Had I been present at the creation, T would have given some useful hints for the better ordering of the Universe. e Wise, 1221-1284 The chessboard is the world; the pieces are the phenomena of the Universe; the rules of the game are what we call the Laws of Nature. The player on the other side is hidden from us. Thomas Wuxley, 1825-1895 Man builds no structure that outlives a book. Eugene Fit& Ware, 1841-1911
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J* rookline Technologies,Ballston Spa, New York, USA
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tio To the memory of
John Herbert 919-1985 Wise, vigorous, effective advocate of the relevance and value of scientific research in industry. His strong belief in the synergetic interaction of Principles and Practice in the field of metallurgy impelled him to assemble an innovative, diverse staff at General Electric, and to inspire independent exploration that benefited both science and engineering.
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Contents
............................................. Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preface to 1995 edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ListofAcronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Crystal Structure Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Some Intermetallic Families Defined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Contributors
I STRUCTUREA
COMPOSITION
............................ ..............................
1 Structural Classification and Notation Jose' Lima-de-Faria 2 Amalgams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cezary Guminski 3 Beryllides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Loren A . Jacobson, Robert J . Hanrahan, Jr., and James L. Smith 4 Precious Metal Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ira M . Wolf 5 Rare-Earth Metal Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Maria L. Fornusini, Franco Merlo, and Marcella Pani 6 Zintl Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Slavi C. Sevov
NDING AND STABILITY
................................
7 Spectroscopic Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Esther Belin-Ferre' 8 Effects of Pressure on Stability and Properties . . . . . . . . . . . . . . . . . . . . . . . Y. V. Levinsky 9 Magnetic Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. M. Cadogan 10 Calculation of Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Didier de Fontaine
vii
xi XiX
xxi xxiii
xxxi xxxv
1 3
21 37
53 85 113
133 135 153 165
185
Contents
viii
. . . , . . . . . , ... ... . . . , .......,. ... . . ...... . ., .....
PROPERTIES AND PHENOMENOLOGY
209
11 Free Surface Structure and Properties Mathias Goken 12 Color and Optical Properties . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . S. G. Steinemann, W. Wolf, and R. Podloucky 13 Effects of Mobile Species . . . . . , . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . Marie-Louise Saboungi and David L. Price 14 IonTracks . B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Robert L. Fleischer 15 Thermal Defects and Diffusion . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . Woljgang Sprengel, Markus A. Mdler, and Hum-Eckhardt Schaefer
211
PV MECHANICAL PROPERTIES
...,,.......,............. ....
231 245 263 275
29 5
16 Creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dilip Shah and Eugene Lee 17 Fatigue .................................................. N . S. Stoloff 18 Solution and Defect Hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Robert L. Fleischer 19 Strain Hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . George T. Gray 111 and Tresa M . Pollock 20 Dislocations in Quasicrystals . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Renhui Wang and Chengzheng Hu 21 Twinning and Mechanical Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M . H. Yoo 22 Staclcing-Fault-Type Interfaces and their Role in Deformation . . . . . . . . . . . V. Paidar and V. Vitelt
297
P L I ~ A T ~ O . . .~. ~. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
469
23 High-Temperature Structural Applications . . . . . . . . . . . . . . . . . . . . . . . . Harry A. Lipsitt, Martin J . Blackburn, and Dennis M . Dimidzik 24 Structural Applications for General Use . . . . . . . . . . . . . . . . . . . . . . . . . . . Vimd K. Sikkn and Seetharama C. Deevi 25 Magnetic Refrigeration . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . K. A. Gschneidner, Jr. and V. K. Pecharsky 26 Niobium Silicide High Temperature In-Situ Composites . . . . . . . . . . . , . . . . B. P. Bewlay, M . R. Juckson, and M . F. X . Gigliotti 27 Coating Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P. K. Watta, J . S. Burnell-Gray, and K . Natesan
47 1
325 351 361 379 403
437
50 1 519 541 56 1
...........................
589
28 Casting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Paul A. McQuay and Vinod K. Sikka
591
Contents
29 Forming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Appel. H . Kestler. and H . Clemens 30 Powder Metallury . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Seetharaman and S . L . Semiatin 31 Thin-Film Deposition and Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G. Ramanath. H . S. Goindi. and D . B . Bergstrom 32 Bulk Amorphous Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R . B . Schwartz 33 Sulfidation Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K . Natesan and P . K . Datta
CH TECHNIQUES
..............................
ix
617 643 663 681 707
721
34 Novel Synthesis Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Naresh N . Thadhani 35 Nanostructured Intermetallics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Suryanarayana 36 Defect and Atomic Process Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . M . I . Baskes 37 Molecular Beam Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hock Min Ng and Theodore D . Moustakas
723
.............................. Commercial Impact on the US Economy . . . . . . . . . . . . . . . . . . . . . . . . . . John V. Busch and AIan C. Goodrich Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
789
VIII MISCELLANEOUS TOPICS 38 39
JunLing hi. Chao Liu. and Zhihong X u 40 Computer Design of Materials with Artificial Intelligence . . . . . . . . . . . . . . . Nadezhda N . Kiselyova 41 Alloy Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Naka and T. Khan 42 Intermetallics on the Internet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J . H . Westbrook
749 765 779
791 797 811 841 857
Indexes Authorindex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subject index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compoundindex .............................................
Contents of Volumes 1 and 2
.........................................
875 959 1019 1037
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List of Contributors F. Appel Institute for Materials Research GKSS, Research Center D-21502 Geesthacht Germany
Bernard P. Bewlay General Electric - CR+ D Schenectady NY 12301 USA
Michael I. Baskes Los Alamos National Laborator) MST-8, NS G755 Los Alamos NM 87545 USA
Martin J. Blackburn School of Engineering University of Connecticut North Eagleville Road Storrs CT 06268 USA
Esther Belin-Ferre CNRS LCPMR-UMR 7614 11 rue Pierre et Marie Curie 75231 Paris Cedex OS France
J. S. Burnell-Gray Surface Engineering Research Centre University of Northumbria at Newcastle Newcastle upon Tyne NE1 8ST UK
Daniel B. Bergstrom Intel Corporation Hillsboro OR 97123 USA
John Busch Ibis Associates, Inc Reservoir Place, Suite 164 1601 Trapelo Road Waltham MA 02451 USA
xi
xii
List of Contributors
J. M. Cadogan School of Physics The University of New South Wales Sydney NSW 2052 Australia
Dennis M. Dimiduk USAF Wright Laboratory WL/MLLM 2230 Tenth Street Suite 1 Building 655 Wright Patterson Air Force Base OH 45433 USA
Helmut Clemens Institut ffir Metallkunde Universitit Stuttgart D-70 174 Stuttgart Germany
Robert L. Fleischer Department of Geology Union College Schenectady NY 12308 USA
P. K. Datta Surface Engineering Research Centre University of Northumbria at Newcastle Newcastle upon Tyne NE1 8ST UK
Maria L. Fornasini U.d. Genova Via Dodecanesco 31 116146 Genova Italy
Didier de Fontaine Department o f Materials Science and Engineering Evans Hall University of California Berkeley CA 94720- 1760 USA
Michael F. X. Gigliotti General Electric - CR + D Schenectady NY 12301 USA
Seetharama C. Deevi Chrysalis Technologies, Inc. 4201 Commerce Rd Richmond VA 23234 USA
Harmeet S. Goindi Rensselaer Polytechnic Institute 110 8th Street Troy NY 12180 USA
..I
List of Contributors
Mathias Goken Department of Materials Science University of Saarland Building 43B PO Box 151150 D-66041 Saarbriicken Germany
Robert J. Hanrahan Los Alamos National Laboratories Los Alamos NM 87545 USA
Alan Goodrich IBIS Associates, Inc Reservoir Place, Suite 164 1601 Trapelo Road Waltham MA 02451 USA
Chengzheng Hu Department of Physics Wuhan University Wuhan 430072 China
George T. Gray 111 Los Alamos National Laboratory Group MST-8 MS G755 Los Alamos NM 87545 USA
Melvin R. Jackson General Electric - CR + D MB-223 Schenectady NY 12301 USA
Karl A. Gschneidner, Jr Ames Laboratory Iowa State University Ames, IA 50011 USA
Loren A. Jacobson Los Alamos National Laboratory MS G-770 Los Alamos, NM 87545 USA
Cezary Guminski Department of Chemistry University of Warsaw Pasteura 1 02092 Warsaw Poland
Heinrich Kestler Plansee AC Technology Centre A-6600 Reutte Austria
xn1
xiv
List of Contributors Jose Lima-de-Faria
ONERA 29 Avenue Divise Leclerc BP 72 Chitillon 92322 France
Instituto de InvestigaGlio Cientifico Tropica Centro de Cristalografia e Mineralogia Alameda D. Alfonso Henriques, 41-40 Esquadro 1000-123 Lisboa, Portugal
Nadezhda N. Kiselyova A A . Brtikov Institute of Metallurgy and Materials Science Leninskii Prospect 49 11 7334 Moscow Russia
Harry A. Lipsitt 1414 Birch Street Yellow Springs OH 45387 USA
Eugene S. Lee Pratt & Whitney M/S 114-41 400 Main Street East Hartford CT 06108 USA
Chao Liu Laboratory of Computer Chemistry Chinese Academy of Science PO Box 353 Beijing 100080 China
Y. V. Levhsky Moscow Institute for Fine Chemical Technology Prospect Vernadakogo 86 113571 Moscow Russia
Paul McQuay Howmet Research Corporation 1500 S. Warner Street Whitehall, Mf 49461-1895 USA
JunLing Li Laboratory of Computer Chemistry Chinese Academy of Science PO Box 353 Beijing 100080 China
Franco Merlo U. d. Cenova Via Dodecanesco 31 I16146 Cenova Italy
List of Contributors
Theodore D. Moustakas Molecular Beam Epitaxy Laboratory Boston University 8 St Mary’s Street Boston, MA 02215 USA
V. Paidar Institute of Physics Academy of Science of the Czech Republic Na Slovance 2 18040 Praha Czech Republic
Markus Miiller Institut fur Theoretische und Anpwandt Physik University of Stuttgart Pfaffenwaldring 57 50 Stuttgart Germany
Marcella Pani U. d. Genova Via Dodecanesco 31 I16146 Genova Italy
Shigeshisa Naka ONERA 29 Avenue de la Divise Leclerc Chiitillon 92322 Cedex France
Vitaly K. Pecharsky Ames Laboratory 242 Spedding Iowa State University Ames, IA 50011 USA
Ken Natesan Argonne National Laboratory, D212 9700 South Case Avenue Argonne, IL 60439 USA
Raimund Podloueky Dept. of Physical Chemistry University of Vienna Liechtensteinstrasse 22A/I/3 A- 1090 Wien Austria
H. M. Ng Physical Science and Engineering Lucent Technology Bell Laboratories 600 Mountain Avenue Murray Hill, NJ 07974 USA
Tresa Pollock Dept. of Materials Science and Engineering University of Michigan 2300 Hayward Street Ann Arbor, MI 48109-2136 USA
XV
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List of Contributors
David L. Price Argonne National Laboratory Argonne IL 60439 USA
Venkat Seetharaman Materials and Processes Engineering Pratt and Whitney 400 Main Street East Hartford, CT 06108 USA
G. Ramanath Department of Materials Science Rensselaer Polytechnic Institute Troy, NY 12180 USA
S. Leo Semiatin
Marie-Louise Saboungi Centre de Recherche sur la Matihre Divise CNRS 1B rue de la Ferollerie 4507 1 OrlCans Cedex 02 France
Slavi C. Sevov Department of Chemistry and Biochemistry University of Notre Dame Notre Dame, IN 46556 USA
Ham-Eckhardt Schaefer Institute of Theoretical and Applied Physics University of Stuttgart Pfaffenwaldring 57 Stuttgart D-70569 Germany
Dilip M. Shah Pratt and Whitney MS 114-45 400 Main Street East Hartford, CT 06108 USA
Ricardo B. Schwarz Structure/Properties Relations Group MSTIG755 PO Box 1663 Los Alamos, NM 87545 USA
Vinod K, Sikka ORNL Oak Ridge, TN 37831-6093 USA
USAF Materials and Manufacturing Directorate Wright-Patterson Air Force Base OH 45433-7817 USA
List of Contributors
James L. Smith Los Alamos National Laboratory STC MS K763 Los Alamos, NM 87545 USA
School of Materials Science and Engineering Georgia Institute of Technology 771 Ferst Drive, NW Atlanta, GA 30332-0245 USA
Wolfgang Sprengel Institut fur Theoretisch und Angewandt Physik Universitiit Stuttgart Pfaffenwaldring 57 D-70550 Stuttgart Germany
Vaclav Vitek Department of Materials Science and Engineering University of Pennsylvania 3231 Walnut Street Philadelphia, PA 19104 USA
Samuel G. Steinemann Institut de physique de Ia Matikre Condenske
Renhui Wang Department of Physics Wuhan University Wuhan 430072 China
Codoz 14
CH 1025 Saint Sulpice Switzerland
Norman Stoloff Department of Materials Science and Engineering Rensselaer Polytechnic Institute Troy, NY 12180 USA
Jack H. Westbrook Brookline Technologies 5 Brookline Road Ballston Spa, NY 12020 USA
C. Suryanarayana
Walter Wolf Materials Design s.a.r.1. 44 av. F.-A. Bartholdi 72000 Le Mans France
Department of Mechanical, Materials and Aerospace Engineering University of Central Florida Orlando FL 328 16-2450 USA
xvii
xviii Ira M. Wolff Technologies Group Conor Pacific Environmental Technologies Inc. Suite 920 1500 West Georgia Street Vancouver BC V6G 226 Canada
Zhihong Xu Laboratory of Computer Chemistry Chinese Academy of Science PO Box 353 Beijing 100080 China
List of Contributors
Man H. Yoo Metals and Ceramics Division, MS 6115 ORNL, PO Box 2008 Oak Ridge, TN 37831-6115 USA
reface
The world at present groans under a load of new publications on every branch of science and art, with which no former period of our literary annals can for a moment be compared. The most assiduous students, unable to peruse a thousandth part of the works which are daily soliciting their attention, are quite perplexed and distressed about what to choose and what to reject. This we have frequently found to be the case with ourselves, and while debating the question in our own minds, have lost, in doubt and uneasiness, the time we meant to set apart for practical manipulation. Impressed, therefore, with the unspeakable disadvantages that result from the circumstancesjust stated, and anxious to save others, in some degree, from that unpleasant dilemma in which we have ourselves been so often placed, we have resolved on the present publication, which we hope will to a very great extent accomplish the useful object we have in view. With what judgment, however, the design has been formed, and with what skill it has been executed, it becomes not us to determine - that question, to the result of which we are deeply alive, remains now with a higher tribunal.
It is disconcerting to note that, in fact, the above words were written, not by us, but by another metallurgist almost 150 years ago.* Talk about dejd vu all over again! To assuage, in our own field, the difficulties summarized above was indeed the primary objective of our original 1995 work, Intermetallic Compounds: Principles and Practice, and we could not have better exprcssed our feclings. One might suppose that the extensive treatment and coverage of the 75 chapters of the predecessor volumes 1 and 2 of our treatise would have exhausted such a narrow and, in the view of many, esoteric subject. This is not so! Interest and activity in the field remain high as indicated by the numerous sub-topical conferences and symposia that have occurred since the publication of the first two volumes and by the still increasing level of activity in new research (approximately 1900 literature additions noted in 2000 by the Permuterm Subject Index). Accordingly, in planning the present volume, we had no difficulty in defining many new topics not previously treated (new intermetallic families, new means of assessment of bonding and stability, new properties and phenomena, new applications, new practical processes and phenomena, and new research techniques). Other topics introduced for the first time include: economics, design of intermetallic-based materials, a compilation of data sources, and opportunities for information retrieval from the Internet. Altogether these new topics comprise 27 chapters in the present volume. In other instances (eight chapters) subjects previously treated were reprised, because of the intense current activity and great importance of their topic matter. In the case of seven more chapters, dealing with mechanical properties and phenomena, although their subjects were previously alluded to in one or more chapters, now totally new approaches were undertaken. A final innovation in the present volume is the inclusion in the front matter of a section by one of the editors (JHW) called ‘Some IntermetallicFamilies Defined’, intended as an assist to all readers. Four planned chapters did not eventuate due to over-commitment of the invited contributors and were reluctantly dropped from the book, In recruiting contributors for the present volume, we deliberately chose not to include any authors from volumes 1 and 2 so as to encourage, and profit from, new viewpoints, knowledge, and contacts. As before, we consulted carefully with many people in order to identify authorities for each subject. We sought experts wherever they were to be found, and our international set of 71 authors turned out to be almost equally divided between the United States and 13 other countries (Austria, Australia, China, Czech Republic, France, Germany, Italy, Poland, Portugal, Russia, Switzerland, Union of South Africa, and the United Kingdom). Having recruited contributors for the project, we then strove to assist them in achieving clarity and thoroughness - from outline, i o draft, to final manuscnpt. The contributors cooperated superbly, and we thank them for their hard work and high achievement.
* From the Preface to the First Edition of James Larhn’s Brass and Iron Founders Guide, H. C . Baird & Co.. Philadelphia, 1853. xix
xx
Prefuce
Their affiliations at the time of writing are shown on the title page of each chapter. Since several of these have changed by the time of publication, their current postal addresses are shown with their photos in the List of Contributors, pp. xi-xviii. Just as with volumes 1 and 2, this volume was planned to be an aid to both scientists and engineers. Together with the earlier volumes, this volume can serve as a base for those who wish to know about interrnetallics as an area in which to begin research or for those who wish to exploit the often unique properties of intermetallics in practical applications. Equally, it is a resource for workers who are already active in the field and need, or wish, to expand their knowledge of related science or practical technology. We also expect that many chapters are appropriate source matter for special-topic or seminar courses at the advanced undergraduate and various graduate school levels, Authors were advised to strive for clarity and, while providing copious references to the literature in their field, to present their chapter in such a way that it could stand alone and be fully comprehensible. Each author was asked to set forth the principles of his or her subject in terms that are meaningful to scientists and engineers who are not speclalists in the author’s field, and then to progress to include knowledge that workers in their own areas would wish to have. Concluding sections of most chapters give the authors’ critical assessment of the state of their subject and of where they believe further effort is merited. As an assist to readers, the acronym list in the front matter consolidates new entries from the present volume with those already compiled in volumes 1 and 2. Similarly, the subject, author, and compound indices constitute a consolidation from all three volumes. We have benefited from outstanding secretarial help by Jean Conley of Union College during the three years of this project. Assembly and publication of the final product were eased for us by the continuing efforts and cheerful good counsel of David Hughes, Helm McPherson, Susan Barclay, Samantha Hartley, and Susan Lambert at John Wiley.
J. H. WESTBROOK, Bullslon Spa, New Y o ~ k R. L. FLEISCHER, Schenectady, New I70rk
Preface to t e 1995 Edition
Intermetallic compounds were last comprehensively reviewed in 1967 in a volume that was edited by one of us (JHW). At that time the field was described as of spccial interest because it was undergoing ‘exponential proliferation’. That trend continues to the present. The number of intermetallic entries in the Permuterm Subject Index shows a doubling period of less than nine years, having reached roughly 1880 entries per year in 1993. Apart from scholarly interest, intermetallics have now become of substantial commercial significance; for some, such as Ni,Al, world-wide use is in the 1000s of tons; for others, for example 111-V semiconducting compounds, although the quantities employed are not in tonnage numbers, their value as vital components of electronic circuits is in the billions of dollars. From the 1967 book we remind the reader that ‘Thc first published paper dealing with intermetallic compounds appeared in 1839, and more than sixty years elapsed before.. .the first review paper by Weville in 1900. However, new results were then appearing so rapidly that fifteen years later two books were printed, devoted exclusively to this subject, one by Desch in England and one by Giua and Giua in Italy’. More recently, conference volumes that deal exclusively with intermetallics but typically only within specific, limited sub-topical subject areas have become common. The scope of the present work is as broad as that of its 1967 predecessor. However, the increased volume of activity in intermetallics and the increased significance of their applications have necessitated an expansion from the 27 chapters of the earlier work to the 75 chapters of the present treatise. First, what are intermetallic compounds? Generally, such a compound is a structure in which the two or more metal constituents are in relatively fixed abundance ratios and are usually ordered on two or more sublattices, each with its own distinct population of atoms. Often substantial or complete disorder may obtain, as a result of low ordering energy or the intervention of some external agency, for example extreme cooling rates, radiation, etc. Deviations from precise stoichiometry are frequently permitted on one or both sides of the nominal ideal atomic ratios, necessitating a partial disorder. Here we include as intermetallic compounds all metal-metal compounds, both ordered and disordered, binary and multicomponent. Even the metal-metal aspect of the definition is often relaxed by including some metal-metalloid compounds, such as silicides, tellurides, and semiconductors. We believe this inclusion is appropriate since the phenomenology of many such compounds is nearly identical to metal-metal ones, and they provide useful examples of priiiciples, properties, and practices. The burgeoning literature on intermetallics and the lack of a comprehensive single source of up-to-date descriptions of where we are, what we need to know. and what we can do with intermetallics created the incentive for the present pair of volumes. This work was planned to provide state-of-the-art assessments of theory, experiment, and practice that will form a solid base for workers who wish to know more than their own particular area. Each author was asked to set forth the principles of his or her subject in terms that are meaningful to scientists and engineers who are not specialists in the author’s field, and then to progress to include knowledge that workers in their own areas would wish to have. Concluding sections of most chapters give the authors’ critical assessment of the state of their subject and of where tlicy believe further effort is merited. This work is divided into two volumes in order that each be of manageable size. The first, on the theme Principles, is directed at the science of intermetallics - how do we understand their formation, structure and properties? The Practice volume considers commercial production and engineering applications of intermetallic compounds. The reader who browses carefully will recognize that the immediacy of the practice described ranges from hoped-for use, to beginnings of use, to actual commercial application - depending on the specific subject. Some of the hoped-for uses are fated never to be realized, but the authors have aimed to reveal what the obstacles are so that the reader may make his or her own assessment (and possibly providc a solution!). xxi
xxii
Preface to the 199.5 Edition
We conferred carefully with many people in order to identify authorities for each subject; having recruited contributors for the project, we then strove to assist them in achieving clarity and thoroughness from ouiline to draft to final manuscript. The contributors cooperated superbly, and we thank them for their hard work and high achievement. We sought experts wherever they were to be found, and our international set of nearly 100 authors turned out to be almost equally divided between the United States and 14 other countries. Manuscripts have in fact come from all inhabited continents. We planned this work as an aid to both scientists and engineers. It can serve as a base for those who wish to know about interrnetallicsas an area in which to begin research. Equally it is a resource to workers who are already active in the field and need, or wish, to expand their knowledge of related science or practical technology. We expect that many chapters are appropriate source matter for special topic or seminar courses at the advanced undergraduate and various graduate school levels. It is hoped that passage of the next 25 years will reveal some influence of this treatise on the further development of this field. As an assist to readers we have provided in the following pages a consolidated acronym list and some crystallographic tables. Nomenclature for crystal structure types is often complex, and some of the authors have introduced their own. Generally we have asked authors to includc both o f two commonly used types of symbols as they introduce structures. The two-part table following this preface lists many of the common types - by Strukturbericht symbol, prototype name (termed a structure type), and Pearson symbol. Strukturbericht symbols are only partly significant and systeniatic: A’s are not compound structures but consist of a single lattice of atoms (except for A15!); B’s are equiatomic ordered structures; C’s have 2-to-1 atomic abundance ratios, DO’S340-1. Structure type compounds are the specific ones used to designate a particular structure. Thus B2 compounds are also referred to as CsCl compounds. Many structures are better known to metallurgists and mineralogists by names other than the formula of the structure type chosen by crystallographers, e.g. Laves, fluorite, Heusler, etc. Such names have been added in selected cases. The Pearson symbols tell the crystal symmetry and the number of atoms per unit cell. Thus, B2, CsCl has a primitive (P) cubic (c) structure with 2 atoms per cell and hence the Pearson symbol (cP2). The Pearson designation is informative, but it is not necessarily unique. Although there is only one cP2 structure, W a r s and Calvert list two cP4s, three cF129 and twenty-two hP9s. Thus to be definitive, both the structure type and the Pearson symbol need to be given, or the Pearson and the Strukturbericht symbol. The index in each volume includes the subjects in both volumes of this work, in order that the reader may be able to locate any subject that is addressed. Although the purpose of such combined indices is not to induce the owner of a single volume to purchase the other, it possibly may help to reduce the barrier to such action. We havc bcnefited from outstanding Secretarial help during the three years of this project, first by Phillis Liu, then Constance Remscheid at General Electric, finally Nary Carey at Renssalaer Polytechnic Institute. We appreciate the hospitality of the General Electric Research and Development Center during the inception and middle period of preparing these volumes. Assembling the find product has been eased for us by the continuing efforts and cheerful good counsel at John Wiley of Jonathan Agbenyega, Irene Cooper, Philip Hastings, Vanessa Lutman and Cliff Morgan.
J. H. WESTBROOK, Bullston Spa, New York R. L. FLEISCHER, Schenectudy, New York
Upon these considerations, we have been induced to undertake the present extensive work, the purpose of which is to instruct rather than to amuse; in which nothing will be omitted that is elegant or great; but the principal regard will be shown to what is necessary and useful. - Isaac Ware, 1756
2D 3D 6D
ASA ASB
two-dimensional three-dimensional six-dimensional
ASRP ASTM
angular correlation of annihilation radiation angular correlation of positron ACPAR annihilation radiation atomic environment AE AES Auger electron spectroscopy AET atomic environment type AF anti-ferromagnetic atomic force microscopy AFM AI artificial intelligence AIM argon induction melting ALCHEMI atom location by channeling-enhanced microanalysis atomic layer epitaxy ALE ALICISS alkali-ion impact collision ion scattering spectroscopy air mass AM active magnetic regenerator AMR Advanced Materials Technology, Inc. AMT AN atomic number atomic probe AP AP atomic property APB anti-phase boundary anti-phase domain APD avalanche photodetector APD APE atomic property expression APFIM atom-probe field-ion microscopy APW augmented plane wave antireflection AR ARIPES angle resolved inverse photoemission spectroscopy angle-resolved photo-emission ARPES spectroscopy angle-resolved ultraviolet photoARUPS emission spectroscopy AMPS angle-resolved X-ray photo-emission spectroscopy ACAR
ASW BC bcc BCS bct BDTT BH
BIS BM BSCCO BSE BT BW BZ CAM CANDU CAP CAS CAT CBED CBLM
cc
CCD CCGSE CCIC CCMAI
xxiii
atomic sphere approximation anti-structural bridge (mechanism) advanced sheet-rolling process American Society for Testing and Materials augmented spherical wave bond charge body-centered cubic Bardeen-Cooper-Schrieffer body-centered tetragonal brittle-to-ductile transition temperature buried heterostructure bremstrahlung isochromatic spectroscopy Bowles-Mackenzie (theory of martensitic transformation) bismuth-strontium-calcium-copperoxide back-scattered electrons Bhatia-Thornton ('partial structure factor for liquid alloys) Bragg-Williams (theory of ordering) Brillouin zone c-axis modulated Canadian deuterium-uranium (power reactor) consolidation under atmospheric pressure Chemical Abstracts Service computer-assisted tomography convergent-beam electron diffraction cluster Bethe lattice method cluster center charge-coupled device concentric-circle grating surfaceemitting (laser) cabled conductor in conduit crystal chemical model of atomic interactioiis
List of A c~onyms cubic close-packe~ continuous cooling transformation
direct chill (casting) direct configurational averaging dominant diffusing species density functional (theory) distributed feed-back density-f~nctionaltheory double hetero (junction) double hexagonal close-packed
compact disc cluster e~paiision(technique) ~ontinuo~ electron-beam s accelerator facility dHVA
duplex layer coating directional levitation zone remelting density of states duplex displace~entper atom demonstration poloidal coil diamond pyramid hardness d e ~ ~ g Q nquasi~~ystal a1 dense random packing directional solidification dime~sio~ally stable anode diEerent~a1scanning calorimetry d i s ~ l a c e ~ eshift n t complete di~erent~al thermal analysis
~ n t ~ ~ n a t i oCommission ii~l on tant initial state couiiter-~ravitylow-pressure inert-atmosphere (investment casting)
colossal ~agnetoresistance coordinator number
e/a of comp~terl e ~ r ~ i n g ) coefficie~tof performance coardination polyhedron coheren~poteiitial approxii~ation critical resolved shear stress clie~~sorptioi~ complex stacking fault ~oincide~~ce-site lattice
chemical v a p r deposition luster variation method o ~ i t i n u ~ uwave s cold worked coiicentr~tionwave illiams method (theory of phase transfoima ti ons)
ESCA
FC fcc FGC fct
~ a t ~ a n a~ ~ e~ ~system ~~ e n~ t ~ ~ ~ t ~ l e - t o - b rtransition ittle teniperature direct c ~ ~ r e n ~
elcctron/atom (ratio) e m b e ~ ~ ~ d -method ato~ electron beam physical vapor deposition equal channel angular extrusion effective cluster interaction embedded-cluster method ekctro-optic directional coupler electrodischarge machining ener~y-dispersiveX-ray (spe~troscopy) electron energy-loss spectroscopy electric-field gradient electro~otiveforce eEective pair interaction electron spectro scopy for chemical analysis electrospar~depos~tion extrinsic stacking Cault electroslag remelting (copper) electroly t extended ion fine structure field cooled face-centered cubic fatigue crack growth face-centered ~ e t r a ~ o n a ~ f o r e i g n - a ~ odiffusion ~ finite-element analysis ~ n i t e - e l ~ ~method ent
List of Acronyms
Fusion Engineering International Experimental Magnet Facility field effect transistor field ion microscopy full-potential linearized augmented plane wave full-potential linearized augmented Slater-type orbital full-potential linearized muffin-tin orbital fully lamellar, narrow (spacing) fully lamellar, wide (spacing) ferromagnetic foreign objects and debris figure of merit Fabry-Perot (laser) Finnis-Sinclair (potential) phase transformation field warmed full width at half maximum fluxing followed by water quenching in fused silicon tubes floating zone fusion zone
HDDR
IC IC IC ICSD ICSU
GS GT GTA
gas atomization gainx bandwidth (product) grain boundary Gorsky-Bragg-Williams (free energy) gross domestic product glass-forming tendency generalized gradient approximation galvanostatic intermittent titration technique grazing incidence X-ray spectroscopy gas metal arc (welding) gravity metal mold giant magnetoresistance generalized perturbation method generalized random-phase approximation ground state Goody-Thomas (electronegativityj gas tungsten arc (welding)
HAZ HB HBT HCF hCP HD HD
heat-affected zone horizontal Bridgman heterojunction bipolar transistor high-cycle fatigue hexagonal close-packed hybrid deposition hydrogen decrepitation
FENIX FET FIM F-LAPW F-LAST0 F-LMTO FLn FLw FM FOD FOM FP FS FT FW FWHM FXWQFS FZ FZ GA GB GB GBW GDP GFT GGA GITT GIXS GMA GMM GMR GPM GRPA
HDZ HEMT HIP HOMOLUMO HPT HPT HPTB HR HREM HRTEM HSCT HTS HVEM HVOF HVTEM IAE IAET IBM
IDOS IEM IGC IHPTET ILS IM IMC IMC IMPATT IPES IPM IPS 1QC ICR IRR ISF ISM IT ITER
xxv hydrogenation-decompositiondesorption-recombination heat-and-deformation zone high-electron-mobility transistor hot isostatic pressing highest occupied molecular orbitallowest unoccupied molecular orbital heterojunction phototransistor high-pressure turbine high-pressure turbine blade high resolution high-resolution electron microscopy high-resolution transmission electron microscopy high-speed civil transport high-temperature superconductor high-voltage electron microscopy high-velocity oxy-fuel high-voltage transmission electron microscopy irregular atomic environment irregular atomic environment type International Business Machines Corporation intermetallic compound integrated circuit investment cast inorganic crystal structure database International Council of Scientific Unions integrated density of states interstitial electron model Intermagnetics General Corporation integrated high-performance turbineengine technology invariant line strain ingot metallurgy intermetallic compound inverse Monte Carlo (method) impact ionization avalanche transit time inverse photo-emission spectroscopy independent-particlemethod invariant plane strain icosahedral quasicrystal infrared internal rate of return intrinsic stacking fault induction skull melting (positive) inner tetrahedron International Thermonuclear Experimental Reactor
xxvi IUCr IUPAC
List of Acronyms
IV
International Union of Crystallography International Union of Pure and Applied Chemistry intermediate valence
J-FET
junction fiela-effect transistor
KHN KKR
Knoop hardness number Korringa-Kohn-Rostoker (bondcalculation method) Khantha-Cserti-Vitek (deformation model) potassium titanyl phosphate Kear-Wilsdorf (dislocation locking mechanism)
KSV KTP KW LA LAPW LAST0 LCAO LCF LCT LCW LD LDA LEG LED LEED LEISS LWC LKKR LM LMC LME LMTO Ln LNT LO LPCVD LPE LPPS LPS LPT LRO LSDA LSI MA MAPW MASC
longitudinal acoustic (wave) linearized augmented plane wave linear augmented Slater-type orbital linear combination of atomic orbitals low-cycle fatigue large-coil task Lock-Crisp-West (radiation analysis) laser diode local-density approximation liquid-encapsulated Czochralski (technique) light-emitting diode low-energy electron diffraction low-energy ion scattering spectroscopy Large Hadron Collider layered KKR (structure calculation) lattice mismatch liquid-metal cooling liquid-metal embrittlement linearized muffin-tin orbital lanthanide liquid-nitrogen temperature longitudinal optical (wave) low-pressure chemical vapor deposition liquid-phase epitaxy low-pressure plasma spraying long-period superstructure low-pressure turbine long-range order local spin-density approximation large-scale integration mechanical alloying modified augmented plane wave metal and silicide composite (a specific Nb,Ti,Hf,Cr,Al,Si alloy)
MB MBE MBT MC MCE MCS MD MEAM MEE MESFET MF MFM MFTF MG MH MIG MISFET MJR MLR Mm MMC MMC MN MO MOCVD MOS MOSFET MOVPE MQW MR MR MRI MRSS MRT MS DOS PSR MT MTD MVA MXPS NAICS NASA NASP ND NET
Martinov-Basanov (electronegativity) molecular beam epitaxy metal-base transistor Monte Carlo magnetocaloric effect Monte Carlo simulation molecular dynamics modified embedded-atom method migration-enhanced epitaxy metal Schottky field-effect transistor mean field magnetic force microscopy Mirror Fusion Test Facility miscibility gap metal hydride metal-inert gas (welding) metal-insulator-semiconductor field effect transistor McDonald jelly roll (superconducting cable construction) multilayer reflector misch metal metal-matrix composite metal mold casting Mendeleev number magneto-optical metal-organic chemical vapor deposition metal-oxide-semiconductor metal-oxide-semiconductor field-effect transistor metal-organic vapor phase epitaxy multiple quantum well magnetoresistance magnetic refrigerator magnetic resonance imaging maximum resolved shear stress orthodontic NiTi alloy Microsoft disk operating system muon spin relaxation muffin tin martensite transformation diagram million volt-amperes monochromatized X-ray photo-electron spectroscopy North America Industry Code System National Aeronautics and Space Administration (USA) National Aerospace Plane N-dimensional next European torus (fusion device)
xxvii
List of Acronyms
NMI NMR NN NNH NNN NOR NPV NSR
normal hydrogen electrode nano indentation neutral impact collision ion-scattering spectroscopy National Maglev Initiative (US) nuclear magnetic resonance nearest neighbor nearest-neighbor histogram next-nearest neighbor negative OR (logic operator) net present value notch strength ratio
OAZ OB OD ODR ODS OEXC oh OIFZ OIM ORNL OT
oxidation-affected zone occupied band outer diameter oxygen dissolution reaction oxide dispersion-strengthened opto-electronic integrated circuit octahedron optical-imaging float zone (process) orientation-imaging microscopy Oak Ridge National Laboratory (negative) outer tetrahedron
NHE NI NICISS
PA PAC PAM PAS PBC PBN PBR PBT PCM PCM PCT PD PDF PDOS PECVD
primary annealed perturbed angular correlation plasma-arc melting positron-annihilation spectroscopy periodic bond chain pyrolytic boron nitride Pilling-Bedworth ratio permeable-base transistor phase-change material point-charge model pressure-composition-temperature phase diagram pair-distribution function phonon density of states plasma-enhanced chemical vapor deposition PES photo-emission spectroscopy PFC planar flow casting PGM platinum-group metals PH Pearson’s Handbook PHACOMP phase computation (program) PIGA plasma-melted, induction-guided, gas atomization PKA primary knock-on atom PL photoluminescence PM powder metallurgy PM paramagnetic
PMTC
PVD PVDF PWHT PZT
phenomenological martensitic transformatioii concept periodic number type of photothyristor partial pair distribution function parts per million path-probability method Paidar-Pope-Vitek (L12 hardening model) plasma-rotating-electrode process Pearson symbol polysynthetically twinned phase transformation phenomenological theory of martensite crystallography physical vapor deposition polyvinyl difluoride post-welding heat treatment lead zirconate titanate (ceramic)
QC QCSE QENS QFD QN QSD QW
quasicrystalline or quasicrystals quantum-confined Starke effect quasi-elastic neutron scattering quantum formation diagram quantum number quantum structural diagram quantum well
RBS RC RCS RCP RD RD RDF RDS RE REP RF RHE RHEED
Rutherford back scattering ribbon comminution replacement-collision sequence relative cooling power rate dependent rolling direction radial distribution function rate-determining step rare-earth (metal) rotating-electrode process radiofrequency reversible hydrogen electrode reflection high-energy electron diffraction reactive hot isostatic pressing rate independent radiation-induced ductility rigid-ion model Ruderman-Kittel-Kasuya-Y oshida (electronic interactions) refractory-metal intermetallic composite root mean square remote plasma-enhanced chemical vapor deposition
PN PnPn PPDF PPm PPM PPV PREP PS PST PT PTMC
RHIP RI RID RIM RKKY RMIC rmS
RPECVD
xxviii
List of Acronyms
RRR RS RS RSP RSS R-T RT
residual resistivity ratio rapidly solidified reaction synthesis rapid solidification processing resolved shear stress rare-earth transition-metal (compounds) room temperature
SAD SAED SAGBO SAM-APD
selected-area diffraction selected-area electron diffraction stress-assisted grain-boundary oxidation separate absorption and multiplication avalanche photodetector simple cubic semiconductor standard calomel electrode self-diffusion specific damping capacity spin-density wave scanning electron microscopy superlattice extrinsic stacking fault stacking fault stacking-fault energy spin glass self-propagating, high-temperature synthesis semi-insulating VLSI self-interstitial atom self-interaction correction stress-induced martensite secondary-ion mass spectrometry superconductor-insulatorsuperconductor superlattice intrinsic stacking fault static inductance transistor semimetal second-moment approximation shape-memory alloy shape-memory effect superplastic forming scanning probe microscopy superparamagnetism superconducting quantum interference device short-range order solid-state amorphizing reaction structural stability diagram superlattice stacking fault Atlas of Crystal Structure Types scanning transmission electron microscopy scanning tunneling microscopy
sc
sc
SCE SD SDC SDW SEM SESF SF SFE SG
SHS SIjVLSI STA SIC SIM SIMS SIS SISF SIT SM SMA SMA SME SPF SPM SPM SQUID
SRO SSAR SSD SSF STA STEM STM
STN
sv sw sx
TA TB TCP TD TD TDFS TE TE TEC TEG TEM TEP TGW TIP TK TM TM TMA TMD TMF TMS TO TOF TPA TRIP TS TSRO tt TTS TTT UB UES UHF UHV ULSI UNESCO UPS UPS USAF
usw
Scientific-Technological Network (of CAS) Sodani-Vitole version of the Paidar et al. model spin waves single crystal transverse acoustic (wave) tight binding topologically close-packed thoria dispersion transverse direction temperature dependence of the flow stress thermo-electric transverse electric (field) thermo-electric cooler thermo-electric generator transmission electron microscopy triethyl phosphene Teatum-Gschneidner-Waber (atomic radius) thermally induced porosity Takeuchi-Kuramoto (dislocation locking mechanism) transition metal transverse magnetic field Ti-MO-Al (alloy) theoretical maximum density themon~echanicalfailure The Metallurgical Society (of AIME) transverse optical (waves) time of flight two-photon absorption transformation-induced plasticity tensile strength topological short-range ordering truncated tetrahedron tubular tin source time-temperaturetransformation unoccupied band universal equation of state ultra-high frequency ultra-high vacuum ultra large-scale integration United Nations Educational, Scientific, and Cultural Organization ultraviolet photo-electron spectroscopy ultraviolet photo-emission spectroscopy United States Air Force ultrasonic wave
List of Acronyms
xxix
WQFS
water quenching in ftised silica tubes Wigner-Seitz (cell) Winterbon-Sigmund-Sanders (model of irradiation damage) weight parts per million
UTS
ultimate tensile strength ultraviolet
VAR VAR VCSEL VEC VGF VGS VHF VHN VIM VINITI
vacuum-arc refined vacuum-arc remelting vertical-cavity surface-emitting laser valence-electron concentration vertical gradient freezing Van Gogh’s sky very-high frequency Vickers hardness number vacuum induction melting Russian Institute of Technical Information vapor-liquid-solid very large-scale integration vapor phase epitaxy Vickers pyramid number vacuum plasma spraying vacuum ultraviolet
uv
VLS VLSI VPE VPN VPS
vuv
WB WGPD WLR
weak beam waveguide photodetector Weclisler-Lieberman-Read (theory of martensitic transformation)
ws wss
wt.ppm
xuv
X-ray absorption near-edge structure X-ray (photo) absorption spectroscopy exchange correlation exothermic dispersion (synthesis process) X-ray emission spectroscopy X-ray inspection module X-ray photo-electron spectroscopy X-ray photo-emission spectroscopy X-ray diffraction extreme ultraviolet
YAG
yttrium aluminum garnet
ZFC ZIF
zero-field cooled zero insertion force
XANES XAS
xc
XDTM XES XIM XPS XPS XRD
This Page Intentionally Left Blank
tructure Nomenchture* Arranged Alphabetically by Pearson-Symbol Designation Pearson symbol cF4 CF8 cF12 cR6 cn4 cF32 cF52 cF56 cF68 cmo c m 12 cF116
c12 cI16 c128 cI32 c140 cI52 cI54 cI58 cI76 c180 cI96 cIl62 cP1 CP2 cP4 cP5
Prototype
Struktufbericht designation
cu C (diamond) NaCl (rock salt) ZnS (sphalerite) CaF, (fluorite) MgAgAs AlCu,Mn (Heusler) BiF, (AlFe,) NaTl AuBe, SiO, (B cristobalite) Cu,Mg (Laves) CuPt, UB,, Al,MgO, (spinel) c03s4
COJ, Sb203(senarmonite) Fe,W,C (q carbide) NaZn,, Cr23C6
Mn,,Th,,Cu,,Mg,Si, (G-phase) W cou Th,P* CoAs, (skutterudite) Ge,Ir, pu2c; Cu,Zn, (y brass) Fe,Zn,, ( y brass) Sb,Tl, ciMn (pphase) Cu,,Si, Md;O, AILi,N2 Mg,,(A1,Zn)49 ciP0 CSCl AuCU, ReO, AIFe,C (perovskite) CaTiO, (perovskite) Fe,N
Space group
Pearson symbol
Fmh Fd!m Fm3m Fdzm Fm3m Fdzm Fmzm Fm2m Fd3m F43m FdJm Fd 3-m Fm2c Fm3m Fdzm Fdzm Fm3m Fdzm Fd 3m Fm2c Fm3m Fm3m Im3m 1213 I43$ Im3 Im3m I23d I2zm Im2m Im3m 143m Zd3d Ia!
cP6 cP7 cP8 cP12 cP20 cP36 cP39 cP52 hP1 hP2 hP3
hP4
Ag*O CaB, Cr,Si (Bw) FeSi Cu3VS, (sulvanite) FeS, (pyrite) NiSbS (ullmanite) BMn BaHg,I Mg2Zn11 Cu,A14 (y brass) HgSn€-,o Mg
wc
AlB, Cdl, FezN LiZn, YSe ciLa BN C (graphite) NiAS
ZnS (wurtzite) hP5 hP6
hP8
10;
Im? Pm3m Pm3m Pm2m Pm3m Pmzm Pm3m P43m
Prototype
hP9
hPlO hP12
Ni,Al, CaCu, CoSn C%Te HgS MoS, Ni,In Na,As Ni,Sn TiAs CrSi, Fe,P WgZn SiO, (high quartz) Pt,Sn, cus MgZn, (Laves) SiO, (p tridymite)
Strukturbericht Space designation group ~3 02, A15 B20 H24
c2 8f)i
A13 02,
08, 083
Af A3 Bh C32 C6 L’3 ck
A8 A3’ Bk A9 B81 B4 D52
D513 D2d
B35
ch B9 C7
B82 0018 Do19
B, C40 C22 86
C8 DSb
818 C14 C10
pn3m Pmlm Pm3n P213 P43m Pa3 P213 P4122 Pm3~ pm3 P43m P6lmmm P6311wp2c P6m2 P6lmmm Plml P63tmmc P6s/mmc P3121 P6+~nc P6~lmmc P63/mmc P63lmmc P63mc P3ml Phl P6lmmm P6/mmm P6/mmm P3,21 P63lmmc P6smmc P63/mmc P63lmmc P63/mmc Pc222 P62m P3 P6222 P63lmmc P63/mmc P63lmmc P63/mmc continued
*Adapted (with additions and corrections) from ASM Handbook, Vol. 3, 10th ed, ASM International, Materials Park, OH.
xxxi
xxxii
Crystal Structure Nomenclature
Arranged Alphabetically by Pearson-Symbol Designation (contmued) Pearson symbol hP14 hP16 hP18 hP2O hP24 hP28 hR1 hR2 hR3 hR4 hR5 hR6 hR7 hRlO hR12 hR13 hRl5 hR20 hR26 hR32 mC6 mC8 mC12 mC14 mC16 mP12 mP20 mP22 mP24 mP32 mP64 oc4 oC8
oc12 oC16 oc20 oC24 oc28
of% oF40 oF48 OF72 oF128 0112 0114
0120
on8 0140 oP4
aP6 oP8
Prototype W*B, Mn&, Ni,Ti Al,C,Si A1,FeMgtSi, Mg,N1 Fe Th, -dS,, CU,P MgNi, (Laves) Co,AI aHg or BPo aAs aSm NaCrS, BiZTe, N G CaSi, NiS (millentel ' Al,C, MoA cyAI,O, (corundum) BaPb, Fe,W, (p-phase) B4C HoAI. Cr,Ali CuPt AuTe, (calaverite) CUO (tenonte) ThC, SNi,Sn4 FeKS AgAuTe, (syfvanite) ZrO, As,SA CO AI, FeksS ASS (realgar) BSe aSe
NU CaSi ctGa CrB I P (bkck) ZrSi, BRe, PdSn, PdSn, AI Mn T!Si Mn4b CuMg, GeS, aS
SiS, TaA AI,U
?%:f
AuCd
Strukturbericht designation
Space group P63lmmc P63/mcm P63/mmc PGmc P62m P6222 P63mc %/m P63cm P63/mmc P&l_mmc R2m R3m Rjm R3m R3m R32 R2m Rzm R3m R3_m Rjc R3m R2.m R3m R3m RJm R3m C2jm c2/c c21c C2/m a l C
P2/c P21Ic P2dC P21Ic P21lc P21lC P2llC p211c Cmcm Cmmc Cmca Cmcm Cmca Cmca Cmcm Cmcm Aba2 Aba2 Cmcm Fddd Fddd Fddd Fdd2 Fddd Ibam Immm Imma Ibam Imma Pmma Pnnm Pnnm Pnma Pbnm
Pearson symbol oP8
oP12
oPl6
Prototype
BCu Ti Feb GeS SnS MnP TiB CozSi, NiSiTi (E-phase) CozSi HgCh Al3Ni AsMn3
E&
oP20
CdSb CuS,Sb (wolfsbergite) Fe$ (cementite) cr3c2
oP24
oP40 tI2
Sb,O, (valentinite) AuTe, (krennerite) CuFe S (cubanite) Nis Ifmillerite) TiO, {brookite) CrG
t I4
116
tI8 tIlO
w:
MoSi, ThH, AI,Ti ALBa
Strukturbericht Space designation group Pmmn Pilmfl Pnma Pnzcn Pnma Pnma Pnma Pbnm Pmnb Pnma Pmmn P411t71 Pbca Pnma Pnma Pnma Pccn Pma2 Pn-ma R3m Pbca Pnma I41mmm I4lmmm 141lamd I4/mmm R3m I4/mmm I4jmmm I4lmmm 14/mmm
14/m
I4lmcm 1411gmd
t112
14
2114 2116
I4/mmm 142d 142m I4/mcm I41lamd I4lrncm I41mmm I4/mmm I4/mcm I4/mcm
?I18 1126 1128
2132
14
tP2 tP4
tP6 tPl0 tP16 tP20 tP30 tP40 tP50
PNP AuCu CuTi, yCuTi PbO Pb,Sr PtS Cu,Sb PbFCl TiO (rutile) $b4Pt Si,U, PdS B Th
b-J
crCrFe AI,Cu,Fe Zn,P, YB
I4/mcm P4lmmm P42.12 P4/mmm P4lmmm P41nmm P4/nmm P4/mmm P42/mmc P4lnmm P4/nmm P42lmnm P4lnbm P4lmbm P42/m P4/mbm P42lmnm P4zlrnnm P4/mnc P4zlnrnc P42lnnm
xxxiii
Crystal Structure Nomenclature Arranged Alphabetically by Stmkturbericht Designation StTukturbericht designatlon Aa Ah A, Ad Ar A, Ah Ai Ak AI
A1 A2 A3 A3' A4 A5 A6 AI A8 A9 A10 A1 1 A12 A13 A14 A15 A16 A17 A20 Bo Bb B, Bd B.? BA= B33) BB Bh Bi Bk Bi Bm B1 B2 83 B4
B 1 B82 B9 B10 B11 B13 B16 B17 B18 B19
Prototype aPa PU RNP PNP HgSn,,,
YB
aP0 BPO aSe PSe cu
w
Mg aLa C (diamond) BSn In aAs YSe C (graphite) aHg or BPo aGa aMn (X-phase) PMn I* Cr,Si @W) CCS P (black)
aU cou o w n CaSi ?Nisi CdSb CrB MOB
wc
TiAs BN ASS (realgar) TiB NaCl (rock salt) CSCl ZnS (sphalerite) ZnS (wurtzite) NiAs Ni,In HgS (cinnabar) PbO yCuTi NiS (millerite) GeS PtS (cooperite) CuS (rovelite) AuCd
Pearson symbol
Space group
t12 tP30 oP8 tP4 hP1 tP50 CPl hR1 mP64 mP32 cF4 CI2 hP2 hP4 CF8 t14
I4lmmm P42lmnrn Pnma P4212 P61mmm P42/gnm Pm3m R3m P21Ic P2LlC Fm>m Im3m P63lmmc P63/?mc Fd3m 141lamd I4/mmm R3m P3121 P63jmmc R3m C-mca 143m P4132 Cmca Pm3n Fddd Cmca Cmcm n,3 P3 Cmmc Pbnm Pbca Cmcm 141!amd P6m2 P63/mmc P63/mmc P21 lc Pnma Fmzm Pm3m F43m P63mc P63mmc P63mmc P3121 P4/nmm P4/pmm R3m Pnma P421mmc P63lmmc Pmma
ti2
hR2 hP3 hP4 hR1 oC8 cI58 cP20 OC8
cP8 oF'l28 oC8 OC4 cI16 hp9 OC8 oP8 oP16 OC8 tI16 hP2 hP8 hP4 mP32 oP8 CF8
CP2 CF8 hP4 hP4 hP6 h P6 tP4 tP4 hR6 oP8 tP4 hP12 OP4
Stmkturbericht designation B20 B26 B21 B29 B3 1 832 B33(= Bf) B34 B3 5 B31 Ca cb
CC C,
c, c h
ck
c1 clb
c2 c3 c4 C6 c7 C8
c9 c10
c11, cl l h c12 C14 C15 Cl5b C16 C18 CI 9 c 2I c22 C23 C28 C32 c33 c34 c 35 C36 c37 C38 C40 C42 c43 c44 C46 c49 c54 DO, DO:
Prototype FeSi CuO (tenorite) FeB SnS MnP NaTl CrB PdS CoSn TlSe Mg,Ni CuMg, ThSi, PdSn, ThC, Cu,Te LiZo, CaF, (fluonte) MgAgAs FeS, (pyrite) Ag2O TiO, (rutile) Cdl, MoS2 SiO, (high quartz) SiO, (p cristobalite) SiO, (@ tridymite) CaC, MoSi, CaSi,
FeS, (marcasite) aSm TiO, (brookite) Fe,P Co,Si, NiSifi (E-phase) HaCI, AIB, Bi2Te, AuTe, (calaverite) CaC1, MgNi, (Laves) Co,Si Cu,Sb CrSi, SiS, ZrO, GeS, AuTez (krennerite) ZrSi, TiSi, PCu,Ti SiU,
Pearson symbol
Space group
cP8 mC8 oP8 oP8 oP8 cF16 oC8 tP16 hP6 1116 hP18 oF48 2112 oC24 mC12 hP6 hP3 cFl2 cF12 cP12 cP6 tP6 Iz P3 hP6 hP9 cF24 hP12 tI6 tl6 hR6 hP12 cF24 cn4 tIl2 oP6 hR3 oP24 hP9 oP12 oP12 hP3 hR5 mC6 aP6 hP24 oP12 tP6 hP9 oI12 mP12 OF72 oP24 oc12
P213 C2/c Pnma Pmcn PnFa Fd3m Cmcm P42/m P6/mmm I4lmcm P6222 Fddd I4llamd Aba2 C2jc P6/mmm P63/mmc Fm3m F43m Pg3 Pn3m P42!n?nm P3m 1 P6,lrnmc P6222 Fd3m P&/mmc I4lmmm I4/%mm R3m P63lmmc Fd3m F43m I4/mcm Pnrm R3m Phca P62m Pnma Pmnb P6/mmm R3m W m Pnnm P63 lmmc Pbnm P4lnmm P6222 Ibam p211c Fddz Pma2 Cmcm Fddd Pmmn I4jmcm
On4 oP8 tA6
continued
xxxiv
Crystal Structure ~
~
~
~
~
~
l
a
t
~
~
r
Arranged A ~ p ~ a b e ~ i bc ya StruktL~rbericht ~~y ~esignation~ c o ~ ~ i ~ ~ e ~
trukturbericht des~~nation
Prototype
Ir,Si AsMn, Ni3P CoAs, (~kutterudite) BiF,, AlFe, ReO, Fe,C ( ~ e m e ~ ~ i t e ) BaS, Na,As Ni,Sn A 1,Ni
Ni,Ti ~ o ~ i , A1,U PdSn,
M nu,
czAl,O, ( ~ o ~ u n d u m ) La203 r\/4[n,0, b,O, (seaarmontite) Sb,S, ZnP, Cr,C, Sb,O, (valentinite) Ni,Al, GNi,Sn, Ta43, A4C3 CO,%
Pearson symbol tIl6 0P16 1132 cI32 cF16 cP4 02'16 0Pl6 hP8 11P8 0P16 hP24 118 tIl6 hP16 tll0 0120 o c20 CPlO tP20 oF40 /IRIS tf1O tI26 tI28 hP6 cP36 cF52 tI18 oC28 cP7 cFI 12 rPlO hP1O cI40 h R.5 mP20 hRIO hP5 cI80 CfsO
0P20
tP40 0F20 oP20 hP5 me14 of14 hR7 cF56 cI28
Space group
Strukturbericht designation
Prototype
Co,Al, Mg,,(A1,Zn),g Ge7Ir3 Ga,Mg,
Pearson symbol m P22 ell62 cI40 0128
hP14 hR7 MO,& hP20 Th,S,, tp32 CrA W,Si, t132 cI52 Fe,Zn,, Cu,Zn, y brass cI52 cP52 Cu,Al, cF116 Cr,,C, Fe,W, (@-phase) hI113 c176 Cu,,Si, Mn,Si, hP16 eF68 CO$, CrgAlg hR26 Co,Al, hP28 oP40 CrF3 Fe,Th, hP20 PbFCl tP6 FeAsS mP24 0Cl6 AgAuTe, (sylvanite) mP12 CuFeS, ( ~ h ~ l c o p y ~ - i tIt6 ~~) CaTiO, (perovskite) cP5 Al,CdS, tll4 Al,Cu,Fe tP40 hP18 Al,FeMg,Si, Mn,Al~~i hP26 AlLi,N, c196 CuFe,S, (cubanite) oP24 cF112 Fe,W,C (q carbide) Al,C,Si hP18 cP12 NiSbS (ullrnanite) mC16 FeMS, hR4 NaCrS, CuS,Sb (~ol~sbergite) oP16 AI,MgO, (spinel) cF56 Cu,VS, (sulvanite) cP8 @u,FeSnS, 1116 cP5 Fe,N CuPt, cF32 AuCu tP4 AuCuII 01'40 CuPt hR32 AuCu, cP4 AlFe,C (perovskite) cP5 iiCuTi tP2 ThH, 116 AlCu,Mn (Heusler) cF16 cI54 Sb,TI, hP3 FC,N CuTi, tP4
~ , &
I
Space group
~
tetrahedra~~y coordinated compounds based on the wurtzite B3 (cF8) structures and all other coinpounds with structu stacking or substitutional or vacancy defect variants. There may or may not be ordering on cation and/or anion sites. Examples of both norinal ternary, mid quaternary adamantane compounds include: In ,Te, (*), and AgGd,InTe,. See tetrahedral structures. a
S
a
alloys, binary or ~ u l t i n a r ywhere , one of the components is merc~ry.They may be moiwphase or mlaltipliase, solid, liquid/solid, or liquid. Thus they may be, or contain, i~itermetallicsbut not necessarily so.
