with the stoichiometric amount of Pr6O11 and ground for a few minutes with the addition of some millilitres of dry diethyl ether. The mixture was then transferred into a boron nitride crucible placed into a water-cooled electron-beam gun inside a high-vacuum chamber. The electron-beam bombardment was gradually activated avoiding melting of the reactants from the beginning: this may indeed result in an explosive evolution of the gaseous BO. After melting and re-melting three times, the product was obtained as beautiful brilliant blue lumps. 6.11.1.2 Borides from metallic fluxes. The preparation of several binary borides of lanthanides, vanadium, tantalum, chromium has been performed by using aluminium as a flux. Aluminium has been used also as a reactive flux in the preparation of alumino-borides (of Mo, Fe) which are stable in concentrated HCl solutions. According to Kanatzidis et al. (2005) the gallium flux is another convenient medium for the preparation of silicon-boron compounds because Si and B are soluble in Ga but do not form compounds with it. Liquid tin also has been used as a suitable flux for the synthesis of borides; an example may be the boron-rich compound YB25 (Zhang et al. 2002). The alloys YB25xCy (x 0–5, y 0–2) were prepared from YB4, amorphous boron and carbon which were reacted in a BN crucible, inserted in a graphite susceptor and heated in an RF furnace at 1600°C for 8–12 hours. Single crystals were grown from high-temperature tin or copper solutions. Boron-rich solids are generally stable in acids, so the excess of metal flux, Sn or Cu, may be removed by hydrochloric or nitric acid, respectively. Quoting again Kanatzidis et al. (2005), a copper flux has been used for the preparation of several borides. Crystals of tungsten borides were prepared from copper solutions using tungsten metal and crystalline boron powder as starting materials under an argon atmosphere; similar results were obtained for chromium, manganese, niobium borides. 6.11.1.3 Application of carbo-thermal reduction. This is a synthesis process for the preparation of powders of carbides, nitrides and borides. Carbon may be graphite, coke, pyrolysed organic polymers. A reference process may be the Acheson process for the production of SiC: SiO2 3C : SiC 2CO

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As for the borides, the following examples may be mentioned, with an indication of the minimum temperature at which the reaction may be performed. TiO2 B2O3 5C : TiB2 5CO (1300°C) V2O3 2B2O3 9C : 2VB2 9CO (1300°C) Al2O3 12B2O3 39C : 2AlB12 39CO (1600°C) The formation of by-products and impurities can be observed (carbides, etc.). 6.11.2 Carbides A review of the preparation of transition metal carbides and related compounds was published by Windish and Nowotny (1972). The following methods were considered: Powder metallurgical methods: These include reaction of the elements and carbothermal reduction methods. Fine powders of the metal (Hf, V, Nb, Mo, W, etc.) and carbon (graphite, lampblack) may be mixed, possibly in wet conditions with an organic solvent to be removed later, then pressed and compacted into pellets or bricks to be heated at high temperature (1800–2000°C). To perform the carbothermal reduction, mixtures of carbon with an oxide (of Ti, V, Cr, etc.) are compacted and heated. An additional heat treatment in a high vacuum may be useful to remove O, N, etc. below a low level. Arc-melting: Well mixed (in some cases partially pre-reacted) compacts of carbon and the metal may be reacted by melting; arc-melting may be especially suitable. An advantage of melting in comparison with solid-state reactions may be related to the fact that arc-melted pieces have a smooth surface less susceptible to contamination. This method was found especially effective for refining and for the preparation of solid solutions mainly of the 4th and 5th carbides groups. Menstruum process (flux process): The menstruum process was described for the preparation of carbides which are distinguished by good wettability and a very low content of impurities (such as N, O). As a most suitable auxiliary metal bath for the reaction between transition metals and carbon, a Fe–Ni alloy was suggested. The amount of this alloy (70 Fe–30 Ni mass%) was about four times the volume of the transition metal (Ti, Zr, V). After the reaction the product was crushed and put in a warm HCl solution to dissolve the menstruum alloy. The preparation of high-melting carbides (TiC, WC, UC) by using various metals (Fe, Co, Ni, Al) as fluxes has been used for a long time now. In some ways

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these methods may be related to the early work by Henri Moissan and his attempts to prepare diamonds by rapidly quenching from high temperature a liquid iron solution of carbon. (The crystals he obtained, however, were probably of SiC.). Synthesis by means of volatile compounds: A number of halides (especially chlorides) of the transition metals display a high volatility and in the gaseous state they are easy to mix. They can be synthesized from oxides, or scrap metals, and chlorine; they are highly reactive and can be utilized for the preparation of various compounds, either as powder or a coherent solid or as coatings. Mixtures, for instance, of TiCl4 CH4 H2 have been used to prepare ultrafine TiC powder, to deposit TiC on graphite (at 1200–1300°C), etc. Fluidized-bed process technology: The synthesis of carbides (and nitrides) of iron performed using fluidized-bed reactors has been described by Deevi et al. (1995). In the fluidized-bed process, solid particles upon fluidization with the required gas mixture behave like liquids. Commercially available iron oxide α-Fe2O3 was used for the synthesis of iron carbides and nitrides. A known amount of α-Fe2O3 was fed into the reactor for fluidization with nitrogen prior to heating. The reactor was slowly heated and nitrogen replaced with a reducing gas (H2) or a reducing/carburizing gas (CO). Ammonia was used for nitriding the reduced iron oxide. The exothermicity of the reactions increased the bed temperature; nitrogen was used as a diluent to control the temperature rise. The pyrophoricity of the carbide/nitride powders necessitates the passivation of their surface by controlled oxidation. A survey of preparation methods of binary and ternary carbides of alkali and alkaline earth metals has been reported by Ruschewitz (2003) where a variety of techniques has been presented and discussed.

6.11.3 Phosphides and polyphosphides Preparation methods of phosphides and polyphosphides have been systematically described and discussed by von Schnering and Hönle (1988). The following techniques and remarks, which are also of general interest, may be quoted. In principle phosphides and polyphosphides can be prepared directly from the components. However, the synthesis must be performed carefully owing to the risk of explosion and overheating (often several hundred degrees) caused by the strong exothermic character of the reaction. Attention must be given also to the transformation occurring at high temperature from white to red phosphorous, the vaporization of which is very slow and represents a kinetic hindrance to the achievement of the equilibrium pressure. High temperature may cause decomposition of

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polyphosphides in lower phosphides, reaction with the container material, etc. To perform complete synthesis and obtain uniform samples, a number of subsequent grinding and annealing treatments may be necessary. The reaction can be carried out in ampoules (sealed tubes) of different materials (from steels to Nb, Ta, and Mo). The adjustment of the decomposition pressure of the phosphide with the vapour pressure of phosphorous may be obtained by using a two-temperature furnace and maintaining at a lower temperature the part of the ampoule in which phosphorous has been placed. A fast adjustment of pressure and removal of kinetic hindrance may be obtained by the addition of a small quantity of iodine, which acts as a transport agent. The preparation of phosphides in liquid media have been discussed, for instance the preparation of alkali metal phosphides in a solution of liquid ammonia; the solvated phosphide obtained can be transformed into a solvent-free, amorphous or microcrystalline compound by moderate heating. Examples of synthesis in molten media are the preparation of rare earth phosphides from molten KCl, and the synthesis of CrP4 and MnP4 from molten Sn; for these compounds this technique is alternative to high-pressure methods. In the review by Kanatzidis et al. (2005), the preparation by the tin-flux method is mentioned also for several ternary phosphides and polyphosphides of rare-earth and transition metals. Typically the components (R metal, T metal, P and Sn in an atomic ratio of about 1:4:20:50) in sealed silica tubes were slowly heated, to avoid violent reactions, up to 800°C, annealed at that temperature for 1 week and slowly (2 K/h) cooled to ambient temperature. The tin-rich matrix was dissolved in diluted hydrochloric acid. The authors described the preparation of compounds corresponding for instance to the formula MeT4P12 (Me heavy rare-earth metals and Th and U, T Fe, Ru, etc.) and to the series of phases MeT2P2 (Me is a lanthanide or an actinide and T a late transition metal) having a structure related to the BaAl4 or ThCr2Si2 types. Among other methods, however generally resulting in not very high-purity, replacement reactions (metathesis reactions) have been used in a number of cases to prepare stable phosphides, which will be unaffected by a subsequent dissolution process of the by-products, for instance: Ca3P2 2Ta : 2TaP 3Ca Electrolytic or chemical (by carbon and hydrogen) reduction processes have been employed in a number of cases to obtain phosphides from phosphates. It may finally be mentioned that molecular beam methods have been used for the preparation of semiconductors as GaP and of thin films of higher polyphosphides.

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6.12. THE SYNTHESIS OF InAs: EXAMPLES OF ALTERNATIVE ROUTES OF PREPARATION

6.12.1 Introduction In the In–As phase diagram (see Fig. 6.18), the formation of only one compound, the congruently melting InAs, is observed. The assessed version of the diagram was reported by Okamoto (1992), whereas Chatillon et al. (1990) revised all the thermodynamic data and calculated an optimized version of the diagram. Diagrams similar to the In–As are given by the binary systems of Al, Ga or In with P, As or Sb. In all these systems the 1:1 congruently melting compound exists, forming two eutectic equilibria with the two components. The compositions of these eutectics (especially those rich in Al, Ga or In) are generally very close to (in some cases practically coincident with) the pure component metal. In many cases, in this group of systems, the formation of high-pressure stable phases has been observed and the formation of various metastable phases has also been described. All the 1:1 normal compounds have the cubic structure of the cF8–ZnS (sphalerite) type and have been included by Parthé (for instance, Parthé 1963) in the family of ‘normal tetrahedral structures’. The preparation and the crystal structure of InAs were first described by Iandelli (1941).

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Figure 6.18. In–As phase diagram (at constrained pressure). Notice, (similarly to other III/V phase diagrams) the formation of the congruently melting 1:1 compound which gives two eutectics. The eutectic with In is practically coincident with In. As a consequence, for all the compositions from 0 up to 50 at.% As the primary crystallization of InAs may be obtained.

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All the compounds of the family (Al, Ga, In)–(P, As, Sb) are semiconductors and are well-known electronic and opto-electronic materials. They are often indicated as 13–15 compounds meaning compounds formed by the combination of one element of the 13th group with one of the 15th of the Periodic Table. In the semiconductor nomenclature these compounds are also called III/V compounds on the basis of old conventions in numbering the groups of the Periodic Table. Several synthetic approaches to the preparation and purification of the compounds of this family have therefore been considered. A selection of these methods will be reported as an illustration of the variety of methodologies which find increasing applications in intermetallic and, more generally, in solid-state chemistry. 6.12.2 Preparation of InAs by direct synthesis from the elements The preparation was performed by Iandelli (1941) from the elements closed, in vacuo, in a hard glass ampoule. This was then heated up to about 700°C for 2 weeks. The slow reaction was observed with a gradual consumption of arsenic. 6.12.3 InAs equilibrium with the liquid The possible preparation of InAs by crystallization from the melt depends also on the liquidus shape (especially in the In-rich region). A summary of previous liquidus measurements was reported by De Winter and Pollack (1986) who employed a ‘source dissolution method’ based on the equilibration, at a fixed temperature, of a known quantity of high-purity indium with single crystals of InAs, the weight loss of which was determined. The experiments were carried out under a flux of hydrogen purified via permeation through palladium. 6.12.4 Synthesis of InAs (and III–V semiconductors) by solid-state metathesis Solid-state metathesis reactions as an effective synthetic route to 13–15 compounds have been discussed by Treece et al. (1993). The reaction scheme: MeX3 Na3Pn : MePn 3NaX (Me Al, Ga, In; X F, Cl, I; Pn P, As, Sb). was used to prepare powders of these compounds. The reaction mixtures were either heated in sealed tubes or ignited in a bomb with a hot filament. The by-product salts are then removed by washing with an appropriate solvent (generally methanol, water and diethyl ether). These reactions are highly exothermic and generally self-propagating. Accidental self-detonation of the mixture may be observed on mixing the reactants.

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6.12.5 Synthesis of InAs by reaction of indium halides Wells et al. (1995) used the following process for the preparation of InAs (and similarly of InP): InCl3 As(Si(CH3)3)3 : InAs 3(CH3)3SiCl The reaction of toluene solutions of indium trichloride and tris(trimethylsilyl)arsine resulted in the formation of a very fine dark-brown powder subsequently annealed up to 400°C to drive to completion the elimination of trimethyl-silyl-chloride. Nanocrystalline InAs was obtained. Similar reactions with InBr3 and InI3 and P compounds have been discussed. Previously a similar reaction was described by Uchida et al. (1993) (reaction of indium acetylacetonate with tris(trimethylsilyl)arsine in refluxing triglyme). Subsequently the reaction with InCl3 was used by Guzelian et al. (1996) in the preparation of nano-crystal quantum dots. They compared different preparation methods and techniques useful to isolate specific size distributions. Another low temperature reduction route has been described by Xie et al. (1999). It corresponds to the reaction: 2InCl3 2As 6KBH4 : 2InAs 6KCl 6BH3 3H2 The reactants were ultrasonically dispersed in ethylendiamine, then transferred to a Teflon-lined autoclave and gradually heated up to 160°C. The products were filtered out, washed with absolute alcohol, normal HCl solution and water and finally dried in vacuum. In the product nano-fibres and near single-crystal whiskers were obtained. 6.12.6 Synthesis of InAs by hydrothermal route As reported by Lu et al. (2004), InAs can be prepared according to the reaction: 6Zn 2In3 As2O3 6H : 2InAs 6Zn2 3H2O Typically, indium trichloride with excess As oxide and metal Zn powder were mixed in an aqueous HCl solution, which was sealed in a stainless Teflonlined autoclave. This was heated at 120°C for 18–24 hours, and then cooled to room temperature. The black product was washed with carbon disulfide, anhydrous methanol and distilled water and desiccated in vacuum. The residue was etched and dispersed in an n-butanol dilute solution of HF and water, stirred and centrifugally separated. In the final product, spherical InAs nano-crystals were obtained.

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6.12.7 Single source precursors in the synthesis of triels monopictides In a review, Cowley and Jones (1989) discussed several methods of preparation of semiconductors formed by the 1:1 combination of elements of the 13th (triels) and 15th (pnicogens) groups. They mentioned methods of classical chemistry including organo-metallic chemical vapour deposition, which is often preferred for large scale processes and typically involves the reaction of a group 13 trialkyl with a group 15 hydride. A characteristic, most widely studied reaction is: Ga(CH3)3 AsH3 : GaAs 3CH4 The reaction is carried out at 600–700°C with a carrier gas (H2, He, N2) to sweep the volatile species through the reaction chamber. According to Cowley and Jones (1989), however, a number of disadvantages and drawbacks concerning these methods may be evidenced.

6.12.8 The liquid-encapsulated Czochralski process and the growth of III–V crystals The so-called liquid-encapsulated Czochralski process, a modified version of the Czochralski method, is extensively used for preparing and growing III–V crystals. As reviewed by Mahajan (2004) this method may be used for in situ synthesis of, for instance, InP and growth of its crystals with a reduction of dislocation density. In this method, since the III–V liquids tend to decompose at the growth temperature, to prevent the decomposition, a cap of an inert liquid (boron oxide B2O3) is placed over the melt and an external pressure higher than the vapour pressure of the V group element is produced by an inert gas such as He or Ar. The growth is carried out in a pressure vessel, and the seed, after having been partially melted, is slowly withdrawn from the melt contained in a BN crucible. During the pulling process, the seed and the crucible are rotated in opposite directions around their common axis to reduce temperature inequalities. The crystal pulled out through the boron oxide layer will be covered with a thin coat of the oxide which must be removed. It has been underlined by Mahajan (2004) that the synthesis for instance of InP, prior to the crystal growth, can be performed in a similar apparatus equipped with a reservoir from which phosphorus is bubbled through molten indium. After the synthesis InP is melted for crystal growth (Fig. 6.19). Warning. Notice that this is not a laboratory guide. Only a general description of methods is given, and specifically without indications of safety organization (and related matters such as laboratory organization, evaluation of hazards, protective equipment, handling and sampling techniques, work permits, etc). The reader

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Figure 6.19. Preparation and growth of InP crystals. Scheme of an apparatus for the liquidencapsulated Czochraslki (LEC) method. The conventional Czochralski method corresponds to one of the techniques employed to grow a single crystal from the liquid phase by passing the molten metal through a temperature gradient to initiate solidification at one point and proceed throughout the melt. A cold seed crystal is touched at the surface of the liquid metal and then slowly raised. According to the scheme here shown the growth is carried out in a pressure vessel; molten boron oxide covers the melt surface. The auxiliary reservoir is also shown from which phosphorus is vaporized into liquid indium (adapted from Mahajan (2004)). 1: pull rod; 2: view rod; 3: seed crystal; 4: B2O3; 5: In InP melt; 6: pressure chamber; 7: red phosphorus; 8: P reservoir; 9: heater; 10: crucible; 11: heater; 12: crucible rod.

interested in making practical laboratory work should therefore, together with his/her laboratory management staff, take care to collect the qualified information and competence necessary for a safe planning and carrying out of the experiments.

REFERENCES

Akimitsu, J. (2001) International Symposium Transition Metal Oxides (Sendai, Japan), January 10. Alekseeva, A.M., Abakumov, A.M., Leithe-Jasper, A., Schnelle, W., Prots, Yu., Chizov, P.S., van Tendeloo, G., Antipov, E.V. and Grin, Y. (2006) J. Solid State Chem., 179, 2751.

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Chapter 7

Families of Intermetallic Structure Types: A Selection

7.1. INTRODUCTION AND STATISTICAL REMARKS

Several thousand binary, ternary and quaternary intermetallic phases have been identified and their structures determined. In a comprehensive compilation such as that by Villars and Calvert, about 2200 (first edition, 1985) or about 2700 (second edition, 1991) different types of intermetallic structures are described. The specific data concerning about 17 500 different intermetallic phases belonging to the aforementioned structural types are reported in the first edition, and 26 000 in the second edition. The group of phases described in the compilation by Villars and Calvert (1991) is a good basis for establishing statistical information about the phase and structure type distributions. This indeed can be considered a fairly representative sample even if the number of new intermetallic phases and of structural types is constantly increasing. The first observation is that the number of phases pertaining to each structural type is not at all homogeneous. Just to give a rough indication with the limits of partial statistics, in a sample of about 8000 truly binary compounds, not considering ternary phases and terminal solid solutions, the prototypes more frequently encountered have been selected and reported in Table 7.1 in decreasing order of frequency. A high number of phases crystallize in a few structural types. This kind of distribution seems to be significant even though Table 7.1 contains only an approximate list. Limited changes may actually be obtained by a more accurate attribution of different phases to a certain structural type or to its degenerate or derivative variants. Considering then the phase composition as a significant parameter, we obtain the histogram shown in Fig. 7.1(a) for the distribution of the intermetallic phases according to the stoichiometry of binary prototypes. For instance, the binary Laves phases, the AlB2, CaIn2, etc., type phases are all included in the number reported for the 66–67.99 stoichiometry range, even if the real stoichiometry of the specific phase is different, see Fig. 7.1(b). We may note the overall prevalence of phases and, to a certain extent, of structural types, which may be related to simple (1:2, 1:1, 1:3, 2:3, etc.) stoichiometric ratios. However, in order to better define the indicative value of the data reported in Table 7.1 and their validity, it could be useful to consider also more complete lists 617

618

AB3 A2B3

1000

60

65

70

75 at.% B

A2B17

55

AB5 AB6

50

A3B7 A2B5

A4B5 A3B4

500

AB4

A3B5

Number of phases

1500

AB

AB2

Intermetallic Chemistry

85

90

80

95

B

% Compounds Cu2Mg

Other Unknown

MgZn2 CdI2 Co2Si InNi2 Al2Cu AlB2 CaF2 CeCu2 FeS Cu2Sb 2 MoSi2

Cu2Mg Unknown MgZn2 Co2Si AlB2 Cu2Sb MoSi2 FeS2 CeCu2 CaF2 CuAl2 Ni2In CdI2 Other

12.6 12.0 8.0 5.5 4.7 3.8 3.8 3.6 3.5 3.2 3.1 1.9 1.8 32.5

222 212 140 97 83 67 66 63 62 57 54 33 32 572

100.0

1760

Figure 7.1. (a) Binary phases. Indicative distribution among the more common stoichiometries, according to the data by Villars et al. (1995). (b) Binary phases. The approximate percentage of the different structural types is indicated for the AB2 stoichiometry, according to the data by Villars et al. (1995).

in which binary and complex (mainly ternary) phases are reported (Daams 1995, Ferro and Saccone 1996). A specimen of such a list is given here below, reporting a few prototypes, not selected on the basis of their frequency, characterized by simple structures and unit cells. For these prototypes not only compounds having the

Families of Intermetallic Structure Types: A Selection

619

Table 7.1. Approximate distribution of intermetallic phases among the different structural prototypes (~8000 binary phases considered), according to the data taken as an example in Villars et al. (1995). Rank order 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Structural type

Pearson symbol

Number

Rank order

Structural type

Pearson symbol

Number

CsCl NaCl AuCu3 Cu2Mg Mn5Si3 MgZn2 CrB AlB2 Th3P4 CaCu5 Co2Si Fe3C NiAs AuCu FeB Ni3Sn Cu2Sb MoSi2 Cr3Si FeS2 Sm5Ge4 CeCu2 Th2Ni17 CaF2 CuAl2

cP2 cF8 cP4 cF24 hP16 hP12 oS8 hP3 cI28 hP6 oP12 oP16 hP4 tP4 oP8 hP8 tP6 tI6 cP8 oP6 oP36 oI12 hP38 cF12 tI12

295 279 251 226 176 143 116 107 103 100 97 96 93 75 72 70 69 68 67 65 64 62 60 57 55

26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Th7Fe3 ZnS NbBe3 W5Si3 CrFe Ni2In NaZn13 Th6Mn23 Mg Pd5B2 Cr5B3 ThMn12 ThSi2 Gd14Ag51 Zn17Th2 U3Si2 BiF3 Er2Co7 Mn CdI2 Pu3Pd5 MnP Na3As Pu3Pd4 Sb2S3

hP20 cF8 hR36 tI32 tP30 hP6 cF112 cF116 hP2 mS28 tI32 tI26 tI12 hP65 hR57 tP10 cF16 hR54 cP20 hP3 oS32 oP8 hP8 hR42 oP20

51 51 49 47 46 46 45 44 42 38 38 38 36 35 35 34 33 33 33 32 32 30 29 29 29

parent structure but also a derivative structure (superstructure of the second kind) have been considered. See Table 7.2. Notice, moreover, that for a family of binary and complex phases such as the Laves phases (Cu2Mg, MgZn2, Ni2Mg types) an overall number of about 1400 has been estimated. The restriction of the phase concentration to a limited number of stoichiometric ratios is also valid (and, perhaps, more evident) for the ternary phases. We may notice in Fig. 7.2, adapted from a paper by Rodgers and Villars (1993), that seven stoichiometric ratios (1:1:1, 2:1:1, 3:1:1, 4:1:1, 2:2:1, 3:2:1, 4:2:1) are the most prevalent. According to Rodgers and Villars they represent over 80% of all known ternary compounds.

620

Intermetallic Chemistry Table 7.2. Examples of binary prototype list in which ternary compounds are included. Prototype tI10-BaAl4 oP12-Co2Si hP3-AlB2 tP6-Cu2Sb oS8-CrB

Aggregate number of compounds 723 495 330 197 193

Prototype hP6-Ni2In hP6-CaIn2 oP8-FeB tI12-ThSi2 hP2-WC

Aggregate number of compounds 154 149 121 82 35

Considering only selected groups of binary or complex alloys, quite different stoichiometric ratios may be predominant. As a binary example we may mention the alloys formed by an element such as Ca, Sr, Ba, rare earth metals, actinides, etc., with Be, Zn, Cd, Hg and, to a certain extent, Mg. Many compounds are generally formed in these alloys. Among them, phases having very high stoichiometric ratios are frequently observed, such as, for instance: CaBe13, LaBe13, BaZn13, BaCd11, BaHg6, BaHg11, BaHg13, La2Zn17, LaZn13, La2Cd17, LaCd11, Th2Zn17, Pu3Zn22, Ce5Mg41, La2Mg17, LaMg12, etc.

7.2. A PROTOTYPE DIRECTORY OF SELECTED INTERMETALLIC STRUCTURES

In the following, some structural types are presented. A warning, however, is necessary considering the huge number of intermetallic phases already known and their fast increasing number. This trend indeed results in an aspect that has to be faced by everyone trying to prepare an even small but hopefully representative collection of alloy structural data. ‘Si parva licet comparare magnis’ we would like to illustrate this point by an anecdote which was related by Oswald Kubaschewski, one of the founders of alloy thermochemistry and applied thermodynamics. Recounting a conversation he had with Max Hansen, the writer of the first critical and systematic description of the constitution of the different alloys (Hansen 1936), Kubaschewski wrote: At the official dinner of a meeting in May 1939, I was sitting next to Max Hansen. When I congratulated him on the well deserved success of his ‘Aufbau der ZweistoffLegierungen’, he smiled: ‘yes, it was a struggle with the hydra, and so it has taken me seven years’, meaning that whenever he had thought to have finished the phase diagram of a particular system, new evidence would turn up like the new heads of the Greek monster.

621

Families of Intermetallic Structure Types: A Selection (a)

x

y

2z

C

yz

xz

y 2z

x 2z

1, 1, 1

y 3z

2, 1, 1 2, 2, 1

3, 3, 1 3, 2, 1 4, 4, 1

4, 2, 1

x 3z x 4z

13, 4, 3 4, 3, 1 14, 6, 3 14, 2, 1 6, 2, 1 8, 6, 1

xy

B

3, 1, 1 4, 1, 1

5, 3, 2

x 2y

x 4y

A

x 3y (b)

14,6,3

14,2,1

8,6,1

13,4,3

6,2,1

5,3,2

4,4,1

4,3,1

4,2,1

4,1,1

3,3,1

3,2,1

3,1,1

2,2,1

2,1,1

500

1,1,1

Number of phases

1000

Figure 7.2. Distribution of the more common ternary intermetallic phases according to their stoichiometry. (a) Shows the position of AxByCz phases in a representative portion of a general composition triangle. The hatched region corresponds to composition values for which in general ternary compounds are very seldom observed. (b) An indication is given about the number of phases reported by Rodgers and Villars (1993) for different typical stoichiometries.

622

Intermetallic Chemistry

The problems in collecting and selecting literature data were underlined and a short history was presented of the subsequent publication of a number of monographs on this subject. The Hansen monograph was followed, in 1958, by a revised English edition with K. Anderko and the supplements by Elliot (1965) and Shunk (1969). Then, several books were published reporting collections of data mainly concerning phase diagrams: Moffatt (1986), Massalski et al. (1986, 1990), Villars et al. (1995), Okamoto (2000), Effenberg and Ilyenko (2005 et seq.) or crystal structure data (Pearson 1972, Villars and Calvert 1985, 1991, Villars et al. 1995) or thermodynamic data (Barin and Knacke 1973, Hultgren et al. 1973). From this large amount of data some prototypes have been chosen and listed in the following. The prototypes to be included in this list have been selected on the basis of somewhat arbitrary criteria. Especially the structure simplicity and the high frequency of a structural type or the existence of phases of considerable practical importance or the possibility of presenting some features of general interest have been considered. The list here presented, therefore, should be considered only as an introduction to a vast subject. The formulae of the prototypes have been generally written according to the previously adopted rules, with the element symbols arranged according to increasing Mendeleev numbers (see § 2.2.1.3). For all the prototypes listed, space group, Pearson symbol and atomic positions are generally reported. A few comments have been added in order to present some characteristic features of the structures and their relationships with other structures and to underline that often a given structural type may be viewed as pertaining to certain structural families. To this end, coordination formulae, environment symbols, layer stacking symbols, etc. have been considered. For all the structures included, the environmental data by Daams et al. (1991) are given indicating for every atom the corresponding coordination number (CNE) and the polyhedron code. The symbols of the elements at the vertices of this polyhedron are then listed in the order of increasing distances from the central atom. Generally, for each of the Wyckoff positions the coordinates of all the equivalent points have been indicated. In some cases, however, to avoid long repetitions or for complex structures, an abbreviated indication has been used. So, for instance for body-centred lattices (I-space groups), the different coordinates may be summarized according to the International Tables of Crystallography conventions, explicitly indicating the centring translations (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) , characteristic of these lattices before representative coordinate triplets. The symbol means that, in order to obtain the complete set of Wyckoff positions the components of these centring translations have to be added to each of the listed triplets.

Families of Intermetallic Structure Types: A Selection

623

For the structural type: tI8-NbP (body-centred tetragonal, space group I41/amd), for instance, the atomic positions: 1 1 ⁄2, 1⁄2, 1⁄2; ⁄2, 0, 3⁄4 4 Nb in (a) 0, 0, 0; 0, 1⁄2, 1⁄4; 1 1 3 1 1 1 4 P in (b) 0, 0, ⁄2; 0, ⁄2, ⁄4; ⁄2, ⁄2, 0; ⁄2, 0, 1⁄4 could also be indicated as: (0, 0, 0; 1⁄2, 1⁄2, 1⁄2), 4 Nb in (a) 0, 0, 0; 0, 1⁄2, 1⁄4 4 P in (b) 0, 0, 1⁄2; 0, 1⁄2, 3⁄4 1 1 1 1 3 1 3 (We have indeed: ⁄2 ⁄2 0; ⁄2 ⁄4 ⁄4; ⁄2 ⁄4 1⁄4; etc.)

Notice moreover that the symbol (x, y, z) includes x, y, z and x, y, z whereas means a cyclic permutation that is: xyz includes yzx and zxy. The Strukturbericht symbols, which in some cases are still used (see Appendix) have generally also been included, and illustrative short lists of phases pertaining to each prototype have often been added. For the different types, the values of the lattice parameters and, if relevant, of the free positional parameters of the prototype have been reported: this may indeed be useful in comparing different structures and in order to get a better idea of the real atomic packing. Notice, however, that generally, several slightly different values have been reported in literature for the various phases (owing to different preparation and measurement techniques and/or to the existence of certain, often not well defined, homogeneity ranges). The reader interested in accurate values of the lattice parameters should therefore consult the original literature; this is also true for the atomic positional parameters. Notice, moreover that, on passing from one compound to another of the same structural type, due to slight changes in the unit cell axial ratios and in the free positional parameters, small variations in the coordination numbers and polyhedra (here presented for the prototype) may be observed. 7.2.1 On the schematic representations of crystal structures As in previous chapters, the reader will find below for a number of structures a schematic representation, generally through a number of sections and/or projections of the unit cells, often together with a few adjacent cells. As an exercise and an introduction to the subsequent descriptive paragraphs, a few examples with indications about their interpretation are given here. 7.2.1.1 Structure and structure component sections: the tI2-αPa, cI2-W, cF8-ZnS and tI8-NbAs types as examples. tI2-αPa and cI2-W types. The cells of these two structures correspond to a bodycentred tetragonal prism and to a body-centred cube, respectively, see Fig. 7.3. The

624

Intermetallic Chemistry

z0 tI2-αPa (I4/mmm) 2 Pa in (a) 0, 0, 0;

1 1 1 , , 2 2 2

1 1 1 , , 2 2 2

z1

a 392.1 pm, c 323.5 pm, c/a 0.825

z0 cI2-W (Im3m) 2W in (a) 0, 0, 0;

1

z 2

1

z 2

z1

a 316.5 pm (by definition c/a 1)

Figure 7.3. Pa and W structure types: perspective view and section sequences of the unit cells.

significant sections of the cells, passing through some atoms, show an identical sequence of atoms: in the corners of a square, at level 0, in the centre of a square at level 1⁄2 of the cell height, in the corners of a square at level 1, etc. The level 1 is identical to level 0 and then all the levels are repeated periodically. In both cases from these sections, one atom may be easily seen between two groups of four atoms each (eight nearest neighbours). A sketch of the cell shape or considerations based on the unit edge a and c values and especially on the c/a ratio shows, however, that in the two cases a different coordination geometry occurs. cF8-ZnS type. The section sequence of the unit cell of the cubic cF8-ZnS type structure, which is fully discussed in the following, is shown here to underline a few general points. Zn

z −0.25

S

0

0.25

0.50

0.75

1

1.25

Above and below the position of the Zn atom at level 0 or 1 in the centre of the square base of the unit cell there are two pairs of S atoms, at levels 0.25 and 0.75

625

Families of Intermetallic Structure Types: A Selection

(that is 0.25), forming the tetrahedron characteristic of the bond geometry of this type of substances. The equivalent situations presented by all the Zn atoms may be more easily evidenced by considering not only the sections of one unit cell but those of a group of adjacent cells.

cF8

y

ZnS

Zn

0

0.25

S

0.5

0.75

1

(z)

x

Often, in order to give a more realistic indication of the structure, more that one single unit cell is shown. The structure results from placing identical three-dimensional (3D) repetitive cells side by side. In every section, therefore, a small group of unit cells is generally shown (the one in bold for easier comparison with the listed numerical data, parameters, etc.). tI8-NbAs type. As a final example, the characteristic section sequence of the tI8NbAs type structure is shown here. It is evident that this structure may be considered as resulting from similar layers (corresponding to the same square net of points) differently shifted from the origin and differently ‘decorated’ (either by Nb or As atoms). tI8

y x

NbAs

0

Nb

0.17

0.25

As

0.42

0.5

0.67

0.75

0.92

1 (z )

7.2.1.2 Structure and structure component projections: the cP1-Po, cI2-W and hP3-AlB2 type structures as examples. In a number of cases a structure may be conveniently described by using projections of the unit cell (or of a number of adjacent cells), instead than by means of sections. See Fig. 7.4(a) and (b).

626

Intermetallic Chemistry

cP1-Po unit cell: 1 Po in (a) 0, 0, 0

Projection of the structure on the ‘base’ plane (001)

Projection of the structure on the ‘diagonal’ plane (110)

Figure 7.4a. cP1-Po unit cell. Open circles represent atoms on the ‘paper’ plane, dashed circles atoms on other parallel planes.

cI2-W unit cell

Projection of the structure on the ‘base’ plane (001)

Projection of the structure on the ‘diagonal’ plane (110)

Figure 7.4b. cI2-W structure type. Unit cell and characteristic projections. Open circles represent atoms on the reference plane, dashed circles atoms on the other parallel planes.

This will result in more compact, even if slightly more complex, drawings. Notice, moreover, that different projections of the same structure, taken along different directions, may complete each other for a more comprehensive description. The hP3-AlB2 type is presented as another example of the use of characteristic projections. A perspective view of the unit cell and the section sequence along the c axis of the cell are depicted in Fig. 7.5. Convenient representative projections in this case may be those on two perpendicular planes, that is: on plane (001) and (110). The projection on the plane (001) of a portion (nine cells) of the structure is shown with the trace of the conventional hexagonal cells and the rectangular trace of the equivalent ortho-hexagonal cell (see the § 3.6.1.3). The projection on a diagonal vertical plane (110), is also shown. 7.2.2 Examples of common structure types and of their characteristic fragments In Chapter 3 it was underlined that several interrelations between different structures may be described in terms of ‘recombination structures’, evidencing the ‘structural

627

Families of Intermetallic Structure Types: A Selection (a) x

y

x

z=0

y

z = 1/2

(b)

a = 300.0 pm, c = 324.5 pm, c/a = 1.082

hP3-AlB2 (P6/mmm) 1 Al in (a) 0, 0, 0 1 2 1 2 B in (d) , , ; 3 3 2

(large circles) 2 1 1 , , 3 3 2

(small circles)

Figure 7.5. AlB2-type structure: (a) unit cell view and sections and (b) projections of the structure on the ‘base’ plane and on the ‘diagonal’ (110) plane. In the projections open circles correspond to atoms on the reference plane, dashed circles atoms on other parallel planes.

modules’ in common. Classification of various structural types can be based on a construction procedure corresponding to a few combination operations applied to a small number of building units. Several variants of this concept have been considered and alternative or complementary descriptions have been adopted in terms of stacking variants of the same layer, or ‘slab’, types, or of different assemblies of similar polyhedra, and, more generally, of different combinations of similar structural fragments. In § 3.9 examples of these descriptions have been shown. A few more examples will be discussed here as a further introduction to the description of selected structural prototypes, of their role in the intermetallic crystal chemistry and of a method of analysis and comparison of crystal structures (see Fig. 7.6).

628

Intermetallic Chemistry

AlB2 W AlB2 W AlB2 W AlB2 R(T,X) CrB

R5T2X4 V5B6

R3T2X2 Ta3B4

R2T2X V2B3

R(T,X)2 AlB2

Figure 7.6. Examples of binary and ternary structures which may be described in terms of combination of ‘fragments’ of the W and AlB2 types (adapted from Rogl 1992).

Structures which can be interpreted as intergrowth of fragments (such as blocks, or 1D columns, 2D slabs, etc.) corresponding to simpler structures (parent structures) may be especially significant. Families of structures may be obtained in which simple basic motifs are combined to give more complex arrangements; changing the proportions of the segments leads to the definition of members of a structural series. Parthé and Chabot (1984) studied several cases of this type in a systematic description and classification of the ternary compounds formed by a large number of ternary alloys, such as those given by the rare earth metals. As an example, Fig. 7.7 adapted from Parthé and Chabot (1984), shows a generic R–T–M ternary composition diagram (R rare earth metal, T transition metal, M B, Si, etc.). In this diagram the composition lines are shown for a few ‘structural series’ which can be considered as built up of the combination of the same well-defined ‘slabs’ in different proportions: in particular R2nT43nM2n from MgZn2 (and its derivative type Mg2Cu3Si) and CeCo3B2-type slabs, R2nT35nM from Mg2Cu3Si-type and CaCu5-type slabs, RmnT5m3nM2n with intergrown CaCu5 and CeCo3B2 slabs and the structure series R2nT45n as obtained from the stacking of RT5 blocks (isostructural with CaCu5) with RT2 blocks (Laves type).

629

a t.

%

R

Families of Intermetallic Structure Types: A Selection

40

6

17

30 5 4 3 2 1

12

13 14

11 7

8

15

9 10

16

1: CaCu5 2: RT4 3: Sm5 Co19 4: Ce2Ni7 5: CeNi3 6: MgZn2 7: Nd3Ni13 B2 8: CeCo4B 9: Ce3Co11B4

10: Ce2Co7B3 11: R4T13 M 12: Ce3Co8Si 13: Dy3Ni7 B2 14: Ce2Co5 B2 15: R5T13 M6 16: CeCo3 B2 17: Sc2Co3Si

10

T 10

20

30

40 at.% M

Figure 7.7. A number of structural types are indicated as found for the given stoichiometries (according to Parthé and Chabot 1984) in the composition triangle of a generic R–T–M system (R rare earth metal, T transition metal, M B, Si, etc. ). The following structural series can be noticed: R2nT35nM (along the 1–17 line) R2nT43nM2n (along 6–16), RmnT5m3nM2n (along 1–16), R2nT45n (along 1–6).

It has already been noticed (see § 3.9.4) that according to the mentioned concepts several ternary compounds may be considered as the result of a sort of structural interaction between binary compounds. As a consequence some regular trend could also be predicted for their occurrence in their phase diagrams and in the description (and perhaps modelling) of their thermodynamic properties. A few details about this type of structural relationships will be considered in the following and, in this introduction, examples of blocks of simple structural types and of their combination in more complex types will be described. Segments of common, simple, ‘parent’ structures making up typical structure series correspond for instance to the types: cP1-Po, cI2-W, cF4-Cu, hP3-AlB2, cP4-AuCu3, cF12-CaF2. Relevant parts (sections, projections) of these types, which have been used in the description (in the construction) of complex structures, are presented in the Figs. 7.4, 7.5 and 7.8. Notice that the slicing of the parent structures into segments can be done in different ways; however a number of requirements, symmetry conditions, etc., should generally be fulfilled. References to these points have been added in the following structural types list.

630

Intermetallic Chemistry

Au Cu

Ca F

Ca Cu

Figure 7.8. Projections on the (001) and (110) planes of the cP4-AuCu3, cF12-CaF2 structures and the hexagonal (c/a 0.80) hP6-CaCu5 structure.

7.2.3 Polyhedra projections As a conclusion to these introductory notes and as ideal models of coordination polyhedra, perspective views and projections along selected symmetrical directions are shown (in Figs. 7.9(a) and (b) of a few polyhedra. The five regular polyhedra (platonic solids) are shown which are the only polyhedra having congruent faces (each composed of a regular polygon) which meet at congruent vertices. Considering also the Euler relation generally valid for a polyhedron

631

Families of Intermetallic Structure Types: A Selection d

a

a

d

d

b

(a)

a d

b

b

c c

b

c

c c

b

a(e)

c

a

b(f)

d

c

d(b)

d

a

a(g)

b

f

h

g h

e

d(h)

c(g)

e

g

h(f)

a

a

a

c

d

c e

d

a

d e

b

c

a(d)

e

b

f

f

c

d (c)

e (b)

(f)

b

a

e

f

f c(f)

a

b

c

b(a)

c

d

e

f

e(d)

f

b b(e)

d

e

f

Figure 7.9a. Perspective views (first column) of the regular tetrahedron, cube and octahedron and the trigonal prism and their projections. For each of the polyhedra the same letters are used for labelling the same vertices in the different projections; two letters (one within brackets) in the same position correspond to two vertices superimposed in the projection.

632

Intermetallic Chemistry

Figure 7.9b. Different perspective views of the regular dodecahedron and icosahedron.

(F V E 2 where F, V and E are the numbers of faces, vertices and edges) the following properties of the regular polyhedra are relevant: Regular polyhedron F Tetrahedron 4 Cube 6 Octahedron 8 Dodecahedron 12 Icosahedron 20

V 4 8 6 20 12

E 6 12 12 30 30

(The 4 faces are equilateral triangles) (The 6 faces are squares) (The 8 faces are equilateral triangles) (The 12 faces are regular pentagons) (The 20 faces are equilateral triangles)

A trigonal prism (F 5, V 6, E 9) is also shown in Fig. 7.9(a). 7.3. UNARY STRUCTURES

7.3.1 General remarks In this paragraph a short description is given of a representative number of prototypes of the element structures. Typical sections and/or projections are shown, also in order to present a few more complex (derivative) structures. Crystal details and numerical values (such as lattice parameter data, etc.) for the different elements are reported in Chapter 5 together with other elemental properties. Crystal data summarized first are those characteristic of structures of metallic elements, typically having highly symmetric and ‘dense’ atomic arrangements. Only a few notes are reported for the close-packed structures (Mg, Cu types), since for these structures several details are presented in § 3.7.6 and 3.9.2.1. Subsequently, particular structures observed for a few selected specific metals and, finally, a few typical structures of non-metallic elements are described.

Families of Intermetallic Structure Types: A Selection

633

Notice that the structures presented in this paragraph are unary structures, that is one species only is present in all its atomic positions. In the prototypes listed (and in the chemically unary isostructural substances) this species is represented by a pure element. In a number of cases, however, more than one atomic species may be equally distributed in the various atomic positions. If each atomic site has the same probability of being occupied in a certain percentage by atoms X and Y and all the sites are compositionally equivalent, the unary prototype is still a valid structural reference. In this case, from a chemical point of view, the structure will correspond to a two-component phase. Notice that there can be many binary (or more complex) solid solution phases having for instance the Cu-type or the W-type structures. Such phases are formed in several metallic alloy systems either as terminal or intermediate phases. 7.3.2 Metallic element structures 7.3.2.1 The close-packed element structure types (Mg, Cu, La, Sm types) and simple derivative types. The Mg, Cu, La and Sm types form a typical set of homeotect structure types (see § 3.7.6 and 3.9.2) characterized by close-packed stacking variants of atomic nets (Figs 3.20 and 3.21), and corresponding to sequences of 2, 3, 4 and 9 triangular nets, respectively. Their space filling parameter is ideally 74% (see § 4.3.2.5) and the coordination number is 12. A high percentage of metals crystallize in one of these structures. Their conventional crystallographic descriptions are reported here. 7.3.2.1.1 Mg, hP2 structural type. Hexagonal, space group P63/mmc, N. 194. Atomic positions: 1 2 2 Mg in (c) ⁄3, 2⁄3; 1⁄4 ⁄3, 1⁄3, 3⁄4; Coordination formula: 3[Mg(66)/(66)] and ideally: 3[Mg12/12] For the prototype, Mg, a 320.89 pm, c 521.01 pm, c/a 1.624. Environment data: Mg (c) CNE 12,

122.2 (h)

(6Mg, 6Mg)

Strukturbericht designation A3. A description of the Mg structure can be found in Fig. 3.16, where the trend of the interatomic distance against c/a is also shown. In an ‘ideal’ hexagonal close— packed structure with c/a 8/3 1.633, there are 12 nearest neighbours at the — same distance. For c/a values different from 8/3 there are two groups of six distances each. One group forms a hexagon on the same plane and the second group consists of three atoms on the layer above and three on the layer below. See the polyhedron 122.2 (h) in Fig. 3.18.

634

Intermetallic Chemistry y hP2 Mg

x

c/a 1.62 Mg y hP2 WC

x

c/a 0.98 W

C

y hP3 CdI2

x

c/a 1.62 Cd

I

y hP4 NiAs

x

c/a 1.39 Ni

As

y hP3 AlB2

x

c/a 1.08 Al

B

y hP6 Ni2In

x

c/a 1.23 Ni z0

0.25

0.5

0.75

In

1

Figure 7.10. Section sequences, parallel to the x, y plane, of Mg-related hexagonal structures. The z coordinate is shown.

In the Mg structure the atoms are arranged in close-packed layers stacked in the sequence ABAB… (equivalent to BCBC…, etc); the corresponding layer symbol (triangular nets) is MgB0.25MgC0.75. Compare this symbol with those relevant to Cu, La, Sm.

635

Families of Intermetallic Structure Types: A Selection

In the schemes of Fig. 7.10, typical sections of a few adjacent cells of this structure are shown; these are also compared with those of a number of related hexagonal structures, some of which are described in the following paragraphs. Notice that important filled-up derivatives can be considered among the ordered structures derived from Mg. Typical examples are the hP4-NiAs type with occupied octahedral holes and the wurtzite (hP4-ZnS) type with one set of occupied tetrahedral holes. Several metals have been reported with the hP2-Mg type of structure, such as: αBe, Cd, εCo, αDy, Er, Ho, Lu, Mg, Os, Re, Ru, Tc, αY, Zn, etc. For Zn, Cd, Hg, a covalent bonding contribution results in an increase of the c/a values: 1.856 for Zn, 1.886 for Cd with bonds stronger in the layers than between the layers. Several binary (and complex) phases have also been described with this type of structure. These are generally solid solution phases with a random distribution of the different atomic species in the two equivalent positions. 7.3.2.1.2 Cu, cF4, structural type – Face-centred cubic, space group Fm 3m, N. 225. Atomic positions: 1 4 Cu in (a) 0, 0, 0; 0, 1⁄2, 1⁄2; ⁄2, 0, 1⁄2;

⁄2, 1⁄2, 0

1

Coordination formula: 3[Cu12/12] Environment data: Cu (a) CNE 12,

122.2(c)

Layer stacking symbols: Triangular (T) nets: Square (S) nets:

(12Cu)

CuA0 CuB1/3 CuC2/3 Cu10Cu40Cu51/2

For the prototype, Cu, a 361.46 pm. Strukturbericht designation A1. The section sequence of the cF4-Cu type structure is shown in Fig. 7.11.

cF4 Cu Cu y x

z=0

0.5

1

Figure 7.11. Section sequence parallel to the base plane of the cF4-Cu type structure.

636

Intermetallic Chemistry

The atoms are arranged in close-packed layers stacked in the ABC sequence (see the triangular net stacking symbol). Several metals, such as Al, Ag, Au, αCa, αCe, γCe, αCo, Cu, γFe, Ir, βLa, Pb, Pd, Pt, Rh, αSr, αTh and the noble gases Ne, Ar, Kr, Xe crystallize in this structural type. Several binary and complex phases having this structure have also been reported (solid solutions with random distribution of several atomic species in the four equivalent positions). Cu-derivative, substitutional and interstitial superstructures. As discussed in § 3.8.1 ff, the Cu-type structure is also an important ‘reference’ structure because it may be considered the ‘ancestor’ of several derivative structures. Derivative structures may be obtained from the Cu-type structure by ordered substitution or by ordered addition of atoms. As examples of derivative structures obtained by ordered substitution (and/or distortion) in the Cu type we may mention the AuCu3, AuCu, Ti3Cu types, which are described in this chapter. For a systematic description of the derivative structures which may be obtained from the Cu type by ordered filling-up, it may be useful to consider that in a closest packing of equal spheres there are, between the spheres, essentially two kinds of interstices (holes). The smallest holes surrounded by a polyhedral group of spheres are the tetrahedral holes. The larger holes (octahedral holes) are surrounded by octahedral groups of six spheres. In an infinite assembly of close-packed spheres the ratios of the numbers of the tetrahedral and octahedral holes to the number of spheres are, respectively, 2 and 1. These holes and their coordinates are shown in Fig. 3.35. A number of filled-up derivatives of the cubic close-packed structures have been mentioned in § 3.8.1.1. NaCl, CaF2, ZnS-sphalerite, AgMgAs- and Li3Bi-type structures can be included in this family of derivative structures; in the same paragraph the dimensional conditions which must be fulfilled in order to give full meaning to such descriptions and derivation schemes are discussed. Relationships between the filling-up of the Cu structure and structures such as CsCl (see Fig. 3.31), Li3Bi and MnCu2Al have also been considered. Notice that similar remarks can be made with reference to the other simple close-packed structure, that is the hexagonal Mg-type structure. 7.3.2.1.3 La, hP4 and Sm, hR9, structural types La: hexagonal, space group P63/mmc, N. 194. Atomic positions: 2 La in (a) 0, 0, 0; 0, 0, 1⁄2 1 2 2 La in (c) ⁄3, 2⁄3, 1⁄4; ⁄3, 1⁄3, 3⁄4 For the prototype, αLa, a 377.0 pm, c 1215.9 pm, c/a 3.225.