,
structure^, g e o ~ ~ e t r i c aidentical ll~ with the ~ u o r i t es~ructure(c the positions of positive and negative ions interchanged. Thus, whereas in Buorite (CaF,) each Ca' is surrounded by eight F- ions at the corners of a cube and each F-- ion by four Ca', ions at the corners of a t e t r a h ~ d r o ~in; the a n t i - ~ ~ o r i t e structure Li, Na, and oxides, sulfides, selenides, and tellurides, the chalcogen ions are close-packed with the alkali ions in tetrahedral interstices. and tellurides would usually be classed with I anti-fluorides also exist, e.g. digenite, (Cu9U)' sites are empty.
complex crystalline phases c o n ~ a i ~ large i ~ g clusters of atoms in nearly perfect tetrahedral coordination that approximate the local structure of a quasi-crystal il is an a~proximantto the icosahedral ~ u a s i - c r ~ ~int athe l Frank-Kasper phases (c1.v.) with the (cI162) structure; an example i s ~g~,(Al,~n)49 erthollides are iiiter~etall~cs in which s i g n i ~ ~ ~deviations nt from etry are allowed; thus these compounds must have CO concentrations of substitutional (antisite) or vacancy dcfects. Ternary have a mare complex definition. *
eta-
electron phases (S.V.)~ stable at an e/a ratio of 3/2, which are bcc structures, usually disordered at high temperatures, but may become ordered, CsCl temperatures, e.g. Cu n. Other exaniples are Ag,In, Al,Ce,,and
eta-
complex cubic (cP20) phases with /3 Mn the Frank-Masper phases (q.v.). Example
ructure; they are related to
*We define only compound families whose structure and/or composition are not obvious (from the term itself) and exclude tradenames, e.g. Alnico, Nitirial, Tribaloy, ctc.
xxxv
Some I ~ t ~ ~F~~ilies ~ e ~~~~~d t ~ l ~ ~ ~
XXXVi
A,B compounds AB (cP8) structure, isomorphous with Cr30 (W,O was ); include: Cr,Si, previously thought to be a tungsten ~ o l y m o r ~ h examples Nb,Sn, and Ti,Pt.
a nickname for the C60polymorph of carbon in allusion to the resemblance of its soccer-ball-like structure to the geodesic domes designed by ~uckminsterFuller.
es
62
literally all compounds formed between metallic elemen I s and the chalcogens, those of column VIB of the periodic table. Only selenides, tellurides and polonides are usually classed as inter~etallic~; they may be either binary, e.g. ZnSe or niultinary~ e.g. NaVTe,. cornpounds with the chalcopyr~te(CuFeS,) structure, (t116), related to zinc blende and having two general compositions: 136,. e.g. CuAlTe,, or 245,, e.g. MgSiP,, ZnSnSb,, and CdGeAs,.
c
compounds whose electronic bonding is neither wholly ionic nor wholly covalent, but a blend of the two; see also Zintl phases. ses
ternary compounds of the type M ~ where~M is a ometal, X, ~ a chalcogen ~ (S, ~ , Te), and x is a number between 0 and 4. ~tructurallythey may be regarded as med by stacking of Mo,X, building blocks wherein the M atom occupies large (x=l) or sinall (x> I) interstices. Many Chevrel phases are type 11 superconductors.
es
e
y intermetallics having ordered arrangements of the a-Mn 58) where the occupancy o f four crystallograpliical~ydifferent by atomic size factors; examples include F e , ~ ~ r ~ , M and o~,
~ g, 7A 1~ 2. a family of ~ o m p o u n TEX,,(2 ~s 2 m > 1.E),discovered where T is a transitio~metal and is from Croups I1 TiSi, structure (oF24) forms the basis of a large family of tetragonal superstructures embracing 35 crystal structure types, some of which have >GO0 atoms per unit cell. The T atoms form a ‘chimney’ of y1 p s e u ~ o c ~within l ~ s which ‘ladders’ of tn pseudocells of X atom pairs are drawn up to an equal height. Electron concentration plays some role in control of this family, and ternary compounds exist where a third element may partially substitute for either T or X, r other discrete structures. Examples include RuaSn3, V17Ce31, Ru,,(d;a,.,,ce,.gP;>1,4, and (Mn, RCr0.2)29Si51. compounds with large framework or cage stru~tures,analogous to zeolites, which can acco~modateother atoms within the cavities; examples include Ma8Si,, and Na24Ge,,,. compoLinds that are strictly stoichiometr~cwith no disce~niblehomogeneit~range; see line compounds.
e co
s 8
a class of quasi-crystals (q.v.) which have 10-fold rotational symmetry in the quasiperiodic plane, while being periodic i third dimension (also called t-phases). (A1,Si)-Go-Cu, and Al-Mn-Pd systems, Decagonal phases are found in the A1 among others. one of a family of related tcp phases iiic~uding6, p, g, P, and R viewed as hybrids constructed of various arrangements of Cr3Si (hP12) blocks; the prototype phase, MoNi, (oP56) is the (hP7), and MgZn, merous ternary phases with this structure (cPll2) occur, for
Some r n t e r ~ ~ ~ tFamilies a l l ~ ~ Defined
xxxvii
compounds analogous to metal hydrides but based on deuterium, the heavier, stable isotope of hydrogen, with twice the nzass of ordinary hydrogen, phases which form at certain ratios of the number of valency electrons contri by all atom species present to the total number of atoms in the unit cell* ratios near or about the . Examples include: @U ,Sn (7/4). Using various d e ~ n i ~ i o of n svalence electrons, tlie concept has also been extended to transition iitctal compounds such as s i phase (q.v.). of exceptional stability (ty~icallym.p electronic structure correlation, e.g. such a compound was first discovered in the Ni-Ti-Si system at the e ~ u i a t o ~ i c compositioii, hence E-phase; atoms occupy three independent site sets in the C0,S.I s t ~ ~ c t u so r e that ordered ternary alloys o Examples include: NiTiSi, CoGe’V, LalrAl a compound of different structure, ZrZn,,, is
one of the Humery electron phases e/a=7/ 4 (actual 1.65 to 1.89). Ex LiZn4. Other unordered hcp phases with a soniewhat larger c/a ratio and less restricted e/a range (1.22-1.83) are known as zeta phases (q.v.). S
aeei %
ees9
compounds isomorphous with Fe3W,C (q carbide) stabilized ternaries, e.g. Ta,Pt,O and silicides, e.g. Ni,T ternaries, e.g. Ni, considered as filled or partially fille
a type of one-dime~isiona~ quasi-crystal of mult~layered,related GaAlAs, usually formed by molecular beam epitaxy, where the ~ l t e r ~ aof t ~the o~ and B layers follows the Fibonacci rule (a numeric sequence in which each member is the sum of its two predecessors 1,1,2,3,5,8,13.. .).
etures
those structures with large voids into which other ato electronic s ~ ~ u c tcan ~ r ebe inserted, thus ‘filling’ or ‘s Examples include tlie Chevrel phases (q.v.)s Hf5Sn,C structure, filled gainina brass, e.g. Tl,Sb,, filled skutt fulleranes, e.g. Na,7,1n,97Z2 where Z=Ni, Pd, or
ppropriate size and
topologically close-packed (tcp) structures a c c o ~ i ~ o d aatoms t i ~ ~o~f ~ i ~ e rsizes ~nt
ses
See Laws phases. all-metal c o ~ ~ o u n dbased s 11) s t ~ u c t u ~exam on the c60 ful e~ Pd, or Pt), -LiMg include: Na961i~97Z, (Z=Ni, Pd, or at), Na172 where the @ symbols indicate onionskin-lik~c o n ~ e n t r ~ c (Mzmixed Li and A,(CT6, intercalation compounds formed between C6*fullerite (buckyballs) and an alkali metal, where the alkali metal ions can be a c ~ Q m ~ o ~ aint ethe d t e t r a ~ ~ dor r~1
~
~
xxxviii
Some ~ ~ t e r ~ n ~~t aal ~l i i~ DeJined l ~ e ~ octahedral interstices of the fullerite. Strictly speaking, these are not true I a kind of carbide. However, analogous true IMCs exist (see fulleranes).
G-phases
ordered ternary compounds of the Mn,,Th, D8, (cFll6) structure. The first-known example was dubbed 'G-phase' because of its presence as an embritting precipitate, 011 grain boundaries o f Ni-base high-temperature alloys. Other examples Ni16Ti6§i7. include Co16Hf6Si7CoI6Zr6Si7, and Cu16 electron compounds or Hume- othery phases (q.v.) with an e/a ratio of 21/13 and (~152)crystal structure. They are built up from 26-atom clusters in various ng arrangements. The architecture of these clusters consists of an inner tetrahedron (4 atoms), an outer tetrahedron (4 atoms), an octahedron (6 atoms) and a cubo-octahedron (12 atoms), sites which inay be variously occupied. Examples include: CusZn 8, gamma phase (cI52); Cr,A18 (h 26); Cu9A14(cP52) and Cu41Snll(cF416). these phases are covalently bonded coinpounds, with a zinc blende (sph~leriteor wurtzite) structure, formed between elements lying equally to the left and right of Group IQ elements, thus 111-V, 11-QI, and I-VII compounds (4.v.).
ses
hexagonal analogs of perovslcite phases with formula type T, Tztransition metal, M=non-transition metal, and X is a metalloid; examples include Ti,AlC, Ti,lnC and Cr,AlC. ternary sulfides, selenides, and tellurides of the defect tetrahedral class with one ordered vacancy per formula unit. Int e~et al l i cexamples include: ZnA12Se4(cF5&), HgGa,Te, (tll6), CuSbSez (oP16), and CdIn,Te4 (tI14). nds or half-filled (also known as sem Whereas Heusler all0 formulation, struc interpenetrating fcc sublattices, the half-Heusler phases possess the same cubic structural motif but in them, as indicated by their XYZ fornzulation, half of the X sites are empty in an ordered array. The resulting narrow bands and gaps in the energy spectra lead to semiconducting, half-metallic conducting, paramagnetic or ferromagnetic behaviors. So mising thermo-electric rm in the same system, as is sometimes properties. Even if both XYZ the case, it does not imply a c id-solution between them. Examples of half-Heusler phases include T1 hexagonal or rhombohedral phases formed by various stackings of Laves and CaCllrs layers. Examples include: CeNi, (hP24), Ce,Ni7 (hP36), and Co,,Sm, (hR24).
ounds
a class of IMCs whose low-temperature properties are characterized by a huge magnification of the density-of-states of charge carriers near thc Fermi level and the appearance of quasi-pa~ticleswith eKective masses of the order of 102-103 times the free electron mass; in some cases they have been treated as 'concentrated Kondo systems'. They usually contain a rare-earth or actinide element with a partially filled 4f or 5f electro shell; they are divided into two subclasses: those with no~~integral valence ) and those with nearly filled valence (#). Examples include: UBe13*, U6Fe, URu,Si,*, CeA12#, CeNi," CePdAl, CeAs, and NbNiSn. compounds which crystallize
(cF16), some of which s; other (non-magnetic)
Some ~ ~ t e ~ m e t uFumilies l l ~ c Dejned
ses
s
phases which form at characteristic ratios of valence electrons to atoms, 312, 21/13, and 7/4. See electron phases. Beta brass, ganiina brass, epsilon pliase, and zeta phase are such phases in the Cu-Zn system. so~~etimes called i-phases; a major class of ~uas~-crystals whose c o m ~ o ns inotif is a group of 20 slightly distorted tetrahedra packed around a comnioxi vertex; the struct~rehas no transl~tionalperiodicity. i(CuFe), i(TiMnSi), and i ( ~ t ~ S i ) . compounds in which metals play both cation and anion roles; normal valency rules are followed; they are densely packed, highly symmetric $tructure~with little or no directional bonding; stoichiometry is very closely observed with no signi~cant homogeneity range; and properties exhibit characteristic behaviors of ionic bonding. Examples are Mg,Si, Fe,NiN, and e (see normal valence ~~mpounds).
cs
iO
xxxix
ternary coinpounds whose prototype is Fe3AlC,, which may st~ucturesstabilized by interstitial carbon or as a perczvskite examples are: Ti3AlC, Fe,NiN, and Mn,AlC.
haws
a series af structurally related phases, carbides, borides, oxides, and all-metal prisms, icosahedra, intermetallics formed from M,M’4 building and octahedra, variously filled andlor o,W,, (hP34). F&IfgRe,
ases
topologically close-packed compounds formed by stacking of rows of icosahedra (or layers o f pentagonally coordinated atoms in (1 phases (q-v.), but here with 5, 6, 8, 9, or 10 layers, g(NiC42, and ~ ~ ( ~ n , A g ) , * lattices (both metallic solid solutions and IMCs) coiitaini~ a small con~entration of ma~neticimpur~tiesin a non-magnetic matrix. A cha~~cteristic ~ i ~ i m inL the ~ i ~ resistivity vs. 2”’is shown by these systems at very low temperatures; below the m i n i ~ u m the , resistance increases logarithmically and then becomes temperature i~dependent. Interesting pheno~ena that have been de~onstrated by these materials: the possibility to become s~perconductingand yet not possess a superconducting energy gap; to become superconductors at one tenip~ratureand at lower te~peratureto come out of the superc~nductin~ state. E dilute Fe in Cu, dilute Cr in Cu, dilute Fe in Au, dilute Ge in (La (La, Ge)B,. OV CO
s
compouii~sformed, not from a liquid alloy, but by orderi terminal solid solution or intermediate phase, e.g. Cu3Au, Fe,
~ ratio close-packed AB, compounds, whose stability derives from both a t o size three basic structu~~s: and electron c o ~ c e ~ t r a t i and o ~ , posses (hP24). They may be (liP12); MgCu, C15 (cF24); and MgNi, formed by the stacking of two kinds of la one puckered h ~ m o ~ e n e o layer u s of atoms of different sizes, designated by T, and the other a 3636 k Thus the structural formulas of the common Laves phases are: [[CU,][M~]](~~)~’, and [ [ ~ i 2 ] [ M g ~ ~ ( S ~true r ~ )tures c h . derivalive fro ~ultilayerstacking (see Kornura phases), ordering in ternary or ~ u a t ~ r ~ a r y compounds, or deformation. Other examples are: Al,iZr, FeSi FeNiTa (cF24); and NbZn,, Cu6Ga4Mg, (hP24). The iii derivative type are the AuBe, (cF24) structures and the CaCu,
Some I
~ F ~ ~ iDefined ~l i ~ ~
formed by a combination of orde include: PdBe,, UNi, (cF24) and 8
~
~
~
n. Examples of this subclass
compounds that are strictly stoichiometric with no discernible range of composition (see Daltonides). of the marcasite structure (q.v.) named after the mineral loellingite, (oP6), having a e/b cryst~~llo~rapliic ratio of about 0.485, lower than that of the other marcasites (-0.615). Examples include: As,Os, CrSb,, and RUP,. alloys (either ordered solid solutions or conventional IMCs) exhibiting stable periodic displacements in the ordering scheme by interposition o f antiphase b o u n ~ ~ r i ethus s , extending the unit cell. The period may be in one, two, or three directions in the antiphase domains and rnay vary from 2-10 as a function of teniperature and composition; it rnay even be non-integral due to mixing of two or more regions with integ of 1-d LPS in ordered alloys include CuAu 21, Au3Cd, and in ordered alloys include: Cu,Pd,-,, Au3+Zn, and Au3Mn. Examples of conventional IMCs with LPS include ZrSi2, @e,U, and Nb,Ga,,. belong to the F r a n ~ - ~ a s p efamily r (q.v.) of t o p o l o ~ i c a close-packed ~l~ structures with prototype A l , ~ N b 4 ~(0~ i 3 ~ this group, named after the mineral marcasite, FeS, derivative from the NiAs type. Examples include: As2 those in which a commensurate or incoinrneiisurate modulation is superposed on the basic ordering scheme. Examples are: Ta,-,Nb,Te, and Zr, superlattices). one o f a faniily of related tcp phases, including 6 , p , 6,P, an as hybrids constructed of various arr~ngementsof Cr, gZn, (hP12) blocks; the prototype for mu is the rhombo ,, and ~ a , M ib19. i ~ ~ ~ other examples are: C o ~ ~Fe,SiRe,,
a compound is called a normal valence compound if, under the assumption that the cations 63 formally transfer all their valence electrons, their number is just correct for all the anions A to be able to complete their octets without sharing electrons. Thus in normal valence conipounds one finds neither cation-cation nor anionanion bonds nor lone electron pairs on the cations (see ionic inte~etallicsand octet compounds). a populous group of coinpounds where electronic factors, as well as size factors, play a role; they rnay be binaries as in the prototypes ,(hP16) and VV5Si3 D8, (tI32), but iiiore often ternaries: C, N,0, Gd,Ce, and CHo,Si,, or even all metal ternaries, et Q:
also known as normal valence compounds (q.v.), a subgroup of valence compounds nce electrons per AB unit; examples 452ternary ~ o m p o u n also ~ s occur, e.g. nGeAs,. See also normal valence compounds and
a transition phase displacive and ordering r e a c t ~ Q ~ $
f certain Ti alloys undergoing both
a family of ternary s~perstruct~re of D
is AlNbTi,. The structure is oC16, a of Ti and Nb on mixed sites of the
~
Some ~ n t ~ r m e t a lFamilies li~ Defined
xli
hexagonal planes; alternatively, it may be regarded as related to the structure through the intermediate B 19 (op4) phase. AlNbTi, is remarkable among IMCs for its relative ductility. one of a Pdmily of related tcp phases, including 6, p, U, P, and R phases, that can be viewed as hybrids constructed of various arrangements of Cr,Si A15 (cP8) , Zr,Al, (hP12) blocks; they have the (oP56) structure; an example is
ases
intermetallics whose structures derive from the 3-d analog of Penrose tilings. quasicrystals and pentagonal intermetallics.
llics
those with a 5-fold symmetry in their x-ray diffraction patterns, the first such discovered being i(A1Mn). This pentagonal character is also manifested in pentagonal Facets on or pentagonal channels through quasicrystals (q.v.) and related structures. It has been shown that such structures relate to Penrose tilin which are non-periodic ways of tiling a plane or 3-d space. It can also be demonstrated that all 3-d Penrose tilings result from the projection of part of a 6-d lattice onto a 3-d space. A currently proposed model postulates that 3-d quasicrystals are formed from arrangements of a single type of building block, an atomic cluster, where neighboring clusters overlap by sharing atoms. Examples of peiitagoiial intermetallics include: Al,,Co4, Al,Mii, and Cu9,,TeSb,. d after the mineral or L1; (Fe,AlC), (cP5), p from cubic-close-packed layers; the A atoms fill some of the octahedral holes in the ccp stacking and are thus surrounded by six X atoms. Although the majority of perovskites are oxides or , or 0 can stabilize metal atoms in this structure, e.g. and O,PtV,. There are also cases where only sub-sto of the interstitial are needed at the A sites to stabilize the rnetal atoms in this structure, e.g. NZn2Ti, or CGe4Co12,or where non-adherence to the A formulation can be accounted for by random inter-substitution af A and X atoms on their normal sites. rnetastable upe er conducting phases formed by rapid quenching or ~igh-p~essure synthesis of a combjnation of noble metals with group elements or of two different group B elements and having an e/a ratio of 4-5. They have the PO (cP1) structure. Examples include: AuBi,, Pd3Sb17,and SnTe,,
es
literally all compounds formed between metallic elements and those of column V of the periodic table. Only arsenides, antirnonides, and bismuthides are usually classed as intei-metallics.
s in these compounds, homocatenation or polymerization occurs via linkage of like ions to form ‘polyanions’. Thus in polyanionic compounds the number of valence electrons transferred by the cations is i n s u ~ c i e for ~ t the anions to complete their octets, and ions of the higher valence element tend to cluster, forming bonds between themselves. For polya~ioniccompounds we have CsPb (Pb4 tetr~hedra), NaGe (Ce, tetrahedra), and CaSi (Si zig-zag chains). In polycat~oniccompounds such as GeAs, Case, and GaTe, more valence electrons are available than necessary for octet completion, so the catio (GaSe) or have lone electron pairs at polycationic compounds (principally cha stackings (not close-packed) of four close-packed layers of atoms in triangular istances between chalcogenide atoms are such that van der Waals
xlii
Some ~ ~ t e ~ m~ e~~ ~~ ~i~ l le ii ~~ e n~ ~e ~ bonds exist, and the separation of cation pairs from those in an adjacent layer is such that the compounds are not metallic conductors but semiconductors. The polytypic stacking types include ABC as in hex GaSe, rhoinbohedrat GaSe or complex stacking as in monoclinic C stable or metastable phases characterized by non~crystallographic orie~ta~ional symmetry and quasi-periodicity~ these comprise: icosahedral compounds (q.v.), decagonal compounds (e.g. t-phase), and even one-diniensional compounds. one of a family of related tcp phases, including 6, p , CT, P, and R phases viewed as hybrids constructed of various arrangements of Cr,Si Zr,Al, (hP7), and MgZn, 614 (hP12) blocks; the prototype phase (hR5 Co-Cr-Mo system; other examples are Fe, iV,, Mn,Ti, A13&4g2,, and Ni3SiV6. phases possessing orientational as well as translational disordering. ~nterinet~l~ic examples include NaSn and CsPb.
a more complex d~velopmentof the Frank-Kasper family (q.v.1 which consists of arrangements of ftised, high-coordination polyhedra rather than fully interpenetrating polyhedra as m the Frank-Kasper phases. The family, studied principally by S. 0. Samson, is of partic~ilarinterest because of the very large unit cells with > 1000 atoms. Exttmples include: Mg NaCd,, and Cu,Cd3.
a phase first found in Fe-Cr alloys, t e t r a ~ o ~ tcp, al
(tP30), a member of the Frank-Kasper family where full or partial ordering can occur on three of the five sets of crystallographic positions in the structure. Examples include: FeCr, CrRe, AlMoNb, Ir4Moll,and Ni,SiV,, compounds whose structure and stability are dominated (but not exclusively) by geometric packing considerations; examples include Laves, Frank-Kasper, and trigonal prismatic phases (q.v.). intermetallics isomorphous with the cobalt-rich mineral skutterrudite, (~#~Ni,Fe)As,, with cIJ2 structure. They include the analogous Pt-group arsenides, binary and ternary antimonides, and certain phosphides~e.g. IIrAs,, CoSb,, FeNiSb6, and PdP,. spinels are mostly oxides and sulfides whose general structural formula is AtB,O[G,T (where t and o mean tetragonal and octahedral coordination respectively and c, cubic closest-packing) and with (cF56) structure, but inany other, more nearly intermetallic, isomorphous compounds e or Te, e.g. Al,CuSe, and CuCr,Te4, and even all metal compound A atom occupies tetrahedral sites are tetrahedral sites and some A atoms in octahedral site general structural formula o f the inverse spinels is Bt (also known as fast ion conductors or mixed conductors) compounds in which a significant fraction of the current is carried by ions as well as electrons. Most such compoun~sare oxides, chalcogenides~or iodides, but intemetallics such as LiAl and Mg3Bi2also belong to this class. See decagonal phases. carbides, borides, or carbo-borides that are stabilized Cr,,C, structure types; exaniples are Crl,Fe,NiC,, Ni20Ti,B,, and IFe23C3B,. those in which every atom has four neighbors s u r r o u n ~ i nit~t e t ~ ~ h e ~ r adefect lly~ tetrahedral structures have some vacant coordination sites. ln such M,N,
Some ~ n t e ~ ~ n e t Fumilies ~ l l i c Defined
xliii
compounds, ~/~ = (eN-4)/(4--eM)where eNand eMrepresent the number of valence electrons on each atom. Examples of normal tetrahedral 1 ~ include ~ 1iiSb s and ZnAs, in the binaries, Cu,SiTe3 and Cu,AsSe, in the ternaries, and ~nIn,GeAs4 and ~ g C d ~ I n T ein, the quaternaries, Defect tetrahedral struct~resinclL~defor e3, Iii&s4Te3, HgGaTe,, and CuSbSe,. ee also ndainantane structures. phases comprising atoms of unequal size in which pscki packing in various ways. Examples include sigma, Lwes, a r4Al,, and various hybrids of these.
~ses
binary phases c o ~ p r i s i natoms ~ with radius ratios subst~~tially greater than one3 the larger atoms forming a triangular prism, ceiitered by the smaller atoms. They are found p r e d o ~ ~ i ~ a nin t l yborides, carbides i n t e ~ e t a l i ~ cexist. s Dy5Ru2 (mCZS), Th
s
phases which require vacancies for stabilization of the structure for either lattice strain or electronic reasons. They are of three types: those whose stoichio deviation is fulfilled by'the presence of vacancies on the minority atom sites, Nil-,Al and Pdl-, In, botli(cP2); those where the vacancies form an ordered superstructure of a simpler basic structure, e.g. As,Cd, (tII6O) derived from the CaF2 structure (32 vacancies per unit cell); and those where a cer vacancies is required but no defect ordering occurs, e.g. In,Te, (cP52). In the latter two types, the vacancies may occur on either or both of the two metal sites. In at least one conipound, PtCe1.619 phases with ordered and disordered vacancies co-exist. compounds in which all atoms, either accept, provide, or share valence electrons to obtain stable octet con~gurations,ns2np6; they may arise either by ionic interaction (a~eptance/donationof electrons) or covalent interaction (sha electrons); most compounds exhibit a hybrid or intermediate type of bo Examples include: Pb e, Cu,Mg, KGe, and CuSi,. Normal valence compounds are those where the ratio of total valence electrons per anion=& Tn a broader sense, valeiice compounds also include those (polyionic valence compounds, q.v.) where this ratio i s 8 (polyanionic compounds) and where it is r compounds). ternary silicides and germanides, A4B4C,, tI60 structure, prototype where A is a transition metal, B can be Mn, Fe, CO, Ni, or Cu, and C is Other examples are: Nb4C04Ge7 and Fe4Hf4Ce7; they have crystal characteristics similar to both Frank-Kasper and Laves phases (q.v.). electron phases with disordered hexagonal close-packed structure occurring over the e/a range of 1.22 to 1.83 and with c/a=1.633. Examples include: ~ u ~Ag,Al, ~ a , and Auslii. lsostructural related phases with c/a=1.57 and more restricted e/a range (1.65-1.89) are known as epsilon phases (4.v.); metastable zeta phases are commonly formed by rapid quenching; many of them are superconductors. phases formed by metals from opposite sides of the periodic table, characterized by ~on~pletely filled electronic orbitals, normally a full octet shell; their bondin be ionic, metallic, covalent, or mixtures thereof, and they CLlr in a variety of crystal structures. Examples iiiclude: NaTl, Mg2Si, &1 3, MgLiSb, arid ~~~gAuSn.
xliv
Some In fermptcdlic Families DefiBed the 12 compounds of the group IIB elements (Zn, Cd, and Hg) with the group VIB chalcogens (0,S, Se, and Te); only the selenides and tellurides would be classed with intermetallics. Many of these and their alloys are of interest for electronic applications.
CQ
a class of covalent semiconductor materials formed as a combiiiation of group IIIB elements (B, Al, Ga, In, and Tl) with group V elements (N,P,As,Sb, and Bi). The B, N, and P compounds are not normally regarded as intermetallics, although their structure and properties may be similar.
the equiatomic chalcogenides formed by combination of the group 1V elements (Si, Ge, Sn, and Pb) with the chalcogens ( S , Se, PO,and Te); only the siilfides would not normally be regarded as internietallics. potentially semiconducting cornpounds formed between group VB and VIB elements. Intermetallic examples include: Bi,Se, and Sb,Te3.
Q ~ Y f~ ~Ssome r
of the define
American crystallographer (1942- ) who worked with the Shoemakers at California Institute of Technology. is
French physical chemist (1 748-1 822) ~ a i ~ t a i n that, e d under certain ~ircu~stances, there could be variable combining ratios in chemical reactions. American physical chemist (1919- ), long-time member of the faculty at Uiiiversity of California-~erkeleyand staff member at Lawrence iation Lab.; espoused ctronic structure in the and promoted Engel's unconventional view of the role o stability of IMCs. French mineralogist and chemist (1931- ). At CNRS, ennes, France, known for his synthesis of ternary molybdenum sulfides, which have striking superconducting properties. English chemist (1766-1 8441, enunciated the chemical law of definite ~roportions; hence IMCs which admit no deviation froin stoich~o~etry are called Daltonides. ~anish-Ainericanphysical chemist (1904- ) who proposed rules for the existence of particular phases and crystal structures dependent upon electronic structures, not only the average number of unpairecl electrons available for bonding, but also involving roles for the s, p, d, and f electrons. Italian-American theoretical physicist (190 1-1954) who studied electronic structure of a toms (Fermi surface) and who argued from quantum-mechanical principles that in certain cases at low temperatures huge magnifications of the density of states of charge carriers should occur. Italian mathematician ( w 1170-1230), also known as Leonard of Pisa. Published several books and was arguably the most outstanding niatliematician of the Middle Ages. He popularized the modern decimal system of numbers and is best known for conceiving the mathematical series, the value of each tern of which is equal to the sum of the two preceding terms, IY,,+~=U~, iU,.
~r~~~
British physicist (1911-1998), served in scientific intelligence at the British Defence Research Establislimeiit during the war years and iininediately thereafter, professor of physics at University of Bristol for most of his career; worked on dielectrics,
Same ~ ~ t e r ~ e t ~F al l~i ic ~ i e ~ ~~~~~~
xlv
dislocation theory, and polymers in addition to his collaboration with understanding the structures of complex IMCs. American electrical engineer (1896-1972) who first determ~ned the crystal structures of MgCu, and MgZn, while at Carnegie Institute 1927, and later worked for the Navy Dept, Bu. Ordnance, and
ria
Ameri~anarchitect and designer (1895-1983) who conceived and ~ u i l tgeodesic domes, the structure of which was seen by crystallographers as analogous to the structures of the C6*polymorph of carbon, hence ‘Buc~yballs’. Geman physical chemist (1887-1958), at University of ~ u n i c hstudied the nature of bonding, especially in inorganic compounds. German inorganic chemist and crystal~ographer(1915- ) at the University of Geman inorganic chemist and crystallogra~herat TechnischeHochschule, German i~dustrialist(1866-1947) at ~sabellenhutte,GmbH in ~ i l l e n ~ u who r g ~ in 1914 serendipitously discovered certain nonferrous alloys which were magnetic, e.g. Cu-Mn-Al, although containing no ferromagnetic elements. Nfeusler’s son, 0 years later determined that the magnetic behaviors derived from the c o ~ p o u n dC , u ~ M n ~hence l , Heusler alloys.
am
English metallurgist (1899-1968), long-time member of the fxulty of University of Oxford, a ~ t h o of r several books on the structure of metals and alloys; showed that electron concentration controls the structure of many intermeta1lic phases. American crystallographer (19 15- ), at General Electric R D Center for most of his career, ~ursuedX-ray and neutron diffraction studies of crystals, es~ecially complex intermetallic compounds. Japanese crystallographer, originally at Osaka City ~niversity and later at Hiroshima University and Tohoku University. Japanese theoretical physicist (1917- ) who was able to account for anomalies in the electrical resistivity, specific heat, and magnetic properties of certain alloys and intermetallic compounds.
kov, olai
ovic
Russian metallurgist and physical chemist (1 860-1 941), studied phase equilibria in salt systems and alloys, recognized metallic phases of variable c o ~ ~ o s i t i o n (~erthollides)and ordering of solid-solution alloys. German-Swiss crystallographer (1906-1978) who affiimed that the existence of certain intermetallics and their crystal structures could be understood in terms of ion of dense packings of atoms of different sizes and specific proportions, We now understand that both size and electronic effects are operative. ~ u s t r i a n metallur~ist and crystallographer (19 1 1- ) contri~uted ~ ~ ~ e r o u s publications on structural, mineralogical and metallurgical chemistry. r ~tiling patterns, which ~ n ~ l~ ia ts~ ~e m a ~ i c(1931i a n ), worked on the g e o m ~ t of turned out to be the basis for the atomic arra~igeme~t in ~uasicrystals. Swedish-American crystallographer (19 17-1 993), at California Institute of Tecliiiology, known especially for studies of ~ n t ~ ~ ~ e twith all~ i ~ si cells ~ (>n1000 ~~to~s). German physicist (1868-1951). For most of his career, professor of theoretical physics at University of Munich; explained the role of the electron in the metallic state.
German chemist (1898-1941) at Technisclie Hochschule, Dai-instadt, proposed a rule di~erentiatingintemetallics whose bonding is essentially ionic or heteropolar and which possess ionic-type crystal structures from those whose bonding and structures are more typically metallic. ques and otlier input to these definitions were contributed by R. W. Cahn, J. Lima-de-Far~a, Pearson, and R. M. Waterstrat. Any remaining errors are the responsibility of the author J. El.
Socrates: ‘But why should we dispute about names when we have realities of such importance to consider?’ Claucon: $Why, indeed, when any name will do which express the thought of the mind with clearness?’ 0 427-347 BC
. . . a man that seeketh precise truth, had need to remember what every name he uses stands for; and to place it accordingly; or else he will find himselfe entangled in words, as a bird in lime-twigs; the more he struggles, the more belimed. s 1588-1679 There can be nothing clearer or more conve~i en~ for the purpose of setting one’s ideas in order and for conducting an abstract discussion, than precise definitions and inviolable lines o f demarFation. 0 ~ t ~ 0 184.5-1923
~
~ ~ l en ~ e ~n~~t e~ upun t~ ~r ~~ ~r ~t solo. i ~~ te ~ o much can elements do when nothing cre
11 things began in order, so shall they end, and SO shall they begin again, according to the ordainer of order and mystical mathematics of the 2
. . . all the work
of the crystallographers serves only to demonstrate that there is only variety everywhere where they suppose ~ n i ~ o r m .i t.~. that in nature there is notliing absolute, nothing perfectly regular.
Chapter 1 Structural ClasslJication and ~ o t a ~ i o ~ Josk Lima-de-Faria Centro de Cristalograjia e Mineralogia, Instituto de Investigaq?o Cientgca Tropical, Lisboa, Portugal
1. Introduction Similar to chemical elements, the inorganic crystal structures call for some display scheme, such as a map or a table may provide, if their individual organization and mutual relationships are to be easily recognized. The systematic knowledge of such organization is synonymous with structural classification and, to move within such a large domain, a ‘vehicle’ should be used which would facilitate the recognition of these relationships, namely, a good notation. The aim is to understand how the chemical elements are linked together in order to reveal the rules, laws, tendencies, principles, etc., of the architecture of inorganic crystal structures. 2. The Structural Classification of Inorganic Compounds Several attempts have been made in the past to present general classifications of the crystal structures (Table 1). Laves (1930) was possibly the first to propose a classification of crystalline structures, as a kind of extension of the structural classification of silicates to all crystal structures. Niggli (1945), Gdrrido and Orland (1946), Bokii (1954), and De Jong (1959), proposed similar classifications. In all of these attempts only a general approach was proposed but was not applied systematically to existing compounds. In 1976, Lima-de-Faria and Figueiredo made the first systematic approach to a general classification of inorganic structure types, and applied it to 782 structure types, which corresponded to approximately
5200 compounds (Table 6). Not only chemical composition but also, and mainly, the crystal structure determines the properties of a compound. This is why structural classification is the natural classification of inorganic cornpoundy. Later, Hawthorne (1983) also suggested a structural classification of crystal structures based on the polymerization of the coordination polyhedra with higher bond valence as a consequence of the application of the bond valence theory to inorganic structures, and considered four main categories: clusters, chains, sheets and frameworks. In 1989 Jensen proposed a classification based on Mdchatschtki (1947) and Niggli’s (1945) ideas, also considering four main categories: molecular, chain, layer and framework, and developed a complex notation, the crystal coordination formulas. Kitaigorodskii (1955) studied the organic compounds and considered only four categories of organic structures: molecules, chains, sheets and frameworks. Consequently the classification of inorganic structures by Lima-de-Fark and Figueiredo (1976), which acknowledges five main categories, namely, atomic, group, chain, sheet and framework, may be applied not only to inorganic structures, but also to crystal structures in general, either inorganic or organic. The term coordination structure used by Bokii (1954) and by Dc Jong (1959) characterized certain structures that are homodesmic (structures in which all bonds are generally similar in kind, though not identical), the particles of which are surrounded by adjacent particles more or less evenly (De Jong, 1959, p. 144). They considered as an example the halite
Intermetallic Cornpounds:Vol. 3, Principles and Practice. Edited by J . W.Westbrook and R. L. Fleischer. 02002 John Wiley & Sons, Ltd.
Structure and ~ o ~ p o ~ ~ i t i ( ~ n
4
General classification of crystal structures Laves 1930 kikdlld§
Chains Sheets Frameworks
Niggli 1945 Isolated particles Molecules radical^ Chains Sheets Frameworks
Garrido and Orland 1946
Bokii 1954
De Jong 1959
Isolated groups
Coordination Islands
Chains Sheets Frameworks
Chains Sheets Frameworks
Coo~~ination Molecules Radicals Chains Sheets Frameworks
wever, this term presents a certain framework class, for which they selected, as an example, the cristobalite structure of i02. This ambiguity disappears if halite is considered close-packed structure, and cristobalite a framework r fact balite is a closest packing s t r ~ ~ c tAs ~ ~a e~ .a t t e of of the C1 atoms with Na atoms occupying the hedral voids; and cristobalite is a framework of tetrahedra. lose-~acked structures are dense tures, and frameworks are less dense; they are open structures, containing large voids. The structural classificat~oiiof inorganic compounds i s based on the ~ o ~ d - s ~ rdistribution e ~ ~ t h and also on the directional character of the bonds. These factors define the so-called struct~rulunits, which are the parts of the structure more tightly linked together internally ed in various ways to form different The main structural cate close-packed (UP utomic), where the structural units are i n d ~ ~ ~ datoms ual - g ~ o ~ p( ~ s ~ ~ b b e ltrian~les, ls, rings, small chains, etc.) - ~ ~ ~ ~chains n i t e i ~ ~ n~ i t ~ e ~ ~ ~ s -
I
-~
~ u ~ e ~ o ~ * ~ s .
For a more detailed description of our structural c~assificatio~~ see Lima~~e-Faria and Figueiredo (19’76) or Lima-de-Faria (1994).
3.
In order to relate easily the inorganic structures we use structural formulas, that is, chemical formulas to whkh is added the structural information. The main structural factors to be indicated are: the structural unit, i t s category and way of packing, a i d the c o o r ~ i ~ a t i oofn the atoms:
Lima-de-Faria and Figueiredo 1976 Atomic (or close-p~cke~) Croups Gbains Sheets Frameworks
the structural unit is placed within square brackets the category of the s t ~ u c t unit ~ ~ (x) r ~is~placed within curly brackets just before the symbol of the structural unit the packing ofthe ~~ructurul unit (y) is indicated as a superscript at the right-hand side of the structural unit the c o o r ~ i ~ ~o tj ithe ~ ~atoms ~ s (a, 8, y , 3 , . . .) are represented as ~uperscripts~within small square brackets, at the right-hand side of the syinbol of each chemical element.
The category of the structural unit is expressed by its dimensionality with the aid of the symbol 00, for the structural units of infinite diinensionality like chains, sheets or framewor~s.The ~~rresponding symbols are { 1CO 1, (2 CO 3 , and (3CO) respectively. They correspond to the Machatschki syinbols &, A) but written in a com~uter-frien~ly way. For finite dimens~oiiality we use the symbol instead of writing zero infinity, {g) for group, and for the structural units of individual atoms of the close-packed structu~esno symbol is used. When there are no i~terstitialatoms and the structural formula starts with the infinite dimensionality symbol, the curly brackets can be omitted. The structural formula of a compound corresponds therefore to its cheinical formula, complemented with the structural information mentioned above. Accordingly, the general structural notation for a c a ~ p o u n d
(A, A,
For instance, for pyrite, FeS,, the structural forinula is Feo&) [SzIc,meaning that the sulphur atoms farm S, groups which pack to ether in such a way that the centers of gravity of th pairs of sulphurs form a facecentered-cubic lattice, that is a cubic closest packing c, and the iron atoms occupy the voids of this packin with an octahedral coordination 0. The structural formula for halite is Na0[CIIc. The structural units c h are formed by the individual Cl atoms, ~ ~ i are
T a ~ 2l ~Various
chemical formulas and corresponding
of higher dimension. Examples of structural formulas are given in Table 2. The cubic body-centered packing is re~resentedby Bb, where B means the nature of the layer of this packing parallel to (010) (Figure 1); and the symbol b, the stacking at a half of the side of the plane unit cell of this layer. The various sym~olsfor the stacking of layers are given in Figure 2. 21 is More complex layers are the formed by interconnected triangles and squares, with tetragonal symmetry, in the proportion o f two triangles for one square. An example is Cuacb f meaning the kind of stacking. R2I is formed by rows of triangles and rows 2 to 1 (Figure I}. An For inore commo hexagonal closest packings, and their co~binations c/h, and also for the cubic ~ody-cente~ed packing the symbol for the kind of layer is omitted, and ch, . . . b are used.,The Laves phases can be as decomposed In T layers means puckered, the dot
structural formulas Structural formula
Chemical f o ~ u ~ a Cu (Copper) NaCl (Halite) Mg,SiO, (For~terit~) AI,MgO, (Spinel) TiCaO, (Perovskit~) S (Sulphur) FeS, (Pyrite) CaMgSi,O, ( ~ ~ o p s ~ d e )
KAl~(OH),Si~AIO~o (~uscovite) C (Diamond) KSi,AlO, (Microcline)
packed in c, the cubic closest packing, with Na atoms occupying the octahedral voids 0. The category of the structural unit (in this case the close-packed} i s not des~gnated,because, by convention, it only need be represented for structural units
( w
N 2'
T
T
K
i ~ ~ 1r eSome homogeneous and other ~eterogeneou~ layers (after L~~a-de-Faria and ~igueiredo,1978)
6
Structure and Composition
C
e 2 Cicneratized stacking symbols. T stands for triangular tesselntion; Q, R and 0 mean quadrangular, rectangular, and ue unit cells respectively (Lima-cte-Faria, 1994; adapted from Lima-de-Faria & Figueiredo, 1976). The arrows indicate the d i s ~ l a c e ~ eofn the ~ ~uccessivelayers from the origin of the unit cell
means heterogeneous layers of atoms of different sizes, and T triangular tesselation) and a K layer (the kagomk layer). These two layers and K have only one way of stacking together, but the assemblage (T?' K) may be stacked in two diff'erent ways, c or h, as in the erefore to the more comnion Zn,Mg, and Ni,Mg, correspond [[Cud [Mg]]@"k, [[Zn,] [Mg]J@K)h,
The structural. formiila of GaCu, is [[Ca] [Cu,]lT, where T corresponds to another heterogeneous puck-
ered layer [CaCuJT and K. to the kagonik layer [CL@ (Figure 1). Some compounds, like CrB and MO tures based on puckered simple hexagonal packings of Cr or MO, with boron atoms in prismatic voids. The packing is puckered because of the relative displncement of certain parts. These packings are denoted by x Ts, where w means puckered by d i s p l a c e ~ ~ e ~ t . Some crystal structures like stibnite, mosaic of linked close-packed blocks (Wellner, 19SS>, They are called r e c o i ~ b i ~ a ~structures ~on (Lima-de-
Structural ClusslficatioPz and Notation
Faria et al., 1990) and the corresponding structural foriiiula is [Sb2S3J#3 where # means linked close-packed blocks, or a recombination packing (previously represented by c t h, Lima-de-Faria, 1994). However, this notation does not describe the way the blocks are linked together and needs some improvement, possibly based 0x1 the work on sulpbosalts by Makovicky (1985, 1997a,b). According to Parthi: and Chabot (1984) and Partlit: (1990), some strul;tures may be decomposed into slabs of other known structures. Examples are CrzAl B2 and Ce Co4B. However, these prticular structures can also be described as a stacking of layers. In fact these structures may correspond to the structural formulas: AICb B! [Cr,lRl1 and [[Ce] [CO,] JJ3]]T1c respectively (Figure 3), where R11 is a layer with rows o f tnangles and squares in the proportion 1 to 1, parallel to the sheet, and k and K are the layers already described for CaCu, running perpendicular to the plane of the sheet. The frameworks can be imagined as decomposed into special layers, the so-called connected units, because they are not individual layers but are linked to the rest of the structure. An example is diamond, C, where the connected units are puckered hexagonal layers fi of carbon atoms, and the corresponding structural formula is 3i;c[CtjHc. When the layer description.is not applicable, because the packing is three-dimensional? as in garnet,
7
C a p Ali SiTs[012]*7the thre~-dimen§ioiialpacking is represented by an asterisk *, In fact the garnet structure has a high packing coefficient of approximately 60%, which is com~arableto that of forsteriie, Al; Mgt[OJh, with 70°/0, and Eorstei-ite is certainly based on a hexagonal closest packing of the oxygens, Other kiiids of structural units also tend to pack together as closely as possible. When the ~ t ~ u c t u r ~ 1 units are groups, they tend to behave as organic molecules. The molecu~esstack in such a way that the . bumps in one are inserted in the hollows of a n ~ t h e rA coiiiplete study of the packing of* finite iiiolecwIcs, infinite molecular chains, and i ~ ~ nmolecular ~ t e sheets in organic structures has been made by (1955). This study may be applied to the categories of inorganic structural units. For the coordination of the atoms two levels of symbols have been proposed: complete and simplified. Each complete synibol gives the total number of atoms coordinated to a certain atom and the type of coordination ~oly~iedron, indicated by lower-case letters. The symbols for the most common coordirration polyhedra are presented in Table 3. For the sake qf s ~ ~ p ~ ~ c athe t i ~xtructural Pz . f ~ ~ ~ usually includes only the already inentioazed ~~~~~r~ st~Ucdzrrcll~~aCtors. However, it may be useful in mrtain cases to add more ~ t r u c t u r ~information, l either to describe more coinpletely tlie structure, or to compare
CeCo,
3 ~ e c o ~ p o s i t i oofnsome structures into slabs of other known structures aiid the co~respondings t r u c ~ ~ rformulas: al (a) AI B,,,(ParlhC, 1990) -+AICbBg[Cr,]R"s (layers parallel to the plane o f the sheet); (b) CeCo,B ( ~ ~ and a Ghabot, r ~ ~ ~ -+[[CeB,]I [Co,lK[CeCo,]' [Co3IK](layers perpendicular to the plane of the sheet), corresponds to Ce2Go,B,, or [[Ce] [CoJ [ the several square brackets meaning heterogeneous packing of Ce, CO and €3 atoms ( ~ e p r o ~ uwith c e ~permission) UP(:
Symbols for common coordination polyhedra (adapted from Lima-de-Faria et al., 1990, reproduced by permission of TUCr) Coordinatioti polyhedron around atom A Single neighbor Two atoms colliiiear 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 tbe ceiiter of the base T~t~d~iedron quare coplanar with atom A Squarc lion-coplanar with atom A Pentagon coplanar with atom A Tetragonal pyramid with atom A in the center of the base Trigonal b i p y r ~ ~ i d Octahedron Trigoiial prism Trigonal antiprism ~ e n t a ~ o nb~pyramid al Monocapped trigonal prism Bicapped trigonal prism Tetragonal prism Tetragonal antipri~ni Cube Anticube ~odecahedronwith triangular faces He~agonalbipyram~d Tricapped trigonal prism Cuboctahedron Anticuboct~~edron (twinned cuboctahedron) Icosahedron Trunca ted tetrahedron Hexagonal prism Fran~-Kasper polyh~drawith: 14 vertices 1.5 vertices 16 vertices
Complete symbol
~ i m p l i ~ esymbols d
tr 2
s*
*
0
P aP
ch acb do
CO
aco E
“Also [4s], ** or sq.
complex structures. For instance, if we consider do[I2Ihwe do not know hew the Cd atoms are distributed in the octahedral voids, and the structural formula may be confused with that of rutile Tio[827h. In rutile the Ti atoms are distributed in rows and in CdIz they alternately fill these layers. To complete this structural infor~ationone could write Cdo@[I2lh, the /a meaning alternately filled layers, and Tio’r[O,]h, the /r meaning rows of filled voids. It has also been recognized that when a structure is not close-pack~d,but belongs to another structural category, it can still be sliced in layers, and, in most cases, the stacking of the layers corresponds to one of the generalized stackings c or h, that is ABC or ABA, as in the closest packings. Even with more complex structures such as the barates where the atoms form simple icosahedra BI2 or truncated
icosahedra B,,, the stacking in c or h applies (Pearson, 1972). For instance, in the case of U the structural formula is U (g>[B,J coilsidering the €Ilz icosahedra as though they were spherical atoms in cubic closest packing (~ullenger and Kennard, 1966) (Figure 4). The fulleranes, e.g. Na1721n,,,Z, where 2 = Ni,Pd,Pt, although much more complex, also present similar truncated icosahedra of In7* (Sevov and Corbett, 1996) (Figure 4), which also behave as large spheres packed in hexa packing. The Subcommittee on Nomenclature of the International Union of ~ryst~llographyhas s t ~ ~ e e o ~ ~ the e ~used oef ~ ~ t ~ ~ ~c tou rr ~ l~in ~order l ~ s , to facilitate the progress of crystal ~ ~ e ~ ~Every ~ s t r ~ worker in this field is advised to adhere to such recommendations and to make a point of using
~ t r ~ c t u r Classjficntion nl and Notation
9
Figure 4 (a) Cubic closest packing (ABC) o f B,, groups (icosahedra) and (b) truncated icosahedron of boron atoms ( S u l l e ~ ~ e r and Kennard, 1966): (c) truncated xcosahedron of In7, in fulleranes (Sevov and Corbett, 1996, reproduced with p e r ~ i s s ~ oofn Acadeiiiic Press)
structural formulas whenever they can be substituted for conventional chemical formulas alone.
e Axes of the Unit Cell There is a tendency to represent crystal structures on the basis of projections along the crystallographic axes. However, in many cases, these axes have no structural
interest and the projections along them may render structural understanding difficult. Many structures which were not considered as closepacked have been found really to be close~~acked structures. For instance, hodgkinsonite, (OH),, in projection along the crystallog (Figure 5) does not disclose that it is based on a slig~tly distorted hexagonal closest packing of the oxygens and hydroxyls with Mn in octahedra1 voids and Zn and Si in tetrahedral holes. The corre§~on~ing structural
Packing r e ~ r e s e ~ t a tand i o ~projection along the crysta~~og~aphic axes of the structure of hodgkrnsonite (after Wyckof-, 1968)
formula is by Rentzeperis, in 1963, and further described in terms of a condensed model by Figueiredo (1976); the structure being built by equal layers (see Lirna-deoore (1 992) considers that the structure representation is very important, and has claimed that he has discovered many structures based on close packings that previously had not been described as such (Moore, 1995). Another curious example is tolbachite, CuCI,. yckoff was a crystallographer very interested in and acquainted with close packings, but did not notice that tolbachite i s a close-packed mineral (Wyckoff, 1963). The same happened with Burns and Hawtharne (1993). This structure is in fact based on a slightly distorted, cubi~-closest-packingof' the C1 atoms, with Cxi atoms occupying o ~ ~ a h e d rvoids a ~ in alternate layers, and should be considered as a distortion derivative of cadinium chloride, Cdo[CIJc. These s t r ~ ~ t u rcorrespond es to the same atomic arrange~ent, but have been considered different because they were
regarded under different projections (Figure 6). A sphere-packing model of cadniiwxn chloride, and the use of the ICSD (Inorganic Crystal Structures Database) and the 'Diamond' com~uterprograms, organized by Bergerhoff (1995, 1997), have helped to confirm this relationship. This is a typical example where the distortion by lowering the syi~metry,and the corresponding projections alon the crystallograpliic axes, niasks the real structural nature of the compound.
~ o r ~ a l lthere y are several inorganic compounds reIated to a given one, and they are considered as pertaining to the same hmily, e.g. the perovskite family (Lima-de-Faria, 1994, p.74), or to an homologous series such as the plagisclases. There are various processes or mechanisms which enable one to relate one struct~re to another, either by sli distortion, by replacement of one kind of atom by
me 6 Structural reprcsentation of the tolbachite structure, Cu"[Cl,]", C2/m: (a) after Wyckoff, 1963; (b) after Burns and wtharne, 1993 (Reproduced with permission of the Mineralogical Society of America). (c) Packing representation of the structure of cadmium chloride, Cd" [Cl$, R3m, after Wyckoff, 1963. These three representations correspond to the same structural arrangement; tolbachite i s only a distortion derivative of Cd"[Cl,]C
S~ructuraL~ L a ~ ~ s i ~ cand a t iNotation o~
two or more kinds of atoms, by insertion of atoms within the voids of the packing of the structural units, or even by subtraction of certain atoms. The more important degrees of similarity among crystal structures have been defined by the IUCr Conimission on Nomenclature in a paper by Lima-dent Faria et al. (1990). Structures with i n v a r ~ ~e~uivalent positions, the same space group and the same occupied equivalent positions normally lead to the same structure type; but, if the e~uivalentpositions are not invariant, the variables inay drastically change the coordination and give rise to a completely different atomic arrangement. Three main de~reesof similarity among structures have been considered in the definitions that follow in rank order: ~ . ~ # p o i ~have t ~ Z : the same symmetry (space group), and the same occupied equivalent positions - i s o c o ~ ~ g ~ r ~ t i oare n a zisopointal and the atoms have the same coordinations - isotypic: are isoconfigurational and have the same structural units packed in the same way. -
For more detailed considerations on these three definitions see Lima-de-Fa~iaet al. (1 990). There are many inorganic compounds with the same structure, and we are mainly interested in dealing with the different atomic ar~angements, therefore we assemble the isotypic compounds (with the same ~ e The structure) under the concept of ~ t r u c t ~type. number of structure types is obviously much less than that of the inorganic compounds, which will greatly facilitate our study. For instance there are approximately 200 compounds pertaining to the halite structure type, NaOEGl]". Halite itself, or NaC1, is called the p r o t o t y ~ eor a r c ~ e ~ y(or p ~even ari~totypein the sense of Megaw, 19731, that is the structure chosen to represent the structure type, and the 200 compounds are its popu~a~ion. When comparing structures differing only by the values of their variable parameters, that is, isopointal
11
structures, in order to assemble them in structure types, we have to consider limits of this variability that do not change the coordination of the atoms. According to Bergerhoff et al. (19991, to each pair of isopointal structures there corresponds a value of the difference of their coordinations, expressed by a parameter called A. The value of h will det er~i neif the structures should be considered i~ocon~gurational and will measure their similarity. A nomenclature for the structure types was first proposed by Ewald and Hermann in the ~ t r u k t ~ r ~ e richt in 1931, however, this notation has not been much used due to the fact that it was not self-explanatory~A l , A2.. .B1, B2, B3. .. are arbitrary letter codes, the meaning of which has to be memorized. In 1965 Hellner proposed another symbology based on the lattice complex concept, which is useful for very simple compounds, but this notation rapidly becomes very complicated for more complex compounds. Many chemists have already used the chemical formula of the prototype to symbolize the structur~type, but this is still not self-explanatory, and it is impossible to imagine the corresponding atomic arrange~entunless we are very familiar with the particular structure type. In 1965 Lima-de-Faria suggested the use of general structural formulas for the symbols of the structure types, and the concept was further extended when in 1976 Lima-de-Faria and Figueiredo (1976) proposed structural formulas of the prototype structures (Table 4).
There are some relationships which are of special interest, and among them the s ~ r u c ~ u~~ ae l~ ~ v ~are~ t i ~ ~ e of particular importance. We shall consider first the derivatives in the sense of uerger (1947), which include two categories, distortion and substitution
Various symbol~smsproposed for the structure types
cu M& NaCl ZnS (sphalerite) Al,Mg04 (spinel) Mg,SiO, (olivine)
Ewald and ~ e r m a SB ~ n (1931)
Hellner (1 965)
A1 A3
F or (c) H E or (h) H F+F' F + F" F;;,+D, T (h)nC,,+00, 1/2, 12xy;AzI11/4,1/4, E;
1 B3
HI 1 1332
Lima-de-Faria (1965)
Li~ia-de-E;ariaand Figueiredo (1976)
xc
[cur
Xh AoXc A")(" A'jB'XC, A'jB'X;
P%Ih
NaO[C11" Znt[SIc AliMgL[04]' Mg$3it[04]"
12
Structure and Composition
derivatives. A distortion derivative of a certain comThe domain of synthetic inorganic crystal structures pound corresponds to another compound that can be has become more and more complex, leading to atomic derived from it by a slight distortion. A s u ~ ~ ~ ~ t u f i arrangements on difficult to describe in simple terms. The structural not at i o~concept i s still at the beginning deriv~tiveis obtained by replacing one kind of atom by two or more atoms. However, there is another stage, and ~ ~ p r o v e m ewill ~ t sbe necessary in order to category that Buerger did not consider, the defect make it possible to use such notation when dealing derivatives, which are derived by subtraction of some with more complex structures. atoms, generating vacancies. These vacancies are important because they are fundamental to defining the packing. An example of a defect derivative of perovskite, Tio[CaQJC, is dzhalindite, Ino[O(OH),IC, which belongs to the R e 0 [ ~ 0 , l cstructure type. When considering two structures one of which is a distortion derivative of the other, the distortion With the structural classification and the correspondderivative is the one with less symmetry, and the ing notation we can order the inorganic structures. other is called the basic structure. To decide which is However, we realize that many structures have the the s t ~ c t u r ewith less symmetry we need to know how same atomic arran~$ment,that is, belong to the same to i~z~asurethe s y ~ ~ e t rofy a crystal structure. structure type, and instead of ordering the inorganic Attempts to measure the symmetry of a structure structures we ordered the inorganic structure types, were once based on group-subgroup relations, but this which greatly simplified our work. gave rise to contradictory results. A definition of the Work on this problem, first approached by Lima-demeasure of the symmetry of a crystal structure was Faiia { 1965) and Lima-de-Faria and Figueiredo presented by Lima”de~Faria(1988); it corresponds to (1969), led to a table reproduced as Table 6, containing the ~ ~ ~ t ~ l iofc ithe t y general p o s ~ t i ~ofn the space 782 inorganic structure types, corresponding to group. This definition is the natural extension to space approximately 5200 crystal structures (Lima-de-Faria groups of the one adopted for point groups. In fact the and Figueiredo, 1976, 1978). This table was presented multiplicity of the general form in point groups in improved form in a book by Lima-de-Faria (1994). corresponds to the multiplicity of the general position In the horizontal direction, five structural categories in space groups. For further details on this definition are shown in their order of increa§in~complexity; see ~ima-de~Faria (199 1 and 1994). vertically, various structural formulas are listed, from simple atomic ratios of binary compounds to the more complex formulations of ternary and higher order compounds. One can notice that most of the intermetallic compounds are located within the close-packed category of structures, on the left-hand side of this table. As Belov (1947) said: ‘In spite of the variety of The structural notation we recommend has been the mineral crystalline world, the whole “mineralogiapplied to approximately 70% of all the structure cal game” just reduces to various modes of filling prototypes described in the table ‘Crystal Structure gaps in uniform close packings with the various ~omenclature’which is presented at the beginning of corresponding patterns’. The same happens with the n ~~ ~i , c and the book, ~ n ~ e ~ C~ o ~~ p~ oa ~ ~Principles intermetallic compounds. We realize that most of the ~ r ~ c ~vol. ~ c 1,e edited , by Westbrook and Fleischer, classified prototyp~sincluded in Table 5 are based on 1995 (Table S). Out of the 220 listed structure close packings, approximately 80%. However, among prototypes 155 have been classified: 124 are closethe chemical elements, there are some structures packed structures,‘ and 31 are of the other structural which have higher dimensionality, e.g. groups, chains, categories. sheets, and frameworks: sulphur (g)[S,], selenium 1 There i s a difference between close-packed and closest~ ] ]tin ~ ~ 1300) ~, (1 CO] [Set2]], arsenic { 2 o o ) [ A ~ [ ~ ~and packed structures, The close-packed structur~sinclude all the [SntINHC. Also for AmB, com~ounds,including interstructures which are not group, chain, sheet, or framework metallics, there are among the non-close-packed structures. Therefore they include the closest packed, the category such examples as CoAs,-Co: (g}[As& body-centered cubic-packed, simple hexagonal and simple (skutterudite), ~ ~ S b ~ ~ o o { g (~drcasite), ~ [ S b 2 ~ ~ ~ cubic packed, etc.
13
Structural Classification and ~ o t ~ t i o ~ Table 5 A ~ p l i ~ a t of ~ othe n s t ~ c t u r notation a~ to the intemetallic protot StPukturbeberieht designation A, A, A, Ad
4
A, A,
4
A, A, A1 A2 A3 A3' A4 A5 A6 A7 A8 A9 A 10 A1 1 A12 AI 3 A14 A15 A16 A17 A20 Be Bb
Be
4
4 Bm
Structure type
Prototype
Pearson symbol 812 tP30 OP8
t P4 hP1 t P50 CP1 hR1 mP64 mP32 c cdz
hP2 hP4 C B
fI4 f I2 hR2 hP3 hP4 hR 1 OC8
s presented in the table 'Crystal structures nomenclature'
Space group
Strukturbericht designation B1 B2 B3 B4 B81 B8,
B9 B10 311 813 B16 B17 B18 319
B20 B26 327 B29 B3 I 332 B33 I334
c158
m5
CP20
B37
OCIS
cP8
OR28 oC8 OC4
cI16 hP9 OC8 OPS oP16 oC8 tB 6 kP2 hP8 hP4 mP32 oP8
'h
cc c e
C, Ch
Ck C1 cl h c2 C3 424 C6 C7 C8 c9 c10
Structure type
Prototype
estbrook and Fleischer, 1995) Pearson symbol
Space group
c n CSCl cP2 ZnS (s~hale~ite) C B ZnS ~ ~ r t z i t ~ ) hP4 NiAs hP4 Ni,h hP6 HgS (cinna~ar) hP6 Pb0 tP4 yCuTi tP4 NiS ~ ~ 1 1 ~ r ~ t hR6 e ~ CeS aP8 tS (cooperite) CuS (rovelite) AuCd oP4 FeSi CP8 GuO (tenorite) mC8 FeB oP8 oP8 oP8 cF16 CrB oC8 PdS tB16 CoSn hP6 TlSe tIl6 hP18 oF48 t112 oC24 PdSn, ThC, mc12 Cu,Te hP6 LiZn2 hP3 cH2 cF12 CP12 cP6 ~g,O Ti02 (mtile) tP6 hP3 h S Si cF24 SiO, (8 t ~ ~ ~ ~ hP12 ~ t e )
contimed
14
Stmkturbericht d e s i ~ a t ~ o n $tr~cturetype Cl 1, C l 1, CI 2 CL4 cl5 C15, C16 Cl 8 Cl 9 c2 1 c22 c23 C28 c32 c33 c34 c35 C36 c37 C38 C40 c42 c43 e44 C46 c49 6-54 DOa DO, DO: D0d
DO, DO2
Do3 f309 DO1 1 DO17
Do18 Do19 0020 DO21 DO22
rototype
arson mbol if6 lr6
Space group
Strukturbericht ~esignation
Stru~turetype
rototype
Pearson symbol tri fi hPli 4
trio
[CU, Sbf" [Cr Siz]" Si'[S,fc ZlF[QJQS
3 00 [GetSd Auo[TeJh
pi SiJTd [Cu, Tilh [Si UJ [Ir,Sir
hP12 cn4 cn4 $112 oP6 hR3 oP24 bzP9 oP12 oP12 hP3 hR5 AuTe, ~ c a ~ a v e ~ t ~nzc4 } CaCl, oP6 ~ g(Laves) ~ j hP24 ~ Co,Si oP12 Cu2Sb rP6 CrSi, hpst SiS, of12 mP12 ZrQ, OF72 GeS, AuTe, ~ k r e n ~ e r i ~ ~oP24 ) ZrSi, OC12 TiSi, on4 PCu,Ti oP8 SiU, tfl6 Ir,Si oP16 1132 er32 cFI 6 cP4 oP16 oP16 BaS, faP8 Ma,As hP8 oP16 ~ ~ , S n hP24 tI8 AI,Ti r116
OI20 OC20 LPlO
tP20 oF40 hRl5 t1lO ti26 t128 hP6 cP36 cF52 tIl8 oC28 cP7 CF112 tPl0 hPl0 cI40 hR5 mP20 hRlO hP5 CI80 C
0
LP40 OP20
O r i4
hR7 cF56 cf28 cFll4 tP3O eP39 mP22
Space group
~ t ~ ~ cClassification t u ~ ~ l and Notation
Strukturbericht designation
Structu~etype
35
~rototype Mg32tA1,Zn)49 Ce,Ir, 5
Th731, @r,%
%G
Fe,W6 (p-phase) Cu,,Si, Mn,Si, CO&* Cr,AI, Co,G1 Cr,C, Fe,Th,
cooco',[s,i"
,
PbFCl FeAsS MgCuAl, AgAuTe, (sylvanite) CuFeS, (chalcopyrite) CaTiO, (perovskite) A1,CdS4
Pbl911[F]IC1](Q2'.Qlff'f Feo{g)[AsSch)y
AgoAu"[TeJ" Cut Fef[SJ' Tio[CaOJ Alt,Cdf[SJ
Pearson Space s y ~ ~ o l group ell62 cI4140 on8 hP14 hR7 hP20 tI32 t132 cI52 c152 cP52 cF116 hR13 cf76 hP16 cF68 hR26 hP28 oP40 hP20 hP28 tP6 mP24 oC16 mP12 t1l6 cP5 tIl4
Strukturericht esignation
S t ~ c t u r etype
ro totype Al,Cu2Fe
FeKS, NaCrS, Cu,VS, (sulvanite) Cu2FeSnS4 Fe,N AIFe,C (perovskite) ThH2 Fe,N CuPt, AuCu CuPt AuCu, GCuTi A ~ C u 2 ~~ n ~ e Sb2T17
CuTi,
Pearson symbol tP40 hP18 h~~ c196 on4 cF112 hP1S cP12 mC16 hR4 oP16 cF56 cP8 tI16 cP5 cP5 $16 hP3 cF32 t P4 AR32 cP4 tP2 u cF16 ~ ~ d54 tP4
Space group
~
r
~
Structure and ~ o ~ p o ~ i t i o n
16
Note: symbols A, €3, and R represent interstitial atoms; X, Y, and Z represent packing atoms
f
N:'
[o&
01'
[Cu Mg Sn Cl]'
Structural Classification and Notation
17
Table 6 (continued)
P HOMOOENEOUS
4ETEROOLNEOUS
HOMOGENEOUS
Sirnplr and fiomwaiih
S,rnp\o
n
**.I
I
I
K1
*I'
,,*I
...
18
Structure and Composition
Table 6 (continued)
I
I
I
I
I
1
Struct~ralCluss$cntion and Notation ~ b ~ ~ ~ - 1~00b)[Pb"O,] ~ 3 n 1 ~ (minium) and As,S,--.f200)[As~~]S~] (orpiment). We therefore conclude that there is a great tendency for inor~anicc o m ~ o u ~to~.form s close-~ackedstructures. Only when special direc~ionalbonds (normally covalent) exist, does the structure tend to form a less dense, open str~cture,giving rise to large voids within of the structural units. also notice that the kayer descr@ton is u ~ p l i c ~ b lto e most i ~ o r g u ~ i~c ~ t r ~ c enabling ~~res a simple description of the structural atomic arrangement. Tlirs is a consequelice of the fact that ia general nd in m a ~ ycases less than I5 A (Lima-de~Faria,19 Another important CO s that the generalized s t ~ c ~siyn~~b o cl and ~ h are ~ r e ~ o m i n a nand t , are even applicable to complex structures such as borates and fulleranes. Furthermore, the layer descr@tion obeys certain ~ s i m ~rules ~ l e (Lima-de-Faria, 1978). The other ~mportantfeature to notice is a kind of p o l y ~ e r i ~ ~ process t ~ o n qf the ~structur~l units, condensing atoms into groups, those into chains, chains into sheets, and eventually into frameworks. This process is very clear in the silicates through the polymeri~atio~ of chains into sheets of tetrahedra (Belov, 1956; Liebau, 1956) and later generalized by Lima-de-Faria and ueiredo (1976). It also applies to octahedra (Moore, 1974) and to other polyhedra. This process of poly~erizationis inherent to the basis of the structural classi~cationwe propose. Many structures are derivatives, either by distortion or substitution of certain basic structures. This means that the v ~ r io~~ ta ~t o ~aircr u n ~ ~ ~ eisnnot t s so large as might appear. These relationships will reduce the number of structure types to be inemorized, and many others can be simply derived from them. According to van Spronsen (1969) 'the periodic system of the chemical elements has passed through three d i ~ ~ r e nstages: t that of initiation, that of ~he~omenological development and that of theoretical development'. The table of inorganic structure types will possibly have to go through similar stages. We are now on the first stage, that of initiation, and much work has still to be done.
I am very grateful to my wife, Natasha, and to Ana Luisa Cunha for revision of the text and also for helping me with the use of the computer.
19
My friend Arnaldo Silvkrio, as usual, made himself available to peruse the ~ a n ~ ~ s c rfor ~ pwhich t , 1 tkank him most heartily.
Belov, N. V. (1947). Structure of Ionic Cr,vstuls a ~ t d~ e ~ a l j i ~ Phases. Izd. Akad. Nauk SSSR. Moscow. Belov, N. V. (1956). Essays of structural niincralo ~ ~ 10, ~ 10-3 l Russian). ~ ~ nSb.e (Lvov), Bergerhog, G., Berndt, M., Br~~ndenbur~, (1999). Concerning inorganic crystal structure types. Acta
Bokii, G. B. (1954). Ilatroduction to Crystal Chemistry. Russian original: I%date17stvo Mo~covs~o English translation: United States Joint Service, New York, 1960. Buerger, J. M. (1947). Derivative crystal stru~ures.J. C ~ ~ Physics, 15, 1-14. Burns, P C., and ~awthorne,I?. C. (1993). Tolbachite, CuCI,, the first exaniple of Cu2+octahe~raIlycoordirzated by Cl-. Amer. ~ i ~ i ~78,r 187-189 . , De Jong, W. F. (1959). General ~rystallography.A San Francisco. C o ~ p e n d i Freeman, ~~. Ewald, P. P., and Hennann, C. editors (1931). S t ~ ~ ~ t u r ~ e r i c j z t (for 1913-1928), Akade~ische ~erlagsge$ellschaft M.B.H., Leipzig. Figueiredo, M. 0. (1976). Private communication on condensed models. Garrido, J., and Orland, J. (1946). Los r ~ ~ la ~o s ~~ ~- ~ ~ c ~ fina de 10s cristales. Dossat, Madrid. Hawthorne, I;. C. (1983). Graphical enumeratio~ of polyhedral clusters. Acta Cryst., Hellner, E. (1958). A s~ructuralscheme for sulp~ideminerals. f. Geology, 66, 503-525. Hellner, E. (1965). Descriptive symbols for crystal structure types and h o ~ e ~ t y p based es on lattice complexes. Acta Cryst., 19, 703-712. Jensen, W. B. (1989). Crystal coordination formulas. In The Structup~~s of Binary C o ~ p o u n d s(eds F. D. G. Fettifor). Elsevier Science Publishers. Kitaigorodskii, A. 1. (1955). Organic Chemical C r y s ~ a l l o ~ r a p(in ~ y Russian). Press of the Academy of Sciences of the ISRSS, Moscow. English translation and revision (1 961). Consultants Bureau Enterprises, New York. Laves, F. (1930). XVI. Die B a u - ~ u s a ~ e n h ~innerhalb ~ige der Kristallstrukturen. 1 Teil. Zeit. Krui., Liebau, F. (1956). Bemerkungen der Systeniatik der Kristallstruk turen vo rnit hochkondensiert~n Anionen. Chim. Phys 6, 73-92. Lima-de-Faria, J. (1965) derivation of inorganic close-packed structures. AX and AX, compounds, sequence of equal layers. 22%. Krisf., 1
20
Structure and Composition
Moore, P. B. (1992). Betpakdalite unmasked, and a comment on bond valences. Aust. J . Chem., Moore, P. B. (1995). Closest-packed Franklin-Ogdensburg: Kepler's gift o f the snowflake (private comm~~ication}. Niggli, P. (1945). Grundlagen der Stereochemie. Verlag Birkhauser, Basel. French translation Leks Bases de 10: StdrPochinzie, Dunod, Paris (1952). Parthk, E. (1 990). ~ l ~ ~of e~ n~ o~r gs~s~ruc~ural nzc ~~e~zs~ry. Linia-de-Farm, a. (1994). S ~ r ~ c ~~~~ rn ae ~r a l oAn ~~. First edition (page VIII-70) Pety-Lnncy (Geneva): Introducrion. Kluwer Academic Publishers, Dordrecht. Katharina Sutter Parthi Editor. Lima-de-Faria, J., and Figueiredo, M. 0. (1969). A table Parthi, E., and Chabot, B. (1984). Crystal structures and IC close-packed structure types. crystal chemistry of ternary rare earth, transition metal Figueiredo, M, 0. (1976). bodies, silicides and homologues, In Handbook on the, ~lassi~cation, notation, and ordering in a table of ~ h y s ~ and ~ . sChemistry of Rare Earths, Vol. 6 (eds K. A. inorganic structure types. J . Solid State Chem., 16, 7-20. Cschneidner, Jr., and L. Eyring). Elsevier Science Lima-de-Faria, J., and Figueiredo, M. 0. (1978). General Publishers, Amsterdam, p. 188. chart of inorganic structural and building units. Pearson, W. B. (1972). The Crystal Chemistry and Physics of Garcia de Orta, SPrie Geologia, Metals and Alloys. Wiley Interscience, New York. Lima-de-Fana, J., Hellner. E., Li Rentaeperis, P. J. (1963). The crystal structure of and ParthC, E. (1990). Nomenclature of inorgaiiic hodgkinsonite Zn,Mn [(OH),SiO,]. Zeit. Krist., 119, structure types. Report of the International Union of 117-1 3s. ~ r y s t a l ~ o g r a p ~ y~. o m ~ i s s i o non Crystallog~aphic Sevov, S . C., and Corbett, .?. D. (1996). A new indium phase Nomenclature, Subcommittee on the Nomenclature of with three stuffed and condensed fullerane-like cages: Inorganic Structure Types. Actu Cryst., A46, 1-1 1 . Na,,,ln,,,Z, (Z= Ni, Pd, Pt). J . Solid State Chern., 123, ac~dtschki~ F. (1 947). Konstitutio~s~ormeln fur den festen Zusldnd, ~ ~ n a t sChenz., ~ h . 77, 333-342. 344-370. Makovicky, E. (1985). The building principles aiid Sullenger, D. B., and Kennard, C. H. L. (1966). Boron classification of sulphosalts based on the SnS archetype. crystals. S c i e n t ~ cA ~ e r ~ ~ u n , van Spronsen, J. W (1969). The Periodic System of Chemical akovicky, E. (1997a). Modular crystal chemistry of Elements. Elsevier, New York. sulpliosalts and other complex sulphides. EMU Notes in Westbrook, J. H., and Fleischer R. L. (eds) (1995). Mineralogy, 1, chapter Intermetallic C o m ~ o u ~~rin~iples ~s, and Practi~e,Vol. 1 . Makovicky, E. (1997b). Wiley, Chichester, UK. approaches. EMU Nor Wyckoff, R. W G. (1963). Crystal Strucfures, vol. 1. Megaw, H. D. (1973). Crystal Striactwr.es. A Working Second edition. John Wiley Interscience Publishers, New aunders Company, P h ~ l a d e l p ~ a . York. oore, P. B. (1 974). Structural hierarchy among miiierals Wyckoff, R. W. G. (1968). Crystal Structures, vol. 4. John containing octahedrally coordinating oxygens, 11. N . JD. Miner. Abh., 120, 205-227. Wiley Interscience Publishers, New York.
Lima-de-Farm, J. (1978). Rules governing the layer organi~~tion of iiior~aniccrystal structures. Zeit. k'rzsf., 1-5. c-Faria, J. (1988). The hierarchy of symmetry. Presented at the Xl European (Vienna). Abstract published in Lima-de-Faria, J. (1 99 1). On the p the symmetry of crystal structures. Garcia de Orta, SPrie
er
Mankind was probably acquainted with mercu even in prehistoric times. It is certain that Hg compounds were well known in the Mediterranean area in the fourth century before Christ, but probably Hg had been applied in China, India and Egypt even earlier (Barnes and Bailay, 1972; Weeks, 1968). Metallic Hg possesses unique physical properties (Guminski, 1992). It is a relatively noble metal with and boiling poiiits of all metals (at 0.101325 MPa) of - 38.8290 and 356.623 "C, respectively. Gaseous Hg consists almost entirely of moiioatomic species. The element loses its metallic character above the critical point at 1492°C and 151 MPa, Solid Hg exists in several allotropic forms labelled ay /3, y and 6. Gamma Wg appears only after inducing a tensile strain. The hexagonal bHg is slowly formed at pressures > 24 GPa at room temperature; thermodynamic equilibrium aHg % 6Hg is estin~ated at 30 t- 6 GPa. The rhombohe~rala H g is stable at normal and moderately elevated pressures at above - 194 "C. The tetragonal PElg is formed at lower temperatures by applying high pressures or by hammering at -268 "C. The aHg % PHg transition is of martensitic nature.
Hg is a rather rare element, seldom found in the native state. The most frequently inet minerals are: HgS (cinnabar), HgSe (tieinaniiite), HgTe (cologSe (onofrite) and solid amalgams of Ag (m~schellandsb~~~ite, ~araschachner~te, schach-
nerite, and weishanite) and Au (weishaiiite). Small amounts af Hg c o ~ p ~ u n are d s formed in volc~ni~al1y active regions. All these minerals are insoluble in
performed from larger amounts of the low-grade ores (typically 0.3 to 3.0% Hg). The usual way of obtaining Hg from HgS consists af roasting its concentrate in air. The conceiitrates can be aiso roasted with CaO or scrap Fe. ~ h e m i ~ a l pure ly recovered by distillation at reduced pressure. Further purification may be attained by pro1 tion while mixing liquid Hg with a solution of ~ g ~ ( ~ ~~b s e~ q u~e n t) ~ . Hg is recommended. Governments in some countries still treat Hg as a strategic mate~ial, production estimates may be erroneous. production of Hg is of the order of ~ 0 0 tons/year. 0 ~
Despite the significant toxicity and scarce o c c u r r e ~ ~ e , Hg and its alloys have always played 8 very important role in the developnieiit of science aiid technology. Although numerous endeavors of a l c ~ e ~ i sto t $transform Hg into Au were fruitless, nevertheless they 'Much rarer minerals include the ainalgams of Gu (kolymte), Pb ( a l t ~ a r k ~ t eand ) , Pe (poterite).
~ n t e ~ ~ e t aCornpounds: ll~c Vol. 3, Principles und Practice. Edited by J. H. Westbrook and R. L. Fleischer. 0 2 0 0 2 John Wiley & Sons, Ltd.
22
Structure and Composition
contributed a lot to the collection of important information for experimental physics, chemistry, and nzedicine. At the turn of the nineteenth~twentieth centuries, the alloys of Hg (also known as amalgams) started to be objects of intensive scientific investigation. Phenomena o f mutual solubility, activity coe~cientsof ~omponents,heats of dissolution and other thermodynamic parameters, viscosity, diffusion and chcmicdl reactions occurring in liquid Hg were widely invest~~ated. Generally, amalgams are good model systems for liquid alloys, and their features may be easily and exactly ineasured at room and near-room ue to its noble character, the clean and removable surface when liquid, the high overpotential for hydrogen ion djscharge, and the possibility to dissolve many metals, Hg was a real driving force in electro~hemsitry as an econoniic electrode material. Electrocheinists were able at last, with liquid mercury electrodes, to verify theoretical equations which had not been c o n f i ~ m eexperimentally ~ by means of solid electrodes. ~lectroanalysisstill continues to profit from olarography by Heyrovsky in the 1920s (and many related techniques later on). Stripping analysis with the use of hanging drop and thin Fbm Hg elcctrodes is an important tool in the trace determination of metals at 10-6--10-9 mol/did (Galus, 1994). The 100-year-old Weston cell: sat./Hg-Cd (12.5 mass% Cd) which contains Cd amalgam on the right-hand side is the best with which to calibrate potentiometric sjistems because of its stability and a very low temperature coefficient (see Westbrook, 1995).
itio ~ m a l ~ ~are m ~s e ~ as ~ alloys e d where one of the compone~tsconsists of Hg. Simple amalgams contain combiiied with Hg, and complex in more than one metal alloyed with . The name amalgarn is used for either mono-phase (homogeneous) or multi-phase (heterogeneous) syss exist a solid, solidlliquid or liquid2 forms. stable molecules have ever been detected in the gas phase in measurable concentrations, therefore gaseous amalgams ought rather to be treated as a mixture of atoms or as dimers (M2). Melting one or more metals with Hg may lead to formation of either 2See p. 26ff. for discussion of short-range order in liquid mercury alloys.
I
10 I
20 I .
30 I
40 I
50 i
80 I
70 I
80' I
A t o m i c number ~ i ~ 1 ~ S~lLibility r e of elements in mercury at 25 "6.Circular and triaiigular symbols represent data from exact deterinitiations and minimum detection levels respectively; open symbols the formation of an IMC; filled symbols nonformation of an IMC
solutions or defined intermetallic compounds (lMCs) as well as their mixtures. The degree of solubility of NI in liquid Hg and the tendency of M to form a stable IMC with Hg are the two major factors that should be taken into account in amalgam classification. The selected solubilities of elements in Hg at 25 OC are collected in Figure 1, and nurncrical values for metals are to be found in Guminski and Galus (1986) or Guminski (1989a). The solubility values denoted by circles and triangles come from exact d e t e r ~ i n a t i o ~ and s rninimum detection levels, respectively. Eventual formation of an IMC or its non-formation in a denoted by empty and full symbols, respectively. The solubility changes with the atomic number of an element reflect changes o f the physical properties of elements throughout the Periodic Table. Taking into account properties of simple amalgams in the sense of: the type of phase diagram for a Hg-M system (Massalski et al., 1990), the solubility of M in Hg, the heat of the dissolution process, the activity and diffusion coefficients. and the kinetics of electroreduction of M"+ on a Hg electrode with the corresponding a ~ ~ a l ~faom~ a t i o(Gumins~i, ~ 1989a), one may formulate a classification of simple amalgams into four groups (Guminski, 1989b). This is not the first attempt at an arrangement, since various generalizations have been done several times before, but this classification has the most general character, is based on the most contemporary knowledge of amalgam
Amalgams features, and is of essential service for practical applications of amalgaiiis,
The first group contains: alkali metals (also ammonium aiid substituted ammonium radicals), Mg and alkaline-earth metals, lanthanides (Ln's) and actinides (An's), All these metals dissolve at 25 "C in Hg to levels higher than 10-3~molYO(with the exception of a few heavy Lns). Due to the large difference in electronegativity of M and Hg, these metals form IMCs of partly ionic bonding. The most stable IMC formed in a g-M system melts congruently at a temperature higher than the corresponding melting point of pure M (with the exception of Th, U, and heavy Lns which possess quite high melting points). In the case of IMC melting points being higher than the boiling point of Hg at normal pressure, one should consider the M-Hg phase diagranis established at an applied pressure to keep the com~onents in the condensed state; see the example of the Ba-Hg phase diagram shown in Figure 2. The saturated liquid a m a l g a ~ are s always in eq~~libriuni with their IMCs in . The majority of the ~~~s are line compounds. ctrode processes at ~ ~ - ~ / interfaces M n are relatively fast; they are fastest for the alkali metals and slowest for Lns and Ans. The amalgam half cell H g - ~ / ~ npotentials + are well defined, and these amalgams may be effectively used in technological processes connected with electrochemical reactions. Use of aprotic solvents and a strictly 0-free atmosphere is recommended. Formal potentials of pure metals EfMiMn+ are always more negative than the n + . experimental a ~ a l g a m potentials E f ~ g - ~ , MThe solubility values are typically lower than those predicted by the theory of ideal solutions. Since the dissolution process is markedly exothermic, preparation of these amalgams by electrolysis or cementation is suggested instead. The liquid homogeneous amalgams deviate strongly froni Raoult's law, activity coefficients of these metals in their dilute solutions (referred to pure metals) are very small, and the liquid phase contains M exclusively in the form of MHg, molecules, but not o f free atoms. This situation is also reflected in the difference between diffusion coe~cients predicted f the simple theory of Sutherlan~-Einstein) and e x p e ~ ~ e n t a l l measured y values; the experimental values are always smaller than the theoretical ones. +
a
20
40
60
I
I
I
1
80
w
ure 2 Assessed Ba-Hg phase diagram at c o ~ ~ t ~ ~ i i ~ e d pressure (from J . Phusc &'@I.)
The second group c or d valence electrons (Al, Ga, In, Cu, Ag, Au, Zn, and Cd). All the soluble in liquid Hg to levels higher than 10 -3 mol% at room temperature. weakly. Even if an it displays a certain decomposes much below the meltin the example of the T1- g phase ~ i a ~ r asmh o ~ nin Figure 3. These amalgams are simply prepared by direct dissolution of the metals, ceme~itatio~, or cation electroreductio~.~nthalpiesof the are small, negative, or positive. slight deviations from Raoult's law (positive or negative) are observed, and the activity c o e ~ c i ~ n t s o f the oscillate around unity. The formal ~~otentials EfHg-M,Mn+ and EfMiMn+ half cells are placed closely together on the potential scale, and the electr~redL~ctions of these cations are the fastest elect~odeprocesses known. The predicted and ex coefficients are quite similar; only and T1 (which form relatively st show measured values lower than those from the predictions. The M-Hg interactions typically have metallic character.
.3
Ps
The third group contains high melting d metals and p elements of aiiiyhoteric character (V, Nb, $a, Cr
24
Structure and Composition
TL w e 3 Assessed Hg-TI phase diagram (from J. Phase Equil.j
g at room temperature are at concentrations below 10-3mol% and in some cases at immeasurably low levels. The experimental values are always lower than those predicted for the ideal solution. The Ce- g phase diagram as a typical representative is shown in Figure 4. Practically pure metals are the saturatin~solid phases. These amalgams may be obtained by electroreduction or chemical reactions, The products are frequently oversaturated by several orders of magnitude. However, quite large amounts (up to 20mol%) of Cr, Fe, or CO have been introduced into Hg by electrolysis, forming products with an initial consistence of milk, then cocoa with
aoo
I
L M.P.
0
Ge-Hg phase d i ~ g r (from a ~ J. Phase ~ ~ ~ i 1 . j
increasing concentration of M, then cream, butter, and finally a plasticine-like paste. Therefore formation of such colloidal dispersions must not be treated as evidencing good solubility of these metals. The dissolution of metals in this group is always an endothermic process. Aquo-cations of these elements are poorly reducible at a FEg electrode (slowly, with a large overpotential). Since these metals do not undergo a stable solvation by Hg, their diEusion coefficients should be similar to those predicted by the SutherlandEinstein equation. Activity coefficients of the metals in their amalgains are much higher than unity aiid the deviations from RaouWs law should be positive. Due to the very low solubility of the majority of these metals, we can experimentally verify only a limited number of features of the selected a~al gam s.The MHg interactions have a dominantly Van der Waals character.
The fourth group of amalgams contains the rest of the d metals and probably Be. Their solubilities are lower than 10-3mol% at room temperature; the experimental values are frequently higher than those predicted by ideal-solution theory. These amalgams can be prepared by direct contact of the elements at elevated temperatures. Often a poorly soluble film of the reaction product (M-Hg) inhibits the reaction progress at lower teinperatures. These amalgams are effectively obtained by the electroreduction, cementation, and chemical reactions. The saturated amalgams are in equilibrium with their, most frequently linear, IMCs which are stable up to 600°C at normal pressure. As an example the Ni-Hg phase diagram is shown in Figure 5. The thermal effect of the dissolution process is the algebraic sum of the significant endothermic surmounting of the cohesioii forces in pure M and the exothermic energy of the IMC (M-Hg) formation^ finally the heat of the dissolution in this group may in some cases be endothermic as well as exothermic. Activity coefficients of these metals in their amalgams are lower than unity. The cation electroreduction processes on Hg electrodes are rather slow and occur at moderate overpotentials. The diffusion coeflicients of known metals are much lower than those calculated from the ~utherla~d-Einstein theory. Negative deviatioiis from Raoult’s law are expected for these amalgams; however, they have not been confirmed experimentally due to the low solubility of these metals. Bonding between Hg and M has a metalliccovalent character.
25
0 M.P.
4400
0
30
10
50
70
90
1200
. 9000 s!
400
200 0
M.F?
0
20
40
60
80
100
i Figure 5 Assessed Hg-Ni phase diagram at 0.101 MPa (from Phase Diagrams of Binary Nickel Alloys)
From our definition, the systems of Hg with nonmetals should not be named amalgams. Nevertheless, such systems may be divided into two categories. Noble gases, 13, C, Si, N, P, and As do not interact spontaneously with Hg and, due to their very low solubility (with the probable exception of P), may be safely included in the third group of amalgams. 0, S, Se, Te, F, C1, Br, and I form stable ionic, rather linear, compounds with Hg which melt above the corresponding melting points of the elements; see the exaniple of the Hg-I phase diagram shown in Figure 6. Since solubilities of such compounds In liquid Hg at room temperature are quite limited, these systems should rather be included with the fourth group of the simple amalgam classification. One could also divide the amalgams according to the s, p, d, and f valence electrons of the metals, but such systematization would be much less informative for practical and theoretical goals. This is ftilly obvious when one would compare for example Be and Ba, Mn and Re, or Ge and Pb amalgams of metals belonging to the same groups of the periodic table.
~~~~r~ 6 Assessed Hg-E phase diagram at constrained pressure sufficient to keep the coiiiponents as liquids (from J Phase Eguil.)
The easiest way of amalgam p r ~ p a r a ~ i oisn direct solution of M in Hg, if the corresponding solubility i s sufficient and the surface is not chemically passivated. The kinetics of the process may be increased by increasing the temperature. 5.2 ~
~
~
~
~
~
c
~
e
Electrochemical reduction of metallic ions on a cathode from aqueous or non-aqueous solvents as as from molten salts allows the introduction of both soluble and insoluble metals into the Deposition of a M away from the very seldom observed; therefore this be quite universal. Some amalgams may be obtained by simultaneous reduction of their soluble salts in a solution. Hg2' may be reduced on noble metal (Ag, Au, Pd or Pt) electrodes with formation of their amalgams. A i ~ m o n i uand ~ alkylammonium radical amalgams are most effectively obtained by electroreduction of airunonium and a l k y l a ~ m o n i ~ions m on a Hg electrode.
5.3 ~ Depending on the kind of metal and available technical possibilities, ainalgams may be prepared by means of any of five groups of methods (Kozlovskii et al., 1971).
e
e
~
~
e
n
t
~
~
Cementation is almost as effective as the ele~trolytic method, but its application makes estimation of the amalgam concentration more difficult; there are problems as well with the comp~etenessof the reaction and
~
~
26
StrLictzive and Composition
the product purity. of preparation: La3
+
+ Na-Hg-,
ere are two examples of this type
La-Hg + Na
+
5.
hemical rea~tionsmay be used for preparation of some kinds of amalgams. Carbonyls of Fe, Ni, CO,MO decomposition at 300 "G In sequent amalgam formation. metallo-organic compounds may also lead to the amalgam formation as in the following example:
Also hydrides of several metals may react with Hg or its compounds:
Taltacs (2000) described an ancient mechanochemical reaction for recovery of mercury from native cinnabar, rubbed with vinegar in a brass mortar with a brass pestle. In the opinion of this author the brass metals are partly transform~d into sulphides and partly dissolved in Hg in the course of this process.
6, ~ t ~ ~ ofc Amalgams ~ u ~ e Amalgams have been investigated with the use of the following physico-chemical techniques: thermal analysis, vapor pressure, density, viscosity, surface tension, hardness, i~iagnetics~sceptibility,diffusion coefficient, calorimetry. enif, electroanalysis, conductance, metallography and x-ray, electron or neutron diflraction. These properties and methods allow for distingLiishing between homogeneous and heterogeneous systems, because formation of a new phase generally produces an abrupt change in the parameters measured. Every techni~ueinforms us to some extent about a particular phase structure. Structures of solid amalganis have mainly been investigated by diffraction techniques. Hg
and M may combine in various stoichiometries from MEZg,, (as in BaMg,,) to HgM,, (as in MgIn,,). The crystal structures and lattice parameters of IMCs have been collected by Villars (1997). It is rather difficult to ascribe certain crystallographic structures to selected stoichiometries of amalgam IMCs. Such general rules could only be observed for Ln-Hg and probably An-Hg IMCs (Iandelli and Palenzona, €979). Structures of liquid amalgams have been deduced from a variety of investigations (see also Singh and March, 1995). For example, in the Hg-Na system, analyzing the thermodynamic functions, Ace*, A H , and A F y , and the concentration Auctation function, Scc(0)= (S2AG/SC2)-' where 4 G is the Gibbs energy and C is concentration), the structure Pictor a J r ) from diffraction experiments, magnetic susceptibility, viscosity, vapor pressure, electrical resistivity and molar volume versus composition for the liquid alloys at 100400 OC, one may find unequivocal iriformation about the existence of a large amount of this liquid amalgam, both below and above the liquidus line (Tamaki et al., 1982; Kozin et al., 1977). The S,,(O), AGex,A H , A F X ,the electronic part of the magnetic susceptibility, the electrical resistivity and the molecular volume, all show a niininmm but viscosity a maximum, at about 33 mol% Na (corresponding to Hg,Na) in the concentration dependence of these functions. Similar conclusions may be drawn from measurements for the Hg-Tl, Hg-In, Hg-K, and Hg-Cs systems where minimal values of the structureinforming functions point to the typical compositions of the Hg-M complexes foiined in the corresponding liquid phases. Around room temperature and in dilute amalgam solutions, information about the liquid amalgam structures may also be obtained from analysis of diffusion coefficients (Guniinski, 1989a) and emf measurements (Korshunov, 1990). metric experii~ents with amalgam cells one may estimate the thickness of the Hg solvation sphere around a dissolved M atom. In case of the alkali metals, such values range between 1.2 (for Li) to 1.8 (for Cs); and, in the case of the alkaline-earth metals, they are between 1.9 (for Ca) and 2.1 (for Ba) atom layers of Hg around these atoms. Quite similar numbers may be deduced from analysis of the diflusion coefficients of these metals. A starting point for an analysis of the diffusion coefficients in a liquid amalgam medium at high dilution is the Sutherland-Einstein equation:
D, = kT/4nrmrl,,
A vnalgams
relating the diffusion coeEcient of the metallic solute
27 I
D M ,the temperature T, the radius of the diffusing entity TM and the viscosity of the dilute amalgam qHg (the last one being practically equal to the viscosity of pure Hg). A correlation between selected experimental values of D M and YM is shown in Figure If one knows D M , one may estimate the radius of the particle that diffuses in Hg. It was demonstrated that such metals as Zn, Cd, Hg (self-diffusion), Al, Ga, In, Ge, Sn, Pb, Sb, Bi, Cr, and Fe diffuse in Hg in the form of naked atoms because the calculated radius from equation (1) is equal to or very near to the effective radius of pure M. All the metals mentioned are known to interact very weakly with Wg, and most of them do not form IMCs or intermediate phases with Hg. Atoms of the alkali metals, akaline-earth metals, lanthanides, and part of the transition metals are solvated by Hg atoms to different degrees, and their experinieiital diffusion coefficieiits are always lower than would be predicted with the help of equation (1). In several cases (Hg,Li, Hg,Na, Hg,Ca, Hg,Tb, Hg, &fn, Hg, 25Ag), the formula estimated from the experimental value of the diffusion coeEcient is equal to the formula of the solid phase (IMC) being in equilibrium with the saturated liquid amalgam at room temperature. However, some metals show explicitly larger or lower solvation numbers than would be deduced from the corresponding binary Hg-M phase diagrams. Foley and Reid (1963) measured diffusion in concentrated T1 amalgams between 0 and 40mol% Tl. These authors observed a distinct decrease of the mean diffusion coefficient near 25 mol% T1 which may indicate that Hg,Tl complexes dominate in the liquid amalgam at room temperature. The coniposition of the equilibrium solid phase in the Hg-Tl phase diagram is Hg5TI2,(28.5 at%), and thus is quite similar. ‘Viscosity and thermodynainjc functions of T1 amalgams similarly show extremal values at compositions from 2528 m01% T1.
1.a
1.
2.
Figure Dependence of the reciprocal diffusion coefficients of metals in liquid mercury on the effective radius of metal at 25 “C
metals with the Hg solvent, two limiting cases will be considered for the solutes: (i) metals that do not interact insofar as could be experimentally detected; and (ii) cases where they interact to such extent that an IMC, M,MI is formed in the Hg medium. The first investigations on this field were performed by Tamniann and Jander (1922) who discovered fomation of Bi3Ce4, Cd-Gu, CeSn2, C L I Z ~AuZn, , and Mg,Sn in relatively dilute amalgams, but detected no IMCs in the Ag-Cd and Ag-Zn amalgam systems. The nature of such compounds has been discussed for years, but now we find an. overwhelming amount of proof that the compounds are very seldom soluble but are typically precipitated in Hg ( ~ u ~ i n s k 1986a). i, The correspon~ingequilibria may be described according to the following schemes:
+ yM’-Hg 4 M x M & - ~pre~ip~tation g xM-Hg + yM”-Hg % M,M&-Hgsoluble product xM-Hg + yM’-Hg It.i:~ ~ ~ soluble ~ - W g
xM-Hg
Although many quarternary systems coiitaining Hg have been i~vestigated, so far most o f them are pseudobinary systems of the type HgX-MX (where X and X’ are non-metals). The corresponding phase diagrams are collected by Tomashik and Grytsiv (1982). However, we are concerned in this paragraph only with systems where Hg has but two metals introduced into it. In addition to interactions of solute
product % precipitation
(2) (3)
(4)
The equilibrium (4) seems to be the most general case that should be true for all reacting systems. However, the results of many experiments show unequivocally that the conce~trationof ~ ~ M ~ soluble , ~ Hmolecules g
28
Structure and Composition
is undetectably low, and most systems in fact obey equilibrium (2). Accordingly, the equilibria (2) and (3) may be expressed as the solubility product: (5) or as the equilibrium constant:
K= [M*M~l/[M]x~M’]y
(6)
The equilibrium concept of formation of solid IMCs in ternary solid-liquid alloys, as expressed by equation (5), was originally proposed by Hume-Rothery (1936) and applied by Zebreva to amalgams (1958). Using various physico-chemical and e~ectroa~alytical techniques, about 7 ~ M - ~ ’ - Hsystems g in the Hg-rich corners of the phase diagrams have been quantitatively investigated (Gumi~ski and Galus, 1992). It was observed that the TMCs formed in Hg solution have simple formulae and their compositions correspond to the most stable compounds in the M-M’ binary systems, as for example: AuCd, AuCu, AuMg, AuMn, AuSn, Pb, BiK,, CdSb, Cu,Sn, , and SbZn. There are CuZn, InSb, n ~ e r o u systems s where two or even more IMCs are formed, as for example: Au,Cd-AuCd, Au,In-AuIn, AuSn-AuSn,, Cu,Sn-CuSn, Cu,Zn-CuZn-CuZn,, and Ni~n-NiZn,. It appears that I-Ig seldom forms the third compoiient of an IMC being precipitated, as for example Mn,Zn,oHg, or HgTlTe,. Here is a typical example of the analysis of the solubility data of CdTe and Cd,Hg,-,Te alloys being introduced into liquid Hg. HgTe and CdTe are almost line compounds which are completely miscible in the solid as well as in the liquid state. Several authors measured the solubility of CdTe in pure Hg (at 250600 “C), in Te amalgam (at 230-530 “C) and performed thermal analysis at higher temperatures (>730 “C). Guminski (198617) showed that KgdTe= [Cd][Te] best described the equilibria in dilute Cd-Te amalgams; see Figure 8. Most of the reliable data lay on or very near to the straightforward relationship of log&, vs. I/??. The positive deviations from this line in the high temperatur~ range are probably due to signi~cant changes of the activity coefficients of the components in the Hg-poor melt. One may consider a t h e r ~ o d y n a m icycle ~ and compare the c o r r ~ ~ ~ o n d ti hn ~g r m o d y n a ~functions ic for the formation of an IMC in a Hg medium and in a related binary system. Such an analysis was performed by Guminski (1986a) on 23M-M”-Hg systems taking into account the enthalpic eEects of reactions:
M + H g ~ M ~ I - I g AHM
(7)
t
0‘1
0.01
TW4x 1
-1
Figure 8 Dependence of the CdTe solubility or the square root of its solubility product in Hg vs. reciprocal temperature ( ) A. V. Vanyukov, I. 1. Krotov and A. I. Ermakov, I d. Nauk SSSR, Neorg. Mater., 13 (1977) 815; ( 0 ) J. Y. Wong (1980), as cited by C. H. §U, P. IS.Liao, T. lectron, Mater., 11 (1982) 931; J. Electron. Mater., 13 (1984) L. Schmit, C. J. Sperschneider Trans. Electron Devices, 27 (1980) 24; (A) A. V. Vanyukov, I. J. Mrotov and A. I. Ermakov, tzv. Akad. Nauk SSSR, Neorg. Mater., 14 (1978) 657; (+) F. R. Szofran and Lelioczky, J. Electron. Mater., 12 (1983) 713; ( x ) P. J. Tung, J. Electron. Mates.,
Equations (7) and (8) denote M and M’ dissolution; (9), precipitation of an IMC in Hg; and (lO), formation of an IMC in the corresponding binary system. Balancing equations (7-10) we may write:
A~ a l g a ? n s
+ yAllpf,l + A H ~ ~ ~ ~ ( H g )
29
Ti, Mn, Fe, Ni, Zn, Cd, Al, Ga, In, Tl, Pb, Sb, Th, and U by means of these procedures. Hg can also be useful - AHMXM~~ (1 1) in metal separation. For example, a Ce-Fe alloy, used in lighter flints (see Chapter 31, Vol. 2), is d e c o ~ ~ o s e d If hH[,,) approaches 0, then we have an additional in liquid Hg at elevated temperatures; then Ce proof that an IMC formed in the Hg medium and in dissolves the Hg, and Fe forms an undissolved scum. the corresponding binary system are the same. HowAfter filtration and evaporat~onof Hg from the filtrate ever, without further investigations we must not to recover the Ce, and from the scum to recover the Fe, ascribe a non-zero enthalpic effect, AH(Hgl,to either both the Ce and the Fe are ultimately separated. formation of an IMC with Hg as the third component, Kozin (1964, 1970) described the essential technical f o ~ a t i o nof a soluble form of an IMC, or surface details important to electrore~ningof metals to high f, crystals by Hg, The AH(Hg)values purity (> 99.9999%) by means of polarization of the approach 0, within experiniental error, for the most and M, amalgam cells: M, M’, M”, . . . Hg/M2~/M-Hg exhaustively investigated compounds, such as: AuCd, M’, M”’, . . . Hg/M2+/M.Electrolysis carried out with AuCu, AuIn, AuSn, AuZn, CdTe, CuZn, LiSn, the use of direct current brings about subsequent Ni,Sn,, and PdZn. Assuming the validity of equation deposition of M or its amalgam on the right side. M’ (1 1) one may predict experimentally unknown A H M ~ M ; and M” are impurities which remain in the Hg phase, if values for several INICs, as - 1222 15 kJ/mol for they are more noble than M, and are in the electrolyte AuMg or - 105.7$. 1.6 kJ/rnol for KPb. phase in the form of ions, if they are more electroactive than M. When the process is continuously repeated several times, then the M is considerably enriched at every stage of the process and the content of impurities decreases. If an M amalgam is finally formed instead of M, Hg is distilled off at high temperature and reduced Hg was used even in antiquity for extraction and pressure. Applying this inethod of multistage electrorefining of Au and Ag from ores as well as for silvering lysis Kozin (1964, 1970) obtained Cd, Ca, In, Tl, Pb, and gilding; see Chapter 24, Vol, 2 and Weeks (1968) and Bi, all at a purity higher than is obtained from the for more details. Knowledge about the safe perforzone melting technique. mance of these processes is very essentials3 The recovery of noble metals from ores may be based on either dissolution in Hg with subsequent formation of IMCs with them (as in the case of Ag and Au) or even surface wetting (as in the case of Pt-like metals). Amalgams prepared by reacting liquid mercury with Amalgams of Zn or Fe have been used for the wetting various metals can also create starting materials for of Pt, Pd, Rh, Ir, and Cu which are present in the powder metallurgy operations. The metals which have autogenous Pt ore. It was found that a process is most high solubility in liquid Hg (Ag, Au, Zn, Cd, Sn, Pb, effective when the input amalgam contains 5 mass % Bi, Mg, Ca, Ba, Li, Na, and K), give up Hg at high Zn and the electrolyte of pH2-3 contains 2mol/ temperatures and form macrocrystalline and poorly dm3NaCl (Shemyakin et al., 1979). Hg may also be sintered sponges. The slightly soluble or insoluble exploited for extraction and refining of various other metals (Al, Ti, Zr, V, Ta, Cr, MO, W, Mn, Fe, CO,Ni, metals. Differences in their solubilities and normal Pt, and U) after similar treatment form fine powders electrode potentials in Hg are the primary basis of the whose particle sizes depend on the formation (or not) corresp~ndingtechnologies. Jangg and Bach (1961) of TMCs by these metals with Mg. The particle size described methods of preparation of the alkali metals, increases with time and temperature during the process. From a fresh Fe amalgam one obtains 3Quite recently this author spent three weeks at a provincial particles of 2-5 pm diameter, and after 1 h of conuniversity in Peru gwing lectures on hydromet~llurgy.All ditioning the amalgain at 300 “C the diameter increases participants in this course were especially interested in Au recovery from ores with the help of Hg, asking for very to 25 prn. If a metal forms an IMC with Hg (the fourth specific details. They were fortunate to learn how to improve a group of amalgams) then the metal particles are even primitive apparatus for Au extraction so that the Wg could be smaller after the Hg isolation (Jangg, 1965). Finely safely reused for the next process and would not poison their divided transition metals from this process are valuable environment. One may therefore deduce that this old and primitive method of Au acquisition is still in practice there. catalyzers for chemical synthesis. AH(HgI = xnHM
30
Structure and Composition
There are many examples of the useful formation of alloys and defined IMCs with the amalgam method. Two metals introduced into Hg may react inimediately lloy may be formed after the g is distilled oE. In this way powders of CO-Fe A13Ni2,Al,Ni, A N , Cu-Zn, nd Bi-Mn (Kozlovskii et al., alloys with Fe, CO, Ni, Ag, and Au (ICirchmayr, 1965), rare earth metals, Mn, Ni, i and Ge (Mayer et al., 1967) have been prepared.
After successful enrichment of OLi isotope in a Hg phase from an equilibration of Li amalgam with a %i+ and 7Li+ mixture, the phenomenon was utilized for separation of H and D, 14M and 15N, 39Mand 41K (Kozlovskii et al., 1971). The interphase exchange between the ionic solutions aiid amalgams compared to the aiialogous exchange with solid M is quite fast, a characteristic essential for practical separation kinetics. ~ i x t u r e s of radioisotopes are effectively separated by this method. Amalgams of the transamericium elements were the first alloys investigated. The radiopolarograp~ymethod allows for reduction on a Wg electrode of Cm, Bk, Cf, Es, Fm, Md, or No ions to the metallic state at concentrations as low as 10-8 to 10-11m01/dm3. The partial excess Gibbs energies of formation of these amalgams were estimated from the po~arographichalf-wave potentials by
amounts of these metals. Liquid alloys of Ln, such as La,Ni, were proposed as possible getters for tritium (3H) in a fusioii reactor operation, Such alloys have low equilibrium pressure, large capacity, and their surfaces are not regeneration may be performed to the following scheme: 5 3H2+ La,Ni-+(La 3W2),Ni Hg
absorption at 530 “C
+ (La ’ H , ) , N ~ ~ ~ a ~ ~+i 5- W ,H2g amalgamatioii at 250-300°C i
+ Hg
regeneration at 400-430°C
as reported by Carstens and David (1983).
~~v~st~gatio~s
The ab0ve”mentioned formation of stoichiometric AuZn in liquid Hg was first utilized by Tammann and Kollinanai (1926) as a kind of potentiometric titration of Au (present in Hg) by Zn introduce^ into it). After detailed investigation of the Hg-rich corners of the Au-Zn-Hg system, (Guminski and Galus, 1971), the Pd-Zn-Wg system (Dergacheva et al., 1978) and the Pt-Zn-Hg system (~um i nskiet al., 1983), the K,, values of AuZn, PdZn, and PtZn, were determined to be 7 x 10-*0nio12/dmA,4 x 10-9 iiio12/dniA,and 1 x 10-14m013/dm9at 25 ‘C, respectively. The fast precipitation of these IMCs in Wg was used to determine the Au diffusion coefficient (Guminski and Galus, 1977) and concentrations (solubilities) of Au, Pd, and Pt in Hg (Guminski, 1991) based on amperometric, voltammetric, and chronopotentiometric experiments. All these noble metals are not electroactive at negative patentials in an amalgam form, but their concentrations and diffusion coefficients are precisely traced by electroactive Zn reacting . formation of vigoro~s~y with them in a Hg m e d i u ~A IMCs in Hg may sometimes complicate electroanalytical processes and especially the stripping analysis; the most typical disturbance is caused by reaction of Cu and Zn on a Hg electrode. Therefore one should be very careful during aiiterpretation of the voltainmetric curves which should have purely di~usionalcharacter in oxidation steps. The catalogue of possible interactions between metals being introduced into Hg was compiled by Guminski and Galus (1992).
Reduction r e a c t i o ~with ~ the use of a ~ a l g a ]nave ~s occasionally been used to obtain chemical csnipounds (Smirnov, 1970). The classical example is the reaction of Na-Hg (obtained at the g cathode from electrolysis of NaCl solution with C1, by-product at the graphite anode) with H28:
+
2H20 2Na-Hg+H2
+ 2NaOH + 2
where pure NaOH and gaseous H are produced; the Hg is then reused after the reaction is complete. Hydroxides of alkali metals, alkaline-earth metals, Ln, An, and A1 are formed in a similar way. The analogous reactions of Na-Hg with alcohols lead to formation of alkali metal alcoholates and hydrogen. The action of 0,, CO,, NO,, ClO,, SO, and Na2S4on Na-IIJg leads to the formation of Na,O,, Na2C204,NaNO,, NaGlO,,
Na2S204,and Na2S, respectively. Na amalgams are frequently utilized in organic chemistry for hydrogenation, reduction of hydroxide-, carboxyl-, nitro-, nitrozo-, azoxy-, hydrazo-, oxime-, halogen-, sulphur-, or arsenic-containing groups. In some cases even the C-C or C-N bondings may be broken. In the reaction of alkyl chloride with Na-Hg, the very poisonous mono- and di-substituted allcyl and aryl compounds of Hg are formed. The HgC $- ion is probably the most ubiquitous. Substantial amounts of Hg are consumed in paints while lesser quantities are used for production o f agricultural and medical chemicals (Vcnetsky, 1981).
Froni a historical perspective several applications of anialgams werc once significant. An alchemist at the enry VI discovered that Cu rubbed with Hg acquired a silvery tint; soon, on the King’s order, Cu coins in masses were coated with Hg counterfeiting the Ag coinage (Venetsky, 1981). Early electrical machines used Hg or amalgams to establish good contacts; especially Hg-In alloys with a certain admixture of 0 have the advantage of well wetting all metallic surfaces at temperatures even below 0 “C (Westbrook, 1986). Hg was applied to join Sn foil to glass in forming ~nirrors.~ The first successful tungsten lamp lament was prepared by ~ ~ t r u d i nBi-Cd-Hg-W g alloy from which the Bi, Cd, and Hg were subsequently removed by heating (Coolidge, 1965). Ag, Cu, and Sn amalgams and combin~tionsthereof have been used as dental restorative materials for almost 500 years and are still important today (Waterstrat and Okabe, 1994). Due to their highly toxic properties, where possible Hg and its alloys are substituted by other materials. However, since Hg is easy to purify to a spectacular degree, it is still used as the working fluid in therniometers, barometers, electric resistance standards, circuit breakers, switches, diffusion pumps, seals, lasers, and electrode materials in pure and applied electrochemistry. Miiiimal interaction of constructional materials with Hg is quite essential for long-time employment of such instruments. Partial solutions, IMC formation at the solid-liquid interface, grain boundary grooving, embrittlement, and wetting have been investigated in several papers (Barlow and Pla~ting,1969; Bennett, 1977; Lahiri and Gupta, 1980; Sudarshan et al., 1984). Hg has a higher thermal 4See insert, above right,
Little Willie from the nzirror, Licked the mercury all off, Thinking in his childish error, It would cure the whooping cough, At the funeral, Willie’s mother Sadly said to Mrs. Brown, “Twas a chilly day for Willie When the mercury went down”. This anonymous bit of doggerel, in two short verses, manages to allude to three different qualities of mercury. fin D. NcCord, What Cheer, Longmans, 1945
conductivity coefficient, boiling point and critical point than water has. These are quite promising factors in the case of using Hg as a circulating coolant in thermal reactors. Hg was used successfully in a fast breeder nuclear reactor coolant, in a turboelectric power conversion system for space craft, in (Fleitman and Weeks, 1971), and as a ~agnetohydrodynamic working fluid (Branover and Lesin, 1995). Fleitman and Weeks (1971) performed and summarized many efforts to establish the ~orrosion resistance of metallic and non-metallic materials in Hg between 250 and 700 “C. Pure Fe, and graphite best withstand the Hg at forming IMCs with Hg such as Ti, Zr, Mn, Ni, and Pt are not recommended for application in construction, although these metals show quite resistance to Hg, even for long tiine temperature. Steels and other alloys sliow preferential leaching of Cr, Ni, and Mn as well as other readily soluble constituents at high temperatures (Suzuki and Mutoh, 1992). it was found that addition of Ti or Zr to liquid Hg inhibits its corrosive action due to formation of highly protective Ti-C-N or Zr-C-N films on the steel surfaces. Cu, Pb, or Sn dissolved in Hg accelerate the corrosion. Graf et aE. (1985) found that amorphous 78Ni-8%-14B glass showed quite good corrosion resistance to Ng attack at room temperature. The Cd-Hg-Te system and many related systems ( Hg-Se and M-Hg-S) have been frequently investigated (Tomashik and Grytsiv, 1982). Much of work has been devoted to the Cd-Hg-Te materials. Solid solutions formed between CdTe and HgTe are semicond~ctors with an energy gap increasing between -0.3 and 1.6eV as a nearly linear function of the CdTe molar fraction content. These materials are used in the Fabrication of infra-red detectors in both military and civilian applicatioiis such as surveillance and in space. Iii order to obtain these alloys with desired electronic
32
Figure 9 Margaret Weiler's research on mercury-cadmiumtelluride photovoltaic detectors has helped Lockheed-Martin TJR Imaging Systems develop arrays such as this, in which each 60 ~ m - s q u amesa-~elineated ~~ pixel is capable of detecting on the order of IOpm infrared light with w~velength~
properties, their growth, optical, dielectric, thermodynamic, t h e ~ o p h ~ s i c and a l mechanical properties, solid state diffusion, defects, and band structure have been widely studied. The corresponding information has been collected in numerous papers, separate books, databases aiid conference proceedings (Mercury Cadaterial Properties Database, 1994; Capper, 1994; Procee~~ngs, 1989). As an example of significant achievement in this field Figure 9 shows a Cd-Hg-Te plio tovoltaic device made according to the accomplishments of M. H. Weiler (Young, 1999). Small amounts of Hg are introduced into glass tubes of fluorescent lamps because Hg vapors emit radiation with high efficiency. To decrease the toxicity of Hg vapors and to adjust the light characteristics, several substitute alloys (Hg-Ni, Hg-Na, Hg-Zn, HgCd, Hg-Sn, Hg-Pb, and in the form of solid pellets were proposed and applied instead. After heating the amalgam, they are decomposed to give the proper Ilg vapor pressure, The amount of Hg intro~ucedcan also be reduced by employing sintered pellets o f a porous Cu-Fe-Hg alloy containing Hg in its capillaries. The Cu-Fe a ~ a l g awas ~ prepared by electrolysis, then tempered at 250°C for 1h, and the Hg excess filtered off and pressed away. These alloys are readily reproducible lamp fillings, they show reduced environmental contaminat~onand also possess useful ferromagnetic features (Schuster, 1986; Guminski, 1990a). Tubes filled with gaseous mixtures of Ar, Ne, and Hg gave lighting of various colours
depending on the gas composition, tube geometry, and mode of the discharge (Lee et al., 1997). When large amounts of Fe or CO, exceeding their saturation levels by a million times, are introduced into Hg (most easily by electrolysis), the still liquid product possesses durable inagnetic properties at room temperature, To prevent an agglomeration of the Fe and CO particles of a colloid-like nature, addition of Sn, Ga, or Na to the amalgam was found to be effective. Then Sn or Ga form monolayers of IMCs on the Fe or Go particles that do not significantly decrease the magnetic properties of the liquid magnets, keep their viscosity low, and inhibit the particle growth experienced on typical crystallization of these metals. An excess of Sn or Ga leads to the destruction of the magnetic moment of the particles (Windle et al., 1975; Keeling et al., 1984). The Ga-Hg (20vol.%) alloy was selected to investigate the stability of a metallic dispersion under microgravity conditions in the Space Shuttle. The Ga-Hg binary system shows an extended niiscibility gap. The dispersed state of Hg was recorded on x-ray sensitive film. The sample was cooled at different cooling rates from 220"C, where the sample was homogeneous. It was observed that the required homo~enizationtime of the sample at 220°C was half as much in space. When cooling the sample into the miscibility gap, precipitation of Hg droplets occurs rapidly by ~eterogeneousnucleation at the Ga surfwe. Supercooling o f the melt appears to be less than 20 "C. At higher cooling rates convective, non-diffusional material transport is likely to contribute to Hg particle growth. Hg droplets near the alloy surface seem to be stationary (Otto, 1984). 8.6
~ ~ s t i ~ ~
This author and his colleagues have been asked many times to prepare so-called red mercury and were offered a very good remuneration, even without giving a recipe. No metallic amalgams are knowii to possess a red colour (see Stein~mannet al. this volume). One can imagine that a red-coloured Hg could arise from an adsorbed film of a red dye on its surface, but such a product would be highly expensive and for what? Any serious information about red mercury could not be found in the open scientific literature. The recent reports by Orlov (2001) and Ladika (2001) put more light on this matter. It seems the most reliable explanation that the name Red Mercury was given to the amalgams o f the transuranium elements. They are relatively well soluble in mer~ury,easily a ~ ~ l g a ~toa t e
33
Amalgurns
form IMCs, and the Elg medium attenuates the radioactivity, making transportation and handling potentially easier. Pu-Hg intermetallic is a reddish powder according to Ladika (2001). A capsule filled with Red Mercury is hot and contains the dangerous stuff inside; therefore the adjective Red seems to be ap~ropriatein the figurative sense as well.
Problems of contamination and poisoning by Hg have been known for centuries. The action of Hg and its cornpounds is frequently not immediate but generally causes irreversible damage in human organs. Due to the high volatility of imtallic H g and the relative ease with which Hg compounds decompose at elevated temperatures, all operations with Elg, amalgams, and Hg compounds must be performed in tightly closed containers placed in a well-ventilated system, in case of any failure of the apparatus. Therefore it is fundamental to collect and keep products containing Hg in absolutely safe places. Even very low concentrations of Hg and its compounds present in water are absorbed by some kinds of bacteria, then accumulated in the bodies of water animals, and may finally be consumed by hui~ans,causing serious diseases. Recovery (recycling) of Hg from waste materials may be carried out by thernial decomposition and es distillation of Hg. Selection of proper t e ~ ~ e r a t u r for such processes should be done only after studies of the corresponding binary and ternary phase diagrains collected in ~ a s s a l et ~ ~nl.i (1990), Toiiiashik and Grytsiv (1982), ~ ~ l ~of eAlloy t i Phase ~ Diagrams, and Jourizal of Phase ~ ~ ~ i l i b r i a . orgstedt et al. (1994) proposed a special method of Hg extraction from waste batteries: steel, iZln-Hg/ KOH/HgO,C,steel. Such batteries, having been cracked open, were treated with liquid Na in an Ar i i ~ red~ictionof Zn and ~ ~ t ~ ~ o s pNhR~~rde~. i t i acaused Hg from their oxides to their metallic states. The NaZn amalgam, after separation from the solid bodies, was electrolyzed in a solid electrolytic cell: Hg-Zn-Na/ beta alumina/Na. In this way the Na was almost quantitatively separated from the Hg (but contaminated by Zn and other metallic impurities). The electrolytic Nn may then be reused, and the only byproduct of the process is Na,O as a scum on the amalgam.
oys to
The question as to whether other low-melting alloys possess properties similar to the am al ga~s,is easy to answer affirmatively; however, our experimental ~ ~ o w l e about d g ~ them is of ~ o ~ s i d e r alesser ~ l y degree. al Guminski (1990b) compared the e ~ p e r i ~ e n tsollxbilities of metals in liquid, low-melting metals such as Gta, In, Sn, Pb, Bi, Li, Na, K, demonstrated that metallic solutes, well soluble in one metallic solvent, are usually well soluble in another one. Similar observations were established with sparingly soluble metals. In every metallic solvent the solubilities, ordered according to the atomic number of the metallic solute, form dependencies similar to that shown in Figure 1. Exceptions are observed for Lns and Ans which are well soluble in p metals but not in the alkali metals. Ln and An do not form IMCs with the alkali metals, but the p metals do. Analyzing diffusion coefficients of various solutes in dilute solutions of 20 liquid metallic solvents ( ~ u m i n s ~ , 1995) one may observe that if an IMC is formed in a binary system solute-solvent, then its diAFusion coefficient is lower than predicted by Equation (1). If no specific interaction between a solute and a solvent exists, then the diffusion coefficient is near to the prediction of equation (1). It was further shown by Guminski (1996) that taking into account the type of binary phase diagram, the solubility, the heat o f the dissolution process, and the activity and diffusion coefficient of metals in liquid Al, Ga, In, or T1 may be divided into four groups in the same ~ a n n e as r was described for the binary amalgams in section 4 of this chapter. The first paper dealing with specific i ~ t ~ r R c ~ini o ~ i ~ liquid ternary metallic systems was published by Tamniann and Schafmeister ( I92S), who observed that partition of a third metal between two im~iscible liquid metals is not in general equal. Concerning solutions of some metals in liquid Ga (sometimes named ‘gallams’)Kozin et al. (198 1) observed that nine metallic solutes, dissolved in p o ~ ~ ~l y~ ~ i sGa-Hg ~ibl~ alloys at 35 “C, always showed a higher concentration in the Elg phase than in the Ga phase (the highest partition coefficient was observed for Mn (= 2 x 105) and the lowest for Sn (= 2). In monographs devoted to Ga (Yatsenko, 1974) and In (Yatsenko, 1987), their author collected experimental data on the binary phase t i these ~ ~ ~ l i t d ~ a ~ asr well ~ ~ as ~ 0~11 sthe c ~ ~ ~ ~ a of metallic solvents with pure metals and alloys. By g such as W, Re, analogy to Hg, the high ~ e l t i n metals
e, Ta, Nb, and OS are the most resistive to corrosive dissolution in both Ga and In (700-1200 "C). Soine struct~ralalloys show etching of the more soluble metals by these liquid metals. Additions of Ti or A1 inhibited corrosion which was also diminished by the on of Cr protective layers. Ceramic materi, AlN, A1203,SiO,, graphite, and ZrO, are als not ed by Ga and In at temperatures lower than 850 "C. Examples of interactions similar to those observed in amalgams may be found for other liquid metal solvents. ~ a r t m a n n et al. (1959) observed precipitation of Cu,Sb, Cu3Sn, and Cu,As in liquid osa et al. (1981) showed the appearance of In3Sb, InSb, and Zn4Sb3complexes in liquid In-SbZn alloys. Solution chemistry in the liquid alkali metals also shows some similarities to amalgams. However, the specific influence of oxygen on the solubilities and corrosion of the transition metals in liquid Na, K, Rb, and Cs has a spectacular character, as does the presence of nitrogen in liquid Li (Borgstedt and Guminski, 2000). The presence of 0 in the Cr-Na system leads to the formation of NaCr02, which is more soluble than pure metallic Cr in liquid Na. Si and N introduced into liquid Li react with precipitation of Li,SiN3, whereas solid Fe,P introduced into Li is decomposed into dissolved P and Fe precipitated in Li. u m m i ~ gup, the amalgams do not seem to be a peculiar kind of alloy, and many features first observed in amalgams have been later discovered in solutions of other lowmelting metals.