Families of Intermetallic Structure Types: A Selection

637

Layer stacking symbols: Triangular (T) nets: LaA0LaB0.25LaA0.5LaC0.75 Environment data: La (a) CNE 12, La (c) CNE 12,

122.2 122.2

(6La, 6La) (6La, 6La)

Strukturbericht designation A3 . – Sm: rhombohedral, space group R3m, N. 166. Atomic positions: 2 ⁄3, 1⁄3, 1⁄3; 3 Sm in (a) 0, 0, 0; 6 Sm in (c) 0, 0, z; 0, 0, –z ; 2 1 ⁄3, 1⁄3, z– 1⁄3; ⁄3, 2⁄3, z 2⁄3;

⁄3, 2⁄3, 2⁄3 ⁄3, 1⁄3, z 1⁄3; 1 ⁄3, 2⁄3, z– 2⁄3; 1 2

For the prototype, αSm, (for its triple primitive hexagonal cell), a 362.90 pm, c 2620.7 pm, c/a 7.222, and z 0.222. Environment data: Sm (a) CNE 12, Sm (c) CNE 12,

122.2 122.2

(6Sm, 6Sm) (3Sm, 3Sm, 6Sm)

Strukturbericht designation C19. Layer stacking symbols: Triangular (T) nets: SmA0 SmC0.11 SmA0.22 SmC0.33 SmB0.45 SmC0.55 SmB0.67 SmA0.78 SmB0.89 The La- and Sm-type structures belong to the same homeotect type set as Mg and Cu. All these close-packed element structures are stacking variants of identical slab types (monatomic triangular nets). An example of a more complex stacking variant of this series may be represented by a statistically disordered form of Co which, conveniently annealed, can show a ….ABABAB…. sequence disturbed by the insertion of a few ….ABC…. groups. For the crystal structures of the lanthanides and actinides see also a few comments in § 5.5.5. 7.3.2.2 The body-centred cubic W-type structure. The W-type structure is another important structure of metallic elements: it is common to a number of metals: Li, Na, K, Rb, Ba, Cs, Eu, Cr, Mo, V, Ta, W, etc. (as the only room temperature stable form), Be, Ca, Sr, several rare earth elements, Th, etc. (as a high-temperature form) and α and δ Fe forms. The data relevant to the prototype are reported in the following.

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7.3.2.2.1 W, cI2, structural type. – Body-centred cubic, space group Im3 m, N. 229. Atomic positions: 1 2 W in (a) 0, 0, 0; ⁄2, 1⁄2, 1⁄2 Coordination symbol:

3 [W8/8]

Layer stacking symbols: Triangular (T) nets: WA0WB1/6WC1/3WA1/2WB2/3WC5/6 Square (S) nets: W10W41/2 Environment data: W (a) CNE 14,

80.360.4

(8W, 6W)

Space filling parameter corresponds to 68% (see § 4.3.2.5 and § 4.3.2). For the prototype, W, a 316.5 pm. Strukturbericht designation A2. The section sequence of the cI2-W structure type is shown in Fig. 7.12. The same structure is formed in a number of binary (or ternary) phases, for which a random distribution of the two (or three) atomic species in the two equivalent sites is possible. Typical examples are the β-Cu–Zn phase (in which the equivalent 0, 0, 0; 1 1 1 ⁄2, ⁄2, ⁄2 positions are occupied by Cu and Zn with a 50% probability) and the β-Cu–Al phase having a composition around Cu3Al (in which the two crystal sites are similarly occupied, on average by Cu, with a 75% occupation probability, and by Al, with a 25% occupation probability). A number of these phases can be included within the group of the ‘Hume-Rothery phases’ (see § 4.4.5). The W body-centred cubic structure can be compared with the simple cubic CsCl-type structure (which can be obtained from the W type by an ordered substitution of the atoms) and with the MnCu2Al-type structure (‘ordered’ superstructure of the CsCl type); see Fig. 3.31 and notice the typical eight (cubic) coordination.

cI2 W W y x

z=0

0.5

1

Figure 7.12. Section sequence parallel to the base plane of the cI2-W type structure.

Families of Intermetallic Structure Types: A Selection

639

7.3.2.3 Two body-centred tetragonal structures (In- and αPa-type structures) 7.3.2.3.1 In, tI2, structural type Body-centred tetragonal, space group I4/mmm, N. 139. Atomic positions: 1 1 1 2 In in (a) 0, 0, 0; ⁄2, ⁄2, ⁄2 Environment data: In (a) CNE 12,

122.2

(4In, 8In)

For the prototype, In, a 325.1 pm, c 494.7 pm, c/a 1.522. Strukturbericht designation A6. Several, disordered binary alloys of In, with Li, Mg, Pb, Sn, Pb Sn, Tl, Bi, Cd, etc., have the In-type structure. The In cell may be considered a distortion of the Cu type, face-centred cubic, cell. The unconventional — face-centred tetragonal cell (equivalent to the tI2 cell), corresponds to a a 2 459.8, c c 494.7 and c /a 1.076. Protactinium has a similar structure, which however with a c/a value lower than one, can be considered a distortion of the body-centred cubic structure. 7.3.2.3.2 Pa, tI2, structural type. Body-centred tetragonal, space group I4/mmm, N. 139. Atomic positions: 1 1 1 2 Pa in (a) 0, 0, 0; ⁄2, ⁄2, ⁄2 The unit cell edges are a 393.2 pm, c 323.8 pm, c/a 0.823. Environment data: Pa (a) CNE 14,

80.360.4

(8Pa, 2Pa, 4Pa)

Strukturbericht designation Aa. Notice that, in this structural type, space group and atomic positions are the same as in the tI2-In type. The different c/a axial ratio, however, results in different atomic environment. 7.3.2.4 Special structural types of selected metals. In this paragraph a few selected special structures peculiar to some metals, generally located in particular positions of the periodic table, are described. Some very simple structural types have to be considered (the simplest one is the αPo-cP1) and some having rather complex atomic arrangements, for instance αMn, cI58. For indications about rare crystal forms possessed only by a few, or just by one, metals see in Chapter 5 the paragraphs dedicated to the various specific elements, where structure type and lattice parameter data are listed for all the allotropes.

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7.3.2.4.1 Po, cP1, structural type – Cubic, space group Pm3m, N. 221. Atomic positions: 1 Po in (a) 0, 0, 0 For the prototype, Po, a 334.5 pm. Environment data: Po (a) CNE 6,

64.0

(6Po)

The simple structure of this semimetal, not very compact, has a space filling parameter ϕ 0.524. 7.3.2.4.2 Hg, hR3, structural type. The hR3-αHg structure can be considered a distorted cubic close-packed structure compressed along the three-fold axis. In the rhombohedral primitive unit cell there is one atom; three atoms are in the equivalent triple primitive hexagonal cell (a 346.0 pm, c 670.2 pm, c/a 1.937) in the positions 3 Hg in (a) 0, 0, 0; 2⁄3, 1⁄3, 1⁄3; 1⁄3, 2⁄3, 2⁄3 in the space group – R3 m, N. 166. The environment data are Hg: CNE 12 (122.2) (66 Hg) The Strukturbericht designation is A10. At high pressure various allotropic forms of Hg are known. 7.3.2.4.3 Ga, oS8, structural type The crystal characteristics of orthorhombic gallium are a 451.86, b 765.70, c 452.58. Space group Cmca, N. 64. 1 1 Atomic positions: (0, 0, 0; ⁄2, ⁄2, 0) 1 8 Ga in (f ) 0, y, z; 0, ⁄2 y, 1⁄2 z; 0, 1⁄2 y, 1⁄2 z; 0, y–, –z ; y 0.155, z 0.081 Environment data: Ga (f ) CNE 7, 33.124.015.012.1 (1Ga, 6Ga) 3 In this modification Ga forms 6 layers of distorted hexagons parallel to the y, z plane at heights x 0 and x 1⁄2.

7.3.2.4.4 Sn, tI4, structural type. The tI4-βSn structure (a 583.2 pm, c 318.2 pm) (4 Sn in (a) 0, 0, 0; 0, 1⁄2, 1⁄4; 1⁄2, 1⁄2, 1⁄2; 1⁄2, 0, 3⁄4; space group I41/amd, N. 141) can be considered a very much distorted diamond-type structure. Each Sn has four close neighbours, two more at a slightly larger (and four other at a considerably larger) distance. The βSn unit cell is depicted in Fig. 7.13. Environment data: Sn (a) CNE 10, 82.224.0 Strukturbericht designation A5.

(4Sn, 2Sn, 4Sn)

Families of Intermetallic Structure Types: A Selection

641

Figure 7.13. Unit cell of the tI4-βSn structure.

The tI4-βSn structure, under high pressure is observed also for other elements of the 14th group, that is by Si and Ge. 7.3.2.4.5 αMn, cI58, structural type (and derivative types Ti5Re24 and Mg17Al12) – Body-centred cubic, space group I43m, N. 217. Atomic positions: (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) 2 Mn in (a) 0, 0, 0; 8 Mn in (c) x, x, x; x–, x–, x; x–, x, x–; x, x–, x– 24 Mn in (g1) x, x, z; x–, x–, z; x–, x, z–; x, x–, z–; z, x, x; z, x–, x–; z–, x–, x; z–, x, x–; x, z, x; x–, z, x–; x, z–, x–; x–, z–, x 24 Mn in (g2) (with the same list of coordinate triplets as in (g1) but with different values of x and z) For the prototype, Mn, a 889.4, x(Mnc) 0.317 and x(Mng1) 0.356, z(Mng1) 0.042, x(Mng2) 0.089, z(Mng2) 0.278. Environment data: (12Mn, 4Mn) Mn (a) CNE 16, 125.046.0 Mn (c) CNE 16, 125.046.0 (9Mn,1Mn, 3Mn, 3Mn) Mn (g1) CNE 13, 85.024.123.116.0 (1Mn, 1Mn, 2Mn, 2Mn, 4Mn, 2Mn, 1Mn) Mn (g2) CNE 12, 125.0 (1Mn, 2Mn, 1Mn, 2Mn, 2Mn, 2Mn, 1Mn, 1Mn) Strukturbericht designation A12. Several phases belonging to ordered or disordered variants of this structure are also called χ phases. Among the different binary phases having structures related to the αMn type, three different cases may be considered: (i) The structure is disordered with almost identical occupancy on all Wyckoff positions (the structure can be properly described as αMn-type).

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(ii) The structure is ordered as in the case of the Ti5Re24 phase second kind superstructure (see § 3.8.5), where Ti preferentially occupies the 2a and 8c Wyckoff positions (with CNE around 16) while Re is predominant in the 24g(1) and 24g(2) positions with coordination around 12–13. Notice that in Mn the two sets of atoms in the g Wyckoff positions have slightly different environments, owing to the different values of the x and z parameters. (iii) The structure is ordered as in the case of Mg17Al12 phase, which can be considered another type of a second kind superstructure of the Mn type. In this structure Mg preferentially occupies 2a 8c 24g atomic positions (with high values of CNE) while Al is predominant in the other 24 g set. With reference to thermodynamic implications of a convenient crystallographic description of the phases, a three-sublattice model has been proposed for the description of both disordered and ordered Mn-derivative structures. In the case of the Er–Mg–Al system, two phases have been identified as solid solutions based on Mg17Al12 and Er5Mg24, respectively; they have been conveniently modelled as one single phase using the three-sublattice model: (Er, Mg)5(Al, Mg)12(Al, Mg)12 (Cacciamani et al. 2002). This model can correspond both to Mg17Al12 and to Er5Mg24 depending on the specific site occupancies. 7.3.2.5 A few comments about uranium and plutonium elemental structures. Data concerning the unit cells of the lanthanides and actinides are reported in § 5.5. In the ‘generalized lanthanide phase diagram’ the stability regions of their various allotropes are shown as in the ‘combined actinide binary diagrams’ (Figs. 5.10 and 5.11). The complex behaviour displayed by the light actinides (especially U, Np, Pu) is evident. A few more details about uranium and plutonium crystal structures are reported in the following. 7.3.2.5.1 αU, oS4, structural type It is orthorhombic, space group Cmcm, N. 63. Atomic positions: (0, 0, 0; 1⁄2, 1⁄2, 0) 4 U in (c) 0, y, 1⁄4; 0, y–, 3⁄4; y 0.105 Unit cell parameters are: a 285.37 pm, b 586.95 pm, c 495.48 pm CNE 12, 122.2 Strukturbericht designation A20. βU ( 668°C) has a tP30 structure, tetragonal (a 1075.9 pm, c 565.6 pm, c/a 0.526) space group P42nm, N. 102, with the 30 atoms in the unit cell distributed in six different Wyckoff positions and CNE ranging from 12 to 14 and 15. Strukturbericht designation Ab. γU ( 776°C) has the cI2-W type structure with a 352.4 pm.

Families of Intermetallic Structure Types: A Selection

643

7.3.2.5.2 Plutonium. The different crystal forms of Pu are the following (stable at ambient pressure and increasing temperatures). αPu-mP16, βPu-mS34, γPu-oF8, δPu-cF4 (Cu type), δ Pu-tI2 (In type), εPucI2(W type). The unit cell data (and the temperature ranges of stability) are listed in Table 5.16. Notice the molar volume increase (and density decrease) on passing from the α form up to a maximum for the δ. αPu-mP16 (monoclinic, space group P21 /m, N. 11) has a complex structure with the 16 atoms, in the unit cell, in eight different groups of 2e (x, 1⁄4, z) positions. This structure has a high packing density, about 20% higher than in the cF4, δ (Cu type) plutonium and may be described as a distorted hcp structure. The CNE for the different Pu atoms ranges in this structure from 12 to 16. The βPu-mS34 (monoclinic, space group C2/m, N. 12) has a complex structure too, with the atoms in seven different sites (Wyckoff positions) and CNE ranging from12, to 13, 14 and 15. The γPu-oF8 structure corresponds to the following positions in the orthorhombic face-centred cell: 1 1 1 (0, 0, 0; 0, 1⁄2, 1⁄2; ⁄2, 0, 1⁄2; ⁄2, ⁄2, 0) 1 1 1 8 Pu in (a) 0, 0, 0; ⁄4, ⁄4, ⁄4 The δPu (Cu type), δ Pu (In type), and εPu (W type) allotropes stable at higher temperatures correspond to typical common metal structures. At high pressure ( 40 GPa) a plutonium modification is also known: it is ζPu-hP8. 7.3.3 A selection of non-metallic elemental structures 7.3.3.1 Boron: remarks on its crystal structure. The atomic and physical properties of boron are reported in § 5.13.2 with a few data about its crystal structures in the elemental state. A few more comments will be added here in order to insert also boron in this short summary of the crystal properties of the various elements. In this general although partial picture, the peculiar characteristics of boron have indeed to be underlined. According to Greenwood and Earnshaw (1997) the following points may be mentioned to emphasize the diversity and complexity of boron inorganic chemistry. The small atomic size of boron, its high ionization energy and the electronegativity value close to those of carbon and hydrogen result in an extensive covalent molecular chemistry. The electronic structure of boron (2s 22p1) is well reflected in its general trivalent behaviour: no tendency is observed to give monovalent compounds (which are more important on passing in the Al, Ga, In and Tl group from one element to the next one). The availability of three valence electrons and of four valence orbitals (s, px, py, pz) results in the capability of acting as an electron pair acceptor (Lewis acid) and of forming multi-centre bonding. Boron can form chains (branched and unbranched), 2D networks and 3D arrays. Owing to its small atomic

644

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dimensions interstitial compounds and alloys can also be formed. These characteristics are reflected also in the structural complexity of its allotropic modifications. A typical building block used to construct several solid-state structures (boronrich borides and allotropes of elemental boron) is the B12 icosahedron. According to King, (1993) an icosahedral B12 building block in which each of the 12 vertices contributes a single electron for an external two-electron two-centre (2e, 2c) bond to an external group implies the following electron count: Electrons for each of the 12 external bonds: Electrons for the 12-centre core bond of the B12 icosahedron: Electrons for the surface binding: Corresponding to the total number of electrons required:

12 electrons 2 electrons 24 electrons 38 electrons

Considering that 12 B atoms have a total of 12 3 36 valence electrons, the B12 unit will be stable as the anion B2 12 . Several allotropic forms of boron are known which are based on various ways of joining B12 icosahedra (using the external orbitals on each boron atom). α rhombohedral boron (12 B atoms in the rhombohedral unit cell: a 505.7 pm, α 58.06°) consists of nearly regular B12 icosahedra arranged in a slightly deformed cubic close packing. β rhombohedral boron (105 B atoms in the rhombohedral unit cell: a 1014.5 pm, α 65.28°), is the most thermodynamically stable allotrope. Its structure may be described as a rhombohedral packing of B84 units (known as Samson complexes) linked by B10 polyhedra and an interstitial B atom between two adjacent B10 units (that is B84(B10)6/3B B105). The B84 unit can be considered as a central B12 icosahedron surrounded by an icosahedron of (partially shared) icosahedra. In more details, it can be described as 12 B7 units arranged so that their apices form the central icosahedron (with the remaining 6 B of each unit having the structure of a pentagonal pyramid, that is of a half icosahedron).The full stoichiometry of the Samson complex may therefore be represented as B12(B6)12 B84. Other boron modifications have been described and also compounds such as B50C2 or B50N2, previously believed to be pure boron forms. For a detailed discussion on the bonding in boron modifications and boron-rich compounds see King (1993). An example of an extremely boron-rich metal boride is given by YB66 (ThB66) having boron sub-networks mainly based on B12 icosahedra (B156 icosahedron of icosahedra, etc.). The crystal structure data of ThB66 corresponds to a very large face-centred cubic unit cell containing 1880 atoms. 7.3.3.2 The 8 eat rule. For a number of non-metal (or semimetal) elements a contribution to the systematics of their crystallography may be given in terms of a

Families of Intermetallic Structure Types: A Selection

645

simplified version of the valence rule, that is of the 8 eat rule where eat is the number of valence electrons of the atom of the element involved. This rule, valid for a number of covalent structures, may be related to the tendency for an element to attain the electron configuration of the noble gas following it in the periodic table. For every covalent bond in which an atom is involved it takes one electron. The element considered are the ‘main groups’ elements from the group numbers 14–17 (except for hydrogen), having 4–7 (s or p) valence electrons. The noble gas type configuration is obtained when the atom is involved in a number of 8 eat simple covalent bonds. Typical structures obeying this rule correspond to four bonds (CN 4) for the elements of the 14th group (diamond-type structure for C, Si, Ge), three bonds for the 15th group (three-connected structures for some forms of P, As, Sb, etc.), two bonds for the 16th group (ring and chain molecules of S, Se) and one bond for the 17th group (diatomic molecules Cl2, I2, etc.). Notice that in the following only a selection is presented of the crystal structures of the elements of the 14th to 17th groups. A few more details and data are reported in the specific paragraphs of Chapter 5. 7.3.3.2.1 C (diamond), cF8-C, structural type – Face-centred cubic, space group Fd3m, N. 227. Atomic positions: 8 C in (a) 0, 0, 0; 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0; 1 1 1 ⁄4, ⁄4, ⁄4; 1⁄4, 3⁄4, 3⁄4; 3⁄4, 1⁄4, 3⁄4; 3⁄4, 3⁄4, 1⁄4 This group of atomic positions corresponds to the so-called invariant lattice complex D; see § 3.7.1 and Fig. 3.14. The coordination formula is: 3[C4/4] The layer stacking symbols are: A B C1/3CB7/12CC2/3CC11/12 Triangular (T) nets: CA0 C1/4 1 4 6 Square (S) nets: C 0 C 0 C 1/4C51/2C73/4 For the prototype, C diamond, a 356.69 pm. Environment data: C (a) CNE 4, 43.0

(4C)

Strukturbericht designation A4. The diamond structure, see Fig. 7.14 below, is a 3D network in which every atom is surrounded tetrahedrally by four neighbours. The eight atoms in the unit cell may be considered as forming two interpenetrating face-centred cubic networks. If the two networks are occupied by different atoms, the derivative cF8-ZnS (sphalerite) type structure is obtained. As a further derivative structure, the tI16-FeCuS2 type structure can be mentioned. These are all examples of a family of ‘tetrahedral’ structures which have been described by Parthé (1964).

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Intermetallic Chemistry

cF8 C (diamond) C y x

z=0

0.25

0.5

0.75

1

Figure 7.14. The diamond-type structure.

The other14th group elements, Si, Ge and αSn have the diamond-type structure. The tI4-βSn structure (observed for Si and Ge under high pressure) can be considered a very much distorted diamond-type structure. Each Sn has four close neighbours, two more at a slightly larger and another four at a considerable larger distance. Fig. 7.13 shows the βSn unit cell. Lead, at ambient pressure, has a facecentred cubic cF4-Cu type structure. For carbon, the diamond-type structure is metastable at room conditions it is stable at high pressure. See the phase diagram of carbon shown in Fig. 5.37. 7.3.3.2.2 C (graphite), hP4, structural type. In comparison with the tetrahedral structure of C diamond a very different structure is adopted by carbon in graphite. hP4-C graphite Hexagonal, space group P63 /mmc, N. 194 Atomic positions: 2 C in (b) 0, 0, 1⁄4; 0, 0, 3⁄4 2 C in (c) 1⁄3, 2⁄3, 1⁄4; 2⁄3, 1⁄3, 3⁄4 Coordination formula: 2[C3/3] The lattice parameters are a 246.4 pm, c 671.1 pm, c/a 2.724. Environment data: 3-ring (3C) C (b) CNE 3, C (c) CNE 3, 3-ring (3C) Strukturbericht designation A9. The hP4-C (graphite) structure is shown in Fig. 7.15. Different varieties, however, of graphite may be considered. The actual structure and unit cell dimensions and layer stacking can vary depending on the preparation conditions, degree of crystallinity, disorientation of layers, etc.

Families of Intermetallic Structure Types: A Selection

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Figure 7.15. hP4-C (graphite) structure. The unit cell and a carbon atom layer are shown.

In crystalline hP4-graphite, sheets of six-membered rings are situated so that the atoms in alternate layers lie one over the other, and the second layer is displaced according to the stacking symbol Cb1/4C c3/4. Whereas in diamond the bond length is 154 pm, in graphite the C9C minimum bond length is 142 pm in the sheets and 335 pm (c/2) between sheets. This relates to the highly anisotropic properties of this substance. It may be said, for instance, that the properties of graphite in the sheets are similar to those of a metal, while perpendicularly they are more like those of a semiconductor. In conclusion, notice also that in terms of combinations of invariant lattice complexes, the positions of the atoms in the level 1⁄4 can be represented by 2⁄3, 1⁄3, 1⁄4 G, and those in the level 3⁄4 by 1⁄3, 2⁄3, 3⁄4 G (where G is the symbol of the ‘graphitic’ net complex, here presented in non-standard settings by means of shifting vectors). 7.3.3.2.3 C (lonsdaleite), hP4, structural type. In § 7.4.2.3, dedicated to the description of a few representative 1:1 compounds, a number of simple binary

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tetrahedral structures and polytypes are described. Reference structures are the ZnSsphalerite (cF8-ZnS), and ZnS-wurtzite, (hP4-ZnO), structural types. The degenerate structures of sphalerite and wurtzite (when, for instance, both Zn and S are replaced by C) correspond to the previously described cF8 diamond-type structure and, respectively, to another carbon form: the hP4-hexagonal diamond or lonsdaleite, which is very rare compared with the cubic gem diamond. The unit cell of lonsdaleite (prepared at 13 GPa and 1000°C) are: a 252 pm, c 412 pm, c/a 1.635. 7.3.3.2.4 C, other modifications. For different crystal forms of C, for fullerenes, etc. see the comments in § 5.14.1. 7.3.3.3 Typical structures of elements of the 15th group (As, Sb, Bi). A typical structure shown by various elements of this group is the hR6-As type structure, corresponding to the stable grey (rhombohedral, metallic) αAs modification. 7.3.3.3.1 As, hR6, structural type – Rhombohedral, space group R3 m, N. 166. Atomic positions (in the triple primitive hexagonal cell): 2 1 1 6 As in (c) 0, 0, z; 0, 0, –z ; ⁄3, ⁄3, ⁄3 z; 2 1 – 1 1 2 2 ⁄3, ⁄3, z ⁄3; ⁄3, ⁄3, ⁄3 z; 1⁄3, 2⁄3, z– 2⁄3 For the prototype, As, a 376.0 pm, c 1054.7 pm, c/a 2.805 and z 0.2271. Layer stacking symbols: AsC0.11AsA0.23AsB0.44AsC0.56AsA0.77 AsB0.89 Environment data: As (c)

CNE 6

Around each As atom there are three As at 251.7 pm and three As at 312.0 pm forming a polyhedron, code 64.0. Strukturbericht designation A7. The section sequence of the hR6-As structure is shown in Fig. 7.16. This structure can be described as a (puckered) layer type (See Fig. 7.17). In each layer the As–As distance (d1) is considerably shorter than the As–As interlayer hR6

As

As

y x

z = 0.11

0.23

0.44

Figure 7.16. The arsenic-type crystal structure.

0.56

0.77

0.89

Families of Intermetallic Structure Types: A Selection

649

distance (d2). In Table 7.3 the values observed for the three 15th group elements having this structure are summarized. Both the data for the primitive rhombohedral unit cell, containing two atoms and for the equivalent triple primitive hexagonal cell are given. According to Pearson (1972) the rhombohedral structure of these elements can be considered a distortion of a simple cubic structure in which the d2/d1 ratio would be 1. The decrease of the ratio on passing from As to Bi, and the corresponding relative increase of the strength of the X–X interlayer bond (passing from a coordination nearly 3, as for the 8 eat rule, to a coordination closer to 6) can be related to an increasing metallic character. 7.3.3.4 Comments on other structures of 15th group elements. The first element of the group, nitrogen, has three different solid modifications (two stable at normal pressure, the third one under high pressure) which differ in the packing of the N2 molecules. Phosphorus exists in many allotropic modifications which correspond to the variety of ways of obtaining catenation. Phosphorus vapour contains tetrahedral P4 molecules (the coordination number of all the atoms is 3) which only at high temperatures decompose in P2 and P molecules. By condensation of the vapour the white, waxy, α P4 is formed which also, as the liquid, contains P4 molecules. The αP4 white form is the most volatile, reactive (and highly toxic) and thermodynamically the least stable solid modification. The slow oxidation of the vapour over the solid results in the phosphorescence characteristic of this element. By heating above 180°C, white phosphorus is transformed into red phosphorus which (a)

(b)

Figure 7.17. The As-hR6 structure: (a) a puckered layer of As atoms is viewed along the c axis of the hexagonal cell and (b) lateral view of two superimposed layers. Notice the coordination 3 of the atoms, characteristic for the element of the 15th group (five valence electrons).

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Table 7.3. Unit cell data of the hR6-As type elements. Unit cell parameters

X–X distances

d2/d1

Rhombohedral description a (pm), α

Hexagonal description a (pm), c (pm)

Within the layer d1 (pm)

Interlayer d2 (pm)

As

413.2; 54.13°

252

312

1.24

Sb

450.7; 57.11°

287

337

1.17

Bi

474.6; 57.31°

376.0; 1054.7 c/a 2.803 430.84; 1127.4 c/a 2.617 454.6; 1187.2 c/a 2.612

310

347

1.12

Element X

is amorphous or microcrystalline, existing in several modifications. Violet (Hittorf’s) phosphorus was obtained by slow crystallization in molten lead. It has a complex, monoclinic, structure in which, according to the 8 eat rule, every P atom is bonded with three other atoms. Black phosphorus, the thermodynamically stable modification at normal conditions, orthorhombic, forms only under special conditions (high pressure, crystallization from liquid Bi). It consists of layers having six-membered rings in a chair conformation. Within the layer each P is connected to other three P atoms. The white and black phosphorus structures have been observed also in metastable arsenic modifications. 7.3.3.5 Typical structures of 16th group elements. For the 16th group elements (the chalcogens, with eat 6) the 8 eat rule corresponds to a ‘first range’ coordination of 2, that is to structures in which two bonds (characterized by the shortest bond length) may be recognized as the main bonds. This bonding behaviour, often resulting in the formation of chain structures, may be identified in several chalcogen compounds and also in the structures of the elements themselves. Several modifications of these elements are known. This is especially characteristic for sulphur; no element indeed shows so many different structure as sulphur. This is related to the great variety of molecular forms that can be achieved by 9S9S9 catenation and also to the different ways in which the molecules may be packed within the crystal. Crystal structures have been described for the following species: S6, S7, S8, S10, S11, S12, S13, S18, S20 and S (in a number of cases more than one modification for each species). Just as an example the structure of αS-oF128 is presented here.

Families of Intermetallic Structure Types: A Selection

651

7.3.3.5.1 αS-oF128 structural type Fcc orthorhombic, space group Fddd, N. 70. 1 1 Atomic positions: (0, 0, 0; 0, 1⁄2, 1⁄2; ⁄2, 0, 1⁄2; ⁄2, 1⁄2, 0) – – –x , y, z–; 32S in (h1) x,y, z; x , y , z; – – – – – 1 1 1 x, y , z ; x ⁄4, y ⁄4, z ⁄4; x 1⁄4, y 1⁄4, z– 1⁄4; x 1⁄4, –y 1⁄4, z 1⁄4; –x 1⁄4, y 1⁄4, z 1⁄4; x 0.9808, y 0.0777, z 0.0765 –x , –y , z; –x , y, z–; 32S in (h2) x, y, z; – – – 1 – 1 – 1 x, y , z ; x ⁄4, y ⁄4, z ⁄4; x 1⁄4, y 1⁄4, z– 1⁄4; – – 1 1 1 x ⁄4; y ⁄4, z ⁄4; x 1⁄4, y 1⁄4; z 1⁄4; x 0.8323, y 0.1048, z 0.1291 32S in (h3)

x, y, z; x, –y , z–; x 1⁄4, –y 1⁄4, z 1⁄4; x 0.9092, y 0.1552, z 0.2012

–x , –y , z; –x , y, z–; –x 1⁄4, –y 1⁄4, z– 1⁄4; x 1⁄4, y 1⁄4, z– 1⁄4; –x 1⁄4, y 1⁄4, z 1⁄4;

32S in (h4)

–x , –y , z; –x , y, z–; –x 1⁄4, –y 1⁄4, z– 1⁄4; x 1⁄4, y 1⁄4, z– 1⁄4; –x 1⁄4, y 1⁄4, z 1⁄4;

x, y, z; x, –y , z–; x 1⁄4, –y 1⁄4, z 1⁄4; x 0.9110, y 0.0327, z 0.2545

The structure of αS-oF128 is shown in Fig. 7.18: the unit cell is represented together with two different projections of the cyclo-octa-sulphur molecule. 7.3.3.6 Remarks on the structures of 17th group elements (I2 ). As a conclusion to the description of the element structure and as another example of the application of the 8 eat rule along the different groups of the periodic table, the crystal structure of a halogen (iodine) is presented. In this case the number of valence electrons is eat 7 and from the rule we have to 8 eat 1 corresponding to the formation of a structure with a coordination number 1. This is obtained in the diatomic molecules of the halogens. In Fig. 7.19, the structure of I2 (and of the isostructural Cl2 and Br2) is shown. Parallel layers of I2 molecules are formed. The I–I distance is 271.5 pm between the atoms of the same molecule, whereas the shortest interatomic I–I distance between the molecules is 350 pm within a layer, and 427 pm between different layers. The crystal data of the I2-oS8 structure are the following: Orthorhombic, space group Cmca N. 64: Atomic positions: (0, 0, 0; 1⁄2, 1⁄2, 0) 8 I in (f) 0, y, z; 0, –y 1⁄2, z 1⁄2; 0, y 1⁄2, z– 1⁄2; 0, –y , z–; y 0.116; z 0.149 a 718.02 pm, b 471.02 pm, c 981.03 pm.

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Intermetallic Chemistry (a)

b a (b)

Figure 7.18. The structure of sulphur αS-oF128: (a) The unit cell. The atoms pertaining to the same molecule have been similarly coloured. The content of one unit cell corresponds to 16 S8 molecules. (Notice however that only two of the molecules are fully included in the cell depicted, the others extend into the adjacent cells.) (b) Two different projections of a single molecule, as identified in the structure of αS-oF128, are shown.

Figure 7.19. A packing drawing of iodine molecules in its crystal structure.

7.4. BINARY STRUCTURES: A SELECTION OF COMMON PROTOTYPES

7.4.1 Preliminary remarks With reference to their ‘ideal’ stoichiometries a few ubiquitous crystal structure prototypes will be presented in the following. Attention will be especially given to some structures corresponding to simple stoichiometric ratios. Notice however that, in several cases, a given prototype may be represented by a point compound but also,

Families of Intermetallic Structure Types: A Selection

653

depending on the specific alloy system, by a solid solution phase corresponding to a composition range, more or less close to the ideal composition. In a number of cases, similarities or other relationships between the prototype under consideration and other structure types have been underlined, so that a number of derivative structures are presented all together, even if corresponding to different stoichiometries. 7.4.2 Simple 1:1 prototypes and derivative structures 7.4.2.1 Introduction. A number of common structures, ideally corresponding to a 1:1 stoichiometry, are presented in this chapter. Some of them are not specifically characteristic of intermetallic compounds only. The CsCl and NaCl types, for instance, are observed for several kinds of chemical compounds (from typical ionic to metallic phases). Notice that for a number of prototypes a few derivative structures have also been considered and described, underlining crystal analogies and relationships even if with a change in the reference stoichiometry. 7.4.2.2 cP2-CsCl, cF8-NaCl and cF16-NaTl types and NaTl-related structures. 7.4.2.2.1 CsCl, cP2, structural type – Cubic, space group Pm3m, N. 221. Atomic positions: 1 Cs in (a) 0, 0, 0 1 Cl in (b) 1⁄2, 1⁄2, 1⁄2 Coordination formulae: 3 3 [CsCl]8/8 or [CsCl]8cb/8cb (ionic description) 333 333 [X6/6][Y6/6]8/8 or [X6o/6o][Y6o/6o]8cb/8cb (metallic description) Environment data: Cs (a) CNE 14, Cl (b) CNE 14,

80.3,60.4 80.360.4

(8Cl, 6Cs) (8Cs, 6Cl)

Layer stacking symbols: B A CsC1/3Cl1/2 CsB2/3ClC5/6 Triangular (T) nets: CsA0 Cl1/6 1 4 Square (S) nets: Cs 0 Cl 1/2

For the prototype, CsCl, a 411.3 pm. Strukturbericht designation B2. The section sequence of the cP2-CsCl is shown in Fig. 7.20. See also Fig. 3.8. where the nearest-neighbour number (NNN) of the two atomic species is evidently eight. A list and the histogram of the atomic distances with the corresponding number of the equidistant neighbours are shown in Fig. 3.17. The resulting CNE is 14. In Fig. 3.31 the derivative CsCl superstructure MnCu2Al type

654

Intermetallic Chemistry

y x

z=0

0.5

1

cP2 CsCI Cs

CI

Figure 7.20. Section sequence parallel to the base plane of the cP2-CsCl type structure.

is presented: it is shown that the W-type structure can be considered a degenerate structure of the CsCl-type structure (in the W structure the two atomic sites are equivalent). The CsCl-type structure is adopted by a few halide and chalcogenide 1:1 (ionic) compounds for which, however, it is in competition with the NaCl-type structure. Of the monohalides only CsCl, CsBr, CsI, TlCl, TlBr and TlI (and of the monochalcogenides only, ThTe) have the CsCl-type structure, while the rest with a lower atomic (ionic) ratio have the NaCl-type structure, corresponding to a lower NNN, 6 instead of 8. These (ionic) compounds generally may be considered point compounds. However the CsCl-type structure is observed also in many of the 1:1 intermetallics for which it often corresponds to a solid solution range. Among the intermetallic binary phases one may mention compounds such as those of alkaline earth and rare earth elements with Mg, Zn, Cd, Hg (and often with In, Tl, Ag, Au), those of Al and Ga with Fe and Pt group metals. The β Cu–Zn phase (stable at room temperature) belongs to this structural type; at higher temperature it undergoes the order–disorder transformation into the disordered cI2-W type, β phase. FeAl is another example of a phase having this (more or less) ordered structure. It corresponds to a solid solution range from 23 to 55 at.% Al. It forms through ordering of the αFe, cI2-W type, phase which has a solubility range from 0 to 45 at.% Al. Other interesting phases belonging to this structural type are: NixAl1x (homogeneous between 42 and 69 at.% Ni) with good mechanical and oxidation resistance properties. By quenching from high temperatures the formation of an ordered martensite is obtained which can be considered for its shape memory behaviour. For a discussion on substitutional additions to CsCl-type alloys (site preference for dilute additions to NiAl, FeAl, CoAl, etc.) see Kao et al. (1994).

655

Families of Intermetallic Structure Types: A Selection

CoxAl1x (48 to 79 at.% Co), CoxBe1x (26–53 at.% Co), NixBe1x (25 to 52 at.% Ni), PdBe (50 at.% Pd), CuxBe1x (51 to 53 at.% Cu), etc. Finally, TixPd1x (47 to 53 at.% Pd) and TixPt1x (46 to 54 at.% Pt) have the CsCl-type structure at high temperature and the oP4-AuCd structure at low temperature. See the space filling curve characteristic for this structure type in Fig. 4.22. 7.4.2.2.2 NaCl, cF8, structural type. – Face-centred cubic, space group Fm3m, N. 225. Atomic positions: 4 Na in (a) 0, 0, 0; 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0 4 Cl in (b) 1⁄2, 1⁄2, 1⁄2; 1⁄2, 0, 0; 0, 1⁄2, 0; 0, 0, 1⁄2 For the prototype NaCl, a 564.0 pm. Environment data: Cl (a) CNE 6, Na (b) CNE 6,

(6Na), (6Cl),

64.0 64.0

Coordination formula: 333 [Na12/12][Cl12/12]6/6 Layer stacking symbols: B Triangular (T) nets: NaA0 ClC1/6 Na1/3 ClA1/2 NaC2/3 ClB5/6 1 4 5 1 Square (S) nets: Na 0 Na 0 Cl 0 Cl 1/2 Cl41/2 Na51/2 The space filling curve characteristic for this structure type is shown in Fig. 4.22. Strukturbericht designation B1. The characteristic sections of a few adjacent cells of NaCl are shown in Fig. 7.21. A perspective view of the cell is shown in Fig. 3.33. A large number of compounds belong to the NaCl-type structure; for instance those given by the alkaline earths with O, S, Se, Te, Po, etc. and nearly all the (partially ionic–covalent and metallic) 1:1 compounds formed by the rare earths and the actinides with N, P, As, Sb, Bi, S, Se, Te, Po. Notice that this structure may also be described as a derivative of the cubic close-packed structure (cF4-Cu type) in

cF8 NaCl Na

y x z=0

0.5

Cl

1

Figure 7.21. Section sequence parallel to the base plane of the cF8-NaCl type structure.

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Intermetallic Chemistry

which the octahedral holes have been filled-in. This description, however, may be especially convenient when the atomic diameter ratio between the two elements is close to the theoretical value 0.414. In this case the small spheres will fit exactly into the octahedral holes of the close-packed arrangement of the metal atoms. This could be the case of a number of ‘interstitial compounds’. Hägg phases. Compounds of the transition metals having relatively large atomic radii with non-metals having small radii (H, B, C, N, possibly O) may be simple examples of ‘interstitial compounds’. General properties of these compounds were discussed by Hägg (1931). Examples of typical phases belonging to this group are a number of ‘mono’ carbides, nitrides, etc. often called Hägg phases. A list of systems forming Hägg phases and some comments about their properties have been presented in § 3.8.4. 7.4.2.2.3 NaTl, cF16, structural type. – The cF16-NaTl type structure is face centred, cubic, space group Fd3m, N. 227. Atomic positions: 8 Tl in (a) 0, 0, 0; 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0; 3 1 3 ⁄4, ⁄4, ⁄4; 3⁄4, 3⁄4, 1⁄4; 1⁄4, 1⁄4, 1⁄4; 1⁄4, 3⁄4, 3⁄4 8 Na in (b)

⁄2, 1⁄2, 1⁄2; ⁄4, 3⁄4, 1⁄4;

⁄2, 0, 0; ⁄4, 1⁄4, 3⁄4;

1

1

1

1

0, 1⁄2, 0; ⁄4, 3⁄4, 3⁄4;

3

0, 0, 1⁄2; ⁄4, 1⁄4, 1⁄4

3

For the prototype, NaTl, a 747.3 pm. Environment data: Tl (a) CNE 14, 80.360.4 Na (b) CNE 14, 80.360.4

(1Na, 4Tl, 9Na) (1Tl, 2Na, 3Tl, 2Na, 6Tl)

A characteristic section sequence of the NaTl structure is shown in Fig. 7.22 together with a few other related structural types. The space filling curve characteristic for this structure type is shown in § 4.3.2.5 and Fig. 4.22. Strukturbericht designation B32. LiZn, LiCd, LiAl, NaIn have this structure. This structure may be regarded as a completely filled-up face-centred cubic arrangement in which each component occupies a diamond-like array of sites. The structure may thus be presented as NaTl: D D (see the descriptions in terms of combination of invariant lattice complexes reported in § 3.7.1). The coordination formula is: 3 Na [Tl4/4]4/4. NaTl has been traditionally considered as a typical representative of the Zintl phases and described as NaTl with Tlcorresponding to a diamond like framework (See § 4.4.3.1). The NaTl-type structure may be conveniently compared with the Li3Bi and MnCu2Al types: all these structures which have cF16-unit cells may be considered as

Families of Intermetallic Structure Types: A Selection

657

composed of four interpenetrating face-centred cubic arrays (F F F F ) and correspond to the same space filling as in eight cubic (or in 8 CsCl type) cells (see Fig. 3.31). The layer stacking symbols and the section sequences of the cF16-NaTl structure are compared in Fig. 7.22 with those of the cF16-Li3Bi and cF16-MnCu2Al types. 7.4.2.2.4 Comments on some NaTl-related structures. Li3Bi, cF16, structural type – cF16-Li3Bi type is face-centred cubic, space group Fm3 m, N. 225. Atomic positions: 1 4 Bi in (a) 0, 0, 0; ⁄2, 1⁄2, 0; 1⁄2, 0, 1⁄2; 0, 1⁄2, 1⁄2 1 1 1 4 Li in (b) ⁄2, ⁄2, ⁄2; 0, 0, 1⁄2; 0, 1⁄2, 0; 1⁄2, 0, 0 1 1 1 3 3 1 8 Li in (c) ⁄4, ⁄4, ⁄4; ⁄4, ⁄4, ⁄4; 3⁄4, 1⁄4, 3⁄4; 1⁄4, 3⁄4, 3⁄4 3 3 3 1 1 3 ⁄4, ⁄4, ⁄4; ⁄4, ⁄4, ⁄4; 3⁄4, 1⁄4, 1⁄4; 1⁄4, 3⁄4, 1⁄4 Coordination formula: 3 [BiLi8/4Li6/6] (ionic description) For the layer stacking symbols, see in the following. For the prototype, Li3Bi, a 672.2 pm. Strukturbericht designation D03. This structure could also be described as derived from a cubic close-packed array of atoms (Bi atoms) by filling all the tetrahedral and octahedral holes with Li atoms. Binary phases pertaining to this structural type (also named as BiF3 type or Fe3Al type) are Fe3Al, Fe3Si, Li3Bi, Li3Sb, K3Bi, Cs3Bi, Cs3Sb, Ca3In, Ca3Tl, Li3Pb, RMg3 (with a number of rare earth metals R). Among the several ternary alloys described as pertaining to this type, a number of Al alloys may be mentioned (AlCo2Fe, AlCo2Hf, AlCo2Ta, AlCrNi2, AlHfCu2, AlCrFe2, AlMn2V, etc.). Compare this structure with the cF16-MnCu2Al type described in the following. MnCu2Al, cF16, structural type. – Face-centred cubic, space group Fm3m, N. 225. Atomic positions: 4 Al in (a) 0, 0, 0; 1⁄2, 1⁄2, 0; 1⁄2, 0, 1⁄2; 0, 1⁄2, 1⁄2 4 Mn in (b) 1⁄2, 1⁄2, 1⁄2; 0, 0, 1⁄2; 0, 1⁄2, 0; 1⁄2, 0, 0 8 Cu in (c) 1⁄4, 1⁄4, 1⁄4; 3⁄4, 3⁄4, 1⁄4; 3⁄4, 1⁄4, 3⁄4; 1⁄4, 3⁄4, 3⁄4 3 3 3 ⁄4, ⁄4, ⁄4; 1⁄4, 1⁄4, 3⁄4; 3⁄4, 1⁄4, 1⁄4; 1⁄4, 3⁄4, 1⁄4 Coordination formula: 3 [AlCu8/4Mn6/6] For the prototype, MnCu2Al, a 596.8 pm. For the layer stacking symbols, the data are reported in comparison with the Li3Bi and NaTl-type structures Strukturbericht designation L21.

658

Intermetallic Chemistry

Layer stacking symbols of the NaTl type and of the NaTl-related types are here reported: Triangular (T) nets: NaTl type: B A A NaA0 Tl1/12 TlC1/6 Na1/4 NaB1/3 TlC5/12 Tl1/2 NaB7/12 NaC2/3 TlA3/4 TlB5/6 NaC11/12 Li3 Bi type: B A B A BiA0 Li1/12 LiC1/6 Li1/4 Bi1/3 LiC5/12 Li1/2 LiB7/12 BiC2/3 LiA3/4 LiB5/6 LiC11/12 MnCu2 Al type: B A B A AlA0 Cu1/12 MnC1/6 Cu1/4 Al1/3 CuC5/12 Mn1/2 CuB7/12 AlC2/3 CuA3/4 MnB5/6 CuA11/12 Square (S) nets: NaTl type: Na10 Na40 Tl50 Na61/4 Tl71/4 Tl11/2 Tl41/2 Na51/2 Tl63/4 Na73/4 Li3 Bi type: Bi10 Bi40 Li50 Li61/4 Li71/4 Li11/2 Li41/2 Bi51/2 Li63/4 Li73/4 MnCu2 Al type: Al10 Al40 Mn50 Cu61/4 Cu71/4 Mn11/2 Mn41/2 Al51/2 Cu63/4 Cu73/4 The characteristic sections of a few adjacent cells are shown in Fig. 7.22 for these structures. A perspective view of the AlCu2Mn structure and a comparison with the CsCl-type structure. Notice that if the two (a) and (b) sites are occupied by the same atomic species, the cell degenerates into a block of eight equal cells (of the CsCl type), on the contrary, if a single atomic species were assigned to the (b) and (c) sites, the ordered structure corresponding to the 1:3 stoichiometric ratio (Li3Bi type or BiF3 type) would be obtained. Finally if all the three, (a), (b) and (c), sites are occupied by the same atomic species the cell degenerates into a block of eight equal, cI2-W type, cells. In several compilations the phases belonging to the MnCu2Al and Li3Bi types are listed together. Among the ternary alloys, several Me MeMe 2 phases can be mentioned (with Me Al, Ga, Ge, Sn; Me Ti, Zr, Hf, V, Nb, Mn, etc. and Me Co, Ni, Cu, Au, etc.). The compounds which crystallize with the MnCu2Altype structure (and particularly the magnetic compounds having this structure) are called Heusler phases. In the specific case of the Al–Cu–Mn system, this phase is ferromagnetic and stable above 400°C, but it can be frozen by quenching to room temperature. It is assumed that its whole moment is due to the spin moment of Mn which has an unfilled d shell (five electrons). The magnetic properties of Heusler phases are strongly dependent on the ordering of the atoms. 7.4.2.3 Simple binary tetrahedral structures and polytypes (ZnS-sphalerite, cF8-ZnS and ZnS-wurtzite, hP4-ZnO, structural types). The sphalerite- and wurtzite-type structures (together with C diamond) are well-known examples of the

659

Families of Intermetallic Structure Types: A Selection

cF16 NaTl y

Na

Tl

x

cF16 Li3Bi y

Li

Bi

x

cF16 MnCu2Al Mn

y x z=0

0.25

0.5

0.75

Al

Cu

1

Figure 7.22. Section sequences parallel to the base plane of the three cF16-related structures NaTl, Li3Bi and MnCu2Al.

‘normal tetrahedral structures’. See a few general remarks on these structure types in § 3.9.2.2 and 4.4.2.1. 7.4.2.3.1. ZnS, cF8, structural type (sphalerite). – Face-centred cubic, space group F4 3m, N. 216 Atomic positions: 4 Zn in (a) 0, 0, 0; 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0 1 1 1 4 S in (c) ⁄4, ⁄4, ⁄4; 1⁄4, 3⁄4, 3⁄4; 3⁄4, 1⁄4, 3⁄4; 3⁄4, 3⁄4, 1⁄4 In terms of a combination of invariant lattice complexes the sphalerite structure may therefore be described as: ZnS: F F. Coordination formulae: 3 [ZnS4/4] (ionic or covalent description) 333 [Zn12/12][S12/12]4/4 (metallic description) For the prototype, ZnS sphalerite, a 541.1 pm. Environment data: Zn (a) CNE 4, S (c) CNE 4,

43.0 43.0

(4S) (4Zn)

Strukturbericht designation B3. The section sequence of the cF8-ZnS type structure is shown in Fig. 7.23.

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Intermetallic Chemistry

cF8 ZnS Zn

y

S

X

z=0

0.25

0.5

0.75

1

Figure 7.23. Section sequence parallel to the base plane of the cF8-ZnS sphalerite-type structure.