Barlow, M. and Planting, P. J. (1969) Z. Metalll~.,60, 292. Barnes, J. W. and Bailay, E. H. (1972) ~ o r l ~ M i n i25, n ~49. , Bennett, 3. E. (1977) Microstr. Sci., 5, 395. Borgstedt, H. U., Guminski, C. and Perk, Z. (1994) Abstraeks of ~ a p e r sp ~ e s c n ~ eat d the 6th Intl. Symp. on Solublity Phenomena, Buenos Aires, Argentina, p. 0-12. Borgstedt, H. U. and Guminski, C. (2000) Monatsh. Chew.., 131, 917. g ran over, H. and Lesin, S. (1995) ~ i q u i~ ~e t a Systems, l H. U. and G. Frees, eds. Plenum, New York, p. 377. Cammarota, V. A. (1975) ~ ~Facts and ~ Problems, e ~U S . ~ Bureau of Mines. Capper, P, (1 994) Pro~ertiesof narrow gap cad~~um-based cornpourin's. EMTS Data Series, LEE, U.K., 640pp. Carstens, D. H. W. and David, W R. (1983) J. Nuclear Mat", 115, 203. Coolidge, W. D. (1965) Sorby ~ e r ~ t e n n ~ S ayl ~ ~ o on s ~theu ~ History of ~ekullurgy.C. S. Smith, Ed., Cordon & Breach, New York, p. 443.
David, F., Sarnhoun, IS.,Lougheed, R, W., Dougan, R. J., Wild, J. F., Landrum, J. H., Dnugan, A. D. and Hulet, E. K. (1990) S u d i o c h ~ Acta, ~ . 51, 65. Dergacheva, M. B., Kozin, L. F. and Panova, N. L. (1978) VINTTI Dep. 3595-78, Moscow. Fleltman, A. H. and Weeks, J. R. (1971) N L L CEng. ~ . Design, 16, 266. Foley, W. T. and Retd, L. E. (1963) Can. 1.Chem., Galus, Z. (I 994) Fundamental~sof ~lectroche~ic~il Analysis, 2nd ed., Horwood, Chichester and PWN, Warsaw. Graf, K. H., Lohmann, W. and Ribbens, A. (1985) Rapidly ~ u e n c h e d~ e t a l s ,Steeb, S. and Warlirnont, H., eds. Elsevier, Amsterdam, p. 1411. Greenwood, N. N. and Earnshaw, A. (1984) C h ~ ~ ~ i soft rthe y E l e ~ e ~ tPergainon, s, Oxford, p. 1395. Guminski, C. (1986a) Z . Metaflk, 74, 87. Guminski, C. (1986b) 9. ~ e . s ~ ~ - C o m ~ ~116, L15. 1. Guminski, C. (1989a) J. Mater Sci., Guminski. C. (1989b) J . Mater. Sci. 5. Guminski, C. (1990a) Technical Report to POLAM (Light Sources Producer), Warsaw, Poland; unpublished. Gurninski~C. (1990b) Z . met all^,, 81, 105. m ? ~ 16 on Guminski, C. (1991) J . ~ ~ s ~ ~ " C o Met., Guminski, C. (1992) J Phase Equil., 13, 657. Guminski, C. (1995) ~ i~ e t ~a Systems, l ~ €3.i U. Borgstedt ~ and G. Frees, eds., Plenum, New York, p. 345. Guminski, C. (1996) Abstracts of papers prcrscnted at the 7th Intl. Symp. on Solubility ~l~enow.ena, Leoben, Austria, p. 0-28. Gurninski, C. and Galus, 2.(1971) Bull. Acad. Pol. Scz., Ser. Sci. Chim.,19, 771. Guminski, C. and Galus, 2;. (1977) J. ~ f e c t r o a n aChem., ~. 83, 139. p. 1395. Guminski, C. and Galus, Z. (1986) Metals in ~ e ~ c u ~ ~ Solubility Data Series, Vol. 25, C. Hirayama, ed., Pergamon, Oxford. Guminski, C. and Galus, 2. (1992) I n t e r ~ ~ ~ aCl lo~~c p o u n ~ in Mercury, Solubility Data Series, Vol. 51, J. G. Osteryoung and M. N. Schreiner, eds., Pergamon, Oxford. and Galus, Z. (1983) J . Hartmann, H., Ensselin, IF. and Wunderlich, F. (1959) Z. E r ~ b e r ~ b aMetallhuttenw., u 12, 374, 437, and 537. Hurne-Rothery, W. (1936) Phil. Mag., 22, 1013. Iandelli, A. and Palenzona, A. (1979) ~ u ~ d b oono the ~ Physics and ~ l ~ e m ~ sof ~ rthe y Rare ~ a r t h s , K. A. Cschneidner and L. Eyring, eds., Vol. 2, Ch. 13, NorthHolland, Amsterdam. l Janng, G. (1965) et all., 18, 442. Janng, G. and Bach, H. (1961) ~ u e c k ~ ~ i fand ~er A m a l g a ~ ~ ~ e t a l l u r gi~ne ~ a ~ d b ~ i cder h Technische ~lektrochemie, Band 1, Teil 1, Akademie Verlag, Leipzig, 592. Keeling, L., Charles, S . W. and Popplewell, J, (1984) J. Phys. F., 14, 3093. Kirchmay~,H. R. (1965) Z. Metallk., 56, 767.
Korshunov, V. N. (1 990) Amalgam Systems, Moskovskii Unsversitet, Moskva, Ch. 2 and 9 (in Russian). Kozin, L. F. (1964) Ph.ysi~o-cher~~ca1 F~~ndamen~als oj Anzalgam Metallurgy, Na~il~a, Alina-Ata (in Russian). Kozin, L. F. (1970) A ~ a ~ g a~m e t a l ~ u r gTekhnika, y, Kiev (in Russian). Kozin, L. F., Nigmetova, R. Sh. and Dergacheva, M. B. (1977) T1~ermodynamic.s of Binary Am&am Systems, Nauka, Alma-Ata (in Russian). Kozin, L. F., Sarmuzina, R. G. and Popova, T. V (1981) Tr. Inst. Org. Kutal. Elektrochim. Kaz. Akud. Nauk, Kozlovskii, M. T., Zebreva, A. I. and Gladyshev, V. Amalgams and Their ~ p ~ l i c a t i ~ )Nauka, ns, Alma-Ata (in Russian). Ladika, S. (2001) Science 292, 64. Labiri, S. K, and Gupta, D. (1980) J . Appl. Phys., Lee, J.-Ch., Kang, D.-Y., Park, D.-H., Ham, J.-K., and Aono, &$.-A. (1997) Proc. 5th lnt. Con$ P~iip.Appl. Dielectr. Mater., Institute of Electrical aiid Electronic Engineers, New York, 1, 154. Luborsky, F. E. (1961) J. Electrochern. Soc., 108, 1138. Massalski, T. R., Subrainanian, P. R., Okainoto, €3. and Kacprzak, L. (1990) Binary Alloy Phase D~agr~ms, 2nd ed., ASM, Materials Park, OH. Mayer, I., Shidlovsky, 1. aiid Yanir, E. (1967) J. Less-
Singb, R. M. and March, N. H. (1995) in rnter~nefallic Co~t~ouP i ~r ~i n~~: ~ ~and l e ~Practice, Vol. 1, Wiley, Chichester, IJK, p. 661. Siniriiov, V. A. (1970) Reduction with A m a l ~ a Khimiya, ~~, Leningrad (in Ruswan). Sudarshan, T. S., Lim, M. H., Nefley, P. L. and Thornpson, J. E. (1984) J. Appl. Phys., 56, 2236. ture Suzuki, T. and Mutoh, I. (1992) High T ~ ~ F ~ ~ e r aCorroszon of Advanced ~ c t t e r z ~and l s Protecfive ~ o u ~ i n gV. s , Saito, Ea. Onay and T. Maruyama, eds., Elsevier, Amsterdam. Takacs, L. (2000) J. of ~ e t ~Jan. l ~p., 12. Tamaki, S., Waseda, U,,Takeda, S. and Tsuchiya, Y. (1982)
Tammann, G. and Jander, W (1922) Z. Anorg. Chem., 105. T a m ~ a n n G. , and Scbafmeister, P. (1925) 139, 219. Tammann, G. and Kollman, K. (1926) Z.Amrg. Ctzem., 269. ~s Tomashik, V. N. and Grytsw, 'v. I. (1982) State ~ i a g r a m of Systetm Based on A"Bvl S e ~ ~ c o ~ ~ ~ C~~mI~ounds, uci~3r Naukova Dumka, Kiev (in Russian). Venetsky, S. (1981) Tales about ~ e t a l s , Villars, P. (1997) Pearson's Handbook of Alloys, ASM Intl,, Materials Park, OH. Mercury Cadmium Telluride Material Properties Database Waterstrat, R. M. and Okabe, T., Ch.27 in Interme~allic (1999) Advanced Materials and Processes Technology Compounds: Principles and Practice, J. HI. Westbrook and Information Analysis Center, 201 Mill Str., Rome, N.Y. R. L. Fleischer, eds., Wiley, Chichester, UK, Vol. 2, Nugent, L. J. (1975) J. Znorg. Nucl. Chem., 34, 1767. p. 575. Orlov, V. A. (2001) Addressing the Challenge of Illicit Weeks, M. E. (1968) Discovery c?f' the E l e ~ ~ n7th t ~ edn. ~ , J. Niiclear Trafficking, in Symp. How ro Harnzonize Chem. Educ., p. 46. Peaceful Uses of Nuclear Energy and N o n - P r o l ~ ~ ~ r u ~ i o nWestbrook, ~, J. H. (199.5) Ch. 31 in I n t e ~ ~ e t a l l iCom~ound~s: c Japan Atomic Industrial Forum, Tokyo, Japan, 12 pp. ~ r ~ n c i p l eand s Prctctice, J. H. ~ e s t b r o o kand R. L. Otto, G. H. (1984) European Space Agency Rep. ESA SPFleischer, eds., Wiley, Chichester, UK, Vol. 2, p. 645. 219, p.43. Westbrook, J. H. (1986) Encyc~o~edia of ~ ~ ~ eScience r ~ ~ l s Proceedings of the 1989 U S . Workshop on the Physics and and ~ngzneering.M. B. Beyer, Ed., Pergamon, Oxford, Chemistry of Mercury Cadmium Telluride and Related p. 2548. 11-VI compounds, 3-5 October 1989, San Diego, CA. Windle, P. L., Popplewell, J. and Charles, S. W. (197.5) IEEE Rosa. C. J., Sonimer, F., Rupf-Bolz, N. and Predel, B. (1981) Trans. Mugrzet., 11, 1367. Z . M e t ~ l l k72, . ~ 47. ns ~ e ~ ~ l Yatsenko, s. P. (1974) ~ctllium- ~ n t e r a c ~ ~ owith Samhoun, K. and David, E; (1979) J . Inorg. Nucl. Chem., Nauka, Moskva (in Russian). 357. ~ ~~pp~ications, ~ e s Yatsenko, S. P. (1987) I n d i u ~- ~ r o ~ e and Schuster, W. (1986) 4th Intl. Symp. of Science and Technology Nauka, Moskva (in Russian). of Light Sources, U. of Karlsruhe, Karlsruhe, G e ~ a n y , Young, P. Irtdustr. Phys. 1999, no.4, 40. p. 263. Zebreva, A. 1. (1958) Vesfn. Akacl. ~ a Kaz.~ SSR, ~ no..1 1 , Sheniyakm, V. S., Rrik, K. A., Bukman, S. P. and Karasev, M. A. (1979) Zzv. Akad. Kaz. SSR, Ser. K h m No. 3, 73. 88.
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Chapter 3 eryElides Loren A. Jacobson, Robert J. Hanrahan, Jr. and James L. Smith Los Alamos National Laboratory, Los Alamos, N M , USA
1. Introduction Forty years have passed since the first major investigation of beryllide intermetallic compounds was conducted, and this early work was based primarily on the high melting points and excellent oxidation resistance associated with these materials. This work, which was sponsored by the United States Air Force over the time period March 1956 to December 1961, was performed by the Brush Beryllium Company (Booker et al., 1962). Oxidation rate results were reported for various beryllide compounds including TaBe,,, Ta,Be,,, ZrBe,, and Zr,Be,, over the temperature range from 2300" to 2750 "F. Ternary systems of beryllium and silicon with molybdenum, niobium, tantalum, tungsten and zirconium were also studied. A mixed phase material with the stoiclziometry MoBeSi proved to be the most promising ternary system, but very little follow-up work was done to exploit the outstanding high temperature oxidation resistance and strength properties that were measured for these beryllium-containing intermetallics. G. V. Samsonov (1966) published an extensive compilation of beryllide properties. This article, which was condensed from a larger monograph, discusses the beryllides as they form with the elements in groups across the periodic table. Some phase diagram information is presented, and there are 179 references to other work. One revealing statement in this review has to do with the peculiarities of the electronic structure of the beryllium atom. The normal electronic configuration of beryllium is 1s22s2 but in solid beryllium and its compounds there can be a single s to p promotion, giving a configuration of ls22s2p, and it is the sp configuration that brings about the
formation of covalent bonds between beryllium atoms, particularly in the lattices of its intermetallic compounds (Samsonov, 1966). In the late 1980s, renewed interest in the beryllide intermetallics was generated in part by the National Aero-Space Plane project. In 1995 a review volume by Dudley and Desai (1995) compiled the data available up to that time. This review is very thorough and presents the available property data including mechanical properties and oxidation behavior, as available, for compounds beginning with CrBe, and ending with Zr,Be,, + Ta,Bel,, arranged in alphabetical order. The presentation is detailed, including many charts and graphs, and the reader is referred directly to the review for information on specific compounds. Updated tabular data on many beryllides is given in Tables 1 to 3. Other unusual physical and structural properties that these compounds exhibit have contributed to the renewed interest in the beryllide intermetallics in the 1990s. For example, beryllide intermetallics with actinide metals exhibit unusual superconducting properties based on a solid-state entity called a heavy fermion, more generally described by Aronson and Coies (1994). Several other efforts to investigate the structure and properties of beryllides have also been conducted with the aim of developing better understanding of the behavior and potential of these materials. This chapter will first describe the various types of beryllide intermetallics that have been characterized, then will summarize the information that is presently available on mechanical, chemical, thermal, magnetic, and other physical properties of these materials. Methods of synthesis will be treated, and the chapter will conclude with some possibilities for application of beryllide intermetallics toward the
Intermetallic Compounds: Vol. 3, Principles and Practice. Edited by J. H. Westbrook and R. L. Fleischer. 0 2 0 0 2 John Wiley & Sons, Ltd.
38
Structure and Composition
Table 1 Physical constants of beryllides of Group IVRVIIB elements Beryllide
Crystal Structure Lattice Parameters Pearson Symbol a, c (A) -__ CrBe, hP12 4.260, 6.988 CrBe,, tI26 7.23, 4.173 HfBe hP3 3.787, 3.1 59 HfBe hP6 4.534. 3.471 cF112 10.00 HfBei3 a-Hf2Be,, hR1Y 7,494, 10.93 hP38 7.44. 7.38 P-Hf,Be,, MnBe, hP12 4.231, 6.909 MnBe, 5.931 cn4 MnBe,; tI26 7.276, 4.256 4.89 Mo,Be cP8 MoBe, hP12 4.433. 7.341 MoBe,, tI26 7.271, 4.234 11.636 cFI84 MoBe2, tPlO 6.49, 3.35 Nb,Be, NbBe, cm4 6.535 MBe, hR12 4.561, 21.05 hP6 NbBe, N/A tI26 7.376, 4.258 NbBe,, hR19 7 409, 10.84 NbzBe,, ReBe, hP12 4.354, 7.101 ReBe, N/A N/A ReBe,, N/A NIA cF24 N/A Re0 9zBe1, 11.54 cF184 ReBe,, 6.010, 4.89 t112 Ta,Be 6.50, 3.32 tPlO Ta,Be, 6.51 TaBe, cF2.4 4.53, 20.95 hR12 TaBe 7.334, 4.267 TaBe,, tn6 hR19 7.388, 10.74 Ta2Be,, , CP2 2.94 TiBe (metastable) 6.450 TiRe, cn4 4.49, 21.32 TiBe, hR12 TiBe,, 7.35, 4.19 tn6 7.392, 10.79 hR19 a-Ti,Be,, 7.36, 7.30 hP38 fi-Ti,Be,, VBe, hP12 4.394, 7.144 t126 7.278, 4.212 VBe,, 4.446, 7.289 hP12 WBe, 7,362, 4.216 tI26 WBe,, cF184 11.628 WBe2, 3.82, 3.24 ZrBe, hP3 4.564, 3.485 ZrBe, hP6 10.047 C F I 12 ZrBe,, 7.548. 10.997 hR19 Zr,Be,,
Melting Temperature Specific Gravity (K)
solution of several challenging technological problems. Finally, some general comments are made regarding the toxicity of beryllium, and beryllium-containing alloys and compounds. In the year of writing, 2000, this is one of the primary reasons why this promising class of materials has not been more thoroughly investigated.
-21 10 - 1610 1603+60 1858+ 10 1963+ 10 2043 70 2043 & 70 N/A N/A N/A 1173&100 2300 & 200 1973 (?) 1573 I863 19033.30 2353 f 50 N/A 1945+5 2073-50 N/A N/A N/A N/A N/A > 1300 N/A <2070 N/A 2123 +28 2263 t28 N/A 1623& 50 1723+50 1823+60 1943+50 1943+50 N/A N/A c 2520 <2020 N/A 1510 1750 2200$.28 2255 & 28
+
4.34 2.44 8.322 6.006 3.93 4.66 4.66 4.494 N/A 2.40 8.425 6.12 3.02 2.51 NIA 5.28 4.72 N/A 2.88 3.28 11.632 N/A N/A N/A 3.38 N/A 13.270 9.79 8.19 4.18 5.05 N/A 3.27 3.01 2.26 2.43 2.42 3.834 2.37 10.2 4.57 3.27 4.32 3.60 2.72 3.05
Ref. 3,4 5 6.31 6,3 1 6,31 6,3 1 6,31 3 Okamoto and Tanner (1987) 5 7 396 9,lO 7,ll 12,153 6,13,30 13,145 Okamoto and Tanner (1987) 5,30,60 14,30,73 3 Okamoto and Tanner (1987) Okamoto and Tanner (1987) Okamoto and Tanner (1987) 11,15 16 6 5,6 6 3,4,60 6,60,73 Okamoto and Tanner (1987) 3,4,31 6,3 1 6,17,31 6,17,31 6,17,31 3 5,17 3 5 7,11 18 19 20,32,60 19,21,73 (Numbered references from Dudley and Desai (1995))
2. Types of Beryllides and their Structure
2.1 MBp,, This compound has a cubic structure, based on the ZrZn,, analog. The Pearson symbol for this structure is cFI84 and the space group is Fd3m. Examples are the compounds WBe,, and MoBez2.
39
Beryllides Table 2 Physical constants of reported beryllides of group VIII elements __
Beryllide CoBe CoBe,, (metastable) &(Co2Be17?) p' (metastable)
c Co5Be2, Fe,Be FeBe, FeBe, eFeBe, FeBe,,, IrBe IrBe, IrBe, 1r2Be17
Ni,Be (metastable) p' NiBe Ni,Be,, OsBe, (metastable) OsBe, Os,Be,7 Os,Be OsBe Pd,Be Pd,Be, Pd,Be, PdBe PdBe, PdBe,, Pt,,Be PtBe Pt,B% PtBe, PtBe,, RhBe RhBe, RhBe6.6 Rh2Be17 Ru,Be, RuRez Ru3Be1, Ru,Be,, Ru,Be,, RuBe,, RuBe,
Pearson Symbol
Lattice Parameters
cP2 tI26 hP19 CR
2.611 7,237,4.249 4.128.10.717
cR?
2.658,3.16 8.3783,13.7652 7.6136& 1.525
hP96 cI52 & c9-416 cFl6 hP12 cn4 hP19,h P48?
Melting Temperature (K)
Specific Gravity
6.307
N/A
N/A
2.49
4.221,6.848 5.890
4.632 3.298
4.193,10.89
5.38
2.611 7.62& 1.53
6.248 3.688
11.342 4.221.10.94 11.350,10.628,8.4803
6.586 5.27
2.819 5.994 7.271,4.251
8.54 4.670 3.169
CP2 cI52
2.80
N/A
~$24
6.004 7.237,4.252 2.7397
4.521
tetragonal
cP2 hP7 tP
cP2 cI52 & cF416 hP* hP12 ell60 hP? mP7 N/A N/A N/A
CP2 cn4 1126
N/A
hP*
1126 cP2
NIA
N/A
hP*
hP7 cI80
hP12 CP
cl160 hP?
4.191,10.886 4.203.10.90 1.142 5.96,9.18 11.03 11.337 4.2036.10.90
hP*
mP*
2.2 MBe13
This compound has a face-centred cubic structure with 112 atoms in a unit cell, the binary prototype of which is NaZq3. The Pearson symbol for this structure is cF112 and the space group is Fm%. The metals Mg,
N/A N/A
3.60
4.158 3.54 N/A N/A
Ca, Pu, Sb, Sc, Sr, Zr, Hf and Y form compounds with beryllium that have this structure, as do all of the lanthanide and all of the actinide series metals investigated to date. This structure is illustrated in Figure 1, which also depicts various coordination arrangements for the different types of atoms.
Structure and Composition
40
Table 3 Physical constants of rare-earth and selected actinide beryllium compounds Beryllide Pearson Lattice Melting Specific Symbol Parameters Temperature Gravity (A) (K)
- _ _ _ _ _ _ I
CeBe,, DyBe13 ErBe,, BuBe,, GdBe,,
HoBe,, LaBe,, LuBe,,
NdBe,, NPB% PrBe,, PuBe,, ScBe, ScBe,, SmBe,, ThBe,, ThBe,, TmBe,, UBc,, YBe,, YbBe,3
cFll2 cFl12 cFt 12 cFI12 cF112 cF112 cF112 cF112 cF112 cFll2 cFl12 cF112 hP6 C F I 12 cFl12 cFl12 cFl12 cA12 cF112 cF112 cF112
10.376 10.237 10.209 10.291 10.280 10.221 10.456 10.173 10.355
3.060 3.463 3.551 3.280 3.361 3.509 2.979 3.686 3.128
found in the scandium, niobium, hafnium and zirconium systems. Other MBe, compounds with AuBe, (cF24) structure include tiose where M = CO, Fe, Pd, and Pt. 2.6 MBej This type of compound exists in a number of different crystal structures. In the Cu-Be system, the structures have Pearson symbols cF24 and hP3. In the Ti and Nb systems the compound has a crystal structure with the Pearson symbol hR12. These compounds have not been very well investigated.
N/AN/A 10.368
3.076
2.7 MBe,
N/AN/A 4.55,3.500 10.102 10.304 10.252 10.395 10.193 10.256 10.238 10.184
2.382 2.089 3.249 3.404 4.169 3.588 4.371 2.552 3.650
These phases are generally Laves phases, and can have all three of the crystal structures that are members of this group, Cubic C15 (cF24), Hexagonal C14 (hP12) and C36 (hP24). Most of the work on these phases has been related to their potential for storing hydrogen, and their unusual magnetic properties, as will be discussed later on. Representatives are found in the Ti, Cr, Cu, Fe, Hf, Mn, MO, Nb, Ta, Ti, V, W and Zr systems.
2.3 MBe,,
This type of compound is the D2, body-centered tetragonal in structure with 26 atoms in a unit cell, and with a binary prototype of ThMn,,. The Pearson symbol for this structure is t126. The metallic elements Ag, Au, Cr. Mn, MO, Nb, Pd, Pt, Ti, V and W are known to form beryllides with this stoichiometry and structure. The structure is shown in Figure 2. 2.4 M2Be17
This compound can exist in two crystal structures, a hexagonal lattice with the Pearson symbol hP38 (i.e. with 38 atoms per unit cell), and a rhombohedral structure, hR19. Two compounds, Ti2Bel7and Hf2Be17 are known to exhibit both structures, while Nb, Ta and Zr beryllides of this type appear to exist only in the hR19 form.
2.8 MBe These compounds generally have the CsCl or B2 crystal structure. The most extensively investigated compound with this structure is NiBe, which will be discussed more thoroughly later. The Be-Co and BeCu systems also have stable compounds with this composition. Another example of this structure was found in the Ti-Be system where a metastable ordered B2 phase formed on devitrification of amorphous alloys that were obtained by quenching melts of approximately the eutectic composition between the metal and the nearest stable beryllide, TiBe, (Tanner and Giessen, 1978). Two additional metastable compounds of the MBe stoichiometry were found in the Zr-Be and the Zr-Hf systems, where the ordered structures were determined to be the orthorhombic B,, or the CrB structure type (Tanner and Ray, 1979; Tanner, 1980).
2.5 MBe, This type of compound, with the CaCu, type D2, structure with a Pearson symbol hP6 has been observed in beryllium metal as an impurity phase, but has not been investigated as a single-phase intennetallic. Representatives of this compound are
2.9 Other Compounds and Phases There are several other beryllide intermetallics, none of which has been extensively studied. Such compounds include Nb,Be,, Mo,Be, BeFe, (D03, cF16 cubic), compounds in the Be-Co and Be-Fe systems with
Beryllides
41
Figure 1 Metal-beryllium,, structure. A. The overall arrangement of the 112 atoms in the unit cell. Note the FCC symmetry for Type I Be atoms. Atomic sizes are not to relative scale. B. Coordination of Type I Be atoms about the metal atom. Atoxrnc sizes are drawn to scale. C. Coordination of Type I1 Be atoms about a Type I Be atom. Because of the difliculty of visualivng this coordination, D. shows the same arrangement of atoms with the Type II Be atoms at half their actual diameter. E. Coordination of Type 11Be atoms about the metal atom. Agam it is difficult to visualize the actual arrangement, so F. shows the coordination with half of the Type II Be atoms removed. In G the metal atom has been scaled to the size o€ the hole within the polyhedron of Type I1 Be atoms. The radius ratio for the metal atom to the hole radius IS 1.1/1.9
42
Structure and Composition
Ni-Al-Be system, compositions based on the L12 phase Ni,(Al,Be) also showed the presence of Ni solid solution and the B2 phase NiBe (Matsuo et al., 1994). Good room-temperature ductility was found for the alloy Ni-20 at%Al, 10 at%Be. Much more useful work could be performed to investigate multicomponent beryllide phases and alloys based on them. 3. Properties of Beryllides 3.1 Mechanical Properties Figure 2 The MBe,, (tI26, I4/mmm) structure illustrating the body-centred tetragonal symmetry. Note the similarity to the MBe,, structure shown 111 Figure I
uncertain stoichiometry, and compounds in the Be-Pd, -Pt and -Ru systems. An unusual feature of the MBe,, and the MBe,, compounds is the extensive solubility of other elements that can form one or another of these phases, probably due to the stiffness of the beryllium sublattice cages, which can accommodate other metals. It was observed that dilute alloys of beryllium with titanium in the 1-2 weight percent range, processed by centrifugal atomization, had unexpected impurities of vanadium, zirconium and molybdenum, some of which originated with the starting materials, and some from the process (Jacobson et al., 1991). The impurities were all concentrated in the particles of TiBe12,and no other phases were found, despite the fact that the lowest metal concentration beryllide for zirconium is ZrBe,,, and for molybdenum, the lowest metal concentration phase is MoBe,,. Other observations of this phenomenon were made by Brimhall et al. (1992) who found that in sputter deposited alloys with both Nb and Zr, which form NbBe,, and ZrBe,, respectively, the compound phase was always MBe12 when the Nb concentration exceeded the Zr concentration, and was MBe,, when Zr was in the majority. It was also observed that on annealing at elevated temperatures the phases (Nb,Zr)Be,, + (Nb,Zr),Be17 or (Nb,Zr)Be,, +(Nb,Zr)2Be,, were present. In no case was the coexistence of (Nb,Zr)Be,, and (Nb,Zr)Be13observed. Samsonov (1966) refers to work on the ternary UTh-Be system in which there is a continuous phase between UBe,, and ThBe13.One can perhaps assume that this observation would hold for other pairs of elements in MBe,, and MBe13 intermetallics. Interesting work on a multi-phase system containing two phases that involved beryllium showed that in the
3.1.1 Elastic Properties
It should be noted that the elastic moduli of the beryllide intermetallics are quite high and compare very favorably with other high-temperature intermetallics (Fleischer et al., 1989; Fleischer, 1991). The low densities of these compounds, coupled with the high elastic moduli, result in truly remarkable specific moduli, generally higher than most other intermetallic compounds. While the characteristic of high specific modulus may be useful for stiffness-limited structural applications, it may be counterproductive in the context of fracture toughness, which is generally thought to be proportional to the reciprocal of the elastic modulus, and in the prospects for lowtemperature ductility, for which the possibility of a large Burgers’ vector and a high shear modulus may lead to more brittle than ductile behavior. 3.1.2 High-Temperature Strength
The refractory metal beryllides of the compositions MBe13,MBe12and M2Be,7have unique combinations of properties that include good high-temperature strength, oxidation resistancc, and low density. For example, the strength (modulus of rupture) of Ta,Bei7 at 1060°C is 420MPa, and its density is 4.99Mg/m3. At the same temperature the strength of Incone1825 is only 42 MPa, at a density of approximately 8 Mg/m3. The strength to density ratio for the beryllide is thus about 16 times that of the nickel-base alloy, at temperature. One of the high-strength nickel-base alloys, Inconel 718, has a comparable strength to density ratio, but at a lower temperature of 760°C. Unfortunately, the beryllides have poor ductility and toughness at ambient temperature, which is believed to be related to their complex crystal structures, that were described above. Thus, their potential usefulness in engineering structures is presently quite limited.
Beryllides An interesting exception is the CsCl (B2) structure beryllide, NiBe. Samples of different stoichiometry were prepared by casting, and hardness was measured as a function of composition (Nieh et al., 1989). A minimum was found at the stoichiometric composition, similar to the aluminides NiAl and CON, which have the same crystal structure. Some roomtemperature ductility was inferred from the fact that there was no cracking associated with hardness indentations. Later work on extruded NiBe (Pharr et al., 1991) showed that the strain to failure at room temperature is 1.3% in tension and 13% in compression, with failure controlled primarily by the cohesive strength of grain boundaries. At temperatures above 400°C strains of 30% in compression could be achieved before failure, and the strength levels at elevated temperatures compared favorably with those of NiAl, but they were somewhat lower than CoAl strengths (and CoAl is brittle at room temperature).
3.1.3 Hardness und Ductile-Brittle Transition Temperature Several investigations have been performed on the relationship between hardness and test temperature for many of the interesting beryllide mtermetallics. Fleischer and Zabala (1989) measured the hardness of Nb2Be17,ZrBe,,, NbBel, and TiBe,,, and at 1000 "C the hardnesses were 9.5, 6.0, 5.8 and 4.7GPa, respectively. These hot hardness levels compare favorably with many other intermetallic compounds that are presently being investigated for possible high temperature application. For example, the compound NbCr, has a hardness of about 6.5GPa at 1000°C (Fleischer and Zabala, 1990). The data of hardness vs. temperature for these beryllides did not give a clear indication of a ductile-to-brittletransition temperature (DBTT), but from an observation of the absence of cracking associated with the hardness indentations, the temperatures were estimated to be 1050, 840, 1000 and 840"C, for the four compounds in the order of decreasing hardness listed above. An investigation of the hardness of three of these same beryllides, and substituting TaBe12for TiBe,,, was also performed at different temperatures (Nieh and Wadsworth, 1990). The materials were prepared by vacuum hot pressing, and hardness samples were sectioned directly from the hot pressed materials. These investigators found that by plotting the logarithm of the hardness vs. the reciprocal of temperature, a clearer indication of a ductile to brittle transition could be determined. Table 4 below compares the DBTT results of the above
43
investigations, along with those from Bruemmer et al. (1993).
3.1.4 Toughness and Creep
These high values for DBTT are undoubtedly sufficient to discourage the application of these complex crystal structure beryllides in low teniperature structural components. The estimate of 750 "C for the DBTT of VBelz by Nieh comes from a more extensive study of this compound which measured room temperature properties, including fracture toughness, as well as elevated temperature creep behavior (Nieh et al., 1992). The fracture toughness was estimated from the microcracking associated with a hardness indentation and found to be 0.84 MPa rnl/,. Steady-state creep rates were compared for vacuum hot pressed and hot isostatically pressed material for different stress levels at 1100°C and 1150 "C. At low strain rates the stress exponent was found to be near 4, consistent with dislocation climb as the rate-controlling mechanism. This is similar to the stress exponent found for other intermetallics such as TiAl, Ti,A1, NiAl and CoAl. At higher stresses the power law appears to break down. At low strain rates the creep activation energy was found to be 270 kJ mol- l, which again is close to the activation energies observed for the other intermetallic compounds. Nieh and co-workers (Nieh et al., 1993) have also investigated the creep behaviour of the beryllide NbzBe17.Again using the microcracking associated with a hardness indentation, the room temperature fracture toughness was found to be 1.1MPam1!2. For this compound, the stress exponent for steady-state creep was found to be close to 3, a value that is associated with dislocation glide as the rate-controlling mechanism. The activation energy was determined to be approximately 575 kJ mol-', a value which is higher than that found for other beryllides. It was not possible Table 4 Ductile-brittle transition temperatures for several beryllide intermetallic compounds Compound
TiBe,, NbBe,, Nb,Be,, ZrBe,, TaBe,, VBe,,
DBTT, "C DBTT, "C DBTT, "C (Fleischer and (Nieh et al.) (Bruemmer et al., 1993) Zabala, 1989) 840 1000 1050 840
770 815 740 790 750 (est.)
700 955
690
44
Structure and Composition
to associate this activation energy with any specific diffusion process because of the lack of data for the compound. Observation of the absence of intergranular crack formation after 15% deformation in creep was also cited as evidence for dislocation glide as the rate-controlling mechanism. This brings us to the concluding part of this discussion of mechanical properties of beryllides, in which we summarize the results of several research efforts done jointly by Battelle-Pacific Northwest Laboratories, and Washington State University (Bruemmer et al., 1992; Henager et al., 1992, 1993; Sondhi et al., 1993). These studies have shed some important new light on deformation mechanisms and dislocation structure in the niobium beryllides, NbBe12 and Nb2Be17.For the former compound, dislocations were observed to be partials bounding planar faults, with slip systems that were identified as 1/2(101){121}, 1/2(101){101) and 1/2(100){011>.The partial dislocations were related to the possible phase transformation from NbBe,, to Nb,Be,, (the latter structure is very closely related to the former) and could account for enhanced dislocation mobility and the promotion of high-temperature deformation. Atomistic modeling has been performed for a[lOO] edge and screw dislocations, and an a/2[1001 screw dislocation (Sondhi et al., 1992). Other results of these investigations compare favorably with prior measurements; in particular it was found that the room-temperature fracture toughness of NbB,, was 4MPam1/,, which is higher than that measured by other investigators. In general, it was found that hot isostatic pressing (HIP) gave better properties for this compound; but intermediate temperature tests revealed that intergranular enbrittlement may be present in HIPed material. Twinning modes in vacuum hot-pressed and HIPed NbBe,, were also investigated by these workers (Charlot et al., 1991), who found that twins and extended faults have (101) habit planes and (011) twinning directions, while shorter range faults have an (001) habit plane. This extensive collection of work should be consulted by future investigators into the mechanical behavior of the MBe12 intermetallic compounds. 3,2 Oxidation and Thermal Properties
The oxidation behavior of beryllides is enhanced by the fact that beryllium forms a protective oxide, BeO, which has two allotropes of which only the alpha phase is usually observed. Doychak (1994), Brady and Doychak (1999) provide a comparison between some
thermodynamic and oxidative measurements of beryllium and other metal/oxide systems. Among the beryllides are some of the highest melting intermetallic compounds, as well as some of the lowest density refractory metallic phases. These densities range from 2 to 4Mg/m3. Despite the attractive properties of beryllides, only a handful of studies on the oxidation of these compounds has been conducted since the 1960s. In addition to the serious safety issues which must be dealt with in order to work with beryllides, there are two technical reasons which are often cited to explain the dearth of research into the oxidation of beryllium compounds. Historically, the majority of the research was conducted on complex line compounds, all of which were brittle to very high temperatures. This may have contributed to a decision not to pursue these efforts further. Most significantly, however, the few studies which were published on the oxidation of beryllides found significant problems of intermediate temperature disintegration and/or oxide volatility in the presence of water vapor. The reaction between beryllium oxide and water vapor at elevated temperatures (Stuart and Price, 1964) may be simplified as: BeW) -I-H20(g) = Be(OH),(g) This reaction has also been implicated in the accelerated oxidation of beryllides at intermediate temperatures (a 'pest' reaction, for example see Doychak, 1994), and at high temperatures (Aitken and Smith, 1962: Perkins, 1963; Dudley and Desai, 1995). A review of the effects of moisture on the oxidation of beryllides is provided by Hanrahan (1999). Based on both the early data and recent work on the compounds TiBe,,, CrBe2, and alloys of NiAl and Be, he concludes that the effects of water vapor on compounds that form continuous Be0 scales is only significant at temperatures above 1100"C. The rates observed are comparable to the Si0,-H,O reaction (Opila, 1999), hence in stagnant environments and/or low partial pressures of moisture, beryllides might be successfully employed at considerably higher temperatures. Nonetheless, this may be considered the upperuse temperature for beryllides exposed in moist environments. Why should we be interested in beryllides today? The simplest answer is that for some applications, there are no other materials with the properties of beryllium and the beryllides. The problems that have been observed in studies of the oxidation of beryllides were based on a very limited amount of work, which did not eliminate possible improvements through
45
Beryllides
alloying additions. In fact, some early reports show that minor alloymg additions could result in dramatic improvements (Paine et al., 1963; Perkins, 1963) although this information has somehow been overlooked in recent years. Finally, the beryllides deserve further investigation in order to understand the properties of beryllium modified intermetallics. Such materials may very well represent the last and best available options for improving both the mechanical and oxidative properties of this class of compounds. Hanrahan et al. (1998,1999) have demonstrated that alloys based on NiAl with beryllium substituted for aluminum will form a previously unreported protective oxide, chrysoberyl BeOAI,O,. This phase is orthorhombic, with an oxygen sublattice that is very similar to that of alpha alumina. Unlike alumina, chrysoberyl is only observed in the highest density allotrope, therefore it is not surprising that the alloys that form continuous chrysoberyl scales actually demonstrate significantly better oxidation resistance than even binary NiAl at temperatures up to at least 1100°C. The addition of Be to NiAl also improves the creep resistance and hardness of NiAl, although it does appear to increase the DBTT (Levit, Hanrahan and Noebe, unpublished work).
3.3 Magnetic and other Physical Properties Beryllide intermetallics have many unusual properties, and this includes electrical and magnetic properties. For example, the compound TiBe, was claimed by Matthias et al. (1978) to be an itinerant antiferromagnet. The ‘itinerant’ qualifier was based on the fact that the elements that make up the compound display no local magnetic moments in their metallic alloys and compounds. However, the cubic (cF24) Laves phase, TiBe,, does have an inverse magnetic susceptibility that increases with increasing temperature, shows metallic behavior in its increase of electrical resistivity with increasing temperature, but was later recognized not to be an antiferrornagnet.The compound has been studied with ternary alloying additions such as copper (Giorgi et al., 1979) and gallium (Giorgi and Stewart, 1982). Modeling of the structure predicts further anomalous behavior of TiBe, in high magnetic fields (Yamada and Terao, 1998). The misinterpretation of TiBe, as an antiferromagnet occurred because it was one of the first of many compounds in which at very low temperature, the electrons exhibit highly correlated behavior; that is, no simple model can predict the behavior.
The most extreme example of a highly correlated electron compound also contains Be. The compound UBe,, has been found to be an unconventional superconducting material (Ott et al., 1983). Earlier work on the magnetic properties of UBe,, had assumed that because of the large U-U distance in this compound of 5.13 A, the uranium ions had a tetravalent configuration with two well-localized Sfelectrons. The specific heat of the compound was observed to increase with decreasing temperature from above l S K , and strong diamagnetic signals were observed below 1K. However, the possibility of bulk superconductivity was discarded, and the results were ascribed to precipitated uranium filaments in the bulk samples. It was subsequently found by Ott et al. (1983) that UBe,, was indeed a genuine superconductor, albeit a very unusual one. Single crystals were grown by slowly cooling U and Be in a flux of aluminum. The temperature dependence of the resistivity of the single crystal sample is shown in Figure 3, also from the work of Ott et al. The magnetic susceptibility measurements were consistent with an electronic system that could be described as a Fermi liquid. (A Fermi liquid is just the next step after the simple free electron gas, which shows that interactions between electrons are making the properties more complicated in the same way that a liquid is more complex than a gas.) And that the presence off electrons is essential for the occurrence of superconductivity in UBe,,. But it was the fact that the heat capacity increased to a value three orders of magnitude higher than all but one other superconductor (CeCu,Si,) that led to intense study of
*(.
0.5
0
0
I
0
50
I
1.5
I
2
26
I
......**.,.
3
I
100 150 200 Temperature [Kj
I
250
300
Figure 3 The temperature dependence of the resistivity of single crystal UBe,,, from the work of Ott et al. (1983)
Structure and Composition
46
UBe,, around the world. Study of other compounds with similar properties suggested that the Fermi liquid had effective particles called quasiparticles, which replaced the electrons; such particles had extremely large effective mass, and hence these solids were called heavy Fermion materials. Soon after the Ott letter was published, additional investigation was made of other beryllides of actinide elements - NpBe,,, Npo,,,Uo 32Be13 and PuBe,,, and the same kind of heavy Fermion behavior as was observed for UBe13was noted for all these systems (Stewart et al., 1984). However, as an additional f electron is added to UBe,, by substituting Np for U, the superconductivity is suppressed, while the heavy Fermion behavior remains, and some form of itinerant-electron magnetism appears. The additional f electron for Pu leads to a Kondo-resonance type of behavior. These phenomena were summarized by Fisk and his colleagues in a later publication (Fisk et al., 1988) in which they described more of the unique features of the low-temperature normal state properties of heavy electron systems. Other related work on MBe,, compounds includes the magnetic properties and specific heat measurements of GdBe,, made by Besnus et al. (1996). The role of the Be in TiBe, and UBe,, is probably best thought of as an inert metallic spacer. Because Be has only Is, 2s and sometimes 2p electrons, these electrons cannot hybridize with d or f electrons. So when the 3d electrons of Ti or the Sfelectrons of U are spread out by the Be atoms, whose electrons cannot hybridize with those of the heavier metal, it is similar to making an insulator out of these atoms with a partially filled electron shell that is likely to possess a magnetic moment. But the Be still conducts electricity. So in a few compounds, this competition between spreading atoms out to make them magnetic but forcing them to stay electrically conducting produces properties that fascinate physicists. Only Be can perform this trick in a binary compound. It takes a ternary to do it without Be, as in CeCu,Si,. Beryllium here is so important because it has so few electrons that they cannot hybridize with d or f electrons.
growth rate of the intermetallic compound YbBe,,, f o m n g between molten Yb and solid Be, is governed almost exclusively by the diffusion of beryllium through the compound toward the liquid, and the diffusion of vacancies from the liquid toward the compoundberyllium interface. Conversely, for the lower atomic number rare-earths such as Ce or Pr the growth of the intermetallic is principally via diffusion of the lanthanide. Intermediate lanthanides such as SniBeI3grow by diffusion of both species. In all cases, lattice diffusion of both species occurs by vacancy motion on the Be sublattices. Therefore, the concentration of vacancies within a particular compound controls the mobility and hence the growth rate of the intermetallic compound. The mobile species on the other hand, is dictated by the valence structure of the particular lanthanide, and its ability to occupy (albeit temporarily) beryllium sites. Another work that deals with diffusion and beryllide intermetallics is that of Brimhall and Bruemmer (1992). They investigated the reactions between the beryllide NbBeI2and refractory metals MO,Ta, and W. Also the ceramics Sic, MoSi, and AI@, were studied. Diffusion couples were prepared between NbBe,, and the other materials, and in no case was the diffusion of other metallic elements into the beryllide observed. Rather, it was primarily the diffusion of Be from the intermetallic into the other materials that governed the interfacial reaction. with some evidence that the compound Nb2Be17 was formed due to the depletion of beryllium in the intermetallic phase. It was observed that Si from the silicon-bearing ceramics diffused into the beryllide. The extent of the reactions that were observed was considerable, and since this study was done with the possibility in mind that the beryllide could ultimately be combined with the other materials in a composite; it was concluded that some form of reaction barrier would have to be used in order to limit the degradation of the interface. It seems clear that the high mobility of beryllium at elevated temperatures is a factor that contributes to the reactivity of beryllium and high melting point beryllides with other refractory materials and molten metals. (Conversely, this also explains why relatively small alloying additions of beryllium can result in the growth of continuous beryllium oxide scales in high temperature exposure.)
3.4 D@usion
There is work at Los Alamos on the reaction rates between liquid rare-earth metals and beryllium (Kanrahan et al., 1997). The differences in diffusion behavior between the higher atomic number rare-earths (Er, Yb) and the lower members of this grouping (Ce,Nd, Sm) have been clearly demonstrated. For example, the
4. Methods of Synthesis
4.1 Powder Reactions
Most of the work on the high beryllium intermetallics (M,Be,, and up) has been performed on materials
47
Beryllides
synthesized by mixing and reacting elemental powders. This form of synthesis has the advantage of forming fine-grained, robust samples for study. However, because the reaction is usually done by grinding up the initial product and reacting and grinding it one or more additional times, there is usually a fairly significant amount of oxide included in the compound sample. One recent example of such a procedure is contained in the work of Nieh et al. (1993). The measurements are nearly always complicated by the presence of this oxide, and, to some extent, by other beryllide phases that can form when the intended stoichiometry is not maintained. 4.2 Liquid and Liquid-Solid Reactions Because of their low-temperaturebrittleness, it has not been very straightforward to prepare beryllides by melting a stoichiometric mixture of the constituents. However, it has been demonstrated that large crystals of some beryllides can be grown from a molten aluminum solution, as described below. Studies of the reaction between liquid metals and solid beryllium have demonstrated that the beryllide intermetallic phase can form, but so far this method has not been used for the preparation of specimens for further measurements of mechanical or electrical properties. The compound TiBe, can be prepared easily by arc melting. Like most C15 structures, it is quite brittle, and likely to shatter as a result of thermal shock. So making very small samples or flipping large samples and remelting while still hot are necessary. Apparently the vapor pressure of the Be is well suppressed by oxide on the surface. If there is excessive oxygen in the beginning constituents, the black powder that comes off is not Be0 but TiO, which is critical if one is trying to compensate for weight loss. If arc-melted TiBe, is melted and slow cooled in a Be0 crucible in He or Ar gas, the resulting huge grains can be cut out as unstrained single crystals. However, significant Be losses do occur on arc melting of the higher beryllides such as MBe,3. This might be explained by the lack of a protective oxide, however the results of Paine et al. (1963) show that these compounds, while reacting somewhat more rapidly than some of the lower beryllides, do form continuous Be0 scales and exhibit somewhat protective oxidation. The loss of Be upon melting of the MBel, compounds is therefore interpreted as demonstrating that the activity of Be in these compounds is considerably higher than in the lower beryllides, and may indeed be higher than that of pure Be (Smith and Hanrahan, unpublished observations).
The MBe13compounds are easily prepared by using molten aluminurn as a solvent. Stoichiometric quantities of U and Be can be dissolved in aluminum in an outgassed Be0 crucible heated to 1200°C and slow cooled to the melting point of AI. Then the A1 is dissolved in a concentrated NaOH solution, and faceted single crystals remain. The ratio of UBe,, to A1 can be as low as 1:lO. However, the quality of the crystals can be improved by adjusting the atomic ratio of U:Be:Al. A slight excess of Be helps them not to stick to the crucible. High ratios of A1 help to avoid the modest substitution of A1 on the Be sub-lattice, which is easily seen by measuring the lattice parameter. Slower cooling yields larger crystals with fewer regions of pure A1 trapped inside the large voids that form with fast cooling. So a 200-400 hour cooling of U:Be:Al in a ratio such as 1:14:200 is close to optimal. 4.3 Thermal Spraying and Sputtering
Plasma spraying of beryllium has become a wellestablished technology, and is a principal candidatefor the fabrication of first-wall components of a fusion reactor (Castro et al., 1996). There should, in principle, be no significant technological barrier to the plasma spraying of beryllide intermetallics. One reference was found for work on flame spraying of zirconium beryllide as a protective coating for Zircaloy-clad reactor fuel rods. The coating was said to improve the steam-oxidation resistance and the high temperature oxidation resistance of the rods (Unknown, 1988). The use of sputtering for the preparation of thin coatings of beryllides has been reported by Brimhall et al. (1992a). The as-sputtered coatings were initially amorphous, and the beryllide phases were formed upon elevated temperature heat treatment. 4.4 Mechanical Alloying Only one reference to mechanical alloying as a method of preparing beryllide intermetallics was found (Chou et al., 1992). The authors investigated compositions corresponding to NbBe,, and NbzBe17,starting with the appropriate ratios of elemental powders. After 72 hours of ball milling in a tungsten carbide vial, using tungsten carbide balls, the resulting powders were amorphous. The desired beryllide phase, along with minor amounts of other phases, was obtained after annealing the amorphous mixture for 4 hours at 1000 "C. In both cases, some contamination from the tungsten carbide was noted.
48
Structure and Composition 5. Opportunities for Application
5.1 Refractory Structures
The high melting temperatures and thermodynamic stability of many of the beryllide intermetallic compounds has encouraged their study as hightemperature structural materials. Unfortunately, the brittleness and low toughness of the high beryllides has not given a great deal of encouragement to the possibility of developing useful engineering materials for application even at high temperatures. However, the compound NiBe has revealed potentially useful ductility and toughness, and it is likely that useful structural materials could be developed from this compound or its alloys with NiAI. As has been discussed above, the high mobility of beryllium at elevated temperatures also suggests that there will be great difficulty associated with the use of beryllides in refractory composites; developing useful coatings containing beryllide phases may be possible.
5.2 Hydrogen Storage It has been found that three intermetallic compounds of beryllium form definite hydride phases. These compounds are TiBe,, ZrBe, and HfBe, (Maeland and Libowitz, 1983). The compound TiBe,, when heated in H2 to 375 "C at atmospheric pressure forms a limited solid solution of composition TiBezHo,os, which involves a small expansion of the cubic TiBe2 lattice. When an applied pressure of 1.5 x 104kPawas used, a hydride of approximate composition TiBe,H, was formed. However, when the pressure was lowered to atmospheric pressure, all of the hydrogen was released, indicating that the hydride was unstable, with a dissociation pressure between IOOkPa and 1.5 x 104kPa. The compound ZrBe, reacted spontaneously with hydrogen at atmospheric pressure and room temperature, to form the phase ZrBe,H, S. The dissociation pressure at room temperature was too low to measure accurately. The hydrogen content of the hydride appears to increase with increasing pressure: at 13kPa the composition was found to be ZrBe,H,,. The compound HfBe, behaves similarly to ZrBe,, but the hydrogen content is less, at a composition HfBqH,.,. Other beryllium compounds including VBe2 and ZrBes were investigated, but not found to have significant hydrogen absorption. The same was true of HfBes and TiBe,. The conclusion was that although the hydrogen storage efficiencies of the three Group IV di-beryllides were not as great as
BeH2, they still compare favorably with some of the hydrides of other intermetallics that are being investigated as hydrogen storage media, particularly on a weight percentage basis (Schlapbach, 1994). The hope was expressed that additional investigation would uncover practical ways to lower the dissociation pressure of TiBe2H, or raise that of ZrBe2H,,5so that the dissociation pressure of the hydride would fall in a range suitable for practical use. The possibility of developing a useful hydrogen storage material using a beryllide has not been investigated recently. Study of the structure of the ZrBe,H,,, phase showed that deuterium occupied tetrahedral sites in a partially ordered configuration at T = 12K, and continuously transformed to a disordered structure at T = 298 K, in which it occupied trigonal bi-pyramidal sites (Hauback et al., 1995). Hydrogen diffusion in this phase has also been investigated, with the interesting finding that hydrogen diffusion is restricted to two dimensions within individual powder particles (Kimmerle et al., 1998). Practical hydrogen storage using beryllide intermetailics could become useful. 5.3 Oxidation Resistant Coatings
Beryllide compounds may form protective oxides based on Be0 or chrysoberyl. These may be applied to service conditions up to at least 1000°C in moist exposure and possibly as high as 1500°C under dry conditions. The resistance of beryllia- or chrysoberylforming alloys to more complex environments (such as combustion environments) has not been investigated to date. The simple beryllium oxides are among the very few systems (the others being alumina, silica, and chromia) which can be grown as protective layers on metals, hence it is inevitable that some of the beryllides will be used at least as oxidation resistant coatings or bond coats on materials for high-temperature oxidation resistance, if not as structural materials. 5.4 Other Applications
The primary importance of the actinide-beryllium compounds so far has been their impact on condensed-matter physics (where they have been very difficult to understand). Now, many years after their special properties were discovered at Los Alamos, they are briefly discussed in introductory textbooks but not explained, because they are still not understood. There are some possible practical applications. As simple refrigerators are needed that can go below l K , the
Beryllides record-setting large heat capacity of UBe,, would be useful in the regenerator of a closed-cycle refrigerator. Similarly, the enormous thermopower of UBe,, can be used for thermoelectric cooling, for example in Peltier refrigerators that work close to 1K. Such low temperatures are not needed in many applications, and the thought of using U and Be in commercial products puts fear into design engineers. However, in time computers will need these temperatures in very tiny volumes, and U and Be will be used.
5.5 Ternary and Higher Order Beryllide Intermetallics It has often been observed that, in order to achieve significant improvements in the properties of intermetallics, particularly with regard to ductility, one of the most attractive approaches is to alloy with elements that may substitute for one or both of the elements in a binary compound. The expectation is that by introducing compositional defects the compound may more easily accommodate antisite defects and vacancies, possibly activating additional slip systems. This approach has only been investigated in a few beryllide systems, despite the fact that there are numerous possible systems in which ternary alloying may be tested. Many of the binary beryllides exhibit mutual solubility (e.g. the MBe,, compounds), however, in these systems the substitutions tend to be principally on the M sublattice so it is unlikely that any significant changes in physical properties will be achieved. There are, however, a large number of ternary beryllides which have been identified which may represent substitution on more than one sublattice. In addition to the B2-B2 NiAl-NiBe system mentioned above, particularly noteworthy are compounds based on the C14 and C15 Laves phases. One of the first of these identified was Be4AlFe, which has been observed as a precipitate in commercial beryllium (Rooksby, 1962) and in welded beryllium (Cotton and Field, 1997). This is a C15 phase, similar to the unusual C15 Be,Fe. The broad solubility range and stoichiometry (Okamoto and Tanner, 1987) of the latter compound (and the adjacent C14 Be,Fe) suggests that the structure accommodates both antisite defects and constitutional vacancies. Assuming this holds true for the higher order C15 beryllides, there may be a route to test the possibility of the ductilizing mechanism outlined above. Aldinger and Petzow (1979) list some 14 C14 and 3 C15 ternary beryllides (and 74 compounds in all) identified as of 1977. As of the present date, however,
49
the potential for these compounds as structural materials has remained largely unexplored. Beryllides have also been investigated as reinforcing second phases in other intermetallics. Tien et al. studied Fe-40% AI reinforced with TiBe12, ZrBe,,, TazBe17,and Nb,Be,,. They noted remarkably good compatibility between the matrix and reinforcing phases which they attributed to the formation of a reaction zone which acted as a ‘diffusional lock’ minimizing further reaction. Taksugi et al. (1986) investigated Ni,A1 modified with Be. They reported improved ductility and high-temperature strength, attributed to both solid-solution strengthening and (at higher Be levels) second-phase precipitates. Mishima et d. (1994) investigated even higher Be content alloys in the same system, and produced a series of NiBe-Ni,Al alloys. Finally, Hanrahan et al. (2000) have investigated the NiAI-NiBe system. In the middle of the NiAl-NiBe quasi binary system remarkably fine lamellar microstructures were developed which may indicate a route to improved mechanical properties. These few studies serve to illustrate the broad range of higher order beryllide systems which remain to be investigated.
6. General Comment As a family of materials, the beryllide intermetallic compounds have many very interesting properties. Unfortunately, the toxicity of beryllium for some percentage of the human population has made the safety of working with these materials a primary concern, and has discouraged investigators from working with these compounds. Thus, the many potential contributions that beryllides could make toward improved performance, particularly of hightemperature structural materials, has not been realized. We hope that the understanding of the factors that govern the toxic nature of beryllium will improve, even to the extent that chronic beryllium disease can eventually be eliminated. Then the beryllides will be able to take their long overdue place among the materials making significant contributions to the performance of high technology systems.
7. Acknowledgments The authors wish to acknowledge the support of the U.S. Department of Energy under Contract W-7405ENG-36 with the University of California. LAJ also
Structure and Composition
50
wishes to acknowledge Dr David Fanning for his help with the IDL computer program by which the views contained in Figure 1 were generated.
8. References Aitken, E. A. and Smith, J. F. (1962). Oxldation. J. Nucl. Mats., 6, 619. Aldinger, F. and Petzow, G. (1979) Constitution of Beryllium and its Alloys. Beryllium Science and Tecknology (eds D. Webster and G. J.). London, Plenum Press, 1, 235-305. Aronson, M. C. and Coles, B. R. (1994). Heavy fermion compounds. Intermetallic Compounds: Principles and Practice (eds J. H. Westbrook and R. L. Fleischer). New York, Wiley, 1, Principles, 21 1-223. Besnus, M. J., Fraga, G. L. F. and Schmitt, D. (1996). Magnetic properties and specific heat of GdBe,,. J. Alloys and Compd~.,235, 59-61. Booker, J., Paine, R. M. and Stonehouse, A. J. (1962). Investigation of Intermetallic Compoundy for Very High Temperature Applications, Technical Report No. WADDTR-60-889, part JI. Brady, M. P. and Doychak, J. (1999). High Temperature Oxidation and Corrosion of Intermetallics. Weinheim, Germany, Wiley-VCH. Bnmhall, J. L. and Bruemmer, S. M. (1992). Compatibility of hgh temperature materials with Be,,Nb. Scripta Met. et Mater, 27, 1747-1752. Brimhall, J. L., Charlot, L. A. and Bruemmer, S. M. (1992). Phase stability in Be-Nb and Be-Nb-Zr intermetallics. Mater. Sci. and Eng.. A152(1-2), 76-80. Bruemmer, S. A., Charlot, L. A., Brimhall, J. L., Henager, C. H. and Hirth, J. P. (1992). Dislocation structures in Be,,Nb after high-temperature deformation. Philosophical Magazine. A, 65(5), 1083-1094. Bruemmer, S. M., Arey, B. W., Brimhall J. L. and Hirth, J. P. (1993). Hot-hardness comparisons among isostructural Be,,X intermetallic compounds. J. Mater. Res., 8(7), 1.550-1 557. Castro, R. G., Stanek, P. W., Elliott, K. E., Youchson, D. L., Watson, R. D. and Walsh, D. S. (1996). The structure, properties and performance of plasma-sprayed beryllium for fusion applications. Phydca Scr&ta, T64,77-83. Charlot, L. A., Brimhall, J. L., Thomas, L. E. and Bruemmer, S. M. (1991). Twinning relationshp in Be,,Nb, Scripta Metall. et Mater., 25, 99-103. Chou, T. C., Nieh. T. G. and Wadsworth, J. (1992). Structural evolution in niobium beryllides dunng mechanical alloying. Scripta Metall. et Mater., 27, 881886. Cotton, J. D. and Field, R. D. (1997). Microstructural features of cracking in autogenous beryllium weldments. Metall. and Mater. Trans. A , 28A (March 1997), 673480. Doychak, J. (1994). Oxidation of Intermetallic Compounds. New York, Wiley.