The space filling curve characteristic for this structure type is shown in Fig. 4.22. 7.4.2.3.2 ZnO, hP4, structural type (or ZnS wurtzite) Hexagonal, P63mc, N. 186. Atomic positions: 1 2 2 Zn in (b) ⁄3, ⁄3, z; 2⁄3, 1⁄3, z 1⁄2; (z z1) 1 2 2 O or 2 S in (b) ⁄3, ⁄3, z; 2⁄3, 1⁄3, z 1⁄2; (z z2) Coordination formula: 3 [ZnO4/4] For the prototypes: ZnO: a 325.0 pm, c 520.7 pm, c/a 1.602. ZnS: a 382.3 pm, c 626.1 pm, c/a 1.638. Both types of atoms have similar coordinate groups (pertain to the same Wyckoff positions) with different values of the z parameter. For ZnO zZn 0, zO 0.3825 and for ZnS zZn 0, zS 0.371. Environment data: Zn (b) CNE 4, O or S (b) CNE 4,

43.0 43.0

(4Zn) (4S)

Strukturbericht designation B4. The section sequence of the hP4-ZnO (ZnS wurtzite) is shown in Fig. 7.24. 7.4.2.3.3 Sphalerite and wurtzite structures: general remarks. Compounds isostructural with the cubic cF8-ZnS sphalerite include: AgSe, AlP, AlAs, AlSb, BAs, GaAs, InAs, BeS, BeSe, BeTe, BePo, CdS, CdSe, CdTe, CdPo, HgS, HgSe, HgTe, etc. The sphalerite structure can be described as a derivative structure of the diamond-type structure. Alternatively, we may describe the same structure as a derivative of the cubic close-packed structure (cF4-Cu type) in which a set of tetrahedral holes has been filled-in. This alternative description would be especially convenient when the atomic diameter ratio of the two species is close to 0.225; see the comments reported in § 3.7.3.1. In a similar way the closely related hP4-ZnO

661

Families of Intermetallic Structure Types: A Selection y x

hP4 ZnO c /a = 1.60 Zn z=0

0.25

0.5

0.75

O

1

Figure 7.24. Section sequence parallel to the base plane of the hP4-ZnO (ZnS wurtzite) type structure.

structure can be considered as a derivative of the hexagonal close-packed structure (hP2-Mg type) in which, too, a set of tetrahedral holes has been filled-in. Compounds isostructural with ZnO include: AgI, BeO, CdS, CdSe, CuX (X H, Cl, Br, I), MnX (X S, Se, Te), MeN (Me Al, Ga, In, Nb), ZnX (X O, S, Se, Te). In order to have around each atom in this hexagonal structure four exactly equi–– distant neighbouring atoms, the axial ratio should have the ideal value 8/3 that is 1.633. The experimental values range from 1.59 to 1.66. This practical constancy of the axial ratio, in contrast with what is observed for other families of isostructural compounds such as those of the NiAs type, may be attributed to a sort of ‘rigidity’ of the tetrahedral (sp3) chemical bonds. As for the atomic positional parameters, the ideal value of one of the parameters (being the other one fixed at zero by conventionally shifting the origin of the cell) is z 3/8 0.3750. The C diamond, sphalerite- and wurtzite-type structures are well-known examples of the ‘normal tetrahedral structures’ (see § 3.9.2.2). Several superstructures and defect superstructures based on sphalerite and on wurtzite have been described. The tI16-FeCuS2 (chalcopyrite) type structure (tetragonal, a 525 pm, c 1032 pm, c/a 1.966), for instance, is a superstructure of sphalerite in which the two metals adopt ordered positions. The superstructure cell corresponds to two sphalerite cells stacked in the c direction. The c/2a ratio is nearly 1. The oP16-BeSiN2 type structure is another example which similarly corresponds to the wurtzite-type structure. The degenerate structures of sphalerite and wurtzite (when, for instance, both Zn and S are replaced by C) correspond to the previously described cF8-diamond-type structure and, respectively, to the hP4-hexagonal diamond or lonsdaleite, which is very rare compared with the cubic, more common, gem diamond. The unit cell dimensions of lonsdaleite (prepared at 13 GPa and 1000°C) are a 252 pm, c 412 pm, c/a 1.635 (compare with ZnS wurtzite). The sphalerite- and wurtzite-type structures belong to a homeotect structure type set. The layer stacking sequence symbols (triangular nets) of the two structures are: Sphalerite: Wurtzite:

A ZnA0 S1/4 ZnB1/3 SB7/12 ZnC2/3 SC11/12 B B Zn 0 S 0.37 ZnC1/2 SC0.87

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Intermetallic Chemistry

In the first case, along the direction of the diagonal of the cubic cell, there is a sequence ABC of identical ‘unit slabs’ (‘minimal sandwiches’), each composed of two superimposed triangular nets of Zn and S atoms, respectively. The ‘thickness’ of the slabs, which include the Zn and S atom nets, is 0.25 of the lattice period along the superimposition direction (that is along the cubic cell diagonal: a3). It is (0.253 541) pm 234 pm. In the wurtzite structure there is a sequence BC of similar slabs formed by sandwiches of the same triangular nets of Zn and S atoms. Their thickness is 0.37 c 0.37 626.1 pm 232 pm). With reference to the aforementioned structural unit slab the Jagodzinski–Wyckoff symbol of the two structures is: ZnS sphalerite: c; ZnS wurtzite: h. In the same homeotect set (equiatomic tetrahedral structure type) many more structures occur, often with very long stacking periods. Several other polytypes of ZnS have been identified and characterized. The largest number of polytypic forms and the largest number of layers in regular sequence have been found, however, for silicon monocarbide (‘carborundum’). A cubic form of SiC is known, as well as a variety of rhombohedral and hexagonal polytypes. In commercial SiC a six-layer structure, hcc, is the most abundant. All have the same ahex 308 pm; the chex of their hexagonal (or equivalent hexagonal) cells are all multiples of 252 pm and range from 505 pm to more than 150 000 pm (up to more than 600 Si–C slabs in a regular sequence). 7.4.2.4 hP2-WC and hP4-NiAs types and examples of NiAs-derivative structures 7.4.2.4.1 WC, hP2, structural type. – Hexagonal, space group P6 m2, N. 187. Atomic positions: 1 W in (a) 0, 0, 0 1 C in (d) 1⁄3, 2⁄3, 1⁄2 For the prototype, a 290.6 pm, c 283.7 pm, c/a 0.976. Environment data: W (a) CNE 14, C (d) CNE 14,

66.063.029.0 66.063.029.0

(6C, 2W, 6W) (6W, 2C, 6C)

Strukturbericht designation Bh. This structure type with the axial ratio c/a close to 1 is an example of the Hägg interstitial phases formed when the ratio between non-metal and metal radii is less than about 0.59. The structure can be described as a 3D array of trigonal prisms of W atoms (contiguous on all the faces). Alternate trigonal prisms are centred by C atoms. Compounds belonging to this structure type are for instance: IrB, OsB, RuB, MoC, WC (compare, however, with the NaCl-type phase), NbN, WN, MoP, etc.

Families of Intermetallic Structure Types: A Selection

663

See the characteristic section sequences of the WC structure and a few related structures in Fig. 7.10. 7.4.2.4.2 NiAs, hP4, structural type. Hexagonal, space group P63/mmc, N. 194. Atomic positions: 2 Ni in (a) 0, 0, 0; 0, 0, 1⁄2 2 As in (c) 1⁄3, 2⁄3, 1⁄4; 2⁄3, 1⁄3, 3⁄4 Coordination formula: 13 [Ni2/2]As6/6 For the prototype, a 362.4 pm, c 503.9 pm, c/a 1.393. The layer stacking sequence symbols are: A AsC3/4 (see Fig. 7.10). Ni0AAsB1/4 Ni1/2 Environment data: Ni (a) CNE 8, As (c) CNE 6,

65.023.0 61.2

(6As, 2Ni) (6Ni)

The As atoms form close-packed layers in the hexagonal stacking sequence … BC…. The Ni atoms (on sites A) are placed in the centres of all the octahedral interstices in the As layers. Ni has 6 As neighbours and As is surrounded by 6 Ni (forming a right trigonal prism). Strukturbericht designation B81. According to Hyde and Andersson (1989), the data reported have to be considered as corresponding to an average slightly idealized structure, corresponding for several compounds to the form which is stable at high temperature. At room temperature, in the real structure, there are very small displacements of both Ni and As from their ideal average positions. The structure should, therefore, be better described by: 2 Ni in (a) 0, 0, z; 0, 0, z 1⁄2 (z 0) 1 2 2 2 As in (b) ⁄3, ⁄3, z; ⁄3, 1⁄3, z 1⁄2 (z 1⁄4) in the space group P63mc, N. 186. The small displacements of the atoms produce several sorts of modulated structures. 7.4.2.4.3 hP4-NiAs derivative structures. A defect derivative: hP3-CdI2; a filled-up derivative: hP6-Ni2In and a distorted derivative structure oP8-MnP. The NiAs structure is an important reference type because of its several (filled-up and defect) derivative structures. If atoms are left out of the metal layers in an ordered way, defects superstructures are obtained: the CdI2 type is obtained when all the metal atoms are omitted in alternate layers. On the contrary other derivative structures (filled-up structures) may be obtained by adding atoms in the same layers as

664

Intermetallic Chemistry

the anions at the positions (2⁄3, 1⁄3, 1⁄4); when all of these positions are occupied, the Ni2In-type structure is obtained. A comparison between these structures may also be made by considering their reported characteristic triangular net stacking sequences: hP3-CdI2 hP4-NiAs hP6-Ni2In

B C CdA0 I1/4 I 3/4 A B A Ni 0 As1/4 Ni1/2 AsC3/4 A C B A Ni0 Ni 1/4 In1/4 Ni1/2 NiB3/4 InC3/4

On passing from CdI2 to the NiAs type the insertion of a new layer is found at level ⁄2 as well as, from NiAs to Ni2In, the ordered addition of atoms at levels 1⁄4 and 3⁄4. Compare their characteristic section sequences in the paragraph dedicated to Mg, § 7.3.2.1.

1

CdI2, hP3, structural type (NiAs defect derivative) – Hexagonal, space group P3 m1, N. 164. Atomic positions: 1 Cd in (a) 0, 0, 0 1 2 2 I in (d) ⁄3, 2⁄3, z; ⁄3, 1⁄3, –z Coordination formula: 2 [CdI6/3] Environment data: Cd (a) CNE 6, I (d) CNE 3,

64.0 loose 3-ring

(6I) (3Cd)

For the prototype, CdI2, a 424.4 pm, c 685.9 pm, c/a 1.616 and z 0.249. Strukturbericht designation C6. Typical phases pertaining to this structural type are CoTe2, HfS2, PtS2, etc. and also Ti2O, which, owing to the exchange in the unit cell of the metal/non-metal positions may be considered to be a representative of the CdI2 antitype. The cP3-CdI2 structure type may be compared with the hP4-NiAs and hP6Ni2In types. A comparison between these structures may also be made by considering their reported characteristic triangular net stacking sequences. Ni2In, hP6, structural type (NiAs filled-up derivative) Hexagonal, space group P63/mmc, N. 194. Atomic positions: 2 Ni in (a) 0, 0, 0; 0, 0, 1⁄2 1 2 1 2 1 3 2 In in (c) ⁄3, ⁄3, ⁄4; ⁄3, ⁄3, ⁄4 1 2 3 2 1 1 2 Ni in (d) ⁄3, ⁄3. ⁄4; ⁄3, ⁄3, ⁄4

Families of Intermetallic Structure Types: A Selection

Environment data: Ni (a) CNE 14, In (c) CNE 11, Ni (d) CNE 11,

665

122.226.0 92.220.3 92.220.3

Coordination formula: 3 [InNi6/6Ni5/5] For the prototype, a 417.1 pm, c 512.1 pm, c/a 1.222. Strukturbericht designation B82. Typical phases assigned to this structural type are, for instance: Zr2Al, Co2Ge, La2In, Mn2Sn, Ti2Sn and several ternary phases such as: BaAgAs, CaCuAs, FeCoSn, LaCuSi, VFeSb, KZnSb, etc. A distorted variant of the Ni2In-type structure is the oP12-orthorhombic structure of the Co2Si, (or PbCl2) type: 3 [SiCo6/5Co4/5], that is total coordination 10 of Co around Si with 6/5 4/5 10/5 2 Co atoms for each Si atom). A ternary derivative of this type is the oP12-TiNiSi type (prototype of the so-called E phases). NiAs distortion structures. The characteristics of a number of structures have been described by Pearson (1972) in terms of distortions of the NiAs type. Different variants have been considered, of which the following new prototypes having a 1:1 stoichiometry are typical examples: mS8-CrS, oP8-MnP, oP16-NiP, hP24-αFeS. The oP8-MnP type is described here below. MnP, oP8, structural type (NiAs distorted derivative) Orthorhombic, space group Pnma, N. 62. Atomic positions. 4 P in (c) x, 1⁄4, z; 4 Mn in (c) x, 1⁄4, z;

–x 1⁄2, 3⁄4, z 1⁄2; –x 1⁄2, 3⁄4, z 1⁄2;

–x , 3⁄4, –z; –x , 3⁄4, –z;

x 1⁄2, 1⁄4, –z 1⁄2 –x 1⁄2, 1⁄4, –z 1⁄2

For the prototype, MnP: a 525.8 pm, b 317.2 pm, c 591.8 and xP 0.189, zP 0.569; xMn 0.005, zMn 0.197. Environment data: Mn (c) CNE 12, P (c) CNE 8,

45.043.127.024.0 24.123.121.215.013.0

The structure of MnP along [100] can be compared with the NiAs structure along [001]. In comparison with Ni in NiAs, Mn in MnP is surrounded by a distorted octahedron of P atoms (6 P); phosphorus is surrounded by a distorted trigonal prism of Mn atoms (6Mn). Strukturbericht designation B31.

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Intermetallic Chemistry

Typical compounds pertaining to this type of structure are: VAs, CrP, CrAs, WP, MnP, MnAs, FeP, FeAs, CoP, CoAs, NiSi, NiGe, RhSi, RhGe, RhSb, RuP, PdSi, PtSi, PtGe, IrSi, IrGe, MnTe, FeS and ternary phases for compositions (solid solutions) around the following ones: FeWP2, CrFeP2, FeVAs2, MnVAs2, MoTiAs2, MoVAs2, MoFeAs2, TiVAs2, Cr2AsSb. 7.4.2.5 oS8-CrB and oP8-FeB structure types (two triangular prism-based structures, similar in coordination). The oS8-CrB and the oP8-FeB type structures are examples of structures based on trigonal prisms. Parthé and Chabot (1984), in discussing structures or rare earth alloys, in an analysis of structures built up exclusively by centred R trigonal prisms, observed that these structures may be classified according to the number of directions of the trigonal prisms axes. The following classes were defined: (i) Only one direction: all the prisms are parallel and identical (except for a rotation around their axis or a shift along it). The oS8-CrB type structure belongs to this class. (ii) There are two directions for the prism axes. A first subclass is characterized by two perpendicular directions (tI16-MoB is an example of this type of structures). In a second subclass, exemplified by the oP8-FeB type, the two directions are not perpendicular. A short description of the two CrB- and FeB-type structures is given in the following, together with a few comparative comments. 7.4.2.5.1 CrB, oS8, structural type Orthorhombic, space group Cmcm, N. 63. Atomic positions: 4 B in (c) 0, y, 1⁄4; 0, y–, 3⁄4; 1⁄2, y 1⁄2, 1⁄4; 4 Cr in (c) 0, y, 1⁄4; 0, –y, 3⁄4; 1⁄2, y 1⁄2, 1⁄4;

⁄2, –y 1⁄2, 3⁄4 1 – ⁄2, y 1⁄2, 3⁄4 1

For the prototype, CrB, a 296.9 pm, b 785.8 pm, c 293.2 pm and yB 0.44, yCr 0.146. Environment data: B (c) CNE 9, Cr (c) CNE 17,

65.034.0 61.244.124.223.221.414.0

Layer stacking symbol: Square (S, crystal plane a,c) nets: B40.06Cr 10.15 Cr40.35 B10.44 B20.56 Cr30.65 Cr20.85 B30.94 Strukturbericht designation Bf (or B33).

667

Families of Intermetallic Structure Types: A Selection oS8 CrB

Cr

B

(a)

a b

0.25

0.75

(z)

0

0.5

(x)

(b)

c b (c)

c b

Figure 7.25. oS8-CrB structure type. Sections of a few cells (four cells are outlined) along the x/y (a) and the z/y (b) planes and (c) a projection on the z/y plane. Notice that this projection, in which the Cr6B prisms parallel to the x axis have been evidenced, corresponds to the superposition of the two sections shown in (b), where the larger circles represent atoms in the x 1⁄2 layer and smaller circles represent atoms in the x 0 layer.

The section sequence of the oS8-CrB structure type is shown in Fig. 7.25. The crystal structure of CrB is made up of independent layers of Cr atom prisms parallel to (010) with the prism axes running in the (100) direction. The prisms are centred by B atoms which form zigzag chains running in the (001) direction. This structure may also be considered as a development from the AlB2 in which the contiguous triangular prisms are separated into independent layers and displaced relative to each other by a/2, c/2 referred to the axes of the CrB cell (Pearson 1972). 7.4.2.5.2 FeB, oP8, structural type Orthorhombic, space group Pnma, N. 62. Atomic positions: 4B in (c) x, 1⁄4, z; –x 1⁄2, 3⁄4, z1⁄2; x–, 3⁄4, z–; – 1 1 3 1 4Fe in (c) x, ⁄4, z; x ⁄2, ⁄4, z ⁄2; x–, 3⁄4, z–;

x1⁄2, 1⁄4, –z 1⁄2 x1⁄2, 1⁄4, –z 1⁄2

668

Intermetallic Chemistry

For the prototype, FeB, a 549.5 pm, b 294.6 pm, c 405.3 pm and xB 0.036, zB 0.610, xFe 0.180, zFe 0.125. Environment data: B(c) CNE 9, 65.034.0 Fe(c) CNE 17, 46.025.124.123.122.121.215.214.013.2 Strukturbericht designation B27. In the FeB structures, Fe atoms form columns of triangular prisms (by each sharing two rectangular faces). The two, CrB and FeB, structures according to Parthé and Chabot (1984) can be considered as stacking variants of each other. Several ternary compounds, moreover, can be described as hybrid structures (periodic intergrowth structures) containing CrB and FeB segments. Notice, finally, that the CrB- and FeBtype structures may be considered as belonging to the same ‘coordination type’ (similar in coordination). According to Daams (1995) two structures are defined as pertaining to the same coordination type when the same atomic environments and the same number of atomic environments are realized. 7.4.2.6 AuCu(I), tP2, and AuCu(II), oI40, structural types (ordered derivatives in the Cu–Au system). As underlined by Okamoto et al. (1987), the Au–Cu system is one of the earliest systems for which several order–disorder transformations were established. A schematic representation of the equilibrium diagram is shown in Fig. 2.20 with an indication of the various phases formed in the solid state represented by a continuous solid solution phase, below the solidus, which on cooling tends to form several ordered phases. General indications about the structures of these phases are shown in Table 7.4. The structure of AuCu3 has been fully described in § 3.7.7 and 3.8.2 and the special case of the long-period structure of AuCu(II) (which has 1D substitutional and displacive modulations) has been shown in Fig. 3.41. tP2-AuCu(I) is tetragonal, space group P4/mmm, N. 123. Atomic positions: 1 Au in (a) 0, 0, 0; 1 Cu in (d) 1⁄2, 1⁄2, 1⁄2; For the prototype, AuCu(I), a 280.4 pm, c 367.3 pm, c/a 1.310. This structure is closely related to that of Cu. This is apparent from Fig. 3.12 where the relation between a small tetragonal cell (tP2 or tI2) and a larger (nearly cubic) cell is shown. The large cell has ac 280.4 2 396.5 pm and c c 367.3. It is similar to a Cu-type cell, slightly compressed (c/a 0.926) and in which the atoms placed in the centre of the side

669

Families of Intermetallic Structure Types: A Selection Table 7.4. Crystal structure data of Au–Cu alloys (after Okamoto et al. (1987). Phase Au–Cu hT solid solution Au3Cu AuCu (I) AuCu (II) AuCu3 (I) AuCu3 (II)

Composition at.% Cu

Pearson symbol prototype

Strukturbericht designation

0–100 10–38.5 42–57 38.5–63 67–81 66–?

cF4-Cu cP4-AuCu3 tP4-AuCu oI40-AuCu (II) cP4-AuCu3 tP28-PdCu3

A1 L12 L10 L12

tP2 AuCu (I) c/a = 1.31 Cu Au y x z=0

0.5

1

Figure 7.26. Section sequence parallel to the base plane of the tP2-AuCu (I) type structure. A tP4 pseudo-cell is outlined by dotted lines.

faces have been orderly substituted. The coordinates in the tP4 super(pseudo)cell (dotted lines in the layer sequence) are: 1 Au in (a) 0, 0, 0 1 Au in (c) 1⁄2, 1⁄2, 0 2 Cu in (e) 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2 and the corresponding square nets stacking sequence is Au10Au40Cu51/2. Environment data: Au (a) CNE 12, Au (c) CNE 12, Cu (e) CNE 12,

122.2 122.2 122.2

(8Cu. 4Au) (8Cu, 4Au) (8Au, 4Cu)

The section sequence of the tP2-AuCu (I) type structure is shown in Fig. 7.26. A special type of modulated superstructure (long-period superstructure) is known for AuCu (AuCuI) and results in the oI40-AuCu (II) type. This antiphase-domain structure has been discussed in § 3.11.1 (Fig. 3.41). 7.4.2.7 oS16-CeAl and oP16-DyAl structure types. The structures of the rare earth monoaluminides CeAl and DyAl can be considered together: parallel

670

Intermetallic Chemistry

pentagonal–triangular nets are important components of both structures. Notice, moreover, in the following descriptions the similarities between the coordinations and the values of CNE. 7.4.2.7.1 CeAl, oS16, structural type (and Na2AuAs-type structure) Ortho-rhombic, space group Cmcm, N. 63. Atomic positions: 1 1 4 Al in (b) 0, 1⁄2, 0; 0, 1⁄2, 1⁄2; ⁄2, 0, 0; ⁄2, 0, 1⁄2 – 1 3 1 1 1 1 4 Al in (c) 0, y, ⁄4; 0, y, ⁄4; ⁄2, y ⁄2, ⁄4; ⁄2, y–1⁄2, 3⁄4 – – – 1 3 1 8 Ce in (g) x, y, ⁄4; x , y, ⁄4; x , y, ⁄4; x, –y , 3⁄4 – – – x 1⁄2, y 1⁄2, 1⁄4; x 1⁄2, y 1⁄2, 3⁄4; x 1⁄2, y 1⁄2, 1⁄4; x 1⁄2, y– 1⁄2, 3⁄4 For the prototype, CeAl, a 927.0 pm, b 768.0 pm, c 576.0 pm and yAl(c) 0.79, xCe(g) 0.179, yCe(g) 0.161. Environment data: Al (b) CNE 12, 125.0 Al (c) CNE 10, 45.043.122.2 Ce (g) CNE 15, 75.026.024.123.113.212.2 A number of RAl compounds of the light rare earths have this structure. The Na2AuAs-type structure may be considered an ordered derivative structure (derivative of the second kind) of the CeAl type. In the same space group, in the same positions we have indeed: 4 Au in (b) 0, 1⁄2, 0; 4 As in (c) 0, y, 1⁄4 8 Na in (g) x, y, 1⁄4; x 1⁄2, y 1⁄2, 1⁄4;

0, 1⁄2,1⁄2; 0, –y , 3⁄4; –x , –y, 3⁄4; x– 1⁄2, y– 1⁄2, 3⁄4;

1 ⁄2, 0, 0; ⁄2; 0, 1⁄2 1 1 ⁄2, y 1⁄2, 1⁄4; ⁄2, –y 1⁄2, 3⁄4 –x , y, 1⁄4; x, –y , 3⁄4; – 1 1 1 x ⁄2, y ⁄2, ⁄4; x 1⁄2, y– 1⁄2, 3⁄4 1

a 887.1 pm, b 712.9 pm, c 576.0 pm and yAs(c) 0.213, xNa(g) 0.321, yNa(g) 0.349. Na2AuSb, K2CuP, K2CuAs, K2CuSb pertain to this structural type. 7.4.2.7.2 DyAl, oP16, structural type Orthorhombic, space group Pbcm N. 57. Atomic positions: 4 Al in (c) x, 1⁄4, 0; –x , 3⁄4, 1⁄2; –x , 3⁄4, 0; 4 Al in (d1) x, y, 1⁄4; –x , y–, 3⁄4; –x, y 1⁄2, 1⁄4; 4 Dy in (d2) x, y, 1⁄4; –x, –y, 3⁄4; –x, y 1⁄2, 1⁄4; 4 Dy in (d3) x, y, 1⁄4; –x, –y, 3⁄4; –x, y 1⁄2, 1⁄4;

x, 1⁄4, 1⁄2 x, y– 1⁄2, 3⁄4 x, y– 1⁄2, 3⁄4 x, y– 1⁄2, 3⁄4

Families of Intermetallic Structure Types: A Selection

671

For the prototype DyAl: a 582.2 pm, b 1136.9 pm, c 560.4 pm and xAl(c) 0.931; xAl(d1) 0.668, yAl(d1) 0.102; xDy(d2) 0.160, yDy(d2) 0.015; xDy(d3) 0.402, yDy(d3) 0.333. Environment data: Al (c) CNE 12, Al (d1) CNE 10, Dy (d2) CNE 15, Dy (d3) CNE 15,

125.0 45.043.122.2 75.026.024.123.113.212.2 75.026.024.123.113.212.2

7.4.2.8 FeSi, cP8, structural type Cubic, space group P213, N. 198. Atomic positions: 4 Fe in (a) x, x, x; x– 1⁄2, –x, x 1⁄2; 4 Si in (a) x, x, x; –x 1⁄2, –x, x 1⁄2;

–x, x 1⁄2, –x 1⁄2; –x, x 1⁄2, –x 1⁄2;

x 1⁄2, –x 1⁄2, –x x 1⁄2, –x 1⁄2, x–

For the prototype, FeSi, a 448.9 pm, xFe 0.137, xSi 0.842. Binary representatives of this structure are found among the Mn, Cr, Fe, Ru, Rh, Os monosilicides and germanides, Zr and Hf monoantimonides, AuBe and Al (or Ga) compounds with Pd and Pt. Ternary phases such as CrMnSi2, CrFeSi2, CrCoSi2, FeMnSi2 have been described. Environment data: Fe (a) CNE 13, Si (a) CNE 13,

65.046.034.0 95.036.013.0

Strukturbericht designation B20. 7.4.2.9 The tI8-NbAs type (and related structures) and the tI8-NbP type 7.4.2.9.1 NbAs, tI8, structural type Body-centred tetragonal, space group I41md, N. 109. Atomic positions 4 Nb in (a1) 4 As in (a2)

0, 0, z; 0, 0, z;

0, 1⁄2 , z 1⁄4; 0, 1⁄2, z 1⁄4;

⁄2, 1⁄2, z 1⁄2; 1 1 ⁄2, ⁄2, z 1⁄2; 1

⁄2, 0, z 3⁄4 1 ⁄2, 0, z 3⁄4 1

For the prototype, NbAs, a 345.2 pm, c 1168 pm, c/a 3.384 and zNb 0, zAs 0.416. Environment data: As (a) CNE 6, Nb (a) CNE 6,

61.2 61.2

(2Nb, 4Nb) (2As, 4As)

The section sequence of the tI8-NbAs type structure is shown in Fig. 7.27.

672

Intermetallic Chemistry tI8

NbAs

Nb

c/a = 3.38

As

y x z=0

0.17

0.25

0.42

0.5

0.67

0.75

0.92

1

Figure 7.27. Section sequence parallel to the base plane of the tI8-NbAs type structure.

The three structural types tI8-NbAs, tI8-AgTlTe2 and tI10-BaAl4 (with its ordered ternary variants such as the tI10-ThCr2Si2) belong to a group of interrelated structures. All these structures contain among their building parts layers of (metal atoms) triangular prisms with specific distributions of the (non-metal) atoms centring the prisms. The prisms are parallel to the basal planes of the tetragonal unit cells. Features of the hP2-WC type structure (characterized by an array of trigonal prisms alternatively centred by C atoms) are therefore present in the aforementioned structures. In the hP2-WC structure, of course, the prism axes are lying in the c direction of the hexagonal cell. Another convenient description of these group of structures may be in term of 44 net layer stacking. The corresponding square net symbols for the eight-layer stacks are the following: tI8-NbAs: Nb10 As20.17Nb30.25 As10.42Nb40.5 As30.67 Nb20.75 As30.92 tI8-AgTlTe2: Tl10 Te40.13 Ag30.25 Te10.37Tl40.5 Te10.63 Ag20.75 Te40.87 tI10-ThCr2Si2: Th10 Si40.13 Cr50.25 Si10.38 Th40.5 Si10.63 Cr50.75 Si40.88 Compare also with the description reported in § 7.5.1.3 and the schemes there shown. 7.4.2.9.2 NbP, tI8, structural type Body-centred tetragonal, space group I41/amd, N. 141. Atomic positions: 4 Nb in (a) 4 P in (b)

0, 0, 0; 0, 0, 1⁄2;

0, 1⁄2, 1⁄4; 0, 1⁄2, 3⁄4;

⁄2, 1⁄2, 1⁄2; ⁄2, 1⁄2, 0;

⁄2, 0, 3⁄4 ⁄2, 0, 1⁄4

1

1

1

1

For the prototype, NbP, a 332.5 pm, c 1138.0 pm, c/a 3.423. Environment data: Nb (a) CNE 4, P (b) CNE 4,

4-ring 4-ring

(4P) (4Nb)

673

Families of Intermetallic Structure Types: A Selection tI8 NbP c/a = 3.42 Nb

y x z=0

0.25

0.5

0.75

P

1

Figure 7.28. Section sequence parallel to the base plane of the tI8-NbP type structure.

The NbP structure corresponds to the NbAs type (previously described) in the special case that zNb 0 and zAs 1⁄2. The section sequence of the tI8-NbP type structure is shown in Fig. 7.28. 7.4.3 Remarks on structures of some 1:2 compounds 7.4.3.1 Introduction. The 1:2 stoichiometry is frequently found in binary and complex intermetallic phases, both as the formula of a point compound or as a reference composition within a range of solid solutions (see the histogram reported in Fig. 7.1). Several structural types have been described for 1:2 phases often corresponding to quite different bonding mechanisms and packing conditions. An important group of phases pertaining to this stoichiometry are, for instance, the cF12-CaF2 type (and antitype) phases which however include a number of intermetallic alloys and several ionic compounds. In a comparison between compounds having 1:2 stoichiometry with 1:1 compounds, the CaF2-type structure may be related to the CsCl type. In the CaF2 structure there are CaF8 cubes which share all edges. Similar CsCl8 cubes are present in the CsCl structure, however they all share faces. Different structural characteristics and properties may be found in another very important group of intermetallic 1:2 phases frequently formed in alloy systems: these are the so-called Laves phases, which include three main structural prototypes (hP12-MgZn2, cF24-Cu2Mg and hP24-Ni2Mg) with several derivative types all pertaining to the large ‘family’ of tetrahedrally close-packed structures. These phases and their structures have been previously discussed at length (§ 3.9.3.1); only a short mention is given here. A few other 1:2 structures are described in this paragraph in order also to discuss some general question relevant to intermetallic chemistry. Attention is given for instance to the numerous group of phases which pertain to the interrelated structural types tI12-αThSi2 and hP3-AlB2 or to their derivative structures. A large number of AlB2-derivative structures are known, and a short list of them may be useful to present the variety of characteristics and of peculiar structural details often observed within schematically similar groups of alloys. In conclusion of this section an example will be reported of a family of compounds having (in a composition range close to 1:2) a sequence of progressively

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Intermetallic Chemistry

changing stoichiometries, corresponding to a variety of gradual changes in the structural atomic arrangements. 7.4.3.2 CaF2 type (and its ordered AgMgAs-derivative structure) 7.4.3.2.1 CaF2 , cF12, structural type – Face-centred cubic, space group Fm3 m, N. 225. Atomic positions: 4 Ca in (a) 8 F in (c)

0, 0, 0; ⁄4, 1⁄4, 1⁄4; 3 1 3 ⁄4, ⁄4, ⁄4; 1

0, 1⁄2, 1⁄2; ⁄4, 1⁄4, 3⁄4; 3 1 1 ⁄4, ⁄4, ⁄4; 1

⁄2, 0, 1⁄2; ⁄4, 3⁄4, 3⁄4; 3 3 1 ⁄4, ⁄4, ⁄4;

⁄2, 1⁄2, 0 ⁄4, 3⁄4, 1⁄4; 3 3 3 ⁄4, ⁄4, ⁄4

1

1

1

1

For the prototype, CaF2, a 546.3 pm. Coordination formula: 333 [Ca12/12] [F6/6]8/4 Environment data: Ca (a) CNE 8, F (c) CNE 10,

80.3 66.043.0

(8F) (4Ca, 6F)

As pointed out in the description of the cubic close-packed structure (cF4-Cu type), this structure may be described (especially for certain values of the atomic diameter ratio) as a derivative of the Cu-type structure in which two sets of tetrahedral holes have been filled-in. Strukturbericht designation C1. A ternary ordered derivative variant of this structure is the cF12-AgMgAs type (Strukturbericht designation C1b). 7.4.3.2.2 AgMgAs, cF12, structural type – Face-centred cubic, space group F43m, N. 216. Atomic positions 1 4 As in (a) 0, 0, 0; 0, 1⁄2, 1⁄2; ⁄2, 0, 1⁄2; 1 1 1 1 3 3 3 1 3 4 Ag in (c) ⁄4, ⁄4, ⁄4; ⁄4, ⁄4, ⁄4; ⁄4, ⁄4, ⁄4; 3 3 3 3 1 1 1 3 1 4 Mg in (d) ⁄4, ⁄4, ⁄4; ⁄4, ⁄4, ⁄4; ⁄4, ⁄4, ⁄4;

⁄2, 1⁄2, 0 ⁄4, 3⁄4, 1⁄4 1 1 3 ⁄4, ⁄4, ⁄4 1 3

For the prototype, AgMgAs, a 624 pm. The structure has often been described with an origin shift and also with reference to LiAlSi as prototype. The structure is an ordered derivative of the cF12-CaF2 type. Each of the three elements forms a face cubic array (F F F ; see § 3.7.1).

675

Families of Intermetallic Structure Types: A Selection

Environment data: As (a) CNE 8, Ag (c) CNE 10, Mg (d) CNE 10,

80.3 66.043.0 66.043.0

(1Mg, 3Ag, 3Mg, 1Ag) (4As, 6Mg) (4As, 6Ag)

The section sequence scheme of the CaF2 and AgMgAs types are shown in Fig. 7.29. The layer stacking symbols of the two structures are the following: Triangular nets: CaF2: AgMgAs:

A A Ca A0 FB1/12 F1/4 CaB1/3 FC5/12 FB7/12CaC2/3 F3/4 FC11/12 AsA0 MgB1/12 AgA1/4As B1/3 MgC5/12 AgB7/12AsC2/3 MgA3/4 AgC11/12

Square (S) nets: CaF2: Ca10 Ca40 F61/4 F71/4 Ca51/2 F63/4 F73/4 AgMgAs: As10 As40 Ag61/4 Mg71/4 As51/2 Mg63/4 Ag73/4 As for the CaF2-type structure, several more or less ionic compounds such as CeO2, UO2, ThO2, etc. belong to this type. Several Me2X compounds, with Me Li, Na, K, X O, S, Se, Te, Po, also belong to this type. In this case, however, the cation and anion positions are exchanged, with Me in (c) and X in (a) and these compounds are sometimes referred to as CaF2 antitype. Typical (more metallic) phases having this structure are also, for instance, AuAl2, PtAl2, Mg2Pb, Mg2Sn, Mg2Ge, Mg2Si.

cF12 Ca

CaF2 F

y x

cF12 Mg

AgMgAs As

y x z=0

0.25

0.5

0.75

1

Figure 7.29. Section sequences parallel to the base plane of the cF12 CaF2- and AgMgAs-type structures.

Ag

676

Intermetallic Chemistry

As for the AgMgAs type, in a systematic investigations of MeTX ternary alloys (Me Th, U, rare earth metals, etc., T transition metal, X element from the V, IV main groups) scores of phases pertaining to this structure type have been identified. For the same group of alloys, however, other structural types are also frequently found. The hP6-CaIn2 type and its derivative types often represent a stable alternative. The relative stabilities of the two structures (especially as a function of the atomic dimensions of the metals involved) have been discussed, for instance, by Dwight (1974), Marazza et al. (1980, 1988), Wenski and Mewis (1986). 7.4.3.3 Laves phases. A very large number of intermetallic (binary and complex) alloys both point compounds and solid solution phases pertain to the family of the Laves phases. The structures considered as reference types for this group of alloys and ideally having a 1:2 composition correspond to the hP12-MgZn2, cF24-Cu2Mg and hP24-Ni2Mg types. General features of these phases, and of a number of their variants, have been presented in § 3.9.3.1 and were there described in the framework of a family of tetrahedrally close-packed homeotect structures (see also § 3.9.2.3). The conventional crystal structure descriptions (summarized in Table 3.7) of these types are presented in the following, together with some figures showing typical sections and projections. 7.4.3.3.1 MgZn2, hP12, structural type (and ordered derivative U2OsAl3, hP12, type) Hexagonal, space group P63/mmc, N. 194. Atomic positions: 2 Zn in (a) 0, 0, 0; 0, 0, 1⁄2 1 2 2 4 Mg in (f) ⁄3, ⁄3, z; ⁄3, 1⁄3, z 1⁄2; 2⁄3, 1⁄3, –z ; 1⁄3, 2⁄3, –z 1⁄2 6 Zn in (h) x, 2x, 1⁄4; 2x–, –x, 1⁄4; x, –x , 1⁄4; –x, 2x–, 3⁄4; 2x, x, 3⁄4; –x , x, 3⁄4; For the prototype, MgZn2, a 517.0 pm, c 850.0 pm, c/a 1.640 and zMg 0.062, xZn 0.830. Coordination formula: 333 [Mg4/4][Zn6/6]12/6 Environment data: Zn (a) CNE 12, 125.0 Mg (f) CNE 16, 125.046.0 Zn (h) CNE 12, 125.0

(6Zn, 6Mg) (3Zn, 6Zn, 3Zn, 3Mg, 1Mg) (2Zn, 2Zn, 2Zn, 4Mg, 2Mg)

Layer stacking symbols, triangular, kagomé (T,K) nets: ZnA0 MgB0.06 Znβ0.25 MgB0.44 ZnA0.50 MgC0.56 Znγ0.75MgC0.94 Strukturbericht designation C14.

677

Families of Intermetallic Structure Types: A Selection cF24

Cu2Mg

0

0.125

0.25

0.375

0.625

0.75

0.875

1

Mg

Cu

y x

0.5

(z )

Figure 7.30. Section sequence parallel to the base plane of the cF24-Cu2Mg type structure.

A ternary ordered variant of this structure corresponds to three different atomic species in the three equipoint set. For instance: hP12-U2OsAl3 (2 Os in (a), 4 U in (f ) and 6 Al in (h)). 7.4.3.3.2 Cu2Mg, cF24, structural type (and ordered derivatives cF24Cu4MgSn and cF24-AuBe5) – Face-centred cubic cF24-Cu2Mg, space group Fd3m, N. 227. Atomic positions: (0, 0, 0; 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0) 8 Mg in (a) 0, 0, 0; 3⁄4, 1⁄4, 3⁄4; 5 5 5 16 Cu in (d) ⁄8, ⁄8, ⁄8; 3⁄8, 7⁄8, 1⁄8; 7⁄8, 1⁄8, 3⁄8; 1⁄8, 3⁄8, 7⁄8; For the prototype, Cu2Mg, a 699.0 pm. Coordination formula: 333 [Mg4/4][Zn6/6]12/6 Environment data: Mg (a) CNE 16, Cu (d) CNE 12,

125.046.0 125.0

(12Cu, 4Mg) (6Cu, 6Mg)

The section sequence of the cF24-Cu2Mg type structure is shown in Fig. 7.30. Face-centred cubic cF24-Cu4MgSn and cF24-AuBe5 Ordered variants of the Cu2Mg type of structure are the Cu4MgSn-type structure and the AuBe5-type structure. The atomic positions of the two structures correspond to – the following occupation of the same equipoints in the space group F43m, N. 216.

678

Intermetallic Chemistry cF24

Cu4MgSn

0

0.125

0.25

0.375

0.625

0.75

0.875

1

Mg

Cu

Sn

y x

0.5

(z )

Figure 7.31. Section sequence parallel to the base plane of the cF24-Cu4MgSn type structure.

Equivalent positions: (a) (c) (e)

0, 0, 0; ⁄4, 1⁄4, 1⁄4; x, x, x; x–, x, x–; (x 0.625 5/8) 1

(0, 0, 0;

0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0) in Cu4MgSn in AuBe5 4 Sn 4 Au 4 Mg 4 Be –x , –x , x; 16 Cu 16 Be x, x–, x–;

Notice that, even if with a different description, the same sets of positions are all involved in the three structures. We can see that the eight atom equipoint of the Cu2Mg-type structure has been subdivided into two different, ordered, four point – – subsets in the two derivative structures passing from Fd3m to F43 m space group. A comparison with other types of Laves phases may be conveniently made in terms of stacking of similar slabs formed by three 36 nets of atoms followed by a 3636 net as summarized in §.3.9.2.3. The section sequence of the cF24-Cu4MgSn type structure is shown in Fig. 7.31. As for the three cubic structures here presented, their layers stacking symbols in terms of triangular and kagomè (T,K) nets are: MgA0Cuα0.13MgA0.25CuC0.29MgB0.33Cuβ0.46MgB0.58CuA0.63MgC0.67 Cuγ0.79MgC0.92CuB0.96 γ Cu4MgSn: MgA0Cuα0.13SnA0.25CuC0.29MgB0.33Cuβ0.46SnB0.58CuA0.63MgC0.67 Cu 0.79SnC0.92 CuB0.96 Cu2Mg:

679

Families of Intermetallic Structure Types: A Selection

AuBe5:

Au A0 Be α0 . 1 3 Be A0 . 2 5 BeC0 . 2 9 Au B0 . 3 3 Be β0 .46 Be 0B . 58 Be A0 . 63 AuC0 . 6 7 γ Be 0.79BeC0.92BeB0.96

Strukturbericht designation Cu2Mg: C15, AuBe5: C15b. An interesting comparison may be finally made between the intermetallic Cu2Mg structure type and the MgAl2O4 type. This is the representative of the spinel family of oxide minerals in which the presence of oxide anions can be assumed. A shortened description of the cF56-MgAl2O4 type structure is reported in this chapter (in § 7.6.9); its layer sequence shown here may be compared with that of the Cu2Mg type: we may notice that the oxygen atoms form a face-centred cubic arrangement and the Mg and Al atoms (inserted inside oxygen tetrahedra and octahedra) form, as a partial structure, the structure of the Cu2Mg-type Laves phase. This is a case in which the cation distribution (in the oxide) is isotypic with the complex structure of an intermetallic phase. Various examples of oxides described as stuffed alloys have been mentioned by Nesper (1991), see § 7.6.9. 7.4.3.3.3 Ni2Mg, hP24, structural type Hexagonal, space group P63/mmc, N. 194. Atomic positions: 4 Mg in (e) 4 Mg in (f ) 4 Ni in (f ) 6 Ni in (g) 6 Ni in (h)

0, 0, z; 1 ⁄3, 2⁄3, z; 1 ⁄3, 2⁄3, z; 1 ⁄2, 0, 0; x, 2x, 1⁄4;

0, 0, z 1⁄2; 2 ⁄3, 1⁄3, z 1⁄2; 2 ⁄3, 1⁄3, z 1⁄2; 0,1⁄2, 0; 2x–, x–, 1⁄4;

0, 0, –z ; 2 ⁄3, 1⁄3, –z; 2 ⁄3, 1⁄3, –z ; 1 1 ⁄2, ⁄2, 0; x, x–, 1⁄4;

0, 0, –z 1⁄2 1 ⁄3, 2⁄3, –z 1⁄2 1 ⁄3, 2⁄3, –z 1⁄2 1 ⁄2, 0, 1⁄2; – x , 2x–, 3⁄4;

0,1⁄2,1⁄2; 2x, x, 3⁄4;

⁄2, 1⁄2, 1⁄2 – x , x, 3⁄4 1

For the prototype, Ni2Mg, a 482 pm, c 1583 pm, c/a 3.284 and zMg(e) 0.094, zMg(f) 0.8442, zNi(f ) 0.1251, xNi(h) 0.1643. The structure can be described by the following layer stacking sequence triangular and kagomé (T,K) nets: γ Niα0MgA0.09NiB0.13MgC0.16Ni 0.25MgC0.34NiB0.37MgA0.41Niα0.50MgA0.59NiC0.63MgB0.66Niβ0.75 MgB0.84NiC0.87MgA0.91 Environment data: Mg (e) CNE 16, Mg (f ) CNE 16, Ni (f ) CNE 12, Ni (g) CNE 12, Ni (h) CNE 12,

125.046.0 125.046.0 125.0 125.0 125.0

(3Ni, 6Ni, 3Ni, 3Mg, 1Mg) (3Ni, 6Ni, 3Ni, 3Mg, 1Mg) (3Ni , 3Ni, 6Mg) (4Ni, 2Ni, 6Mg) (2Ni, 4Ni, 6Mg)

Coordination formula: 333 [Mg4/4][Ni6/6]12/6 Strukturbericht designation C36.

680

Intermetallic Chemistry

7.4.3.4 tI6-CaC2 and MoSi2-type structures 7.4.3.4.1 CaC2, tI6, structural type Body centred tetragonal, space group I4/mmm, N. 139. Atomic positions: 2 Ca in (a) 0, 0, 0; 4 C in (e) 0, 0, z;

⁄2, 1⁄2, 1⁄2 0, 0, –z ; 1

⁄2, 1⁄2, z 1⁄2;

1

⁄2, 1⁄2, –z 1⁄2

1

For the prototype, CaC2, a 389 pm, c 638 pm, c/a 1.640 and zC 0.4068. Strukturbericht designation C11a. Typical compounds pertaining to this structural type are dicarbides of Ca, Sr, Ba, rare earths, Pa, Th, U, dioxides of K, Rb, Ca, Sr, Ba. A comparison with the tI6-MoSi2 structure (Strukturbericht type C11b) may be useful. In CaC2, Ca and C are, respectively, in the same Wyckoff positions as Mo and Si in MoSi2 (in the same space group I4/mmm). The unit cell dimensions, however, correspond to different axial ratios (c/a 1.640 in CaC2 instead of 2.452 as in MoSi2) and the free parameter z has the value 0.4068 (instead of 0.333). These differences result in two different space arrangements (see also § 3.6.2 and Fig. 3.7). Diatomic groups, such as C2, clearly evident in CaC2 (and in a number of isostructural dicarbides and peroxides) are not formed in MoSi2. 7.4.3.4.2 MoSi2, tI6, structural type Tetragonal, space group I4/mmm, N. 139. Atomic positions: 2 Mo in (a) 4 Si in (e)

0, 0, 0; 1⁄2, 1⁄2, 1⁄2 0, 0, z; 0, 0, –z

⁄2, 1⁄2, z 1⁄2;

1

⁄2, 1⁄2, –z 1⁄2

1

For the prototype, MoSi2, a 320.6 pm, c 784.6 pm, c/a 2.4447 and zSi(e) 0.333. Environment data: Mo (a) Si (e)

CNE 14, CNE 14,

84.142.224.0 42.342.140.318.010.4

Strukturbericht designation C11b. The section sequences of the tI6-MoSi2 and tI6-CaC2 type structures are shown in Fig. 7.32. 7.4.3.5 oI12, CeCu2 and KHg2 structural descriptions (an exercise on isotypism and ‘normalization’ of crystal structure data). The crystal structure of these isotypic compounds (either oI12-CeCu2 or oI12-KHg2 type) is a derivative structure of the hP3-AlB2 type, a distortion of the hexagon mesh layers of which results in

681

Families of Intermetallic Structure Types: A Selection

y x 0 0 0 0

0.17 131 0.09 57

0.33 262 0.41 260

0.5 393 0.5 319

0.67 523 0.59 378

0.83 654 0.91 581

1 785 1 638

ZMoSi2 d/pm MoSi2 ZCaC2 d/pm CaC2

Figure 7.32. Crystal structures of MoSi2 (c/a 2.445) and CaC2 (c/a 1.640). The similar characteristic sequences of the structure sections (4 2 adjacent unit cells) are compared. Notice that the different c/a values and the different heights of the atomic planes (d/pm) result in different structural arrangements.

an orthorhombic symmetry (see AlB2). The CeCu2 and the KHg2 structures correspond to the same type even if in the original presentations of their structures, as well as in many subsequent compilations, different descriptions were reported. It may be a useful exercise to recall the two original different descriptions and see how they may be reduced to the same one. 7.4.3.5.1 CeCu2 vs. KHg2 the original structural description as oI12-CeCu2 type CeCu2, body-centred orthorhombic, space group Imma, N. 74. Atomic positions: (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) 4 Ce in (e) 0, 1⁄4, z; 0, 3⁄4, z– 8 Cu in (h) 0, y, z; 0, y– 1⁄2, z; 0, y 1⁄2, –z ; 0, –y, –z For the prototype, CeCu2, a 443.0 pm, b 705.0 pm, c 745.0 pm and zCe 0.5377 yCu 0.0510, zCu 0.1648. This structure type has been described as a member of the AlB2 structure family. The structure of KHg2 may be recognized as isotypic with that of CeCu2, even if this is not immediately apparent from the data (axes orientation, positional parameters) reported in the original structure determinations and, consequently, in various compilations. See a few comments in the following. 7.4.3.5.2 KHg2 vs. CeCu2 the original structural description as oI12, KHg2 type KHg2, body-centred orthorhombic, space group Imma, N. 74. Atomic positions: (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) 0, 3⁄4, –z 4 K in (e) 0, 1⁄4, z; x–, 1⁄4, z; x–, 3⁄4, –z ; x, 3⁄4, –z 8 Hg in (i) x, 1⁄4, z;

682

Intermetallic Chemistry

b c Ce

y=0 y = 0.5

Cu

y=0 y = 0.5

K

y=0 y = 0.5

Hg

y=0 y = 0.5

a c

Figure 7.33. A comparison between the structures of CeCu2 and KHg2. For the two compounds projections (of four cells) are shown, according to the original descriptions of the two structures. Notice that by a convenient axis exchange and origin shift a new cell may be identified in KHg2 (dashed lines) which is identical with that of CeCu2.

Families of Intermetallic Structure Types: A Selection

683

For the prototype, KHg2, a 810.0 pm, b 516.0 pm, c 877.0 pm and zK 0.703, xHg 0.190, zHg 0.087. The data quoted above (unit cell edges, positional parameters) are those given in the original structure determination and reported in compilations such as the Atlas of Crystal Structure Types (Daams et al. 1991). From a comparison of this numerical data with those previously reported for CeCu2 it is not immediately apparent that the two structures are isotypic. This, however, could be recognized after drawing and comparing the two atomic arrangements (see the sketches shown in Fig. 7.33). In a simpler way this may be checked by a re-description of the KHg2 cell in terms of a CeCu2-type cell. This can be done by applying to the descriptions of all the atomic positions (to their coordinates) a set of transformations which, of course, should be compatible with the symmetry characteristics of the space group concerned. In the specific case these transformation include an axis interchange and a shift of the origin of the coordinate system (of the unit cell). The reader interested in performing such a crystallography exercise should carry out the following sequence of arithmetic operations: (i) Preparation of the complete list of all the 12 atomic positions with the numerical values of x, y and z as obtained from the data previously reported for KHg2. (ii) Interchange the parameters x and y in all the positions listed. In the unit cell description reported for KHg2 we have the edges in the order b a c, whereas for CeCu2 we have a b c: in this case, owing to the symmetry elements of the structure any alternative labelling of the axes is possible. To be coherent with the criterion adopted for CeCu2 we have to interchange the a and b axes and, therefore the x and y parameters. (iii) Addition of 1⁄4, 1⁄4, 1⁄4 to all the 12 atomic positions: this correspond to the shift of the origin needed to superimpose the description of the KHg2 to that of CeCu2. The atomic position list so obtained for KHg2 is indeed practically identical to that which can be built for CeCu2 from its original data. In view of the many possibilities of describing a crystal structure, the ‘normalization’ of crystal structure data (that is the obtainment of their standardized presentation) is not always a simple procedure. For this reason a computer programme (STRUCTURE TIDY) has been written which will standardize data (Parthé and Gelato 1984). 7.4.3.6 Co2Si (PbCl2 ), oP12, and TiNiSi, oP12, structural types. Orthorhombic, space group Pnma, N. 62. In these structural types the atoms are distributed in three groups of positions corresponding (obviously with different values of the x and z free parameters) to the same type of Wyckoff positions (Wyckoff position c).

684

Intermetallic Chemistry oP12 TiNiSi

Ti

Ni

Si

c a

y = 0.25

y = 0.75

Figure 7.34. Projection of four cells of the oP12-TiNiSi type structure.

Atomic positions: (c1) x, 1⁄4, z; x–, 3⁄4, –z ; (c2) x, 1⁄4, z; x–, 3⁄4, –z ; (c3) x, 1⁄4, z; x–, 3⁄4, –z

x– 1⁄2, 3⁄4, z 1⁄2; x 1⁄2, 1⁄4, –z 1⁄2; x– 1⁄2, 3⁄4, z 1⁄2; x 1⁄2, 1⁄4, –z 1⁄2; x– 1⁄2, 3⁄4, z 1⁄2; x 1⁄2, 1⁄4, –z 1⁄2;

in Co2Si 4 Co

in TiNiSi 4 Ti

4 Co

4 Ni

4 Si

4 Si

Environment data (Co2Si): Co (c1) CNE 13, 62.225.024.123.116.0 Co (c2) CNE 13, 62.244.125.014.0 Si (c3) CNE 10, 45.043.122.2 The coordination formula is: 3 [SiCo6/5Co4/5], that is total coordination 10 of Co around Si with: 6/5 4/5 10/5 2 Co atoms for each Si atom. A ternary derivative of this type is the oP12-TiNiSi type (prototype of the so-called E phases). For the prototypes: Co2Si: a 491.8 pm, b 373.8 pm, c 710.9 pm, a/c 0.692; xc(1) 0.038, zc(1) 0.782; xc(2) 0.174, zc(2) 0.438; xc(3) 0.702, zc(3) 0.389. TiNiSi: a 614.84 pm, b 366.98 pm, c 701.73 pm, a/c 0.876; xc(1) 0.0212, zc(1) 0.8197; xc(2) 0.1420, zc(2) 0.4391; xc(3) 0.7651, zc(3) 0.3771. This structure is a distortion of the Ni2In type which is described in § 7.4.3.14 together with a AlB2-derivative structure family. The cell projection of the oP12-TiNiSi structure is shown in Fig. 7.34.

Families of Intermetallic Structure Types: A Selection

685

Co2Si is the prototype of a group of phases (also called PbCl2 type) which can be subdivided into two sets according to the value of the axial ratio a/c which is in the range from 0.67 to 0.73 for one set (for instance, Co2Si, PdAl2 , ZrAl2, Rh2Ge, Pd2Sn, Rh2Sn, etc.) and in the range from 0.83 to 0.88 for the other set (for instance PbCl2, BaH2(h), Ca2Si, Ca2P, GdSe2, ThS2, TiNiSi, etc.). The ternary variant TiNiSi type is also called E-phase structure. Many ternary compounds belonging to a MeTX formula (Me rare earth metal, Ti, Hf, V, etc., T transition metal of the Mn, Fe, Pt groups, X Si, Ge, Sn, P, etc.) have this structure. Strukturbericht designation C23. 7.4.3.7 CuAl2, tI12, structural type Body-centred tetragonal, space group I4/mcm, N. 140. Atomic positions: (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) 4 Cu in (a) 0, 0, 1⁄4; 0, 0, 3⁄4 1 8 Al in (h) x, x ⁄2, 0; x–, x–1⁄2, 0; x–1⁄2, x, 0;

x1⁄2, x–, 0

For the prototype: a 606.3 pm, c 487.2 pm, c/a 0.804 and xAl 0.1541. Environment data: Cu (a) CNE 10, Al (h) CNE 15,

85.024.0 45.044.143.136.0

Strukturbericht designation C16. This structure, according to Pearson (1972), is included within a group of structures generated by square-triangle nets of atoms. In particular the CuAl2-type structure is made up of 32 434 nets of Al atoms at z 0 and z 1⁄2 which are oriented anti-symmetrically relative to each other; the squares of these layers are centred by the Cu atoms of the nets at z 1⁄4 and 3⁄4. Examples of other structure types included by Pearson within those characterized by 32 434 nets of atoms are: oP16-CdSb, tI16-TlSe, tP30-Tl2Se, oP24-AuSn2, tI48-PdSn2, oS32-PdSn3, oS24-CoGe2, mS12-PdP2 (NiP2), tP16-CoGa3 (FeGa3), oS32- and tI64-ZnAu3 (R2 and R1 phases), oP16-Fe3C, tP10-PtPb4, oS20-PtSn4, tI24-PdGa5, oP36-Sm5Ge4, tI32-Cr5B3, mP22-Co2Al9. Details about the tI32Cr5B3 and the oP16-Fe3C types are given in the specific paragraphs of this chapter. 7.4.3.8 Cu2Sb, tP6, structural type Tetragonal, space group P4/nmm, N. 129. Atomic positions: 2 Cu in (a) 0, 0, 0; 1⁄2, 1⁄2, 0 2 Cu in (c) 0, 1⁄2, z; 1⁄2, 0, –z 2 Sb in (c) 0, 1⁄2, z; 1⁄2, 0, –z For the prototype, Cu2Sb, a 399.2 pm, c 609.1 pm, c/a 1.526 and zCu 0.270, zSb 0.700.

686

Intermetallic Chemistry

Environment data: Cu (a) CNE 12, Cu (c) CNE 9, Sb (c) CNE 9,

44.143.142.2 45.043.114.0 45.043.114.0

Strukturbericht designation C38. Typical compounds pertaining to the tP6-Cu2Sb type structure are: AmS2, AmSe2, AmTe2, CmS2, CmSe2, CmTe2, PaAs2, ThAs2, ThSb2, ThBi2, UAs2, USb2, UBi2, NpAs2, several rare earth disulphides (selenides, tellurides), and Mn2As, Mn2Sb, Cu2As, etc. A ternary variant of the Cu2Sb-type structure is represented by ZrSiSe corresponding to the following atomic positions: 2 Si in (a) 2 Zr in (c) 2 Se in (c)

0, 0, 0; 0, 1⁄2, z; 0, 1⁄2, z;

⁄2, 1⁄2, 0 ⁄2, 0, z– 1 ⁄2, 0, z– 1

1

For ZrSiSe, a 362.4 pm, c 836.0 pm, c/a 2.307 and zZr 0.257, zSe 0.622. 7.4.3.9 Fe2 P, hP9, structural type – Hexagonal, space group P6 2m, N. 189. Atomic positions: 1 P in (b) 0, 0,1⁄2 1 2 2 P in (c) ⁄2, 2⁄3, 0; ⁄3, 1⁄3, 0 3 Fe in (f) x, 0, 0; 0, x, 0; –x, –x , 0 –x, –x ,1⁄2 1 3 Fe in (g) x, 0, ⁄2; 0, x,1⁄2; For the prototype, a 586.5 pm, c 345.6 pm, c/a 0.589 and x(f) 0.256, x(g) 0.594. Environment data: P (b) CNE 9, P (c) CNE 9, Fe (f ) CNE 12, Fe(g) CNE 18,

65.034.0 65.034.0 64.125.024.023.1 74.064.128.027.012.2

Strukturbericht designation C22. In the Fe2P-type structure there are four different groups of equipoints. The distribution of P and Fe atoms in different groups of positions is reported. A number of isostructural binary compounds are known. To the same structure, however, ternary or even more complex phases may be related if different atomic species are distributed in the different sites. This structure can be considered as an example of more complex structures built up by linked triangular prisms of Fe atoms.

Families of Intermetallic Structure Types: A Selection

687

Several ordered ternary phases have structures related to the Fe2P type. A distinctive feature of this structure, indeed, is that both Fe (in (f) and (g)) and P (in (b) and (c)) occupy two sites. Thus many mixed, but ordered, compositions are possible in higher-order compounds (Chen and Corbett 2004). Derivative ordered intermetallics with two metals in the Fe sites are common (ZrNbP, RAgGe with R Y, Sm, Gd, … Lu). Compounds in which the two P sites are distinguished in their occupation may be represented by Zr6CoAl2 and several R6TX2 phases (with R Sc, Y, Dy, etc., T late transition metal, X Te, Sb). Ternary germanides LnAgGe (Ln Y, Sm, Gd–Lu) with an ordered Fe2P-type structure have been described by Gibson et al. (1996). 7.4.3.10 TiSi2, oF24, structural type Face-centred orthorhombic, space group Fddd, N. 70. Atomic positions: (0, 0, 0; 0, 1⁄2 , 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0) 8 Ti in (a) 0, 0, 0; 1⁄4, 1⁄4, 1⁄4; –x 1⁄4, 1⁄4, 1⁄4; x 1⁄4, 1⁄4, 1⁄4 16 Si in (e) x, 0, 0; –x , 0, 0; For the prototype, TiSi2, a 823.6 pm, b 477.3 pm, c 852.3 pm and xSi 0.333. Environment data: Ti (a) CNE 14, Si (e) CNE 14,

83.241.224.0 72.241.320.316.0

Strukturbericht designation C54. 7.4.3.11 UPt2, oS12, structural type. Orthorhombic, space group Ama2. N. 40. Atomic positions: (0, 0, 0; 0, 1⁄2, 1⁄2) 4 Pt in (a) 0, 0, z; 1⁄2, 0, z 4 Pt in (b) 1⁄4, y, z; 3⁄4, –y , z 4 U in (b) 1⁄4, y, z; 3⁄4, y–, z For the prototype, UPt2, a 560.0 pm, b 968.0 pm, c 412.0 pm and zPt(a) 0.0, yPt(b) 0.38, zPt(b) 0.0, yU(b) 0.17, zU(b) 0.50. 7.4.3.12 MoPt2, oI6, structural type Orthorhombic, space group Immm, N. 71. Atomic positions: (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) 2 Mo in (a) 0, 0, 0 4 Pt in (g) 0, y, 0;

0, –y , 0

For the prototype, MoPt2,: a 276.5 pm, b 829.6 pm, c 393.8 pm, y 0.353.

688

Intermetallic Chemistry

It is a close-packed superstructure based on a face-centred cubic pseudo-cell. Distorted close-packed triangular layers are stacked in close-packed ABC sequence. 7.4.3.13 FeS2, cP12, structural type (pyrite) – Cubic, space group Pa3 , N. 205. Atomic positions: 4 Fe in (a) 0, 0, 0; 1⁄2, 0, 1⁄2; 0, 1⁄2, 1⁄2; 1⁄2, 1⁄2, 0 – 1 – 1 8 S in (c) x, x, x; x ⁄2, x , x ⁄2; x–, x 1⁄2, x– 1⁄2; x 1⁄2, x– 1⁄2, x–; x– x– x–; x1⁄2, x, x– 1⁄2; x, x– 1⁄2, x 1⁄2; x– 1⁄2, x 1⁄2, x; For the prototype, FeS2, a 540.4 pm, xS(c) 0.384. In the FeS2 (pyrite), cP12, structure, the Fe atoms form a face-centred cubic array, the S atoms are arranged in pairs across the midpoints of the cell edges and the cell centre. The structure can (formally) be regarded as a NaCl type in which Na atoms are replaced by Fe and Cl by pairs of S atoms aligned at an angle to the axes directions. Fe is surrounded octahedrally by 6 S atoms, S is tetrahedrally surrounded by 3Fe1S. Notice that pyrite, cP12, is the β-FeS2 form, high-temperature (T 425°C) form, the α-FeS2 modification (room temperature form) is marcasite (oP6). 7.4.3.14 The AlB2, hP3, type and its structural family 7.4.3.14.1 AlB2, hP3, structural type Hexagonal, space group P6/mmm, N. 191. Atomic positions 1 Al in (a) 0, 0, 0; 2 B in (d) 1⁄3, 2⁄3, 1⁄2; 2⁄3, 1⁄3, 1⁄2 For the prototype, a 300.0 pm, c 324.5 pm, c/a 1.0817. Coordination formula: 323 [Al8/8][B3/3]12/6 Environment data: Al (a) CNE 20, 121.264.220.6 B (d) CNE 9, 65.034.0

(12B, 6Al, 2Al) (3B, 6Al)

Compare these data with those reported for the tI12-ThSi2 type which belongs to the same ‘coordination type’. The Strukturbericht designation is C32. The AlB2-type structure can be considered a filled-up WC structure type. The B atoms form a hexagonal net and centre all the Al trigonal prisms. The arrangement of the boron atoms in their layers is the same as that of carbon in graphite (63 layers). (See also the αThSi2, tI12, description for a comparison between the planar

Families of Intermetallic Structure Types: A Selection

689

graphitic net and similar 3D networks.) Aluminium atom layers with triangular mesh (36) alternate with the B layers. Several B, Si, Ge, Ga, etc., binary and ternary compounds have been described as pertaining to this structure or, possibly, to its variants (many of them deficient in the second component and corresponding to different stoichiometries in the 1:2 to 1:1.5 range). The axial ratio of phases with this structure varies between very wide limits. The relationships between axial ratio, atomic radius ratio of the elements involved and the role of the different bonds have been discussed by Pearson (1972). In the specific case of AlB2 (c/a 1.08) the important role of the graphite-like net of B atoms in determining the phase stability has been evidenced. Finally, while considering the structural characteristics of the AlB2-type phases, it is found that boron-centred triangular metal prisms are the dominating structural building elements in the crystal structures of simple and complex metal borides. Building blocks of centred triangular prisms as base units for classification of these substances have been considered by Rogl (1985, 1991) in a systematic presentation of the crystal chemistry of borides. We may mention here, also as an example of ‘modular’ description, that several structures may be described in terms of cyclic repetitions around a 63 axis of AlB2-type columns (see Fig. 3.39). Examples of intergrowth structures containing AlB2-type fragments are cited in the following. 7.4.3.14.2 AlB2-type variants and derivative structures. A number of AlB2type related structures are here presented in order to emphasize the role that structural characteristics such as those present in the AlB2 type may play in a variety of intermetallic phases and to illustrate an example of a structure family containing numerous members interrelated by various kind of more or less large deformations or substitutions. Reference to a seminal paper by Gladyshevskii et al. (1992) will especially be made. A few derivative structures of the hP3-AlB2 type, have been introduced in § 3.8 and Fig. 3.32 as examples of this kind of relations. These are the hP3-ThAuSi type, and, as an example of a more complex derivative structure, the hP24-Er2RhSi3. The hP3-ThAuSi type (isostructural with hP3-BaPtSb) is hexagonal, with space – group P6 m2, N. 187. BaPtSb, hP3, structural type – Hexagonal, space group P6 m2, N. 187 Atomic positions: 1 Ba in (a) 0, 0, 0 1 2 1 1 Pt in (d) ⁄3, ⁄3, ⁄2 2 1 1 1 Sb in (f) ⁄3, ⁄3, ⁄2 For the prototype, BaPtSb, a 453.5 pm, c 488.4 pm, c/a 1.077.

690

Intermetallic Chemistry y x

hP3 ThAuSi c /a = 0.977 Th

Au

Si

y x

hP3 AlB2 c /a = 1.08 z=0

Al 0.5

B

1

Figure 7.35. The hP3-AlB2 type structure and its derivative structure hP3-ThAuSi.

Environment data: Ba (a) CNE 20, Pt (d) CNE 9, Sb (f) CNE 9,

121.264.220.6 65.034.0 65.034.0

The isostructural ThAuSi may be described as having Th in (a), Au in (d) and Si in (f) (see Fig. 7.35). The layer stacking sequence symbol of this structure may be compared with those of the hP2-WC and hP3-AlB2 types: B WC type, triangular (T) nets: WA 0 C0.5 A a AlB2 type, triangular, hexagonal (T, H) nets: Al0 B0.5 B C ThAuSi type, triangular, hexagonal (T, H) nets: ThA0 Au0.5 Si0.5 Notice, on passing from the AlB2 type to the ThAuSi type, the change of the space – group from P6/mmm to P6 m2 and the ordered splitting of the B positions into two sets of Au and Si. Another, previously mentioned, ordered derivative structure of the AlB2 type is the hP24-Er2RhSi3 type, hexagonal, space group P63/mmc, N. 194. In the past a – slightly different description of the structure was given in the space group P6 2c, N. 190, with, however, very small deviations from centro-symmetricity. Its atomic positions are: 2 Er in (b): 0, 0, 1⁄4; 0, 0, 3⁄4 1 2 1 2 – 2 1 – 2 1 4 Rh in (f): ⁄3, ⁄3, z; ⁄3, ⁄3, z 1⁄2; ⁄3, ⁄3, z ; ⁄3, ⁄3, z 1⁄2 – – – 1 1 1 6 Er in (h): x, y, ⁄4; y , x y, ⁄4; x y, x , ⁄4; y, x, 3⁄4; – – – x y, y , 3⁄4; x , x y, 3⁄4 – 12 Si in (i): x, y, z; y, x y, z; x– y, –x , z; x, y, –z 1⁄2; –y, x y, –z 1⁄2; –x y, –x , –z 1⁄2; –x , –x y, –z ; y, x, –z ; x y, –y, –z ; y, x, z 1⁄2; – – – x y, y, z 1⁄2; x , x y, z1⁄2. (with zRh 0; xEr 0.481; yEr 0.019; xSi 0.167; ySi 0.333; zSi 0).

Families of Intermetallic Structure Types: A Selection

691

For the prototype a 803.6, c 771.2, c/a 0.9597. Environment data: Er (b) CNE 20, 124.038.036.029.0 Rh (f) CNE 9, 65.034.0 Er (h) CNE 20, 45.044.043.038.036.029.0 Si (i) CNE 9, 65.034.0 7.4.3.14.3 Examples of derivatives of the AlB2 type. Following a seminar paper by Gladyshevskii et al. (1992) a selection of simple derivative structures of the AlB2 type is here collected. Their projections along [001] and [110] are shown, followed by their full crystallographic descriptions. A first group of members of

AlB2

EuGe2

UHg2

, Al

, U

, Eu

, B

, Hg

, Ge

CeCd2

CaIn2

KHg2

a c ,

Ce

,

Ca

,

K

,

Cd

,

In

,

Hg

Figure 7.36. Projections on characteristic planes of the unit cells of AlB2-derivative structures (binary deformation variants). Open circles represent atoms on the projection plane, dashed circles atoms on other parallel planes. For AlB2 compare with Fig. 7.5 and, for KHg2, with 7.33. (Adapted from Gladyshevskii et al. 1992)

692

Intermetallic Chemistry

this family corresponds to a number of binary deformation variants a few examples are presented in the following (Fig. 7.36): hP3-UHg2: For this compound we have a significant deformation of the cell with a c/a ratio (0.65) smaller than for AlB2 (1.08). As a consequence we have an increase of the coordination. hP3-ω,Cr–Ti: This structure is formed on quenching several close-packed hexagonal solid solutions of Ti, Zr, Hf with other transition metals. It is not an ordered structure and is approximately isotypic with AlB2 with smaller axial ratio (0.62). hP3-CeCd2 (c/a 0.68) and hP3-EuGe2 (c/a 1.22): In these compounds the atoms (Cd or Ge) centring the trigonal prisms are displaced along the prism axis and form puckered hexagon mesh layers. hP6-CaIn2: This compound too presents puckered layers formed by indium atoms and interconnected. Consecutive layers are related by a mirror plane so that, in comparison with the AlB2 cell, the c axis is doubled. oI12-KHg2: A distortion of the hexagon mesh layers results in an orthorhombic symmetry. The trigonal prisms are deformed in such a way that each prism has one smaller and one larger triangular face. The Hg atoms are displaced towards the larger face and form a 3D framework, where each atom is surrounded by four other atoms in a tetrahedral coordination. The KHg2 type is isotypic with the CeCu2 type, for which a different description was reported: see a discussion on this point in § 7.4.3.5. Different projections of these structures are shown here, and a short description is given in the following. UHg2, hP3, AlB2-derivative structural type Hexagonal, space group P6/mmm, N. 191. Atomic positions 1 U in (a) 0, 0, 0 2 Hg in (d) 1⁄3, 2⁄3, 1⁄2; 2⁄3, 1⁄3, 1⁄2 For the prototype, UHg2, a 497.6 pm, c 321.8 pm, c/a 0,647. Notice, in comparison with AlB2, the considerable change in the c/a value. EuGe2, hP3, structural type – Hexagonal, space group P3m1, N. 164. Atomic positions: 1 Eu in (a) 0, 0, 0 2 Ge in (d) 1⁄3, 2⁄3, z; 2⁄3, 1⁄3, –z z 0.405 For the prototype, EuGe2, a 410.2 pm, c 499.5 pm, c/a 1.218.

Families of Intermetallic Structure Types: A Selection

693

CeCd2, hP3, structural type – Hexagonal, space group P3 m1, N. 164. Atomic positions: 1 Ce in (a) 0, 0, 0 2 Cd in (d) 1⁄3, 2⁄3, z; 2⁄3, 1⁄3, –z ; z 0.42 For the prototype, CeCd2, a 507.3 pm, c 345.0 pm, c/a 0.680. Environment data: Ce (a) CNE 14, Cd (d) CNE 14,

122.226.0 40.334.231.230.413.0

Notice, in comparison with AlB2, the different value of c/a and the free parameter in the positions of Cd atoms (0.42 instead of 0.509) which results in puckered layers. CaIn2, hP6, structural type Hexagonal, space group P63/mmc, N. 194. Atomic positions: 2 Ca in (b) 0, 0, 1⁄4; 0, 0, 3⁄4; 1 2 4 In in (f) ⁄3, ⁄3, z; 2⁄3, 1⁄3, z 1⁄2; 2⁄3, 1⁄3, –z ;

⁄3, 2⁄3, –z 1⁄2;

1

Layer stacking symbol: B A C A C Ca1/4 InB9/20 In11/20 Ca3/4 In19/20 Triangular (T) nets: In1/20 For the prototype, a 489.5 pm, c 775.0 pm, c/a 1.583, and z 0.455. Environment data: Ca (b) CNE 14, In (f) CNE 10,

122.226.0 36.035.034.013.0

This structure can be described as a derivative form of the AlB2-type structure (Fig. 7.37). Ca atoms form trigonal prisms alternatively slightly off-centred up and down by In atoms. Notice also, in comparison with AlB2, the nearly doubled value of c (and c/a). Compounds pertaining to this structural type are MgGa2, CaGa2, CaIn2, SrIn2, SrTl2, BaTl2 and a number of (nearly) equiatomic ternary phases such as RCdIn, RCuSn, RCuPb, RPbSb, RZnTl (R rare earth metal). In a number of cases the structure is really CaIn2 type with 2R in (b) and 4Me in (f) (Me is a disordered mixture of, say, 1Cd and 1 In). For a number of similar compounds, however, a derivative ordered structure has been proposed. This may be obtained by ‘splitting’ the four equivalent positions (f) into two sets with a consequent lowering of the symmetry in another space group. The new structure is the LiGaGe type described in the following. Owing to the particular values of the z parameters, the layer stacking symbol and the environment data are very similar to those of the CaIn2 type.

694

Intermetallic Chemistry hp6 y

CaIn2

Ca

c /a = 1.58

In

x

z = 0.045

0.25

0.455

0.545

0.75

0.955

Figure 7.37. Sequences of characteristic sections of the hP6-CaIn2 type structure.

NdPtSb

,

Nd

, ,

Pt Sb

LiGaGe

ZrBeSi

,

Li

,

Zr

, ,

Ga Ge

, ,

Be Si

Figure 7.38. Projection of hP6-AlB2 derivative structures. Crossed discs indicate superimposed different atoms in projections in the translation units.

Compounds described as pertaining to this type are for instance: LiZnSb, LiZnBi, KSnAs, CaZnSn, CaAgBi, PrPtSb. oI12, CeCu2 or KHg2 type This structure, considered either as CeCu2 or as KHg2 type, may be described as a member of the AlB2 structure type family. See the description reported in § 7.4.3.5. 7.4.3.14.4 Substitution derivatives of the AlB2 type. The closely interrelated structures of NdPtSb, LiGaGe and ZrBeSi are described here below and shortly commented according to Gladyshevskii et al. (1992). In the deformation derivative NdPtSb, the layers are slightly puckered whereas a strong distortion is observed in LiGaGe. In ZrBeSi subsequent layers formed by the prism centring atoms (Be and Si) are rotated by 60° around the c axis with respect to each other. More complex ternary substitution derivatives of the AlB2 type are schematically shown in Fig. 7.38.

Families of Intermetallic Structure Types: A Selection

695

NdPtSb, hP6 and LiGaGe, hP6, structures (AlB2-derivative types) Both structures are hexagonal, space group P63mc, N. 186. with the following atomic positions: 2 Nd (2 Li) in (a) 2 Pt (2 Ga) in (b) 2 Sb (2 Ge) in (b)

0, 0, z; ⁄3, 2⁄3, z; 1 ⁄3, 2⁄3, z; 1

0, 0, z 1⁄2 2 ⁄3, 1⁄3, z 1⁄2 2 ⁄3, 1⁄3, z 1⁄2

zNd 0.000 zPt 0.286 zSb 0.736

zLi 0.247 zGa 0.059 zGe 0.444

For the prototypes: NdPtSb, a 453.4 pm, c 786.6 pm, c/a 1.735. LiGaGe, a 417.5 pm, c 678.3 pm, c/a 1.625. The NdPtSb and LiGaGe structures have similar atomic positions but in NdPtSb the layers are slightly puckered whereas in LiGaGe we have strong distortions resulting in a 3D framework of Ga and Ge. Each Ga is surrounded by a Ge4 tetrahedron and each Ge by a Ga4 tetrahedron. Environment data for LiGaGe structure: 122.226.0 Li (a) CNE 14, Ga (b) CNE 10, 36.035.034.013.0 Ge (b) CNE 10, 36.035.034.013.0 The LiGaGe structure can also be considered an ordered derivative of the CaIn2 type with the passage from the space group P63/mmc to P63 mc and the splitting of the four equivalent positions of the In atoms into two sets of positions (2 Ga and 2 Ge). The atomic positions of the 2 Li in LiGaGe are very close to those of Ca in CaIn2. ZrBeSi, hP6, structure (a AlB2-derivative type) Hexagonal, space group P63/mmc, N. 194. Atomic positions: 2 Zr in (a) 0, 0, 0; 0, 0, 1⁄2 2 Be in (c) 1⁄3, 2⁄3, 1⁄4; 2⁄3, 1⁄3, 3⁄4 2 Si in (d) 1⁄3, 2⁄3, 3⁄4; 2⁄3, 1⁄3, 1⁄4 For the prototype, a 371 pm, c 719 pm, c/a 1.938. This structure, as remarked in the following ‘Note’, can also be described as a Ni2In-derivative type structure. CaPtP, oP12, structural type Orthorhombic, space group Pmc21, N. 26. Atomic positions: 2 Ca in (a1) 0, y, z; 0, –y , z 1⁄2; y 0.5860 2 Ca in (a2) 0, y, z; 0, –y , z 1⁄2; y 0.8722 1 2 P in (b1) ⁄2, y, z; 1⁄2, –y , z 1⁄2; y 0.3836 1 2 P in (b2) ⁄2, y, z; 1⁄2, –y , z 1⁄2; y 0.0733 1 2 Pt in (b3) ⁄2, y, z; 1⁄2, –y , z 1⁄2; y 0.1698 2 Pt in (b4) 1⁄2, y, z; 1⁄2, –y, z 1⁄2 y 0.3420

z 0.5719 z 0.1362 z 0.7562 z 0.3321 z 0.0000 z 0.3778

696

Intermetallic Chemistry

For the prototype, CaPtP, a 434.4 pm, b 831.1 pm, c 651.9. Ca (a1) Ca (a2) P (b1) P (b2) Pt (b3) Pt (b4)

CNE 16, CNE 16, CNE 9, CNE 3, CNE 10, CNE 10,

63.0.0.142.0.0.127.026.024.0.0.1 44.0.0.143.0.0.142.0.0.126.017.015.0 65.034.0 3-ring 55.026.024.013.0 55.026.024.013.0

This structure may be described as an orthorhombic distorted variant of the AlB2 structure type family. The prisms surrounding half of the Ca atoms are transformed to nearly pentagonal prisms. A ‘Note’ on the Ni2In, hP6, structural type This structure and its relation with the NiAs type is described in § 7.4.2.4.3. The scheme of the sequence of unit cell sections of Ni2In is shown here together with that of its (second kind) derivative structure ZrBeSi (Fig. 7.39). A distorted variant of the Ni2In-type structure is the oP12-orthorhombic structure of the Co2Si, (or PbCl2) type which is described in § 7.4.3.6. Complex stacking variants. More complex stacking variants in the ternary AlB2 substitution derivatives may be considered. In Fig. 7.40 the structures of hP9LiCaSn, hP12-YPtAs and oP36-CaCuGe are schematically shown. These can be described as three, four and six slabs variants of a similar arrangement (compare also with the two slabs structures of KHg2, Fig. 7.33).

y x

hP6 Ni2In c /a = 1.23 Ni

In

y x

hP6 ZrBeSi c /a = 1.94

z=0

Zr 0.25

0.5

0.75

Si

1

Figure 7.39. Sequences of characteristic sections of the hP6-Ni2In and ZrBeSi structures. Four adjacent cells are shown.

Be

Families of Intermetallic Structure Types: A Selection

697

7.4.3.14.5 AlB2 ‘fragments’ as components of complex intermetallic structures. The role and the ubiquity of AlB2-type atomic arrangement may be further underlined considering that the AlB2 type is the basis of a number of intermetallic structures also through the intergrowth mechanisms (see § 3.9.4). An example may be given by the homologous series TmnT n X2m (T, T transition metals, X p-block element) described by Zaremba et al. (1991) where m and n are the numbers of fragments of AlB2 and CsCl types, respectively. For the tP10Mo2FeB2 structure, here shown in Fig. 7.41, m/n 1/1. In this figure the structure fragments are clearly identified. Other compounds of the same series are, for instance, the R5Ni2In4 phases, where R is a rare earth metal. As for the role of AlB2-type fragments as constituent of various structures we may mention Parthé and Chabot (1984) who described series of structures which can be interpreted as intergrowth of W-type and AlB2-type slabs, series resulting from the intergrowth of AlB2 BaAl4 segments, series containing AlB2 BaAl4 AuCu3 segments, etc. 7.4.3.15 αThSi2, tI12, and LaPtSi, tI12, structural types. The αThSi2-type structure, and its lattice-equivalent ternary LaPtSi-type derivative, can be considered filled-up tI8-NbAs-type derivative. These structures can be described in terms CaLiSn

YPtAs

CaCUGe

a

b ,

Ca

,

Y

,

Ca

,

Li

,

Pt

,

Cu

,

Sn

,

As

,

Ge

Figure 7.40. Structures of ternary derivative of the AlB2 type. The 3-, 4-, 6- stacking variants hP9LiCaSn, hP12-YPtAs and oP36-CaCuGe are shown. Crosses indicate superimposed different atoms in projection of the translation unit.

698

Intermetallic Chemistry

CsCl

AlB2

Figure 7.41. Mo2FeB2: the projection of the structure on the x,y plane is shown; the CsCl-type and AlB2-type fragments are also shown which, when packed together in a 1:1 ratio, may result in an atomic arrangement of the Mo2FeB2 type.

of layers of (metal atoms) triangular prisms parallel to the basal planes of the tetragonal cells; the prism axes in one layer being rotated 90° relative to those of the layers above and below. In the NbAs-type structure the As atoms only centre alternate Nb prisms. In the αThSi2-type structure all the Th prisms are centred by Si instead of only half of them (Pearson 1972). It is also possible to compare the three structures in terms of 44 net layer stacking (along the c direction of the tetragonal cells). See Figs. 7.42, 7.43 and, for NbAs, Fig. 7.27. tI8-NbAs: Nb10 As20.17 Nb30.25 As10.42Nb40.5As30.67Nb20.75As30.92 tI12-αThSi2: ThSi10 Si40.08 Si20.17Th30.25Si20.33Si10.42Th40.5 Si10.58 Si30.67Th20.75 Si30.83Si40.92 tI12-LaPtSi: La10 Pt40.08 Si20.17 La30.25 Pt20.33Si10.42La40.5Si10.58Si30.67 La20.75 Pt30.83Si40.92 7.4.3.15.1. Structural type: tI12-αThSi2. Body centred, tetragonal, space group I41/amd, N. 141. 1 1 1 1 4 Th in (a): 0, 0, 0; 0,1⁄2, 1⁄4; ⁄2, ⁄2, ⁄2; ⁄2, 0, 3⁄4 – 8 Si in (e): 0, 0, z; 0,1⁄2, z 1⁄4; 1⁄2, 0, z 3⁄4; 1⁄2,1⁄2, –z 1⁄2 1 1 ⁄2, ⁄2, z 1⁄2; 1⁄2, 0, z 3⁄4; 0,1⁄2, –z 1⁄4; 0, 0, –z For the prototype a 412.6 pm, c 1434.6 pm, c/a 3.477 and zSi 0.4165. Environment data: Th (a) CNE 20, Si(e) CNE 9,

121.244.242.4 65.034.0

699

Families of Intermetallic Structure Types: A Selection tI12

ThSi2

Th

c/a = 3.48

Si

y x

tI12

0

0.084

0.166

0.25

0.334

0.416

0.5

0.584

0.666

0.75

0.834

0.916

LaPtSi

La

Si

(z )

c /a = 3.42

Pt

y x

0

0.085

0.169

0.25

0.335

0.419

0.5

0.585

0.669

0.75

0.835

0.919

(z )

Figure 7.42. Characteristic sections of the tI12-α ThSi2 type structure and of its ordered derivative LaPtSi.

Compare these data with those reported for the hP3-AlB2 type which belongs to the same ‘coordination type’. Strukturbericht designation Cc. 7.4.3.15.2 Structural type: tI12-LaPtSi Body centred, tetragonal, space group I41md, N. 109. 4 La in (a1): 0, 0, z; 0, 1⁄2, z 1⁄4; 1⁄2, 1⁄2, z 1⁄2; 1⁄2, 0, z 3⁄4; 4 Pt in (a2): 0, 0, z; 0, 1⁄2, z 1⁄4; 1⁄2, 1⁄2, z 1⁄2; 1⁄2, 0, z 3⁄4; 4 Si in (a3): 0, 0, z; 0, 1⁄2, z 1⁄4; 1⁄2, 1⁄2, z 1⁄2; 1⁄2, 0, z 3⁄4 For the prototype, a 424.90 pm, c 1453.9 pm, c/a 3.422 and zLa 0 (fixed conventionally), zPt 0.585, zSi 0.419. Environment data: La (a1) CNE 20, 43.142.128.026.226.025.024.223.0 Pt (a2) CNE 9, 65.034.0 Si (a3) CNE 9, 65.034.0

700

Intermetallic Chemistry

ThSi2

LaPtSi

NbAs

Th

La

Nb

Si

Pt

(vac)

Si

Si

As

Figure 7.43. Unit cells of tI12-ThSi2 type, of its substitution derivative LaPtSi and of its defectderivative tI8-NbAs types.

The ThSi2-type structure according to Pearson (1972) is primarily controlled by the Th–Si contacts, with the Si–Si contacts exerting a certain influence. Each Si atoms has three close Si neighbours resulting in the 3D connected framework schematically shown in Fig. 7.43. This framework (and the Si–Si coordination) can be compared with the planar graphite hexagonal nets and therefore with, for instance, the hP3-AlB2 type structure (and its ordered variants). In the case of ThSi2, however, one vertex of each hexagon is always missing and we have parallel sets of planar chains interconnected to similar perpendicular sets. It may be interesting to mention that the characteristic structure of this network described as ‘hinged’ network should have the peculiar feature that the entire framework could undergo reorganization by a nearly barrier-less twisting type motion. According to Baughman and Galvao (1993) and Moore (1993), unusual mechanical and thermal properties may be predicted for substances having all their atoms arranged in such a framework. These special properties, therefore, may be envisaged for hypothetical compounds such as polyacetylene, polydiacetylene, polyphenylene, (BN)x phases, etc. and

Families of Intermetallic Structure Types: A Selection

701

perhaps for substances containing the hinged network as a part of their structure (‘crowded’ hinged network crystals) such as ThSi2 compounds. Finally, Considering the AlB2 and the α-ThSi2 type structures we may notice that the similarity of their bonding arrangements may be further confirmed by the existence of the AlB2 structure also for a different form of ThSi2 (high-temperature form) and (as a defective structure) for Th3Si5. Following the description presented by Baughman and Galvao (1993) the AlB2-type structure could be called a ‘crowded’ graphitic network structure. For a discussion on general properties for the three-connected nets (the AlB2 and ThSi2 structures and their transition metal derivatives) see Zheng and Hoffmann (1989). Characteristic band structures were presented for these two compounds and their derivative structures (CaCuGe, LaPtSi) and other three-connected nets (SrSi2, LaIrSi). 7.4.3.16 RGe2x (rare earth ‘digermanides’): an example of a family of compounds with structures related to the ‘coordination similar’AlB2 and ThSi2 types. The two structural types hP3-AlB2 and tI12-αThSi2 are closely interrelated: their structures may be described in terms of triangular prisms of metal atoms (Al or Th) centred by B or Si. In the AlB2-type structure we have a 3D array of parallel trigonal prisms that are contiguous on all the faces. The B atoms form hexagonal (graphite type) parallel nets. In the αThSi2-type we have layers of trigonal prisms parallel to the basal plane of the cell, the prism axes of one layer being rotated 90° relative to those of the layers above and below. As for B in AlB2, each Si in αThSi2 has three close Si neighbours, resulting however in a 3D connected framework (see Fig. 7.44). According to a definition given by Daams (1995) the AlB2 the αThSi2 structure types belong to the same ‘coordination type’: two structures, indeed, are considered pertaining to the same coordination type when in them the same atomic environments and the same number of environments are realized. Several derivatives of these structural types have been described. A large number have been identified in alloy systems of silicides or germanides of metals such as the lanthanides or the actinides. In a number of papers Venturini et al. (1999a, b, c) systematically investigated RGex phases (R rare earth element, x 1.5–1.8 Ge 60–64 at.%), making a thorough study of their structures and presenting a comprehensive description of their structural properties. These structures may generally be summarized as superstructures of AlB2-or αThSi2-type germanides, which are characterized by different ordering schemes of Ge vacancies. An idea of the complexity of such systems and of their crystal–chemistry may be grasped from Fig. 7.45 where a summary is shown of the stoichiometries of the compounds formed in the Ge-rich regions of R–Ge systems.

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Intermetallic Chemistry

Figure 7.44. Scheme of the 3D connected framework of Si atoms of the structure of tI12-αThSi2.

Lanthanide radius (Å) 0.90

0.88

1.74

0.92

0.94

0.96

Gd

Sm

0.98

1.00

1.02

ThSi2 type

x (Ge)

1.70 1.66 1.62 1.58

AlB2 type

1.54

Tm Er Y

Dy

Tb

Nd Pr

Ce

La

Ho

Figure 7.45. Rare earth germanides. Summary (according to Venturini et al. 1999a,b,c) of the crystal–chemistry of RGex phases in the composition range RGe1.5 to RGe1.8. The stoichiometries observed in the various compounds of the different R, are shown as a function of the R atomic dimensions (ionic radius of R3). Notice (for x 1.625) the separation line between the two structural types the αThSi2-derivative types and the AlB2-derivative types.

Families of Intermetallic Structure Types: A Selection

703

7.4.4 Examples of structure types with a 1:3 stoichiometry 7.4.4.1 Introductory remarks. Phases related to the 1:3 stoichiometry and their derivative structures, either as point compounds or as solid solution ranges, are frequently found in binary and ternary intermetallic alloy systems. Various prototypes are known, often displaying quite different bonding mechanisms and involving metals of different regions of the Periodic Table. In the following paragraphs a few selected prototypes will be presented corresponding to several phases and pertaining to certain groups (families) of interrelated structures which could be relevant to a discussion on some points of general interest in the intermetallic crystal–chemistry. Notice that a number of important 1:3 prototypes, owing to their relationships with other structure types, are described in other paragraphs; so the cF16-Li3Bi type (and the related cF16-MnCu2Al type) is described in § 7.4.2.2 together with the cF16-NaTl reference type, whereas in § 7.6.5 and 7.6.6 the cP4-ReO3 and the related cP5-CaTiO3 structural types are discussed. 7.4.4.2 A polytypic structure family consisting of close-packed stacking of layers composed of triangular and kagomè nets (the hP8-Ni3Sn, cP4-AuCu3, hP16TiNi3, hP24-VCo3, hP24-PuAl3 and hR36-BaPb3, types). Structural details are reported, in a few paragraphs below, for a number of interrelated structures XY3 which may be described as constituted by the stacking of arrays, each of which has the XY3 stoichiometry with the X atoms forming a triangular (sub)net 36 A, B or C and the Y atoms a kagomé 3636 (sub)net α, β or γ. These close-packed layers are stacked one above the other according to the normal close-packed positions (A, B or C) so that an X atom has only Y atoms as nearest neighbours. A discussion of the characteristics of a number of ordered layer superstructures involving a XY3 stoichiometry has been reported by Massalski (1989). Sequences of layer structures (among which those corresponding to the cP4-AuCu3, hP16TiNi3, hP24-VCo3, hR36-BaPb3 types) as observed in V (or Ti) alloys with Fe, Co, Ni, Cu are described. The relative stabilities of the different stacking sequences have been analysed in terms of a few parameters which characterize the interactions between various layers. The various possible stacking sequences generate a family of polytype structures, a few examples of which are listed here: hP8-Ni3Sn: cP4-AuCu3: hP16-TiNi3: hP24-VCo3: hP24-PuAl3:

β SnB0.25 Ni0.25 SnC0.75Niγ0.75 A α Au 0 Cu 0 AuC0.33 Cuγ0.33AuB0.67Cuβ0.67 γ TiA0Niα0 TiB1/4 Niβ1/4 TiA1/2 Niα1/2TiC3/4Ni 3/4 γ β γ A VA0 Coα0 VC0.17 Co 0.17VB0.33Coβ0.33V0.5 Coα0.5VB0.67Co 0.67VC0.83Co 0.83 β α γ α Al 0.08PuB0.09Al 0.25PuA0.25PuB0.41Alβ0.42 Al 0.58PuC0.59 Al 0.75PuA0.75 PuC0.91Alγ0.92

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Intermetallic Chemistry

Or in short: hP8-Ni3Sn: cP4-AuCu3: hP16-TiNi3: hP24-VCo3: hP24-PuAl3:

Bβ-Cγ Aα-Cγ-Bβ Aα-Bβ-Aα-Cγ Aα-Cγ-Bβ- Aα-Bβ-Cγ Bβ-Aα-Bβ-Cγ-Aα-Cγ

...(BC)... ...(ACB)... ...(ABAC)... ...(ACBABC)... ...(BABCAC)...

The layer stacking must be considered along the c axis in the hexagonal compounds (Ni3Sn, hP16-TiNi3, hP24-VCo3 and hP24-PuAl3) and along the cell diagonal in the cubic AuCu3. More complex representatives of this family are the types hR36-BaPb3, hR48-PuGa3, hR60-HoAl3, etc. However, notice that, for the structures previously mentioned, besides the 363636 layer description, different representations may be useful in order for instance to underline relationships with other prototypes (a special case may be the AuCu3type structure). Notice in the following description of this group of structures the coordination 12 around all the atoms. 7.4.4.2.1 Ni3Sn, hP8, structural type Hexagonal, space group P63/mmc, N. 194. Atomic positions: 2 1 3 2 Sn in (c): 1⁄3, 2⁄3, 1⁄4; ⁄3, ⁄3, ⁄4; 1 6 Ni in (h): x, 2x, ⁄4; 2x–, –x , 1⁄4; x, –x , 1⁄4; –x , 2x–, 3⁄4 2x, x, 3⁄4; –x, x, 3⁄4 For the prototype, a 527.5 pm, c 423.4 pm, c/a 0.802 and x 0.833. Environment data: Sn (c) CNE 12, Ni (h) CNE 12,

122.2 (h) 122.2

Strukturbericht designation D019. z = 0.75 hP8 Ni3Sn

Ni

Sn

y x z = 0.25

z = −0.25

z = −0.25

0.25

0.75

Figure 7.46. hP8-Ni3Sn structure. The Ni coordination around Sn is shown and the sequence of typical sections of the structure (four adjacent cells are shown). Notice the coordination polyhedron, already shown in Fig. 3.18 (12d). Compare with the Mg structure.

Families of Intermetallic Structure Types: A Selection β

705

γ

B C The layer stacking symbol, Sn0.25 Ni0.25 Sn0.75 Ni0.75, may be compared with the B C symbol Mg0.25 Mg0.25 of the Mg type. This type, indeed, is a superstructure of the closed-packed (hP2-Mg) hexagonal structure in the same way as the AuCu3 type is of the close packed cubic (cF4-Cu) structure. It can, therefore, be considered a stacked polytype of the AuCu3 type. Several phases belong to this type, for instance, Ti3Al, Fe3Ga, Fe3Ge, Fe3Sn, ZrNi3, ThAl3, YAl3, etc. In the specific case of the rare earth trialuminides RAl3, the NiSn3-type structure has been observed for LaAl3 to GdAl3 (and YAl3). For ErAl3 to YbAl3 and ScAl3 the AuCu3-type structure is formed (Fig. 7.46). For the intermediate RAl3, intermediate stacking variants of similar layers have been described and their relative stabilities discussed (Van Vucht and Buschow 1965). A close relationship with the oP8-βTiCu3 type structure has been also underlined.

7.4.4.2.2 AuCu3, cP4, structural type – Cubic, space group Pm3m, N. 221. Atomic positions: 1 Au in (a) 0, 0, 0 3 Cu in (c) 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2 1⁄2, 1⁄2, 0; For the prototype, AuCu3, a 374.8 pm. Coordination formula: 333 [Au6/6][Cu8/8]12/4 Environment data: Au (a) CNE 12, Cu (c) CNE 12,

122.2(c) 122.2(c)

(12Cu) (4Au, 8Cu)

Strukturbericht designations L12. The layer stacking symbol in terms of triangular and kagomé (T,K) nets is: γ

β

AuA0 Cuα0 AuC1/3 Cu 1/3AuB2/3 Cu 2/3 which may be compared with those of Ni3Sn, TiNi3, and VCo3. On the other hand in terms of square (S) nets (that is examining the structure along the cell edge instead of the diagonal) we have the sequence: Au10Cu40Cu51/2 which, in the following pages, is shown in comparison with those of Cu (a reference structure) and of other XY3 compound (the tetragonal tI8-TiAl3 and tI16-ZrAl3 type structures). For more details on this structure, see also § 3.7.7 and Figs. 3.27–3.30. This structure can be considered a derivative structure (ordered substitution) of the cF4-Cu type. Other examples of substitutional superstructures based on facecentred cubic pseudo-cells are the tI8-TiAl3, tI16-ZrAl3, tI10-MoNi4, oI16-MoPt2 types (described in § 3.8.3 and Fig. 3.36). As for TiAl3 compare its layer sequence

706

Intermetallic Chemistry

not only with those of the cF4-Cu and cP4-AuCu3 structures here reported, but also with that of ZrAl3 shown in Fig. 7.47. These different interrelated structures, with special attention to their occurrence in Al–X–Y ternary alloys (X Ti, Zr, Hf, V, Nb, Ta, Mo; Y V, Cr, Mn, Fe, Co, Ni, Cu, Zn) have been considered by Kumar (1990). According to differences in chemical bonding, mechanical and physical properties, Kumar considered (for various stoichiometries) three main groups of structures: 1. Geometrically close-packed structures, cP4-AuCu3 (L12), tP2 (tP4)-AuCu (L10), hP8-Ni3Sn (D019), tI8-TiAl3 (D022), tI16-ZrAl3 (D023), hP16-TiNi3 (D024). 2. Body-centred cubic structures and their derivatives, cP2-CsCl (B2), cF16Fe3Al (D03), cF16-NaTl (B32), cF16-MnCu2Al (L21). 3. The topologically close-packed structures which tend to be quite brittle, cP8Cr3Si (A15), cF24-Cu2Mg (C15), hP12-MgZn2 (C14), hP24-Ni2Mg (C36). 7.4.4.2.3 TiNi3, hP16, structural type Hexagonal, space group P63/mmc, N. 194. Atomic positions: 2 Ti in (a) 0, 0, 0; 0, 0, 1⁄2 1 2 1 2 1 3 2 Ti in (c) ⁄3, ⁄3, ⁄4; ⁄3, ⁄3, ⁄4 1 1 1 1 6 Ni in (g) ⁄2, 0, 0; 0, ⁄2, 0; ⁄2, ⁄2, 0; 1⁄2, 0, 1⁄2; 0, 1⁄2, 1⁄2; 1⁄2, 1⁄2, 1⁄2 – – 1 1 6 Ni in (h) x, 2x, ⁄4; 2x , x , ⁄4; x, –x , 1⁄4; –x, 2x–, 3⁄4; 2x, x, 3⁄4; –x, x, 3⁄4 For the prototype, TiNi3, a 510.1 pm, c 830.7 pm, c/a 1.629 (2 0.815) and xNi 0.833. Environment data: Ti (a) CNE 12, Ti (c) CNE 12, Ni (g) CNE 12, Ni (h) CNE 12,

122.2 122.2 83.1446.0 44.144.026.022.2

Strukturbericht designation D024. 7.4.4.2.4 VCo3, hP24, structural type – Hexagonal, space group P6 m2, N. 187. Atomic positions: 1 V in (a) 0, 0, 0; 1 V in b) 0, 0, 1⁄2; 1 2 2 V in (h) ⁄3, ⁄3, z; 1⁄3, 2⁄3, z–; 2 1 2 V in (i) ⁄3, ⁄3, z; 2⁄3, 1⁄3, z–; 3 Co in (j) x, –x, 0; x, 2x, 0; 2x–, –x , 0;

Families of Intermetallic Structure Types: A Selection

3 Co in (k) 6 Co in (n1) 6 Co in (n2)

x, –x, 1⁄2; x, –x , z; x, –x , –z; x, –x , z; x, –x ,–z;

x, 2x, 1⁄2; x,2x, z; x, 2x, –z; x, 2x, z; x, 2x, –z;

707

–, –x, 1⁄2; 2x 2x–, –x , z; 2x–, –x , –z; 2x–, –x , z; 2x–, –x , –z;

For the prototype, VCo3, a 503.2 pm, c 1227.0 pm, c/a 2.438 (3 0.813), and zV(h) 0.333, zV(i) 0.167, xCo(j) 0.5, xCo(k) 0.5, xCo(n1) 0.167, zCo(n1) 0.167, xCo(n2) 0.833, zCo(n2) 0.333. Environment data: V (a) CNE 12, V (b) CNE 12, V (h) CNE 12, V (i) CNE 12, Co (j) CNE 12, Co (k) CNE 12, Co (n1) CNE 12, Co (n2) CNE 12,

122.2 122.2 122.2 122.2 46.043.124.022.2 46.043.124.022.2 52.244.123.114.0 52.244.123.114.0

7.4.4.2.5 PuAl3, hP24, structural type Hexagonal, space group P63/mmc, N. 194. Atomic positions: 2 Pu in (b) 0, 0, 1⁄4; 0, 0, 3⁄4 1 2 2 4 Pu in (f) ⁄3, ⁄3, z; ⁄3, 1⁄3, z 1⁄2; –, –x , 1⁄4; 1 6 Al in (h) x, 2x, ⁄4; 2x – 2x, x, 3⁄4; x , x, 3⁄4; 12 Al in (k) x, 2x, z; 2x–, –x , z; 1 2x, x, z ⁄2; x–, x, z 1⁄2; –x, x, –z ; 2x–, –x , –z 1⁄2;

⁄3, 1⁄3, –z ; x, –x , 1⁄4;

⁄3, 2⁄3, –z 1⁄2 – x , 2x–, 3⁄4;

2

1

x, x–, z; 2x, x, –z ; x, 2x, –z 1⁄2;

x–, 2x–, z 1⁄2; x–, 2x–, –z ; x, –x, –z 1⁄2

For the prototype, PuAl3, a 610.0 pm, c 1447.0 pm, c/a 2.732 and zPu(f) 0.0892, xAl(h) 0.5160, xAl(k) 0.8337, zAl(k) 0.0815. Environment data: Pu (b) CNE 12, Pu (f) CNE 12, Al (h) CNE 12, Al (k) CNE 12,

122.2 122.2 44.144.026.022.2 52.243.124.116.0

The PuAl3-type structure (a slightly distorted form of the VCo3 type) results from the stacking of six (slightly non-planar) close-packed layers, stacked along [001] in a sequence of the type BABCAC.