Dudley, R. D. and Desai, P. D. (1995). Properties of Intermetallic Alloys III. Beryllides and Miscellaneous Intermetallic Alloys, West Lafayette, Indiana, Metals Information Analysis Center. Fisk, Z., Hess, D. W., Pethick, C. J., Pines, D., Smith, J. L., Thompson. J. D. and Willis, J. 0. (1988). Heavy electron metals: new highly correlated states of matter. Science, 239, 33-42. Fleischer, R. L. (1991) Alloys for Future Structural High Temperature Intermetallic Compounds. International Symposium on Intermetallic Compounds, Sendai, Japan, Japan Institute of Metals. Fleischer, R. L., Gilmore, R. S. and Zabala, R. J. (1989). Elastic moduli of polycrystalline high-temperature binary intermetallic compounds. Acta Metall., 37(10), 2801-2803. Fleischer, R. L. and Zabala, R. J. (1989). Mechanical properties of high-temperature beryllium intermetallic compounds. Metall. Trans. A , 2QA(7), 1279-1282. Fleischer, R. L. and Zabala, R. J. (1990). Mechanical properties of diverse binary high-temperature intermetallic compounds. Metall. Trans. A, 21A, 27092715. Giorgi, A. L , Matthias. B. T., Stewart, G. R., Acker F. and Smith, J. L. (1979). Itinerant ferromagnetism in the C-15 Laves phase: TiBe,-,Cu,. Solid State Comm., 32(6), 455458. Giorgi, A. L. and Stewart, G. R. (1982). Expansion of the Laves phase TiBe, by addition of gallium with anomalous results. Solid State Comm., 44(1 I), 1465-1469. Hanrahan, R. J., Jr. (1999). Molsture Effects on tke Oxidation of Beryllides, High Temperature Corrosion and Materials Chemistry: Per Kofstad Memonal Symposium, P. Y. Hou et al., eds. Honolulu, HI, The Electrochemical Society. Hanrahan, R. J., Jr., Butt, D. P., Chen, K. C., Taylor, T. N., Maggiore, C. J. and Thoma, D. J. (1999). High Temperature Oxidation of Ni,(AI,Be),. Elevated Temperature Coatings: Science and Technology 111, TMS, Warrendale, PA, p. 305. Hanrahan, R. J., Jr., Chen. K. C. and Brady, M. P. (1998). The Effects of Berylkm Additions on the Oxidation of Nickel Aluminide and Titanium Aluminide Based Intermetallics, The Electrochemcal Society, Pennington, NJ. Hanrahan, R. J., Jr., Zocco, T. G., Thonia. D. J., Jacobson, L. A., Lowery, J. L. and Pereyra, R. (1997). Surrogate Studies of the Pu-Be Reaction II, 21st DOE Compatibility, Aging and Stockpile Stewardship Conference, Albuquerque, NM. Hauback, B. C., Fjellvag, H. and Maeland, A. J. (1995). Temperature-induced structural changes in Be,ZrD, studied by powder neutron diffraction. J. Alloys and Compds., 224(2), 241-243. Henager, C. H., Bruemmer, S. M. and Hidh, J. P. (1993). Strength and toughness of beryllium niobium intermetallic compounds. Mater. Sci. und Eng. A, 17Q(1-2), 185-197.
Beryllides Henager, C. H., Jacobson, R. E. and Bruemmer, S. M. (1992). Elevated temperature mechanical properties of Be,,Nb. Mater. Sci. and Eng. A , 153(1-2), 416-421. Jacobson, L. A., Stanek, P W.. Castro, R. G., Elliott. K. E. and Martin, P. (1991). Unpublished work. Kimmerle, F.. Majer. G . , Kaess. U,, Maeland, A. J., Conradi, M. S. and McDowell, A. F. (1998). NMR studies of hydrogen diffusion in ZrBe,H, 4' J. Alloys and Compdr.. 264(1-2), 63-70. Maeland, A. J. and Libowitz, G. G. (1983). Hydrides of berylliuni-based intermetallic compounds. J. LessCommon Met., 89, 197-200. Matsuo, T., Hosoda, H.. Miura, S. and Mishima, Y . (1994). Phase Stability, Microstructure and Mechanical Properties in the Multi-Phase Alloys Based on the LI,Ni,(Af,Be). Materials Research Society Symposium Proceedings, Boston, MA. Matthias, B. T., Giorg, A. L., Struebing, V. 0. and Smith, J. L. (1978). Itinerant antiferromagnetism of TiBe,. Phys. Left., 69A(3), 221. Mishima, Y., Miura, S., Suzuki, T., Matsuo. T. and Hosoda, H. (1994). Design of ductile Ni,Al being two phase with NiBe. Alloy Modelling and Design (eds G. M. Stocks and P. E. A. Turchi). Warrendale, PA. TMS, pp275-282. Nieh, T. G. and Wadsworth, J. (1990). Hot indentation tests of refractory metal beryllides. Scripta Metall, et Mater., 24, 1489-1494. Nieh, T. G., Wadsworth, J., Chou, T. C., Owen, D. and Choksht, A. H. (1993). Creep of a niobium beryllide, Nb2Be,,. J. Muter. Res.. 8(4), 757-763. Nieh, T. G., Wadsworth, J., Grensing, F. C. and Yang, J. M. (1992). Mechanical properhes of vanadium beryllide. VBe,,. J . Mater. SCL.,27, 2660-2664. Nieh, T. G., Wadsworth, J. and Liu, C. T. (1989). Mechanical properties of nickel beryllides. J . Muter. Res., 4(6). 13471353. Okamoto, H. and Tanner, L. (1987). Phase Diagrams of Binary Beryllium Alloys. Metals Park, OH, ASM International. Opila, E. J. (1999). Vanation of the oxidation rate of silicon carbide with water vapor pressure. J. Am. Ceram. Soc., 82(3), 625-636. Ott. H. R., Rudigier, H., Fisk, Z. and Smth, J. L. (1983). UBe,,: an unconveiitional actinide superconductor. Phys. Rev. Lett., 50(20), 1595-1598.
51
Paine, R. M., Stonehouse, A. J. and Beaver. W W. (1963). High temperature oxidation resistance of the beryllides. Corrosion. 20, 307-3 13. Perkins, F. C. (1963). Intermediate Temperature Oxidation of Beryllides, USAEC Report DRI, 2128. Pharr, G. M., Courington, S. V., Wadsworth, J. and Nieh, T. G. (1991). Deformation of an extruded nickel beryllide between room temperature and 820°C. J. Mater. Res., 6(12), 2653-2659 Rooksby, H. P. (1962). Intermetallic phases in commercial beryllium. J. Nuc. Mater., 7(2), 205-21 1. Samsonov, G. V. (1966). The chemistry of the beryllides. Recssian Chemical Reviews (Uspekhii Khrmii), 35(May), 339-361. Schlapbach, L. (1994). Intermetallic hydrides and their applications. Ch. 21. Intermetallic Compounds: Principles and Pracrice (eds J. H. Westbrook and R. L. Fleischer) New York Wiley, 2, Practice, 475-488. Sondhi, S., Hoagland, R. G. and Hirth, J. P. (1992). Atomistic modeling of dislocations in Be,,X compounds. Mater. Sci. and Eng. A, 152(1-2): 103-107. Sondhi. S., Hoagland, R. G., Hirth, J. P., Brimhall, J. L., Charlot, L. A. and Bruemmer, S. M. (1993). Deformation Mechanisms in Bel$ Compoundr. Boston, MA, USA, Materials Research Society. Slewart, G. R., Fisk. Z., Smith, J. L., Willis, J. 0. and Wire, M. S. (1984). New heavy fermion system, NpBe,,, with a comparison to UBe,, and PuBe,,. Phys. Rev B, 30(3), 1249-1252. Stuart. W 1. and Price. G. H. (1964). Reaction between Be0 and water. .I. Nucl. Mats., 14. 417-433. Takasugi, T., Imm, 0. and Masahashi, N. (1986). Improved ductility and strength of Ni,Al compound by beryllium addition. Scrzpta Metal., 20(lO), 1317-1322. Tanner, L. E. (1980). Stable and metastable phase relations in the Hf-Be alloy system. Acta Metall., 28(12), 180.5-1816. Tanner, L. E. and Giessen. B. C. (1978). Structure and formation of metastable phase M-TiBe. Metall. Trans. A, 9(1), 67-69 Tanner, L. E. and Ray, R. (1979). Metallic glass formation and properties in Zr and Ti alloyed with Be. 1. Binary ZrBe and Ti-Be systems. Acta Metall., 27( I l), 1727-1747. Tien, J. K., Vignoul, G. E. and Kopp, M. W. (1991). Materials for elevated temperature applications, Materials Sciences & Engineering A , A143, 43-49. Unknown (1988). Evaluation of Fuel Cladding Properties at High Temperatures, Electric Power Research Institute.
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Chapter 4
Precious Metal Compoupz Ira M. Wolff Mintek, Randburg, South Africa*
1. Introduction Of all the classes of intermetallic compounds (ICs) jockeying for adoption as advanced industrial materials, those based on precious metals enjoy a surprisingly wide applications base and extent of conimercial adoption. Their success is based on circumstances of a historical, techno-economical and property-related nature. They were among the first actual examples of intermetallic compounds recognized historically, and also provided fruitful grounds for early research in the evolving science of intermetallics. Modern-day usage of the precious metal ICs continues to be governed by their unique properties on the one hand, and their relative scarcity 011 the other. This chapter confines itself to underlining some of the recent studies in which the precious metal ICs have surfaced, with emphasis on the more mainstream commercial developments in the PGMs (the platinum group metals Pt, Pd, OS,Rh, Ru and Ir) and also gold (although elements such as Ag and Re might arguably also have been included). Four classes of intermetallic compounds receive particular attention, namely: 0
0
0
The CsCI (B2) systems, of interest in hightemperature structural and coating applications, Compounds comprising the precious metals as a minor alloying addition, Precipitation-strengthened alloys, particularly the fcc/LI, compounds, which have drawn interest as analogues of the nickel-base superalloys,
*See List of Contributors for present address.
0
The coloured ICs, in which the cubic crystal structures predominate. In these, ornamental applications are often juxtaposed with their more prosaic industrial applications.
Brief consideration is given to the prevalence of precious metal ICs in other applications, and their wider exploitation is evaluated vis-a-vis the underlying market fundamentals governing availability and supply.
Reviews of our constitutional knowledge of the precious metal compounds are incomplete and somewhat dated, and have only been attempted by a few authors. Raynor (1976) has delineated the main classes of gold compounds, including the 312, 21/13 and 714 electron compounds, noting also the wide range of intermediate compounds identified in the literature. A more current description is in preparation (Rapson, in press). A very limited treatment of some of the PGM IC classes has been provided by Darling (1973) and Savitsky et al. (1978), and a compilation of published binary, ternary and quaternary equilibrium diagrams lists about 570 systems involving the PGMs (He et al., 1983, 1993). An unexpectedly large number of systems are absent from, or only partially determined in the literature, although a growing number of binary and ternary equilibrium phase studies have recently been added to the precious-metal knowledge base. This reflects emergent interest in the precious metals as they come to the fore in new applications. However, outside of a few key applications, thermodynamic
Intermetallic Compounds: Vol. 3 , Principles and Practice. Edited by J. H. Westbrook and R. L. Fleischer. @ 2002 John Wiley & Sons, Ltd.
and ~ i n e t ~know~edge c is poorly developed, and the underlyin~platform for product developnicnt consequently fa~lsshort in inaiiy respects, compared with most of the other rans sit ion metal systems. Some of the reasons for this state o f affairs are:
eiivironment in some app~ications (corrosion and oxidation), and their highly sekctive action on the environment in others (catalysis) provide most of their development impetus. It i s particularly the former that attracts attention in the field of structural intermetallics.
The precious metals are almost by definition scarcer ity spectrui~,and their restricted ~ ~ b u n d ~limits ~ i c ~ possible mass engineering e the products further above the An illustrative accouiit of historic intermetallic-based
eographic constra~~i~s. The largest proportion of the precious metals, particularly the PCMs, is sourced from just two geo-political regions (~outhernAfrica and the fornier Soviet Union), uring the ~ ~ m e d ~ apast t e years of economic isolation of the above countries, free markets not research these elements, but was actively undertaken to ence on these elements for (for example Fogg and
Global trends have nevertheless fuelled a growing a p ~ ~ i ~ ~ t base, i o n s particularly in roles where the precious metals have suites of properties not available to the designer elsewhere. Examples of such trends are: estricted automob~leemissions, widely enforced y legislation in most developed countries. More % respectively of Pt and Pd c o n s u ~ ~ t i oisn used in catalytic converters for emission control (Johnson Matthey, PZatinum t r a ~ ~ ~ t ~power t i o ngene~~tion, particularly in the land-based emissions; here the rature properties, particularly i ~ ~ r t n eto~ sattack, make the PGMs frontline materials for ~ ~ ~ t - g e ntion e r aalloys, In aircraft engines goals of lower noise levels, greater fuel e~ciencyand higher thrust-to- ass ratios, all in the wake of h i ~ ~turbine e ~ - temperatures, ~ x t e n ~ service ed intervals, and reduced ~aintenance (auto~otive component^ such as spark plugs and catalytic converters, spacecraft), Higlier quality standards, including purity (for example the ~pecialityglass industry). Other than the purely ornaiiieiital or investment attributes of the ~reciousmetals, their inertness to the
record, and are cited in applications as diverse as relig~ousicons (a gold amal~amdating to twelfth- or thirtee~th-century India), fish-hooks used by preColumbian South Americ Indians (AuCu and/or Cu,Au), imitation gold (C t), pen nibs and instruments of ~ ~ ~ , C uand ) ~metallic t , mirrors (Fe with large amounts of P the CsCl structure Several precious modern developments in the science and application of etallics. Two are worth singling out: the study of range ordering p h e n o ~ in ~ ~thea ~ u ~ and C ~ II systems, and the early observation of shape memory behaviour in the Au-Cd system. remain archetypes for ongo~ngstudies into st~uctural order. The first recorded account (c. 1905) of an alloy ~ardenableby slow cooling from elevated t e m ~ ~ r a t u r ~ s appears to be of an alloy of composition 64Au-12.5Ptl6.5Ag-7Cu, actually predating the discovery of precipitation age-hardening in ~ u r a ~ u m i nin 1911 (Chaston, 1971). During the 193Os, this came to be recognized as being the result of atoms taking up preferred locations in the lattice, often accompanied by dramatic shape deform~tion, and changes in the mechanical properties, hence order hardening. The concept of ordering has become central to many important industrial processes, such as the magnetic CO-Pt alloys, and the hardenable 18ct gold jewellery alloys (which are strengthened by a complex combination of order and age hardening, depending on composition). Pertinently, it is in the f u ~ d a m e ~ t a l studies of the Au-Cu and Pt-Cu systems where much of the unde~standingof ordered structures and i n t e ~ e tallic compound behaviour has evolved (see for example Warren (1965), Mitchell et al. (1973, Maluff and Cahn (1985) and Rapson, Chapter 26, Vol. 2).
~
Precious Metal Cornpounds Curiously, the ordering phenomenon in equiatomic Au-Cu, and the accompanying crystallographic changes, showed behaviour consistent with the phenomenological theory of martensitic transformations, which were becoming topical in the study of shape memory phenomena. Wayman and Harrison (1989) note that by 1950, martensites with twinned lamellar structures had been observed in FePt, CoPt, AuCd, fnT1, CrMn and BaTiO,. The evolutionary spread of studies following from Chang and Read's (1951) report of rubber-like behaviour (and shape recovery) in AuCd has been treated extensively by Warlimont and Delaey (1974) and Wayman and Harrison (1989). The first patent for a shape memory device was for an Au-AgCd alloy (Muldawer and Feder, 1961). Some of the other precious metal systems exhibiting crystallographic transformations of relevance to shape memory and related phenomena are summarized in Table 1. Thc cited works are offered as being representative of the great number of studies, rather than comprehensive. For a more detailed treatment, the reader is referred to Schetky (Chapter 25, Vol. 2) and Otsuka and Wayman (1998). Modern precious metal IC development has shifted in emphasis to the high-temperature structural intermetallics. Much of this work has paralleled research into high-temperature alternatives to the nickel-base superalloys, or augmented superalloys. The titanium and nickel aluminides make up the mainstream of structural IC research (for a more indepth treatment, see Chapters 1-5, Volume 2). The B2 nickel aluminide NiAl has received special emphasis owing to its excellent corrosion resistance, higher melting point and low density. In addition, the pNiAl structure is the operative phase in many aluminide diffusion coatings for oxidation resistance (National Research Council, 1996). Applications remain somewhat tentative, since the requisite niechanical properties (room-temperature toughness and hightemperature strength) have to date not been achieved by alloying or microstructural control. This has encouraged investigations into related systems that show promise of converging their superior properties with those of NiAl by inter-alloying. In this respect, the PGM-based B2 aluminides have attractive attributes. The precious metals also preside over another major attribute - notably the existence among them of an fcc crystal structure. Their substitutability for nickel makes them almost unique among the refractory transition metals, and forms the basis of attempts to provide augmented or alternative superalloys. The following sections examine progress in these fields.
55 4. The B2 Compounds
B2 aluminide structures have been reported for all six of the PGMs, although PtAl is not an equilibrium B2 phase at room temperature. RuAl and IrAl in particular have attracted a good deal of interest for high-temperature use, and common features in their binary phase diagrams have often led to parallel studies (Figure 1). The RuAl compound has recently been reviewed in the context of its potential applications (Wolff, 1997). and its main features are summarized below. The recurring interrelationship with IrAl is highlighted. 4.1 The RuAl System
Initial work by Fleischer (1992a) gave prominence to a small cluster of PGM-based intermetallics - IrNb (Llo), RuTa (Llo), RuSc (B2) and RuAl (B2)-all exhibiting credible room-temperature ductility. These compounds have enjoyed varying degrees of attention (see Chapter 11, Vol. 2), but RuAl in particular has derived development impetus from its singular combination of thermodynamic stability (Jung and Kleppa, 1992), toughness (Chapter 11, Vol. 2), corrosion resistance (McEwan and Biggs, 1996), oxidation resistance (Fleischer and McKee, 1993), electrical and thermal conductivity (Smith and Lang, 1995; Anderson and Lang, 1998) and amenability to substitutional alloying (Fleischer, 1993a,b; Wolff and Sauthoff, 1997). In addition, useful gains in oxidation resistance. high-temperature strength and cost-effectiveness can be achieved by ternary alloying. The structure-property evolution of RuAl can be traced from its early identification (Obrowski, 1963) and subsequent findings by Wopersnow and Raub (1979) that the compound exhibited unusual resistance to attizck in hot mineral acid environments, R U N was reported to remain immune to concentrated HNQ3. aqua regia, FeCl, and H F rmxtures, and this list was confirmed and subsequently expanded to include a range of other aggressive chemical media (McEwan and Biggs, 1996). In combination with useful oxjdation resistance up to about I 100"C, the corrosion resistance of RuAl has profiled it for exploitation in coatings, electrodes, and high-temperature structural applications (WoB, 1997). The early Ending (Wopersnow and Raub, 1979) that RuAl had only 'medium brittleness", especially in combination with the (Ru,AI) solid solution, was borne out by the classic 'chisel toughness' tests reported by Fleischer (Chapter 11, Vol. 2). While not
56
Structure and Composition
Table 1 Shape deformation and related transformations rn precious metal ICs Compound
System
Reference
TaRu, NbRu NbIr, NbRh
B2(~)-,Ll,@”)+orthorhombic (lp”)
TiPd
B2-+B19 (orthorhombic)
TiPd-Fe Ti,Pd,,-,Cr, AuCuAl
B2-+B19 B2-tB19 B2 +tetragonal
TiAu, TiNiAu AuTi, PdTi, PtTi AuCd AuZn Au-Cu-Zn AuCuZn, (Heusler phase)
B2-+B19[2H) B2-tB19
Ritter et al. (1964) Schmerling et al. (1970) Das and Liebeman (1975) Das et al. (1976) Fleischer et al. (1990) Fleischer et al. (1991) Fonda et d.(1998) Otsuka et ai. (1993) Golberg ei al. (19953 Otsuka and Ren (1999) Enami et al. (1986) Schwartz and Tanner (1992) Japanese Patent (1991) Jp 3013535 Wolff and Coitie (1994) Levey et ul. (in press) Wu and Wayman (1987) Donkersloot and Van Vucht (1970) Warlimont and Delaey (1974) Ridley and Pops (1970) Brook and Iles (1975) Maluta and Nagasawa (1984) Tadaki et al. (1990) Oshima et al. (1988) Muto et al. (1988) Yuasa et a2. (1994) Baranov and Barabanova (1995) Yi et ai. (1988) Semenova et al. (1995) Warlimont and Delaey (1974) Warlimont and Delaey (1974) Chen and Franzen (1990) Marezio et al. (1971) Asada et al. (1985) Oota et al. (1985) Jorda et al. (1988) Semenova and Kndryavtsev (1994) Kudryavtsev and Semenova (2000) Giessen et al. (1964)
Fe,Pt Fe,Pd FeRh + Ni,Pt,Pd,Ir RhTi TiNi-TiRu CuPd AuMn ‘0
VRu
46
B
B2
P
P-tB2-+L2, LI,-tbct
bee-bct b c c jbct-+monoclinic B2-t rhombohedtal+monoclimc B19’ B2-+fcc B2 4tetragonal tetragonal-+orthorhombic B2-t tetragonal
ZrRh, ZrIr
B2-tB19‘
TaRh
?+tetragonal
fully understood, various aspects of the unusual plastic flow behaviour of RuAl have since come to light. The ductility of RuAl lies somewhere between that of Fe& on the ductile side, and NiAl, where deformation is almost exclusively limited to (001) slip. RUM has had a greater number of slip vectors reported than its more brittle counterparts, NiAl and &AI, viz. {loo), (110) and ( I l l ) , thus satisfying the Von Mises criterion for homogeneous deformation (Fleischer et al., 1991; Lu and Pollock, 1999). It remains to establish whether these slip vectors are the result of multiple glide or the product of dislocation reactions, Sabariz and Taylor (1998) found that only ordinary dislocations of { 100) type (not superdislocations) operated in polycrystalline RuAl compressed at
4.2K and 293 K, although (1 Il)-type dislocationswere identified after compression at 1273K. If this is the case, it is difficult to understand the low-temperature ductility observed. From another perspective, atomistic modelling (see for example Lin et al., 1992) predicts:
(i) a lower antiphase boundary (APB) energy for RuAI in the (I 1I} direction (690 mJ/m2) than for NiAl (1000 mJ/m2); (ii) directional charge distribution along the (111) direction in NiAI; and (iii) substantial differences in the charge densities and hybridization states between NiAl and RuAL
1
57
Precious Metal Compound9 f
¶
Ai
RU
h
I
10
20
30
40
50
60
70
80
90
at.% Ir
Figure 1 Binary equilibrium phase diagrams of (a) the Ru-A1 system (after Boniface and Cornish, 1996) (b) the Ir-A1 system (after Hill et al., 199%)
58
Structure and Composition 2500
2000
1500
1000
500
Figure 2 High-temperature behaviour of PGM-base eutectic composites (data after WoH et al. (1997); Hill and WoE(1999))
Thus readier slip processes could by implication be achieved by lowering of the APB energy or modifying the hybridization andtor cohesive energy via ternary alloying between systems that exhibit unlike cohesive properties e.g. within the Ni-AI-Ku system. Studies have been carried out to evaluate the temperature dependcnce of flow stress, and strainrate sensitivities, of a range of RuAL-based alloys relative to those of NiAl (Eow and Pollock, 1998; Lu and Pollock, 1999). At RT and 77 K, RuAl exhibits a much lower temperature dependence than NiAI, in fact by up to an order of magnitude. Saliently, this is not affected by the presence of secondary phases. The question as to whether other ductile ruthenium alumimdes were to be found was raised by Paxton and Pettifor (1992). A trialuminide phase A1,Ru with DO, structure, was predicted to have room-temperature ductility on the basis of density-functional theory. Although its electroiiic structure was such that i t was highly improbable that it could be made cubic by alloying, AI,Ru, unlike other transition metal trialuminides, showed an ideal axial ratio. Subsequent experimentation unfortunately failed to confirm this, and a reassessment of the phase diagram found a
competing phase, AII3Ku4, to be the more stable (Manh et al., 1995).
4.2 The IrAI System
Like KuA1, the B2 IrAl compound is stable in a limited concentration range (48-52 at.%). Both compounds melt congruently, and exhibit a eutectic L-tIrAl (RuA1) + ITsJ(Et%). However, room-temperature hardnesses of over 1000 #" have been recorded for the binary IrAl, and it is considerably more brittle. Whereas RuAl is notable for its room-temperature toughness, IrAl stands out as a candidate for hightemperature strength. Separate studies have therefore focused primarily on its high-temperature capability and improvement of its room-temperature properties: a The Ir-A1 and Ir-Ru-A1 systems have been studied
by Hill et al. (1998a, 1999a). The B2 Ir,-xRuxAl pseudo-binary was found to extend in a continuous series with a very limited width. Room-temperature hardness of RuAl increases sharply if more than 40% of the Ru is replaced.
59
Precious Meifa1 Compounds
The Ir, -,Ni,Al series has been evaluated in compression up to 1400°C (Chiba et al., 1998). The effect of Ni is to improve ductility, but it decreases strength. The specific strength becomes independent of Ni content at temperatures greater than 1200 "C.Significantly, the 0.2% proof stress of IrAl is an order of magnitude greater than NiAl (0.2% PS at 800°C = 1200 MPa, and 350 MPa at 1200°C). Some lOat.% Ir increases the creep strength of NiAl by a factor of 4. Composite 1ameHar eutectic Ir + IrAl structures have been tested in compression to 1300 "C by Wolff and Sauthoff (1996b). The results are compared with those obtained for the Ru-Ni-A1 (mixed eutectic y(Ni) + (Ru) + BRuAl), and Ru f RuAl systems in Figure 2. The oxidation resistance of IrAl has been evaluated for: -1rAl (Lee and Worrel, 1989; Chou, 1990; Hill et al., 1999b) - I N + Si (Lee and Worrel, 1994) -IrAl+ B (Wolff and Hill, 2000) -1rAl + Ru (Hill et al., 2000) -1rAl + Ni (Hosoda et al., 2000a) tudies confirm exceptional high-temperature capability, superior to that of RuAl, but requiring Al-rich stoichiometries, or alloying with Si, for continuous protective scale formation at temperatures beyond about 1550 "C. Ni was reported to reduce mass-loss under isothermal oxidation up to 1400°C. Finally, an assessment of the Ir-based ICs would not be complete without noting the exceptional mechanical properties found among some of the other systems. The Llz compounds are considered in Section 6. Compounds based on the L1, structure additionally deserve mention. Studies by Fleischer et al. (1990) found a promising combination of room-temperature toughness, plasticity and strength among simple binary and ternary formulations such as IrNb, Ir~NbsoNi,,, Irz5Niz5TiS0, Ir&o,,Nb,,, and Ir2,Niz5Vs0.The latter, in particular, showed immense strength in compression, rising to 2500 MPa at room temperature.
4.3 &+fleetof Boron on B2 Compounds In further studies, Fleischer (1991, 1993c) also went on to demonstrate the effectiveness of small boron additions in enhancing the strength and ductility of RUM, This was related to a change in fracture mode from primarily intergranular to primarily transgranular, akin
to the now well-established boron ductilizing effect, featuristic of some other cubic systems, notably Ni,AI. While boron has a clearly demonstrated beneficial effect on the mechanical properties of RuAl, no apparent benefit to room-temperature compressional ductility or strength appears to be gained in the binary Ir-A1 system (Wolff and Hill, 2000). The extraordinarily high hardnesses to be found amongst the IrAl compounds may dictate that any ductilization effects on the part of boron are overridden at room temperature by the inherent resistance to slip. This is in fact the case reported for the B2 NiAl system; boron segregates to the grain boundaries, strengthening them and allowing transgranular cleavage, but the increase in hardness as a result of the boron addition counteracts any potential improvement (Chapter 38, Vol. 1). Support for this premise can be found in the study by Hill (1998), who concluded that boron additions to slightly aluminium-rich alloys in the pseudo-binary series RuxIr50~xA150 allowed reasonable toughness and ductility when the ruthenium content exceeded 20 at.%. The structural distribution of boron in the bcc systems RuAl and IrAl remains to be established. Fleischer (1993c) inferred from RuAl lattice parameter data that boron is more likely to occupy substitutional sites than interstitial sites. The existence of a B2 RUB phase suggests that boron would be likely to substitute for aluminium, but the resulting defect structure is a matter for conjecture. Phases of Is3 stoichiometry have also been reported, but exhibiting orthorhombic or hexagonal symmetries (Villars and Calvert, 1985). Boron additions of up to 0.5 at.% do not appear to influence the microstructure on the Ir-rich side of the Ry,Ir,_,Al series (Hill et al., 1998b). An unexpected finding is the debilitating effect that boron additions of O.Sat.% have on the oxldation resistance of RuAl- and IrAl-based compounds (see below) (Wolff and Hill, 2000). Reduced oxidation resistance in a boron-doped ternary (Ru, 1r)Al alloy has also been observed (Hill et al., 2000). 4.4 Ternavy Alloying
Various ternary substitutional alloying additions have been examined with a view to enhancing the strength and oxidation resistance of RuA1, or incorporating its favourable properties into allied systems. Cr, Si and Y (McKee and Fleischer, 1991), and Ir (Hill et al., 2000) have been shown to improve its oxidation resistance, although at the expense of room-temperature toughness. In the case of Ir, substitutional additions of greater than 20 at.% are required to make a significant difference to
60 30
25
w
20
@ 15 E
10
5
0 CO content, at.%
1800
30
1600
25 1400
20 ae
1200
@ 9
I.I
1000 15
800
600
10
400 5
200 0
0
0
10
20
30
40
60
70
COcontent, a t %
Figure 3 Cobalt substitution, showing the effect of a compliant two-phase necklace structure on the mechalucal properties of RuAt {a) RuAI-CoAl single-phase (b) RuAI-Co,&l, two-phase (after WoIff and Sauthoff, 1997)
61
Precious Metal Compounds
oxidation behaviour at temperatures up to 1300°C. Sc additions of 7-9 at.% improve both room-temperature and high-temperature hardness up to 1150"C (Fleischer, 1991, 1992b), and the alloy has only 'marginally unacceptable' oxidation rates at 1350"C, making it a possible contender for lower temperatures. Several studies have sought to substitute Ru in isostructural series based on (Ru, M)A1, where M has been represented by Fe, Ni and CO, and Ti has been substituted for A1 (Fleischer, 1993a. 1993b; Wolff and Sauthoff, 1997). This has been most successful in two-phase microstructures. Stoichiometries slightly rich in Ru, and Iying just beyond the single-phase RuAl field, can be formulated to give a so-called 'necklace structure' in melt-processed material. A thin film of the Ru-rich solid solution, taking the form of a 'divorced' eutectic, acts as a compliant layer, greatly assisting extrinsic crack-toughening processes. So, for example, up to 40 at.% of the Ru can be substituted in this way by CO without a significant deterioration in room-temperature mechanical properties (Figure 3). The Ru-Ni-A1 ternary, for reasons including those discussed above, has received rather more attention than the other B2 ternaries. The structure of the pseudo-binary Ru,-,Ni,Al series has not been conclusively clarified, although various arguments have been put forward to amount for a pronounced hardness maximum within the series (non-ideal solutioning behaviour) at room temperature. A contributing interest stems from the strong solid-solution strengthening response to either Ru or Ni in the respective NiAl or RuAI B2 phases. Unlike the relatively benign effect of CO or Ti on RuAl, hardnesses of close to 1000 HV can be achieved with substitutional additions of Ni to RuAl (Wolff and Sauthoff, 1996a). The interest in this is obvious, given the possibility of extrapolating this strengthening effect to higher temperatures, but the underlying mechanisms are unclear. The possible existence of a miscibility gap between the NiAl and RuAl phases has been investigated by, inter alia, Tsurikov et al. (1980), Chakravorty and West (1985), W O Eand Sauthoff (1996a), Hark et al. (1997), Hill et al. (1997), Sabariz and Taylor (1997, 1999), and Homer et al. (1998). In essence, early observations pointed to melt-processed material solidifying with a diphasic structure, being the NiAl and RuAl phases with a small lattice mismatch (cO.h%). Such mismatch strain might account for the hardening observed and, provided that a sufficiently fine mixture of these two phases could be achieved and sustained at
high temperature, coherency strains could provide a potentially useful strengthening mechanism. An alternative view put forward is that the sloping liquidus between the high-melting-point RuAl (-2050 "C) and lower-melting-point NiAl (1638 "C) produced a coring effect rather than a two-phase microstructure per se. Material processed via reactive powder processing routes (SHS or RHIP) shows no such coring, nor any evidence of a two-phase structure. The lattice parameters show a linear gradation between RuAl and N N , irrespective of processing route (Figure 4). Thus phase misfit strain does not appear to play a determinate role (Wolff et al., 1997). Curiously, the lattice parameter data in Figure 4 show a singularity corresponding to the RuNiAlz stoichiometry, raising the question of a possible ternary ordering effect, as occurs in the Nb-Ru-A1 and Ti-Ru-A1 systems. A comparison of modelled and experimental data in fact points to a Ni,,Ru2,Al,, alloy as exhibiting the maximum degree of order, i.e. approximately 80% (Harte et al., 1997). In another study by Sabariz and Taylor (1999), on material consolidated by reactive powder processing, peak splitting and broadening in XRD data was noted at the RuNiAl, composition. At the same time, hot hardness measurementsexhibited a departure from the linear variation with temperature at this point. Sabariz and Taylor provide microstructural and X-ray evidence for two co-existing isostructural B2 phases (lattice mismatch 1.3%) to account for this. Whether these observations are compatible with a ternary ordering effect requires further work for clarification. An additional consideration has been raised by the work of Munroe (1996) and Munroe and Kong (1996), who have pointed out that Ni also increases the hardness of B2-structured FeAl beyond that predicted by atomic misfit calculations, and reduces the softening that occurs on low-temperature annealing of this compound. They advance a defect hardening mechanism to account for this, speculating that the structure of the Ni site favours the formation of divacancies in the vicinity of the atom, which are effectively restricted in mobility. The existence of a hardness peak in other Ni-based pseudo-binary series, see for example Ru,Ni,-,Ti (Semenova et al., 1995), has led to the premise that this effect may be intrinsic to Ni in the B2 structure (Wolff et al., 1997).
-
4.5 Production
Given the high melting point of RuA1, its aggressive attack of refractories, and the volatility of its
62
Structure and Composition 0.300
0.298 0.296
I 0.294 ‘ L
,g 0.292 0,
0.298
0.288
a 0.286 0.284
0.282 0.280
I $
5
10
15
25 30 Ni content, at.%
20
35
40
45
Figure 4 Lattice parameter data For RuAI-NiAI alloys prepared by RWIP or melt processing, showing a singularity at RuNiAl, (after Wolff et a?., 1997)
constituents, manufactured quantities of RuAl were initially limited to the capacity of cold-crucible melting techniques. Even then, porosity and inhomogeneous microstructures rendered the product unsatisfactory. Bulk production of RuAl waited on the development of a powder metallurgical processing route, based on reactive hot isostatic pressing (RMIP) (Wolff, 1994, 1996; Ishiyama et al., 1994; Sabariz and Taylor, 1999). Exploiting the primary powder products of the PGM refineries, and the high enthalpy of formation of the PGM-aluminides, thermally efficient production routes at temperatures well below the melting point can be engineered to produce simple near-net-shape components (Figure 5). This production route follows similar industrial temperature and pressure regimes to those used in, for example, WCCO production, placing it within the realms of commercial feasibility. Other production routes for the B2 compounds have been discussed previously (Wolff, 1997). Techniques that remain no more than laboratory curiosities at this stage, but have provided interestiiig possibililies include the production of nano-phase crystallites by high-energy ball milling (Hellstern et aE., 1989), mechanical aUoying (Xu et al., 1994), and liquid solvent precipitation (Johnson and Garland, 1990).
4.6 Composite structures
Two-phase microstructures have been engineered to usefully enhance the mechanical capability of RuAIand IrAl-based materials, and their ternaries. ‘Ductilephase toughening’ is particularly effective in raising both the strength and toughness of these alloys (Wolff and Sauthoff, 1996b). Melt-processed materials around the eutectic composition exhibit classic lamellar eutectics, wth submicron interlamellar spacings. The high interface density leads to increased strength by providing obstacles to dislocation motion in the normal way, but also provides for extrinsic toughening (crack deflection). The fine scale of the lamellar phases does, however, appear to place as upper limit on the high-temperature strength; beyond approximately onehalf o f the melting point, deformation proceeds by interfacial sliding, with a concomitant loss of strength relative to coarser microstructures. Such structures take on the characteristics of superplasticity, and have been studied in, for example, the eutectic AI-PdA& system (Piatti and Bardy, 1981). The production of RLAI by reaction synthesis paved the way for modified microstructures, either by the incorporation of a dispersoid, using the intermetallic as a matrix material, or by exploiting the
Precious Metal Cornpounds
63
Figure 5 Cylinders of RuAl produced by reactlve hot isostatic pressing
intrinsic two-phase microstructure to grow a discrete in situ composite. In the latter, the unusual situation exists where the intermetallic matrix phase (RuA1) is more ductile than the solid solution phase (hcp Ru). An example is shown in Figure 6, where discrete particles of the Ru solid solution are embedded in the intennetallic matrix. The benefits to be had from the composite microstructure in terms of high-temperature strength are shown in Figure 7 for a simple binary (Wolff and SauthoR, 1999). The structure can be refined to a point where the high-temperature strength exceeds that achievable with the lamellar eutectic structure, but with a commensurate loss of lower-temperature ductility.
4.7 ~ i ~ ~ - T e m p e r aPerformance t~re
One of the more demanding service environments targeted for RuAI is that of the automotive spark-plug electrode. Requirements for longer service intervals (60000km in Europe and Japan, 100000 miles in the USA) have focused attention on the PGMs to provide the erosion resistance required (Raw, 1992). The potential of PGM-based iiitermetallic compounds as spark-plug electrode materials was recognized in an early patent (McGitl and Selman, 19781, but the almost universal brittleness of the ICs has doubtlessly prevented their adoption. Given a way to overcome the problems with mechanical robustness, the high thermodynamic stability, environmental resistance and intrinsic resistance to self-diffusion make the ZCs natural candidates. In this regard, RuAl-based materials have shown early promise (Steyn et al., 1994). Their ductility and thermal shock resistance combine with excellent electrical and thermal transport properties
Figure 6 Microstructures engmeered to show: (a) Necklace structure in RuAI-CoAI (after Wolff and SauthoE, 1997); @) lamellar eutectic structure in A1,1r,,Ru,9 (after Hill et aL, 1999a); (c} in situ eutectic composite structure in Ru-rich RuAI produced by reactive hot isostatic pressing (RHIP) (after Wolff et at., 1997)
(Lang, 1999), and environmental resistance. Endurance trials on simple binary compounds have demonstrated them to be well within the capability of meeting the less onerous 60000 km targets, with ternary and higher formulations showing potential for even greater capability.
64
Structure and Composition 1400
.............. .................................
1200
a loo0
P
g.
"
........... ......
.............
_.
......._... "
.I,
.-,,
__.
.
4F&MW(RHIP)
-a- R@ln (RHIP) -A-- RudI,, + B (RHIP)
."'
...... 4 RuAIn (RHIP)
.................................................................
800 ..............................................................
......................................................
s
2
400
.......................
..........................................................
I"
.I.......................
..
0 400
600
800
900
1100
loo0
1200
1300
Temperature, O C
Figure 7 Effect of melt-processing, Reactive Not Isostatic Pressing (RHIP) and composition on the hgh-temperature compression strength of RuAl-based alloys (data after Wolff and Sduthoff, 1999)
.......................................................................
4
.... L
2-
1.5-
1-
0.5
.... ....
-
0-
Figure 8 Erosion rates of RuAl spark plug electrodes as a function of composition (after Wolff and Hill, 2000)
Precious Metal Compounds
Spark-plug development work has also driven a number of investigations into related aspects of RuAI. One of the findings is that optimal erosion resistance is shown by two-phase compositions, around the 68 at.% Ru level (Figure 8). The governing erosion mechanism appears to be the preferential breakdown of the RuAl constituent, ostensibly by the cyclic formation and removal of an aluminium oxide, leaving a rutheniumiich residue at the surface (Wolff et al., 1997).Although elemental Ru exhibits excellent erosion characteristics; its intrinsic brittleness, as with the ICs, has tended to preclude it from application. The effective role of RuAl thus appears to be that of providing the fracture resistance to wrthstand the thermal cycling. Unexpectedly, as can be seen from the chart in Figure 8, the small amount of boron alloyed to the RuAl-based spark-plug electrodes to provide ductility during manufacture (for example, when the insert is crimped into the surrounding nickel sheath) dramatically debilitates the erosion resistance of R u ~ ~ AThis I~~. has been associated with an enhanced propensity for internal oxidation (Wolff et at., 1997). The adoption of ICs in applications like spark-plug electrodes presages requirements for large-scale manufacture, in this case wire, within narrow dimensional tolerances. Some progress has been made with metal powder injection moulding techniques. The (Ru,M)Al materials allow near-full density wire to be achieved with relatively coarse size fractions ( ~ 3 4 p r n )and sintering cycles akin to those of, for example, alumina (DuPreez and Wolff, 1999) (Figure 9). 4.8 Constitutional Studies Development work has been accompanied by a growing experimental base for the more fundamental properties. Recent attention has been given to phase
F i r e 9 Prototype spark plug with RuAl inserts. Also shown is Imm wire produced by PIM, and the associated microstructure
65
relationships in the Ru-AI, Ir-AI, Ru-Ni-Al, Ru-Cr-Al, Ru-Ir-Al and Ru-AI-Y systems (Boniface and Cornish, 1996; Hill et al., 1998a, 1999a; Horner et ai., 1998; Hohls et al., in press; Compton et al., in press). 5. Precious Metals as Minor Alloying Additions
In a number of systems the precious metals play a role in secondary phase formation, or modification of the intermetallic constituent. Examples of the following, discussed below, are noteworthy: e Additions of precious metals modify the structure, 0
0
or kinetics of secondary precipitate formation. Small additions of precious metals provide secondary phases for modifying properties, such as in precipitation strengthening. Alloys in which an intermetallic phase, as with the y' phase in nickel-base superalloys, constitutes the majority volume fraction, and in which the properties are augmented by the precious metal addition.
5.1 PGMs in Sigma Phase Formdon Small additions of PGMs (<0.2 wt.%) are made to passivatable alloys like ferritic stainless steels to effect so-called cathodic modification in reducing acid environments (see for example Higginson, 1989), as well as enhancing the high-temperature oxidation resistance (Wolff et al., 1998). The PGM addition promotes spontaneous passivation in the reducing acid, improving corrosion resistance by up to five orders of magnitude. Extraordinary gains in the hightemperature oxidation resistance can also be engineered. It has, however, been noted that the PGMs can accelerate the formation of the generally slow-forming tcp a-FeCr phase (D8,) at intermediate temperatures (Wolff et al., 1998). This observation leads to an application developed by Cortie et al. (1995) for high-Cr stainless steels, in which the BGM plays an active role in modifying the microstructure. When exposed to intermediate temperatures (<800 "C), ferritic stainlesssteels with Cr contents greater than about 20 wt.% become 'sigmatized'. Although this is generally debilitating to the corrosion and mechanical properties, a fully sigmatized alloy is readily and cost-effectively milled to a fine powder, which has use in thermal spraying, powder metallurgy, etc. Recognizing the propensity of small ruthenium and other additions to enhance the rate of sigma phase formation, fully sigmatized alloys can be made at intermediate annealing temperatures within minutes.
The s i w a phase in the final product is removed by an appropria~e~ i n t ~ r i ntreatment g above the solutioni~ig teiii~erature,with or ~ i t h o uthe ~ benefit of added s ~ g ~ ~ - p hretardants ase ( ~ o n g * ~eta al., n 1998).
oxide under ~put~ering ~ o n ~ ~and ~ ~ (iii)o ~~ is ~, A3~ d ~ r segregation to the unoxidized surface of the samples. It is worth making mention here of the improvements in ductility and fabri~abi~ity brought about by 1-3 at.% a~ditionsof Pd to Ni3A1(Vol. 2 Chapter 2). In this case, the results have been explained in ternis of a reduction in the ordering energy. Although Ir additions of up 5at.% reportedly Alloying additions to the gamma titanium alu~~iinides increase the h ~ r d e n I nrate ~ of Peal (€321, ostensibly seek to improve d~ictilityby one or more of the t y p ~ the ~ ~ ~ r e ds i s at ~ nin ~~an ~~ ~ n f o l l ~ w ~ nmge c h a n ~ s ~~so~ d i ~ sfip, e d ~ i c r o s t r ~ c t u r a ~by v a c a ~ c ~ ~defects, oxygen atmosphere at 1300°C is not i m ~ r o v e ~ re~nement,and ~recipitationof small amounts of the (Hosoda et crt,, ~ O ~ O b ) . vely ductile (bcc) @-phase (Chapter 4, Vol. 2). enium ~dditionsof up to 5 at. % have been found ve strong b e ~ ~ ~ s t a b i l ~ zrotes i n g in Ti-Al-Rti ~ ~ t e r n ~ ~ and t a l three l ~ ~ ~types , of martensite can be m the P-fieId, depending on Tke ~ x ~ e ~~ ti ~g hu ~~ ~~ el ~~ ~ i ~e c~ hr aapropern~i ~ ~~ ~e al., 1989). Alloys based on ties of the nickel-base su~era1loys rely on the 7Al- I Cr-2Nb alloys have precipitation of coherent, ordered ~ ~ ~ A l - t y(fcc pe also been found to have greatly ~ m ~ r o v ethennod L1,) particles in an fcc matrix. mechanical p r ~ c e s s i ~attribut~s g thanks to the addit~mperatureferritic alloys can be engi~eeredaround tion of 1 at.% Ru, which encourages a fine distribution coherent CsC1-type (bcc B2) particles in a bcc matrix, of equiaxed B2 particles (Chen and Wang, 1997). In One of the mare unusual examples i s to be found in addition to distributing strain more evenly, the B2 the Fe-Au-Cu system (~ahlgren,1967). Additions of phase reporte~lyprovides nuc~eat~on sites for static y 3.8at.% each of Au and Cu to iron were found to recrystallization during post heat treatments. result in ordered zones with structures (apparently ~artition~ lend ~ gsite o c c u p a ~ ~ofyRu in t ~ o - p h ~ s e AwGu in c o ~ p o s ~ t i o ~onsistent n~ with the CsCl a2+ y Ti-48at.%A1 alloys have been studied by atomstructure. This is unexpected, since none of the binary probe icroscopy ~ ~ P F(Kim f ~ and ) Smith, Au-Cu c o m ~ o ~ ~have ~ i d sthis structure. No apptications have been reported, 1997; 1999). In alloys with Rti additio~isof Precipitation-strengthened ferritic alloys based on Up u was observed to substit~teyreferentitslly for A1 in the ordered 1' phase, Ru was considered CsC1-type p ~ e c i ~ i ~in~ tFe es - ~ i - ~ l (- ~C o~ ~ ~ ete r o ~ al,, 1988) and Fe-Cr-Al-NI ( ~ a i l and ~ ~Pineau, r ~ 1982; i~g to follow IVb with regard to p a ~ t ~ t i o n behaviour, but to follow Cr with regard to s ~ ~ i f the t ~ (n ~~ * + ~ Zliu ~ /and ~ T'jong, 1997) have enjoyed more interest, but have been limited in appli~letiondue to c o a r s e n i ~of~ boundar~to the Af-rich side in these alloys. No the precipitates at teniperatures much above 700 "C. evidence of Ru segre~atioi~ to a2/y interfaces was NiAl-type p r e ~ i ~ ~ t could ~ t i o si~i1arly ~i be expected in found; nor did Ru appear to si~ificantlyaffect the Fe-Cr-A1 by alloying with Ru. partitioning of interstiti~lelements C and 0. Small additions (-0.2 wt.%) of Ru to ferritic idtoys Single-crystal studies of NiAl, to which 10at.% fr based on Fe-Cr-A1 have been shown to drama~ically was added, have d ~ ~ ~ o n s t r athe t e dbenefits for the flow improve passivity ia both aqueous and oxidation stress and creep resistance up to 1200 "C (Chiba et al., environments (WolR et al., 1998). Increasing the Ru 2000). Flow stresses about it factor of 4, 5 and 8 higher to 4 wt, % ( 2 at, %) provides an age-hardthan those of NiAl were ~ e p o r t ~ atdroom ~ e ~ p e r a t ~ r e addition , enable ~ y s t e with ~ , a fine, s e ~ i - ~ o h epre~ipitate r~~t 900 "C and 1200"C res~ect~vely. A change in the active dispersion in Fe-20Cr-5A1 and Fe-35Crslip plane was oEered to account for this pronounced ~ A1 nya and Wolff, 1999). ~ o w e v e rthe effect of Ir. ~ h i g ~ ~ t e ~ p e ~ ~47:1 ~ u rine these alloys is high, and chemical The role of Pt in e n h a ~ c i nthe found that the p~eci~itate species (in the over-aged oxidation r~sistanceof mQdi~edaluniinide coatings c o ~ d i t i ~ nis) a lower a de, p ~ o b ~ bthe 1 ~lesss Using has been ~ ~ a ~byi ~~ i e ~d ~ etd al.u (1993). symniet~ic(CS4 or C1I) phase, which displays /3-NiAl with (1101, s ~ n g ~ ~ ~st~~dies ~ ~ y ofs tPt-doped ~l little adva~~tage in i ~ i c r o s t ~ c t ustability ~al relative to (100) and ( I l l ) o r ~ e n t ~ t i o nPt~ , was noted to (i) ti sg.Al:Ru ratio in t ~it foro nits base-~etal~ o ~ ~ ~ t e ~r o~ va i~~the ~ ~ c i l i tA1,03 a t ~ ~ ~ ~ un ~(IOO),~ but~ hinder the bulk alloy closer to unity appears to successfully (1 10) and (11I), (ii) provide for a very stable and dense ~~~~~~
-
precious Metal Compounds
induce the B2 RuAl precipitate. Jackson (1991) has claimed a precipitation-strengthened FeCrAlU composition, with Ru additions of up to 20 at.%, and in which the B2 fRu,Fe)Al phase predominates. Patents clainiing the use of RuAl-containing coatings for high-temperature oxidation resistance have issued for the Ru-AI-Cr system (Jackson, 1990, 1998). These devolve from the synergy offered by Cr and A1 for oxidation resistance, and provide for Ru contents of up to 45 at.% to obtain the required microstructures.
5.4 Nickel-base ~ u p e r a l with ~ ~ sPGM Additions Second-generation superalloys, typically containing upwards of 11 different alloying additions, are approaching their asymptote in terms of microstructural stability, environmental resistance and hightemperature creep performance. The last recourse of alloy designers is to the (surprisingly unexploited among the transition metals) PGMs as bulk alloying additions. Although the so-called 'PGM concept' is more than two decades old in the patent literature (Selman and Midgley, 1975). increasing demands for greater Performance, fuel efficiency, and noise reduction have only in recent years propelled such alloys below the cost-benefit curve. (Other factors, particularly for alloys operational in land-based power plants, are the need to reduce emissions, and to cope with dirtier fuels than are typical in aerospace applications.) Overcoming the inherent resistance among alloy engineers to these costly additions has been greatly assisted by two developments: The success of Pt-modified aluminide coatings has inculcated an appreciation of the benefits to be had on the basis of total life-cycle costing. Furthermore, the interaction of these coatings with the substrate has necessitated an understanding of the effects of the Pt when diffused into the nickel-base substrate. This has laid the basis for an early database on the effects of Pt in the superalloy system. Secondly, the advent of the relatively scarce, strategic and expensive Re additions at levels up to 6 wt.% in the current superalloys created a defucto precedent for its PGM counterparts. According to the US Geological Survey (Feb. 1997), only 27200kg of Re were produced in 1996, for an average selling price of $1100/kg (or $33/oz). The USA is the largest producer (68%), but has to import to meet demand. Some 60% of Re production is used in superalloys. For comparative purposes, some 10 000 kg of Ru are taken up by the
67
market each year - the average price (1999) was about $3910~.It can therefore be seen that the PGMs are not as extraneous as might be supposed. Attention among turbine alloy engineers has focused mainly on Pt, Ir and Ru additions, and PGM-modified superalloys have been cited in numerous patents (see for example Coupland and Pearson, 1982; Hill et al., 1984; Duhl and Cetel, 1986; Walston et ul.,1995; and Putatunda et al., 1998). The key issue in achieving greater environmental stability is a combinahon of improved oxidation resistance and hot-corrosion resistance, normally only achievable with higher Cr contents (with implications for microstructural stability), or expensive MCrAlY-type coatings. However, PGM additions dramatically improve both the oxidation and hotcorrosion resistance without debilitating the mechanical properties. There are also a number of associated advantages, as enumerated by Corti et al. (1980): The fcc PGMs, particularly Pt, show a high degree of compatibility and substitutability with nickel. e While MO and Ta are more effective solid solution strengtheners up to about lOOO"C, at higher temperatures Pt shows clear solid-solution strengthening advantages over even M O and Ta (no data available for Re). e All the PGM-modified alloys show improvements in environmental stability over the standard superalloys, although their rankings differ. Cyclic oxidation resistance improves according to the ranking Ru < Rh < Pt
The reported partitioning behaviour of the PGMs between the gamma and gamma-prime phases is not consistent, and appears to be a function of composition. Guard and Westbrook (1959) provide empiricalrules of thumb to predict substitutional behaviour in Ni,AI, viz. o
6
The occurrence of a structurally related Ni3Xphase dictates Al-type substitution (and presumably Nitype substitution can be expected from elements that exhibit an isomorphous X,Al equivalent). Elements most like Ni in electronic configuration (i.e. they foim continuous solid solutions with Ni) will substitute for Ni; those Like AI for Al.
68
Structure and Composition
However, evidence has been advanced to show that the site preference can be modified by the alloying content and multicomponent influences (Ochiai et al., 1984). Of the six PGMs: All, with the exception of Ru, show complete solid solubility in Ni, with no compound formation (Ru and Ni dissolve up to 34.5 and 50 at.% of the other element respectively in their solid solutions at elevated temperatures), e Only Pt has had both a Pt3A1 phase, and a Ni,Pt (LI,) phase reported (Villars and Calvert, 1985), which may account for the inconsistency in its reported partitioning and substitutional behaviour. e
Coupland et al. (1982a) report strong partitioning of all the PCMs, with the exception of Qs, to the y'phase in simple model y/y" systems. A developmental alloy containing 4.5wt.% Pt was found by Coupland et al. (1980, 1982b) to have Pt substituting predominantly for AI. However, Ochiai et al. (1984) invoke a semi-empirical model based on the Miedema formula (incorporating electronegativity, electron density and size) to link the change in total bonding energy to predict the site preference in three-component systems. Both Pt and Pd are shown to have a preference for the Ni sites, in agreement with other investigators cited by them (see also Pd in Ni,AI, Vol. 2, Chapter 2). Similar substitutional behaviour was found for Pt and Pd in the L1, Ni3Ga, Ni,Ge and Ni,Si systems. At high Pt levels, the L1, structure is destabilized, and a ternary tetragonal (Ll,-variant) phase of the type Pt,CuAl forms at stoichiometries of Pt2NiAl (Kamm and Milligan, 1994). The partitioning behaviour of Ir similarly appears to be a function of composition. In Ni-18at.%Al-1, 3, or Sat.%Ir alloys, Ir has a preference to partition to the y phase. (Murakami et at., 2000). However, quaternary Ir-Ta-Ni-AI alloys induce Ir to partition preferentially to the Ll, {Ir,Ta) phase @U' et al., 1999). Atom-probe fieid-ion microscopy studies of the later-generation TMS-79 (Re-free) alloy reveal a slight preference of Ir atoms to partition to the matrix y-phase, but substitute for the A1 site in y' (Murakami et al., 1998), whereas Re-containing TMS-80 exhibits a slight preference for Ir to partition to the y' precipitates (Murakami et al., 2000).
The behaviour of Ru is Iess well documented. A study of the Ni,Al-Ni3Cr-Ni,Ru section of the Ni-CrAI-Ru system indicated a preference of Ru for the matrix y-phase (Chakravorty et al., 1985).
6. The Refimtory Srrpe~all~y~ The concept of supplanting nickel in the ubiquitous superalloys is not new. Analogues based on a gamma/ gamma-prime precipitation-strengthened structure have been sought amongst the higher melting-point refractory transition metals, but invariably within the constraints of much higher densities, poor roomtemperature ductilities, and very poor oxidation resistance. Furthermore, most of the refractory transition metals have open bcc structures, which, although capable of exhibiting coherent structures, exhibit inferior creep properties (Stoloff and Sims, 1987). As noted already, a number of the precious metals have fcc structures, in common with the Ni/Ni,Al system. A quest for alloy systems capable of performance at ultra-high temperatures (defined here as service capabilities at least 200 "C above those of existing nickelbase superalloys) ultimately focused attention on the PCMs, whose relative nobility and excellent environmental resistance complement their higher melting points and desirable crystal structure. A particular subset, developed in the superalloy paradigm of a coherent y/yf structure, are referred to here as 'refractory superalloys', in keeping with the terminology proposed by Yamabe et al. (1996).
6.1 Systems Based on I r Iridium has partmlar merit, based on its fcc structure, high melting point (2443 "C) and intrinsic resistance to deformation. Gamma-fa and gamma-prime L1, microstructures can be equilibrated in the highmelting-point systems Ir-Hf, Jr-Nb, Ir-Ta, Ir-Ti, Ir-V and Ir-Zr (Massalski, 1990). Of these, the fr-M, system has embodied the most impressive resistance to hightemperature deformation to date. Ir,Nb systems (Llz, Tm>24OO0C)have been variously investigated by Bruemmer et al. (1990), Wolff and Sauthoff (1996b), and Yamabe-Mitarai et al. (1997). The most noteworthy characteristic in the simple binary system is a compressive strength comparable with the strongest metallic materials identified to date at temperatures up to A proof stress of 212 MPa at 1800°C has been recorded for Ir-10 at.% Nb (this despite the phase diagram predictmg a single-phaseconditlon, suggesting that Nb also has a potent role to play as a solid-solution strengthening agent), and a compressive stress of over 300 MPa has been reported for Ir-15 at.% Nb at the same temperature. Improvements in high-temperature
69
Precious Metal Compounds
strength appear to correlate with higher degrees of positive lattice misfit (i.e. the precipitate lattice parameter is greater than that of the matrix), but this may not offer optimal creep resistance or resistance to microstructural coarsening at lower strain rates. Interestingly, peak compression strengths appear in the Ir-Ir3Nb system at roughly 50% volume fraction of precipitates (cf. 60-70% volume fraction y' in thirdgeneration nickel-base superalloys) (Yaniabe-Mitarai et al., 1997). Comparable properties have also been reported for two-phase alloys based on Ir-Hf, Ir-Ta and Ir-Zr (Yamabe-Mitarai et al., 1997) (Figure 10). Fundamental deformation studies of the L1, constituents of these systems have received comparatively limited study. In particular, there seems to be some conflicting evidence regarding the existence of a positive dependence of the flow stress on temperature.
A moderate yield strength anomaly has been reported for Ir,Nb in thin film studies (Bruemmer et aZ., 1990), and a pronounced increase in flow stress with temperature up to 800 "C has been noted in compression studies of polycrystalline Ir-25 at. %Nb (YamabeMitarai et al., 1999a). In the latter study it was also noted that, as in the case of Pt,Al, Ir,Nb shows a strong decrease in strength between - 196 "C and RT. In contrast, no anomalous hardening was observed in polycrystalline hardness studies (Gyurko and Sanchez, 1993). Recently, it has been reported that compositions around Ir,Nb also exhibit the characteristic 'boron ductilizing effect' in compression (Wolff and Hill, 2000; Gu et al., 2000). Small additions of boron improve strength and ductility, and change the fracture mode from predominantly intergranular to transgranular in nature.
1600 Ir-Nb Rh-Ta
Figure 10 High-temperature compression strength of Ir and Rh-base alloys (after Yamabe-Mitarai et al.. 1997)
70
Structure and Composition
The high-temperature properties of the EngelBrewer intermetailic, Ir,Zr (Ll,, Tm=2280"C) have been examined by Gyurko et al. (1992). (Engel-Brewer intermetallics are extremely stable compounds between high-melting-point transition metals from the second and third transition series, based on their electronic structure.) k3Zr showed no yield strength anomaly, and compared unfavourably with Ni,AI and Ir3Nb in terms of yield strength at elevated temperature (Ir,Zr had only half the resistance to deformation of Ir3Nb). However, its high ordering energy has been put f o w a d a a basis for excellent creep resistance. Furthermore. preliminary studies of a ternary L1, compound Ir, 71Nboz,Zro,os,show a high-temperature hardness plateau from 600 to 1200"C, outperforming both binary systems (Gyurko and Sanchez, 1993). The system thus shows considerable potential at ternary or higher alloying levels. Precipitation hardening and the associated defomation structwes in Ir-Nb and Ir-Zr have been studied by Yamabe-Mitarai et al. (1997; 1999b,c). Typical microstructures are shown in Figure 11, In order of increasing lattice misfit. A close correlation has been found between lattice mismatch, precipitate morphology, and ffow stress. In general, greater mismatches give rise to an increase in the compressional flow stress, but are associated with microstructural instabilities and d i s ~ o n t i n u o ~coarselung. ~ High mismatches (- 2%) induce plate-like precipitates (Figure I l e and f), while mismatches between 0.3-0.4% are associated with cuboidal precipitates (Figure Ilc and d). As a general observation, extraordinarily close parallels exist between these systems and their nickel-base counterparts in respect of their heat-treatment and deformation response, and much of what has been learnt in the past decades of superalloy alloy engineering appears to be transferable. Two major drawbacks of Ir - its high density, and its relative scarcity - act as incentives to explore at. least partial substitution. Replacement of some of the Ir by Ni in the Ir-l5at.% Nb system has been examined, with improvements in both the roomtemperature compression strength and ductility noted for Ni contents up to 20at.x (Gu et al., 1998). The yield strength at 1200"C was, moreover, comparable with that of the binary Xr-15Nb composition at these nickel levels. Significantly, the nickel appeared to promote an intergranular-to-transgraiiular transition in the fracture mode, Control of the inicrofracture and deformation processes can also be effected by varying the Nb, MO and C contents (Gu et al., 2000).