708

Intermetallic Chemistry

7.4.4.2.6 BaPb3, hR36, structural type – Rhombohedral, space group R3m, N. 166. Atomic positions: (in the triple-primitive hexagonal cell): (0, 0, 0; 2⁄3,1⁄3,1⁄3; 1⁄3,2⁄3,2⁄3) 3 Ba in (a) 0, 0, 0 6 Ba in (c) 0, 0, z; 0, 0, –z 1 ⁄2, 0, 0; 0, 1⁄2, 0; 1⁄2, 1⁄2, 0; 9 Pb in (e) 18 Pb in (h) x, x–, z; x, 2x, z; 2x–, x–, z x–, x, –z ; 2x, x, –z ; x–, 2x–, –z For the prototype, BaPb3, a 728.7 pm, c 2577.0 pm, c/a 3.536(4 0.884) and zBa 0.222, xPb(h) 0.167, zPb(h) 0.111. Environment data: Ba (a) CNE 12, Ba (c) CNE 12, Pb (e) CNE 12, Pb (h) CNE 12,

122.2 122.2 83.146.0 52.244.123.114.0

7.4.4.3 The βTiCu3, oP8, structural type (a Ni3Sn-type related structure). In the preceding paragraph, the Ni3Sn-type structure was described and compared with those of several compounds forming a polytypic family of 1:3 compounds. The Ni3Sn structure will now be compared with that of another important 1:3 prototype: the βTiCu3 type. In βTiCu3 the atoms are arranged in close-packed layers parallel to (010) plane (x/z plane), each Cu has 4 Ti and 8 Cu neighbours (there are no nearest Ti–Ti neighbours). The sequence of characteristic sections of this structure clearly shows analogies with the atomic arrangements observed in the Ni3Sn-type structure. The βTiCu3 structure is orthorhombic, space group Pmmn, N. 59. Atomic positions: 2 Ti in (a) 0, 0, z; 1⁄2, 1⁄2, –z 2 Cu in (b) 0, 1⁄2, z; 1⁄2, 0, z– 4 Cu in (f) x,0, z; –x , 0, z; x– 1⁄2, 1⁄2, z–; x 1⁄2, 1⁄2, –z For the prototype, a 516.2 pm, b 434.7 pm, c 453.1 pm; and z zCu(b) 0.345, xCu(f) 0.250, zCu(f) 0.155. Environment data: Ti (a) CNE 12, Cu (b) CNE 12, Cu (f) CNE 12,

122.2 122.2 122.2

Ti

0.655,

Families of Intermetallic Structure Types: A Selection

709

Strukturbericht designation of the βTiCu3, oP8 type is D0a. 7.4.4.4 The tP4-Ti3Cu, tI8-TiAl3 and tI16-ZrAl3 type structures: tetragonal derivatives of the cP4-AuCu3 type 7.4.4.4.1 Ti3Cu, tP4, structural type Tetragonal, space group P4/mmm, N. 123. Atomic positions: 1 Cu in (a) 0, 0, 0 1 Ti in (c) 1⁄2, 1⁄2, 0 2 Ti in (e) 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2 Coordination formula: 333 [Cu6/6][Ti8/8]12/4 Layer stacking symbols: 5 Square (S) nets: Cu10 Ti40 Ti1/2 For the prototype, Ti3Cu, a 415.8 pm, c 359.4 pm, c/a 0.864.

Strukturbericht designation L60. This structure can be described as a tetragonal distortion of the AuCu3-type structure. It may also be considered a variant of the previously described AuCu(I) type (compare with its tP4 pseudo-cell). 7.4.4.4.2 TiAl3, tI8, structural type Body-centred tetragonal, space group I4/mmm, N. 139. Atomic positions: 2 Ti in (a) 0, 0, 0; 1⁄2, 1⁄2, 1⁄2 2 Al in (b) 0, 0, 1⁄2; 1⁄2, 1⁄2, 0 4 Al in (d) 0, 1⁄2, 1⁄4; 1⁄2, 0, 1⁄4; 1⁄2, 0, 3⁄4; 0, 1⁄2, 3⁄4 For the prototype: a 383.6 pm, c 857.9 pm, c/a 2.236. Environment data: Ti (a) CNE 12, Al (b) CNE 12, Al (d) CNE 12,

122.2 122.2 122.2

Strukturbericht designation D022. The square net layer sequence of TiAl3 is shown in Fig. 7.47; it is compared with those of AuCu3 (and of Cu as reference structures) and of ZrAl3. The TiAl3-type structure is a superstructure of AuCu3 and may be described in terms of two, distorted, AuCu3-type subcells stacked one above the other.

710

Intermetallic Chemistry cF4

Cu

Cu

AuCu3

Cu

Au

Ti3Cu

Ti

Cu

c/a = 0.86

TiAl3

Ti

Al

c/a = 2.24

ZrAl3

Zr

Al

c/a = 4.32

0.25

0.36 0.38

0.50

y x cP4

y x tP4

y x tI8

y x tI16

y x z=0

0.12 0.14

0.62 0.64

0.75

0.86 0.88

1

Figure 7.47. Sequences of sections, parallel to the base plane of the cells, of the cF4-Cu, cP4-AuCu3, tP4-Ti3Cu, tI8-TiAl3 and tI16-ZrAl3 type structures.

Families of Intermetallic Structure Types: A Selection

711

7.4.4.4.3 ZrAl3, tI16, structural type Body-centred tetragonal, space group I4/mmm, N. 139. 1 4 Al in (c): 0, 1⁄2, 0; 1⁄2, 0, 0; ⁄2, 0, 1⁄2; 0, 1⁄2, 1⁄2; 1 1 1 1 1 3 4 Al in (d): 0, ⁄2, ⁄4; ⁄2, 0, ⁄4; ⁄2, 0, ⁄4; 0, 1⁄2, 3⁄4; – 1 1 1 1 – 4 Al in (e): 0, 0, z; 0, 0, z ; ⁄2, ⁄2, z 1⁄2; ⁄2, ⁄2, z 1⁄2; – 1 1 1 1 1 – 4Zr in (e): 0, 0, z; 0, 0, z ; ⁄2, ⁄2, z ⁄2; ⁄2, ⁄2, z 1⁄2; For the prototype: a 400.5 pm, c 1728.5 pm, c/a 4.316 and zAl(e) 0.361, zZr(e) 0.122 Environment data: Al (c) CNE 12, Al (d) CNE 12, Al (e) CNE 12, Zr (e) CNE 12,

44.143.142.2 44.143.142.2 122.2 122.2

Strukturbericht designation D023. This structure may be considered another, more complex, superstructure based on close packing. The height of the superstructure cell in the c direction corresponds to four cubic pseudo-cells. 7.4.4.5 Cr3Si, cP8, structural type: an example of ‘tetrahedrally close-packed’ phases. This structure is also called W3O or β-W type (it was previously believed to be a W modification instead of an oxide, that is a unary structure, a ‘A’ type structure in the Strukturbericht Designation). It has to be underlined that, as for its general structural properties, the Cr3Si type can be included in the description of the group of the so-called ‘tetrahedrally close-packed’ phases (a short description of which is given in § 3.9.3.1 and 7.5.3). In this framework, structural relationships of the Cr3Si type with many other phase types may be mentioned: examples could be the hP7-Zr4Al3, tI12-CuAl2, tI8-Ni3P, hP6-CaZn5 type phases and moreover the σ-Fe–Cr phases, the Friauf–Laves phases, etc. 7.4.4.5.1 Cr3Si, cP8 structural type – Cubic, space group Pm3n, N. 223. Atomic positions: 2 Si in (a) 0, 0, 0; 1⁄2, 1⁄2, 1⁄2 6 Cr in (c) 1⁄4, 0, 1⁄2; 3⁄4, 0, 1⁄2; 1⁄2, 1⁄4, 0; 0, 1⁄2, 1⁄4; 0, 1⁄2, 3⁄4

⁄2, 3⁄4, 0

1

For the prototype, Cr3Si, a 455.5 pm, Strukturbericht designation A15. The section sequence of the cP8-Cr3Si type structure is shown in Fig. 7.48.

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Intermetallic Chemistry

y x z=0

0.25

0.5 cP8 Cr

0.75

1

Cr3Si Si

Figure 7.48. Sequence of cell sections, parallel to the base plane, of the cP8-Cr3Si type structure.

Environment data: Si (a) CNE 12, Cr (c) CNE 14,

125.0 125.026.0

A characteristic feature of this structure is the short Cr–Cr distance in the rows parallel to the directions of the three axes of the cubic cell. The Cr3Si-type structure (also named Nb3Sn-type structure) in terms of a combination of lattice invariant complexes may be described as: Cr3Si: I W. Finally, the particular relationship between the Cr3Si-type structure and the garnet structure (see § 7.6.8) may be pointed out. The position of the cations, indeed, in the garnet structure correspond to the Cr3Si arrangement. 7.4.4.6 Na3As, hP8, structural type (and the ‘bond factor’). According to Pearson (1972), the importance of the chemical bond factor in the Na3As-type phases can be evidenced from the near-neighbour diagram (see Insert 4A). The experimental points corresponding to the different compounds are generally placed along the line corresponding to the Na–As coordination. Crystal data relevant to the Na3As-type structure are: Hexagonal, space group P63/mmc, N. 194. Atomic positions 2 Na in (b): 0, 0, 1⁄4; 0, 0, 3⁄4; 2 As in (c): 1⁄3, 2⁄3, 1⁄4; 2⁄3, 1⁄3, 3⁄4; 2 1 4 Na in (f): 1⁄3, 2⁄3, z; ⁄3, ⁄3, z 1⁄2; 2⁄3, 1⁄3, –z ;

⁄3, 2⁄3, –z 1⁄2

1

For the prototype, Na3As, a 508.8 pm, c 898.2 pm, c/a 1.765 and z (Naf) 0.583. According to symmetry rules, the ideal values of the parameters would be: c/aid 1.78, z(Naf)id 5/12. As Pearson (1972) underlined, the unit cell axial ratio found in several phases is very close to the ideal value.

Families of Intermetallic Structure Types: A Selection

Environment data: Na (b) CNE 9, As (c) CNE 11, Na (f) CNE 11,

713

65.034.0 66.034.023.0 46.035.034.013.0

Strukturbericht designation D018. The layer stacking symbol (triangular nets) is: NaC0.08NaA0.25AsB0.25NaC0.42NaB0.58NaA0.75AsC0.75NaB0.92 Equal numbers of Na and As atoms form hexagonal nets (as in boron nitride), the remaining Na atoms are arranged in layers on either sides of these nets. Typical compounds pertaining to this structure type are: alkali compounds with the 15th group elements (Li3As, Na3P, Na3As, Na3Sb, Na3Bi, K3P, K3As, K3Sb, K3Bi, Rb3As, Rb3Sb, Rb3Bi) a number of actinide hydrides (NpH3, PuH3, AmH3, CmH3, BkH3), some alloys, mainly of magnesium and aluminium (IrMg3, PtMg3, AuMg3, Mg3Hg, IrAl3, IrSi3). Li3Bi cF16 structure. This structure and the related structures NaTl and MnCu2Al have been described in §7.4.2.2. 7.4.4.7 Fe3 C, oP16, structural type Orthorhombic, space group Pnma, N. 62. Atomic positions: 4C in (c): x, 1⁄4, z; –x 1⁄2, 3⁄4, z 1⁄2; x–, 3⁄4, –z ; 4Fe in (c): x, 1⁄4, z; –x 1⁄2, 3⁄4, z 1⁄2; x–, 3⁄4, –z ; 8 Fe in (d): x, y, z; –x 1⁄2, –y , z 1⁄2; x–, y 1⁄2, –z ; x–, –y , –z ; x 1⁄2, y, –z 1⁄2; x, y– 1⁄2, z;

x 1⁄2, 1⁄4, –z 1⁄2 x 1⁄2, 1⁄4, –z 1⁄2 x 1⁄2, –y 1⁄2, –z 1⁄2

x– 1⁄2, y 1⁄2, z 1⁄2

For the prototype, Fe3C, a 507.9 pm, b 673.0 pm, c 451.4 pm and xC(c) 0.881, zC(c) 0.431, xFe(c) 0.044, zFe(c) 0.837, xFe(d) 0.181, yFe(d) 0.063, zFe(d) 0.337. Environment data: C (c) CNE 11, 45.044.036.0 Fe (c) CNE 15, 43.127.026.025.124.123.014.0 Fe(d) CNE 14, 64.126.025.024.023.1 Strukturbericht designation D011. Fe3C, is the metastable phase, cementite, formed in the Fe–C system. (see 5.10.4.5 and Fig. 5.29). Isostructural compounds are Co3C, Ni3C, Co3B, Ni3B, Pd3Si, Pd3P. A number of compounds are also known which have the Fe3C antitype structure, among these we have YF3, AsF3, SbF3, SbCl3, etc.

714

Intermetallic Chemistry

A ternary-derivative structure of the Fe3C type is the oP16-YPd2Si type to which belong several phases such a number of RPd2Si, RPd2Ge, RPt2Si compounds (Parthé and Chabot 1984). Notice that for this ternary stoichiometry other structure types are also very common. An example is the cF16-MnCu2Al type (Heusler type, CsCl derivative) previously described (§ 7.4.2.2). 7.5. A SELECTION OF MORE COMMON INTERMETALLIC PROTOTYPES HAVING MORE COMPLEX STOICHIOMETRIES AND STRUCTURES

The number and variety of intermetallic phases having more complex structure than the simple ones considered in previous paragraphs is very large. The small groups of prototypes here reported are therefore just a few examples of binary (or ternary) phases having odd or very high stoichiometric ratios. 7.5.1 Examples of prototypes corresponding to high stoichiometric ratios

A number of MXn phases (n 3) are reported in the following listed according to increasing values of n. 7.5.1.1 Th6 Mn23, cF116, structural type – Face-centred cubic, space group Fm3 m, N. 225. 1 1 Atomic positions (0, 0, 0; 0, ⁄2, ⁄2; 1⁄2, 0, 1⁄2; 1 1 1 4 Mn in (b) ⁄2, ⁄2, ⁄2; 24 Mn in (d) 0, 1⁄4, 1⁄4; 0, 3⁄4, 1⁄4; 1⁄4, 0, 1⁄4; 1 ⁄4, 0, 3⁄4; 1⁄4, 1⁄4, 0; 3⁄4, 1⁄4, 0 –x , 0, 0; 0, x, 0; 24 Th in (e) x, 0, 0; – 0, x , 0; 0, 0, x; 0, 0, –x –x , –x , x; –x , x, –x ; 32 Mn in (f1) x, x, x; – –x , –x , –x ; x, –x , x; x, x, x ; –x , –x , x; –x , x, –x ; 32 Mn in (f2) x, x, x; – – x, x, x ; x , –x , –x ; x, –x , x;

⁄2, 1⁄2, 0)

1

x, –x , –x ; –x , x, x x, –x , –x ; –x , x, x

For the prototype Th6Mn23 a 1252.3 pm and xTh(e) 0.203, xMn(f1) 0.378 and xMn(f2) 0.178. Strukturbericht designation D8a. Environment data: Mn (b) CNE 8, Mn (d) CNE 12, Th (e) CNE 17, Mn (f1) CNE 13, Mn (f2) CNE 12,

80.3 125.0 84.145.042.210.4 65.034.132.210.3 125.0

Families of Intermetallic Structure Types: A Selection

715

Ternary derivatives of the Th6Mn23 type are the (second kind derivative) Mg6Cu16Si7-type phases (also described as G phases). Binary phases pertaining to this type are: Th6Mg23, Sr6Mg23, Ba6Mg23; ternary examples are: Sc6N16Si7, Ti6N16Si7, Mg6Cu16Si7, Sc6Ni16Ge7, Sc6Ni7Al16, Ti6Co16Si7, etc. According to Parthè and Chabot (1984) the following atomic positions are occupied in the ternary compounds Sc6Ni16Si7 and Sc6Ni7Al16, respectively Sc in 24 (e) Si (or Ni in Sc6Ni7Al16) in 4(b) 24(d) and Ni (or Al) in 32(f) 32(f). Parthè and Chabot (1984) discussed the characteristics of this structure, together with those of a few other prototypes (such as Ti2Ni, Ca3Ag8, Cr23C6, ZrZn22 and their ternary derivatives), in terms of units made up of linked nested polyhedra (cube, tetrahedron, truncated tetrahedron, octahedron, cuboctahedron). 7.5.1.2 Fe4N, cP5, structural type. An interesting example of a fcc-derivative interstitial phase corresponds to the primitive cubic cP5 Fe4N type. It may be described in – – terms of the following atomic positions in the Pm3m, N. 221, (or P 4 3m) space group: 1 Fe in (a): 0, 0, 0; 1 N in (b): 1⁄2, 1⁄2, 1⁄2 3 Fe in (c): 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0 Strukturbericht designation L 1. This filled-up superstructure corresponds therefore to the occupation by N of an interstice (centred in 1⁄2, 1⁄2, 1⁄2) of a Cu-type (or AuCu3-type) structure. The N atom results octahedrally surrounded by 6 Fe atoms. This structure could also be described as a deficient NaCl-type derivative structure; the Fe atoms are in the same positions as the Na atoms in NaCl and one out of the four Cl positions is occupied by the N atoms. This structure may be also compared with that of CaTiO3. 7.5.1.3 BaAl4, tI10, structural type and BaAl4-derivative types 7.5.1.3.1 BaAl4, tI10, structural type Body-centred tetragonal, space group I4/mmm, N. 139. Atomic positions: (0, 0, 0;1⁄2,1⁄2,1⁄2) 2 Ba in (a) 0, 0, 0 4 Al in (d) 0, 1⁄2, 1⁄4; 1⁄2, 0, 1⁄4 4 Al in (e) 0, 0, z; 0, 0, z–; For the prototype: a 453.9 pm, c 1116 pm, c/a 2.459, and z 0.38. Environment data: Ba (a) CNE 22, Al (d) CNE 12, Al (e) CNE 9,

162.244.220.4 44.143.142.2 45.043.114.0

716

Intermetallic Chemistry tI8

Nb

NbAs

c /a = 3.38

As

y x

0

0.17

tI8 AgTlTe2

0.25 Ag

0.42 Te

0.5

0.67

0.75

0.92

1

(z)

0.87

1

(z)

0.88

1

(z)

0.87

1

(z)

0.87

1

(z)

0.92

1

(z)

c /a = 3.88

Tl

y x

0

tI10

0.13 BaAI4

0.25 Ba

0.37

0.5

0.63

0.75

c /a = 2.46

AI

y x

0

tP10

0.12 CaBe2Ge2

0.25 Be

0.38 Ca

0.5

0.62

0.75

c /a = 2.47

Ge

y x

0

tI10

0.13

0.25

ThCr2Si2

Th

0.13

0.25

BaNiSn3

Ba

0.15

0.25

0.39 Cr

0.5

0.63

0.75

c/a = 2.62

Si

y x

0

tI10

0.37 Ni

0.5

0.63

0.75

c /a = 2.27

Sn

y x

0

0.42

0.5

0.65

0.75

Figure 7.49. A comparison between tetragonal structures (see the values of the c/a ratios).

Families of Intermetallic Structure Types: A Selection (a)

717

(b)

Ba

Al

Figure 7.50. tI10-BaAl4 type structure. Perspective view (a) and projection of a few adjacent cells on the plane x, z (b) (open and filled circles represent atoms with y 0 and y 1⁄2).

Strukturbericht designation (tI10-BaAl4 type structure) D13. A number of binary phases (such as CaAl4, SrAl4, BaAl4, EuAl4, BaGa4. EuGa4, BaIn4) have been described as belonging to this structural type; this structure (or one of its derivative variants) has also been attributed to scores of ternary phases. The tI10-BaAl4 type structure belongs to a group of interrelated structures which include the types tI8-NbAs and tI8-AgTlTe2 (see the characteristic sections of these structures shown in Fig. 7.49). It may be considered also a filled-up form of the tI8-AgTlTe2 type. A perspective view of this structure, and its projection on the x, z plane, are shown in Fig. 7.50. Sections along the z axis of a few variants of the BaAl4-type structure are shown in the following (with its ordered ternary variants such as the tI10-ThCr2Si2). An exhaustive description of the BaAl4-derivative structures has been presented by Parthé and Chabot (1984). A number of ordered ternary BaAl4-derivative structures with tetragonal symmetry and a unit cell similar to that of BaAl4 were considered; among these were the types ThCr2Si2 and CaBe2Ge2, for a 1:2:2 stoichiometry, and, for the 1:1:3 stoichiometry, the BaNiSn3 type. A number of more complex variants were also described, and also several intergrowth structures containing BaAl4-type slabs. Examples are oI22-U3Ni4Si4 type (which can be interpreted as intergrowth of BaAl4 AlB2 slabs), oS16-TbFeSi2 (BaAl4 AlB2 slabs), oS14-CeRe4Si2 (BaAl4 Cu slabs), etc. (See also Parthé et al. 1983).

718

Intermetallic Chemistry

7.5.1.3.2 CaBe2Ge2 , tP10, structural type (a BaAl4-derivative type) Tetragonal, space group P4/mmm, N. 129. Atomic positions: 2 Be in (a): 0, 0, 0; 1⁄2, 1⁄2, 0 2 Ge in (b): 0, 0, 1⁄2; 1⁄2, 1⁄2, 1⁄2 2 Be in (c) 0, 1⁄2, z; 1⁄2, 0, –z 2 Ca in (c) 0, 1⁄2, z; 1⁄2, 0, –z 2 Ge in (c) 0, 1⁄2, z; 1⁄2, 0, z– For the prototype, a 402.0, c 992.0, c/a 2.468 and zBe(c) 0.608, zCa(c) 0.249, zGe(c) 0.868. Environment data: Be (a) CNE 12, Ge (b) CNE 12, Be (c) CNE 5, Ca (c) CNE 22, Ge (c) CNE 9,

44.143.142.2 44.143.142.2 42.114.0 162.244.220.4 45.043.114.0

Examples of ternary compounds pertaining to the Be2CaGe2 type are: RSb2Ni2, RBi2Ni2, RGe2Ir2, RSi2Pt2 (U, Th)Ge2Ir2 (R rare earth metal). 7.5.1.3.3 ThCr2Si2, tI10 structural-type (a BaAl4-derivative type) The ThCr2Si2-type structure is one of the ordered ternary variant of the BaAl4 type, frequently found in several ternary compounds. The two structures may be compared considering the occupation of the same atomic positions in the space group I4/mmm (N. 139). In position (a) In position (d) in position (e)

0, 0, 0; 0, 1⁄2, 1⁄4; 1 ⁄2, 0, 3⁄4; 0, 0, z; 1 1 ⁄2, ⁄2, z 1⁄2;

⁄2, 1⁄2, 1⁄2 1 ⁄2, 0, 1⁄4; 0, 1⁄2, 3⁄4; 0, 0, –z ; 1 1 – ⁄2, ⁄2, z 1⁄2; 1

in BaAl4 2 Ba 4 Al

in ThCr2Si2 2 Th 4 Cr

4 Al

4 Si

For ThCr2Si2: a 404.3 pm, c 1057.7 pm, c/a 2.616 and z 0.375. Many ternary alloys MeT2X2 (Me Th, U, alkaline earth, rare earth metal, etc., T Mn, Cr, Pt family metal, X element of the 15th, 14th and occasionally 13th group) have been systematically prepared and investigated (Rossi et al., 1979, Parthé and Chabot 1984). A few hundreds of them resulted in the ThCr2Si2 (or

Families of Intermetallic Structure Types: A Selection

719

other Al4Ba derivatives) structure. The peculiar superconductivity and magnetic properties of these materials have been reported. The ThCr2Si2-type structure, can be described as formed by T2X2 layers interspersed with Me layers. The bonding between Me and T2X2 layers has been considered as largely ionic. In the T2X2 layers, T–X (covalent) and some T–T bonding have to be considered. A detailed discussion of this structure and of the bonding involved has been reported by Hoffmann (1987). In the specific case of the RT2X2 phases (R rare earth metal), the data concerning 10 series (T Mn, Fe, Co, Ni, Cu; X Si, Ge) have been analysed by Pearson (1985). It has been observed that the cell dimensions are generally controlled by R–X contacts. In the case of Mn, however, the R–Mn contact has to be assumed to control cell dimensions. Magnetic phase transition in RT2X2 phases have been described by Szytula (1992). Structural distortions in some groups of RT2X2 phases (RPt2Sn2), leading to less symmetric cells, have been reported by Latroche et al. (1992). An interesting compound belonging to the RT2X2 family is EuCo2P2. In a neutron diffraction investigation of this phase carried out by Reehuis et al. (1992) the positional (nuclear) and the magnetic structures were determined. The ordering of the magnetic moments of the Eu atoms and the relation (commensurability) between this ordering and that of the atomic positions were studied. 7.5.1.3.4 BaNiSn3, tI10, structural type (a BaAl4-derivative type) Body centred tetragonal, space group I4mm, N. 107. Atomic positions: (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) 2 Ba in (a) 0, 0, z; 2 Ni in (a) 0, 0, z; 2 Sn in (a) 0, 0, z; 1 4 Sn in (b) 0, 1⁄2, z; ⁄2, 0, z; For the prototype, BaNiSn3, a 482.0 pm, c 1093.0 pm, c/a 2.268 and zBa 0.000, zNi 0.655, zSn(a) 0.424, zSn(b) 0.249. Environment data: Ba (a) CNE 22, Ni (a) CNE 5, Sn (a) CNE 9, Sn (b) CNE 12,

54.046.044.244.143.118.0 42.114.0 45.043.114.0 44.143.142.2

Examples of ternary compounds pertaining to this structural type are RTX3 phases with R rare earth element, T Ru, Co, Rh or Ir and X Si, Ge or Sn or RTSi3 compounds with R Th or U and T Rh, Ir or Os.

720

Intermetallic Chemistry

7.5.1.3.5 AgTlTe2, tI8, structural type (a defect-derivative form of the BaAl4 type) – Body-centred tetragonal, space group I4m2, N. 119. 1 1 1 Atomic positions: (0, 0, 0; ⁄2, ⁄2, ⁄2) 2 Tl in (a): 0, 0, 0; 2 Ag in (c): 0,1⁄2, 1⁄4; 4 Te in (e): 0, 0, z; 0, 0, –z ; For the prototype, a 392 pm, c 1522 pm, c/a 3.883 and zTe 0.369. Layer sequence: Square (S) nets: Tl10 Tl40.13Ag30.25Te10.37Tl40.5Te10.63Ag20.75 Te40.87 The three structural types tI8-NbAs, tI8-AgTlTe2 and tI10-BaAl4 (with its ordered ternary variants) belong to a group of interrelated structures (see tI8-NbAs). Notice, that even if in a different space group, the (a) and (e) atomic positions of Tl and Te correspond to the (a) and (e) positions of Th (Ba) and Si (Al) in ThCr2Si2 (BaAl4), the two (c) positions of Ag in AgTlTe2, on the contrary correspond only to half of the (d) positions occupied by Cr (or Al) in ThCr2Si2 (or BaAl4). Even if only in a formal way, we may therefore describe the tI8-AgTlTe2 type structure as a defect variant of tI10ThCr2Si2 (or BaAl4). The AgTlTe2 phase with this tI8 structure probably is metastable. The structure was examined by electron diffraction on thin film. 7.5.1.3.6 BaMg2Sn2 , tP20, structural type Tetragonal, space group P4/nmm, N. 129. Atomic positions: 2 Mg in (a) 0, 0, 0; 1⁄2, 1⁄2, 0 2 Sn in (b) 0, 0, 1⁄2; 1⁄2, 1⁄2, 1⁄2 2 Ba in (c1) 0, 1⁄2, z; 1⁄2, 0, –z 2 Ba in (c2) 0, 1⁄2, z; 1⁄2, 0, –z 2 Mg in (c3) 0, 1⁄2, z; 1⁄2, 0, –z 2 Sn in (c4) 0, 1⁄2, z; 1⁄2, 0, –z 2 Sn in (c5) 0, 1⁄2, z; 1⁄2, 0, –z 2 Sn in (c6) 0, 1⁄2, z; 1⁄2, 0, –z 4 Mg in (f) 0, 0, z; 1⁄2, 1⁄2, z 1⁄2, 1⁄2, –z ; 0, 0, –z For the prototype, BaMg2Sn2, a 489.0 pm, c 2420.0 pm, c/a 4.949, zBa(c1) 0.871, zBa(c2) 0.380, zMg(c3) 0.566, zSn(c4) 0.185, zSn(c5) 0.066, zSn(c6) 0.681, zMg(f) 0.252. Mg (a) Sn (b)

CNE 12, CNE 12,

44.143.142.2 44.143.142.2

Families of Intermetallic Structure Types: A Selection

Ba (c1) Ba (c2) Mg (c3) Sn (c4) Sn (c5) Sn (c6) Mg (f)

CNE 22, CNE 22, CNE 9, CNE 9, CNE 9, CNE 9, CNE 12,

721

162.244.220.4 162.244.220.4 45.043.114.0 45.043.114.0 45.043.114.0 45.043.114.0 44.143.142.2

7.5.1.4 MoNi4, tI10, structural type Body centred, tetragonal, space group I4/m, N. 87. Atomic positions (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) 2 Mo in (a): 0, 0, 0; 8 Ni in (h): x, y, 0; –x , –y , 0; –y , x, 0; y, –x, 0 with x 0.2, y 0.4. This structure may be considered a superstructure based on a face-centred cubic pseudo-cell. The atoms form close-packed layers stacked in a 15 layer close packed repeat sequence. For the prototype, MoNi4, a 572.0 pm, c 356.4 pm, c/a 0.623. Environment data: Mn (a) CNE 12, Ni (h) CNE 12,

122.2 122.2

(8Ni, 4Ni) (6Ni, 2Mo, 1Mo, 3Ni)

Strukturbericht designation D1a. 7.5.1.5 CaCu5, hP6 , structural type Hexagonal, space group P6/mmm, N. 191. 1 Ca in (a) 0, 0, 0 2 Cu in (c) 1⁄3, 2⁄3, 0; 2⁄3, 1⁄3, 0 3 Cu in (g) 1⁄2, 0, 1⁄2; 0, 1⁄2, 1⁄2; 1⁄2, 1⁄2, 1⁄2 For the prototype, a 508.2 pm, c 407.8 pm, c/a 0.802. Environment data: Ca (a) CNE 18, Cu (c) CNE 12, Cu (g) CNE 12,

122.1.0.162.2 65.036.034.0 45.044.143.1

(6Cu, 12Cu) (6Cu, 3Cu, 3Ca) (4Cu, 4Cu, 4Ca)

The layer stacking symbol, triangular (T: A, B, C), hexagonal (H: a, b, c) and α . kagomé (K: α, β, γ) nets is: CaA0 Cu a0 Cu0.5 Strukturbericht designation D2d. The section sequence of the hP6-CaCu5 type structure is shown in Fig. 7.51.

722

Intermetallic Chemistry y x

hP6 CaCu5 c /a = 0.80

z=0

Ca 0.5

Cu

1

Figure 7.51. Sequences of characteristic sections of the hP6-CaCu5 type structure.

A large coordination is obtained in this structure: Ca is surrounded by 6 Cu 12 Cu 2 Ca at progressively higher distances and the Cu atoms have 12 neighbours (in a non-icosahedral coordination). Several phases belonging to this structure are known: alkali metal compounds (such as KAu5, RbAu5), alkaline earth compounds (such as BaAu5, BaPd5, BaPt5, CaPt5, CaZn5, etc.), rare earth alloys (such as LaCo5, LaCu5, LaPd5, LaPt5, LaZn5, etc.), Th compounds (such as ThFe5, ThCo5, ThNi5, etc.). Ternary phases have also been described, both corresponding to the ordered derivative hP6-CeCo3B2 type (1 Ce in (a), 2 B in (c) and 3 Co in (g)) and to disordered solid solutions of a third component in a binary CaCu5-type phase. Other CaCu5-type derivative structures are for instance hP18-Nd3Ni13B2, hP12-CeCo4B, hP18-Ce3Co11B4, hP24-Ce2Co7B3 (structures built up of CaCu5 and CeCo3B2 slabs). According to Pearson (1972), the CaCu5 type may be considered the reference arrangement of a family of structures with large coordination polyhedra and in which triangular 36 (and hexagonal 63) nets of atoms are alternatively stacked with kagomè 3636 nets. In particular, a number of structures can be obtained from the CaCu5 type by replacing various proportions of the Ca atoms at the centres of two fused hexagonal anti-prisms by two atoms with their common axis along the axis of the anti-prisms, so that each atom centres one of the hexagonal anti-prisms. Examples of such structures are the tI26-ThMn12 type (by substitution of Mn pairs for half of the Ca (Th) atoms), the hR57-Th2Zn17 and the hP38-Th2Ni17 (by substitution of one third of Ca (Th) atoms by pairs of Zn or Ni atoms). The resulting structures are shown in the specific paragraphs. The relationships existing between the different unit cells of these structures can be seen in Fig. 7.52. As for the building principles of the CaCu5 type, some analogies with the Laves phases may also be noticed. Cobalt-based rare earth alloys such as SmCo5 (hP6-CaCu5 type) are important materials for permanent magnets. A short review on the properties of alloys as permanent magnetic materials is given in Raghavan and Antia (1994). Complex (especially iron) alloys have been mentioned starting from the Alnico (Fe–Al–Ni–Co) alloys introduced in the thirties, followed by ferrites and Co-based rare earth alloys (such as SmCo5) and then by Sm2(Co, Fe, Cu)17 and Nd2Fe14B

Families of Intermetallic Structure Types: A Selection 2 3 Ca, Th Ni, Zn

2

3

CaCu5

1 2

1

Th2Ni17 2

1

Cu, Mn

723

1

Th2Zn17 2

2 3

ThMn12 3

1 3

Figure 7.52. The projections of the unit cells of CaCu5 (on the x/y plane), of Th2Zn17 and Th2Ni17 (on the x/y plane) and of ThMn12 (on the y/z plane) are compared (adapted from Pearson 1972).

(tP68) with progressively decreasing volume and weight of magnets per unit energy product. In an investigation of the ternary Yb–Zn–Al system, Fornasini et al. (2006), identified four ternary phases, hP41(38.6)-Yb3.36Zn30.94Al4.34 (with a structure derived from the SmZn11 type), hP63(56.6)-Yb6.4Zn46.8Al3.4, hP120(113.6)Yb12.4Zn96.8Al4.4 (with a structure related to the U2Zn17 type) and tI100Yb3Zn17.7Al4.3 (with a structure related to the Ce3Zn22 type). These structures are found neither in the Yb–Zn nor in the Yb–Al system. The addition of Al seems to stabilize these otherwise unstable structures in the binary systems. The four structures belong to the same family derived from the hP6-CaCu5 type by replacing part of the Ca atoms with dumbbells of partner elements. Fornasini et al. (2006) observed that these compounds are members of the family which can be described as an intergrowth of the CaCu5 and Zr4Al3 types. 7.5.1.6 CaB6, cP7 structural type (a cross-reference note). This compound is an important example of 1:6 stoichiometry and of octahedral structure. Details about this and the high coordination number and application of the Wade rules are in § 4.4.4.7. 7.5.1.7 Th2Ni17, hP38, structural type Hexagonal, space group P63/mmc, N. 194. Atomic positions: 2 Th in (b) 0, 0, 1⁄4; 0, 0, 3⁄4 1 2 2 Th in (d) ⁄3, 2⁄3, 3⁄4; ⁄3, 1⁄3, 1⁄4 1 2 2 2 4 Ni in (f) ⁄3, ⁄3, z; ⁄3, 1⁄3, z 1⁄2; ⁄3, 1⁄3, –z ; 1 1 1 6 Ni in (g) ⁄2, 0, 0; 0, ⁄2, 0; ⁄2, 1⁄2, 0; 1 1 1 1 1 0, ⁄2, ⁄2; ⁄2, ⁄2, ⁄2

⁄3, 2⁄3, –z 1⁄2 ⁄2, 0, 1⁄2;

1 1

724

12 Ni in (j)

12 Ni in (k):

Intermetallic Chemistry

x, y, 1⁄4; y, –x y, 3⁄4; –x , –x y, 3⁄4; x, 2x, z; 2x, x, z 1⁄2; –x, x, –z ;

y–, x y, 1⁄4; x y, x, 3⁄4; –y, –x , 1⁄4; 2x–, –x , z; –x, x, z 1⁄2; –, –x, z– 1⁄2; 2x

x– y, –x , 1⁄4; y, x, 3⁄4; –x y, y, 1⁄4; x, –x , z; 2x, x, z–; x, 2x, –z 1⁄2;

x– y–, 3⁄4; x y, y–, 3⁄4 x, x y, 1⁄4 –x , 2x–, z 1⁄2; –x, 2x –, –z – x, x, z– 1⁄2

For the prototype, Th2Ni17: a 837.0 pm, c 814.0 pm, c/a 0.973 and zNi(f) 0.110, xNi(j) 0.333, yNi(j) 0.000, xNi(k) 0.167, zNi(k) 0.000. Environment data: Th (b) CNE 18, Th (d) CNE 20, Ni (f) CNE 14, Ni (g) CNE 12, Ni (j) CNE 13, Ni (k) CNE 12,

124.0.0.164.0 124.165.026.0 125.026.0 125.0 105.026.014.0 85.024.123.1

The Th2Ni17- and the Th2Zn17-type structures (and derivative structures) are closely inter-related: they can be considered as stacking variants of similar structural slabs which when stacked in a sequence …ABAB….. or …ABCABC… result in the hexagonal hP38 or in the rhombohedral hR57 structure. Following the systematic description by Parthè and Chabot (1984) we may consider the structures of hP38-Ce2Ni15Si2 (Th2Ni17 derivative) and of hR57-Ce2Co15Al2 (Th2Zn17 derivative) as examples of several compounds ideally having the R2T15X2 composition (R lanthanide, T transition metal, X Al, Si, etc.). The composition, and structure, of the slabs was described as: 2RT5 X2T5 R2T15X2, where RT5 is a segment of the hexagonal CaCu5 type structure, and X2T5 may be described as a CaCu5-type block in which an R atom has been substituted by a pair (a dumbbell) of X atoms. 7.5.1.8 Th2 Zn17 , hR57, structural type – Rhombohedral, space group R3 m, N. 166. Atomic positions: (0, 0, 0; 2⁄3, 1⁄3, 1⁄3; 1⁄3, 2⁄3, 2⁄3) 6 Th in (c1): 0, 0, z; 0, 0, –z ; 6 Zn in (c2): 0, 0, z; 0, 0, –z ; 1 1 1 1 1 9 Zn in (d): ⁄2, 0, ⁄2; 0, 1⁄2, 1⁄2; ⁄2, ⁄2, ⁄2; – 18 Zn in (f): x, 0, 0; 0, x, 0; x , –x , 0; –x , 0, 0; 0, –x , 0; x, x, 0; 18 Zn in (h) x, –x , z; x, 2x, z; 2x–, –x , z; –x , x, –z ; 2x, x, –z ; –x , 2x–, –z ;

Families of Intermetallic Structure Types: A Selection

725

For the prototype, Th2Zn17, a 903.0 pm, c 1320.0 pm, c/a 1.462 and zTh(c1) 0.333, zZn(c2) 0.097; xZn(f) 0.333, xZn(h) 0.500; zZn(h) 0.167. Environment data: Th (c1) CNE 19, Zn(c2) CNE 14, Zn (d) CNE 12, Zn (f) CNE 13, Zn (h) CNE 12,

94.135.135.034.016.0 125.026.0 125.0 105.026.014.0 85.024.123.1

See the paragraph on the Th2Ni17-type structure for a few comments on both structures. – 7.5.1.9 BaHg11 , cP36, structural type Cubic, space group Pm3m, N. 221. Atomic positions: 1 1 Hg in (b) ⁄2, 1⁄2, 1⁄2 1 3 Ba in (d) ⁄2, 0, 0; 0, 1⁄2, 0; 0, 0, 1⁄2 –x , –x , x; –x , x, –x ; 8 Hg in (g) x, x, x; x, –x , –x ; – – – – – – x, x, x ; x, x, x; x, x , x; x , x, x 12 Hg in (i) 0, y, y; 0, –y, y; 0, y, –y; 0, –y, –y; –y, 0, y; –y, 0, –y; y, 0, y; y, 0, –y; –y, y, 0; –y, –y, 0 y, y, 0; y, –y, 0; – 1 1 – 1 1 – – ⁄2, y, y; ⁄2, y, y; ⁄2, y, y; ⁄2, y, y; 12 Hg in (j) – – 1 1 – 1 y, ⁄2, y; y, ⁄2, y; y, ⁄2, y; y, 1⁄2, –y; –y, y, 1⁄2; –y, –y, 1⁄2 y, y, 1⁄2; y, –y, 1⁄2; xHg(g) 0.155; yHg(i) 0.345; yHg(j) 0.275. For the prototype BaHg11, a 960.0 pm Environment data: Hg (b) CNE 12, Ba (d) CNE 20, Hg (g) CNE 15, Hg (i) CNE 10, Hg (j) CNE 9,

122.2 85.084.146.0 125.036.0 45.043.122.2 42.240.314.0

Compounds pertaining to this type are CaHg11, SrHg11, BaHg11 and several RCd11 (with R rare earth metal, Th, U, Np, Pu). In all these compounds the large atom in d) is surrounded by a great number of Hg or Cd atoms. Comments on stuffed variants of cP36-BaHg11 structure type have been reported by Li and Corbett (2006). The ordered structure of cP37-K3Mg20In14 has been described and discussed with particular attention to the role of Mg and its substantial participation in the overall network bonding (see § 5.13.4.2). Variants

726

Intermetallic Chemistry

cP36-37 have been mentioned for alloys such as Me3Au6 xAl26Ti (Me Ca, Sr, Yb) and Y3Ni6xAl26Ta which possibly are partially disordered or must be described with larger cells. According to Pearson (1972) the BaHg11 type represents a structure in which the size (radius ratio) is an important controlling factor. Among the XYn phases with high stoichiometric value n, Pearson considered the following ones: tI26-ThMn12 (coordination CNE around Th 20) and with an ideal radius ratio rX/rY in the range 1.3–1.5 to satisfy the high coordination; cP36-BaHg11 (CNE 20–22, radius ratio1.35–1.65), cF112-NaZn13 (CNE 24, radius ratio 1.6–1.8); cF52UB12 (CNE 24, radius ratio 2.1). 7.5.1.10 ThMn12, tI26, structural type and ThMn12-derivative types Body centred tetragonal, space group I4/mmm, N. 139. Atomic positions (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) 2 Th in (a) 0, 0, 0 3 3 1 8 Mn in (f) 1⁄4, 1⁄4, 1⁄4; ⁄4, ⁄4, ⁄4; 3⁄4, 1⁄4, 1⁄4; 1⁄4, 3⁄4, 1⁄4 – 8 Mn in (i) x, 0, 0; x , 0, 0; 0, x, 0; 0, –x , 0 –x , 1⁄2, 0; 1⁄2, x, 0; 1 – 8 Mn in (j) x, 1⁄2, 0; ⁄2, x , 0 For the prototype, ThMn12: a 874.0 pm, c 495.0 pm, c/a 0.566 and xMn(i) 0.361, xMn(j) 0.277. Environment data: Th (a) CNE 20, Mn (f) CNE 12, Mn (i) CNE 14, Mn (j) CNE 12,

85.084.146.0 125.0 125.026.0 85.024.123.1

Strukturbericht designation D2b. Among the compounds having this structure several berillides of transition elements are known: MeBe12 (Me Ti, V, Nb, Ta, Cr, Mo, W, Mn, Fe, Co, Pd, Pt, Au) and a number of MeMg12, MeMn12, MeZn12 phases with Me corresponding to some elements of the lanthanide family. Several ternary phases are known, often homogeneous in more or less large ranges of compositions: formulae such as MeAl6T6, MeAl8T4 (Me lanthanides, actinides, T Mn, Cr, Fe) are frequently found and also several isostructural phases with Ga instead of Al. According to the systematic presentation and classification of intermetallic phases presented by Parthè and Chabot (1984), some

727

Families of Intermetallic Structure Types: A Selection

more or less ordered variants have been considered for which, in the same space group I4/mmm, the following atomic positions were described: Atoms in the different positions of various tI26-ThMn12 structure variants: tI26-YNi10Si2 tI26-DyFe6Al6 tI26-CeMn4Al8 Wyckoff position (a) (0, 0, 0; ) 2Y 2 Dy 2 Ce (f) (1⁄4, 1⁄4, 1⁄4; ) 8 Ni 8 Fe 8 Mn (i) (x, 0, 0; ) 4 Ni 4 Si 8 Al 8 Al (j) (x,1⁄2, 0; ) 8 Ni 4 Fe 4 Al 8 Al Unit cell edges of the ternary variants a (pm) 820.7 865.0 c (pm) 467.7 500.1 c/a 0.570 0.578

889.0 517.0 0.582

Together with other structural types such as BaHg11, NaZn13, UB12, the ThMn12 type may be considered a structure in which the size factor (the ratio between the radii of the component atoms) plays a significant role. All these structures have high coordination number around the larger atom. 7.5.1.11 NaZn13, cF112, structural type – Face-centred cubic, space group Fm3 c, N. 226 Atomic positions (0, 0, 0; 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 3 3 3 8 Na in (a) 1⁄4, 1⁄4, 1⁄4; ⁄4, ⁄4, ⁄4 1 1 1 8 Zn in (b) 0, 0, 0; ⁄2, ⁄2, ⁄2 96 Zn in (i) 0, y, z; 0, –y, z; z, 0, y; z, 0, –y; – y, z, 0; y, z, 0; – 1 1 – 1 y ⁄2, ⁄2, z ⁄2; y 1⁄2, 1⁄2, –z 1⁄2; 1 ⁄2, z 1⁄2, –y 1⁄2, 1⁄2, z 1⁄2, y 1⁄2; z 1⁄2, y 1⁄2, 1⁄2; z 1⁄2, –y 1⁄2, 1⁄2;

⁄2, 1⁄2, 0)

1

0, y, –z; –z, 0, y; y, –z, 0 y 1⁄2, 1⁄2, z 1⁄2; 1 – ⁄2, z 1⁄2, –y 1⁄2; –z 1⁄2, y 1⁄2, 1⁄2;

0, y–, –z ; –z, 0, –y; –y, –z, 0 –y 1⁄2, 1⁄2, z 1⁄2; 1 – ⁄2, z 1⁄2, y 1⁄2; –z 1⁄2, –y 1⁄2, 1⁄2;

For the prototype, NaZn13, a 1228.4 pm, yZn(i) 0.1806 and zZn(i) 0.1192. Strukturbericht designation D23. Environment data: Na (a) CNE 24, Zn (b) CNE 12, Zn (i) CNE 10,

244.1 125.0 55.026.024.013.0

728

Intermetallic Chemistry

Typical compounds having this structure are several MeBe13 phases (with Me Ca, Sr, Ba, Sc, Y and the lanthanides and actinides, and Zr and Hf), MeZn13 (with Me Na, K, Rb, Ca, Sr, Ba, Eu, Yb), KCd13, RbCd13, CsCd13 and a few compounds such as LaCo13, etc. Several ternary compounds are also known as LaCu6Al6. According to Parthè and Chabot (1984) the body-centred tetragonal Ce2Ni17Si9 structure can be considered a NaZn13-derivative structure (We have tI56-Ce2Ni17Si9 type: I4/mcm a 785.7 pm, c 1150.3 pm, c/a 1.46 with a – – (Ce2Ni17Si9) 1⁄2 2a (NaZn13) and c (Ce2Ni17Si9) a(NaZn13) and c/a 2 and V(Ce2Ni17Si9) 1⁄2V(NaZn13). The rather complex structure of the compound NaZn13 was studied by Ketelaar (1937) and by Zintl and Haucke (1938). Every Na atoms is surrounded by 24 Zn atoms at the same distance. The lattice parameters of several MeZn13 compounds pertaining to this structural type are, in a first approximation, independent of the size of the alkali (or alkaline earth) metal atom. Similar consideration may be made for the MeCd13 compounds. Zintl, therefore, considered the fundamental component of this crystal structure to be a framework of Zn (or Cd) atoms with the alkali (or alkaline earth) metal atoms occupying the holes of the framework. However notice (Nevitt 1967) that in compounds MeX13 radius ratios (rMe/rX) deviating by more than about 15% from the mean value 1.54 are unfavourable for the occurrence of the structure. The NaZn13-type structure, only however in a very formal way, could be compared with the CsCl type in which the anions are replaced by Zn13 centred icosahedra. 7.5.1.12 Relationships among prototypes with high stoichiometric ratios. After having described the structures of a number of compounds characterized by high stoichiometric ratios and especially those corresponding to the hP6-CaCu5, hP38Th2Ni17, hR57-Th2Zn17 and tI26-ThMn12 types it may be useful, according to Pearson (1972), to underline a number of relationships among the unit cells of these structures. This is shown by the diagram of Fig. 7.52 containing projections of the mentioned structures. All these structures are characterized by high coordination numbers around Ca (Th): CNE is 18 (CaCu5), 18–20 (Th2Ni17), 19 (Th2Zn17) and 20 (ThMn12).