-
The above results have also led to an examination of the convergence between the Ir-base and the Ni-base superalloy systems. Studies of the IrlTa-Ni,Al and Ir,Nb-Ni,Al systems have been reported fyu et al., 1999, 2000). Strengths intermediate between those of the nickel-base and the binary Ir alloys at 1200 "C were recorded, but with considerably improved ductilities relative to the binary compositions.
6.2 Systems Based on Rk
Characterization studies of Rh-based systems have also been pursued, where the lower melting point is offset by a more attractive density and oxidation resistance (Yamabe-Mitarai et al., 1997). The assessed phase diagrams suggest that two-phase y/y' structures can be equilibrated in Rh-Am, Rh-Ce, Rh-Hf, Rh-Nb, Rh-Np, Rh-Ta, Rh-711, Rh-Ti, Rh-U, Rh-V and RhZr (Massalski, 1990). High-temperature capabilities much superior to nickel-base superalloy comparitors, but somewhat inferior to the Ir systems, were found for the Rh-15 at.% Nb, Rh-15 at.%X, Rh-15 at.% Ta and Rh-25 at.% Ta systems. Nickel has similarly been investigated as a subsDtutional addition in Rh-15 at.% Nb alloys (Gu et a[., 1999). Up to 30 at.% Ni can be accommodated, although for optimal benefits in compression strength, fracture mode and ductility, no more than 10 at.% Ni is used.
For mainly techno-economic reasons, discussed more fully at the end of this chapter, considerable effort has gone into evaluating Pt as a basis for a refractory superalloy. Platinum has a more modest melting point (1772"C), but has an edge in availability, environmental stability, and density, over Ir. Scope to develop useful (high-temperature) two-phase binary y/y' structures is more limited, being confined to the Pt-Hf, Pt-Ti, Pt-Cr, Pt-Zr and Pt-A1 systems. However, the existence of several L1,-type Pt3X phases (X = Ga, In, Mn, Sn, Zn, CO) with lower-temperature stability, provides scope for ternary or higher alloying to modify the y'-phase. There also exists the possibility of finding some coherency in other Pt3X systems, or even to stabilize an L1,-related structure of Pt3X by alloying (e.g. Pt3V (t18), Pt3Ta (mP48), and Pt,Nb (oP8). This finds concomitance in nickel-base alloys, where Ta and Nb both segregate strongly to, and stabilize, the y'
Precious Metal Compounds
71
Figure 11 Precipitate morphology in heat-treated Ir-1Sat.YoX,where X = (a) V, (b) Ti, (c) Nb, (d) Ta. (e,g) Hf, and (f.h) Zr. The lattice mismatch (L.M.) is shown in each case (after Yamabe-Mitarai e t al., 1997)
72
Structuw and Composition
O ! 0
200
4a0
1005
1200
14
Figare 12 Mechanicalproperties of some Ll, Pt,X compounds and Ir&b (after Wee et aL, 1980; Yamabe-Mitaraiet at., 1999a)
phase, despite the fact that Ni3Ta and Ni,Nb do not exhibit LI, structures). The results of limited high-temperature mechanical (mostly hot-hardness) studies of Pt3X systems are available, including the L1,sti-uctured Pt,Al, Pt,Ti, Pt,Jn, Pt3Sn, Pt,V, Pt3Cr, Pt,Ca and Pt3Mn (Wee and Suzuki, 1979; Wee et al., 1980). Some of these results are reproduced in Figure 12. From a practical consideration of melting points, the In, Sn, Ga and Mn systems are not very useful for high-temperature applications. It can be noted that the Pt,Al and Pt,Ti systems manifest the most promising hot-hardness behaviour amongst the Llz Pt compounds, sustained up to about 900"C, the limit of testing reported. In comparison with Ir,Nb, the Pt,Al single phase exhibits higher flow stresses in this temperature range (see Figure 12). A number o f Pt-Pt,X systems have been evaluated in terms of microstructural stability and oxidation resistance (Hill et al., 2001a). Three systems have enjoyed comparatively more attention, viz. Pt-Zr, PtHf, and Pt-Al. Intermetallic dispersion-strengthened Pt-Hf alloys have been proposed by Wang et al. (1996) and Fairbank et al. (1999). The latter have also
examined the phase equilibria in the Pt-Zr system, as well as Rh additions to both the Pt-Hf and Pt-Zr systems. Revised constructions of the Pt-Kf, Pt-Zr and Pt-Zr-Rh phase diagrams have been proposed, but no mechanical properties have been reported. Pt,Zr and Pt,Hf have also been examined as contact materials, based on their excellent corrosion resistance, hardness and electrical conductivity (see Pecora and Ficalora, 1977). The Pt-AI system has the advantage of a trackrecord, albeit in coating form. Platinum-modified coatings have become the protective aluminide system of choice for high-performance blades (Chapter 22, Vol. 2), representing one of the most adherent, oxidation- and hot-corrosion-resistant formulations identified to date - which provides a basis for believing that structural alloys based on Pt-AI will be similarly endowed. The Pt-AI system is made more complex by the existence of a low-temperature, tetragonal variant of the L1, Pt3Al phase (Oya et al., 1987; Bronger er aZ., 1997; and others). It nevertheless closely emulates the nickel-based systems in terms of electronic structure (Pt and Ni share the same group in the periodic table)
Precious Metal Compounds and the inherent capability of forming its own protective oxidation layer. The evidence to date shows that Pt,Al exhibits only mild manifestations of the so-called yield-strength anomaly. Generally, deformation in L12 compounds is understood to be governed by the intrinsic features of the cores of the screw dislocations. Pt3Alis classified as belonging to that class of L1, compounds where the screws are always sessile, militating against the yield anomaly, or 'Kear-Wilsdorf locking (Vitek et al., 1991). The compressive flow stress of Pt,AI single crystals has been measured in three different orientations ([OOl], [I231 and [ill]) over the temperature range from near liquid He to 1080 K (Wee et al., 1984). The study found: A sharp increase in flow stress with decreasing temperature below room temperature. This dramatic effect has received little attention in the literature, and its practical implications remain uncertain, Two distinct slip systems depending on orientation over the entire test range of temperatures, Constant to slightly increasing flow stresses above 400 K, depending on orientation. The strong low-temperature and weak high-temperatur; dependence of flow stress corroborates earlier hardness studies conducted by Wee et al. (1980). Two approaches to obtaining the coherent precipitation-strengthened microstructures have been considered. Conventional solutionizing and ageing practices, as followed in the nickel-base superalloys, are constrained by the shape of the assessed binary equilibrium phase diagram. Because the trajectory of the Pf, solvus line dictates a relatively small volumefraction of secondary phase ($), as per the lever-rule principle, ternary approaches have been examined as a means of modifying the shape of the Pt solid solution solvus line (Hill and Wolff, 1999). More usefully, composite eutectic structures can be exploited in the Pt-AI system as an alternative approach to achieving a fine phase mix (Hill et al., in press (b)). The as-cast eutectic structure following homogenization is characterized by a fine (< 1pm) discrete particle morphology that similarly shows a high resistance to coarsening. Mechanical testing shows these alloys to be among the strongest Pt-based alloys on record (see for example Figure 2), but to date results are considerably below the strengths achieved in the Ir-based systems. Given the well-known intrinsic resistance of Ir to deformation, and considering that single-phase Pt3AI exhibits higher strengths than the
73
Ir,Nb phase at intermediate temperatures (see above), the Pt solid-solution phase appears to be the critical factor governing the high-temperature resistance to plastic deformation. Further work examining solidsolution strengthening and/or microstructural refinement appears to be indicated. Developmental studies extending to the Pt-A1-X systems (X=Ru, Re, Ta, Ti, Cr) have confirmed the high resistance to oxidation which is a hallmark of the Pt-aluminide coatings (Hill et al., in press (c)), with compression properties above 1200 "C showing a clear ascendance over their nickel-base counterparts (Hill et al., 2001b). Creep behaviour remains to be evaluated. There is some evidence to suggest that the incorporation of other PGMs into the Pt-AI system has additional benefits for the oxidation behaviour of PtAI coatings, that may extend to the bulk alloys (Fisher et al., 1999). Rhodium acting in combination with platinum reportedly increases durability of the coating under oxidizing conditions. Iridium-modified coatings have been found to produce a thinner coating than the simple Pt-A1 system, but with rather less adherence.
6.4 The Occurrence of Short-Range Order (SRO) in Pt-based Alloys Perhaps one of the most intriguing and potentially useful properties to be found in the Pt-based alloys relates to the ability of single-phase Pt solid solutions with relatively small alloying additions to be strengthened by high-temperature treatments. Recent studies have linked this to short-range ordering (SRO) activity. SRO revolves around atomic order on a highly localized scale. Due to the microstructural scale of SRO, it is generally inferred from scattering experiments (XRD, neutron, electron) rather than direct microstructural observation. Although imperfectly understood, evidence for SRO has been offered in a number of systems. However, no unified microstructural description of this phenomenon, other than purely deterministic treatments (see Chapters 2 and 33, Vol. l), is available in the literature. Schonfeld (1999) recognizes four models of SRO, viz. The statistical model - in which SRO exists homogeneously in a one-phase equilibrium state, and in which the occupation of a neighbouring site fluctuates around some value, statistically greater than a random value,
74
Structure and Composition
Disperse order model - SRO is heterogeneous in a two-phase equilibrium state i.e. particles of a longrange ordered phase in a less ordered matrix (the equilibrium interface energy just compensates the elastic energy of the particles, ensuring a maximum particle size of 2 to 5 nm), e- ~ ~ c r ~ d o model m ~ ~- nwell-defined, well-ordered microdomains (a few unit cells in size) heterogeneously embedded in a random matrix, o Lattice defect model - non-homogeneous (melastable) heterogeneous variations in composition because of defects (vacancies, dislocations, etc.) introduced by plastic deformation. 0
The ageing behaviours of these systems are often similar to those of precipitation-strengthened alloys, in that the ordered domains can interfere with the passage of dislocations. With ageing, coarsening of the microdomains can occur, ultimately leading to peak hardening and subsequent overaging (StolofT and Dames, 1966). Recent observations of anomalous hardening in Pt-5 wt.% Ru and R - 5 at.% MO alloys quenched from temperatures up to 1300°C have been inferred to be indicative of changes in the structural order, although this was premised largely on the absence of any information to the contrary (Towle et al., 1998; Towle, 1999). However, in other studies, neutron-scattering experimeilts performed on Pt-10 at.% V and Pd-10 at.% V alloys quenched from 1100"C show satellite diffuse peaks at room temperature (Murakami and Tsunoda, 1999). These have been interpreted in terms of SRO concentration waves, which reflect the characteristic shape of the Fenm surfaces in Pt and Pd. Related studies, in which magnetic SRO has been inferred for Pt and Pd alloys with around 10 at.% Mn, Fe, Cr and Go, were also cited (Murakami and Tsunoda, 1999). The SRO phenomenon has also been studied in Pdbased alloys containing MO, W, Cu and Au (Kim and Flanagan, 1967; Lang and Doyle, 1996; and others). Substitutional additions of transition metals to the solid solution bring about resistivity anomalies that can be interpreted in terms of changes in the structural order above a critical temperature. In effect, SRO appears to be effective in increasing the roorn-temperature hardness of Pt and Pd alloys when they are quenched from above a critical temperature. Exploiting this mechanism to improve the room-temperature mechanical and wear properties of high-caratage jewellery alloys has been proposed (Towle, 1999; Lang et ad., 2000). Of wider interest is its possiblc effect on high-temperature mechanical properties. Tile generally limiting strength of the y solid
solution, rather than that of the y', is widely understood to be the governing parameter inhibilng greater resistance to plastic deformation in the nickel-base superalloys (Giamei et al., 1985). SRO in the Pt-based system potentially offers a mechanism whereby the Pt solid solution can be strengthened in situ at attractively high temperatures. The existence of such high-temperature SRO in nickel-chromium alloys has, in fact, been suggested by Nordheim and Grant (1953) and Akhtar and Teghtsoonian (1971), and has also been advanced as the reason that Re has such a potent effect on creep resistance in superalloys (Blavette et al., 1986). In the case of Pt, the phenomenon usefully applies to systems to which refractory alloying additions have been made, of direct interest to extending the superalloy paradigm. Experimental evidence for this mechanism in two-phase Pt-base systems is yet to be produced, but represents a compelling area for further research. 7. Coloured Inte~meta~e ~ornpoun~$
Investigations into the underlying origins of colour in metals predate even ir consideratioii of their mechanical and other properties (Petersen, 1989). Apart from gold and copper, intrinsic colour in metallic systems is to be found only among the intermetallic compounds. Systematic studies of their optical properties have provided a fairly good, if not comprehensive, basis for understanding the attributes which lead to colour, and various 'conditions' for the occurrence of colour have been proposed for different IC classes (see Chapter 12 by Steinemann et a2.). Thus, an upper limit on the valence electroii concentration has been put forward for the Zintl phases (MgAuSn, LiMgPtSn, etc.), while an electron-to-atom ratio i s stipulated for the WumeRothery phases (Eberz, 1983; Drews et al., 1986). Predominant amongst the coloured intermetallics are the cubic structures, which conform to the general requirement for a highly symmetrical crystalline structure in which the electronic band structure allows sp-d hybridization, with a covalent character, to prevail (Steinemann, 1994). A by no means exhaustive list of the some of the coloured ICs is given in Table 2. 7.1 The CaF2 or Hitorite Structiare
Colour is one of the more notable attributes of this class of intermetallics. It includes PtAl, (deep yellow), AuAI, (purple), and CoSi, (intense blue), all three of which have considerable industrial significance; PtAI2
Precious Metal Compounds
75
Table 2 Coloured compounds based on the precious metals
Compound
System
Colour
Reference
PdIn AuCuAl &AI, + Cu AuAI, AuEn, AuGa LiMgPtSn Li, ,MgPtSn LiMgPdSn LiMgIrSn Li,AuGa Li,AuIn Li,AuSn LL~AuP~ LiPd,Ge LiP4Sn Li,PdPb L1,PtSn Li,Pt,Sn, LiAuSb MgAuSn MgPdSn MgPdSb MgPtSn MgPtSb LiMgPdSn LiMgPtSn LiMgPtSb LiMgIrSn
B2 82 Cap2 CaF, CaF, CdF, Cubic L1,Bi-related
Purple-yellow Yellow-red Orange-pink-yellow Purple Blue Bluish Coppery red Dark red Red/violet Grey-blue Greenish yellow Greenish yellow Orange Violet Brown Yellow Yellow-grey Yellow Yellow Red-violet Violet Yellow Violet Dark red Dark red Violet Bright red Violet Grey-blue
Randin (1994) Levey et al. (in press) Huriy and Wedepohl (I 993) Cahn (1998) Cretu and Van der Lingen (in press) Cretu and Van der Lingen (in press) Eben (1993)
Cubic Li,Bi-related
Cubic Li,Bi-related Cubic Li,Bi-related Cubic Li,Bi-related Cubic Li,Bi-related Cubic Li,Bi-related
is a common constituent of modified aluminide diffusion coatings for high-temperature turbine blades; AuAl, is the basis of the infamous ‘purple plague’, to be avoided in soldering contacts in electronic circuit boards (arising from the interdiffusion of Au and Al) (Cahn, 1998); good lattice matching allows CoSi, to be grown epitaxially on Si (001) surfaces for semiconductor-metal-semiconductor transistors. The fcc structure of these compounds notwithstanding, all exhibit poor fracture toughness - a factor which has nevertheless not precluded their use in ornamental applications, 7.1.1 Platigerns
Caratage platinum alloys have not found wide favour in jewellery, owing to the traditional marketing ethos of platinum within the higher-purity alloy range (greater than 900 parts per 1000). Unlike gold, the alloys of platinum have no intrinsic colour. However, as is apparent from Table 2, a number of brilliantly coloured Pt iiitermetallicshave been identified, with Pt contents varying up to 77 wt.%. Platigeme is based on
Petersen (1989)
Ibid.
Ibid.
Ibzd. Ibid.
Ibid.
the fluorite PtAI, phase. which occurs as an intense yellow compound resembling gold in colour. Additions of copper allow colours ranging from yellow, through orange to pink to be obtained (XIurly and Wedepohl, 1993). A higher caratage white intermetallic compound (consistent with a hallmark of 900 parts per thousand) based on the Pt-AI-Ti system has also been developed vaylor and Biggs, 1996). The overriding attribute of the Platigem compounds i s their high hardness, which allows them to be polished to a high lustre, or even to be faceted (Figure 13). Indeed, the compounds are marketed as synthetic gemstones, and are set in conventional jewellery alloys as an inlay or gemstone (Wolff, 1995). Coloured compounds for jewellery are not the exclusive domain of platinum. The gold counterpart of Platigems, AuAl, (more probably Au6Al,,), or ‘purple glory’, has enjoyed similar applications. Meltprocessing of AuAl, allows the production of robust and durable synthetic gemstones (Figure 13), although high-pressure production techniques reportedly lead to room-temperature decomposition into constituent A1 and AuAl phases (Cahn, 1998).
76
Structure and Composition
Figure 13 Examples of the jeweller’s craft with coloured intermehllics (a) PlatigemB synthetic gemstones based on PtAI, (courtesy Min?ek/Lonrho Platinum}; @) Purple gold based on AuAl, (courtesy M. B. Cortie, Mintek); (c) Spangold@ based on the AuCuAl beta compound (courtesv Mintek/WGC). See also Figure 13 (colour plate section) between pages 870 and 871.
Alternative approaches to accommodating the intrinsic brittleness of AuAI, suggest themselves. Rapson (Chapter 26, Vol. 2) has inquired into a composite structure. The AI-AuAl, phase field would appear to offer the possibility of mixing a ductile AI solid solution with the brittle TC. The eutectic has been studied by directional solidification, but the colour characteristics and mechanical properties were not documented (Piatti and Pellegrini, 1976). Off-stoichiometric compositions to induce a compliant two-phase necklace structure proved to yield little advantage (Suss and Cretu, 1998). Another approach lies in the production of a surface coating of AuAI2. Sequentialfy layered deposits of Au and Al readily interdiffuse at room temperature to form compounds, although the phase formation sequence is problematic, not always yielding the thermodynamically most stable phase (Chapter 26, Vol. 2).
Following the discovery of shape memory in the (brittle) Au-Cd system, some effort was expended in
Precious Metal Compounds
finding gold-based shape memory alloys of sufficient ductility, caratage and colour to allow their use in jewellery. Applications such as clasps for stones have been cited (Brook, 1973; Brook and Iles, 1975; and Japanese Patent JP 30,113,535, 1991). The Spangold@ concept represents an interesting departure from conventional shape memory applications in that the crystallographic memory effect is exploited for decorative rather than thermomechdnical ends (Wolff and Cortie, 1993). The shape deformation accompanying the martensitic transformation is harnessed to give Spangold its characteristic glitter, or ‘spangle’ - heat treatment distorts a prior-polished surface of the parent phase, rendering a myriad of randomly tilted facets, or laths, that scatter incident light (Figure 13~). The convergence of the properties that make Spangold attractive for jewellery applications is somewhat serendipitous, Spangold was originally thought to be a derivation of the AuCu I (Ll,) ordered lattice, that is centred on a composition of Au-50 at.%Cu (75 wt.% Au, or 18 carat, which is the basis of the most widely adopted jewellery in western markets). The hardening associated with the ordering transformation in AuCu, so-called ‘French gold’, has long been recognized and exploited as a strengthening mechanism (Chaston and Sloboda, 1951). As in the shape memory alloys, the ordering transformation of the fcc lattice to a tetragonal AuCu I, and ultimately orthorhombic (AuCu 11) structure is accompanied by a shape deformation. Systematic additions of A1 were found to change both the temperature of transformation, and also the morphology of the resultant lath structure, from fine platelets to broad facets (Wolff and Cortie, 1994; Wolff and Pretorius, 1994). More recently, studies of alloys based on Au - 18 wt.% Cu - 6 wt.% A1 have found that the Spangold structure and phenomenology are consistent with a beta compound (e/a ratio of 3/2), placing Spangold in the family of classic shape memory alloys. Shape deformation proceeds via an ordering reaction of the hightemperature phase from B2 to L2, positions, whereafter a displacive transformation between an incompletely ordered L2, parent phase and a tetragonal product of as yet indeterminate structure occurs (Levey et al., 2000). In addition to its advantageous composition, the 18carat Spangold alloys occupy the yellow to red wavelengths in the colour spectrum, joining the class of intermetallicspossessing intrinsiccolour. Spangold is also relatively malleable (it can be hot-worked), and has excellent castability, all of which make it attractive for jewellery applications. Of equal technological interest is its potential application as a shape memory alloy.
77
A recent addition to the ‘Spangold‘ concept is the 23-carat Au-AI alloy, which exhibits a p-phase akin to the body-centred p-electron compounds (Levey et al., 1998). Light chemical etching of the surface lamellae produces colourful interference effects, that have likewise been proposed for decorative purposes. The narrow range of stability, and brittleness of the alloy unfortunately renders it difficult to work with. For some stunning examples of the jewellers art in coloured gold intermetallics, the reader is referred to Cretu and Van der Lingen,1999.
8. Other Applications
A comprehensive survey of the precious metal compounds in other fields lies beyond the scope of this chapter. However, some unusual areas for further study have emerged in the recent literature, and some examples are given in Table 3. The reader is referred to the chapters in Volume 2 on ‘Shape Memory Alloys’, and ‘Dental IMCs’, and in this volume ‘Color in IMCs’ for a more detailed description of the precious metals in this field.
9. Supply and Availability of the Precious Metals Somewhat different dynamics govern the global gold and PGM markets, and what follows is an overview of the principal features. In recent years, physical demand for gold has comfortably outstripped mining production, but shortfalls have been easily met from the estimated 34000 tons in reserves held by central banks. There is therefore little fear that gold supplies and worldwide resources could not sustain demand from significant new applications. Gold usage is heavily concentrated - by far the largest application is in jewellery (3145.2 tons, or 85% (Gold 1999, Gold Fields Mineral Services Ltd), although industrial demand is substantial. However, gold’s (albeit diminished) monetary role ensures a high degree of elasticity in supply and demand. World PGM markets are considerably less flexible, for a number of reasons, some of which have already been mentioned: 0
World PGM production is geographically highly concentrated, most supplies originating from just two centres (Southern Africa, and the former Soviet Union).
Structure and Composition
78
Table 3 Some novel developmentsin the precious metal ICs
Application
Compound
System
Description
References
Icosahedral
Quasipriodic structures (or quasicrystals) show unusual thermophysical properties.
Anlage, S. M., Fultz, B., and Krishnan, K. M. (1988). J. Mater Res., 3(3), 421. Shield, J. E., Chumbley,L. S., McCallum, R. W., and Goldman, A. I. (1993). J. Mater. Res., 8(1), 44.
Hydrogen precursors
Pd,Mn CeRu,
Ag&k L1, MgCu,
Intermediateprecursors formed by N takeup. In Pd,Mn, an L1, structure can be stabilized with vastly different mechanical properties at RT. CeRu, undergoes amorphization. The systems allow the contributions from order-disorder, and phase transformation to be studied, depending on theintal history.
Nesbit, S., Craft, A., and Foley, R. (1991). Scripta Metall. et Mater., 25, 1183. Kim, Y -G., and Lee, J.-Y. (1990). Scrlpta Metall. et Mater., 24, 2123.
Hydrogen storage
FeTi +Pt.Pd
B2 (CSCI)
The hydrogen-storage capability of FeTi is improved by Swt.O/o additions of Pd w.r.t. activation, reduction in absorption-desorption pressures and reduced hysteresis.
Mulshreshtha. S. K., Jayakumar, 0. D., and Bhatt, K. B. (1993). J. Mater. Sci.. 28, 4229.
Extnnsic toughening
IrNb, Ir,,Nb, RuTa
Ll,, oPI2 Ll,, 3 2
Twm-Iike lamellae provide a mechanism for extrinsic toughenmg, yelding good toughness and plasticity at room temperature.
Ffeischer, R. L. (1992). Platintun Metals Rev., 36(3), 138. Fleischet, R. L., Field, R. D., and Briant, C . L. (1991). Metal]. Trans. A, 22A, 129.
Transfonnaaon induced plasticity (TRIP)
B2
A twinning or martensite-like deformation mode allows unusual room-temperature ductility in this high melting-point alloy (Tm- 1800aC). Sufscient plasticity and wear resistance allows it to be evaluated as a dental alloy.
Watezstrat, R. M. (1993) Platinum Metals Rev., 37(4), 194.
Electrocatalysis Ti,RuFe
cP2-Cscl
The electrocatalytic activity for the hydrogen evolution reaction in chlorate electrolysis can be considerably enhanced by nanocrystalline TiiRuFe application in dimensionally stable anodes (DSA).
Blouin, M., Guay, D., and Schulz, R. (1998) NanoStructured Materials, 10(4), 523.
Raney Ni catalysts find an equivalent in the PGMs. Raney Ru, Jr and Ir-Ru catalysts can be prepared by leaching their aluminides in KOH solution.
Semenova, A. D., Yankovskii, Kh. I., Kropotova, N. V., and Vovchenko, G. D. (1981). Russian Journal of Physical Cizemi.wy, §§(2),271.
Catalysis
RuAI, IrAl, RuIrAl
Not specified
Permanent magnets
FePt, Col?
Tetragonal tP4
Superplasticity
AI-PdAI,
Eutectic fcc/hcp
Darling, A. S . (1973). Znf. Metallurgical Renews, 18, 91. Fully superplastic behawour up to -400% at T>723 K up to strain rates of 3 x 10-2s-'
ThermoeIectncs
Tetragonal Below 1000K, the tetragonally distorted fcc compound delivers the maximum positive thermopower for any metal (see Vol. 2, Chapter 20).
Conducting films
D8b
Thin films of Mo,Ru3 and W,Ru, exhibit high hardness, electncal conductivity, good wear resistance and corrosion resistance.
Piatti, G., and Bardy, M. (1981). Metal Science, Feb., 55. Vdernikov, M. V., Terekhov, G. I., Sinyakova, S . I., and Ivanov, 0. S. (1969) Metals, 4, 191 (in Russian) Testardi. L. K., Royer, W.A., Bacon, D. D., Storm, A. R., and Wernick, J. W. (1973). Metallurgical Transactions34, 2195.
I9
Precious Metal Compounds Palladium
I
I
lrtdium
Ruthenium
I The minor PGMs are produced as by-products (in South Africa, of platinum mining, in Russia of nickel (or, arguably, palladium) mining) - production is thus governed by primary demand in the Pt/Pd markets, and strategic and economic considerations may dictate against increased production. Diversification is poor, placing heavy reliance on a few major applications. This is particularly true of platinum. Emission legislation creates a derived demand for Pt in catalytic converters; the other major application is in the field of jewellery. o Some of the minor PGMs have finite resources. Although, in theory, the PGM deposits in
Year
140,
I
Figure 14 The PGM markets, showing annual price range (dark shaded band) and total demand (bars) (data after Johnson Matthey, Platinum 1990-1999)
concentrations such as the Bushveld Complex are inexhaustible, some occur in concentrations and at depths that make them largely unexploitable. This puts practical limitations on the amount of metal available, irrespective of demand or price. Trends in PGM markets are reflected in Figure 14. The price ranges arc shown on an annualized basis (Platinum 1990-1999, Johnson Matthey). The salient features to note are: Production has steadily risen over the past decade, with producers carefully matching supply with
80
a
e
e
Structure and Composition
demand as far as it is possible to do so. Thus the primary products platinum and palladium have enjoyed a long period of price stability. Uncharacteristic price surges in the period 19991 2000 were largely attributable to legislative export constraints in the former Soviet bloc, leading to temporary shortfalls in the market. Among the minor PGMs, stability can be jeopardized by relatively minor fluctuations in demand. A case in point is the Rh market. In the early 199Os, a refinery bottleneck resulted in a smalt shortfall. The immediate consequence was a price spike, followed by a sustained drop in the Rh price as the effects of substitution took hold. Short-term profits bad to pay for the irrecoverable loss of applications and demand in the longer term. Market volatility is therefore carefully guarded against to ensure the longer-term viability of the market. Current and projected supplies of Ir are limited. Demand arising from significant new applications in recent years have on occasion seen the Ir price overtaking that of Pt. (This may in turn result in the loss of applications ID which its low price made it attractive initially.) Ru is acknowledged to exist in a state of slight oversupply, which has kept it the cheapest of all the PGMs. This situation is likely to be accentuated by increasingly greater recourse to the deeper UG2 reef, the world’s largest PGM resource, and which contains a relatively greater proportion of Ru than the Merensky Reef which has dominated production to date (Edwards, 1988). However, a growing number of new applications for Ru are set to increase demand in future (Wolff, 1999).
An assessment of estimated resources can be made from the data in Table 4.Pt and Pd reserves are vast
and capable of meeting sustained growth of up to 10% per annnm well into the next century. The Pt and Pd markets at the time of publication were balanced on the one hand by a declining trend in sales from Russian stockpiles, that characterized the immediate post-Cold War era, and by expansioii of the South African mines. In 1999, Pt was experiencing a boom, with the three largest producers in the world set to increase produo tion to raise projected Pt availability to 4.7 million tr. oz (-200 tons) per annum by 2004 (Financial Mail (South Afrrca), Oct. 1, 2999). The biggest growth areas are anticipated to be the commercialization of fuel-cell technology, as well as growth in Asian, particularly Chinese, jewellery and investment markets (Johnson Matthey, Platinum 1999). The case for Pd can be made in a similar vein, although the vagaries surrounding Russian production make this less deterministic. A final consideration relates to the PGM cycle, Owing to their nobility and intrinsic worth, the PGMs not only endure, but also provide a built-in incentive to recover as much metal as possible. Significant quantities of secondary metal have started entering the market, notably from recycled autocatalysts, and this trend is set to grow. In this respect, it is worth bearing in mind that the real cost of precious-metal based components is the interest cost plus the cost of refininglrecyclingat the end of the service life. Precious metals in any bulk engineering form are invariably recovered. In conclusion, the point that emerges is that, depending on the application, Au, Pt and Pd are precious metal commodities that can be discussed on a ‘tonnage’ basis for new applications. Use of the other PGMs is more narrowly constrained by physical production. However, the PGMs continue to occupy niche applications on the basis of their properties, and in balance with their price structures.
Table 4 Total PGM reserves of the major deposits (to 1200m depth) (after Viljoen, 1998; V m a a k and Van der Merwe, 2000) ~
PGM (in situ tons)
Pt
Pd
Ru
Rh
Ir
OS
South Africa Merensky Reef UG2 Reef Platreef Great Dyke, Zimbabwe Stillwater, Montana Noril’sk, Siberia Sudbury/Lacdes Isles, Canada
83 235.6 39 544.2 37 110.1 6581.3 10091.0 6627.91 20 255.0 878.9
42 104.6 21 750.4 17 534.1 2820.1 5656.0 1403.8 3985.3 343.1
27 102.9 13204.7 10 693.7 3204.5 3377.0 5058.5 14009.6 442.3
6898.9 2349.1 4287.2 262.6 590.0 33.8 776.4 31.2
4548.6 1419.6 2947.4 181.6 266.0 86.8 614.2 41.0
1618.8 454.1 1104.8 59.9 107.0 31.1 518.2 14.4
961.8 366.3 542.9 52.6 95.0 13.9 351.3 6.9
Total
121 088.4
53 492.8
49 990.3
8330.3
5556.6
2289.5
1428.9
Site ~~
~~~
Precious Metal Compounds
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Steyn, H., DeV., Wolff, I. M., and Goetzee, R. (1994). South Africm Patent No. 94/10180 (Dec. 22). Stoloff, N. S., and Davies, R. G. (1966). Progr. Mater. Scr., 13(1), 3. Stoloff, N. S., and Sims, C. T. (1987). Tn Superalloys II (eds C. T. Sims, N.S. Stoloff, and W. C. Hagel). Wiley. Suss, R., and Cretu, C . (1998). Proc. Micros. Soc. Southern dfrtca, 28, 20. Tadaki, T., Okazaki, H., Nakata, Y., and Shimini, Y. (1990). Mater. Trans. JIM, 31(11), 935. Taillard, R., and Pineau, A. (1982). Mater. Sci. and Eng., 54, 209. Taylor, S, S., and Biggs, T. (1996). South African Patent No: 9618932, Oct. 24. Towle. N. R. (1999). Order ffardeningofPlatinm Al1oy.q MSc Dissertation, University of Cape Town, South Afnca. Towle, N. R., Lang, C. I., and Miller, D. (1998). Proe. Micras. Soc. Southern Africa, 28, 15. Tsurikov, V. F., Sokolovskaya, E. M., and Kwkova, E. F (1980). Vestnik Mosliovskogo Universibeta, 35(5), 512. Vermaak, C. F., and van der Menve, M. J. (2000). The Platinum Mines and Deposits of the Bushveld Complex South Africa. Mintek, Randburg, South Afnca. p. 118. Viefhaus, H.. Row, J. P., and Grabke, H. J. (1993). Steel Research, 64(7), 369. Viljoen, M. (1998). World Platinum Congress, Nov. 18-19, Sandton, South Africa, Centre for Mining and Energy, 42 pages. Villars, P.,and Calvert, L. D. (1985). Pearson’s Handbook of CrystallographieDatafor Intermetallic Phases, ASM, Ohio. Vitek, V., Sodani, Y., and Cserti, J. (1991). Mut. Res. Soc. Proc., 213, 195. Walston, W. S., Ross, E. W., Pollock, T. M., O’Hatd, K. S., Murphy, W. €3. (1995). US Patent No. .5,455,120, Oct. 3. Wang, S.-P,, LI, Y.-J., Chang, X.-M., Yang, Y.-H. (1966). Precious Meials 1996, June, Newport Beach, California, USA, International Precious Metals Institute, 245. Warlimont, H., and Delaey, L. (1974). Prog. Matls Sci., 18. Warren, B. E. (1965). Trans. Metall. Soc. AIME, 233, 1802. Wayman, C. M., and Harrison, J. D. (1989). JOM, September 26. Wee, D.-M., Noguch, O., Oya, Y., and Suzuki, T. (1980). Tranx JIM, 21, 237. Wee, D.-M., Pope, D. P., and Vitek, V. (1984). Acta Metall., 32(6), 829. Wee, D.-M., and Suzuki, T. (1979). Trans. JIM, 20, 634. Westbrook, J. H. (1977). Metall. Trans. A , SA, 1327. Wolff, I. M. (1994). South African Patent No. 9413626 (25 May). Wolff, I. M. (1995). Endeavour, 19(1), 20. WOE, I. M. (1996). Metall. and Mater. Trans. A., 27A, 3688. Wolff, I. M. (1997). JOM, January, 34. Wolff,1. M. (1999). South African Journal of Science, 95, 539. Wolff, I. M., Cornish, L. A., Sauthoff, G., Steyn, H. DeV, and Coetzee, R. (1997). Structurat Intermetallics 1997, Proc. 2nd International Symposium OR Structural Intermetallics, Seven Springs, Champion, 21-26 Sept.
(eds M. V. Nathal, R. Darolia, C. T. Liu, P. L. Martin, D. B. Miracle, R. Wagner, and M. Yamaguchi). Tfhe Minerals, Metals tk Matertals Society, 815. WOW, I. M., Iorio, L, E., Rumpf, T., Scheers, P, V. T., and Potgieter, H. (1998). Mater. Sci. and Eng. A , 241 (1-2), 264. Wolff, I. M., and Cortie, M. B. (1993). South $ric.an Patent No: 9312674. Wolff, I. M., and Cortie, M. B. (1994). Gold BuIieiin, 27(2), 44. Wolff, I. M., and Hill, P. J. (2000). Proc. Iradiwn (eds E. K. Ohnner, R. D. Lanam, P Panfilov, and H, Harada). The Minerals, Metals and Matertals Society, 259. Wolff, I. M., and Pretonus, V. R. (1994). Gold Technology, 12, 7. Wolff, I. M., and Sauthoff, G . (1996a). Metail. and Muter. Trans. A., 27A, 1395. Wolff, I. M., and Sauthoff, G. (1996b). MetalZ. and Mater. Trans. A., 27A, 2642. Wolff, I. M., and Sauthoff, G. (1997). Acra Mater., 45(7), 2949. Wolff, I. M.,and Sauthoff, G. (1999). Unpublished research, Mintek, South Africa. Wong-Kian, M., Cortie, M. B., and Cornish, L. A. (1998). Meter. Sci. and Tech., 14, 1242. Wopersnow,W., and Raub, Ch. J. (1979). Metall., 33(7), 736. Wu, S. K., and Wayman, C. M. (1987). Meiallography, 20, 359. Xu, Y., Makhlouf, S. A., Ivanov, E., Wakoh, K., Sumiyama, K., and S U M ,K. (1994). Nanostructured Materials, 4(4), -437. Yamabe, Y., Koizurm, Y., M u r a k m , H., Ro, Y.. Maruko, T., and Harada, H. (1996). Scripza Mater., 35(2), 211. Yamabe-Mitarai, Y., Ro, Y., Maruko, T., Yokokawa. T., and Harada, H. (1997). Structural Intermetalks 1997, Proc. 2nd International Symposium on Structural Intermetallics, Seven Springs, Champion, 21-26 Sept. (eds M. V. Nathal, R. Darolia, C. T. Liu, P. L. Martin, D. B. Miracle, R. Wagner, and M, Yamaguchi). The Minerals, Metals & Materials Society, 805. Yamabe-Mitarai, Y., Hong, M.-H., Ro, Y.. and Harada, H. (1999a). Phil. Mug. Leits, 79(9), 673. Yamabe-Mitarai, Y., Ro, Y., Maruko, T,, and Harada, H. (1999b). Scrpta Mater., 40(1), 109. Yamabe-Mitarai, Y., Gu, Y., Ro, Y., Nakazawa, T., Maruko, T., and Harada, H. (1999~).Scriptu Mater., 41(3), 305. Yi, S. S., Chen, B. H., and Franzen, H. F. (1988). J. Less Common Metals, 143, 243. Yu, X. H., Yamabe-Mitarai, Y., Ro, Y., Gu,Y., and Harada. H. (1999). Scripta Mater., 41(6), 651. Yu, X. H., Yamabe-Mitarai, Y., Ro, Y., and Harada, H. (2000). Key Engineering Materfals, 171-174, 677. Yuasa, S., Miyajima, H., and Otani, Y. (1994). J. Physical Soc. Japan, 63(8), 3129. Zhu, S . M., and Tjong, S . C. (1997). Metall. m d M a t . Trans. A., B A , 1095.
are-Earth
mpounds
Marfa L. Pornasini, Franco Merlo and Department of Chemistry and Industrial Chemistry, University of Genova, Genova, Italy
1. I~tro~uction Among intermetallicphases, the compounds containing rare-earth atoms form a numerous class, well studied for many years in both fundamentd and applied research. Nearly all known phases are binary or ternary compounds, with some general features, Binaries, formed by rare-earths with elements from manganese to the nitrogen group, are in most cases strictly stoichiometric, solid solutions being usually rare. Ternaries occur in most cases in R-T-X systems, where R is a rare-earth, T is a transition metal of the titanium to copper groups, and X is a post-transition element. In these phases, homogeneity ranges are frequently observed,coveringin some cases large fields in the compositional phase diagram. The term rare-earth refers to the Lanthanide family (lanthanum to lutetium), and for reasons of chemical similarity usually includes the other two elements of the third group, scandium and yttrium.* For these 17 elements the alloying behavior observed is not uniform, as shown by the experimental data. According to a simple analysis of composition and crystal structure of the existing phases, the rare earths can be divided into three groups: 1. The normally trivalent lanthanides, namely from
lanthanum to Iutetium, save europium and ytterbium, but including yttrium, 2. Europium and ytterbium, which in most systems behave as divalent a t o m , in a similar way to the alkaline-earths (calcium, strontium, barium), 3. Scandium. *See p.108 for a useful and amusing mnemonic for recalling the sequence of the rare-earth elements.
The three different behaviors are due both to the valence situation and for dimensional reasons. Moreover, in some systems cerium and ytterbium (and rarely europium, samarium and thulium) display valence instabilities,giving rise to anomalous physicd properties which are described by several theoretical models (intermediate valence, Kondo systems, heavy fermions).
2. Stability and Crystal Structure 2.1 Thermal Stability
A large number of rare-earth metal phase diagrams, especially of binary systems, has been determined, and the considerable volume of data on melting (or peritectic) temperatures gives information about the thermal stability of the intermediate phases, Figure l(a) reports all the phases found in the binary systems formed by gadolinium with the X elements from 7A to 15B groups of the periodic table. The phase diagrams are known for all Gd-X systems save for X = OS,Ir, Zn, Hg, and As. Considering the proposed Pr-0s diagram (Massalski et al., 1990) and the available thermal data on the Ce-Ir, Sm-Zn, La-Hg and Nd-As diagrams, it is possible to locate the solid phase with the highest melting temperature in each system. In nearly all cases this phase melts congruently, while GdMn,,, Gd,Fe,, and GdMg show a peritectic formation: the lines join these phases within every group, and the corresponding temperatures, indicated as T,,, are plotted in Figure I@). When X is a transition element, the composition of the phase with the maximum thermal stability is rich in X (at least GdX& and the corresponding T,, values are close to the melting temperatures of the X elements, which
Intermetallic Compounds: Vol. 3. Prmczples and Practice. Edited 1)y J. H. Westbrook and R. L. Fleischer. 02002 John Wiley & Sons, Ltd.
Ill I/ I //I I
0 Mn Fe
Rh
RU
OS
eu
Ni
CO
Pd
Ir
Pt
Mg
As
Al
Zn Au
Si
Ga Cd
Hg
As
Ge Ill
n
Sn
sb
Pb
Bi
Figore 1 (a) Schematx representation of the binary phase diagrams, For each system generally gadolinium IS chosen as representative and full circles indicate the existing intermediate phases. The lines join the phases with the highest melting or pentectic temperature (TmM) in each system; (b) Penodic trend of T,,
show a similar periodic trend. These two features indicate a prevailing influence of the chemical bond interactions o f the X sublattice. From the copper group onwards the composition of the most stable compound changes to GdX (or Gd,X, for X = Ge, Sn, or Pb), and the T,, values are considerably higher than the X melting points, reaching a difference of 1740°C for GdBi. This can be imputed to the strengthening of the R-X interactions, indicating a lower metallic character and an increase of the bond ionicity: in other words, a transition from purely metallic phases to true chemical compounds.
2.2 Volume ERects The formation of an intermetallic phase is accompanied by a volume effect. The average volume per atom Vexp, experimentally obtained from the ratio ‘elementary cell volume’/’number of atoms per cell’, is usually different from the ideal value VdCr calculated from the
proper combination of the elemental atomic volumes of the components. In most rare-earth compounds a volume contraction occurs, namely the quantity A V/V = ( Vexp- V&)/ Vcalcis negative, though slightly positive or zero values are sometimes observed. The phases formed by the divalent rare-earths (Eu, Yb) show the maximum AVlV values, and the heavy rareearths (from Gd to Lu) give volume contractions higher than light rare-earths. Within a binary R-X system, the AV/V values are different for each compound, but show a regdar trend versus composition, reaching the maximum for a given phase. Figure 2(a) reports these maximum AV/Vvalues in the binary Gd-X compounds, the observed contractions ranging from 1 to 15%. The 25% contraction shown by silicon and germanium phases (in particular GdSi, and GdGe,) is mainly a geometrical effect, due to the strongly different packing efficiency in the compounds compared to the diamond-type structure of elemental Si and Ge. The other factors influencing the volume
87
O
25-
x
atomic percent
loo
0
100
A V N ["h]
20 15
-
10 -
c-c--J
5-
Figure 2 (a) Periodic trend of the maximum volume contraction values (AV/V) observed in the binary Gd-X compounds; (b) Experimental average atomic volumes (V,,) versus composition in some binary gadolinium systems. Dotted lines show ideal trend; full curves are calculated according to Merlo and Fornasini (1993). The Vex,,scale is indicated only for the Gd-Ni system
deviations from the ideal linear trend between the elemental volumes are the elastic effects (energy necessary to change the volume of the Wigner-Seitz cells up to the equilibrium density in the compound) and the ionic effects (charge transfer due to the electronegativity difference between the component atoms). In Figure 2(b) some examples of average atomic volumes versus composition are plotted, for gadolinium systems with a large number of intermetallic compounds. The dotted lines indicate the ideal trend, while the full curves are calculated following an empirical model (Merlo, 1988; Merlo and Fornasini, 1993), which suggests the main role of charge transfer effects when X is a transition metal, and the greater
influence of elastic effects when X is a post-transition element.
2.3 Binary Compounds From a statistical point of view, the distribution of the intermediate phases in the R-X systems is not much different from that shown by Iandelli and Palenzona many years ago (1979). Taking into account the intennetallic data compilation (Villars, 1997) and the last five years of scientific literature, the current total of about 2500 binary rare-earth phases covers 65 different compositions, going from Sc,,Os,to YB,,. As shown in Figure 3, where the number of phases is reported as a
88
Structure w d Composition
1:2
1:l
400 QD
300 1:3
1 5 217
0
20
60
100
Figure 3 Statistical distributionof the R& phases as a function of the X content. The most frequent compositionsare indicated
function of composition, the most frequent formulae are RX, ,RX ,RX3and R,X,. The structurally known R,X, compounds crystallize in about 200 different structure types, with a large variety of bond-length values and atomic-coordination geometries. This situation i s the main reason behind the unusual chemical behaviors and exceptional physial properties which gwe rise to the numerous practical applications of rare-earth intermetallics. The importance i s clear of any theoretical or empirical method able both to rationalize the existing crystaltographic data and to obtain predictions on the existence, structure and properties of new phases (see chapter by Kiselyova). The method of structural maps, widely used for many years, and extensively applied to intermetallic compounds by Villars (1995), points out the physical factors which influence phase stability. Figure 4 shows the occurrence and the crystal structure of the binary phases with the four most frequent compositions formed by the trivalent rare-earths and yttrium. Only the phases stable at normal temperature and pressure conditions axe rqorted. The X elements are arranged as in the periodic table, and this sequence appears to be
one of the most important rationalizing factors; clustering of most structure types in certain regions is observed. Concerning the RX, phases, a great variety of structural types is observed. Save for the AuCu, (Pearson code cP4) type, which is spread over nearly the whole periodic table, the other types seem stable only in particular regions: from left to right the sequence is NbBe, (hR36) and CeNi, 01p24) first, then TiCu, (oP8), BiF, (cF16). and SnNi, (hP8). It is known that NbBe, and CeNi, are closely related, while the types AuCu,, SnNi,, TiCu,, ErCd, (oC16), HoA13 (hR60). TiNi, (hP16), BaPb, (hR36) and PuGa, (hR48) are all based on different stackings of close. packed layers. Stability domains of the different structural types can be recognized even for the RX2 compounds: for example, the Laves phases (MgCu, (cF24) and MgZn, (hP12) structure types) form mainly with transition elements, then the tetragonal MoSi,! (tI6) is encountered, followed by the AIB2 (W3), CeCu, (0112) and CeCd, (hP3) types, all three strictiy correlated and based on the trigonal prismatic coordination of the X
Rare-Earth Metal Compounds
Rx
Ra
0s
Ir
.I Pt
0
OCsCI
OCrB
mCaAt
oTlrNi(r)
O A
Mg
AI Si I.r901no
1%
Au
Hg
Tl
Bi
0 A O
#
* U
AFeB
1NaCI
Pb
vDyM
89
1
A
oAuCul
(e)
0
MnJSib
OQg&
Aw&$
APU&
t PlWbJsb,
Ph
Sb
fa)
Figure 4 Distribution of the structural types occurring for the known phases with composition RX, (a), RX, (b), RX (c) and R,X, (d), where R =trivalent rate-earths and yttrium. The symbols are drawn if at least one compound within the series exists
atoms. The types CaC, (tI6), a-ThSi, (t112), ZrSi, (oC12), TbGe, (oC24), Lap, (mC48), NdAsz (mP12) and SmSb, (oC24) occur only with the 4B and 5B group elements, and are mainly governed by the bond geometry of the X sublattice. A rather complex situation can be observed in the RX table of Figure 4, where the three most frequent types (CsC1 (cP2), CrB (oC8), FeB (oP8)) appear in partially overlapping domains. As already pointed out (Schob and Parthk, 1965; Hohnke and Parthk, 1966), the CrB- and FeB-type compounds, dominated by the trigonal prismatic coordination of the X atoms, are separated in two classes, and elongated or compressed prisms are found when X is a p-element or a transition metal, respectively. The phases crystallizing in the NaCl (cF8) type are restricted to the 5B group elements, and can be classified as normal valence compounds.
The hexagonal Mn,Si, type (hP16) frequently appears among the R,X3 phases. For many years it has been known that, by filling the octahedral interstices of this structure, a ternary ordered HfsSn3Cu (or MoSSi3C,hP18) type is formed, and several filled-up rare-earth stannides, plumbides and bismuthides have been reported. In more recent years this filled structure has been found for compounds such as LasGe3Z and La5Pb,Z, with a wide range of the Z element going from transition metals to halogens (Kwon et al., 1990; Guloy and Corbett, 1992, 1993, 1994). The corresponding binary compounds exist with the same unfilled MnsSi, structure, but in La&$ with Z = C,,O, this structure type is stabilized only by the insertion of the third element, whilst the parent compound LasSn3 crystallizes with the tetragonal WsSi3 (tI32) structure. Moreover, the filling with some particular elements may cause a structure
Structure and Composition
90
change, as in La,Pb,2 with Z = N , 0,where an interstitial derivative of the tetragonal Cr,B, (tI32) type is formed. Examples of contamination by hydrogen, probably present in the starting, commercial purity, rare-earth metals, were found in R5X3 phases with R = Eu, Yb and X = Sb, Bi, previously reported in the literature to have the orthorhombic P-YbsSb3 (oP32) structure type. They are really R,X3H, compounds, with hydrogen atoms in the tetrahedral interstitial sites, but after heating these products under high vacuum, high temperature conditions, hexagonal Mn,Si,-type phases can be obtained (Leon-Escamilla and Corbett, 1998). So, the capability of inserting a variety of elements in the host lattice in a controlled way can be useful either to stabilize compounds with that structure, or to obtain compounds with interesting physical and mechanical properties (Corbett et al., 1998). 2.4 T e m q Conrpoinndr
A compilation of crystal data and a discussion of the crystal chemistry of ternary rare-earth intermetallics were made by Parthe and Chabot (1984). Their proposed division of these phases into three classes is still valid: 1. Truly ternary phases, where the different elements
occupy different crystallographic sites. In some cases the structures are ternary ordered derivatives of binary types. 2. Truly ternary phases, where certain crystallographic sites are randomly occupied by different atoms. Extended homogeneity ranges are often observed. 3. Ternary solid solutions formed by binary phases with the third element. An updating of ternary phase equilibria and crystal chemistry in ternary rare-earth systems was reported by Gladyshevskii et al. (1990). The total number of known ternary phases increases every year, and nowadays about 5500 compounds are known, covering 21 1 different compositions. Figure 5 shows the distribution and the number of the 20 more common phases versus stoichiometry: RTX, RT,X, and RTX, are the most frequent formulae, which go from ScgFeGa (01142) to CeCr,Al, (cF184). The structurally known ternary compounds crystallize in at least 360 different structure types. Figures 6, 7 and 8 show the Qccurrence and crystal structure of the RTX, RT2X2and RTX, phases, respectively, considering only the trivalent rare-earths and yttrium. The T
X
Figure 5 Distribuhon of the 20 niore frequent RT rareearth intermetallic compounds versus composition base of each bar). The corresponding number of phases is proportional to the bars length, considering that about 1000 RTX phases are known
&
and X elements are placed on both axes and arranged according to the chemical scale proposed by Pettifor (1986a,b); the crystal structure symbols in each T-X box indicate the occurrence of one or more out of the 14 possible rare-earth phases. The triangular graph of the RTX phases IS complete on both axes, while for the other two compositions only the rectangular region containing all known phases is reported. The simplest crystal-chemical situation is shown by the RT,X, phases, which mostly belong to the very similar ThCr2Si2(tIl0) and CaBe,Ge, (tP10) types, two ordered derivatives of the B A 4 (t110) structure. The X atom is always an element of the 3B, 4B or 5B groups. A little more complex distribution is found for the RTX, phases, owing to the occurrence of 14 different structure types. If we regard the X atoms in phases crystallizingwith the three most frequent types, a general glance at the graph shows that the CeNiSi, type (oC16) occurs only with the 4B group, HfCuSi, (tP8) with the 5B group and YNiA1, (or MgCuAl,, oC16) with the 3B group elements. Most of the CeNiSi,-type phases are non-stoichiometric, with wide homogeneity ranges, and the true formula is
Rare-Earth Metal Compounds
91
Figure 6 Distribution of the crystal structure types for the RTX compounds (R=tnvalent rare-earths and yttnum; T, X =elements of the BA to 5B groups and Li, Ti, Mn). Both axes report the T and X elements arranged according to Pettifor's chemical scale. Each T-X box includes the 14 RTX systems, and the symbols refer to the structure type of the existing phases. The outlined region corresponds to four electron concentration values: 25/3, 26/3, 2713, 28/3 electrons/atom
usually R T a 2 with 0.1<x<1. An interpretation of such a situation was given in terms of a variable interstitial solution of the T atoms in a ZrSi,-type (oC12) RX, sublattice (Francois et al., 1990; Venturini et al., 1990). The maximum number of structure types (24), of observed T-X combinations (105) and compounds formed (more than 1000) is shown by the equiatomic RTX class. A four-dimensional structure map can be applied to these compounds, using the same parameters employed to analyze a part of these phases (Fornasini and Merlo, 1995): the size parameter Ar) = r ~ / ( ~ + c yQ), considering the elemental radii for coordination 12 (Teatum et aZ., 1968); the electrochemical parameter A@*)= -@ - @ff, where @* is the Miedema electronegativity (de Boer et al., 1988); the periodic parameter Px,namely the period number of the X element; and the valence electron concentration VEC. The problem in evaluating
+
this last quantity can be solved by taking the corresponding group number (e.g. 3 for La, 8 for Fe, or 14 for Si). These values reproduce the sequence of the elements in the periodic table, whose influence on crystal structure distribution is recognizable in Figure 6: as can be seen, most phases occur in the systems with four VEC values, from 25/3 electrons/atom (e.g. for the WeSi phases) to 28/3 electrons/atom (e.g. for RNiP). The corresponding region, outlined in the figure, contains 181 different T-X pairs, with 2534 possible RTX compounds. About 980 phases are structurally known, crystallizing in 2 1 structure types. Therefore, the structural map contains the eight sections corresponding to VEC = 2513, 261'3, 2713, 28/ 3 electrons/atom; Px = 3;4 and Px = 5;6 (Figure 9). The graph reports only some border points within each series of 14 possible phases for a given T-X pair. Half of the structure types (PrPdSi (mP24), ScAuSi (hP6), MgZn, (hP12), LaIrSi (cP12), CeRhAl COP%),
92
Structure and Composition
Figure 7 Distribution of the crystal structure types for the RT,X, compounds (R=trivaIent rare-earths and yttrium; T, X = elements of the SA to SB groups and Cr, Mn, Re)
V
Figure 8 Distribuhon of the crystal structure types for the RTX, compounds (R= trivalent rare-earths and yttrium; T, X = elements of the 8A to 5B groups and Li, Mn, Re)
93
Rare-Earth Metal Compounds
....
f(4j*l 7
6 5 c
.5
.... ....
.6 @) .7
7
6
5
Fignre 9 Structural map for the RTX phases (R = trivalent rare-earth and yttrium; T, X =elements of the 8A to 5B groups). The coordinates are the combination of the elemental radii,Ar) = r ~ / (+r px), ~ the combination of the electronegativitieson the Miedema scale&#*)= @ + @$the valence electron concentration ( Y E Q and the period number of the X element (Px). The symbols indicate the structure types
e,
CeGoAl (mC12), LuNiGe (oc48), EuNiGe (mP12), WdSi (oP24), gYbAuGe (oP36), TiFeSi (0136)) occur rarely, and orrly in limited regions of the map. Some types are frequent and well localized, such as the LiGaGe (hP6) and MgAgAs (cF12) types, whose occurrence appears mainly related to the VEC value of 28/3 electrons/atom, and the GeFeSi (tP6) phases, clustered in a region defined by Px=3;4 and VEC= 2513; 26/3 electrons/atom. On the other hand, the very frequent TiNiSi (oP12) and ZrNiAl (hP9) types spread over a large tridimensional region, and nearly everywhere the correspondingdomains overlap. Though the spatial separation of the different structural domains appears incomplete, this type of data representation can be considered useful, as some predictions of the structure of the unknown phases are possible, The imperfect structural definition of the map i s mainly due to the small energy differences among structure types which are geometrically related.
The best example is the structural family derived from the AlB, type. As pointed out by many authors (e.g. see Gladyshevskii et al., 1992; Kussmann et a[., 1998), all these types are based on the trigonal prismatic coordination of the non-rare-earth atoms, and can be obtained from the parent type by different ordering on the T and X sublattices, and/or deformation of the elementary cell. Figure 10 reports some examples of 1:1:l types, which maintain the hexagonal symmetry, while Figure 11 shows some orthorhombic and monoclinic variants, usually derived from the simplest form, the CeCua type. 2.4.1 Crystal Structure qf the
Nd, (Fe, -xTiJ29- Type Phases awing to their interesting magnetic properties, a particular note on the crystal chemistry of the novel R,(Fe, --xMx)29phases is given. The magnetic ternary
94
Structure and Composition n
2
YbAgPb
LiGaGe
ScAuSi
nisa
Figure 10 Hexagonal structures denved from the AIB, type. The AIB, cell is viewed along c; all others are projected along the [I 101 direction. R, X and T atoms are represented by large, medium and small circles, respectively. Open and full circles are at heights 0 and ;in the case of YLiSn the double circles are at heights $ and $. The lines connecting the R atoms show the trigonal prisms. For YbAgPb, see Merlo et nl. (1996); for all other structures, see W a r s (1997)
4
phase Nd,(Fe, -xTix)29 was reported with monoclinic symmetry (Li et al., 1994). This phase is not formed in binary alloys of rare-earths with iron, but a third element, such as Ti, V, Cr, Mn, Nb, MO, or Re, is necessary to stabilize it. The quantity of additional element can bc as small as x=0.022-0.067 for Ti, larger as x = 0.14-0.17 for Cr and x = 0.39 for Mn, or a mixture of additive elements can be used. Owing to the potential application of these materials for permanent magnets, a lot of work has been done in recent years on their characterization and magnetic properties determination. Several phases were studied R,(Fe,Ti),, with R = Ce, Pr, Nd, Sm, Gd, Tb, Dy, or Y (Fuerst et al., 1994a; Ibarra et al., 1994; Margarian et al., 1996; Li et aZ., 1996; Yang et al., 1997); R,(Fe,M),,
-
with R = Ce, Nd, Sm, Gd, Tb, Dy, or Y and M V, Cr, or MO (Han et al., 1997; Hu et al., 1998); Nd,(Fe,Mn), (Fuerst et aZ., 1994b); Sm3(Fe,Re)29 (Ivanova et al., 1996) and Gd,(Fe,Nb),, (Huang et al., 1999). By powder neutron diffraction the site occupation of some phases was determined (Yelon and Hu, 1996), while recently success in single-crystal growth has been obtained (Courtois et al., 1998; Mendoza and Shaheen, 1999; Yang et al., 1999a,b). The structure of Nd,(Fe,Ti)29(mS64) was described as belonging to the monoclimc A2/m space group (Kalogirou et al., 1995) and to contain 2 Nd and 11 Fe/ Ti sites. It belongs to the series of structures derived from RT5 (CaCurtype), where R is a me-earth (or actinide) element and T is a transition element, by
95
Rare-Earth Metal Compounds
a
b
EuAuln {Ti~iSi)
EuAuGe
a
a-U FeGe a
b YPdSi
b
EuAuSn
CaAuSn Figure 11 RTX structures derived from the CeCu, type by different ordering of the T, X atoms and/or deformation. Large, medium and small circles: R, T and X atoms. Open and full circles represent atoms on layers separated by half the period along the projection axis. To facilitate the comparison,the R distorted trigonal prrsms are connected by lines. The references are: oc- and y-YbAuGe (Merlo et al., 1998), YPdSi (Prots’ ef al., 19981, EuAuGe (Psttgen, 1995), EuAuSn (Pottgen er al., 1997), EuAuIn (Pottgen, 1996), oc-UFeGe (Canepa eb al., 1996), CaAuSn (Kussmann et al., 1998)
96
Structure and Composition
a43 Th22n17
a
ThMn, Rgure 12 Sectionsat zero height of the Nd,(Fe,Ti),,, Th,Zn,, and ThMn,, cells. Large circles: Nd or Th; small circles: Fe/Ti, Zn or Mn in the section plane; double circles: Fe/Ti, Zn or Mn atoms above and below the section plane. The segments of the '€h,Zn,-, and ThMn,, structures forming the Nd,(Fe,TiX, structure are outlined
replacing some R a t o m with T-atom pairs (dumbbeus) coaxial with the hexagonal c axis of the CaCu, cell. A classification of these structures was made by Stadelmaier (1984), who proposed the formula Rm-nT3mc2n, where m denotes the number of units RT, making up the new structure, and n is the total number of R atoms being replaced. For the 3:29 phase we have m = 5 and n = 2. This series also includes the well-known 2:17 stnictures (hexagonal Th2Ni,7 and rhombohedral ThZZnl7) and the tetragonal ThMn,, structure. So, it is not surprising that the structure of the 329 phase can be regarded as formed by an intergrowth of the Th2Zn,, and ThMn,, types, as already mentioned by several authors. The structure of Nd,(Fe,Ti), is represented in Figure 12 together with the Th2Zn17and T W n l 2structures, the axis perpendicular to the sheet being b for the monoclinic 329 cell, a
for the orthohexagonal 237 cell and a2 for the tetragonal 1: 12 cell. Along !his common direction the lattice translation is -&SA. Only the basal plane of each ?I1 is drawn, but the entire outlined blocks, 8.5 A thick, are identically reproduced in the 329 structure, maintaining the same composition of the component 2:17 and 1:12 structures.
-
3. PhyslcaI Properties
Many technological applications are based upon those special thermodynamic, magnetic, electronic, optical and purely chemical effects of solid materials, that are mostly found in intermetallic systems. Table 1 reports a fist of such effects, their main applications and one example of a useful material for each effect. Some
97
Rare-Earth Metal Compounh Table 1 Examples of technological applications based on physico-chemicalproperties of IMCs
Physico-chemicaleffect
Application
Material
Magnetic ordering Kerr effect Magnetostriction
Hard and soft magnets Magneto-optical data storage Actuators Read heads Cryogenerators Energy storage Refrigerators
Nd2Fe,,B BiMn, amorphous Tb-Fe-Co Tb, ,Dy, ,Fe, (“Terfenol-D’) InSb-NiSb, La,,,Ca, ,,MnQ, Gd, @,Gel -J6
Magnetoresistance Magnetocalonc effect Hydrogen absorption Peltier effect Chemical reactivity Thermionic effect Secondary emission Semiconductivity
Superconductivity
Getters Electron guns
Photomultipliers Electromc devices
Charge transport
substances have been in use for many years, others are not yet commercially employed, but the role played by rare-earths is very important. The 1995 edition of Intermetallic Compounds and the present one consider in detail nearly all the listed applications, and some other important topics such as structural superalloys uses. In the following, a sampling of literature data of the last five years will be given for five different applications of rare-earth intermetallics.
3.1 Magnetic Properties An overview of magnetic properties and applications of intermetallics was given in Vol. 2 of this treatise by Stadelmaier and Reinsch (1995). The properties of ordered magnetic systems have been described by theoretical models, showing the role of the different types of interactions in determining the material performance. The following general reviews may be cited: Gignoux and Schmitt (1995), Duc (1997), Richter (1998). Cadogan, in another chapter of this work, extensively reviews magnetic interactions of IMC constituents and in particular magnetic phase diagrams. Here we summarize the structures and properties of rare-earth intermetallics of magnetic interest. 3.1.1 Nd2Fe,,B Phase
Nd2Fe14Bis the well-known basis of high performing hard magnets and for several years its manufacture has entered into commercial production. Recent developments have increased coercivity and corrosion resistance and decreased material and production costs. Other efforts have been directed to overcome the poor thermal stability of this compound, due to its
LaNi,
Bi,Te, Ba,A1,3 LaB, Cs,Sb GaAs
Nb,Sn, Nb-Ti solid solution
low Curie temperature and the strong temperature coefficient of remanence and of coercive field. Several types of substituent or additive elements were studied, but the problem is that each of them, while improving some properties, is unfavourable for others. So, a proper control of the amounts of the added elements is essential. Typical substitutions are made by replacing the Nd atoms with Dy or Tb, and Fe atoms with CO,Ni or Cr, thereby achieving a considerable change of intrinsic properties, such as the magnetization, the Curie temperature, and the magnetocrystalline anisotropy. Additive refractory elements such as Nb, MO, V, W, Zr. or Ti both suppress to some extent the formation of iron particles, which could act as nucleation centers for Bloch walls, and inhibit grain growth during sintering, which would reduce the coercivity (Buschow et al., 1995). In order to obtain a uniform, fine grain size, stable during thermal processing, a dispersion of a stable second phase may be used. The addition of Ti + C, which produces particles of T i c in the form of a fine precipitate, improves the microstructure of the Nd,Fe,,B phase without changing the properties of the base alloy (Branagan and McCallum, 1995). With an addition of 0.25 at.% Cu to a NdI6Fe,,B8 alloy during a powder metallurgy processing route a coercivity HC> 1000kA m-l was obtained while maintaining a remanence of 1.3 T (Ragg and Harris, 1987); a further improvement with H,= 3290 kA m- was reached by substituting Dy for 30 at.% Nd in melt-spun Nd-rich alloys (Harland and Davies, 1998). The Dy snbstjtution is effective also for high-temperature properties. For better corrosion resistance, it is necessary to change the Nd-rich grain boundary from a reactive to a non-reactive phase. It was found that a combined addition of very small quantities of Cu,CO and 0 in
98
Structure and Composition
(Nd,Dy)-Fe-B alloys substantially improves the coercivity, high-temperature properties and corrosion resistance, without a reduction of the remanence (Rim and Camp, 1996). Furthermore, the addition of V and Nb decreases the oxidation rate in sintered NdFe-B phases (Steyaert et af., 1998). Herbst (1991) has provided a detailed review of R2Fe14Bcompounds. A precise crystal and magnetic structure determination of Nd2Fe14Bwas made 011 a single crystal by neutron diffraction, in order to better understand the nature of the spin reorientation transition, which occurs below 14OK. It was shown that this transition, besides changing the anisotropy from an easy c axis to a canted structure, causes a lowering of the crystal symmetry, which changes to the monoclinic Cm space group (Wolfers et al., 1996). This monoclinic distortion was also confirmed by a single-crystal X-ray detennination (Obbade et al., 1996). 3.1.2 R2(Fe,M)17 Phases
During the last five years, much work has been carried out on the R2Fel7-,M, compounds with M =AI, Ga or Si, studying also the effects of interstitial H, C, and W atoms. Some regularities are observed. The maximum numher of iron atoms being replaced by A1 or Ga is x = 8-9, and generally this substitution, even in sniall quantity, stabilizes the Th,Zn,, structure (space group Rgm). This is also the case for the heavy rareearths. Since the atomic size of AI or Ga is larger than that of Fe, the guest elements firstly replace iron in the I8h site, and then in sites 6c and 18f,always avoiding Pd, the site with the smallest WignerSeitz cell. However, a limited quantity of Si enters into the host structure (x = 3-44), and only the f8h site is occupied. The introduction of Al or Ga atoms increases the cell volume, while the Si introduction causes a decrease. In any case, a significant effect on the magnetic properties of this family of ferromagneticphases is observed. An x increase leads to an increase of the Curie temperature Tc and in some cases to a change of the anisotropy from an easy plane to the easy c axis. As T, often passes through a maximum for M =AI or Ga, and the magnetization always decreases with x,a compromise has to be chosen. Though several rare-earths were examined, the most promising is Sm, for which a substitution of 2-3 A1 or Ga atoms for Fe reaches the maximum T, value and is more than enough to get uniaxial anisotropy (Cheng et aZ., 1995; Li and Morrish, 1995). The combined effect of the iron replacement and the insertion of interstitial atoms (€3, C, or N) is
particularly interesting. It is known that the interstitial compounds Sm2Fel,N, and Sm2Fe17Cy fy = 2-3) have excellent properties relative to the parent compound, such as a noticeable increase of Tc and spontaneous polarization, due to the lattice expansion, and a strong uniaxial magnetic anisotropy. Another example is the spectacular effect given by nitrogen insertion in CeJ?e17:a transition from an antiferromagnetic state with T, =225K in the starting compound to a ferromagnetic state with Tc = 728 K in Ce,Fe17N, (Tsnard et al., 1996). The problem with these materials, that they decompose when heated above 900 K, can be overcome by a substitution of iron with AI, Ga or Si, which stabilizes the phases and allows the use of high-temperature powder metallurgy to form dense magnets ( M U k et al., 1996). For Sm2Fel,66Gao.,4Ny an anisotropic field MA= 18,4T, a rernanence B,.= 12.3kG, a coercive field H, = 10kOe, a saturation magnetization M, = 137 emu g-l, with T, = 751 K (Yu et al., 1995) are realized; while for the Sm-rich srn2Fe,4si2N,,6 phase, HA= 157kOe, M, = 117emu g- I, and Tc=602K (Hadjipanayis et al., 1995) were obtained. Substitution of iron with other d-elements (Ti, V, Cr, Nb, Zr, etc.) was also examined by neutron diffraction (Luo et al., 1997), since the diversity in site preference of the substituents could give different modificaQons of the Fe-Fe exchange in the Fe sublattice. Moreover, it was found that the insertion of carbon in Nd2Fe,7-xTi, induces a change in the Ti site occupation, passing from the Fe 6c site to the 18f and 18h sites. Recently, new routes were explored in preparing these materials. A carbonitride Sm,Fe,,(C,N),,, obtained by the economical method of mechanically grinding Sm,f;e17 with pyrazine, without crystallization treatment, showed a coercivity of 0.7 T (Jakubowicz and Jurczyk, 1998). An HDDR-processing (hydrogenationdecomposition-desorption-recombination)applied to Sm,Fe,,M (M = AI, Ga and Si) and their nitrides and carbides achieved high coereivities up to 3 T and 2.3 T for nitrogenated and carburized samples, respectively (Kubis et a€., 1999). For special applications at temperatures higher than it is necessary to improve the long-term thermal stability of the material, and this can be obtained in cobalt-rich compounds. In sintered Sm(Coo92_xFe,C~.06Zr~.",7.~ magnets, with TCmIlOOK, an HC=8.3kOe at 400 "C is found when x = 7 wt,% Fe (Chen et al., 1998). More recently, the compound Sm2Co,,A12 shows Tc=904K, M,=61.3em~g-~at 1.5K and &HA=8.4T at room temperature (Shen et al., 1999).
Rare-Earth h4etaE Compounds
3.1.3 R(Fe,M)IzPhases The RFe,,-xMx compounds with ThMn,, structure form another family with interesting ferromagnetic properties. Here the presence of a metal M = Ti, V, Cr, Mn, N13, MO, Ta, W, Re, or Si partially replacing iron is necessary to stabilize the phase. Since the introduction of the above elements always has the negative effect of decreasing both the Curie temperature and the magnetization, a minimum substitution is called for, typical values being x = 1 for Ti, x= 1-2 for V, Cr, MO,W, or Si and x = 0.5-0.7 for Nb and Ta. Out of the three Fe sites present in the ThMn,, structure (space group 14/mmm), the guest element (except Si) always occupies the 8i site, since it has the largest Wigner-Seitz cell and only one rare-earth atom neighbor. This behavior is in agreement with the greater size of the guest element and with its low affinity for the electropositive rare-earths. On the contrary, Si generally prefers the other two Fe sites, Sj and SA allowing contacts with two rare-earth atoms (Lin et al., 1995; Moze and Buschow, 1996; Ayres de Campos er al., 1998; Tang et al., 1999). As for the R2Fet7compounds, the introduction of interstitial H, C, or N atoms improves the Curie temperature and magnetization. By neutron diffraction on RFe,2-xM,Hy phases, hydrogen was found to occupy firstly the octahedral 2b site (2R-4Fe) up to y = 1 and then partially the triangular bipyramidal 8h site (lR-2Fe/M-2Fe) (Obbade et al., 1997), while carbon and nitrogen, absorbed in a smaller amount, enter the 2b sitc too. These materials have the advantage of a good corrosion resistance, but it is difficult to reach high coercivities for application as permanent magnets. Among the rare-earths, Pr, Nd, Cd, Dy, or Y or a mixture of them seem to be the most promising. Good values were obtained for NdFe,Co3TiN, with T, = 860 K, M , = 150emu g-I and &,HA=7.2T (Fujii et al., 1995) and for (Pro.8Dyo.z)Fei,5V1.5Nywith Tc = 815K, M, = 146emug-I and hHA=13.2T (Yang et al., 1996). The new tantalum-containing series and their hydrides and carbides form stable phases only with the heavy rare-earths p e r t et al., 1999). A comprehensive review on the magnetic properties of the ThMn,,-type compounds was made by Suski (1996).
,
3.1.4 R,(Fe,M), Phases
The physical properties of the R3(Fe.M),, phases reflect the characteristics of their crystal structure,
99
composed of blocks of the rhombohedral Th,Zn17 and tetragonal ThMn,, structures in the ratio 1:1. So, in examining the ferromagnetic properties of this family, it was pointed out that the saturation magnetization of compounds containing a low concentration of stabilizing M element (M = Ti, V, or Cr) can be roughly calculated from a combination of the saturation magnetization of the component 217 and 1:12 units (Han et al., 1997; Fang et al., 1997). As already found for the ferromagnetic R2Fe,, and R(Fe,M)lz compounds, the introduction of interstitial H, C, or N atoms here too strongly enhances both the Curie temperature and the magnetization, in relation with a cell volume increase of 2.3-2.8% for H, 4 6 % for C and 5-8% for N insertion. The two positions occupied by nitrogen in the unit cell were determined by neutron diffraction and found to be the same as in 2:17 and 1:12 structures, midway between two neighboring rare-earth atoms, reaching octahedral 2R-4Fe environments (Hu et al., 1996). According to the available nitrogen sites, the maximum number of N atoms per formula unit should be four, but several authors reported also 5-8. A farmation of rare-earth nitrides was proposed as a possible explanation. Another important point concerns the easy magnetization direction in these phases. It is not unique, as in the 2:17 and 1:12 phases, where, when uniaxial anisotropy is reached, it is always found along the c axis. In the monoclinic 3:29 structure the directions [ 1021 and [ZOl] correspond to the c axis of the 2: 17 and 1:12 units, respectively (see Figure 12). Thus we have two directions in competition, the choice depending on several factors, such as the type of rare-earth, the Mstabilizing elements and the presence of interstitial atoms. For instance, for Srn,(Fel-,M$, phases with M=Ti, V, or Cr it was found that the parent compound and the hydrogenated compound show the easy magnetization direction along [ZOl], while nitrogenated compounds show [102] as the easy axis (Koyama et al., 1996). As for the 2:17 phases, Sm seems to be the most promising rare-earth. For Sm~(Fe~,~3~Tio.o~,)29N~ a Curie temperature T, = 750 K, a saturation magnetization M , = 140emu g-l, an anisotropy field p0HA= 12.8 T and a coercivity of 0.83 T were reported (Yang et al., 1994). For S r n 3 ~ e o , ~ ~ * C r oa. , ~ ~ ~ C coercive field of 0.80 T was obtained, with a good corrosion resistance in comparison with a powder sample of commercial Nd-Fe-B (Wang et al., 1997).
100
Structure and Composition
3.1.5 Tetragonal Phases Derived from the NaZn,,
M-doped R-Fe-B permanent magnets, improving the corrosion resistance and coercivity of the alloys. The crystal structure was firstly determined for La6Co,,Ga3 The body-centered-tetragonal CeNi, sSL,5 (tI56) struc(t180) with space group I4/mcm (Sichevich et al., 1985), ture (Bodak, 1979) represents a ternary derivative of where the Ga atoms completeiy fill the 4a site and the well-known cubic NaZnI3 (cF112) type, with partially substitute for CO in a 162 site. When the M partial ordering of the Ni and Si atoms. Several atoms occupy only the 4a site, the structure becomes RT13-xMxcompounds were studied with T = Fe, CO, perfectly ordered and corresponds to the Nd6Fe13Si or Ni and M=Al, Ga, Si, or Ge (Villars, 1997). In type (Allemand et d.,1990). This relatively complex some cases a small amount of p-element stabilizes the structure contains two rare-earth and four iron sites. cubic structure, with a transition to the tetragonal Regarding magnetic properties, in some cases structure with a greater amount. For instance, in the magnetic order near room temperature was observed, PrCo,,-,Si, system for x = 0, no 1:13 phase is formed, but with very low magnetization values. Antiferrowhile for 1 Cx$2 a NaZn13-type phase and for magnetic ordering of the four Fe and two R sublattices 2.5GxG4.5 a CeNi8,,Si45-type phase are found was determined by neutron diffraction, for example in (Huang et al., 1995). A perfectly ordered structure Pr6Fe,,Si and Nd6Fe,,Au (Schobinger-Papamantellos was also reported for compounds with stoichiometry et a).,1999). However, for some NdFe13Mcompounds 1:9:4, for example, LaFe9Si4 (Tang et al., 1994), conflicting magnetic results were reported, probably PrCo,Si, and NdCo,Si4 (Tang et al., 1995). The due to traces of ferromagnetic NdzFe17impurity. transition from cubic to tetragonal seems also to be Even though these materials appear to be of no induced by a prolonged annealing, as was observed in interest for commercial permanent magnets, a number the system LaCo,,-,Si, for as-cast samples with x = 2 of interesting properties has been pointed out. and 2.5 (Rao et al., 1994). Different magnetic anisotropy directions were found In the binary rare-earth-transition element systems by changing the M atom in Nd6FeI3Mphases: for a 1:13 phase exists only for LaCo13(NaZn13-type),with M=Cu, Ag, Au, Sb, or Bi a basal anisotropy, for interesting ferromagnetic properties: a magnetization M=In, T1, Sn, or Pb an axial anisotropy, and for of 126emug-I and a Curie temperature of 1290K M = Si, or Ge a basal anisotropy at low temperatures, (Velge and Buschow, 1968). The combined occurrence but an axial anisotropy at room temperature were of this transition-metal-rich compound and the reported (Hautot et al., 1998). The influence of the possibility of changing to a tetragonal structure upon non-magnetic element on the direction of the magnetic appropriate CO replacement, thus improving the anisotropy may be related to the particular features of magnetocrystalline anisotropy, have raised the interest this structure, where slabs of iron atoms alternate with of many researchers. Several types of element subslabs containing rare-earth and M atoms only. So, it is stitution have been tried, extending the study also to proposed by the same authors that the magnetic other rare-earths and to Fe-containing phases, and anisotropy may be controlled by the s-p hybridization nitrogenation of the alloys has also been explored, in of the Nd-M bonds. analogy with what was successfully attained for the Another property seemingly related to the crystal 2:17 phases (Huang et al., 1996; Liu et al., 1995). structure is the noticeable hydrogen uptake of these Unfortunately, in this case the introduction of nonphases, where 13-20 H-atoms per formula unit are magnetic elements was found to strongly deteriorate absorbed, with a strong anisotropy in the lattice the magnetic properties necessary for a good permaexpansion, an order of magnitude greater along c nent magnet. than along a (Leithe-Jasper et al., 1996). Hydrogenated compounds such as Nd6Fe&UH2*,@(Coey et al., 1994) and Nd,Fe,,GaW,, (Yartys et al., 1997) were reported 3.1.6 R&,-,M, Phases in which a cell volume expansion of about 15% was reached. Remembering that hydrogen is preferentially Phases with the composition R6Fe14-,M, = La, Pr, bound to rare-earth atoms, a favourabie situation for Nd, or Sm; M = 1B to 5B group element; x = 1-32 its absorption i s given by the several available have been studied by several groups over the I'dst few tetrahedral and octahedral interstitial sites inside the years (Weitzer et al., 1993; Weitzer et at., 1994; rare-earth slabs. Kuncser et al., 1997; Hautot et al., 1998). The interest In Figure 13 the structures of LaFe9S& and comes both from their structural and magnetic properNd6Fe13Siare represented together with the related ties and from their occurrence as secondary phases in
Rare-Earth Metal Compounds Ce(Mn,Ni),, (Kalychak et al., 1975) and the ferromagnetic Th4Fe13Sn5(Manfrinetti et al., 1997). These are four tetragonal structures characterized by the same slabs, formed by iron atoms in Nd6Fe13Siand Th,Fe,,Sn,, and by Fe/Si and MnlNi atoms in LaFe9Si4 and Ce(Mn,Ni), respectively. These slabs, which contain an extended network of bonds, highlighted in the figure by icosahedra around the most symmetric atom, alternate with slabs formed by the other atoms of the structure: Nd bicapped square antiprisms centered by Si in Nd,Fe13Si, Th octahedra centered by Sn and layers of Sn in Th4Fel,Sn5. In LaFe9Si4the Fe/% slabs are simply separated by a La layer, while in Ce(Mn,Ni),, the Mn/Ni icosahedra are joined by an edge giving rise to chains parallel to the c axis.
101
3.1.7 Permanent Magnet Preparation
A brief survey of the main manufacturing routes follows, mostly referring to Nd2Fe,,B production. The starting alloys are usually prepared by induction melting of the constituent elements in a protective atmosphere. The second step is magnetic hardening, to obtain fine-grained powders with high coercivity. The main processes, namely metallurgical sintering, melt spinning, HDDR process (Takeshita, 1993) and mechanical alloying are schematized in Table 2. In powder metallurgical sintering the cast alloy is milled, and the powder aligned, pressed and vacuum sintered. After a heat treatment the material is again machined and finally magnetized. The first milling step can be replaced by the so-called hydrogen
Figure 13 Four tetragonal structures characterized by the same slabs of centered icosahedra (dark stippling). The c axis is vertical. In Ce(Mn,Ni),, and LaFe,Si, the atoms belonging to the icosahedra are Mn/Ni or Fe and Si and circles represent Ce or La atoms. In Nd$e,,Si and Th,Fe,,Sn, the slabs of iron icosahedra alternate with slabs of Nd bicapped square antiprisms centered by Si (light stippling) or with slabs containing Th octahedra centered by Sn (light stippling) and layers of Sn (full circles)
Structure and Composition
102
decrepitation @ID) technique, where the coarsegrained alloy is broken up into a fine powder by exposure to hydrogen at around 1 bar pressure and room temperature. The metallurgical route is fairly expensive, but anisotropic magnets are achievcd (Buschow, 1998). Melt spinning i s a rapid-quenchingtechnique. A fine jet of molten alloy, directed onto the outer surface of a rapidly spinning wheel, produces a thin solidified ribbon. The ribbons are then typically ground down into a fine powder. This process produces isotropic powders, due to the random orientation of the grains (Croat, 1997). Another fairly economical way is the HDDR technique. proposed by Harris and McGuiness (1991) and Nakayama and Takeshita (1993). This process i s applied to the Nd-Fe-B magnets and consists essentially of four steps: hydrogenation of Nd2Fe14Bat low temperature, decomposition of Nd2Fe14BH, into NdH, +8 -i- Fe -i- Fe2B, desorption of H, gas from NdH,+I, and, finally, recombination of Nd + Fe + FezB into NdzFe14B.Because the formation of Nd2Fe,J3 grains in the last step is a solid-state reaction, it proceeds at a much lower rate than during normal solidification from the melt. The average grain size remains small, about 0.3pm, and leads to large coercivities.This process was also adapted for magnetic hardening of interstitial Sm2Fe,7N,compounds applying the RDDR treatment to Sm2Fe17N, before nitrogenation (Takeshita, 1993; Muller et al., 1996). In the mechanical alloying technique, the initial alloy preparation is avoided. Powders of the constituent elements are mixed and directly cold worked in a ball mill under an inert atmosphere to yield amorphous
or layered nanostructures, which are then heat treated to induce crystallization. This method, initially used for making highly coercive Sm,Fe,,N, magnets, was successfully applied also to Nd-Fe-B (Harada and Kuji, 1996). Melt-spun Nd-Fe-B may be further treated to produce dense, well-aligned magnets. Full density is achieved by hot pressing, typicaUy at I kbar and 973K under an inert atmosphere. A second hot pressing in a larger die cavity to allow deformation transverse to the press direction (die upsetting) introduces a preferred magnetization direction parallel to the press direction (Lee, 1985). An increase in remanence and fairly large energy products are thus obtained. The die upsetting technique can also be applied to mechanically alloyed material to produce dense anisotropic magnets. Considering the final manufacturing of these materials, bonded magnets constitute a significant fraction of large-scale production. They are prepared by encapsulating the magnetic powder in a resin or polymer and then compacting or molding the material to the final shape. The principal advantages are their good mechanical properties and the possibility of having shaped parts practically ready for use. Normally, the magnetic powder i s obtained by melt spinning, but more recently the HDDR technique was applied and anisotropic bonded magnets produced. Indeed, the grains formed by the HDDR process are aligned to some extent, in the same direction as the parent grains in the original precursor alloy. A proposed explanation for this ‘memory’ i s the presence of fine, undissociated Nd2Fel,B particles which serve as nucleation centres for the recrystallized HDDR grains (Coey and O’Donnell, 1997). A
Table 2 Scheme of the main processes used in permanent magnet preparation
SINTERING
RAPID QUENCHING
ALLOY PREPARATION
ALLOY PREPARATION
i
MILLING
I
I
MELT SPINNING
I
MECHANICAL ALLOYlNG ALLOY PREPARATION
1
HOMOGENIZATION
I
CRUSHING
CRUSHING
1
-1
SINTERING
HEAT TREATMENT
RDDR
i
1
PARTICLE ALIGNMENT AND PRESSXNG
1
HEAT TREATMENT
1
MAGNET
MAGNET POWDER
i
CRUSHING
1
MAGNET POWDER
MILLING OF ELEMENTS
1
HEAT TREATMENT
1
MAGNET POWDER
Rare-Earth Metal Compomds
comprehensive review on processing and applications of rare-earth iron permanent magnets can be found in the book edited by Coey (1996).
3.2 S ~ p e r c ~ ~ ~ c ~ ~ ) ~ t y Stekly and Gregory (1995) presented an overview of superconducting behavior and applications of intermetallics as appeared in the early 1990s. However, the discovery of superconductivity in rare-earth transition metal borocarbides (Nagarajan et al., 1994; Cava et al., 1994d) has opened up a new area of research. These compounds have the formula RNi2B2Cwrth R =: rareearth and have a crystal structure of the tetragonal LuNi,B,C (tI12) type (Siegrist et al., 1994b). The highest critical temperatures in this family were found for LuNi,B,C with T,= 16.6K and YNi,B,C with T, = 15.6K, both containing non-magnetic rareearths; but magnetic rare-earths such as Dy, Ro, Er, Tm also form the same phase, showing interesting phenomena associated with the interplay between superconductivity and magnetic order, never observed before for any type of superconducting material. Moreover, in a multiphase sample of composition YFd,B3Co superconductivity at 23 K was found. which is the highest T, reported for a bulk rare-earth intermetallic alloy (Cava et aZ., 1994c) and close to the record T, of Nb,Ge, 23.2K. A review of the vanety of effects shown by the RNi,B2C phases was made by Gupta (1997). Indeed, DyNi,B,C orders antiferromagnetically at TN= I1 K and becomes a superconductor at 6K, whereas ErNi2B2Cand TmNi2B2Cbecome superconductors at T, = 10.5 K and 11 K, respectively, but order antiferromagnetically at 6.5K and l S K , this long-range order coexisting with superconductivity. HoNi2B2C shows first a magnetic transition and then goes into the superconducting state at almost the same temperature, T C a8 K. So, three different behaviors are encountered with T,< TN,T,> TNand T,x TN.DyNi2B2Cpresents the rather rare transition to superconductivity in an already magnetically ordered lattice. Its magnetic structure is formed by layers of iso-oriented Dy moments stacked antiferromagnetically along the c axis. In ErNizBzC the Er moments undergo an incommensurate antiferromagnetic ordering, being again confined in the ab plane, whereas in TmNi,B2C they are oriented along the c axis. A remarkable feature of HoNi,B,C is its double re-entrant superconducting transition. This compound undergoes a first magnetic transition at 8.5 K and then goes into the superconducting state at almost the same N
103
temperature ( T c z8K). Next it re-enters the normal state at.., 6 K with a change in magnetic structure, and finally regains superconductivity below 5 K, with a commensurate antiferromagnetic order, similar to that of the Dy phase. This behavior, which is very sensitive to the chemical composition and heat treatment of the sample, has been observed for the first time under the condition of zero applied field. Modifications in the nature of the magnetic ordering, in particular the occurrence of incommensurate structures, seem to be responsible for the disappearance of superconductivity. Superconducting RPt2B,C phases, crystallizing with the same structure type, were reported for R = La, Pr and Y, with T, approximately 10K, 6K, and 10K, respectively (Cava et al., 1994b). Moreover, it was observed that, in light rare-earth phases. substitution of Au for Pt and appropriate annealing improve phase purity, while maintaining the same properties (Cava et al., 1994a). Superconductivity is found also in metastable, as-melted ScNi,B2C samples, with T, = 15-16 K (Ku et aZ., 1994), and in an annealed sample of YRu,B,C with T, = 9.7 K (Hsu et al., 1998). With reference to the multiphase U-Pd-B-C alloy showing Tc=23K, much work has been done to identify the superconducting phase. Some authors reached the common conclusion that the phase has a composiQon close to YPd2R2C,with a body-centered tetragonal structure, identical or closely related to the LuNi2B2Ctype, but, owing to the probable metastable nature of this phase, attempts to prepare single-phase specimens have not yet been successful (Jia et al., 1994; Sun et al., 1994; Tominez et aE., 1998). Other superconducting phases, but with different compositions, were found in borocarbide and boronitride systems. In RNiBC compounds, crystallizingwith the LuNiBC (tP8) structure (Siegrist et al., 1994b), upon substitution of Cu for Ni two phases were obtained, for example YNi,-,CqBC with TCz8.9K and LuNi,_,Cu,BC with T,w6.4 K (Gangopadhyay and Schilling, 1996). Superconductivity wa5 also found in the boronitride La,Ni,B,N, with T c z13K (Cava et al., 1994e). Physical properties measurements have been made on both polycrystalline samples and single crystals. Within two months after the discovery of superconductivity in these materials a method of singlecrystal growth based on a Ni,B ffux technique was developed at the Ames Laboratory and extensively applied in the following years to the study of all heavy rare-earth RNi2B2C phases (Canfield et al., 1997). Crystals of YNi2B2C and HoNi,B,C with centimeter dimensions were also grown using a floating-zone
104
Structure and Composition
method (Takeya et al., 1996). In recent years, alternative preparation routes were explored, in view of possible practical applications. Rapidly quenched YC(NiB), alloys with x = 2,3,4 were prepared by both splat-cooling and melt-spinning techniques, obtaining a critical temperature of 16K in a rapidly quenched YNi3B3C ribbon sample (Kim et al., 1998). In nanocrystalline or amorphous YNi,B,C, produced under different conditions of ball milling, it was observed that superconducting properties deteriorate upon milling and disappear when the amorphous phase is achieved. However, upon annealing the amorphous phase recovers its superconductivity (Ledig et al., 1999). Once again the superconducting state appears closely connected with the crystalline nature of the material. The LLIN~~B,C structure (Siegrist et al., 1994b) can be considered a filled-up variant of the well-known ThCr2Si2type, where the insertion of carbon into the rare-earth plane causes an expansion of the cell along the c axis. NaCl-type layers with composition LuC alternate with Ni2B, layers, where nickel is tetrahedrally coordinated by four boron atoms. Even though the structural framework is three-dimensional, the layered nature is pointed out by the results of Mossbauer studies on the isotypic DyNi,B2C (Cupta, 3999, suggesting that the Dy-C plane is insulating and electric conduction takes place within the Ni2B2layers. A drawing of the LuNi2B2C structure and related ThCr,Si,-type LuFe2B, (Villars, 1997) structure is reported in Figure 14. A detailed analysis of this structure in the RNi2B2C series and in other isotypic borocarbide compounds was made by Siegrist et al. (1994a). Strong anisotropy throughout the RNi,B2C series is observed: while the a constant of the tetragonal cell decreases regularly from La to Lu, following the normal lanthanide contraction, the c constant, on the contrary, increases. The proposed explanation for this anomalous trend is closely related to the structural features of these phases. The chain element B-C-B. aligned along the c axis, is very rigid, the B-C distanceo maintaining practically the same value of 1.47-1.48 A through the entire series. Thus, the radius variation of the rareearth will affect only the R-C distance within the NaCltype plane, regulating the a-constant value. without changing the B-C distance. On the other hand, since the Ni-B distance in the Ni2B, layers is also constant through the series, this constancy can be obtained only by an increase of the B-Ni-B tetrahedral angle on going from La to Lu, with a consequent thickening of the Ni2B2layer and c-constant expansion.
The structures of LuNiBC and La,Ni,B,N, (tI20) (Zandbergen et al., 1994b) are also given in Figure 14. It is easy to see that all these structures are related and the quaternary phases in particular can be described by a general formula (RX),(Ni,B,) with X = C or N. The first members of this family, LuNi2B2C,LuNiBC and La,Ni2B2N,have n = 1, 2 and 3, respectively, where n represents the number of NaC1-type layers inserted between two Ni,B, layers. Other quaternary nonsuperconducting phases found in these systems are LaNiBN, isotypic with LuNiBC (Zandbergen et al., 1994b) and Lu2NiBC2, identified by high resolution electron microscopy, and containing also a 6, layer between two lutetium layers (Zandbergen et al., 1994a).
3.3 Magmtoresistmce Magnetoresistance (MR) is the change in the electrical resistance that occurs under application of magnetic fields. The materials with giant magnetoresistance (GMR) and colossal magnetoresistance (CMR) show giant values (Aplp = 1040%) or colossal values ( A p [ p = 100% or more) of MR, usually in the vicinity of an order-disorder magnetic transition temperature. The applications of these materials can be as magnetic field sensors, read heads for hard drives, magnetic random access memories, or galvanic isolators. An explosion of research work has occurred on the perovskite-like manganites derived from LaMnO,. Partial substitution of lanthanum by an alkalineearth element produces spectacular effects, such as the appearance of a mixed valence state (Mn+3/Mn+4), the shifting of the magnetic ordering temperature, the competition between ferro- and antiferromagnetic interactions, the occurrence of a metal-insulator transition near the magnetic transition temperature, and correspondingly huge MR values. CMR materials are found also in rare-earth intermetallics, but their application is difficult because of the operating temperature, which is usually well below room temperature. Some examples are Tb,Ni,Si, with magnetoresistance change Aplp = 85% in an applied field B= 5T at T = 9 K (Mazumdar et al., 1997); CeAg,Sb, with Aplp = 40%, 3 = 5 T, T = 9 K (Guzik and Pierre, 1998); DyNiSb with A p / p = 32%, B = 4T, T = 2 K (Karla et al., 1998); Er0,4T~,&Oz with Ap/p = 300%, B = 10T, T = 0.5K (Hauser et al., 1999). The only rare-earth materials which show high MR values at slightly higher temperatures are Eu,,MnSb,, and Eu14MnBill,with magnetic ordering points at 92K and 32K, respectively (Chan et al., 1998).
105
Rare-Earth Metal Compounds
LaN LaN Ni2B2 LaN
LUC
LaN
LUC
Ni2B2 Y1
Ni262
Y I
LaN LaN
La3Ni2B2N3 Figure 14 Tetragonal structure types in superconducting borocarbides. The LuFe,B, structure (ThCr,Si,-type) is also reported for comparison. The c axis is vertical. Large open circles: Lu or La; medium full circles: Ni: small open circles: B; small full circles: C or N. The characteristic tetrahedral connection of Ni with four boron atoms and the 15°C or 8-N bonds are drawn
properties were favourab~e,the lattice t h e r ~ a lconductivity was too high and could not be s~~fficieiitly For many years compounds with the~oelectric lowered by part~alreplace~ent of the constituent as electric power g e n e ~ ~ t o r s ~lemeiits.Best results were o b t ~ ~ n ewith d a closely The chapter by V e ~ e r ~ i k o ~ ~ related class of compounds called ‘filled s k ~ t t e r u ~ i t e s ~ , 111 the preceding edition of ~ ~ ~ where t ~ ~ atoms ~ ~ up ~ the voids ~ lin the l ~ rare-earth fill provides a basis for both pr~ncip~es and s~utterLid~te s t r ~ ~ t u rThese e. phases have the ~ o r ~ u I a practical applications of the classical ther~oelectric RT4X12,where R = rare-earth r generally La-Nd, Sm, yed in a certain range of EL$, or Yb), T = Fe,Ru, or OS and X = P, As, or Sb, ?Se3alloys below 500 K, The series RCO~P,, is also known, while several ~~~~~~~~, and Si-Ge alloys above a n t i ~ o n i ~ eare s formed by the al~aline~earths (Ca, roblem of ther~oelectricdevices is and a r s ~ i i i d eby~ Sr, or Ba) and a few ~hosp~iides asured by the dimensionless figure aiid U (Villars, 1997; Even et al., 1995; Kaiser and ere T is the t e m ~ e r a t ~and ~ r eZ = ~~~x ~eitschko,1998), eebeck coefficient, ~i aiid x A p e c ~ I i a r iof t ~ several of these phases is that the R are the elect~icaland thermal ~ o ~ d u ~ t i respecy ~ t y ~ atoms ~~~~n~ the voids are loosely bound and show actually used, the m a x i ~ ~ m unusually large thermal d~spla~enient para~eters,For 1 Since good ther~noelectric an enhanced effect the R atom should find an oversized ~ ~ t e r shou~d ~ a ~ sbe n 1 i ~ ~ abetween y metals (high cage, and this is realized in some a ~ i t ~ ~ ~ n iIn des. elec~rical~ o ~ i d u ~ t ibut v i tlow ~ see be^^ c ~ e ~ c iand e~t thermal d ~ s p ~ a c e m parameter e~t in ermal co~ductivity~ and insula4Sb,2 and ~ a ~ e is4about ~ b four ~ ~ coeEcicnt arid low thermal times, and in ~ d ~mores than ~ six~times~ that~of 2 ~ o i i ~ ~ ~ c t i vbut i t yalso , low electrical c o n ~ ~ c t i v i tity ~ ~ the other Fe or Sb atoms. Figure 15 is a d ~ a w ~ of n gthe is clear why s e i ~ i c o i ~ d ~have ~ ~ treceived o r ~ most of the LaFe4Sb12structure. The structure is c o ~ p o s e dof a t r i d i n ~ e ~ s i oarray n ~ l of distorted FeSb, ~ o ~ i e r - ~ h a ~ i n ~ the search for more e ~ c i e materials, ~t comoctahedra. This arrangement gives rise to rectangu~ar ~ O L ~ such r ~ ~as S CoSb,, rSb3, c ~ s t a l l i ~ i ning planar Sb4 units which co~nectadjacent o c t ~ ~ e d r a , ucture (CoAs,-type, cf32) and form nearly icosahedral voids where the large rareet al., 1995; Tritt et al., 1996; earth atoms are located, being ~ ~ r r o ~ ibyi d12eSb. ~ A Caillst et al., 199 ever, although the electronic partial occupancy of the R site is often observed; for instatice, it is 9496 for LaFe,Sb,, arid 83% for NdFe,Sb, ?. The ~ n ~t s~ ~e vibr~tion ~~ l~ aa i ~~ ~ ~ l i tof u ~the e sR atoms in the ant~nionidec o ~ ~ o u n dconfer s a very favourable efTect in enhancing thernioelectric properties, since this ‘rattling’ motion gives rise to strong phonon scattering and, as a consequence, to a remarkable reduction of the lattice thermal ~ ~ n d L ~ c ~ ~ ity. On the other hand, these materials maintain relatively good electronic c~nductiont ~ o u g hthe framework formed by t ~ d n s i t i o n ~ ~ eand t a i anti~11ony andb ~ ~ atoms. The c o ~ ~ studied, o ~ ~ ~n ~~ e ~4 S =La - ~ F e 4 - ~ ~ 0with ~Sb~ ~ or Ce seen1 to be the most ~ ~ o m~ ~~ so i rand ~~ ~l eisner, ~ i 1995; Sales et al., 1996, 199’7; Chen et al., 1997; Sales, 1998), as theimal c ~ n d u c t i v is ~strongly ~~ reduced coinp~redto unfilled ~kutterudite§,being 6-8 times lower at room t e m p e ~ ~ t u with r e ~ values a p p r ~ a c ~ i nthose g of amorphous SiO,, The partial replacei~entof CO for Fe has two main effects: it inc~ease~ the ~ e e b e cc o~e ~ c i ~up nt Crystal ~ t r u ~of ~ the u ~ f ~i l l e d - ~ ~ ~ ~ t t ~ r u d i ~ ~ to a ~ ~ ~ b s t level i t not ~ ~ exceeding ~ o ~ x=2.5, and it (~134).Sb, ~ ~ ~ l i around ~ d r athe Fe atoms are decreases the rare-earth o c c ~ p ~ n c factor. y For . Large circles: La; small circles: Sb ~~~~~~~~~~~
I
Rare-Earth Metal Compounds
Lao,9Fe,CoSb,, and Ceo,9Fe,CoSb,, a Seebeck coefficient Sx 100,uV/IC, an electrical conductivlty o x 1000R-l cm-I, a lattice thermal conductivity ~ ~ x 0 . 0W 1 5K-l cm-' are reported at room temperature, and for the Ce compound ET is greater than one at temperatures above 700K. A similar behavior was recently observed in the nickel-substituted compounds Ce,Fe,-,Ni,Sb,,, where, upon substitution, the Seebeck coefficient increases up to 180pV/K at x = 1.1, but for x = 1,5 becomes small and negative, while the Ce content regularly decreases (Chapon et aE., 1999). Filled skutterudites MxCo4Sb,2with partial occupation of the voids by M = Sn or Pb were also prepared by a high pressure-high temperature treatment (Takizawa et al., 1999). An improvement of the electric and thermal properties of these materials should be achieved by varying the carrier concentration througb an accurate electronic balance, of course preserving the low lattice thermal conductivity, which is a peculiarity of the filled skutterudites. This should be possible, because the lattice contribution to the thermal conductivity is higher than the electronic term and does not depend strongly on carrier concentration.
-
3.5 Energy Storage The commercial production of Ni-MH batteries started nearly ten years ago as described by SchEapbach et al. (1995) and quickly increased, reaching 570 million cells in 1997, representing 40% of the market for small rechargeable batteries. As is well known, this system is based on the noticeable property of the intermetallic compound LaNi, to absorb, rapidly and reversibly, more than six hydrogen atoms per formula unit. The electrochernical reactions involved are: Negative Positive Overall
charge M + H 2 0+ e- 2 MH + OHdischarge
Ni(OH),
+OH- 2 NiOOH +H 2 0+e-
M + Ni(OH), 2 MH + NiOOH
The charge-discharge mechanism is simply a movement of hydrogen between a metal hydride (MH) electrode and a nickel hydroxide (Ni) electrode in an alkaline electrolyte, typically 6M KOH. The MH electrode is formed by an alloy powder pasted onto a nickel-plated steel sheet. The alloy
107
composition is MmNi, & O ~ , ~ M ~ ~ ,37, A where ~ , La is substituted by the more economical mischmetal (Mm) and Ni is partly replaced by elements chosen for improving the performance of the cell. In particular, the combined substitution of cobalt and aluminum for Ni results both in corrosion inhibition and in considerable reduction of the volume expansion from hydrogen absorption, which is about 24% for pure LaNi,, and is responsible for a pulverization of the alloy and a consequent loss o f capacity during repeated charge-discharge cycles (Sakai et al., 1995). Moreover, cobalt lowers the hardness of the alloy, another important point for a high-cycling stability (Chartouni et al., 1996). The presence of Mn is useful from several aspects. During the activation cycles the alloy is cracked by the hydridingldehydridingvolume changes, allowing diffusion of the electrolyte solution inside the particles. This operation is required prior to the alloy cycling process between the hydride and metal phase. The addition of Mn to the alloy produces small equiaxed grains in the ingot, facilitating cracking and improving rate capability. Manganese, together with aluminum, contributes also to a decrease in the hydrogen pressure in the alloy, favouring hydrogen diffusion inside the cell and maintaining charge efficiency. Other essential requirements for an MH electrode are a homogeneous microstructure, obtained by a suitable heat treatment of the MmNi,-based alloy produced by rapid solidification, and a large, wellconducting surface area obtained on forming a nickelrich layer. Practical capacities per volume are in the range 9001200mA-h/cm3, with an energy density per unit volume of 360 W-h/l and an energy density per unit weight of 70 W-h/kg. These cells are used in various portable appliances such as cellular phones, video cameras, and lap-top computers, where compactness is very important; and recently, a high-power Ni-MH battery has been placed on the power-tool market. Other applications are in the field of the electric vehicles, where high power Ni-MH batteries either are directly employed, or in fuel cell systems assist a methanol reformer in hydrogen production (Sakai et al., 1999). Basic research and technology for applications have been closely connected in this field, more so thm in others. Research and development efforts are now directed on the one hand, to improving technology and producing light and compact batteries with high power, and on the other hand toward reducing costs. The cost per cell has greatly decreased to about onethird of its initial value, but still remains high,
108
Structure and Composition
primarily because of the incorporation of cobalt in the alloy. A partial substitution of CO with Fe, which maintains good cycle stability and rate capability, was proposed by Ziittetel et al. (1997), while an alioy with the cobalt completeiy replaced by a mixture of Cu, Fe, and Cr, and a small fraction of the rare-earths replaced by Ti showed good cycling stability although with a lower capacity (Hu, 1999). Chemical treatments of the electrode surface were also studied. By dipping and stirring the alloy in an aqueous HCl solution, several beneficial effects are observed: a partial solution of rare-earihs and Mn generates micropares, which increase the specific surface area and activate the discharge reaction; the outer surface area is enriched in Ni and CO metal, enhancing electric conductivity and catalyzing hydrogen absorption and desorption reactions (Imoto et at., 1999). Treatment of the allay powder with KOH solution at 80 "Cproduces a surface containing Mm hydroxides, Mn oxides and metallic Ni, and prevents the alloy bulk from further corrosion, enhancing the cycle life (Ikoma e t al., 1999). Moreover, it was found that surface deposition of trace amounts of platinum-group metals on the MH electrode considerably improves absorptioafdesorption rates and increases resistance to deactivation ('Willey e t at., 1999). The more than 50 papers on the MH electrodes and Ni-MH batteries, presented in the 1998 International Symposium on Metal-Hydrogen Systems - Fundamentals and Applications, held in Hangzhou, China, and published in J. A l b y ~Compd., 293-295 (1999), form a basis for updating the research and bibliography, and demonstrate the continuing interest in this subject. The search for new energy-storage alloys of high performance. and IOW costs is still an open field.
Ac~nQwled~e~e~t Dedicated to Professor Erwin ParthC.
Note: The sequence of the rare-earths (Sc, Y, La, Ce, Pr, Nd, Pm,Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) is readily recalled with the following mnemonic:
-Some young Ladies gan't
e t Nickels groperly into
-Slot-machines: Every S r l Tries Daily However Every Time u o u Look.
J. C. Chaston
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Rare-Earth Me fa[ Compounds
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Slavi G,Sevov Department of Chemistry and Biochemistry, University of Notre Dame,IN, USA
1. Intxodnction The subject of this chapter is a special class of intermetallics called ‘Zintl phases’ named after Edward ZintS who pioneered their exploration and the rationale for their structures (Zintl and Dullmkopf, 1932; Zintl and Brouer, 1933; Zintl, 1939). Zintl’s view applied to the classical Zintl phase NaTl assumes compSete electron transfer from the more electropositive sodium to the more electronegative thallium (Zintl and Woltersdorf, 1935}, just as in genuine ionic salts such as NaCI. The difference is that the resulting anions do not necessarily achieve an electronic octet as isoErated species but may rather bond to each other in order to do so. Thus, 3-in Na+TY behaves like an element of the group to the right, group 24, and forms a diamond network, typical for the elements of that group, that is stuffed by the Na+ cations. Such phases are the link between the metallic, alloy-type intermetallics on the one hand and the typical valence cornpounds on the other. The number of Zintl phases has increased many-fold since Zintl’s time, and a number of reviews on the subject have been published in recent years (Corbett, 1996, 1997, 2000a; Miller, 1996; Eisemann and Cordier, 1996; van der Lugt, 199% Belin and Tillard-Charbonnel, 1993). Since the definition of a ‘Zintl phase’ has never been very exact, often compounds that include nonmetals have been considered in this class. The intent here is to concentrate more on clearly intermetallic ZintI phases, i.e. phases that contain main-group metals, semimetals, or semiconductorsonly. Thus, only compounds of the alkali metals with groups 13 (without B and AI), 14 (without C), and 15 (without N and P) will be discussed here.
1.1 Def&ion and Synthesis
For the purposes of this chapter ‘classical’ or true Zintl phases are defined as follows. They are compounds that: 1. contain an alkali or alkaline-earth metal and a p-
element (or elements) that is a metal, semimetal, or small-gap semiconductor; 2. are electronically balanced or closed-shell compounds, i.e. the number of electrons provided by the constituting elements equals the number of electrons needed for covalent bonding in the structure; 3. have very narrow or no homogeneity width, i.e. they are line compounds; 4. are semiconductors or poor conductors; 5. are diamagnetic or show very weak, temperatureindependent paramagnetism; 6. are brittle. Criteria (2) through (6) are the same as for normal valence compounds, while (1) provides the connection to the general class of intermetallics. Requirement (2) needs to be explained in some more detail, especially the meaning of ‘number of electrons needed for covalent bonding’. For structures with ‘normal’ 2center-2-electron localized bonds this number is simply the sum, 2 x (number of bonds) t 2 x (number of lone pairs), where all atoms follow the octet rule. For compounds with delocalized bonding, on the other hand, the valence rules are different. The bonding electrons in compounds with deltahedral clusters are calculated by Wade’s rules (Wade, 1972, 1976) that have been deveIoped for the borane c a p but also work equally well for naked main-group clusters. Furthermore, there are combinations of the two, i.e.
Interwetalfic compound^: Vol. 3, Principles and Practice. Edited by J. R. Westbrook and R. L. Fleischer. 02002 John Wiley & Sons, Ltd.
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compounds that contain networks of deitahedral clusters bonded to each other via localized bonds, and the sum of bonding electrons for such systems will include the electrons for cluster bonding, those for intercluster bonding, and the lone pairs (usually on cluster atoms not involved in intercluster bonding). Since the Zintl phases usually contain alkali or alkaline-earth metals and are also air- and moisturesensitive themselves, their synthesis and handling is carried out in vacuum or inert atmosphere. Typically, they are synthesized by heating (anywhere between 300 and 9OO0C) mixtures of the constituting elements sealed in containers made of ductile and high-melting niobium or tantalum. Since the latter are easily oxidized at these temperatures they are additionally 'jacketed' in evacuated ampules of fused silica.
1.2 Histopicat Ovepvicw For alloys and intermetallic compounds made of similar elements, the correlation between structure and valence electron concentration (VEC) had been established before Zintl's time. The rules developed by Hume-Rothery and Westgren were already stated, and explained why different structures form for different VECs (Hume-Rothery, 1926; Westgren and Phragmen, 1926). Also prior to ZintI the GrimmSomnierfeld rule for tetrahedral frameworks was suggested (Grimm and Sommerfield, 1926). Zintl also studied intermetallic compounds but only those made of elements with very different electronegativities, i.e. combinations of the very electropositive alkali or alkaline-earthmetals with the post-transition elements. It W B Sclear that the phases in these systems behaved quite differently than Hume-Rothery's metallic phases and were rather saltlike since they had melting points higher than the elements, were brittle, and conducted poorly, It was also noticed that all compounds that were not Hume-Rothery phases exhibited atomic volume contraction, presumably due to contraction of the more electropositive atoms. This suggested that the 'latter were cations in the structure, or in other words, they have transferred their electrons onto the more electronegative atoms. This was realized by Zintl and became the basis for rationalizing the electronic structure and bonding in the new class of compounds, now called Zintl phases. Thus, instead of using VEC for the prediction of the structure, it was proposed to look at the electronic state of the more electronegative element after assuming complete transfer of the valence electrons from the more electropositive element (Zintl and Woltersdorf, 1935). Later, Klemm
developed the idea further into what is known as the 'pseudo-atom' concept, the negatively charged atom would behave structurally similar to the corresponding isoelectronic neutral element of a group to its right (Klemm, 1956, 1959). This concept, combined nowadays with the electronic requirements for delocalized bonding in closed-sheil clusters, is a very powerful tool correlating the structures of the Zintl phases with their stoichiometnes.
2. Zintf Phases with Ddocaiized Bonding 2.1 Isolated Clusters
Usually deltahedral clusters are associated with the borane cages and their derivatives of the type B,,H&-, B,&?;, etc. The bonding electrons in such species are delocalized, i.e. they are shared by all atoms of the cluster. Therefore, the electronic requirements in such species can not be described by simple 2-center-2electron bonding but rather by rules developed by Wade (Wade, 1972, 1976) and known as Wade's rules. The latter postulate that closo- (no vertices missing), nidn- (one vertex missing), and arachrzo(two vertices missing) species require 2n+2, 2n44, and 2n -I-6 ebctrons for bonding, respectively, where n is the number of vertices of the cluster. The same rules can be applied for main-group 'naked' deltahedral clusters, i.e. clusters without ligands, where one has to consider the fact that each vertex will carry a lone pair of electrons. With this requirement in mind we can review the suitability and potential problems for forming such clusters from different main-group elements. The isolated borane-type deltahedral clusters of the closo-type of groups 13, 14 and 15 will have formulas E$"2)-, E;-, and respectively. The nido-species will have charges of (n+4)-, 4-, and (n-4)+, respectively, and the charges for the corresponding arachno-species will be (n f 6) -, 6 -, and (n-6)+, respectively. One can clearly see that formation of negatively charged clusters of group 15 is basically impossible. The only two possibilities for elements of this group are arachno Ej- (square) and E,- (pentagon). None of them has been observed in neat solids (solids made directly by solid-state reactions from the elements and that do not contain organic or similar moieties), although the former anion can be crystallized from ethylenediamine solutions of K,Bi, in the compound E-cryptJ2B4 where crypt = 4,7,13,16,21,24-hexaoxa-l, 10-diazabicyclo[8.8.8]hexacosane (Cisar and Corbett, 1977). For
Zintl Phases clusters of group 13, on the other hand, the negative charges are going to be too high. For example, a closo-cluster of 11 atoms will require the enormous charge of 13- . Its 10 and 9 atom nzdo- and avachnoversions will have even higher charges of 14- and 15-, respectively. Therefore, it is very unlikely that such clusters will fonn for this group either. The charges in group 14 are independent of the cluster size, they are always 2 -, 4 - , and 6 - , for closo, nido, and arachno species. The charge of 2- is perhaps too small for a relatively large cluster since it will require only two countercations in a compound such as A,[E,,]. The two cations will be too few and too small for packing eficiently with the large clusters and for separating and screening them effectively from each other. No such clusters have been found in neat solids, although they exist in compounds precipitated from ethylenediamine solutions with huge countercations such as [A-crypt]. Known in such compounds are E?- trigonal bipyramids (Edwards and Corbett, 1977; Campbell and Schrobilgen, 1997), and E:tricapped trigonal prisms (Belin et al., 1977). Until recently, the nido and arachno clusters of group 14 were also thought to have charges too low for formation in neat solids. However, in recent years this concept has been proven wrong with the synthesis of a number of Zintl phases with stoichiometry A,E, that contained the nid0-E;- clusters (Queneau and Sevov, 1997a, 1998a,b; Todorov and Sevov, 1998; von Schnering et al., 1997). 2.1.1 Group 14
Small tetrahedral species El- in the equimolar Zintl compounds AE (= A,E4) are known for all elements of this group (Schafer and Eisenmann, 1985). Counting electrons in the tetrahedron is somewhat debatable, since there are two different, but equally satisfactory, ways to do that. One way to look at it is as a nido deltahedron derived from the closo trigonal bipyramid E:- by removing a vertex, despite the fact that all of its faces are triangular and that it does not really look like a geometrical body with a missing vertex. Nevertheless, when taken as such, i.e. assuming delocalized bonding, its charge is going to be 4- as for any nido species of this group. The second rationalization of the electron count is to assume simple 2-center-2-electron localized bonding between all the vertices. Thus, the tetrahedron has 6 edges which require a total of 6 x 2 = 12 bonding electrons. When the 8 electrons for the 4 lone pairs are included, the total for the cluster becomes 20 electrons, or the available 4 x 4 = 16 electrons provided by the 4
115
atoms are again 4 electrons short from the 20 needed by the cluster. Yet a third and perhaps the best way to view these compounds is to use the pseudo-atom concept where E- in AE is a pseudo-element of group 15 such as phosphorus, and as such it forms tetrahedra that are typical for one of the allotropic forms of that element. Tt should also be mentioned here that pseudophosphorus can be made not only from atoms of the neighboring group, but also from atoms of group 13, i.e. two groups to the left of phosphorus. Thus the compounds A2E (= A,E,) where E = In or T1 contain the same tetrahedral species although with a doubled charge, E:- (Smith and Hansen, 1967; Sevov and Corbett, 1993a). Larger deltahedral clusters of this group have been known for quite some time but all in compounds crystallized from ethylenediamine solutions with cryptated alkali metal countercations (Corbett, 1997, 2000a. and references therein). The synthetic niethodology starts usually with the preparation of a precursor AXE, by melting the two elements. It was always thought that these precursors were simple featureless melts or alloys with no particular structure, or even less likely, structures with clusters. The precursor is dissolved in ethylenediamine which usually also contains 2,2,2-crypt as an additive designed to capture the alkali metal. It was thought that the cluster formation always occurred at this step during the dissolution of the precursor. Nevertheless, our and others’ studies have shown that many of the precursors in these systems are Zintl phases with already pre-existing clusters, and that the dissolution process often is reduced to simply extracting them into the solution (Queneau and Sevov, 1997a. 1998a,b: Todorov and Sevov, 1998; von Schnering et al., 1997; Somer et al., 1998; Xu and Sevov, 1999). The first structurally characterized compound with isolated 9-atom deltahedral clusters was Cs,Ce9 (tP208) shown in Figure 1 (Queneau and Sevov, 1997a). Choice of this particular combination of elements for study was not accidental; it combines the largest cation, Cs, and the smallest element of this group, Ge, for which a 9-atom cluster has been characterized from solution. As already discussed, it was thought that E$- clusters cannot exist in neat solids due to the mismatch of large clusters and small cations, and therefore the best chance for formation of such species had the smallest clusters combined with the largest cations. With the knowledge that at least Ge$- exist in neat solids it was more than logical to test thc possibilities for similar clusters of the heavier analogs Sn and Pb.
116
Structure and Composition
Figure 1 The structure of Cs,Ge, (left), the first Zintl phase with isolated %atom clusters of group 14.The clusters Ge;- (right) are nzdo deltahedra with the shape of monocapped square antipnsms. There are 208 atoms in the unit cell
Thus, the next step was to investigate the combination of the largest cation and the largest cluster, Cs4Pb, (mP52) (Todorov and Sevov, 1998). Again, it was somewhat surprising to discover that the corresponding Zintl phase can be synthesized. Although the atomic ratio is the same as in Cs4Ge, the packing and therefore the structure of Cs4Pb9is different. Lastly, the other extreme combination of cation and anion, K4Pb9(mP52), with a very small cation and the largest cluster was tried (Queneau and Sevov, 1998a). The compound forms, the structure is different from the above two (Figure 2), and contains two different types of Pbg4- clusters, labeled A and B (Figure 3). The clusters of type A have the expected geometry for this charge, i.e. monocdpped square antiprisms, but those of type B are rather like tricapped trigonal prisms. This latter geometry indicates, of course, closo species of %atoms, and those therefore should rather
carry a charge of 2 - . Nevertheless, this particular cluster is elongated along the three-fold axis, and, as a result of this, one otherwise antibonding and empty orbital becomes bonding and filled, and the charge is again 4-. It should be mentioned here that compounds with Sn$- clusters were also made. Furthermore, in addition to the structural characterization most compounds were also studied by Raman spectroscopy (von Schnering et al., 3997). It was shown that the 9-atom clusters exhibit a very characteristic set of vibrations that can be easily recognized in these spectra. Thus, Raman spectroscopy can be a very useful tool for identification of compounds with isoIated ionic clusters of different sizes by simply matching experimental spectra with spectra from a database. AI1 the 9-atom clusters of group 14 mentioned so far, Gey, Sn,, and Pb,, were known from solution work
Zintl Phases
117
Figure 2 The structure of K,Ph, w t h two different types of Phi- clusters, monocapped square anhprisms (darker polyhedra) and elongated tricapped trigonal prisms (lighter polyhedra). The potassium cations are shown as isolated spheres
prior to finding them in Zintl phases. The element missing from this collection is obviously silicon since no silicon clusters (larger than the tetrahedra found in A,Si4) had ever been made either from solution or in the solid state. Nevertheless, with the knowledge that clusters of the heavier analogs can be made in neat solids, it was natural to explore the possibility for similar silicon clusters. Thus, reactions with stoichiometry A&, were carried out, and the resulting phase indeed contained Si$- deltahedral clusters although the stoichiometry of the compound was somewhat different (Queneau and Sevov, 1998b). The new compound, AI2Sil7where A=K, Rb, Cs (mP464), contains not only 9-atom clusters but also the tetrahedral species Sii- (Figure 4). The formula can therefore be rewritten as 12A++ 2(Si$-) + Si$-.