7.5.2 γ-brass: Cu5Zn8, cI52 structural type The Cu5Zn8 (Cu5Zn6.9 Cu5Zn9.7) phase is a classical example of a HumeRothery phase (“electron compounds”, brass-type phases) that is of a phase in which there is a structure-determining influence of the VEC (valence electron concentration, see § 4.4.5).

729

Families of Intermetallic Structure Types: A Selection

– Body-centred cubic, space group I 4 3m, N. 217. Atomic positions (0, 0, 0;1⁄2,1⁄2,1⁄2) 8 Zn in (c) (2 IT) x, x, x; –x , x–, x; –x , x, –x ; 8 Cu in (c) (2 OT) x, x, x; –x , –x , x; –x , x, –x ; 12 Cu in (e) (2 Oc) x, 0, 0; –x , 0, 0; 0, x, 0; 24 Zn in (g) (2 Co) x, x, z; –x , –x , z; –x , x, –z ; –z , –x , x; –z , x, –x ; x, z, x;

x, –x , –x x, –x , –x 0, –x , 0; 0, 0, x; x, –x , –z ; z, x, x; –x , z, –x ; x, –z , –x ;

0, 0, –x z, –x , –x ; –x , –z , x

For the prototype, a 884.0 pm and xCu(c) 0.828, xZn(c) 0.110, xCu(e) 0.355, xZn(g) 0.313, zZn(g) 0.036. The γ-brass Cu5Zn8 structure can be described and presented in several ways, one way is to describe it as a super-structure of the body-centred cubic packing with a tripled unit cell edge. The cell volume is then 33 27 times larger than the volume of the cI2 cell. The cell contents should be: 2 27 54: but instead it is 52. There are two vacancies, which are orderly distributed (the atoms ‘missing’ in the large cell correspond to the positions 0, 0, 0 and 1⁄2,1⁄2,1⁄2 of this cell). The atomic positions are of four kinds in a ratio of 2:2:3:6 and a random distribution may occur to some extent. The structures Fe3Zn10 and Cu9Al4 may be related to a different occupation of the same sites. With reference to a description of the γ-brass Cu5Zn8 structure in terms of polyhedra (and clusters), two clusters (each containing 26 atoms) may be considered. These have their centres in 0, 0, 0; and 1⁄2, 1⁄2, 1⁄2 and each is composed by an internal tetrahedron (IT), followed by a large outer tetrahedron (OT), then a larger octahedron (Oc) and a still larger, slightly irregular; cuboctahedron (Co). 7.5.3 Tetrahedrally close-packed phases, Frank–Kasper phases (cross-reference note) General characteristic of the so-called tetrahedral close packing have been described in § 3.9.3.1 where a list of important prototypes of such phases is reported together with an indication of the specific coordination polyhedra. For a few other phases of this group a crystallographic description is given below. 7.5.3.1 Zr4Al3, hP7, structural type (a tetrahedrally close-packed phase) – Hexagonal, space group P6, N. 174. Atomic positions: 1 Zr in (b) 0, 0,1⁄2 2 1 Zr in (f) ⁄3, 1⁄3,1⁄2 1 1 2 Zr in (h) ⁄3, 2⁄3, z; ⁄3, 2⁄3, z– – –0 3Al in (j) x, y, 0; y , x y, 0; x– y, x,

730

Intermetallic Chemistry

For the prototype, a 543.3 pm, c 539.0 pm, c/a 0.992 and zZr(h) 0.250, xAl(j) 0.333, yAl(j) 0.167. Environment data: Zr (b) CNE 15, Zr (f) CNE 15, Zr (h) CNE 14, Al (j) CNE 12,

125.036.0 125.036.0 125.0236.0 125.0

7.5.3.2 σ Cr-Fe, tP30, structural type (a tetrahedrally close-packed phase). In the space group P42/mnm, N. 136, the two atomic species Cr and Fe are distributed in several sites with a nearly random occupation. Different atom distributions have been proposed in the literature (also owing to different preparation methods and heat treatments). The following distribution is one of those reported in Daams et al. (1991). It corresponds to the reported percentage occupation probabilities of the different positions by the Cr and Fe atoms. 2 M1 in (a) 4 M2 in (f) 8 M3 in (i) 8 M4 in (i) 8 M5 in (j)

0, 0, 0; x, x, 0; x, y, 0; y, x, 0; x, y, 0; y, x, 0; x, x, z; x, x, z–;

M1 88% Fe 12% Cr M2 25% Fe 75% Cr M3 38% Fe 62% Cr M4 84% Fe 16% Cr M5 34% Fe 66% Cr

⁄2, 1⁄2, 1⁄2 – x , x–, 0; x–, y–, 0; y–, x–, 0; x–, y–, 0; y–, x–, 0; x–, x–, z; x–, x–, z–; 1

x– 1⁄2, x 1⁄2, 1⁄2; y– 1⁄2, x 1⁄2, 1⁄2; x– 1⁄2, y 1⁄2, 1⁄2; y– 1⁄2, x 1⁄2, 1⁄2; x– 1⁄2, y 1⁄2, 1⁄2; x– 1⁄2, x 1⁄2, z 1⁄2; x– 1⁄2, x 1⁄2, z– 1⁄2;

x 0.3986 x 0.4635, x 0.7393, x 0.1827

x 1⁄2, x– 1⁄2, 1⁄2 y 1⁄2, x– 1⁄2, 1⁄2 x 1⁄2, y– 1⁄2, 1⁄2 y 1⁄2, x– 1⁄2, 1⁄2; x 1⁄2, y– 1⁄2, 1⁄2 x 1⁄2, x– 1⁄2, z 1⁄2; x 1⁄2, x– 1⁄2, z– 1⁄2

y 0.1312 y 0.0661 z 0.2520

The structure can be considered as made up of primary hexagon–triangle layers containing 3636 3262 and 63 nodes (in a 3:2:1 ratio) at height 0 and 1⁄2 separated (at height 1⁄4 and 3⁄4) by secondary 32434 layers (that is layers, in which every node is surrounded, in order, by two triangles, one square, one triangle and one square). Strukturbericht designation D8b.

Families of Intermetallic Structure Types: A Selection

731

7.5.3.3 W6Fe7, hR39, structural type (μ phase) (a tetrahedrally close-packed phase) – Rhombohedral, space group R3 m, N. 166. 2 Atomic positions: (0, 0, 0; ⁄3, 1⁄3, 1⁄3; 1⁄3, 2⁄3, 2⁄3) 3 Fe in (a) 0, 0, 0 6 W in (c) 0, 0, z; 0, 0, –z 6 W in (c) 0, 0, z; 0, 0, –z 6 W in (c) 0, 0, z; 0, 0, –z 18 Fe in (h) x, –x , z; x, 2x, z; 2x–, –x , z; –x , x, –z ; 2x, x, –z ; –x , 2x–, –z ; For the prototype, W6Fe7, a 475.7 pm, c 2584.0 pm, c/a 5.432 and zW(c1) 0.167, zW(c2) 0.346, zW(c3) 0.448, xFe(h) 0.833, zFe(h) 0.257. Environment data: Fe (a) CNE 12, W (c1) CNE 15, W (c2) CNE 16, W (c3) CNE 14, Fe (h) CNE 12,

125.0 125.036.0 125.046.0 125.026.0 125.0

Strukturbericht designation D85. 7.5.4 Samson phases (a cross-reference note) In addition to the Frank–Kasper phases, other structures may be considered in which the same four types of coordination polyhedra prevail although some regularity is lost. A few notes about these phases are reported in § 3.9.3.2. 7.5.5 Chevrel phases, structures containing Me6X8 clusters (cross-reference note) The Chevrel phases are structure containing ‘clusters’ as building blocks and they may be considered as phases having characteristics at the borderline between those of compounds containing ‘molecular-like’ units and of solids containing infinitively extended units. Such phases have been described in § 4.4.4.7 together with Mo6X8 clusters and the products of their condensation. 7.5.6 A miscellany of stoichiometries and prototypes (short notes) In this last paragraph, only the essential crystal structure information is given for a couple of stoichiometries that are frequently found in several families of intermetallic compounds.

732

Intermetallic Chemistry

7.5.6.1 Selected structures corresponding to a binary 5:4 stoichiometry 7.5.6.1.1 Eu5As4 oS36, structural type (and Tm5Sb2Si2, oS36) Eu5 As4: Orthorhombic, space group Cmca , N. 64. Atomic positions: (0, 0, 0; 1⁄2, 1⁄2, 0) 4 Eu in (a) 0, 0, 0; 0, 1⁄2, 1⁄2 – –x , 0, 0; 8 As in (d) x, 0, 0; x, 1⁄2, 1⁄2; x, 1⁄2, 1⁄2 – – 1 1 1 1 8 As in (f) 0, y, z; 0, y ⁄2, z ⁄2; 0, y ⁄2, z ⁄2; 0, –y , –z – – – 1 1 x , y 1⁄2, –z 1⁄2; x, –y , –z ; 16 Eu in (g) x, y, z; x , y ⁄2, z ⁄2; –x , –y , –z ; – x, y 1⁄2, z 1⁄2; x, –y 1⁄2, z 1⁄2; –x , y, z For the prototype, Eu5As4, a 1580.2 pm, b 802.1 pm, c 805.8 pm and xAs(d) 0.8014, yAs(f) 0.1118, zAs(f) 0.6111, xEu(g) 0.8539, yEu(g) 0.8303, zEu(g) 0.6648. The coordinations and environment data are: Eu (a) CNE 14, 86.0 64.0 As(d) CNE 7, 54.0 25.0 As (f) CNE 9, 65.0 34.0 Eu (g) CNE 17, 35.1 33.1 32.1 26.1 17.0 15.0 14.1 14.0 13.2 11.2 Compounds pertaining to this structural types are phosphides and arsenides of Sr and Eu and Ba3P4. Several R5Sb2X2 compounds (with R Y or a lanthanide and X Si or Ge) have the Tm5Sb2Si2-type structure which is an ordered superstructure (of the second kind) of the oS36-Eu5As4 type and corresponds to the following data: Tm5Sb2Si2: Orthorhombic, space group Cmca, N. 64 (oS36-Eu5As4-derivative structure). Atomic positions: (0, 0, 0; 1⁄2,1⁄2, 0) 4 Tm in (a) 0, 0, 0; 0, 1⁄2, 1⁄2 –x , 0, 0; 8 Sb in (d) x, 0, 0; –x , 1⁄2, 1⁄2; x, 1⁄2, 1⁄2 – – 8 Si in (f) 0, y, z; 0, y 1⁄2, z 1⁄2; 0, y 1⁄2, z 1⁄2; 0, y–, z– –x , y 1⁄2, –z 1⁄2; x, –y , z–; 16 Tm in (g) x, y, z; –x , y– 1⁄2, z 1⁄2; –x , y–, –z ; x, y 1⁄2, z– 1⁄2; – – 1 1 x, y ⁄2, z ⁄2; x , y, z For the prototype, Tm5Sb2Si2, a 1476.8 pm, b 772.3 pm, c 774.1 pm and xSb(d) 0.2049, ySi(f) 0.3608, zSi(f) 0.1380, xTm(g) 0.1291, yTm(g) 0.1650; zTm(g) 0.3355. The structure of Tm5Sb2Si2 is closely related to the orthorhombic oP36-Sm5Ge4 and tetragonal tP36-Zr5Si4 types (Kozlov 2004). All these structures can be described as built up from fragments taken from the same basic structural types (namely CuAl2, U3Si2 and α-Po).

Families of Intermetallic Structure Types: A Selection

7.5.6.1.2 Sm5Ge4 oP36, structural type Orthorhombic, space group Pnma, N. 62. Atomic positions: 4 Ge in (c) x, 1⁄4, z; x– 1⁄2, 3⁄4, z 1⁄2; –x, 3⁄4, –z ; 4 Ge in (c) x, 1⁄4, z; x– 1⁄2, 3⁄4, z 1⁄2; –x, 3⁄4, –z ; 4 Sm in (c) x, 1⁄4, z; x– 1⁄2, 3⁄4, z 1⁄2; –x , 3⁄4, –z ; 8 Ge in (d) x, y, z; x– 1⁄2, y–, z 1⁄2; x–, y 1⁄2, –z ; x–, y–, –z ; x 1⁄2, y, –z 1⁄2; x, –y 1⁄2, z; 8 Sm in (d) x, y, z; x– 1⁄2, y–, z 1⁄2; x–, y 1⁄2, –z ; –x, y–, –z x 1⁄2, y, –z 1⁄2; x, –y 1⁄2, z; 8 Sm in (d) x, y, z; x– 1⁄2, –y, z 1⁄2; x–, y 1⁄2, –z ; –x , y–, –z ; x 1⁄2, y, –z 1⁄2; x, y– 1⁄2, z; Ge(c) Ge(c) Ge (c) Ge (d) Sm (d) Sm (d)

CNE 9, CNE 9, CNE 14, CNE 9, CNE 15, CNE 15,

733

x 1⁄2, 1⁄4, –z 1⁄2 x 1⁄2, 1⁄4, –z 1⁄2 x 1⁄2, 1⁄4, –z 1⁄2 x 1⁄2, y– 1⁄2, –z 1⁄2; –x 1⁄2, y 1⁄2, z 1⁄2 x 1⁄2, y– 1⁄2, –z 1⁄2; x– 1⁄2, y 1⁄2, z 1⁄2 x 1⁄2, y– 1⁄2, –z 1⁄2; x– 1⁄2, y 1⁄2, z 1⁄2

65.034.0 65.034.0 86.064.0 65.034.0 45.036.024.023.118.015.114.113.0 43.0.1.036.027.024.123.114.01.014.013.0

For the prototype, Sm5Ge4, a 775.0 pm, b 1494.0 pm, c 784.0 pm and xGe(c1) 0.9132; zGe(c1) 0.1115; xGe(c2) 0.1761; zGe(c2) 0.6333; xSm(c3) 0.2880; zSm(c3) 0.0024; xGe(d1) 0.2206; yGe(d1) 0.9551; zGe(d1) 0.5312; xSm(d2) 0.1205; ySm(d2) 0.1157; zSm(d2) 0.3388; xSm(d3) 0.9747; ySm(d3) 0.1004; zSm(d3) 0.8219. The prototype structure may be described according to Pearson (1972) as made up by layers parallel to the (010) plane (44 and 32434 atomic nets, see § 7.4.3.7). Several R5Si4, R5Ge4, R5Sn4 and R5Pb4 (with R Y or a lanthanide) compounds have this structure. Isostructural compounds are also found among R5T4 phases formed by rare earth metal, and plutonium, with T Rh, Ir, Pt . 7.5.6.1.3 Zr5Si4 tP36, structural type Tetragonal, space group P41212 , N. 92. Atomic positions: –x , –x ,1⁄2; –x 1⁄2, x 1⁄2, 1⁄4; 4 Zr in (a) x, x, 0; x 1⁄2, x– 1⁄2, 3⁄4; –x , y–, z 1⁄2; 8 Si in (b1) x, y, z; y– 1⁄2, x 1⁄2, z 1⁄4; –x 1⁄2, y 1⁄2, z– 1⁄4; x 1⁄2, –y 1⁄2, –z 3⁄4; y, x, –z ; y 1⁄2, x– 1⁄2, z 3⁄4; –y , –x , z– 1⁄2

734

Intermetallic Chemistry

8 Si in (b2) x, y, z; –x 1⁄2, y 1⁄2, –z 1⁄4; y 1⁄2, –x 1⁄2, z 3⁄4; 8 Zr in (b3) x, y, z; –x 1⁄2, y 1⁄2, z– 1⁄4; y 1⁄2, x– 1⁄2, z 3⁄4; 8 Zr in (b4) x, y, z; x– 1⁄2, y 1⁄2, –z 1⁄4; y 1⁄2, x– 1⁄2, z 3⁄4;

–x , –y , z 1⁄2; x 1⁄2, y– 1⁄2, –z 3⁄4 –y , –x , –z 1⁄2 –x , –y , z 1⁄2; x 1⁄2, y– 1⁄2, –z 3⁄4; y–, x–, –z 1⁄2 x–, y–, z 1⁄2; x 1⁄2, y– 1⁄2, –z 3⁄4; –y , –x , z– 1⁄2

y– 1⁄2, x 1⁄2, z 1⁄4; y, x, –z ; y– 1⁄2, x 1⁄2, z 1⁄4; y, x, –z ; y– 1⁄2, x 1⁄2, z 1⁄4; y, x, –z ;

For the prototype, Zr3Si4, a 712.3 pm, c 1300.2 pm, c/a 1.825 and xZr(a) 0.1743 xSi(b1) 0.0513; ySi(b1) 0.2982; zSi(b1) 0.8109; xSi(b2) 0.2949; ySi(b2) 0.3590; zSi(b2) 0.6752; xZr(b3) 0.9997; yZr(b3) 0.1454; zZr(b3) 0.6240; xZr(b4) 0.9969; yZr(b4) 0.3491; zZr(b4) 0.2153. Environment data: Zr (a) CNE 14, Si (b1) CNE 9, Si (b2) CNE 9, Zr (b3) CNE 16, Zr (b4) CNE 18,

86.064.0 65.034.0 65.034.0 54.037.036.033.028.0 76.054.045.027.0

Zr5Ge4 and binary Me5Si4 compounds (with Me La, Ce, Pr, Nd, Ti, Zr, Hf) have this structure. 7.5.6.2 Selected structures corresponding to a binary 5:3 stoichiometry. The seminal work by Corbett (Cordett 1996, 2000, Corbett and Leon-Escamilla 2003) may be quoted as an introduction to this paragraph for the presentation of aspects of general interest and for the description of some structure types and compound families. During their systematic studies of solid-state chemistry, Corbett and co-workers performed an accurate analysis of the preparation methods, structure and properties of the families of compounds having structures related to the Mn5Si3 and Cr5B3 types (here described in the following). Especially, a thorough examination of the Me5X3 compounds containing a divalent Me metal (alkaline earth metal, Sm, Eu, Yb ) with pnicogens (X As to Bi) or tetrels (X Si to Pb) was performed. It was underlined that the divalent metals have often contributed substantial amounts of hydrogen and this fact has led to several erroneous reports of supposed binary compounds many of which are really ternary phases stabilized by an interstitial element (hydrogen). The ability of the Mn5Si3-type structure to take up a third element in a preformed interstitial site was first described by

Families of Intermetallic Structure Types: A Selection

735

Nowotny et al. (1956) who initially thought that all these phases were ternaries (Me5X3Z) According to Corbett and Leon-Escamilla (2003) the preparation of a hydrogen-free compound and of a ternary hydride can be summarized by the following reaction examples: 5Ca(Hx) 3Sb : Ca5Sb3 5x/2 H2 (800°C, 5 hours, in Ta under dynamic vacuum); Ca5Sb3 is hexagonal Mn5Si3 type. 4.5Ca 0.5 CaH2 3 Sb : Ca5Sb3H (cooled in 40 hours from 1100°C to 650°C, in Ta container enclosed in a sealed SiO2 phial); Ca5Sb3H is orthorhombic Ca5Sb3F type. According to the first reaction to ensure the absence of hydrogen and its removal from the alkaline earth metal, with which it generally forms appreciable solid solution, the preparation must be performed in Ta (or Nb) crucibles relying on the special properties of these metals. Ta is selectively permeable to hydrogen at high temperature. Hydrogen dissolved in the otherwise pure reactant can be removed from the container when this is maintained in a high vacuum (dynamic vacuum) at high temperature. The preparation of the hydride can be performed in a Ta crucible loaded with hydrogen (for instance as CaH2) and sealed within an evacuated SiO2 container. In a classification of the compounds of the divalent metals, the following families of binary Me5X3 (and related ternary Me5X3H phases) were described (Corbett and Leon-Escamilla 2003): (i) Systems giving the binary tetragonal Cr5B3-type compounds and the ternary hydrogen-stuffed Cr5B3(H)-type phases. They correspond to Me Ca, Sr, Ba, Eu and X Si, Ge. (ii) Systems forming only the ternary hydrogen-stuffed Cr5B3H-type phases are Ca–Sn, Sr–Pb, Ba–Sn, Ba–Pb, Eu–Sn, Eu–Pb, Yb–Sn. In the Ca–Sn system the hydrogen content was quantified by using deuterium and neutron powder diffraction (Ca5Sn3D1.04). No stable binary Cr5B3-type compound was found in these systems. (iii) Systems giving the binary hexagonal Mn5Si3-type compounds and the ternary hydrogen-stuffed Mn5Si3Hx-type phases (x 1). These include the arsenides of Ca, Sr, Eu and Yb, the antimonides of Ba and Sm and the bismuthide of Ba. The binary compound is able to absorb hydrogen. (iv) Systems forming the binary hexagonal Mn5Si3-type compounds which take up some amount of hydrogen and then transform into another structure, the orthorhombic Ca5Sb3F-type structure. In an investigation of Mn5Si3-derivative phases (Mn5Si3-type hosting structures), Zheng et al. (2002) remarked that extended structures featuring polyhedra or condensed polyhedra are ubiquitous in chemistry. Octahedron-based frameworks of reduced halides are known to be very versatile hosts, as they can accommodate

736

Intermetallic Chemistry

very different interstitial atoms ranging from the main groups (B, Al, Ga, C, Si, Ge, N, P, As, Sb) to several transition metals (Mn, Fe, Co, Ni, Ru, Rh, Os, Ir, Pt). On the other hand intermetallic phases are known in which polyhedra enclose metal ions. Between these two categories, the Mn5Si3-type host structures have been defined as electronically very tolerant and, with reference to the work by Corbett (1996, 2000, 2003) and to the pioneering activity of Nowotny. (for instance Nowotny et al. 1956, Zheng et al. 2002), twenty different interstitial X from different regions of the periodic table (Cr, Mn, Fe, Co, Ni, Cu, Zn, Al, Ga, C, Si, Ge, Sn, Pb, P, As, Sb, O, Cl, Br) were listed, which can be incorporated in several Mn5Si3type compounds giving M5Si3X- type phases. 7.5.6.2.1 Cr5B3, tI32, structural type Tetragonal, space group I4/mcm, N. 140. Atomic positions: (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) 4 B in (a) 0, 0, 1⁄4; 0, 0, 3⁄4 4 Cr in (c) 0, 0, 0; 0, 0,1⁄2 – 1 8 B in (h) x, x ⁄2, 0; x , –x 1⁄2, 0; – 1 16 Cr in (l) x, x ⁄2, z; x , –x 1⁄2, z; –x , x 1⁄2, z 1⁄2; x, –x 1⁄2, –z 1⁄2;

–x 1⁄2, x, 0; –x 1⁄2, x, z; x 1⁄2, x, –z 1⁄2;

x 1⁄2, –x , 0 x 1⁄2, –x , z; –x 1⁄2, –x , –z 1⁄2

For the prototype, Cr5B3, a 546.0 pm and c 1064.0 pm, c/a 1.949. xB(h) 0.375, xCr(l) 0.166 and zCr(l) 0.150. Environment data: B (a) CNE 10, Cr (c) CNE 14, B (h) CNE 9, Cr (l) CNE 16,

85.0, 24.0 86.064.0 65.034.0 43.135.135.024.122.116.116.0

Strukturbericht designation D8l. 7.5.6.2.2 Mn5Si3, hP16, structural type Hexagonal, space group P63/mcm, N. 193. Atomic positions: 1 2 2 4 Mn in (d) ⁄3, 2⁄3, 0; ⁄3, 1⁄3, 1⁄2; ⁄3, 1⁄3, 0; – 6 Mn in (g) x, 0, 1⁄4; 0, x, 1⁄4; x , x–, 1⁄4; 0, x–, 3⁄4; x, x, 3⁄4 1 6 Si in (g) x, 0, ⁄4; 0, x, 1⁄4; x–, x–, 1⁄4; – 3 3 0, x , ⁄4; x, x, ⁄4

⁄3, 2⁄3,1⁄2 – x , 0, 3⁄4;

1

x–, 0, 3⁄4;

For the prototype, Mn5Si3, a 691.0 pm, c 481.4 pm, c/a 0.697 and xMn(g) 0.2358, xSi(g) 0.5992.

737

Families of Intermetallic Structure Types: A Selection

Environment data: Mn (a) CNE 14, 64.163.126.0 Mn (g) CNE 15, 84.132.225.023.1 Si (g) CNE 11, 85.024.016.0 Strukturbericht designation D88. 7.5.6.2.3 W5Si3 , tI32, structural type Tetragonal, space group I4/mcm, N. 140. Atomic positions: (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) 4 Si in (a): 0, 0, 1⁄4; 0, 0, 3⁄4 1 1 1 4 W in (b): 0, ⁄2, ⁄4; ⁄2, 0, 1⁄4 – 1 8 Si in (h): x, x ⁄2, 0; x , x– 1⁄2, 0; 16 W in (k): x, y, 0; x–, y–, 0; x–, y, 1⁄2; x, y–, 1⁄2;

x– 1⁄2, x, 0; y–, x, 0; y, x, 1⁄2;

x 1⁄2, x–, 0 y, x–, 0; y–, x–, 1⁄2

For the prototype, W5Si3, a 964.5 pm, c 497.0 pm, c/a 0.515 and xSi(h) 0.170, xW(k) 0.0746, yW(k) 0.223. Environment data: Si (a) CNE 10, W (b) CNE 14, Si (h) CNE 10, W (k) CNE 15,

85.024.0 125.026.0 45.043.122.2 44.143.135.026.013.212.2

Strukturbericht designation D8m. 7.5.6.3 A selected structure corresponding to the binary 3:4 stoichiometry 7.5.6.3.1 Th3P4, cI28, structural type – Cubic, space group I4 3d, N. 220. Atomic positions: (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) 1 1 12 Th in (a) 3⁄8, 0, 1⁄4; ⁄8, 0, 3⁄4; ⁄4, 3⁄8, 0 3 1 1 3 ⁄4, ⁄8, 0; 0, ⁄4, ⁄8; 0, 3⁄4, 1⁄8 – 1 – 1 16 P in (c) x, x, x; x ⁄2, x, x ⁄2; x–, x 1⁄2, x– 1⁄2; – – 1 1 1 1 1 x ⁄2, x ⁄2, x ; x ⁄4, x ⁄4, x ⁄4; x– 1⁄4, x– 3⁄4, x 3⁄4; – – x 3⁄4, x 1⁄4, x 3⁄4; x– 3⁄4, x 3⁄4, x– 1⁄4; For the prototype, P4Th3, a 860.0 pm, xP(c) 0.083. Environment data: Th (a) CNE 8, 45.044.0 (4P, 4P) P (c) CNE 6, 64.0 (3Th, 3Th) Strukturbericht designation D73.

738

Intermetallic Chemistry

Among the compounds pertaining to this structure type we may mention: U3X4 (X P, As, Sb, Bi, Se, Te), Sr4Bi3, Ba4Bi3, Ba4As2.6 are isostructural and crystallize as anti-Th3P4-type structure. 7.6. REMARKS ABOUT THE CRYSTAL STRUCTURES OF A FEW OXYGEN COMPOUNDS. EXAMPLES OF OXIDES AND MINERALS

7.6.1 Introduction This paragraph describes a few oxygen-containing compounds, including an example of a suboxide (Ta4O), two oxides of relevant interest to metallurgy, TiO2 and Al2O3, and ReO3. The structures of these oxides are the reference prototypes for numerous groups of compounds. A few notes concerning some more complex oxygen compounds are also included, these are: BeAl2O4 (chrysoberil), CaTiO3 (perovskite), MgAl2O4 (spinel), garnets and olivines. These compounds (and/or minerals) are often involved in metallurgical processes and their structures are the reference prototypes of a large variety of phases. Moreover, as especially mentioned in the paragraph dedicated to the MgAl2O4 (spinel) type, in these compounds examples of interesting and intriguing interrelations are often observed between the structures of intermetallics and of complex oxides. 7.6.2 Ta4O, oP5, structural type Orthorhombic, space group Pmmm, N. 47. Atomic positions: 1 Ta in (a): 0, 0, 0 1 1 Ta in (b): ⁄2, 0, 0 1 1 O in (h): ⁄2, 1⁄2, 1⁄2 2 Ta in (l): x, 1⁄2, 1⁄2; –x, 1⁄2, 1⁄2 For Ta4O: a 719.4, b 326.6 pm, c 320.4 pm (c/a 0.445, c/b 0.98 1.0) and xTa 0.225. The cell can be described as formed by two superimposed slightly distorted bcc subcells of the metal atoms. The O atom is surrounded by a slightly compressed Ta atoms octahedron. 7.6.3 αAl2O3, hR30, structural type (and derivative FeTiO3, ilmenite type) The αAl2O3, hR30, structural type (corundum structure) is: – Rhombohedral, space group R3c, N. 167 with the following atomic positions in the equivalent, triple primitive, hexagonal cell: 12 Al in (c): (0, 0, 0; 1⁄3, 2⁄3, 2⁄3; 2⁄3, 1⁄3, 1⁄3 ) (0, 0, z; 0, 0, 1⁄2 z) 18 O in (e): (0, 0, 0; 1⁄3, 2⁄3, 2⁄3; 2⁄3, 1⁄3, 1⁄3) (x, 0, 1⁄4; 0, x, 1⁄4; –x, –x, 1⁄4)

Families of Intermetallic Structure Types: A Selection

739

For the prototype αAl2O3, the lattice parameters (of the hexagonal cell) are a 475.4 pm, c 1299.1 pm, c/a 2.730 and zAl(c) 0.3523, xO(e) 0.3064. Environment data: Al (c) CNE 6, O (e) CNE 4,

64.0 43.0

The structure can be described as composed by a hexagonal close-packed array of oxide ions with aluminium ordered on two-thirds of the octahedral interstices. Along the [001] direction there are six oxygen sheets. The Strukturbericht designation is D51. Al2O3 is a material of great hardness and high melting point. Some isostructural oxides are Ti2O3, V2O3, Cr2O3, α-Fe2O3 (hematite), Rh2O3, α-Ga2O3 (Al2O3 doped with Cr2O3 is the red gemstone ruby, doped with Ti2O3 is sapphire, with Fe2O3 a variety of topaz). An α-Al2O3-derivative structure is the ilmenite, FeTiO3 (Fe2Ti4O2 3 ) structure in which the Fe and Ti atoms are ordered on two distinct sets of cation sites as described in the following. The FeTiO3, hR30, structural type (ilmenite structure) is: – Rhombohedral, space group R3 , N. 148. With the following atomic positions in the equivalent, triple primitive, hexagonal cell: 6 Fe in (c): (0, 0, 0; 1⁄3, 2⁄3, 2⁄3; 2⁄3, 1⁄3, 1⁄3) (0, 0, z) z 0.1446 6 Ti in (c): (0, 0, 0; 1⁄3, 2⁄3, 2⁄3; 2⁄3, 1⁄3, 1⁄3) ( 0, 0, z) z 0.3536 18 O in (f): (0, 0, 0; 1⁄3, 2⁄3, 2⁄3; 2⁄3, 1⁄3, 1⁄3) (x, y, z; –y , x y, z; –x y, –x, z) x 0.295, y 0.022, z 0.2548 Compare this structure with that of α-Al2O3 and notice that they correspond to very similar atomic arrangements with the ordered subdivision of the Al sites in the two groups of positions of the two metals. For FeTiO3, the lattice parameters (of the hexagonal cell) are: a 508.7 pm, c 1404.2 pm, c/a 2.760. 7.6.4 TiO2 , tP6, structural type (rutile) Different crystal forms of titanium dioxide are known: rutile (tP6), anatase (tI12) brookite (oP24). Rutile is the most common form (the others, metastable, transform into it on heating). The ideal structure of rutile can be described as: Tetragonal, space group P42/mnm, N. 136. Atomic positions: 2 Ti in (a) 0, 0, 0; 1⁄2, 1⁄2, 1⁄2 4 O in (f) x, x, 0; –x, –x, 0; –x 1⁄2, x 1⁄2, 1⁄2; x 1⁄2, –x 1⁄2, 1⁄2

740

Intermetallic Chemistry

tP6 TiO2 c /a = 0.64 O Ti

y x z=0

0.5

1

Figure 7.53. tP6-TiO2 rutile. The sequence of characteristic sections of the structure and a perspective view of the unit cell are shown. Notice the Ti atom surrounded by 6 O forming an (irregular) octahedron.

For the prototype, TiO2, a 459.37 pm, c 295.87 pm, c/a 0.644 and xO 0.3048. The Strukturbericht designation is C4. The Ti atoms form a body-centred tetragonal lattice (much distorted from a cube); the O atoms surround the Ti atoms octahedrally (see Fig. 7.53). This, tP6 type, structure of TiO2 (for which other crystal forms are known) is observed for a number of difluorides and di-oxides such as βMnO2, βPbO2, SnO2 (cassiterite) and GeO2. The antitype structure has been described for Co2N, Ti2N. It may now be observed that the binary system of oxygen with Ti (as those of other metals close to Ti in the Periodic Table such as vanadium) is very complex and contains a high number of compounds. Many of these have rutile-related structures. For the Ti–O region around the 50 at.% composition, with NaCl-type structure, see Fig. 3.38. The ‘Reduced Rutiles’ (Magnéli-type phases) are a large number of ordered stoichiometric phases in the composition region between Ti3O5 and TiO2 and corresponding to the general formula TinO2np (n and p are integers), as for instance the following group for p 1 and n 4–9: Ti4O7 (TiO1.75), Ti5O9(TiO1.80), Ti6O11 (TiO1.83), Ti7O13 (TiO1.86), Ti8O15 (TiO1.87), Ti9O17 (TiO1.89). The Ti4O7 phase is metallic at room temperature, the others tend to be semiconductors. These phases

Families of Intermetallic Structure Types: A Selection (a)

(b)

741

(c)

Figure 7.54. Scheme of the reduction of an oxide with the formation of another compound by a crystallographic shear plane (adapted from Greenwood and Earnshaw 1997). (a) With reference to a structure characterized by an octahedral coordination of oxygen around the metal, a section of the original structure (a section through the octahedral equatorial plane) is shown. The MeO6 octahedra share their vertices with each other. (b) In a plane perpendicular to that shown in (a), oxygen is removed: a plane of vacant sites is produced locally and the octahedral coordination destroyed. (c) The movement, the slide, of a crystal slab results, along the shear plane, in linking again the octahedra (by edge sharing).

are built up of slabs of rutile-type structure of a width of nTiO6 octahedra. Adjacent slabs are mutually related by a crystallographic shear which conserves oxygen atoms by sharing between adjacent octahedra. Crystallographic shear plane. Series of discrete shear phases are observed among the oxides of several transition metals. By progressive reduction, series of TinO2n1, VnO2n1 phases are obtained from the dioxides, as MenO3n1 phases may be related to trioxides such as MoO3 or WO3. An example of a crystallographic shear plane formation is schematically shown in Fig. 7.54. 7.6.5 ReO3, cP4, structural type – Cubic, space group Pm3m, N. 221. Atomic positions: 1 Re in (a) 0, 0, 0 3 O in (d) 1⁄2, 0, 0; 0,1⁄2, 0; 0, 0,1⁄2 In the unit cell cube the Re atoms are in the corners and the O atoms in the midpoints of the edges. This structure may be related to a NaCl-type cell in which the three positions at the face centres and that at the body centre are missing. Re is surrounded by an octahedron O6; each octahedron is joined through corners to six others (each oxygen is shared between two Re atoms; the overall formula therefore is ReO6/2). Layer stacking symbols: γ Triangular and kagomè (T, K) nets: ReA0 Oβ0.17 ReC0.33 Oα0.50 ReB0.67 O 0.83 1 5 1 Square (S) nets: Re 0 O 0 O 1/2

742

Intermetallic Chemistry

cP4 ReO3 Re

O

y x

cP5 CaTiO3 Ca

O

Ti

y x

z=0

0.5

1

Figure 7.55. Characteristic sections of the cubic ReO3 and CaTiO3 types.

This structure is closely related to the perovskite structure. Several trioxides (CrO3, WO3, etc.) have this structure. 7.6.6 CaTiO3, cP5, structural type (perovskite) The ideal, reference, perovskite structure corresponds to the following description: – Cubic, space group Pm3m, N. 221. Atomic positions: 1 Ca in (a) 0, 0, 0 1 Ti in (b) 1⁄2, 1⁄2, 1⁄2 3 O in (c) 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0 Layer stacking symbols: Triangular and kagomè (T, K) nets: CaA0Oα0 TiB0.17 CaC0.33 Oγ0.33 TiA0.50 CaB0.67 Oβ0.67 TiC0.83 4 Square (S) nets: Ca10 O40 Ti ⁄ O5 ⁄ Strukturbericht designation E21. The sequence sections of the ReO3 and CaTiO3 type structures are reported in Fig. 7.55. 1

1

2

2

This structure may be compared with the CsCl type (Cs in a, Cl in (b)) with the addition of the 3 O in (c), or with the AuCu3 type (Au in (a), Cu in (c)) with the addition of an atom in the position (b) and therefore described also as a filled-up AuCu3 type. The atom in a (Ca) is surrounded by 12 oxygen atoms and the atom in b (Ti) by 6 O. In order that the atoms (ions) in a and in c form together an ideal cubic close-packed arrangement they should be about the same size and the atom in b should be smaller.

Families of Intermetallic Structure Types: A Selection

743

The structure of perovskite shows several analogies with that of ReO3. For such a comparison a re-description of the CaTiO3 structure may be considered with an origin shift of 1⁄2, 1⁄2, 1⁄2. The different atomic positions will transform in the following new ones: 0, 0, 0 for Ti; 1⁄2, 0, 0; 0, 1⁄2, 0; 0, 0, 1⁄2; for oxygen (similar to those previously reported for ReO3) and 1⁄2, 1⁄2, 1⁄2 for Ca. The analogy between ReO3 and CaTiO3 is not only formal: a partial occupation of the Ca positions with varying amounts of metal ions can be obtained as for instance in the case of the cubic so-called, tungsten bronzes (AXWO3 with x 0.3–0.93 and A alkali metal). The perovskite structure and its variant and derivative structures, and superstructures, are adopted by many compounds with a formula 1:1:3 (and also with more complex compositions). The ideal, cubic perovskite structure is not very common, even the mineral CaTiO3 is slightly distorted (an undistorted example is given by SrTiO3). Along with perovskite, the previously described ilmenite (FeTiO3) is another structure for the composition MeIIXIVO3. In the perovskite the space for the Me2 ion is larger: a criterion for the preferential selection of one of the two structures is based on the values of the ionic radii: r(Me2)/r(O2) 0.7 : ilmenite;

r(Me2)/r(O2) 0.7 : perovskite

7.6.7 BeAl2O4, oP28, structural type (chrysoberil) Orthorhombic, space group Pnma, N. 62. Atomic positions: 1 4 Al in (a) 0, 0, 0; ⁄2, 0, 1⁄2; 0, 1⁄2, 0; – – 4 Al in (c) x, 1⁄4, z; x 1⁄2, 3⁄4, z 1⁄2; x , 3⁄4, z–; x 0.2732 z 0.9940 –x 1⁄2, 3⁄4, z 1⁄2; –x , 3⁄4, –z; 4 Be in (c) x, 1⁄4, z; x 0.0929 z 0.4335 –x 1⁄2, 3⁄4, z 1⁄2; –x , 3⁄4, z–; 4 O in (c) x, 1⁄4, z; x 0.0905, z 0.7902 –x 1⁄2, 3⁄4, z 1⁄2; 4 O in (c) x, 1⁄4, z; x–, 3⁄4, –z ; x 0.4334 z 0.2410 –x , y 1⁄2, z–; 8 O in (d) x, y, z; x– 1⁄2, y–, z 1⁄2; –x , y–, –z ; x 1⁄2, y, –z 1⁄2; x, y– 1⁄2, z; x 0.1632 y 0.0172 z 0.2585

⁄2, 1⁄2, 1⁄2 x 1⁄2, 1⁄4, –z 1⁄2 1

x 1⁄2, 1⁄4, –z 1⁄2 x 1⁄2, 1⁄4, –z 1⁄2 x 1⁄2, 1⁄4, –z 1⁄2 x 1⁄2, y– 1⁄2, –z 1⁄2 x– 1⁄2, y 1⁄2, z 1⁄2

For the prototype BeAl2O4, a 940.41 pm, b 547.56 pm, c 442.67 pm. As reported by Hyde and Andersson (1989) the well-refined structure of mineral crysoberil may be considered the reference for the structures of a number of

744

Intermetallic Chemistry

minerals (and synthetic oxides, sulphides, fluorides, etc.). The very important silicate members of this group (the olivine group X2ZO4) include Mg2SiO4 (forsterite), Fe2SiO4 (fayalite); olivine itself is (Mg, Fe)2SiO4. In the idealized olivine structure (the real structure of BeAl2O4 is very close to the ideal one) the oxygen atoms form a slightly distorted hexagonal close-packed structure: in the interstices of which the metal atoms (cations) are inserted: Be in tetrahedral holes and Al in octahedral holes. For an analogous structure, based however on a cubic close-packed arrangement of oxygen atoms, see the cF56MgAl2O4 (spinel) structural type in § 7.6.9. 7.6.8 Garnet, yttrium iron garnet, cI160, structural type Data for the reference structure of Y3Fe5O12 ( Y3Fe2 Fe3O12) (Hyde and Andersson, 1989). – Body-centred cubic, space group Ia3 d, N. 230. Atomic positions: 16 Fe in (a): (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) (0, 0, 0; 1⁄2, 0, 1⁄2; 0, 1⁄2, 1⁄2; 1⁄2, 1⁄2, 0; 3⁄4, 1⁄4, 1⁄4; 3⁄4, 3⁄4, 3⁄4; 1⁄4, 1⁄4, 3⁄4; 1⁄4, 3⁄4, 1⁄4) 24 Y in (c) (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) (1⁄8, 0, 1⁄4; 3⁄8, 0, 3⁄4; 1⁄4, 1⁄8, 0; 3⁄4, 3⁄8, 0; 0; 1⁄4, 1⁄8; 0, 3⁄4, 3⁄8) 24 Fe in (d) (0, 0, 0; 1⁄2, 1⁄2, 1⁄2) (3⁄8, 0, 1⁄4; 1⁄8, 0, 3⁄4; 1⁄4, 3⁄8, 0; 3⁄4, 1⁄8, 0; 0; 1⁄4, 3⁄8; 0, 3⁄4, 1⁄8; 3⁄4, 5⁄8, 0; 3⁄4, 3⁄8, 1 ⁄2; 1⁄8, 1⁄2, 1⁄4; 7⁄8, 0, 1⁄4;0, 1⁄4, 7⁄8; 1⁄2, 1⁄4, 1⁄8) 96 O in (h)

(0, 0, 0;1⁄2, 1⁄2, 1⁄2) (x, y, z; x– 1⁄2, y–, z 1⁄2; z, x, y; z 1⁄2, x 1⁄2, y–; – y, z, x; y , z 1⁄2, x– 1⁄2; 3 1 – 1 y ⁄4, x ⁄4, z ⁄4; y– 3⁄4, x– 3⁄4, –z 3⁄4; x 3⁄4, z 1⁄4, –y 1⁄4; x– 1⁄4, z 3⁄4, y 1⁄4; z 3⁄4, y 1⁄4, x– 1⁄4; z 1⁄4, y– 1⁄4, x 3⁄4;

x–, y 1⁄2, –z 1⁄2; –z 1⁄2, x–,y 1⁄2; y 1⁄2, –z 1⁄2, x–; y 1⁄4, x– 1⁄4, z 3⁄4; x– 3⁄4, –z 3⁄4, –y 3⁄4; –z 1⁄4, y 3⁄4, x 1⁄4;

x 1⁄2, –y 1⁄2, –z ; –z ,x 1⁄2, y– 1⁄2; –y 1⁄2, –z , x 1⁄2; –y 1⁄4, x 3⁄4,z 1⁄4; x 1⁄4,z– 1⁄4 ,y 3⁄4; –z 3⁄4, y– 3⁄4,x– 3⁄4)

with: xO(h) 0.0269; yO(h) 0.0581; zO(h) 0.1495 Lattice parameter for the prototype Y3Fe5O12: a 1237.6 pm Many hundreds of minerals and compounds have this structure. In the arrangement created by the 96 oxygen atoms, there are three types of sites which may be filled with various atoms (ions).

Families of Intermetallic Structure Types: A Selection

745

The following scheme gives examples of typical compounds and of the distribution (substitution) of the atoms in the different sites:

sites:

Y3 Fe2 Fe3O12 p p p Mg3Al2 Si3O12 pp p c a d

corresponding to the following oxygen coordination and geometry. c: twisted cubic site (CN 8), a: octahedral site (CN 6), d: tetrahedral site (CN 4). This structure may be compared with that of the Cr3Si type. In comparison with this compound the unit cell of a typical garnet has a double length edge, and therefore an eight times larger volume. The garnet unit cell may be described as an assembly of eight cubic subcells each containing a formula unit such as Mg3Al2Si3O12. The arrangement of the non-oxygen atoms in each subcell is similar to that observed for all the atoms in the Cr3Si-type cell (the different subcells, however, are differently oriented inside the garnet cell). In terms of lattice complex symbols the arrangement of the Mg24Al16Si24 atoms (in the large unit cell) corresponds to V* I2 S* that is to W2 I2 (see V* S* W2 in Fig. 3.14) which can be compared with the symbol W I of Cr3Si (see § 7.4.4.5). The garnet-type structure, therefore, may perhaps be described as an example of ‘oxygen stuffed alloy’ similarly to what reported in the following discussion of the MgAl2O4 (spinel), cF56, structural type. In the silicate crystal chemistry, compounds such as Mg3Al2Si3O12 are classified within the orthosilicates owing to the isolated SiO44 tetrahedra existing in their structure, and better described by a chemical formula such as Mg3Al2(SiO4)3. Among the best-known garnets: Y3Fe2Fe3O12 (Y3Fe5O12: yttrium–iron garnet YIG) for its magnetic properties and applications, Y3Al5O12 (YAG, important laser host material). 7.6.9 MgAl2O4 , cF56, structural type (spinel) – Face-centred cubic, space group Fd3m, N. 227. Atomic positions: (0, 0, 0; 0, 1⁄2, 1⁄2; 1⁄2, 0, 1⁄2; 1⁄2, 1⁄2, 0) 3 1 3 8 Mg in (a) 0, 0, 0; /4, /4, /4 5 5 5 3 7 1 16 Al in (d) /8, /8, /8; /8, /8, /8; 1 3 7 /8, /8, /8; 32 O in (e) x, x, x; x–, x– 1⁄2, x 1⁄2; – 3 1 3 x ⁄4, x ⁄4, x ⁄4; x– 1⁄4, x– 1⁄4, x– 1⁄4; x 1⁄2, x–, x– 1⁄2; x– 3⁄4, x 3⁄4, x 1⁄4;

7

/8,1/8,3/8;

x– 1⁄2, x 1⁄2, x–; x 1⁄4, x– 3⁄4, x 3⁄4;

746

Intermetallic Chemistry

For the prototype, a 807.5, xO 0.361. Environment data: Mg (a) CNE 4, Al (d) CNE 6, O (e) CNE 4,

43.0 64.0 43.0

(4 O) (regular tetrahedron) (6 O) (regular octahedron) (1Mg, 3Al)

Strukturbericht designation H11. The section sequence of MgAl2O4 type structure are shown in Fig. 7.56. The structure may be described with reference to a face-centred cubic closepacked arrangement of oxygen atoms (ions) in which the cations are inserted. The distribution of the 32 O atoms corresponds to that of a combination of eight adjacent cells of the simplest cubic close-packed structure (the cF4-Cu type). In this large cell we have therefore eight times as many tetrahedral and octahedral holes as those in one simple cell, that is 32 octahedral sites and 64 tetrahedral sites. Hence, in MgAl2O4 (ideally) one half of the octahedral sites are occupied by Al atoms (Al3 ions) and one eighth of the tetrahedral sites by Mg atoms (Mg2 ions). This distribution of ions is typical of the so-called normal spinels. In Fe2MgO4, on the other hand, half of the Fe atoms are in the tetrahedral sites and the rest of Fe together with the Mg atoms are in the octahedral sites: such a spinel is said to be inverse. For an analogous structure, based however on a slightly distorted hexagonal close-packed arrangement of oxygen atoms, see BeAl2O4, oP28, structural type (chrysoberil) and ‘Olivines’.

z=0

z = 1/8

z = 1/4

z = 3/8

z = 1/2

z = 5/8

z = 3/4

z = 7/8

O

Mg

Al

Figure 7.56. Characteristic sections of the cubic unit cell of MgAl2O4 (spinel). Compare the metal positions with those depicted in Fig. 7.30 for the atoms in the Cu2Mg-type Laves phases.

Families of Intermetallic Structure Types: A Selection

747

A very great number of M 2MX4 (mainly oxides or sulphides) have a spinel-type structure (and also a few binary compounds such as Fe3O4, which can be described as Fe 32 Fe2O4). In any case it may be interesting to observe that the positions of the cations correspond to the same Wyckoff sites as those of the two components in the cF24-Cu2Mg type structure (compare the positions of the metals in the different sections of the unit cells of the two structures). As noticed by Nesper (1991), this means that we may describe the spinel structure as a kind of oxygen stuffed Laves phase. This may be considered a special case of the presentation of ‘oxides as stuffed alloys’ (O’Keeffe and Hyde 1985), having this concept based on the fact that the pure cation distribution in oxides is often isotypic with the structure of a metallic (intermetallic) phase. A list of examples has been presented, among which we may mention the following pairs of interrelated metallic and oxide phases (metallic structure and its oxygen-filled variant): Cu : ThO2 (CaF2 type), Cu : MgO (NaCl type), Cu : Cu2O, Mg : ZnO, Mg : La2O3 , C(diamond) : SiO2 (β cristobalite), MgCu2 : Mg2AlO4, CuPt : NaFeO2, Ni3Sn : Li3PO4, CrB : β-Ga2O3, etc. Nesper (1991) observed that a surprising consequence of such relationships may be found in the question: can we invert this concept ‘oxides as stuffed alloys’ into ‘intermetallic phases as electrides’? In other words: could the electrons find good residence regions at those points in the structure where the favoured anion positions are found?

7.6.10 Olivines Olivines are monosilicates (orthosilicate in the chemical nomenclature, nesosilicates in the mineralogical classification) in which isolated SiO44 groups may be recognized (νη~σος : island). The chemistry of natural olivines is conveniently described in terms of four (isostructural) principal components: Mg2SiO4 (forsterite), Fe2SiO4 (fayalite), Mn2SiO4 (tephroite), Ca2SiO4 (Ca-olivine). Their orthorhombic crystal structure is described in this chapter with reference to the oP28-BeAl2O4, chrysoberil, structural type. Olivine is the principal mineral (in terms of mass) of the earth’s upper mantle where it is present as a combination of the two main components forsterite (85–95 mol.%) and fayalite (5–15 mol.%). In the earth mantle the increase in seismic velocity with depth is believed to be due to the presence of denser modifications of common minerals. Fayalite (melting point 1205°C) and forsterite (melting point 1890°C) form continuous solid solutions (the melting diagram of their binary mixtures correspond to the type exemplified in Fig. 2.28). Phase equilibria as a function of pressure, show, however, transition into the spinel structure. (cF56-MgAl2O4, spinel structural type).

748

Intermetallic Chemistry

REFERENCES

Barin, I. and Knacke, O. (1973) Thermochemical Properties of Inorganic Substances (Springer-Verlag, New York). Baughman, R.H. and Galvao, D.S. (1993) Nature, 365, 735. Cacciamani, G., Saccone, A., De Negri, S. and Ferro, R. (2002) J. Phase Equilib., 23, 38. Chen, L. and Corbett, J.D. (2004) Inorg. Chem., 43, 436. Corbett, J.D. (1996) Zintl phases of the early p-block elements. In: Chemistry, Structure, and Bonding of Zintl Phases and Ions, ed. Kauzlarich, S.M. (VCH, New York, Weinheim). Corbett, J.D. (2000) Inorg. Chem., 39, 5178. Corbett, J.D. and Leon-Escamilla, E.A. (2003) J. Alloy Compd., 356–357, 59. Daams, J.L.C. (1995) Atomic environments in some related intermetallic structure types in: Intermetallic Compounds, ed. Westbrook, J.H. and Fleischer, R.L. (John Wiley & Sons Ltd., Chichester), p. 363. Daams, J.L.C., Villars, P. and van Vucht, J.H.N. (1991) Atlas of Crystal Structure Types for Intermetallic Phases (ASM International, Materials Park, OH). Dwight, A.E. (1974) Proceedings of the 11th Rare Earth Research Conference, October 9–10, Traverse City, Michigan, USA, p. 642. Effenberg, G. and Ilyenko, S. (eds.) (2005 et seq.) Ternary Alloy Systems: Phase Diagrams, Crystallographic and Thermodynamic Data. Landolt-Bornstein New Series, Numerical Data and Functional Relationships in Science and Technologies, Group IV: Physical Chemistry (Springer, Berlin). Elliot, R.P. (1965) Constitution of Binary Alloys, 1st (McGraw-Hill Company, New York). Ferro, R. and Saccone, A. (1996) Structure of intermetallic compounds and phases. In: Physical Metallurgy, eds. Cahn, R.W. and Haasen, P. (North-Holland, Amsterdam), p. 205. Fornasini, M.L., Manfrinetti, P. and Mazzone, D. (2006) J. Solid State Chem., 179, 2012. Gibson, B., Pöttgen, R., Kremer, R.K., Simon, A. and Ziebek, K.R.A. (1996) J. Alloy. Compd., 239, 34. Gladyshevskii, R.E., Cenzual, K. and Parthé, E. (1992) J. Alloy. Compd., 189, 221. Greenwood, N.N. and Earnshaw, A. (1997) Chemistry of the Elements, 2nd Edition (Pergamon, Oxford). Hägg, G. (1931) Z. Phys. Chem., B12, 33. Hansen, M. (1936) Der Aufbau der Zweistofflegierungen (Springer-Verlag, Berlin). Hansen, M. and Anderko, K. (1958) Constitution of Binary Alloys (McGraw-Hill Book Company, New York). Hoffmann, R. (1987) Angew. Chem. Int. Ed. Engl., 26, 846. Hultgren, R., Desai, P.D., Hawkins, D.T., Gleiser, M. and Kelley, K.K. (1973) Selected Values of the Thermodynamic Properties of Binary Alloys (American Society for Metals, Metals Park, Ohio). Hyde, B.G. and Andersson, S. (1989) Inorganic Crystal Structures (J. Wiley & Sons, New York). Kao, C.R., Pike, L.M., Chen, S.-L. and Chang, Y.A. (1994) Intermetallics, 2, 235. Ketelaar, J.A.A. (1937) J. Chem. Phys., 5, 668.

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King, R.B. (1993) Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry (CRC Press, Boca Raton, Ann Arbor). Kozlov, A.Yu., Pavlyuk, V.V. and Davydov, V.M. (2004) J. Alloy. Compd., 12, 155. Kumar, K.S. (1990) Int. Mater. Rev., 35, 293. Latroche, M., Selsane, M., Godart, C., Schiffmacher, G., Thompson, J.D. and Beyermann, W.P. (1992) J. Alloy. Compd., 178, 223. Li, B. and Corbett, J.D. (2006) Inorg. Chem., 45, 3861. Marazza, R., Rossi, D. and Ferro, R. (1980) J. Less - Common Met., 75, P25. Marazza, R., Rossi, D. and Ferro, R. (1988) J. Less - Common Met., 138, 189. Massalski, T.B. (1989) Metall. Trans., 20A, 1295. Massalski, T.B., Murray, J.L., Bennett, L.H. and Baker, H. (1986) Binary Alloys Phase Diagrams (American Society for Metals, Metals Park, Ohio). Massalski, T.B., Okamoto, H., Subramanian, P.R. and Kacprzak, L. (1990) Binary Alloy Phase Diagrams, (ASM International, Materials Park, OH). Moffatt, W.G. (1986) The Handbook of Binary Phase Diagrams (Genium Publishing Corporation, Schenectady, New York). Moore, J.S. (1993) Nature, 365, 690. Nesper, R. (1991) Angew. Chem. Int. Ed. Engl., 30, 789. Nevitt, M.V. (1967) Intermetallic Compounds, ed. Westbrook, J.H. (John Wiley & Sons, New York), p. 217. Nowotny, H., Lux, B. and Kudielka, H. (1956) Monatsh. Chem., 85, 241. Okamoto, H. (2000) Phase Diagrams for Binary Alloys (ASM International). Okamoto, H., Massalski, T.B., Chakrabarti, D.J. and Laughlin, D.E. (1987) The Au–Cu (gold-copper) system. In: Phase Diagrams of Binary Gold Alloys, ed. Okamoto, H. and Massalski, T.B. (ASM International, Materials Park, OH). O’Keeffe, M. and Hyde, B.G. (1985) Struct. Bond. (Berlin), 61, 77. Parthé, E. (1964) Crystal Chemistry of Tetrahedral Structures (Gordon and Breach Publishers, New York). Parthé, E. and Chabot, B. (1984) Crystal structures and crystal chemistry of ternary rare earth-transition metal borides, silicides and homologues. In: Handbook on the Physical Chemistry of Rare Earths (North-Holland Physics Publishing, Amsterdam), Vol. 6. Parthé, E. and Gelato, L.M. (1984) Acta Crystallogr, A40, 169. Parthé, E., Chabot, B., Braun, H.F. and Engel, N. (1983) Acta Crystallogr, B39, 588. Pearson, W.B. (1972) The Crystal Chemistry and Physics of Metals and Alloys (WileyInterscience, New York). Pearson, W.B. (1985) J. Less - Common Met., 114, 17. Raghavan, V. and Antia, D.P. (1994) J. Phase Equilib., 15, 42. Reehuis, M., Jeitschko, W., Möller, M.H. and Brown, P.J. (1992) J. Phys. Chem. Solid., 53, 687. Rodgers, J.R. and Villars, P. (1993) J. Alloy. Compd., 197, 167. Rogl, P. (1985) J. Less-Common Metals, 110, 283. Rogl, P. (1991) Inorganic Reactions and Methods, ed. Hagen, A. (VCH-Publishers, New York), p. 85.

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Rogl, P. (1992) Modern Perspectives in Inorganic Chemistry, ed. Parthé, E. NATO ASI Series (Kluwer Academic Press, Dordrecht, The Netherlands), p. 267. Rossi, D., Marazza, R. and Ferro, R. (1979) J. Less-Common Met., 66, P17. Shunk, F.A. (1969) Constitution of Binary Alloys,2nd Supplement (McGraw-Hill Company, New York). Szytula, A. (1992) J. Alloy. Compd., 178, 1. Van Vucht, J.H.N. and Buschow, K.H.J. (1965) J. Less-Common Met., 10, 98. Venturini, G., Ijjaali, I. and Malaman, B. (1999a) J. Alloy. Compd., 284, 262. Venturini, G., Ijjaali, I. and Malaman, B. (1999b) J. Alloy. Compd., 285, 194. Venturini, G., Ijjaali, I. and Malaman, B. (1999c) J. Alloy. Compd., 289, 168. Villars, P. and Calvert, L.D. (1985) Pearson’s Handbook of Crystallographic Data for Intermetallic Phases (American Society for Metals, Metals Park, Ohio). Villars, P. and Calvert, L.D. (1991) Pearson’s Handbook of Crystallographic Data for Intermetallic Phases (ASM International). Villars, P., Prince, A. and Okamoto, H. (1995) Handbook of Ternary Alloy Phase Diagrams (ASM International, Materials Park, OH). Wenski, G. and Mewis, A. (1986) Z. Anorg. Allg. Chem., 543, 49. Zaremba, V.I., Kalychak, Ya.M., Zavalli, P.Yu. and Bruskov, V.A. (1991) Sov. Phys. Crystallogr. Eng. Trans., 36, 801. Zheng, C. and Hoffmann, R. (1989) Inorg. Chem., 28, 1074. Zheng, C., Mattausch, H. and Simon, A. (2002) J. Alloy. Compd., 347, 79. Zintl, E. and Haucke, W. (1938) Z. Elektrochem. Angew. Phys. Chem., 44, 104.

751

Families of Intermetallic Structure Types: A Selection APPENDIX

Crystal structure nomenclature alphabetically arranged by Strukturbericht designation Strukturbericht Prototype designation Aa Ab Ac Ad Af Ag Ah Ai Ak Al A1 A2 A3 A3

A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 A16 A17 A20 Ba Bb Bc Bd Be Bf (B33) Bg Bh Bi

αPa βU αNp βNp HgSn6–10 γB αPo βPo αSe βSe Cu W Mg αLa C (diamond) βSn In αAs γSe C (graphite) αHg αGa αMn (χ phase) βMn I2 Cr3Si (β-W) αS P (black) αU CoU ζAgZn CaSi ηNiSi CdSb CrB MoB WC TiAs

Pearson symbol

Strukturbericht designation

Prototype

Pearson symbol

tI2 tP30 oP8 tP4 hP1 tP50 cP1 hR1 mP64 mP32 cF4 cI2 hP2 hP4 cF8 tI4 tI2 hR2 hP3 hP4 hR1 oS8 cI58 cP20 oS8 cP8 oF128 oS8 oS4 cI16 hP9 oS8 oP8 oP16 oS8 tI16 hP2 hP8

Bk Bl Bm B1 B2 B3 B4 B81 B82 B9 B10 B11 B13 B16 B17 B18 B19 B20 B26 B27 B29 B31 B32 B33(Bf) B34 B35 B37 Ca Cb Cc Ce Cg Ch Ck C1 Clb C2 C3

BN AsS (realgar) TiB NaCl (rock salt) CsCl ZnS (sphalerite) ZnS (wurtzite) NiAs Ni2In HgS (cinnabar) PbO γCuTi NiS (millerite) GeS PtS (cooperite) CuS (rovelite) AuCd FeSi CuO (tenorite) FeB SnS MnP NaTl CrB PdS CoSn TlSe Mg2Ni CuMg2 ThSi2 PdSn2 ThC2 Cu2Te LiZn2 CaF2 (fluorite) MgAgAs FeS2 (pyrite) Ag2O

hP4 mP32 oP8 cF8 cP2 cF8 hP4 hP4 hP6 hP6 tP4 tP4 hR6 oP8 tP4 hP12 oP4 cP8 mC8 oP8 oP8 oP8 cF16 oS8 tP16 hP6 tI16 hP18 oF48 tI12 oS24 mC12 hP6 hP3 cF12 cF12 cP12 cP6

752 Strukturbericht designation C4 C6 C7 C8 C9 C10 C11a C11b C12 C14 C15 C15b C16 C18 C19 C21 C22 C23 C28 C32 C33 C34 C35 C36 C37 C38 C40 C42 C43 C44 C46 C49 C54 D0a D0c D0 c D0d D0e D02 D03 D09

Intermetallic Chemistry Prototype

TiO2 (rutile) CdI2 MoS2 SiO2 (high quartz) SiO2 (β cristobalite) SiO2 (β tridymite) CaC2 MoSi2 CaSi2 MgZn2 (Laves) Cu2Mg (Laves) AuBe5 Al2Cu FeS2 (marcasite) αSm TiO2 (brookite) Fe2P Co2Si, NiSiTi (E-phase) HgCl2 AlB2 Bi2Te3 AuTe2 (calaverite) CaCl2 MgNi2 (Laves) Co2Si Cu2Sb CrSi2 SiS2 ZrO2 GeS2 AuTe2 (krennerite) ZrSi2 TiSi2 βCu3Ti SiU3 Ir3Si AsMn3 Ni3P CoAs3 (skutterudite) BiF3, AlFe3 ReO3

Pearson symbol

Strukturbericht designation

tP6 hP3 hP6 hP9 cF24 hP12 tI6 tI6 hR6 hP12 cF24 cF24 tI12 oP6 hR3 oP24 hP9 oP12

D011 D017 D018 D019 D020 D021 D022 D023 D024 D1a D1b D1c D1d D1e D1f D1g D13 D2b D2c D2d D2e D2f D2g D2h D21 D23 D5a D5b D5c D5e D5f D51 D52 D53 D54

oP12 hP3 hR5 mC6 oP6 hP24 oP12 tP6 hP9 oI12 mP12 oF72 oP24 oS12 oF24 oP8 tI16 tI16 oP16 tI32 cI32 cF16 cP4

D58 D59 D510 D511 D513 D7a D7b

Prototype

Fe3C (cementite) BaS3 Na3As Ni3Sn Al3Ni Cu3P Al3Ti Al3Zr Ni3Ti MoNi4 Al4U PdSn4 Pb4Pt B4Th Mn4B B4C Al4Ba Mn12Th MnU6 CaCu5 BaHg11 UB12 Fe8N Al6Mn CaB6 NaZn13 Si2U3 Pt2Sn3 Pu2C3 Ni3S2 As2S3 αAl2O3 (corundum) La2O3 Mn2O3 Sb2O3 (senarmontite) Sb2S3 Zn3Pt2 Cr3C2 Sb2O3 (valentinite) Ni2Al3 δNi3Sn4 Ta3B4

Pearson symbol oP16 oP16 hP8 hP8 oP16 hP24 tI8 tI16 hP16 tI10 oI20 oS20 tP10 tP20 oF40 hR15 tI10 tI26 tI28 hP6 cP36 cF52 tI18 oS28 cP7 cF112 tP10 hP10 cI40 hR5 mP20 hR10 hP5 cI80 cF80 oP20 tP40 oP20 oP20 hP5 mC14 oI14

753

Families of Intermetallic Structure Types: A Selection Strukturbericht Prototype designation

Pearson symbol

Strukturbericht designation

Prototype

Pearson symbol

D71 D72 D73 D8a

hR7 cF56 cI28 cF116

E21

CaTiO3 (perovskite) Al2CdS4 Al7Cu2Fe Al8FeMg3Si6 Mn3Al9Si AlLi3N2 CuFe2S3 (cubanite) Fe3W3C (η carbide) Al4C4Si NiSbS (ullmanite) FeKS2 NaCrS2 CuS2Sb (wolfsbergite) Al2MgO4 (spinel) Cu3VS4 (sulvanite) Cu2FeSnS4 (stannite) Fe4N AlF3C (perovskite) ThH2 Fe2N CuPt3 AuCu CuPt AuCu3 δCuTi AlCu2Mn (Heusler) Sb2Tl7 CuTi3

cP5

D8b D8c D8d D8e D8f D8g D8h D8i D8k D8l D8m D81 D82 D83 D84 D85 D86 D88 D89 D810 D811 D101 D102 E01 E07 E1a E1b E11

Al4C3 Co3S4 Th3P4 Mn23Th6, Cu16Mg6Si7 (G-phase) σCrFe Mg2Zn11 Co2Al9 Mg32(Al,Zn)49 Ge7Ir3 Ga2Mg5 W2B5 Mo2B5 Th7S12 Cr5B3 W5Si3 Fe3Zn10 Cu5Zn8(γ brass) Cu9Al4 Cr23C6 Fe7W6 (μ phase) Cu15Si4 Mn5Si3 Co9S8 Cr5Al8 Co2Al5 Cr7C3 Fe3Th7 PbFCl FeAsS MgCuAl2 AgAuTe4 (sylvanite) CuFeS2 (chalcopyrite)

tP30 cP39 mP22 cI162 cI40 oI28 hP14 hR7 hP20 tI32 tI32 cI52 cI52 cP52 cF116 hR13 cI76 hP16 cF68 hR26 hP28 oP40 hP20 tP6 mP24 oS16 mP12 tI16

E3 E9a E9b E9c E9d E9e E93 E94 F01 F5a F51 F56 H11 H24 H26 L l L 12 L 2b L 3 L1a L10 L11 L12 L2a L21 L22 L60

tI14 tP40 hP18 hP26 cI96 oP24 cF112 hP18 cP12 mC16 hR4 oP16 cF56 cP8 tI16 cP5 cP5 tI6 hP3 cF32 tP4 hR32 cP4 tP2 cF16 cI54 tP4

754

Intermetallic Chemistry

Crystal structure strukturbericht designation alphabetically arranged by pearson symbol designation Pearson symbol cP1 cP2 cP4 cP5

cP6 cP7 cP8

cP12 cP20 cP36 cP39 cP52 cI2 cI16 cI28 cI32 cI40 cI52 cI54 cI58 cI76 cI80 cI96 cI162 cF4 cF8

cF12

Prototype

Po CsCl AuCu3 ReO3 AlFe3C (perovskite) CaTiO3 (perovskite) Fe4N Ag2O CaB6 Cr3Si (β-W) FeSi Cu3VS4 (sulvanite) FeS2 (pyrite) NiSbS (ullmanite) βMn BaHg11 Mg2Zn11 Cu9Al4 (γ brass) W CoU Th3P4 CoAs3 (skutterudite) Ge7Ir3 Pu2C3 Cu5Zn8 (γ brass) Fe3Zn10 Sb2Tl7 αMn (χ phase) Cul5Si4 Mn2O3 AlLi3N2 Mg32(Al,Zn)49 Cu C (diamond) NaCl (rock salt) ZnS (sphalerite) CaF2 (fluorite) MgAgAs

Strukturbericht designation

Pearson symbol

Ah B2 L12 D09 L 12 E21 L 1 C3 D21 A15 B20 H24 C2 F01 A13 D2e D8c D83 A2 Ba D73 D02 D8f D5c D82 D81 L22 A12 D86 D53 E9d D8e A1 A4 B1 B3 C1 C1b

cF16

cF24

cF32 cF52 cF56 cF68 cF80 cF112 cF116

hP1 hP2 hP3

hP4

hP5 hP6

Prototype

AlCu2Mn (Heusler) BiF3 (AlFe3) NaTl AuBe5 SiO2 (β cristobalite) Cu2Mg (Laves) CuPt3 UB12 Al2MgO4 (spinel) Co3S4 Co9S8 Sb2O3 (senarmontite) Fe3W3C (η carbide) NaZn13 Cr23C6 Mn23Th6, Cu16Mg6Si7 (G-phase) HgSn6–10 Mg WC AlB2 CdI2 Fe2N LiZn2 γSe αLa BN C (graphite) NiAs ZnS (wurtzite) La2O3 Ni2Al3 CaCu5 CoSn Cu2Te HgS (cinnabar) MoS2 Ni2In

Strukturbericht designation L21 D03 B32 C15b C9 C15 L1a D2f H11 D72 D89 D54 E93 D23 D84 D8a Af A3 Bh C32 C6 L 3 Ck A8 A3

Bk A9 B81 B4 D52 D513 D2d B35 Ch B9 C7 B82

755

Families of Intermetallic Structure Types: A Selection Pearson symbol hP8

hP9

hP10 hP12

hP14 hP16 hP18

hP20 hP24 hP26 hP28 hR1 hR2 hR3 hR4 hR5 hR6 hR7 hR10 hR13 hR15 hR26 hR32 tP2 tP4

Prototype

Na3As Ni3Sn TiAs CrSi2 Fe2P ζAgZn SiO2 (high quartz) Pt2Sn3 CuS (rovelite) MgZn2 (Laves) SiO2 (β tridymite) W2B5 Mn5Si3 Ni3Ti Al4C4Si Al8FeMg3Si6 Mg2Ni Fe3Th7 Th7S12 Cu3P MgNi2 (Laves) Mn3Al9Si Co2Al5 αHg βPo αAs αSm NaCrS2 Bi2Te3 Ni3S2 CaSi2 NiS (millerite) Al4C3 Mo2B5 αAl2O3 (corundum) Fe7W6 (μ phase) B4C Cr5Al8 CuPt δCuTi βNp AuCu

Strukturbericht designation D018 D019 Bi C40 C22 Bb C8 D5b B18 C14 C10 D8h D88 D024 E94 E9b Ca D102 D8k D021 C36 E9c D811 A10 Ai A7 C19 F5l C33 D5e C12 B13 D7l D8i D51 D85 D1g D810 L11 L2a Ad Ll0

Pearson symbol

tP6

tP10 tP16 tP20 tP30 tP40 tP50 tI2 tI4 tI6

tI8 tI10 tI12 tI14 tI16

tI18 tI26 tI28 tI32

Prototype

CuTi3 γCuTi PbO PtS (cooperite) Cu2Sb PbFCl TiO2 (rutile) Pb4Pt Si2U3 PdS B4Th βU αCrFe Al7Cu2Fe Zn3Pt2 γB αPa In βSn CaC2 MoSi2 ThH2 Al3Ti Al4Ba MoNi4 Al2Cu ThSi2 Al2CdS4 Al3Zr CuFeS2 (chalcopyrite) Cu2FeSnS4 (stannite) Ir3Si MoB SiU3 TlSe Fe8N Mn12Th MnU6 Cr5B3 Ni3P

Strukturbericht designation L60 B11 B10 BI7 C38 E01 C4 D1d D5a B34 D1e Ab D8b E9a D59 Ag Aa A6 A5 C11a C11b L 2b D022 D13 D1a C16 Cc E3 D023 E11 H26 D0’c Bg D0c B37 D2g D2b D2c D81 D0e

756 Pearson symbol

oP4 oP6 oP8

oP12

oP16

oP20

oP24

oP40 oS4 oS8

Intermetallic Chemistry Prototype

W5Si3 AuCd FeS2 (marcasite) CaCl2 αNp ηNiSi βCu3Ti FeB GeS SnS MnP TiB Co2Si, NiSiTi (E phase) Co2Si HgCl2 Al3Ni AsMn3 BaS3 CdSb CuS2Sb (wolfsbergite) Fe3C (cementite) Cr3C2 Sb2O3 (valentinite) Sb2S3 AuTe2 (krennerite) CuFe2S3 (cubanite) TiO2 (brookite) Cr7C3 αU CaSi αGa

Strukturbericht designation D8m B19 C18 C35 Ac Bd D0a B27 B16 B29 B31 Bm C23 C37 C28 D020 D0d D017 Be F56 D011 D510 D5l1 D58 C46 E9e C21 D101 A20 Bc A11

Pearson symbol

oS12 oS16 oS20 oS24 oS28 oI12 oI14 oI20 oI28 oF24 oF40 oF48 oF72 oF128 mC6 mC8 mC12 mC14 mC16 mP12 mP20 mP22 mP24 mP32 mP64

Prototype

CrB I2 P (black) ZrSi2 MgCuAl2 PdSn4 PdSn2 Al6Mn SiS2 Ta3B4 Al4U Ga2Mg5 TiSi2 Mn4B CuMg2 GeS2 αS AuTe2 (calaverite) CuO (tenorite) ThC2 δNi3Sn4 FeKS2 AgAuTe4 (sylvanite) ZrO2 As2S3 Co2Al9 FeAsS AsS (realgar) βSe αSe

Strukturbericht designation B33(Bf) A14 A17 C49 E1a Dlc Ce D2h C42 D7b Dlb D8g C54 D1f Cb C44 A16 C34 B26 Cg D7a F5a Elb C43 D5f D8d E07 Bl Al Ak

Formula Index Compound and Prototype Index The formulae of selected compounds and prototypes are listed in alphabetical order. The alphabetical order is also used to define the symbol sequences within all the formulae. Reference is made to the numbers of paragraphs where the specific compound or structure type is described.

AsPtY-hP12 ....................................7.4.3.14.4 AuBe5-cF24 .....................................3.9.3.1.3 ..........................................................7.4.3.3.2 AuCu(I)-tP2 .........................................3.11.1 .............................................................7.4.2.6 AuCu(II)-oI40 ......................................3.11.1 AuCu3-cP4 .............................................3.7.1 ................................................................3.7.7 ................................................................3.8.3 ..........................................................4.3.2.5.4 ..........................................................7.4.4.2.2 AuSiTh-hP3 ..............................................3.8 ........................................................7.4.3.14.2 α Boron ...............................................7.3.3.1 βB-hR315 ...........................................7.3.3.1 B6Ca-cP7..........................................4.4.4.7.1 BCeCo4-hP12.........................................3.9.4 B2CeCo3-hP6 .........................................3.8.5 .............................................................7.5.1.5 B3Ce2Co7-hP24 ......................................3.9.4 B4Ce3Co11-hP18.....................................3.9.4 B3CoW3-oS28 ........................................3.9.4 BCr-oS8 ...........................................7.4.2.5.1 B3Cr5-tI32 ........................................7.5.6.2.1 BFe-oP8 ...........................................7.4.2.5.2 B6Lu5Ni19-hP30 .....................................3.9.4 B2Nd3Ni13-hP18.....................................3.9.4 BaHg11-cP36 .......................................7.5.1.9 BaMg2Sn2-tP20................................7.5.1.3.6 BaNiSn3-tI10....................................7.5.1.3.4 BaPb3-hR36 .....................................7.4.4.2.6 BaPtSb-hP3 ....................................7.4.3.14.2 Be2CaGe2-tP10 ................................7.5.1.3.2 BeSiZr-hP6 ....................................7.4.3.14.4

AgAsMg-cF12 .......................................3.7.1 ..........................................................7.4.3.2.2 AgTe2Tl-tI8 ......................................7.5.1.3.5 AlB2-hP3...................................................3.8 .............................................................7.2.1.2 ........................................................7.4.3.14.1 Al4Ba-tI10........................................7.5.1.3.1 Al2BeO4-oP28 crysoberil.......................7.6.7 AlCe-oS16........................................7.4.2.7.1 Al8CeMn4-tI26 ..................................7.5.1.10 Al7+xCo4Si2-x-mS26 .........................4.4.4.7.8 Al2Cu-tI12...........................................7.4.3.7 AlCu2Mn-cF16..........................................3.8 ..........................................................7.4.2.2.4 AlDy-oP16 .......................................7.4.2.7.2 Al6DyFe6-tI26 ...................................7.5.1.10 Al12Mg17-cI58 ..................................7.3.2.4.5 Al2MgO4-cF56 spinel ............................7.6.9 Al2O3-hR30....corundum........................7.6.3 Al3OsU2-hP12..................................3.9.3.1.3 ..........................................................7.4.3.3.1 Al3Pu-hP24 ......................................7.4.4.2.5 Al3Ti-tI8 .................................................3.8.3 ..........................................................7.4.4.4.2 Al3Zr-tI16...............................................3.8.3 ..........................................................7.4.4.4.3 Al3 Zr4-hP7..........................................7.5.3.1 As-hR6 .............................................7.3.3.3.1 AsAuNa2-oS16.................................7.4.2.7.1 As4Eu5-oS36 ....................................7.5.6.1.1 AsNa3-hP8 ..........................................7.4.4.6 AsNb-tI8 .............................................7.2.1.1 ..........................................................7.4.2.9.1 AsNi-hP4..........................................7.4.2.4.2

757

758

Formula Index

Bi-hR6..............................................7.3.3.3.1 BiLi3-cF16 .............................................3.7.1 ..........................................................7.4.2.2.4 C-cF8 diamond.......................................3.7.1 ..........................................................4.3.2.5.4 ..........................................................7.3.3.2.1 C-hP4 graphite .................................7.3.3.2.2 C-hP4 lonsdaleite .............................7.3.3.2.3 C2Ca-tI6 ..............................................3.6.1.2 ..........................................................7.4.3.4.1 CFe3-oP16 ...........................................7.4.4.7 CW-hP2 ............................................7.4.2.4.1 CaCu5-hP6 .............................................3.8.5 .............................................................7.5.1.5 CaF2-cF12...fluorite ...............................3.7.1 ..........................................................7.4.3.2.1 CaIn2-hP6.......................................7.4.3.14.3 CaCuGe-oP36 ................................7.4.3.14.4 CaLiSn-hP9....................................7.4.3.14.4 CaO3Ti-cP5..perovskite..........................3.7.1 ................................................................7.6.6 CaPPt-oP12 ....................................7.4.3.14.4 Cd2Ce-hP3 .....................................7.4.3.14.3 CdI2-hP3...........................................7.4.2.4.3 CdPt5Zn7-hP8 .....................................3.6.1 CeCu2-oI12 ......................................7.4.3.5.1 Ce5Ni2Si3-hP40 ......................................3.9.1 Ce6Ni2Si3-hP22 ......................................3.9.1 CeRe4Si2-oS14 .................................7.5.1.3.1 ClCs-cP2 ................................................3.6.1 .............................................................3.6.1.2 ................................................................3.7.1 ................................................................3.7.5 ..........................................................4.3.2.5.4 ..........................................................7.4.2.2.1 ClNa-cF8................................................3.7.1 ...................................................................3.8 ..........................................................4.3.2.5.4 ..........................................................7.4.2.2.2 Co2EuP2-tI10........................................3.11.1 Co2Si-oP12..........................................7.4.3.6 Co3V-hP24........................................7.4.4.2.4 Cr-Fe, tP30, σ...................................3.9.3.1.2 .............................................................7.5.3.2 Cr3Si-cP8 ...............................................3.7.1 ..........................................................3.9.3.1.1 ..........................................................7.4.4.5.1

Cr2Si2Th-tI10 ...................................7.5.1.3.3 Cu-cF4....................................................3.7.1 ................................................................3.7.6 .............................................................3.9.2.1 ..........................................................4.3.2.5.4 ..........................................................7.3.2.1.2 Cu2Mg-cF24...........................................3.7.1 .............................................................3.9.2.3 ..........................................................3.8.3.1.3 ..........................................................4.3.2.5.4 ..........................................................7.4.3.3.2 Cu4MgSn-cF24 ................................3.9.3.1.3 ..........................................................7.4.3.3.2 Cu4Mo6Se8 .......................................4.4.4.7.4 Cu2Sb-tP6............................................7.4.3.8 Cu2.1Sc3Zn15.9-cI184 ........................4.4.4.7.9 CuTi3-tP4 .........................................7.4.4.4.1 β Cu3Ti-oP8.........................................7.4.4.3 Cu5Zn8-cI52 γ brass...............................7.5.2 Er2RhSi3-hP24 ..........................................3.8 ........................................................7.4.3.14.2 EuGe2-hP3 .....................................7.4.3.14.3 Fe4N-cP5 ................................................3.7.1 .............................................................7.5.1.2 FeNNi-tP3 ...........................................3.8.4.4 FeO3Ti-hR30 ilmenite............................7.6.3 Fe5O12Y3 cI160...garnet .........................7.6.8 Fe2P-hP9..............................................7.4.3.9 FeS2-cP12 pyrite................................7.4.3.13 FeSi-cP8 ..............................................7.4.2.8 FeSi2Tb-oS16 ...................................7.5.1.3.1 Fe7W6-hR39, μ-phase .........................7.5.3.3 αGa-oS8...........................................7.3.2.4.3 GaGeLi-hP6 ...................................7.4.3.14.4 Ga5Ir3-tP32........................................3.11.2.1 Ga2NdNi-oS16 .......................................3.9.4 Ga2Os-oF24 ......................................3.11.2.1 Ga17Rh10-tP108 .................................3.11.2.1 Ge5Ir4-tP36........................................3.11.2.1 GeMg2-cF12...........................................3.6.1 Ge22Rh17-tI56....................................3.11.2.1 Ge4Sm5-oP36 ...................................7.5.6.1.2 Ge31V17-tP192...................................3.11.2.1 αHg-hR3 ..........................................7.3.2.4.2 Hg2K-oI12........................................7.4.3.5.2 Hg2U-hP3.......................................7.4.3.14.3 I2-oS8 ..................................................7.3.3.6

Formula Index In-tI2 ................................................7.3.2.3.1 InNi2-hP6 .........................................7.4.2.4.3 La-hP4....................................................3.7.6 .............................................................3.9.2.1 ..........................................................7.3.2.1.3 LaPtSi- tI12....................................7.4.3.15.2 Li2PtSn-cF16...........................................3.10 Mg-hP2 ..................................................3.7.1 ................................................................3.7.6 .............................................................3.9.2.1 ..........................................................4.3.2.5.4 ..........................................................7.3.2.1.1 MgNi2-hP24 ........................................3.9.2.3 ..........................................................3.9.3.1.3 ..........................................................7.4.3.3.3 MgZn2-hP12........................................3.9.2.3 ..........................................................3.9.3.1.3 ..........................................................7.4.3.3.1 αMn-cI58 .........................................7.3.2.4.5 MnP-oP8 ..........................................7.4.2.4.3 Mn5Si3-hP16 ....................................7.5.6.2.2 Mn11Si19-tP120 .................................3.11.2.1 Mn12Th-tI26 ......................................7.5.1.10 Mn23Th6-cF116 ...................................7.5.1.1 Mo2N-tI12..............................................3.6.1 MoNi4-tI10.............................................3.8.3 .............................................................7.5.1.4 Mo6PbS8-hR45.................................4.4.4.7.3 MoPt2-oI6...............................................3.8.3 ...........................................................7.4.3.12 Mo3S4-hR42 .....................................4.4.4.7.5 Mo3Se4-hR42 ...................................4.4.4.7.5 MoSi2 tI6................................................3.6.1 .............................................................3.6.1.2 ..........................................................7.4.3.4.1 NaTl-cF16 ..............................................3.7.1 ..........................................................4.3.2.5.4 ..........................................................7.4.2.2.3 NaZn13-cF112 ...................................7.5.1.11 NbP-tI8.............................................7.4.2.9.2 NdPtSb-hP6 ...................................7.4.3.14.4 Ni7Pr15Si10-hP64 ....................................3.9.1 NiSiTi-oP12 ........................................7.4.3.6 Ni4Si4U3-oI22 ..................................7.5.1.3.1 Ni10Si2Y-tI26 .....................................7.5.1.10 Ni3Sn-hP8 ...........................................7.4.4.2 ..........................................................7.4.4.2.1

759

Ni17Th2-hP38 ......................................7.5.1.7 Ni3Ti-hP16 .......................................7.4.4.2.3 O3Re-cP4 ...............................................7.6.5 OTa4-oP5 ................................................7.6.2 .............................................................3.8.4.4 O2Ti-tP6 rutilo .......................................7.6.4 OZn-hP4...........................................7.4.2.3.2 ..........................................................7.4.2.3.3 P4Th3-cI28........................................7.5.6.3.1 αPa-tI2 ................................................7.2.1.1 ..........................................................7.3.2.3.2 αPo-cP1..................................................3.7.1 ..........................................................4.3.2.5.4 .............................................................7.2.1.2 ..........................................................7.3.2.4.1 Pt2U-oS12 .........................................7.4.3.11 αPu-mP16 ........................................7.3.2.5.2 β Pu-mS34 ........................................7.3.2.5.2 γ Pu-oF8 ...........................................7.3.2.5.2 Re24Ti5-cI58 .....................................7.3.2.4.5 Ru2Sn3-tP20 ......................................3.11.2.1 αS-oF128 .........................................7.3.3.5.1 SZn-cF8 sphalerite .................................3.7.1 ..........................................................4.3.2.5.4 .............................................................7.2.1.1 ..........................................................7.4.2.3.1 ..........................................................7.4.2.3.3 SZn-hP4 wurtzite .............................7.4.2.3.2 ..........................................................7.4.2.3.3 Sb-hR6 .............................................7.3.3.3.1 Sb2Si2Tm5-oS36...............................7.5.6.1.1 SeSiZr-tP6...........................................7.4.3.8 αSi2Th-tI12 ....................................7.4.3.15.1 Si2Ti-oF24.........................................7.4.3.10 Si3W5-tI32........................................7.5.6.2.3 Si4Zr5-tP36 .......................................7.5.6.1.3 Sm-hR9 ..................................................3.7.6 .............................................................3.9.2.1 ..........................................................7.3.2.1.3 β Sn-tI4.............................................4.3.2.5.4 ..........................................................7.3.2.4.4 Te4Ti5-tI18........................................4.4.4.7.7 Th2Zn17-hR57 .....................................7.5.1.8 αU-oS4 ............................................7.3.2.5.1 β U-tP30 ...........................................7.3.2.5.1 W-cI2......................................................3.7.1 ..........................................................4.3.2.5.4

760

Formula Index

.............................................................7.2.1.1 ..........................................................7.3.2.2.1 Zn-hP2..............................................4.3.2.5.4 μ Fe7W6-hR39..................................3.9.3.1.1 .............................................................7.5.3.3 σ, Cr-Fe, tP30...................................3.9.3.1.2 .............................................................7.5.3.2 Bergman phases ...............................3.9.3.1.1 Chevrel phases .................................4.4.4.7.2 Frank-Kasper phases ...........................3.9.3.1 Hägg phases ...........................................3.8.4 Hume-Rothery phases............................4.4.5 Laves phases .......................................3.9.2.3 ..........................................................3.9.3.1.3 .............................................................7.4.3.3 Magneli phases.......................................7.6.4 Nowotny phases ................................3.11.2.1 Samson phases ....................................3.9.3.2 Zintl phases ............................................4.4.3 Cementite ............................................7.4.4.7 Chimney ladder phases .....................3.11.2.1 Corundum ..............................................7.6.3 Crysoberil...............................................7.6.7 Diamond.................................................3.7.1 ..........................................................4.3.2.5.4

..........................................................7.3.3.2.1 Ferrite ................................................5.10.4.5 Fluorite...................................................3.7.1 .............................................................7.4.3.2 Garnets ...................................................7.6.8 Graphite............................................7.3.3.2.2 .............................................................7.4.2.2 Ilmenite ..................................................7.6.3 Interstitial phases ...................................3.8.4 Lonsdaleite..........................................7.3.3.2 M phases ..........................................3.9.3.1.1 Olivines ................................................7.6.10 P phases............................................3.9.3.1.1 Perovskite ...............................................3.7.1 ................................................................7.6.6 Pyrite .................................................7.4.3.13 R phases ...........................................3.9.3.1.1 Rutile......................................................7.6.4 Sphalerite ...............................................3.7.1 ..........................................................4.3.2.5.4 .............................................................7.2.1.1 ..........................................................7.4.2.3.1 ..........................................................7.4.2.3.3 Spinel .....................................................7.6.9 Wurtzite............................................7.4.2.3.2 ..........................................................7.4.2.3.3

Index 1:1 prototypes and derivative structures AuCu(I), tP2, and AuCu(II), oI40, structural types, 668–669 cP2-CsCl, cf8-NaCl and cF16-NaTl types and NaTl-related structures, 653–658 FeSi, cP8, structural type, 671 hP2-WC and hP4-NiAs types and examples of NIAs-derivative structures, 662–666 oS16-CeAl and oP16-DyAl structure types, 669–671 oS8-CrB and oP8-FeB structure types, 666–668 simple binary tetrahedral structures and polytypes, 658–662 tI8-NbAs type (and related structures) and tI8-NbP type, 671–673 1:2 compounds, structures of, 673 AlB2, hP3, type and its structural family, 688–697 CaF2 type, 674–676 Co2Si (PbCl2), oP12, and TiNiSi, oP12, structural types, 683–685 Cu2Sb, tP6, structural type, 685–686 CuAl2, tI12, structural type, 685 Fe2 P, hP9, structural type, 686–687 FeS2, cP12, structural type (pyrite), 688 Laves phases, 676–679 MoPt2, oI6, structural type, 687–688 oI12, CeCu2 and KHg2 structural descriptions, 680–683 Rge2–x, 701–702 3rd group metals (Sc, Y, La, Ln, Ac and An), 356–357 actinide concept, 357–358, see also Actinides

chemical properties and reactivity, 370, 373–376 intermetallic chemistry alloy crystal chemistry, 390, 391, 392 melting point and formation enthalpy trends in binary alloys of, 383–387 phase diagrams, see Phase diagrams, of 3rd group metals rare earth metals atomic and physical properties, 366–369 ionization energy, 367 lanthanides, see Lanthanides metallothermic reduction, 362 occurrence and preparation, 361–362 scandium (Sc), 359 yttrium (Y), 359 4th group elements (Ti, Zr, Hf), 393 atomic and physical properties, 394 chemical properties and reactivity, 395–396 hafnium (Hf), 394 intermetallic chemistry alloy crystal chemistry, 400–402 applications of zirconium and titanium intermetalics, 402–404 melting point trend in binary alloys, 398–400 phase diagrams, 396–397 5th group elements (V, Nb, Ta) atomic and physical properties, 406, 407 chemical properties and reactivity, 406, 407 hydrides, 326 intermetallic chemistry crystal chemistry, 409, 412–413 761

762

Index

5th group elements (Continued) melting point trend in binary alloys, 409, 410–411 phase diagrams of, 407–408 6th group elements (Cr, Mo, W) atomic and physical properties, 415–416 chemical properties and reactivity, 417 chromium (Cr), 413–414 intermetallic chemistry alloy crystal chemistry, 418, 421 melting point trends in binary alloys, 417–418, 419 phase diagrams, 417 molybdenum (Mo), 414–415 tungsten (W), 415 7th group elements (Mn, Tc, Re) atomic and physical properties, 423, 424 chemical properties and reactivity, 423 intermetallic chemistry alloy crystal chemistry, 425 phase diagrams, 425, 426–427 manganese (Mn), 421–422 rhenium (Re), 423 technetium (Tc), 422 11th group elements (Cu, Ag, Au) alloys of, applications, 466–467 atomic and physical properties, 459–460 chemical properties and reactivity, 460 copper, 457–458 gold, 459 intermetallic chemistry alloy crystal chemistry, 464–466 phase diagrams, 460–464 silver, 458 13th group elements (B, Al, Ga, In, Tl) aluminium (Al), 481 alloys, 491–493 atomic and physical properties, 482–484 boron (B), 480 chemical properties and reactivity, 484–485 gallium (Ga), 481 indium (In), 481–482

intermetallic chemistry crystal chemistry of, 486, 488–491 phase diagrams, 485–486, 487 14th group elements (C, Si, Ge, Sn, Pb) atomic and physical properties, 500–501 15th group elements (N, P, As, Sb, Bi), 507–509 atomic and physical properties, 509, 510 intermetallic chemistry alloy crystal chemistry, 510–514 phase diagram, 509, 510 16th group elements (O, S, Se, Te, Po) atomic and physical properties, 516–517 binary compounds, 517–518 chalcogenides, 520 chalcogens, 520 cluster compounds, 520 selenides, tellurides and polonides, 518, 520 sulphides, 518 intermetallic chemistry, 516–520 phase diagram, 516–517 oxygen (O), 514–515 polonium (Po), 516 selenium (Se), 515 sulphur (S), 515 tellurium (Te), 515 αThSi2, tI12, and LaPtSi, tI12, structural types, 697–701 tI6-CaC2 and MoSi2-type structures, 680 TiSi2, oF24, structural type, 687 UPt2, oS12, structural type, 687 γ-Brass: Cu5Zn8, cI52 structural type, 728–729 χ Phases, 641 A Acetylides, 504 Acheson process, 602 Acoustic cavitation, 593 Actinides (An) actinium (Ac), 362–363 americium (Am), 363

Index An–An alloys, 379–381 berkelium (Bk), 364 californium (Cf), 364 chemical properties and reactivity, 376–377 crystal structures, lattice parameters, and densities, 372 curium (Cm), 363 einsteinium (Es), 364 fermium (Fm), 364 ionization energies, 371 isotopes, 365 lawrencium, 364–365 mendelevium (Md), 364 neptunium (Np), 363 nobelium (No), 364 occurrence, 365 phase stabilization, 390 physical properties, 370, 371 plutonium (Pu), 363 preparation metallothermic reduction, 365 tantalothermic reduction, 366 Van Arkel process, 366 protoactinium (Pa), 363 refining processes, 366 thorium (Th), 363 uranium (U), 363 AET, see Atomic environment type Aging, 543 Al2S3, 583 AlH3, 329 Alkali metal alloys, 335 atomic and physical properties, 338–340 chemical properties and reactivity, 340–341 crystal structures, 339, 340 intermetallic chemistry alloy crystal chemistry, 344 complex intermetallic compounds, 344–347 melting point trend in binary alloys, 343–344

763

phase diagrams, 341–342 solubility of metals in liquid alkali metals, 342–343 Alkaline earth metals and divalent rare earth metals, 347 atomic and physical properties, 350, 351 chemical properties and reactivity, 350–351 intermetallic chemistry alloy crystal chemistry, 353–356 melting point trend in binary alloys, 352–353 phase diagrams of, 351–352 Alloy 2090, 336 Alloy 2091, 336 Alloy 8090, 336 Alloy CP276, 336 Alloying behaviour of elements of periodic table, see specific entries Alloys, see specific alloys Allylenides, 504 Alpha alloys, 398 Alpha stabilizers, 398 Alpha strengtheners, 398 Alumina, 481 Aluminium (Al), 329, 487, 583 alloys applications, 491–493 glass-forming alloys, 212 highest melting points in, 486, 487 atomic and physical properties, 483 chemical properties and reactivity, 484 crystal structures, lattice parameters, and densities, 483 ionization energy, 483 occurrence and preparation, 480–481 as reactive solvent, 578–579 synthesis of beryllides, 578 Ammonia, 324, 327, 330 chemical reactivity with alkali metals, 340 Amorphous alloys, 207–209 amorphization tendency, 210

764

Index

Amorphous alloys (Continued ) definition, 207 with glass-forming capability, 211–212 radial distribution function, 209 structure of, 209–210 thermodynamic formation functions, 207 time–temperature–transformation (TTT) diagrams, 207 Annealing, 543 Antimonides, 514, 592 Antimony (Sb), 513 alloys, highest melting points in, 513 atomic and physical properties, 510 crystal structures, lattice parameters, and densities, 511 ionization energy, 510 occurrence and preparation, 508–509 Anti-perovskite structure, 553 Anti-phase domain boundaries, 192 Antitypic phases, 114–115 Arachno-boranes, 328 Arachno-clusters, 275, 276, 277, 278 Arc furnaces (cold crucible technique), 534–535 Arc-melting, for carbide synthesis, 603 Aristotype structure, 189 Arsenic (As) arsenic-type crystal structure, 648 atomic and physical properties, 510 crystal structures, lattice parameters, and densities, 511 ionization energy, 510 occurrence and preparation, 508 Atomic dimensions, in intermetallic phases atomic radii and volume, 238–243 formation volume and formation heat, correlation between, 243–244 geometrical principles, about intermetallic crystal structures connection principle, 254–255 space-filling parameter, 255–262 space-filling principle, 255 symmetry principle, 254

and partial molar (atomic) volume, 251–253 role in alloying behaviour, 244–251 Atomic environment and corresponding coordination numbers and polyhedra, 130–136 definition, 130–132 Atomic environment type (AET), 130–136 Au–Cu alloys, 668–669 B Ball milling, high-energy, 568–569 Barium (Ba), 348 chemical reactivity, 350 crystal structures, lattice parameters, and densities, 351 occurrence and synthesis, 349 physical properties, 350 Bauxite, 481 BeH2, 329 Berthollides, 88 Beryllides, 476 Beryllium (Be) alloys, 476 applications of, 476 highest melting points in, 474 intermediate phase in binary, 476 atomic and physical properties, 469 chemical properties and reactivity, 470 crystal structures, lattice parameters, and densities, 470 occurrence and preparation, 467–468 phase diagrams, 471–472 Beta alloys, 398 Beta stabilizers, 398 Bidimensional phase diagrams, 48, 50–51 BiH3, 327 Biltz-Zen’s rule, 242–243 Binary 3:4 stoichiometry, 737–738 Binary 5:3 stoichiometry, 734–737 Binary 5:4 stoichiometry, 732–734 Binary alloys alkali metals

Index formulae and structure types of intermediate phases in, 345 melting point trend in, 343–344 alkaline earth metals crystal chemistry of binary alloys of Eu, Yb and, 353–356 melting point trends in, 352–353 compound formation capability, see Compound formation capability enthalpy of formation of solid and liquid, 17 intermediate phases, 38–40 3rd group metals in actinides, 392 3rd group metals in rare earth metals, 391 4th group elements, 401 6th group elements, 420–421 7th group elements, 428 11th group elements, 464–466 of Al and Ga elements, 489 of Be, 476 of divalent metals, 355 Ir, 445–446 of Mg, Zn, Cd, Hg, 477–478 Os, 444, 446 Pd, 446–448 Pt, 446–448 Rh, 445–446 Ru, 444, 446 of Tl and In elements, 490 iron, 440, 441–443 melting point trends 3rd group metals, 383–387 4th group elements, 398–400 5th group elements, 409, 410–411 6th group elements, 417–418 systematic analysis of, 520–522 Binary Laves phases, 181 Binary phase diagrams, see also Phase diagrams of actinides, 380 ‘building blocks’ of, 25, 26, 27–28

765

of congruently melting ABm compound (hypothetical), 561 intermediate phases formation in alloys, 33–38 in binary alloys, 38–40 of magnesium alloy systems, 247 mutual liquid solubilities, trends in, 30–33 mutual solid solubility of component metals, see Mutual solubility of titanium oxides and sulphides, 398–400 two-phase equilibria, inter-crossing of, 22–24 phase rule, ‘building blocks’ in binary system diagrams, invariant equilibria, 24–28 solubility diagrams, 28–30 Yb–Cd, 206 Binary structures, 652 1:1 prototypes and derivative structures AuCu(I), tP2, and AuCu(II), oI40, structural types, 668–669 cP2-CsCl, cf8-NaCl and cF16-NaTl types and NaTl-related structures, 653–658 FeSi, cP8, structural type, 671 hP2-WC and hP4-NiAs types and NiAs-derivative structures, 662–666 oS16-CeAl and oP16-DyAl structure types, 669–671 oS8-CrB and oP8-FeB structure types, 666–668 simple binary tetrahedral structures and polytypes, 658–662 tI8-NbAs type and tI8-NbP type, 671–673 1:2 compounds, structures of, 673 αThSi2, tI12, and LaPtSi, tI12, structural types, 697–701 AlB2, hP3, type and its structural family, 688–697

766 Binary structures (Continued ) CaF2 type, 674–676 Co2Si (PbCl2 ), oP12, and TiNiSi, oP12, structural types, 683–685 CuAl2, tI12, structural type, 685 Cu2Sb, tP6, structural type, 685–686 Fe2P, hP9, structural type, 686–687 FeS2, cP12, structural type (pyrite), 688 Laves phases, 676–679 MoPt2, oI6, structural type, 687–688 oI12, CeCu2 and KHg2 structural descriptions, 680–683 RGe2–x, 701–702 tI6-CaC2 and MoSi2-type structures, 680 TiSi2, oF24, structural type, 687 UPt2, oS12, structural type, 687 Binodal points, in phase diagram, 56–57 Bismuth (Bi) alloys, highest melting points in, 513 atomic and physical properties, 510 crystal structures, lattice parameters, and densities, 511 ionization energy, 510 occurrence and preparation, 509 Bismuthides, 514 Bismuth sulphides, 581 Black phosphorus, 650 Borane-like cluster nomenclature, for cluster compounds, 275–278 Boranes, 328 Wade rules for, 329 Borides crystal structure, 486, 488 from metallic fluxes, 602, see also Metal borides refractory metal, 480 Boron (B) allotropes, 482 atomic and physical properties, 483 chemical properties and reactivity, 484

Index crystal structures, lattice parameters, and densities, 483 ionization energy, 483 occurrence and preparation, 480 structure, 482 triels, 328 Boronitride, 539 Borothermic reduction, 602 Bravais point lattice type, 96, 98–99 Brazing, 506–507 Brewer multi-diagrams, 299, 306 for 6th period transition metals, 302 for Mo alloys, 303 for Mo–Me systems, 304 and Mo–Me1–Me2 systems, 305 Brine, 324, 545 Building blocks of binary phase diagrams, 25, 26, 27–28 C Cadmium (Cd) atomic and physical properties, 469 chemical properties and reactivity, 471 crystal structures, lattice parameters, and densities, 470 occurrence and preparation, 469 phase diagrams, 471–472 Caesium (Cs), 338 atomic and physical properties, 339 crystal structures, lattice parameters, and densities, 339 occurrence and synthesis, 338 Calcium (Ca), 347 chemical reactivity, 350 crystal structures, lattice parameters, and densities, 351 occurrence and synthesis, 347–348 physical properties, 350 uses, 348 Calcium hexaboride (CaB6), structure, 282–283 CALPHAD methods, 68–74

Index CANDU (Canadian Deuterium Uranium) power reactor, 404 Carbaboranes, 275 Carbides crystal chemistry, 502 interstitial, 164–165 salt-like, 504 synthesis, 592, 603–604 transition metal, 504 Carbon (C), 494 allotropes, 494–497 carbon black, 495–496 coke, 495 diamond, 494 fullerenes, 496–497 graphite, 494–495 microcrystalline and amorphous carbon, 495 atomic and physical properties, 500 crystal structures, lattice parameters, and densities, 501 intermetallic chemistry, 500–501 alloy crystal chemistry, 502–505 phase diagram, 501–502 ionization energy, 500 nanotubes, 496–497 occurrence and preparation, 494 phase diagram, 497 Carbon and graphite resistor furnaces, 532–533 Carbon black, 495–496 Carbo-thermal reduction, application of, 602–603 Carburizing, 543–544 Catenation property, 327, 520, 649 Cementation, 544 Cerium (Ce), see also Lanthanides chemical properties, 370 metallic radius, and valence, in intermetallic compounds, 373 occurrence and preparation, 361, 362 physical properties, 360 Chalcogenides

767

nanostructures, 520 synthesis, 581–582 Chalcogens, 327 nanostructures, 520 structure, 650–651 Chemical bond factor and valence-electron counting rules, 262 Brewer diagrams, 299–306 in cluster compounds, see Cluster compounds electronic counting in intermetallic compounds, 306–312, see also Stability maps and correlation diagrams Hume–Rothery phases and VEC, 296–299 normal valence compound rule, 263–264 in polyanionic compounds, see Zintyl phases tetrahedral structures, 264–265 valence compounds, 265–267 Chemical vapour deposition, 583–584 synthesis of nano-structures alloys by, 597 Chevrel phases, 283, 285, 520, 567 structures containing Me6X8 clusters, 733 synthesis of sulfo-selenide, 567 Chimney-ladder phases, 193–197 Chromium (Cr) alloys, highest melting points in, 419 chemical properties and reactivity, 417 crystal structures, lattice parameters, and densities, 416 ionization energy, 416 occurrence and preparation, 414 physical properties, 416 Closo-boranes, 328, 329 Closo-clusters, 275–276, 277 closo-boranes, 328 holes in, 156–158

768

Index

Cluster compounds, 271 of 16th group elements, structure, 520 arachno-cluster, 275, 276, 277, 328 borane-like cluster nomenclature, 275–278 closo-cluster, 275–276, 277, 328 condensation in, 281–282 condensed and high nuclearity, 279–281 electron-precise, electron-deficient and electron-rich clusters, 278, 279 hetero-atomic clusters, 490 hypho-cluster, 275, 328 interstitial atoms in, 278–279 naked, 275, 277 nido-cluster, 275–276, 277, 328 problems in relations between complex intermetallic alloys and, 291–293 shapes, 273 and solid state intermetallics, see Solid state intermetallic structures thermochemistry of, 293–296 and two electron-two centre (2e, 2c) bonding scheme, 273–275 CN, see Coordination number CO2 laser, 536 Cobalt (Co) alloys, 437–438 highest melting points in, 441–443 chemical properties and reactivity, 433 crystal structures and lattice parameters, 433 ionization energy, 434 occurrence and preparation, 429–430 physical properties, 432 Coinage metals, 236, see also 11th group elements Coke, 495 Combustion synthesis, 566 Commensurate composite crystals, 197–198, 201–202 Complex alloys, 33 of alkali metals, 344–347 alloying behaviour of, 522–524

problems in relations between cluster compounds and, 291–293 Complex intermetallic compounds, see Complex alloys Composite crystals, 190 commensurate and incommensurate periodic ‘substructures,’ 197–198 Nowotny chimney-ladder phases, 193–197 Compound formation capability, 521–522 3rd group elements, 381, 382, 383, 385 4th group elements, 396, 397 5th group elements, 408–409 6th group elements, 417, 418, 419 7th group elements, 425, 426 8th, 9th and 10th group elements, 436 11th group elements, 460–461 13th group elements, 485–486 14th group elements, 501–502 15th group elements, 509, 512 16th group elements, 516, 518 alkali metal alloys, 341 alkaline earth metals and divalent metals, 352 Be, Mg, Zn, Cd and Hg alloys, 471–472 plutonium, 388 uranium, 387 Concentric polyhedral clusters, 290–291 Condensed clusters, 279–281 Conjuncto-boranes, 328 Connection principle, 254–255 Coordination number (CN) atomic environment and, 130–136 concept, 126–130 definition, 126 effective coordination number (ECoN), 130 Frank-Kasper definition, 128–129 and packing geometry, 125–126 Coordination polyhedron, 128, 132 Copper (Cu) alloys, 545–546

Index applications, 466 highest melting points in, 462–463 atomic and physical properties, 459 chemical reactivity, 460 crystal structures, lattice parameters, and densities, 460 niobium–copper system, 560 occurrence and preparation, 457–458 vanadium–copper system, 560 Coupled reductions, intermetallic phase synthesis by base metal preparation, 590 oxide coupled reduction with boron and sulphur, 590–591 with metal and hydrogen, 589–590 Crucibles, refractory materials arc-welding apparatus, 540 ceramic materials, 539–541 crucible-less melting and processing, 542 flame welding of silica (or glass) tubes, 541 metallic welded tubes, reactions in, 542 thorium oxide, 541–542 Crystal coordination formulae, see also Coordination number approximate formulae, 91 ideal formulae, 90 polymorphism descriptors, 92 site occupation formulae, 91–92 variable composition formulae, 91 Crystallographic description, of solid phases, see Solid intermetallic phases Crystallographic nomenclature Bravais point lattice type, 96, 98–99 crystallographic system, 96 space groups, 97, 99 Crystallographic system, 96 Crystal structures, see also Intermetallic chemistry 6th group metals, 415, 416 alkali metal alloys, 339, 340, 344

769

alkali metal–triel alloys, 488, 490–491 borides, 486, 488 hydrogen-metal compounds, 334 of oxygen compounds αAl2O3, hR30, structural type (and derivative FeTiO3, ilmenite type), 738–739 BeAl2O4, oP28, structural type (chrysoberil), 743–744 CaTiO3, cP5, structural type (perovskite), 742–743 garnet, yttrium iron garnet, cI160, structural type, 744–745 MgAl2O4, cF56, structural type (spinel), 745–747 olivines, 747 ReO3, cP4, structural type, 741–742 Ta4O, oP5, structural type, 738 TiO2, tP6, structural type (rutile), 739–741 Cs–Au alloys, 461 Cu4Mo6Se8 cluster, structure of, 284–285 Cubic close-packed structure, 137–138 αHg, hR3, structural type, 640 Cu type, 139 NaCl, cF8, structural type, 655 sphalerite and wurtzite structures, 660–662 Cybernetic computer-learning methods, see Savitskii–Gribulya–Kiselova method D Daltonides, 88 Darken and Gurry diagram, 28–29 Databases, for phase diagrams, 75 Decagonal quasicrystals, 203–204 Defect tetrahedral structures, 264, 265 Degenerate structures, 152 Deltahedral clusters, 275 Derivative structures, 152 AlB2-type variants and, 689–696 of binary structures, 653–658

770

Index

Derivative structures (Continued) defect and filled-up, 155–158 NiAs, 662–666 tetrahedral and octahedral holes in close-packed structures, 156–158 Diamond, 494 applications, 505 DICTRA (Diffusion simulation software) program, 74 Diffusion couple technique, 64–66 Di-hydrogen, 325 Dimensionality index, of structures, 124 Direction indices, of unit cell, 111 Displacive modulations, 191, 202 Distillation and sublimation, 555 Divalent rare earth metals, see Alkaline earth metals and divalent rare earth metals Dodecagonal quasicrystals, 204 E Edge-sharing clusters, see Poly-condensed clusters Effective coordination number (ECoN), 128, 130 Electric arcs, 537 Electric resistance heating coil, 532 Electric resistor furnaces, 532–533 Electric steel process, 452 Electrochemical reduction, 591 on Hg cathode, 592 Electrodeposition of alloys, 591–592 Electron-beam furnaces, 536 Electron-beam melting, 536 Electronegativity, 12–14, 263 Electron localization function, 307 Electron-precise clusters, 278, 279 Electrotransport, 555 Electrowinning, 555 Equilibrium phase diagrams and reaction rate, 7–8, 51–54 spinodal decomposition, 56–58 stable, metastable and unstable states, 54–55

Equilibrium states, 7, 54–55 Europium (Eu), 349, 360, see also Lanthanides chemical reactivity, 351 crystal structures, lattice parameters, and densities, 351 lattice parameter and heat of formation trends in compounds and alloys, 374–376 oxidation state, 373–374 physical properties, 350 Eutectoid reaction, 23 transformation, 543 F Face-sharing clusters, see Poly-condensed clusters Ferro alloy metals, 236, 450, 454 Fluidized-bed process technology, for carbide synthesis, 604 Formation enthalpy, of alloys, 181, 294, 383, 385 Frank–Kasper (F–K) phases, 719–731 structures, 172, 174 Fullerenes, 496–497 G Gallium (Ga) atomic and physical properties, 483 crystal characteristics of orthorhombic, 640 crystal structures, lattice parameters, and densities, 483 ionization energy, 483 occurrence and preparation, 481 as reactive solvent, 579 Gas phase, intermetallics and reactions with chemical transport reactions, 585 single crystal preparation by, 585–586 chemical vapour deposition, 583–584 physical vapour deposition, 582–583 synthesis of metastable Al and Ga monohalide solutions, 586

Index vapour phase transport, 584–585 Germanium (Ge), 499 atomic and physical properties, 500 crystal structures, lattice parameters, and densities, 501 ionization energy, 500 occurrence and preparation, 499–500 Gibbs phase rule, see Phase rule Glasses, 539 Glass-forming metallic alloys, 211–212 Glassy alloys, 568, see also Amorphous alloys Gold (Au) alloys, 461, 467 atomic and physical properties, 459 chemical properties, 460 crystal structures, lattice parameters, and densities, 460 occurrence and preparation, 459 Goldschmidt atomic diameter, 238 Graphite, 494–495 intercalation compound, 495 H Hafnium (Hf) alloys, highest melting point in, 399 chemical properties, 396 crystal structures, lattice parameters, and densities, 395 ionization energy, 394 occurrence and preparation, 393–394 physical properties, 394 Hägg phases, 658 Hägg rules, 165–166 Halides, Mo and W, structure of, 286–288 Hardening, 544 Heating, thermal treatments, 531 crucibles, refractory materials, 539–542 laboratory furnaces, 532–539 Heat treatments, terminologies, 543–544 Heliostat, 537 Hermann–Mauguin symbol, 99 Hetero-atomic clusters, 490 Heusler phases, 660

771

Hexagonal close-packed structure, 137, 138 Homeotect structure types, 170–171 Homogenization, 544 Hume–Rothery phases, 296–299 Hume–Rothery rules, 29 Hydrides, 330 α and β hydrides, 325 application of, 331–334 boranes, 328 chalcogens, 327 covalent hydrides, 327 families of, 326–327 interstitial, 162–164 ionic hydrides, 326 pnicogens, 327 uranium, 326 Hydrogen, 323 and alkali metals, chemical reactivity, 340 di-hydrogen, 325 hydrogen–metal phases, crystal structures of typical, 331 hydrogen storage materials, 333 and its isotopes, 323–324 atomic properties, 323 deuterium, 323 physical properties, 324 tritium, 324 metal hydrides, application of, 331–334 occurrence, 323 phase diagrams of metal-hydrogen systems, 329–331, 332 preparation, 324–325 reactivity with elements, 325–329 Hypho-boranes, 328, 329 Hypho-clusters, 275 Hypoelectronic elements, 480 I Icosahedral quasicrystals, 203, 204 Impurities, role in intermetallics, 552 alloy properties and on synthesis control, effects on, 556–560

772

Index

Impurities, role in intermetallics (Continued) high-purity materials, preparation rare earth metals, 554–555 silicon, 553–554 impurity-stabilized phases, 553 interstitial impurities on phase equilibria, effects on, 560 InAs, alternative routes of synthesis, 606–610 Indium (In), 487 alloys, highest melting points in, 487 atomic and physical properties, 483 crystal structures, lattice parameters, and densities, 483 ionization energy, 483 occurrence and preparation, 481–482 synthesis in liquid, 579–580 Indium halides, 608 Induction furnaces, 533–534 Interatomic distances, reduced, 148 Intergrowth structure series, 185 compositional formulae, 188 construction method, classification, 186 fragments classification, 185–186 Intermediate phases, 8 formation, 33–40 in binary alloys, 38–40, see also Binary alloys, intermediate phases Intermetallic chemistry, of alloy elements 2nd group elements crystal chemistry, 473, 476 melting point trends in binary alloys, 473, 474 phase diagrams, 471–472 3rd group metals alloy crystal chemistry, 390, 391, 392 melting point and formation enthalpy trends in binary alloys of, 383–387 phase diagrams, 377–383 4th group elements alloy crystal chemistry, 400–402 applications of zirconium and titanium intermetallics, 402–404

melting point trend in binary alloys, 398–400 phase diagrams, 396–398 5th group elements alloy crystal chemistry, 409, 412–413 melting point trend in binary alloys, 408–409, 410–411 phase diagrams of, 407–408 6th group elements alloy crystal chemistry, 418, 421 melting point trends in binary alloys, 417–418, 419 phase diagrams, 417 7th group elements alloy crystal chemistry, 425, 428 phase diagrams, 425, 426–427 11th group elements alloy crystal chemistry, 464–466 phase diagrams, 460–464 12th group elements crystal chemistry, 473, 476, 477–478 melting point trends in binary alloys, 473, 474, 475 phase diagrams, 471–472 13th group elements, 485–491 14th group elements, 500 alloy crystal chemistry, 502–505 phase diagram, 501–502 15th group elements, 509, 510–514 16th group elements, 516–520 alkali metal alloys alloy crystal chemistry of, 344 complex intermetallic compounds of, 344–347 melting point trend in binary alloys, 343–344 phase diagrams of, 341–342 solubility of metals in liquid alkali metals, 342–343 alkaline earth metals and divalent rare earth metals alloy crystal chemistry, 353–356

Index melting point trend in binary alloys, 352–353 phase diagrams of, 351–352 hydrogen hydrides, 326–327, 331–334 hydrogen–metal phases, crystal structures, 331 hydrogen reactivity with elements, 325–329 phase diagrams of metal–hydrogen systems, 329–331 iron family metals, 432–434 alloys crystal chemistry, 439–440, 441–444 phase diagram, 439 platinum family metals, 435 alloys crystal chemistry, 439–440, 444, 445–448 phase diagram, 439 Intermetallic compounds, see also Solid intermetallic phases electronic counting, developments in, 306–312 and periodic table, see Periodic table Intermetallic phases atomic dimensions role in, see Atomic dimensions, in intermetallic phases classification, factors for, 237, see also Chemical bond factor composition and compositional formula constituent proportions, indication of, 90–94 order of citation of element symbols in formula, 89–90 distribution among different structural prototypes, 619 Hume–Rothery phases and VEC, 296–299 layer stacking sequences in, 136–145 in liquid states, 82–85 in solid states, see Solid intermetallic phases

773

structure and atomic dimensions, see Atomic dimensions structure families, see Phase structure families, of intermetallics ternary, distribution of, 621 Intermetallic phase synthesis, 560 by coupled reductions base metal preparation, 590 oxide coupled reduction with boron and sulphur, 590–591 oxide coupled reduction with metal and hydrogen, 589–590 melting, 561–565 single crystals (or quasicrystals), growth from metallic solutions, 565–566 solid-state synthesis, 566–575 Intermetallic prototypes γ-brass: Cu5Zn8, cI52 structural type, 728–729 BaAl4, tI10, structural type and BaAl4derivative types, 715–721 BaHg11, cP36, structural type, 725–726 CaB6, cP7 structural type, 723 CaCu5, hP6, structural type, 721–723 Chevrel phases, 733 Fe4N, cP5, structural type, 715 MoNi4, tI10, structural type, 721 NaZn13, cF112, structural type, 727–728 relationships with high stoichiometric ratios, 728 Samson phases, 731 selected structures corresponding to binary 3:4 stoichiometry, 737–738 selected structures corresponding to binary 5:4 stoichiometry, 732–734 selected structures corresponding to binary 5:3 stoichiometry, 734–737 tetrahedrally close-packed phases, Frank–Kasper phases, 729–731 Th2Ni17, hP38, structural type, 723–724 Th2Zn17, hR57, structural type, 724–725

774

Index

Intermetallic prototypes (Continued) Th6Mn23, cF116, structural type, 714–725 ThMn12, tI26, structural type and ThMn12-derivative types, 726–727 Intermetallic structures examples, 626–630 prototype directory of, 620 for structural type:tI8-NbP, 623 structure and structure component projections, 625–626 structure and structure component sections, 623–625 International Temperature Scale (ITS), 551 Interstitial atoms, in clusters, 278–279 Interstitial superstructures interstitial carbides and nitrides, 164–165 interstitial hydrides, 162–164 miscellaneous examples, 166–167 Invariant equilibria, 27 Invariant lattice complexes, see Lattice complexes Ionic hydrides, 326 Ionization energy, 221 Iridium (Ir), 431, 437–438 chemical properties, 434–435 crystal structures and lattice parameters, 435 intermediate phases in binary alloys of, 445–446 ionization energy, 434 physical properties, 433 Iron (Fe) alloys, technical names, 453–454 binary alloys, 440, 441–443 chemical properties and reactivity, 432 crystal structures and lattice parameters, 433 ionization energy, 434 occurrence and preparation, 429 phase diagram of iron-carbon, 451, 452–453

physical properties, 432 production, 450 Iron family metals atomic and physical properties, 432, 433 chemical properties and reactivity, 432–434 cobalt (Co), 429–430 intermetallic chemistry, 435 alloys crystal chemistry, 439–440, 441–444 phase diagram, 439 iron (Fe), 429 and its alloys, 450–457 nickel (Ni), 430 Isobaric phase diagram, 47 Isolobal principle, 272 Isothermal methods, for phase diagram, 59–62 Isotopes actinides, 365 hydrogen, 323–324 Isotypic structures, see Isotypism Isotypism, in inorganic compounds, 114 J Jagodzinski symbol, for layer stacking sequence, 143 K Kagomé net structure, 141–142 Kinetic phase diagrams, 52, 53 L Laboratory equipments, 551–552 furnaces, see specific furnace La–Ni–Mg alloys, 333 Lanthanides cerium (Ce), 360 concept, 357 contraction, 358–359 crystal structures, lattice parameters, and densities, 368–369

Index dysprosium (Dy), 361 erbium (Er), 361 europium (Eu), 360 gadolinium (Gd), 360 holmium (Ho), 361 lanthanum (La), 360 Ln–Ln alloys, 377–379 lutetium (Lu), 361 metallothermic reduction, 362 neodymium (Nd), 360 occurrence and preparation, 361–362 physical properties, 367 praseodymium (Pr), 360 promethium (Pm), 360 samarium (Sm), 360 terbium (Tb), 361 thulium (Tm), 361 ytterbium (Yb), 361 Laser heating, 536 Lattice complexes, 116–121 AuCu3-type structure, 150 Laves phases, 171–172, 619, 676–679 binary, 181 and derivative structures, 178–184 occurrence, 180–181 stability, 180–181 thermodynamic modeling of, 181–184 Laves-type phases, of fifth group elements, 409 Layer position symbols, see Stacking symbols Layer stacking sequences, 136–145 Jagodzinski symbol, 143 Schläfli notation, 138, 140 Lead (Pb), 499 atomic and physical properties, 500 crystal structures, lattice parameters, and densities, 501 ionization energy, 500 occurrence and preparation, 500 in solders, 506 synthesis in lead flux, 580 Leo Brewer, 542

775

Levitation, 534 techniques, 542 Li–Al alloys, 336 Light metals, 235 Li–Mg–Zn alloys, 178 Li–Pb alloys, 82, 83 Liquid alloys, 517 of 16th group, 517 general characteristics, 85–87, see also Zintl phases structural change investigation in, 86 surface tension measurements, 87 Liquid-encapsulated Czochralski (LEC) process, 609–610 Liquid intermetallic phases, 82–85 Liquidus curve, 9, 60 Lithium (Li), 335 alloys, 335–336 atomic and physical properties, 339 crystal structures, 339 occurrence and synthesis, 335 Long-period ordering, 192 M Mackay cluster, 205 Magnesium (Mg) alloys applications, 476 ASTM designation code, 478–479 binary alloys, 477–478 highest melting points in, 474 atomic and physical properties, 469 chemical properties and reactivity, 471 crystal structures, lattice parameters, and densities, 470 occurrence and preparation, 467–468 phase diagrams, 471–472 Magnesium di-boride, 600–601 Magnetic modulated structure, 191 Manganese (Mn) alloys, highest melting points in, 426 crystal structures, lattice parameters, and densities, 424

776 Manganese (Continued) ionization energies, 424 occurrence and preparation, 421–422 physical properties, 424 Martensitic transformations, for steel and iron, 455–457 Mechanical alloying, 567–568, 569 phase sequence during, 568 preparation of rare earth metals and alloys by, 572–573 Mendeleev number, 14, 15 Menstruum process (flux process), for carbide synthesis, 604 Mercury (Hg) alloy, amalgams, 472 atomic and physical properties, 469 chemical properties and reactivity, 471 crystal structures, lattice parameters, and densities, 470 occurrence and preparation, 469 phase diagrams, 471–472 red mercury, 478 Metal borides, preparation methods of, 600–603 Metal joining processes brazing, 506–507 soldering, 506 welding, 507 Metallic glasses, see Amorphous alloys Metallothermic reduction, 362, 554–555, 573 Metastable alloys, 544 Metastable phase diagrams, 52–53 Metathesis (exchange) reactions, intermetallic phase synthesis by, 586 solid-state, 587–589 in solutions, 589 Methanides, 504 Mg8Rh4B, 601 MgB2, 600–601 Mg–Cu alloys, 61 Mg–Pd alloys, 564

Index Microwave heaters, 537–539 Miedema’s model and parameter, 13, 16–21 Miedema’s theory, 311–312 Miscibility gaps, in liquid state, 33, 37, 517 Mo6PbS8, structure of, 283–284 Mo6S8 cluster, structure of, 285–286 Modulated crystal structures, 190 anti-phase domain boundaries, 192 crystallography of, 201–202 displacive modulations, 191 magnetic modulated structure, 191 substitutional modulation, 191 Molten metals, protection of, 565 Molybdenum (Mo) chemical properties and reactivity, 417 crystal structures, lattice parameters, and densities, 416 ionization energy, 416 occurrence and preparation, 414 physical properties, 416 use of, 414–415 Molybdenum or tungsten furnaces, 532 Mo–Re alloys, 414 MoS2, 592 Mo–W alloys, 414 MTDATA, 75 Multi-phase diagrams, 244, see also Brewer multi-diagrams, and VEC Mutual solubility Hume–Rothery rules for, 29 in liquid states, 9 trends, 30–33 in solid states, 9 of component metals in binary phase diagrams, 8, 10–11 effect of atomic properties of components on, 28–30 partial, 21–22 trends, 11–12

Index N Na7Sn12, 504 Na–Cd alloys, 86 Na–K alloys, 336 Nano-structured metals and alloys, synthesis of, 596–597 by chemical vapour deposition and condensation, 598 by inert gas evaporation technique, 597 via mechanical deformation, 597 nanowires, 598–599 from organometallics, 598 precursor preparation by solution chemistry, 597 Nanotubes, see Carbon nanotubes Nb5Si3, preparation, 583 Nd:YAG radiation, 536 Near-neighbour diagram, 260, 261 Nichrome-wound resistance furnaces, 532 Nickel (Ni) alloys, 441–443 chemical properties and reactivity, 433 crystal structures and lattice parameters, 433 ionization energy, 434 occurrence and preparation, 430 physical properties, 432 Nido-boranes, 328, 329 Nido-clusters, 275–276, 277 Niobium (Nb), 405 alloys, highest melting points in, 410 chemical properties and reactivity, 406 crystal structures, lattice parameters, and densities, 407 ionization energies, 407 occurrence and preparation, 405 physical properties, 406, 407 Nitrides, 511 interstitial nitrides, 164–165 Nitrogen (N) atomic and physical properties, 510 crystal structures, lattice parameters, and densities, 511

777

ionization energy, 510 occurrence and preparation, 507 Nomenclature, see Crystallographic nomenclature Non-oxidizing acids, 578 Non-stoichiometric phases, in solids, 88 crystallographic description, 95 Normal tetrahedral structures, 264–265 Normal valence compound rule, 263–264 for tetrahedral structure, 264–265 valence compounds, 265–267 Nowotny chimney-ladder phases, 193–197 O Occupational modulation, see Substitutional modulation Octet rule, 82 Oil-bath method, 538, see also Microwave heaters Optical furnaces, 537 Optical pyrometry, 547 Order–disorder transformation, 158–160 Osmium (Os), 430–431 chemical properties, 434 crystal structures and lattice parameters, 435 intermediate phases in binary alloys of, 444, 446 ionization energy, 434 physical properties, 433 Oxygen (O) atomic and physical properties, 516 crystal structures, lattice parameters, and densities, 517 ionization energy, 516 occurrence and preparation, 514–515 Oxygen compounds, crystal structures of αAl2O3, hR30, structural type (and derivative FeTiO3, ilmenite type), 738–739 BeAl2O4, oP28, structural type (chrysoberil), 743–744

778

Index

CaTiO3, cP5, structural type (perovskite), 742–743 garnet, yttrium iron garnet, cI160, structural type, 744–745 MgAl2O4, cF56, structural type (spinel), 745–747 olivines, 747 ReO3, cP4, structural type, 741–742 Ta4O, oP5, structural type, 738 TiO2, tP6, structural type (rutile), 739–741 P Packing geometry 3D packing, 199 coordination number and, 125–126 Palladium (Pd), 431 chemical properties, 435 crystal structures and lattice parameters, 435 intermediate phases in binary alloys of, 446–448 ionization energy, 434 palladium–vanadium system, 252 physical properties, 433 Pandat software package, 74–75 Partial molar (atomic) volume, of alloys, 251–253 Pauling’s rule, 239 Pearson symbol, 115–116 Penrose tiling, 199–200 Pentatitanium tetratelluride, structure of, 288–290 Periodic table, 220 blocks and subdivisions of, 228 blocks of, 228–229 d block contraction effect, 230 diagonal relationships, 231 ‘divides’ in periodic table, 231–233 geochemical subdivision of, 233–234 lanthanide contraction effect, 229–230

relativistic effects and impact on periodic table, 230 superconducting elements in, 235 technological subdivision, 235–236 coinage metals in, 236 and electron configurations of elements, 219–223 electronic structure of atoms, 224–228 structure of periodic table, 223 ferro alloy metals in, 236 light metals in, 235 precious metals in, 236 refractory metals in, 235 soft solder metals in, 236 Pettifor scale, chemical order of elements by, 15 Pettifor’s structure maps, 308 Phase diagram(s), 1–2, 7 of 3rd group metals An–An alloys, 379–381 Ln–Ln alloys, 377–379 R–Me and An–Me alloys, 381–383 4th group elements, 396–398 5th group elements, 407–408 6th group elements, 417 7th group elements, 425, 426–427 11th group elements (Cu, Ag, Au), 460–464 13th group elements, 485–486, 487 14th group elements (C, Si, Ge, Sn, Pb), 501–502 15th group elements, 509, 510 16th group elements, 516–517 alkali metal alloys, 341–342 alkaline earth metals and divalent rare earth metals, 351–352 assessment of, 67–68 bidimensional, 48, 50 binary, see Binary phase diagrams calculation, thermodynamic optimization and prediction of, 68–69

Index ab initio, first-principle calculations, 71–72 CALPHAD methods, 69–74 databases, 75 DICTRA (diffusion simulation software), 74 MTDATA, 75 Pandat software package, 74–75 semi-empirical methods and rules, 72, 73 Thermo-Calc, 74 thermodynamic calculation, 73–74 carbon, 497 equilibrium diagrams, 51–54 equilibrium states in, 7, 54–55 experimental determination of, 58–59 diffusion couple technique, 64–66 isothermal methods, 59–62 materials microstructure, characterization and 3D representation of, 66–67 polythermal methods, 59 X-ray powder diffraction methods, 62–64 iron–carbon, stable and metastable, 452–453 iron family metals, 439 isobaric, 47 of metal–hydrogen systems, 329–331, 332 platinum family metals, 439 spinodal decomposition in, 56–58 ternary phase diagrams, 41–45 variable pressure phase diagrams, 45–51 Phase rule, 24–26 Phase stabilization, in actinides, 390 Phase structure families, of intermetallics, 151 coordination polyhedra assembly, 173–174 fused polyhedra structures, 184 tetrahedrally close-packed structures, see Tetrahedrally close-packed structures

779

degenerate structures, 152 derivative structures, 152 defect and filled-up, 155–158 Hägg rules, 165–166 homeotect structure types, 170–171, 172–173 close-packed element structure types, 171 equiatomic tetrahedral structure types, 171 Laves phases, 171–172 homogeneous intergrowth structures, 185 inhomogeneous intergrowth structures, 185–186 intergrowth structure series see Intergrowth structure series interstitial superstructures, 162, 166–167 interstitial carbides and nitrides, 164–165 interstitial hydrides, 162–164 modular aspects of crystal structures, 168–170 order-disorder transformation, 158–160 recombination structures, 185 superstructures, 167–168 second kind of, 167–168 substitutional, 160–162 Phosphides, 512, 514 and polyphosphides, synthesis, 604–605 Phosphorus (P), 649 atomic and physical properties, 510 compounds, phosphides, 512, 514 crystal structures, lattice parameters, and densities, 511 ionization energy, 510 occurrence and preparation, 508 Physical vapour deposition, 582–583 Plane indices, of unit cell, 111–113 Platinum (Pt), 431 alloys, applications of, 448–450 chemical properties, 435

780

Index

Platinum (Continued) crystal structures and lattice parameters, 435 intermediate phases in binary alloys of, 446–448 ionization energy, 434 physical properties, 433 platinum alloy wound furnaces, 532 Platinum family metals alloys of, application of, 448–450 atomic and physical properties, 433–434 chemical properties and reactivity, 434–435 intermetallic chemistry, 435–439 alloys crystal chemistry, 439–440, 444, 445–448 phase diagram, 439 iridium (Ir), 431 osmium (Os), 430–431 palladium (Pd), 431 platinum (Pt), 431 preparation, 431–432 rhodium (Rh), 431 ruthenium (Ru), 430 Plumbides, crystal structure, 505 Plutonium, alloying behaviour, 388–390 Pnicogens, 327, 566 Point compounds, 35, 88, 247 Point lattices, see Bravais point lattice type Polonides, 518, 520 Polonium (Po) atomic and physical properties, 516 crystal structures, lattice parameters, and densities, 517 ionization energy, 516 occurrence and preparation, 516 Polyanionic compounds, see Zintl phases Poly-condensed clusters, 290 Polyhedral clusters, concentric, 290–291 Polyhedra projections, 630–632, see also Intermetallic structures Polyhedron code, for AET, 132 Polyphosphides, 512, 514

Polythermal methods, for phase diagram, 59 Polytypic structure, 170–171 Porcelain, 539 Potassium (K), 336 alloys, 337 atomic and physical properties, 339 crystal structures, 339 occurrence and synthesis, 337 Powder metallurgical methods, 603 Precious metals, 236 Pseudo-lanthanides, 249 Pulsed laser ablation deposition (PLAD) technique, 595, 596 Q Quasicrystals, 190, 198–200 3D packing, 199 decagonal quasicrystals, 203–204 dodecagonal quasicrystals, 204 icosahedral quasicrystals, 204 other intermetallic phases and, relation between, 204–206 Quasi-periodic structures, 190 composite crystals, see Composite crystals crystallography of, 200–203 modulated structures, 190–192 quasicrystals, see Quasicrystals Quenching, 544 from liquid, 545 melt-quenching of metastable and nano-crystalline alloys, 546 from solid state, 544–545 R Radial distribution function (RDF), of amorphous alloys, 209 Radium (Ra), 349 crystal structures, lattice parameters, and densities, 351 physical properties, 350 radioactivity, 350

Index Raynor Index, 38 Recombination structures, of solid intermetallic phases, 185–189 Red mercury, 478 Reduced interatomic distances, 148 Refractory metals, 235 borides, 480 Relativistic alkali metal, see Thallium Resistor furnaces, see Electric resistor furnaces Rhenium (Re) crystal structures, lattice parameters, and densities, 424 ionization energies, 424 occurrence and preparation, 423 physical properties, 423, 424 Rhodium (Rh), 431, 437–438 chemical properties, 434–435 crystal structures and lattice parameters, 435 intermediate phases in binary alloys of, 445–446 ionization energy, 434 physical properties, 433 Rubidium (Rb), 337 atomic and physical properties, 339 crystal structures, 339 Ruthenium (Ru), 430 chemical properties, 434 crystal structures and lattice parameters, 435 intermediate phases in binary alloys of, 444, 446 ionization energy, 434 physical properties, 433 S Salt-like carbides acetylides, 504 allylenides, 504 methanides, 504 Samson complexes, 644 Samson phases, 173, 184, 731

781

Savitskii–Gribulya–Kiselova method, 308–309 SbH3, 327 Schläfli notation, 138, 140 Selenides, structure, 518, 520 Selenium (Se) atomic and physical properties, 516 crystal structures, lattice parameters, and densities, 517 ionization energy, 516 occurrence and preparation, 515 Semi-solid processing, 546 Shock-induced and shock-assisted reactions in powder mixtures, 594 Silicon (Si), 498–499, 503 atomic and physical properties, 500 crystal structures, lattice parameters, and densities, 501 ionization energy, 500 occurrence and preparation, 498–499 ‘Silit’ furnaces, 532 Silver (Ag) alloys, 466 atomic and physical properties, 459 chemical reactivity, 460 crystal structures, lattice parameters, and densities, 460 occurrence and preparation, 458 Single-phase alloys, 56 Sodium (Na) alloys, 336 atomic and physical properties, 339 crystal structures, 339 occurrence and synthesis, 336 Soft solder metals, 236 Solar furnaces, 537 Soldering process, 506 Solid–gas equilibria, 31 Solid intermetallic phases, 87–88, see also Amorphous alloys; Quasi-periodic structures crystallographic description

782

Index

Solid intermetallic phases (Continued) Pearson symbols and structure types, 115–116 structural types representation, 113–115 Strukturbericht symbols, 151 by unit cells, see Unit cell description crystal structure of atomic environment and corresponding coordination numbers and polyhedra, 130–136 coordination and dimensionality symbols, in crystal coordination formula, 122–126 coordination number (CN), 126–130 cP4-AuCu3 type structure, notations and symbols for, 145–150 lattice complexes, 116–121 layer stacking sequence description and symbols, 136–145 structural descriptions and symbols, 121–122 identification and characterization, 88–89 structure families, see Phase structure families Strukturbericht symbols, 151 trivial names and symbols, 151 Solid state intermetallic structures, 281–282 calcium hexaboride (CaB6), 282–283 Chevrel phases, 283 concentric polyhedral clusters, 290–291 Cu4Mo6Se8 cluster, 284–285 edge-sharing and face-sharing poly-condensed clusters, 290 Mo6PbS8, 283–284 Mo6S8 and Mo6Se8 clusters, 285–286 Mo and W halides, 286–287 pentatitanium tetratelluride, 288–290 Solid-state metathesis reactions, for InAs synthesis, 607 Solid-state synthesis

combustion synthesis, 569–573 from component powders, 566–567 co-reduction of mixed oxides, 573 ‘extraction’ of a phase from mixture, 574–575 fast, solid state, microwave-assisted, synthesis, 573–574 field-activated, self-propagating, high-temperature synthesis, 573 from solid components by ‘mechanical alloying,’ 567–569 Solidus curve, 9 Solubility diagrams, 28–30 Sono-chemical techniques, 593–594 Source dissolution method, 607 Space-filling parameters, for intermetallic structures, 255–262 Space-filling principle, 255 Space groups, 97, 99–101, 102 internal space, 201 position space, 201 Spinodal decomposition, 56–58 Sputtering, 594–595 Stability maps and correlation diagrams, 307, 310–311 Gschneidner’s relations, 310–311 Miedema’s theory and structural information, 311–312 Pettifor’s structure maps, 307–308 Savitskii–Gribulya–Kiselova method, 308–309 Villars, Villars and Girgis approaches, 309–310 for intermetallics, 307, 310–311 Miedema’s theory, 311–312 Pettifor’s chemical scale and structure maps, 307–308 Savitskii–Gribulya–Kiselova method, 308–309 Villars, Villars and Girgis approaches, 309–310 Stacking symbols, 138, 140, 141, 150 Stannides, crystal structure, 505

Index Stearic acid, 568 Steel production, 450–452 temperature–time–transformation (TTT) diagrams, 454–455 Stibnite (Sb2S3), 509, 594 Stoichiometric phases, in solids, 87–88 crystallographic description, 94 Strain parameter, reduced, 260 Strontium (Sr), 348 chemical reactivity, 350 crystal structures, lattice parameters, and densities, 351 physical properties, 350 Structures, intermetallic, see Solid state intermetallic structures Structure types with 1:3 stoichiometry βTiCu3, oP8, structural type, 708–709 Cr3Si, cP8, structural type, 711–712 Fe3 C, oP16, structural type, 713–714 Na3As, hP8, structural type, 712–713 polytypic structure family, 705 AuCu3, cP4, structural type, 705–706 BaPb3, hR36, structural type, 708 Ni3Sn, hP8, structural type, 704–705 PuAl3, hP24, structural type, 707 TiNi3, hP16, structural type, 706 tP4-Ti3Cu, tI8-TiAl3 and tI16-ZrAl3 type structures Ti3Cu, tP4, structural type, 709 TiAl3, tI8, structural type, 709 ZrAl3, tI16, structural type, 711 Strukturbericht symbols, for intermetallic phases, 151 Sublattice model, 92 for Laves phase types, 183 Substitutional modulation, 191 Substitutional superstructures, 160–162 Sulphides of 16th group elements, 518, 519 binary phase diagrams, 398 Sulphur (S) atomic and physical properties, 516

783

crystal structures, lattice parameters, and densities, 517 ionization energy, 516 occurrence and preparation, 515 Supercrystals, 201 Superspace groups, 201 Superstructures interstitial, see Interstitial superstructures second kind of, 167–168 substitutional, 160–162 W-type, 152 Super-thermite, 572 Symmetry principle, 254 Synthesis in solvents (under fluxes), 575–577 in alkali chalcogenide reactive flux, 581 in alkali poly-chalcogenide flux, 581–582 intermetallic phases in liquid sodium, 577 in lead flux, 580 in liquid aluminium, 578–579 in liquid gallium, 579 in liquid indium, 579–580 in liquid NH3, 582 in mercury solution, 577–578 single-crystal preparation and growth by NaCl/KCl flux reaction, 581 in tin flux, 580 Systematization number (SN), 377–379 T Tammann type furnace, 533 Tantalothermic reduction, 366 Tantalum (Ta) chemical properties and reactivity, 406 crystal structures, lattice parameters, and densities, 407 ionization energies, 407 occurrence and preparation, 405–406 physical properties, 407

784

Index

Technetium (Tc) crystal structures, lattice parameters, and densities, 424 ionization energies, 424 occurrence and preparation, 422 physical properties, 424 Tellurides, 518, 519, 520 Tellurium (Te), see also Tellurides atomic and physical properties, 516 crystal structures, lattice parameters, and densities, 517 ionization energy, 516 occurrence and preparation, 515 Temperature measurement and control radiance measurement, 546–547 resistance temperature detector, 547–548 thermocouple, 548–551 Tempering, 544 Terminal phases, 33 Ternary compounds, 188, 523–524 Zintl phases, 269–271 Ternary phase diagrams, complex representations, 41–45 Tetrahedrally close-packed structures, 174–175 σ-phase type structure (tP30-σ Cr–Fe type), 177 cP8-Cr3Si type structure, 175–177 Laves phases and derivative structures, 178–184, see also Laves phases Tetrahedral structures defect, 265 normal, 264 Thallium (Tl) atomic and physical properties, 483 chemical properties and reactivity, 484–485 crystal structures, lattice parameters, and densities, 483 ionization energy, 483 occurrence and preparation, 482 Thermistors, 548, see also Temperature measurement and control

Thermo-Calc programs, 74 Thermochemistry, of clusters, 293–296 Thermocouples, 548 calibration, 551 characteristics, 549 protection, 551 reference junction, 550 voltage to temperature conversion, 550 Thermopile, 550 Thixoforming, see Semi-solid processing Thorium (Th), 363 alloying behaviour, 387 occurrence and preparation, 365 Three-cap crucible, 565 Ti3Al, 403 Ti5Te4, structure, see Pentatitanium tetratelluride TiAl3, 403–404 Tin (Sn), 503 atomic and physical properties, 500 crystal structures, lattice parameters, and densities, 501 ionization energy, 500 occurrence and preparation, 499–500 tin-containing soft solders, 506 TiO, structure, 166 Titanium (Ti), 393 α/β titanium alloys, phase diagrams, 397–398 chemical properties and reactivity, 395–396 crystal structures, lattice parameters, and densities, 395 intermetallics Ti3Al intermetallics, 403 TiAl3 intermetallics, 403–404 Ti-Al intermetallics, 403 ionization energy, 395 occurrence and preparation, 393 physical properties, 394 Tl2CO3, 484 Transition metal carbides, 504 Travelling floating zone furnace, 537

Index Tungsten (W) chemical properties and reactivity, 417 crystal structures, lattice parameters, and densities, 416 furnace, 532 ionization energy, 416 occurrence and preparation, 415 physical properties, 416 Two electron-two centre (2e, 2c) bonding scheme, 273–275 Two-phase equilibria, inter-crossing of, 22–24 U Unary structures, 632–633 metallic element structures body-centred cubic W-type structure, 637–638 close-packed element structure types, 633–637 special structural types of selected metals, 639–642 two body-centred tetragonal structures, 639 uranium and plutonium elemental structures, 642–643 non-metallic elemental structures 8 – eat rule, 644–648 16th group elements, 650–651 boron, 643–644 structures of 17th group elements, 651–652 Unit cells, description for solid phase structure, 94–95 alternative descriptions of, 106–110 content, 101–105 crystallographic description, 94, 95 crystallographic nomenclature, 96–101 cubic, descriptions of, 108–109 hexagonal unit cell, 107–108 interatomic distances, 110–111 plane and direction indices, 111–113 rhombohedral unit cell, 106–107, 108

785

symmetry operations in, 99–100 volume of unit cell (Vcell), 105–106 Uranium (U), 363 alloying behaviour, 387–388 occurrence and preparation, 365 Uranium hydrides, 326, see also Hydrides V Vacuum melting, 555 plasma heating and spraying, 535 Valence compounds, 265–267 normal, 263–264 tetrahedral structures, 264–265 Valence-electron concentration (VEC) Brewer multi-diagram and, 299, 301–306 Hume–Rothery phases and, 296–299 parameter, 265 Valence-electron counting rules, see Chemical bond factor and valence-electron counting rules Vanadium (V), 404–405 chemical properties and reactivity, 406 crystal structures, lattice parameters, and densities, 407 ionization energies, 407 occurrence and preparation, 404–405 physical properties, 406, 407 Van Arkel method, 584 Van Arkel process, for actinides, 366 Variable pressure phase diagrams, 45–48 partial pressure as variable, 48–51 VEC, see Valence-electron concentration Vegard’s rule, 242 Villars, Villars and Girgis approaches, 309–310 Violet (Hittorf’s) phosphorus, 650 Volumetric index, 258 Voronoi polyhedron, 128 W Wade electron counting rules, for clusters, see Borane-like cluster nomenclature

786

Index

Wade rules, for boranes, 329 Weldalite 049, 336 Welding, 507 Wyckoff sequence, 116 X X-ray powder diffraction methods, 62–64 Y Y–Cu alloys, 563–564 Ytterbium (Yb), 350, 361, see also Lanthanides chemical reactivity, 351 crystal structures, lattice parameters, and densities, 351 lattice parameter and heat of formation trends in compounds and alloys, 374–376 oxidation state, 373–374 physical properties, 350 Z Zinc (Zn) atomic and physical properties, 469 chemical properties and reactivity, 471 crystal structures, lattice parameters, and densities, 470 occurrence and preparation, 468 phase diagrams, 471–472

Zintl, Eduard, 582 Zintl compounds, 580, see also Zintl phases Zintl ions, 85 Zintl–Klemm concept, 268 Zintl–Klemm ions, 85 Zintl phase compounds, 574 Zintl phases, 267–270, 346, 589, 656 criteria for defining, 270 with delocalized bonding, 271 with hetero-atomic clusters, 271 with homo-atomic clusters, 271 with localized bonding, 271 Zirconium (Zr), 393–394 chemical properties, 396 crystal structures, lattice parameters, and densities, 395 highest melting points trends in binary alloys, 400 intermetallics, Zr3Al, 404 ionization energy, 395 occurrence and preparation, 393–394 physical properties, 394 Zone melting, 555 Zone refining, 553 Zr3Al, 404 Zr–Hf–Ir alloys, 564–565

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