2.1.2 Group I3 Although this group was initially thought to be not very promising for deltahedral clusters (see above), it turns out that it actually provides the largest and most diverse collection of clusters with delocalized bonding. The first cluster of this group was found in a phase which, ironically, is not exactly a true Zintl phase
Figure 3 Closer view of the two types of Ph$- clusters found in K4PhP.A) monocapped square antipnsm; and B) elongated tncapped trigonal prism
according to the definition given in the Introduction (above), and the cluster itself is not of borane-type geometry. It is an 11-atom cluster of indium, Inyc, found in the compound &In,, (hR114) shown in Figure 5 (Sevov and Corbett, 1991). The discrepancy between charge and number of cations means that there is an extra electron per formula. Therefore, it is not an electronically balanced phase and cannot be called a true Zintl phase according to our rules. It better fits a group of phases which can be called ‘almost Zintl phases’ or ‘metallic Zintl phases’, discussed later on. The extra electron is apparently
118
Structure and Composition
Figure 5 The structure of K,In,, (rhombohedral. R3c) is of close-packed layers of In:; clusters (polyhedra) stacked tn a cubic fashion along the c =is ( v e r t d ) and separated by double layers of potassium cations (spheres)
Figure 4 Shown is the structure of Rb,,Si,, which contains 9and ‘$-atom clusters of silicon, Sii- and §ij- in ratio 1:2 shown as lighter and darker polyhedra, respectively. The rubidium canons are shown as isolated spheres. This structure and other Zintl structures may be viewed in color at www.nd.edu/ sbobev/interm,htrrd
n
N
delocalized over the alkali-metal atoms and perhaps the cluster antibonding orbitals, and the compound is Paulj-paramagnetic and metallic. Nevertheless, the cluster is deltahedral and exhibits delocalized bonding. Yet, its geometry and electron count differ from that expected for a borane cage of 11 atoms. The cluster in this case is a pentacapped trigonal prism that has been compressed along the three-fold axis (Figure 6), and the number of electrons needed for skeletal bonding within the cluster is not 2n+2 but rather 2 n - 4 = 18, Thus, instead of carrying the enormous charge of 13 corresponding to (n + 2) - for closo species of group 13 (see above), its charge i s the more reasonable 7 - .
Figure 6 A closer view of the indium cluster in K&,. Its shape can be considered as a pentacapped trigonal prism that has been compressed along the threefold axis {vertical). Three of the capping atoms cap rectangular faces at the waist of the prism, and the remaining two cap the two triangular bases, top and bottom of the figure
Zintt Phases
Molecular orbital calculations clearly show that a good size HOMO-LUMO (Highest Occupied Molecular Orbital-Lowest Unoccupied Molecular Orbital) gap of 1.2eV opens at 18 bonding electrons for this geometry, i.e. the cluster IS hypo-electronic with respect to the classical chic, geometry. It can be rationalized in the following way. Starting from a classical tricapped trigonal prism with 2n + 2 = 20 electrons, i.e. In;1-, we add two more indium vertices to cap the triangular bases. This addition does not bring new orbitals, i.e. the number of required electrons remains 20, but only two additional electrons, the p-electrons of the indium atoms, and the cluster becomes In?,-. Next, the cluster is compressed along the three-fold axis, and this distortion makes a formerly bonding a; orbital into an antibonding and empty one (Figure 7). This translates into the lower charge for the cluster, In:, . Besides K81nilthe clusters 1n:T also exist in RbsInil and Cs81nll. Clusters with the same geometry and charge were later found for thallium in A8Tlll where A = K, Rb, or Cs (Dong and Corbett, 1995a), A1,Tl,, (hP42) where A = R b or Cs (Dong and Corbett, 1996a), and K,8T12&u3 (hP443) (Dong and Corbett, 1995b), and for gallium in Cs,Gal, (Henning and Corbett, 1997). Furthermore, it should be pointed out that these AsEl, phases can be made electronically balanced by ‘controlled’ one-electron oxidation without changing their structures. Thus, the chlorineintercalated derivatives Cs,GallC1 and Cs81nl,CI (hR120) contain the same 11-atom clusters and the same overall structure but are semiconducting and diamagnetic (Nenning and Corbett, 1997). The chiorine occupies an available site that is empty in the AsEl, structure. These two phases satisfy all but one requirement in our definition of Zintl phases (see above). Criterion (1) is violated since chlorine is obviously a nonmetal. Nevertheless, CI is one atom out of 20, and furthermore the phase can exist without it. This clearly shows how complicated defining Zintl phases can be! In addition to these compounds, there is also a substitutional phase that is electronically balanced. This is K&n,,,Hg] (hP38) with the same 11-atom cluster as in K,Inll but with one indium atom substituted by Hg, an element from the group to the left (Sevov et al., 1993). Due to the substitution the cluster assumes charge 8-, i.e. [In,oHg]s-, and the compound is a true Zintl phase. Although here we have a ternary system, the heteroatom does not cause changes in the cluster shape. It rather acts only as an electron gatherer and causes localization on the cluster of the otherwise delocalized extra electron.
119
Similarly, there are two denvatives of substitution in the Tl&- clusters. The isoelectronic [TI,CC~~]~~is the result of three thallium atoms substituted by an element to the left, and the cluster keeps the same overall geometry (Huang and Corbett, 1999). Nevertheless, the compound in which it is found, Na9KldTllBCd3 (hP92), is not a classical Zintl phase since it has an extra electron which makes the compound paramagnetic. Another derivative is fr19Au21g- which has even fewer electrons, 2n-6 rather than 2n-4 (Dong and Corbett, 1995b). The pentacapped tngonal prism in this case IS compressed even ftrther, so much so that a bond is formed
-5
-6
/ e’ -7
-8 ISXI (
~
~
H
~
Figure 7 The molecular orbital levels for p orbitals in In,, clusters with D,, symmetry: left, the classical pentacapped tngonal prism with 20 electrons; and right, the observed axially compressed cluster with 18 electrons. The HOMOLUMO separations are shown with broken lines
120
Structure and Composition
et al., 1998). Two of these, Tl:- and Tli-, follow Wade’s ruies and carry the prescribed charges of (n + 2) - . The geometries, as one might expect, are also borane-like, a trigonal bipyramid and an octahedron for the two, respectively. The other three species are again hypoelectronic with nonclassical shapes: T1:and T17- are compressed square and pentagonal bipyramids, respectively, with bonds between the two axial vertices, and TI8- has a strange geometry that is best described as the imaginary product of the removal of four neighboring vertices from a Tl-centered icosahedron (Figwe 9). There are a number of observations that can be Figure 8 The cluster Tl&u?_ XI K,8T120Au3.It can be made at this stage for both groups 13 and 14. One is considered as an extremely compressed pentacapped that clearly nido and arachno species of group 14 have trigonal pnsm (see also Figures 6 and 7) with the gold atoms (light) capping the two triangular bases. The the ‘right’ charges and can form in the solid state. Two, compression leads to the formation of a bond between the the problem of high negative charges of group 13 has two gold atoms been solved by simply forming deltahedral clusters with nonclassical shapes that require fewer electrons between the gold atoms capping the bases (Figure 8). for skeletal bonding, i.e. hypoelectronic clusters. This, Alternatively, the shape can be considered as made of however, is only one of the solutions of the problem. thrce face-fused octahedra, all sharing an edge, the Another solution is to form centered clusters where Au-Au bond. Again, compression and condensation the centerkg atom brings additional electrons and/or lead to a decrease of the number of electrons needed causes geometrical distortions that lead to hypoelecfor bonding and a lower charge. tronic species. This is the case in K,E,Jn (tP38) for For indium and gallium it seems the 11-atom cluster E = In or T1 (Sevov and Corbett, 1993b; Dong et al., is the only isolated species. Thallium, on the other 1997), KloEloM(op252) for E = In or Tl and M = Ni, hand, forms five additional isolated clusters: Tli- in Pd, or Pt (Sevov and Corbett, 1993~;Corbett, 2000a). Na2KzlTlI9 (oCl68) (Dong and Corbett, 1994), and NaloGa,,,Ni (Henning and Corbett, 1999). The ZnNa23K9Tl1533* (hP96) (Dong and Corbett, 1996~)and centered clusters [El&nIs- are close to the classical Na9K,6TllxCd3(Huang and Corbett, 1999), Tli- in shape expected for 10-atom species (Figure lO), a AT1 where A = K or Cs (Dong and Corbett, 1993, bicapped square antiprism, but again compressed 1996b), Tlg- in Na,,K,Tl,,M (hP39) for M = Mg, Zn, Cd, or Hg @ong and Corbett, 1996d), T17- in Kl0Tl7 along the four-fold axis. The compression is clearly a result of the equidistant positioning of all cluster atoms (mP68)(Kaskel and Corbett, 2000) and Na,2K38T14xA~2 from the central zinc. The effect of the compression is (hP100) (Huang et al., 1998), and T18- in Na2K2,TlI9 the same as in all compressed clusters described so far, (Dong and Corbett, 1994) and Na,2K38TbxAu2 (Huang i.e. molecular orbitals that are otherwise bonding and filled become antibonding and empty, and the charge *Non-integral proportions indicate presence of vacancies in on the cluster is lowered. Thus, instead of 2 n + 2 the the position.
Figure 9 Shown are three thallium clusters: left TY- with the shape of a Compressed square bipyramrd; center, T1:- with the shape of a compressed pentagonal bipyramid; and nght, T1;- with the shape of a self-centered icosahedronof thallium where four vertices have been removed
Zintl Phases
121
Figure 10 Two centered In,, clusters: top, In,,,Zns- with the shape of a compressed bicapped square antiptism; and bottom, In,$Ji'o- with the shape of a compressed
tetracapped tngonal prism (capped are the three rectangular faces and the upper tnangular base) Zn-centered cluster requires just 2n = 20 electrons for bonding. The central Zn and the 10 In atoms provide 2 + 10 = 12 electrons (lone pairs are not counted), and the resulting charge is 20 - 12 = 8 - . Exactly the same is observed in the [E,,M]'O- clusters. The clusters are tetracapped trigonal prisms that have been compressed along the three-fold axis (Figure 10). The cause for the distortion i s again the central Ni, Pd, or Pt atom being equidistant from the cluster atoms. The distortion makes the cluster again hypoelectronic with 2n = 20 electrons. In this case the central atoms do not provide bonding electrons, and consequently the charge is 20 - 10 = 10- . Isolated and centered clusters of thallium are again more numerous than those of the lighter analogs. In addition to the above-mentioned centered species it also forms self-centered icosahedra (Tl,,Tl)lo- and (T112T1)*1-(Dong and Corbett, 1995c), Na- and Hcentered icosahedra (T11,Na)13- and an octahedron (T16H)?- (Dong and Corbett, 1995d), and icosahedra
Figure 11 The dimer of corner-sharing, the zinc atom, trigonal hipyramids of Ge,Zn6- found in Cs,Ge,Zn. It can also be considered as two germanium tetrahedra linked by a
zinc atom. The two Zn-capped faces are eclipsed making the zinc in a tngonal prismatic environment centered by two-electron donors (Tl12M)12- where M = Mg,Zn, Cd, or Hg (Dong and Corbett, 1996d). Notice that the self-centered icosahedra can exist with different charges, 10 - and 11 - , and therefore with both even and odd numbers of electrons. More importantly, the cluster with the odd number of electrons (49), (Tli2Tl)10-,is one electron short of the required number for a closed shell. This has apparently been explained with an electron hole localized on the cluster, since the compound is paramagnetic. 2.1.3 Heteroatomic The substituted 11-atom clusters of group 13, &n,,HgI8-, [ v u 2 l 9 - and [Tl,Cd,]'O- have been
122
Structure and Composition
discussed already. For group 14 there are no such substituted species. Rather, all attempted similar substitutions with elements of group 12 lead to species made of tetrahedra of group 14 that are connected by the heteroatom. Thus, Cs,[Ge,Zn] ( o n 50) (Figure 11) contains isolated [GeXZnl6- clusters that can be considered as corner shanng (the Zn atom) trigonal bipyramids or as two Ge4-tetrahedrajoined together via a zinc atom (Queneau and Sevov, 1997b). For the latter, the zinc atoms cap faces of tetrahedra that are eclipsed with rcspect to each other so that the zinc is in trigonal prismatic coordination. Coincidentally, had the zinc substituted for a germanium atom in the G$clusters, the resulting specles would have had the same stoichiometry and charge, [Ge8Znlh-.The explanation of why zinc does not substitute in Geg- and In;, clusters is perhaps the fact that it carries only two electrons and its s-orbital is not inert (stable) enough. Mercury, for example, can and does substitute for In in Inll. The zinc atom prefers a position with rather a sphericalenvironment, a geometry that does not require a lone pair. Cadmium and mercury also do not substitute in the 9-atom clusters of group 14. Instead, they form compounds that are structurally different from Cs,[Ge8Zn] but stoichiometrically equivalent with it. The cadmium analog, K6[Pb8Cd](mC90) (Todorov and Sevov, 1999), contans isolated PbI--tetrahedra as well as tetramers of Pb4-tetrahedra connected via cadmium atoms, [(Pb4)Cd(Pb4)Cd(Pb4)Cd(Pb4)]10(Figure 12). The latter can be also viewed as made of a pair of [PbXCdl6-species analogous to [Ge8ZnI6- that have been further linked by the third cadmium. All tetrahedra are linked via faces, but the faces are
staggered wrth respect to each other, so that the cadmium atoms are in a trigonal antiprismatic environment. Lastly, Hg-connected dimers of tin tetrahedra exist in Cs,[Sn8Hg], but the bridging is between edges rather than faces. The mercury atoms are in elongated tetrahedral coordination. 2.2 Networks of Clusters Besides Zintl phases with isolated clusters there are a number of compounds with networks of interconnected clusters, predominantly in the systems group 13 - alkali metal. Such compounds combine two different types of bonding, delocalized within the clusters and localized between them. Naturally, the intercluster bond distances (exo-bonds) are shorter than those within the clusters (endo-bonds) since the former are ‘normal’ 2-center-2-electron bonds while the latter is delocalized bonding. It turns out that many of the network compounds are not electronically balanced but very close to being such. Many of them have a few extra electrons (or holes) relative to those needed for the bonding. Such compounds can be referred to as ‘metallic Zintl phases’, and in order to consider them in this chapter we have ,to somehow broaden the definition given before. We can extend and paraphrase Hughbanks’ interpretation of Zintl phases as phases with ‘structures for which we can at least think‘ of as valence compounds (Hughbanks, 1992). We will call ‘metallic Zintl phases’ those compounds that conform to all rules outlined in the Introduction (see above) except rule (2). We modify rule (2) to state that the phases
Figure 12 The tetramer of four lead tetrahedra joined by three cadmium atoms, (Pb,)Cd(Pb4)Cd(F‘b4)Cd(Pb4),found in K6Pb,Cd
123
Zintl Phases ‘look like’ they were nearly electronically balanced according to their structures but have a few extra electrons or holes.
2.2.1 Group 13
Gallium is perhaps the element with the greatest tendency to form networks of interconnected clusters, while it has only one compound with isolated clusters. The tendency for network formation diminishes drastically on going down the group, with thallium exhibiting only two such compounds, A,5T127 for A=Rb, Cs (Dong and Corbett, 1996a) and K6Tlll (oC184) (Corbett, 2000b), but a large number of isolated clusters. Tndium is clearly in between with many examples of both networks and isolated species. The structural chemistry of the systems alkali metal gallium has been extensively reviewed by Belin (Belin and Tillard-Charbonnel, 1993). A good example of a gallium network is the structure of KGa, (tZ24) (Belin and Ling, 1982) which contains 8-atom clusters of gallium, each with 8 exo-bonds, and isolated 4-bonded gallium atoms, the two species in equimolar ratio (Figure 13). The clusters are of the closo-type and therefore require 2n+2 = 18 electrons for skeletal bonding. Also, since each exo-bond is a normal 2center-2-electron bond, half of the electrons needed for them, i.e. (8 x 2)/2 = 8, are counted for the cluster as well. The total number of electrons required for the endo- and em-bonding of the cluster is therefore l8+8=26. The eight gallium atoms of the cluster bring 8 x 3 = 24 electrons and the charge of the cluster is 2-, i.e. Gag-. The 4-bonded isolated gaslium is in tetrahedral coordination and therefore has a formal charge of 1 -, i.e. Gal-, in order to achieve an octet. Thus, the equimolar combination of Gai- and Galwill require 3 potassium atoms to balance the charge, and therefore the formula K3Ga, (=KGa,) can be represented as 3K* iGai- +Gal-. The compound is electronically balanced and a true Zintl phase. Other examples o f electronically balanced gallium networks of clusters are: &Gal, (oC128) with 12and 1I-atom clusters, LizGa7(hR18) with icosahedra, Na,Ga13 (kR360) with icosahedra and 15-atom ‘spacers’, RbGa, (hR32) with icosahedra connected via 3-center-2-electron bonds, etc. More complex structures with fused deltahedra and/or partially occupied gallium sites also exist, and these are often ‘metallic Zintl phases’. Such are Li5Gag (oC56), Na,,Ga39 (oZ244), Li,Nn,Ga19 57 (oE896), Li,K3Ga2, (oC328), Na13K4Ga4,,57 (hR138), etc.
Figure 13 The structure of KGa, made of interconnected gallium (dark spheres) 8-atom cfoso deltahedra and isolated atoms
(Belin and Tillard-Charbonnel, 1993, and references therein). There are also many indium networks made up of interconnected deltahedral clusters. Perhaps the simplest such network is found in Rb2fn3(= Rb41n6)(tI20) (Sevov and Corbett, 1993d), layers of 4-bonded octahedra made of indium (Figure 14). The electron count is straightforward: 2n 2 = 14 for skeletal bonding, 2 x 2 = 4 €or lone pairs on the two non-exobonded vertices, and (4 x 2)/2 = 4 for the 4 exo-bonds. This totals 22 electrons required for bonding while the 6 indium atoms of the cluster provide only 6 x 3 = 18 electrons. ?‘lie additional 4 electxons come from the 4 rubidium atoms, and the compound is electronically balanced. This is not the case, however, in K,Naz,In4,
+
Structure and Composition a
Figure 14 The structure of Rb&, made of layers of 4-bonded closo octahedra of indium and separated by the rubidium cations (isolated spheres)
figure 15 The structure of K,N%J%,. The anionic network IS made of intercoiinected icosahedra (darker polyhedra) and avachno 12atom deltahedra (drum shaped, lighter polyhedra) of mdium. The c a ~ o n s of potassiuni and sodium are shown as larger and smaller isolated spheres, respectively
125
Zintl Phases
U Figure 17 A closer view of the 12-bonded closo-In,, found in Na,In,,,. The shape can be considered as a tetracapped truncated tetrabedron. The 4 capping atoms are 6-bonded within the cluster and do not have exo-bonds. The truncated tetrahedron is shown with thicker bonds
Figure 14 The structure of Na,In,,, which contains 12bonded closo-In,, clusters and nido icosahedra
(cP154) (Sevov and Corbett, 1993e), also with a network of clusters (Figure 15). The network is made of 12-bonded icosahedra (closo-Tn,J and 6-bonded hexagonal antiprisms (~rachno-In,~) in ratio 1:3. Each icosahedron requires 2n f 2 = 26 and (12 x 2)/2 = 12 electrons for endo- and exo-bonding, respectively, while these numbers for the aruchno-In12 are 2n I-6 = 30 and (12 x 2)/2 = 12 electrons, respectively. Combined with the available 12 x 3 = 36 electrons from the 12 indium atoms forming the clusters, the charges are 2- and 6- for the closo and aruchno species, respectively, i.e. clom-InfF and urachno-Infy in ratio 1:3. Thus the number of needed extra electrons to balance the charges of 1 x 12 + 3 x 12 = 48 indium atoms is 1x 2 + 3 x 6 = 20. However, available are 3 potassium and 26 sodium atoms according to the formula, and therefore the compound is a ‘metallic Zintl phase’ with 9 extra electrons per formula. Twelve-atom clusters, icosahedra, are typical for this group which is sometimes cdled the group of the icosagens. Nevertheless, indium has shown capabilities to form even larger closo-species. Sixteen-atom clusters of indium havc been found in two different nonstoichiometric compounds, NaJn,, (tP228) and
Na151n27,4 (oc344) (Sevov and Corbett, 1992, 1993a). The network of the former (Figure 16) is made of three different species, 12-bonded closo-in,,, 11-bonded nido-In,,, and 4-bonded isolated indium atoms. The numbers of required and available electrons per cell are 504 and 507, respectively, or only 3 extra electrons (or 0.6%) available per 504 electrons and the compound is metallic. an ‘almost Zintl phase’. The 16-atom deltahedral cluster is a new species found for the first time in this compound (Figure 17). Its shape can be understood starting from a tetrahedron, then truncating its 4 corners to form a 12-atom cluster species with 4 hexagonal faces, and finally capping those hexagonal faces with 4 additional indium atoms. It is highly spherical with the ideal geometry of point group T,. As a result of this particular tetrahedral symmetry, the bonding within the cluster needs rather 2n + 4 electrons instead of the ‘normal’ 2n+2 electrons for closospecies. The cluster is hyperelectronic. 2.2.2 Heteroatomic
In addition to the described networks of homoatomic clusters there are also many group 13-based networks of heteroatomic ones. Such are Nalo2Cu36Ga279 (hR417) and Na,02Zn,2Ga243(hR417) with species of 3 face-fused icosahedra, Na&d2&+aS6 (cF460) and Li3RZn34Ga67 (hP834) with 16-atom tetracapped truncated tetrahedra, and Li,,Cu,Ga2, (~1160)with interconnected icosahedra (Belin and Tilfard-Charbonnel, 1993, and references therein). Indium-based ternary and quaternary compounds with heteroatomic clusters are also numerous, K1n2-,Cd, (hP90) and
126
Structure and Composition
Figure 18 T h e structure of Kh,-,Cd, with arackno-In,, deltahedra (lighter polyhedra) in the shape of double drums and icosahedra (darker polyhedra)
K3,1n,9-xCdx (hR636) (Sevov, 1993) with 12-bonded araclano 18-atom clusters (Figure 18), Na2,In3,,,Zn, and Na,31n,9BAu3,4(hP132) (Sevov, 1993) with 15bonded closo 15-atom clusters that are truncated trigonal prisms (Figure 19), and Naglnl6,,Zn, (cF448) with 16-bonded closo 16-atom clusters (Sevov, 1993). All these are either electronically balanced or very close to being such. Once more, the thallium-based heteroatomic network compounds are only a very few. Known are RI,Cd,T121 (hP88) with interconnected pentagonal bipyramids (TillardCharbonnel et al., 1997) and CssT1,1Cd2with columns of fused Cd-centered pentagonal antiprisms (Corbett, 2000b). Perhaps the most spectacular ternary Zintl phases based on group 13 elements are those with fused ‘fLillerene’4ike cages made of indium (Figure 20), Na&&, (kP195) (Sevov and Corbett, 19930 and Na1721nt92Z2 (oP712) for Z=Ni, Pd, Pt (Sevov and Corbett, 1996). The fullerene cages in these phases are made of pentagonal and hexagonal faces and contain
concentric spheres of sodium where the number of sodium atoms equals the number of fullerene faces (Figure 21). Nickel-centered clusters of Inlo, just like those in K,o[In,oNi](see above) are found inside the sodium spheres. The formula of one fullerene cage can be written as Ni@In,o@Na,,@fn,, where the symbol @ is used for ‘within’ (Figure 21). We should point out here that the stoichiometries of these compounds are extremely close to another Zintl phase, NaIn (=Na,In,) with a diamond framework of indium (Zintl and Dullenkopf, 1932). The difference i s just 2 additional nickel atoms per nearly 200 atoms of sodium and indium! Although there is such a negligible difference in stoichiometry,the two structures, those of Na&r~~~Ni, and Na961np6,have nothing in common. Furthermore, although structurally extremely complicated, the Nag61n9,Z,compounds are diamagnetic, and therefore true Zintl phases. Another group of compounds containing networks of heteroatomic clusters are based on mixtures of groups 12 and 14. Two compounds, Na,,Cd,E,
Zintl Phases
Figure 19 A view of the 15-bonded closo-In,, with the shape of a truncated trigonal prism (the three-fold axis is vertical) found in Na.&,,,,Zn4,, and Na,,In,,Au,,.,
made of Figure 20 The indium framework in NaJn,Ni, face-fused fidlerene-like cages of 74 and 60 atoms. The spheres are ‘stuffed’ with sodium cations and Ni-centered In,, clusters (see Figure 21). The layers of cages are stacked in double hexagonal fashion, ABACAB. along the c-axis (vertical)
127
Figure 21 A closer view of a fullerene-like cage of indium made of 74 atoms. A nickel atom centers the sphere, a cluster of 10 lndium atoms surrounds the nickel, and a sphere of 36 sodium atoms surrounds the indium cluster. The formation can be written as Ni@In,,@Na,,@In,
(cII60) for E = P b , Sn (Todorov and Sevov, 1997a) and Na49Cd58.sSn37,(hR580) (Todorov and Sevov, 1997b), were synthesized recently. Both compounds contain empty icosahedra, the only examples of such species that do not involve group 13 elements. One way to rationalize that is, of course, to consider the isoelectronic relationship between an atom of group 13 and the average of an atom of group 12 and another one of group 14. In addition to the icosahedra, Na,9Cd58,Sn,7,, also contains 12-bonded closo deltahedra of 18 atoms, the largest closo deltahedra known so far {Figure 22). This cluster is also interesting from an electronic point of view since, as in the case of closoIn,,, it is hyperelectroaic and requires 2n + 4 bonding electrons. However, the violation o f Wade’s rules in this case is not due to the particular symmetry as in the case of In,, but is rather due to the size of the cluster. Since the cluster is rather elongated, an ‘extra’ orbital that is bonding withm the two hemispheres and antibonding between them becomes net-bonding and filled. Also of interest here is that the non-exobonded atoms of the cluster do not carry lone pairs of electrons, apparently due to the flatness of the coordination of these atoms. Tlre planarity is a direct result of the size of the cluster, and therefore this cluster is beyond or at some critical size, above which atoms without exo bonds will have empty porbitals.
128
Structure and Composition
Figure 22 The structure of Na,,Cd,,,,Sn,, with the largest closo deltahedron of 18 atoms. The cluster IS 12-bonded to other cluster species in the structure. The potassium cations are shown as isolttted spheres
3. Zintl Phases with Localized Bonding
The compounds in this category contain only regular 2-center-2-electron bonds between the p-elements. Most of them involve the relatively electron-richer pelements, ie. elements from the right-hand side of the p-block. The majority of compounds involve at least two p-elements of different groups and alkali metals, and are therefore mostly ternaries. An excellent review of these compounds by Eisenmann et al. has appeared recently (Eisenmann and Cordier, 1996). Many of the compounds contain tetrahedral units made of one of the p-elements and centered by the other, and often share corners or edges with each other. For example, isolated Sn-centered tetrahedra of antimony, [SnSb,]*-, are found in Na8SnSb4(cF104) (Eisenmann and Ktein, 1988). Chains and higher dimensional motifs of corner-sharing tetrahedra are found in many compounds. Chains characterize the structure of Na,SnSb,, while a 3-0 network of tetrahedra is found in Cs,h4Bi, (aP17) (Bobev and Sevov, 1999a}, for example (Figure 23). There are also structures
Figure 23 The structure of Cs,In,Bi, with chains of edgesharing In-centered tetrahedra of bismuth. The chains are interconnected via In-In bonds (shown) to form a 3dimensional network. The cesium cations are shown as isolated circles
where the tetrahedra are both corner- and edge-shared such as Ga-centered As4-tetrahedra in K,Ga3As, (OR@), In-centered As4-tetrahedra in K,In2As3 (oC64), etc. The number of such heteroatomic compounds and their structural types is very large. In addition to the number of different ways of interconnecting tetrahedra, there are structures with isolated or connected flat AB, units, or mixtures of interconnected tetrahedra and such AB3 units, etc. (Eisenmann and Cordier, 1996). Nevertheless, despite the structural variety, all these compounds have simple bonding, are easily understood by simple octet rule consideration, and since they have been extensively reviewed already (Eisenmann and Cordier, 1996; von Schnering and Hiinle, 1988; Schafer and Eisenmann, 1985; von Schnering, 1981; Schlfer and Eisemann, 1981) they will not be discussed any further in this
Zintl Phases
Figure 24 The structure of Cs3Bi2with isolated dimers of Bif. An extra electron is apparently delocalized on the cesium cations and antibonding Bi-orbitals
chapter. More emphasis will be given to new homoatomic compounds, i.e. one p-element combined with alkali metals.
3.2 Group 15 It is quite surprising that until recently there were blank spots of structurally unknown compounds in the simple binary systems alkali-metatantimony and
129
alkali-metal-bismuth, and even in alkali-metalarsenic. Studies of the corresponding liquid systems (van der Aart et al., 2000) have suggested that structural units such as dimers, tetramers, squares, etc., exist in melts with stoichiometries A5E4and A3E2 Recently, structural studies in these systems revealed that similar units exist in the corresponding solid-state compounds (Gascoin and Sevov, 2000). Thus, compounds A,Bi2 (oC15) were found for A = R, Rb, or Cs. They Fontain Bi2-dimers with a Bi-Bi distance of 2.976A in Cs3Bi2 (Figure 24). Compounds with the stoiclxiometry A5E4 were characterized for both bismuth and antimony with A = K, Rb,or Cs. They contain planar zig-zag tetrameTs of bismuth (Figure 25) wi!h end distances of 2.972 A and a middle oiie of 3,036A. Magnetic and two-probe conductivity measurements suggest that the compounds are metallic. This combined with the stoichiometries and the structures of the compounds (the possible presence of hydrogen has been discarded based on neutron diffraction studies and indirect synthetic evidence) leads to only one possible explanation of their electronic structures. Similar to K&,, which can be written as 8K+ + InTr + e- and other similar ‘metallic Zintl phases’ with extra dectrons (see above), the two compounds A,& (oCl5) and A5E4(oCl8) contain the species E:- and E f - , respectively, and an extra
Figure 25 The structure of Cs,Bi, ulth isolated tetramers of Bi:-. electron that makes the compound metallic
Similarly to Cs,Bi, (see Figure 24) there IS a delocalized
Structure and Composition
I30
electron each. Their formulas can be written as 3A+ + E:- + e- and 5A+ +E!- + e-, respectively. Furthermore, both bismuth compounds dissolve in ethylenediamine, and the compounds that can be crystallized from the solutions contain double-bonded dimeric fBi=Bi12- molecules (Xu et al., 2000). This indicates that the dimer in A3Bi2 also has a double bond, and that the planar tetramer in A,Bi4 has one delocalized double bond with all bismuth atoms in sp2 hybridization, The extra electrons in both compounds are delocalized over the alkali-metal cations and antibonding Bi-Bi orbitals (just as in K81nl,, see above). The latter makes the bismuth distances somewhat longer than for the correspondingmultiple bonding. 3.2 Group 14 Species with multiple bonding have been found for the elements of this group as well. Thus planar rings of silicon and germanium, Sif- and Gej-, isoelectronic with cyclopentene, have been found in LilZE7(oP152) (von Schnering et al., 1980). Also, planar triangular star-shaped Silt- and Ge:- are found in the same compounds. These species are isoelectronic with CO$and similarly have a delocalized double bond. Recently, a class of compounds called clathrates based on group-14 elements have attracted much attention due to their potential for thermoelectric applications. These compounds are AsE46(cP54) and A,E1,6 (cF160) (ideal stoichiometries) where A = alkali metal and E = group-14 element, identified as clathrate-I and clathrate-11, respectively (Cros et al., 1965; Kasper et al., 1965). The structures of both are built of fused cages of 4-bonded tetrahedral E-atoms, and the alkali metals occupy the centers of the cages. C I a ~ a t e - Itype phases (analogous to the zeolite melanophlogite) crystallize in a primitive cubic lattice, space group P m h (Figure 26). The 46 clathrand atoms form two cages of diEerent sizes: one is a 20-atom pentagonal dodecahedron [512], and the other is a 24atom tetrakaidecahedron [512fi2] (the symbol [51262] denotes a polyhedron with 12 pentagonal and 2 hexagonal faces). There are 8 cages per formula unit, 2 smaller and 6 larger, and therefore the clathrate-I formula can be written as A2AiE4;. Clathrate-I1 (analogous to the zeolite ZSM-39) crystallizes in the face-centeredcubic F&rn space group (Figure 27). The framework-building atoms also form two different polyhedra. The difference, however, is that here in addition to the pentagonal dodecahedra [512] the second type of polyhedra are built of 28 atoms, hexakaidecahedra [51264], that have 12 pentagonal
Figure 26 The structure of clathrate-I with cages made of 4bonded elements of group 14,The clathrate has cages of 20 and 24 atoms shown as gray and white polyhedra, respectively. Alkali-metalcations (not shown) center the cages
and 4 hexagonal faces. The ratio of smaller to larger cavities in clathrate-If is 16:8 and therefore the formula can be written as A\6A$E,36. Four-bonded atoms of group 14 should have zero formal charge, and therefore both clathrates should be *metaIlicZintl phases’ considering a full transfer of electrons from the alkali metal atoms to the framework atoms. Nevertheless, there are ways to achieve electronically balanced clathrates, i.e. to ‘stabilize’ true Zintl
Figure 27 The structure of clathrate-I1 with cages of 20 and 28 atoms shown as gray and white polyhedra, respectively. Two types of cations with very different sizes such as Cs+ and Na+ stabilize this structure by occupying the centers of the two different cages
131
Zintl Phases
phases. One way is to form vacancies at the network sites as in A,Sn4u2 where is a vacancy at a tin site. Each missing tin atom leaves the 4 neighboring atoms with incomplete valence shells, i.e. 4 extra electrons will be needed to complete their octet configurations wth lone pairs. Another way to balance the ‘extra’ electrons from the alkali metals is to substitute group14 atoms with an electron-poorer element, from groups 13 or 12 for example. This idea has been widely utilized in the last 10-15 years for making new ternary phases with the clathrate-1-structure. The ideal stoichiometries will be A8EiE3*and &&E42 where E and E are group-13 and -12 elements, respectively. The existence of many of these compositions and their compliance with the Zintl concept have been proven. Even more complicated and difficult for interpretation are the compounds with the clathrate-11-type structure, Until recently, only the non-stoicbiometric NaxSi136 and NaxGe136phases were known in the binary A-E systems (Cros et al., 1965, 1970). The structure of the former was recently refined from X-ray powder diffraction in order to determine the distribution of the sodium atoms within the two available alkali-metal sites, i.e. the centers of the pentagonal dodecahedra and the hexakaidecahedra (Ramachandran et al., 1999; Reny et al., 1998). It was concluded that for xG8, the Na-atoms occupy preferably the larger [512fi2]cage. Until very recently, there was no unequivocal structure determination for compounds with the clathrate-I1 type structure. The first wellrefined structures from single crystal data and reproducible direct syntheses were reported for the stoichiometricand completely-filled silicon and germanium clathrate-I1compounds with mixed alkali metals: C S ~ N ~ ~ , S ~ ,CssNa,6Ge136, ~,, Rb8Na16Si136, and Rb8Na16Ge136 (Bobev and Sevov, 1999b, 2000). These compounds are stoichiometric and due to the extra 24 electrons per 136 group-1.8 atoms, they are also metallic Zintl phases.
a
4. Conclusion
Both the true Zintl phases and the ‘metallic Zintl phases’ are classes of fascinating compounds, some with clusters presenting delocalized bonding and some with ‘normal’ localized bonds. The variety and structural richness is quite obvious, and this is only a small percent of all possible combinations to be explored. The importance of these intermetallic compounds is primarily in the understanding of the chemistry of the p-elements in their negative oxidation
states. When in such unusual oxidation states many of these elements form bonds between themselves, form clusters and networks of clusters. These phases are potential starting materials for deposition of thin films or formation of nanoparticles of the corresponding pelement. Some of them may have good thermoelectric and semiconducting properties, and even may show superconductivity. There are definitely many new and more exciting compounds to be found.
5. References Belin, C., Corbett, J. D., and Cisar, A. (1977). J . Am. Chem. Soc., 99, 7163. Belin, C., and Ling, R. G. (1982). Acad. Sci. Paris, 294, 1083. Belin, C., and Tillard-Charbonnel, M. (1993). Prog. Sotid St. Chem., 22, 59. Bobev, S.,and Sevov. S. C. (1999a). Inorg. Chem.. 38,2672. Bobev, S., and Sevov, S. C. (1999b). J. Am. Chem. Soc., 121, 3795. Bobev, S.,and Sevov, S . C. (2000). J. Solid State Chem., 153, 92. Campbell, J., and Schrobilgen, C.(1997). Inorg. Chem., 36, 4078. Cisar, A., and Corbett, 3. D. (1977). Inorg. Chem., 16, 2482. Corbett, J. D, (1996). In Chemistry, Structure, and Bonding of Zintl Phases and Ions (ed. S. M. ICauzkdrich). VCH, New York, p. 139. Corbett, J. D. (1997). StructureLBonding, 87, 157. Corbett. J. D. (2000a). Angew. Chem. Int. Ed., 39, 670. Corbett, J. D. (2000b). private communicalon. Cros, C., Poucliard, M., and Hagenmuller, P. (1965). Compt. Rend., 260, 4164. Cros, C., Pouchard, M., and NagenmuIIer, P (1970). J. Solid State Chem., 2, 570. Dong, Z.-C., and Corbett. J. D. (1993). J. Am. Chem. Soc., 115, 11299. Dong, L C . , and Corbett, J. D. (1994). J. Am. Chem. Soc.. 116, 3429. Dong, Z.-C., and Corbett, J. D. (1995a). J. Cluster Sci., 6, 187. Dong, Z.-C., and Corbett, J. D. (1995b). Inorg. Chem., 34, 5042. Dong, Z.-C., and Corbett, J. D. (1995~).J. Am. Chem. Soc., 117, 6447. Dong, Z.-C., and Corbett, J. D. (1995d). Inorg. Chem., 34, 5709. Dong, Z.-C., and Corbett, J. D. (1996a). Inorg. Chem., 35, 1444. Dong, Z.-C., and Corbett, .T. D. (1996b). Inorg. Chem., 35, 2301. Dong, 2.-C., and Corbett, J. D. (1996c). Inorg. Chem., 35, 3 107.
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Dong, Z.-C., and Corbett, J. D. (1996d). Angew. Chem. Int. Ed. Engl., 35, 1006. Dong, Z.-C., Henning, R. W., and Corbett, J. D. (1997). Inorg. Chem., 36, 3559 Edwards, P. A., and Corbett, J. D. (1977). Inorg. Chem., 16, 903. fisemam, B., and Cordier, G. (1996). IR Chemistry, Structure, m d Bonding of Zintl Phases and Ions (d. S. M. Kadarich). VCH Pubtishers, Inc., New York. NY,p. 61. Eisenmann, B., and Klein, J. (1988). 2. Naturforschung, 43B, 69. Gascom, F., and Sevov, S. C. (2000). J. Am. Cltern. Soc., 122, 10251. Orimm, H.O., and Sommerfeld, A. (1926). Z . Phys., 36, 36, Henning, R. W., and Corbett, J. D. (1997). Inorg. Chem., 36, 6045. Hennmg, R. W., and Corbett, J. D. (1999). Inorg. Chem., 38, 3883. Huang, D.-P., Dong, 2.-C., and Corbett, J. D. (1998). Inorg. Chem., 37, 5881. Huang, D.-P., and Corbett, J. D. (1999). Inorg. Chem., 38, 316. Hughbanks, T. (I 992). In Inorganometullic Chemistry (ed. T. P. Fehlner). Plenum Press, New York, p. 289. Hume-Rothery, W. (1926). J. Inst. Metals, 35, 295. Kaskel, S., and Corbett, J. D. (2000). Inorg. Chem., 39, 778. Kasper, J. S., Hagenmuller. P., Pouchard, M., and Cros, C. (1965). Science, 150, 1713. Klemm, W. (1956). Trab. Hem, Int. React. Solidos3rd, 1,447. Klemm, W, (1959). Proc. Chem. Soc., 329. Miller, G. J. (1996). In Chemistry, Structure, and Bonding of Zintl Phaseasand Ions (ed. S. M. Kauzlarich). VCH, New York, p. 1. Queneau, V., and Sevov, S. C. (1997a). Angew. Chem. Int. Ed. Engl., 36, t 754. Queneau, V., and Sevov, S. C. (1997b), J. Am. Chem. Soc., 119,8109. Qimeau, V., and Sevov, S. C. (1998a). Inorg. Chem., 37, 1358. Queneau, V., and Sevov, S. C. (1998b). J. Am. Chem. Soc., 120, 3263. Ramachandran, G. K., Dong, J., Diefenbacher,J., Gryko, J., Mamke, R. F., Sankey, 0.F., and McMiIlan, P. F. (1999). J. Solid State Chem., 145, 716. Reny, E., Gravereau, P., Cros, C., and Pouchard, M. (1998). J . Mater. Chenz., 8, 2839. Scliafer, H., and Eisenrnann, B. (1981). Rev. Inorg. Chem., 3, 29. Schiifer, W., and Eisenmann. B. (1985). Rev. Mat. Sci., 15, 1. Sevov, S. C . (1993). Ph.D. Thesis, Iowa State University, Ames, IA. Sevov. S. C., and Corbett, . I . D. (1991). Inorg. Chem., 30, 4875. Sevov, S. C., and Corbett, J. D. (1992). Inorg. Chem., 31, 1895.
Sevov, S. C., and Corbett, J. D. (1993a). J . Solid State Chem., 103, 114. Sevov, S. C., and Corbett, J. D. (1993b). Inorg. Chem., 32, 1059. Sevov, S. C., and Corbett, J. D. (1493~).J. Am. Chcm. Soc., 115, 9089. Sevov, S. C., and Corbett, J. D. (1993d). Z. Anorg. AElg. Chem., 619, 128. Sevov, S. C., and Corbett, J. D. (1993e). Inorg. Chem., 32, 1612, Sevov, S. C., and Corbetl. J. D. (1993f). Science, 262, 880. Sevov, S. C., and Corbett, J. D. (1996). J. Solid State Chem., 123, 344. Sevov, S. C., Corbett, J. D., and Ostenson, J. E. (1993). J. Alloys Comp., 202, 289. Smith J. F., and Hansen, D. A. (1967). Acta Crystallogr., 22, 836. Somer, M., Carrillo-Cabrera, W., Peters, E. M., Peters, I<., and van Schensing, H.-G. (1998). 2.Anorg. dlfg. Chew?., 624, 1915. Tillard-Charbonnel, M., Chahme, A., Belin, C., Rousseau, R.,and Canadell, E. (1997). Chem. Eur. J., 3, 799. Todorov, E., and Sevov, S. C. (1997a). Inorg. Chem., % . , 4298. Todorov, E., and Sevov, S. C . (1997b). J. Am. Chem. Soc., 119,2869. Todorov, E., and Sevov, S . C. (1998). Inorg. Chem., 37,3889. Todorov, E., and Sevov, S. C. (1999). Angew. Chem. Int. Ed., 38, 1775. van der Aart, S. A., Verhoeven, V. W. J., Verkerk. P., and van der Lugt, W. (2000). J. Chem. Phys., 112, 857. van der Lugt, W. (1996). In Chemistry, Structure, and Bonding of Zintl Phases and Ions (ed. S. M. I(aWkmCh). VCH, New York, p. 183. von Schnering, H A . , Nesper, R., Curda, J., and Tebbe, K.-F. (1980). Angew. Chem. Int. Ed. Engl., 19, 1033. von Schnering, H.-G. (198 1). Angew. Chem. Int. Ed. Engl., 20, 33. von Schnemg, H.-G.. and HBnle, W. (1988). Chem. Rev., 88, 243. von Schnermg, H.-G,, Bartinger, M., Bolle, U., CarrelloCabrera, W., Curda, J., Gm, Y., Heinemann, F., Llanos, J., Peters, IS.,Schmeding, A., and Somer, M. (1997). 2. Anorg. Allg. Chem., 623, 1037. Wade, K. (1972). Inorg. Nucl. Chem. Leit., 8, 559. Wade, K. (1976). Adv. Inorg. Chem. Radiochem., 18, 1. Westgren, A. F., and Phragmen, G. (1926). 2. Metaifkunde, 18, 279. Xu, L., and Sevov, S. C. (1999). J. Am. Chem. Soc., 121,9245. Xu, L., Bobev, S., El-Bahraoui, J., and Sevov, S, C. (2000). J. Am. Chem. SOC.,122, 1838. Zintl, E. (1939). Angew. Chem., 52, 1 . Zintl, E., and Brouer, G. (1933). 2.Phys. Chem,, BU1, 245. Zitl, E., and Dullenkopf, W. (1932). Z . Phys. Chem., B16,183. Zintl, E., and Woltersdorf, G. (1935). Z. Elecrrochrm., 41, 876.
Books must follow science, not science books. Francis Bacon, 15
The verb “to theorize” is now conjugated as follows: ‘I built a model; you formulated a hypothesis; he made a conjecture.’ ohn Ziman, 1925-
It is a different sort of genius that audaciously posits the subtIe interactions among a complicated ensemble of atoms. Marry A. A ~ ~ t e 1921r,
Esther Belin-Ferr6 Universitd Pierre et Marie Curie - Centre National de Za Recherche Scientifique, Paris, France
1. Introduction The properties of intermetallics may be better understood through insight into their electronic as well as their atomic structures. Knowledge of the electronic structure and the nature of bonding may also give general trends, helpful when looking either for new intermetallics or for improving physical characteristics along definite lines such as enhancing resistance to corrosion, modifying mechanical properties, etc. Therefore, numerous theoretical as well as experimentalmeans have been developed to analyse the band structure and densities of electronic states (DOS) of these solids. For further background the reader may wish to consult the following chapters from Vol. 1 of this treatise: Turchi, Ch.2, on electronic theories of phase stability; Singh, Ch. 6, on band structures and their interpretation: and pintschovius, Ch.7, on phonon dispersion curves and their interpretation. In this chapter a few experimental spectroscopic techniques will be presented. These are interesting as far as electronic structure is concerned because they investigate transitions between two different quantum states of the solid, each one characterized by its energy and lifetime. Accordingly they provide direct relevant information on the nature and energy distribution of the electronic states and their interactions, therefore on the chemical bonds in the material. Total overlap of partial electronic bands in the valence band of a specimen implies a complete mixing of the corresponding states and suggests metallic or covalent bonding which is generally found for hard materials. Changes of the electronic and physical properties from one sample to another involve modifications in the electronic structure, for example, deviation of the electronic
energy distributions for a given intennetallic with respect to free-electron or d-like metals will underline that the specimen departs from a metallic-like behaviour. Also, shift of the valence and conduction band edges from the Fermi level will end up in the formation of a pseudo-gap or a real gap which clearly will imply deviation from metallic behaviour. We are not going to consider here all of the numerous spectroscopic techniques useful for investigating the electronic structure of solids (visible, UV and infra-red optical spectroscopies, Raman, NMR, ellipsometry . . .) but will restrict ourselves to only a few which we have chosen because they give direct information on the electromc distributions and can be compared directly with DOS calculations with no further assumptions and do not require sophisticated specimen preparation. These are photoemission, soft X-ray emission, X-ray photoabsorption, electron energy loss, and isochromat Bremsstrahlung spectroscopies. The first two techniques allow one to analyse electronic occupied states whereas the last three are well adapted to a description of the electronic distnbutions of normally unoccupied states. For each of these techniques, the underlying general principles will be presented. Their usefulness and main characteristics will be illustrated with only a few selected recent examples of their application to intermetallics presented from the large volume of the experimental information published so far.
2. Investigation of Occupied States
As mentioned,the occupied electronicstates of a solid can be probed by means of photoemission and soft X-ray
Intermetallic Compounuk Vol. 3, Principles and Practice. Edited by J. H. Westbrook and R. L. Fleischer. 02002 John Wiley L Sons, Ltd.
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Bonding and Stability
photoemission process involves three successive steps: first, the excitation of the photoelectron, second, its travel through the solid and third, its ejection into the vacuum from the very surface. This last step is governed by the photoelectron transmission probability. Accordingly, the binding energy EB o f the photoelectron is related to its kinetic energy by:
Figure E Scheme of the energy levels involved in binding energy measurements.EFis the Fermi level. EK(v)is the kinetic energy with respect to the vacuum energy level of the sample, and EB IS the binding energy of the photoelectron created by the incoming photons. It is measured wth a speGtrometer having the work function @'spech.om
emission spectroscopies. For a few decades now, since the original work of K. Siegbahn and his group in Uppsala (Siegbahn cf al., 1967, 1969), so-called ESCA (electron spectroscopy for chemical analysis) or photoemission spectroscopy (PES) has become quite a popular tcchniquc, so much so that very efficient and powerful spectrometers are produced and marketed by various companies. On the contrary, for soft X-ray emission spectroscopy, appropriate spectrometers are not commercially available; they mostly have to be designed and constructed in the laboratories that intend to use this technique. However, this situation will not long prevail for nowadays several groups, all around the world, operate such home-made equipments using the very intense light beams of new generation synchrotron facilities.
2.1 ~~otoerniss~oB Spectpnseollies Photoemission spectroscopies (PES) probe the kinetic energies EK of photoelectrons emitted from inner levels of a solid as well as from the outermost occupied band (OB) as a consequence of the interaction of the solid with an incoming X-ray (XPS) or ultra-violet (UPS) radiation of energy hv. Therefore, the initial state i s the ground state of the system whereas in the final state there is a hole created by the incoming energetic beam. Within the framework of the frozen orbitals (assuming that the presence of a hole in the final state does not affect significantly the remaining orbitals), the
where Q, denotes the difference between the work functions of the spectrometer and of the sample (Figure I). Usually, it is not necessary to know Q, exactly provided the EB scale is properly calibrated, e.g. by referring to a well-known level such as the 1s level of contaminating carbon, always present at the surface of a sample not prepared in a clean, high vacuum, or the Au 4f7j2 levels if Au can be evaporated onto the sample itself, It i s to be noted that the Fermi levels of the spectrometer and metallic specimens adjust to each other, whereas this does not hold true for non-conducting substances for which charging effects induce shifts that can be as large as several eV. As to the final energy resolution of PES measurements, it depends upon the natural energy width of the incident photon beam and the spectrometer experimental fwction. For XPS it is generally about 0.4-O.XeV and for U P S it may be as good as a few tenth of an eV. The binding energies of the inner levels of a specimen are obtained SeparateIy. On the contrary, for the OB, the contributions of all the electrons are summed9 modulated by the photoelectron cross-sections o:
where \Irf and yii denote the wave functions of the final and initial states, respectively. During its travel through the solid, the photoelectron is subjected to inelastic interactions with the electrons of the medium; therefore, the sampled depth is governed by the mean free path of the photoelectrons, denoted A. Thickness up to 3h are generally probed, which makes PES basically a surface-sensitive technique. Consequently, it is necessary to use very careful preparation and characterization of the surface under study. In addition, because of the inelastic interactions, the shape of the background on which the photoelectron peaks are superposed is not a simple function, and it is necessary to model it. In narrow energy ranges, say for instance for inner level peaks, a linear background can be subtracted, but this cannot be done for OB states that usually extend over more than 10-12eV.
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Speetroscopic Approaches
The number n(c) of the emitted photoelectrons is a fmction of several parameters and can be written as
n(&)cx n ( ~ v ) . N ( E ~ i . N ( E ) ~ ~ ~ . a ( E ) . ~(3) (E) where n(hv) is the number of incident photons, N(E), and IV(E)~stand for the DOS at initial and final states, respectively, f& is the Fermi-Dirac temperature function, a(E) is the photoemission cross-section and A(E) is the detector transmission factor. The contribution to the total intensity due to an element E at a depth x in a direction referred to by its angle 9 with the surface of the sample is connected to its concentration and to the electron's mean free path. Therefore, accurate nieasurements of the intensity of a chosen core level of a given element in a sample make it possible to determine its concentration by comparing the same photoelectron peak in the specimen and the pure element. Also, profile variations in concentration can be achieved by tuning the angle 0. There are two kinds of PES techniques by which final states may be explored. In integrated photoernission all possible final states contribute to the spectra. As photoemission cross-sections depend on hv, tuning the energy of the incident photons allows one to achieve some site selectivity and to distinguish between the features due to individual contributions to the OB of an alloy, provided their respective EB values are different enough to be resolved experimentally. Yet, the photoemission cross-sections significantly favour d andf states relative to p or s states (Yeh and Lindau 1985; Yeh, 1993). Accordingly, no features arising from sp constituents are observed in the OB spectra of alloys which contain sp as well as d and f elements. This integrated photoemission technique is mainly applied to polycrystalline specimens. The experimental data are usually compared to total DOS calculations when available. Such comparison is made more meaningful by convoluting the theoretical DOS with appropriate functions to account for the photoemission cross-sections and experimental functions. One example is shown in Figure 2 (Brown et aZ., 1997). Here, the complete overlap between Pt and Mn d-like sub-bands is indicative of a metallic bond in this material. Xn angle resolved photoemission, the photoelectrons are collected over a small solid angle, and their damping is weak enough that only transitions with k momentum conservation are involved. Thus, energy dispersion curves can be probed, which allows one to investigate band structure topology as we11 as Fermi surfaces. The data are often treated using the free-
8
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n
c 8
6
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0
Binding Energy (e Figure 2 Panel (a) PES spectra for Pt,Mn with partial contributions of Pt and Mn. In panel CO) the calculated DOS (Tohyama et al., 1989) (thin solid lines) are properly broadened for a meaningful comparison with the experimental data (thick solid line)
electron final state model; and, when possible, they are compared to band structure calculations. This technique is labelled ARUPS or ARXPS according to whether incident ultraviolet or X-ray photons are used; it is applied mainly to single crystals. In addition to the inner level peaks and to the OB band, the photoelectron spectra show many satellite
Bonding and Stability
radiation emitted by the X-ray tube. It is often difficult to account exactly for this background in the OB range, and models are necessary; however, for core levels, a linear background can generally be subtracted from the raw data. The intrinsic shape of the energy distribution of a core-level peak is a Lorentzian curve whose full width depends at half maximum intensity (FWHM), .4&,1,,, on the life time z of the inner hole through: AE,,,,, =hz-'
7
l , , , . l ~ . . . l . * , , . l . * ~ . *
$IQ
BOO
890
BEO
am
IN^^^ ENERGY (ev) Figure 3 Ce 3d PES spectra in a senes of Ce(Pd,,Cux), IntermeVduics taken at 1486.6 eV incident energy (Ogawa et al., 1993)
contributions that may carry important information about the electronic structure and bonding. They arise from characteristic energy losses, Auger peaks, shakeup and shake-off processes, plasmon excitations, surface states, etc. as well as final-state effects. Piasmon excitations are found towards high I& of the peaks, whereas surface states give a contribution to the low EB side. Final-state effects usually do not dominate in the spectra except for elements with unfilled inner shells, like the 4f levels of rare earths. Then, the photoemission spectra show complex features andlor multiplets involving f", f n + l and fn+2 final state configurations (Figure 3) (Ogawa et al., 1993). In addition to the photoemission peaks that are superimposed on a background which arises from the inelastic diffusion of the electrons; for X P S there is an additional contribution from the Bremsstrahlung
(4)
Therefore, core level spectra are usually decomposed into Lorentzian curves and compared to standards. Actually, for meaningful decompositions, Voigt functions can also be used, since it is commonly admitted that the experimental function of the PES spectrometer is a Gaussian distribution of energy. The PES core-level spectra bring information from both qualitative and quantitative st'andpoints. We already mentioned that their study may be advantageous for measuring concentration. In addition, they are very sensitive to the chermcal environment; hence shape modifications (for example, broadenings in amorphous systems as compared to crystals) as well as shifts up to a few eV (usually less than 5 eV) with respect to pure elements can be observed in different saniples. Indeed, the energy of an electron in a corclevel depends on the attractive potential of the nucleus of the atom and the repulsive interaction due to the other electrons of the surrounding cloud. As during the photoemission process, all the orbitals of the system contribute to the screening of the hole; the screening energy involves two terms, one is dtte to the intraatomic relaxation of the electronic cloud of the perturbed atom itself and the other term comes from the relaxation of neighbour atoms. Therefore, corelevels are affected by any change of the potentials to which they are subjected. To account exactly for such core-level shifts requires reference to models. These involve relaxation energy terms, electronegativities, formation enthalpies, etc. Accordingly, investigation of the chemical shifts in an intermetallic compound is of great interest, as it brings information 011 the chemical state of the probed element. The example of Figure 4 represents the A1 2p3p inner level in fcc Al, an amorphous intermetallic AI-Cu-Fe and the oxide present at the surface of the samples. Note that the feature towards low kinetic energies (high binding energies) at about 3 eV from the maximum is due to the contributioii of the Cu 3p level to the spectrum of the intermetallic sample.
139
Spectroscopic Approaches
fee AI
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netic energy (eV) Figure 4 Core-level peak in amorphous AI-Cu-Fe (open rhombs) and fcc Al (solid line) xn the kinetic energy range around 1404 eV (binding energy around 75 ev). The vertical bars show the maxlma of the AI 2pSizpeaks in the oxide (maximum intensity) and the samples and so illustrate chemical shifts from fcc A1 to the amorphous AI-Cu-Fe alloy (Belin-Fe&, unpublished)
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BINDING ENERGY (eV) Another interesting piece of information is provided by examination of the shape of the Fermi edge in relation to the metallic character of a sample. This comparison requires measurements with a high energy resolution; and, accordingly, UPS experiments are necessary. Many studies have been dedicated to the investigation of the Fermi edge of intermetallics; in recent years the presence of a pseudo-gap at EF in quasicrystalline alloys was verified for icosahedral as well as decagonal phases which gives indication that the electronic properties of such alloys depart from being metal-like. Figure 5 shows the Fermi edges of fcc Al and Au and icosahedrai Al-Cu-Fe and points out a clear deviation of the OB edge of the icosahedral intermetallic with respect to what is expected for a freeelectron-like system (Mori et al., 1991). As mentioned, ARUPS helps to map out the energy bands of a solid. As an example, we show in Figure 6 the binding energies versus k l for the r X direction of €-Fe% (100) measured between the third and fourth Brillouio zones and those calculated using a direct transition model with a free-electron final-state band
Figure 5 From bottom to top, expenmental Fermi edges (dots) and calculated Fermi edges (solid lines) for pure gold, fcc AI and an icosahedral AI-Cu-Fe quasicrystal. For this Iatter, the F e r n edge i s calculated assuming a freeelectronlike behaviour. The discrepancies between calculation and experiment demonstrate that the quasicrystal is by no means a freselectron-like system and emphasizes the low DOS at EF, therefore establishing the presence of a pseudo-gap
(Castro et al., 1997). The data are compared to band structure calculations by Mattheis and Hammann (1993). Topological investigations are based on the fact that the photoelectrons are diracted by the crystal lattice and therefore carry structural information. Fermi surfaces are analysed in such a way (Aebi et al., 1996) as exemplified in Figure 7, which shows the Fermi surface mappings of Pt (111) and its comparison with theoretical calculations (Pilo et al., 1999a and b). In conciuding this section, we note that only in very few cases of ordered alloys, have core-level as well as
140
Bonding and Stability
OB PES photo-diffraction patterns been used to decompose the OB into the partial densities of states of its components. We present in Figure 8 the total and partial DOS of AuCus (001) (Stuck et al., 1990). More information on PES techniques can he found in many textbooks, such as Barr, 1993; Brundle and Baker, 1978; Cardona and Ley, 1978 and 1979, or in Hiifner, 1995, etc. 2.2 X-ruy Emissiorr Spectroscopy
Figure 6 Experimental binding energies (solid dots) versus kL for the rX direction of t--FeSi (100). The solid lines are the calculated bands taken from Mattheis and Hammann (1993). These are shifted by 0.1 eV towards low binding energes for a better adjustment to the experimental results
An ionized or excited system is not stable and evolves spontaneously. Therefore, a hole in a core-level of a solid recombines, radiatively or not, from either a more external level or the OB. The energy implied in this recombination is the difference between the energies of the initial and final states. The initial state presents a hole in an inner level, and there remains a more external hole in the final state. The radiative process is the X-ray emission investigated by X-ray emission spectroscopy (XES). The non-radiative counterpart is the Auger effect, not treated here, which ends up emitting electrons and leaving two holes in the final state. Within the one-electron approximation, thus neglecting relaxation energy terms, X-ray emission involves two steps: first, creation of the inner hole at level L(n, 1, j ) and second, reorganization of the electronic cloud from another level L(d,Z',j') or from the OB. This is schematized in Figures 9a and 9b. The energy distribution of the emitted radiation is given by
Figare 7 Mapping of the Fermi surface of Pt(l1X) (left side) from PES measurements at room temperature with an incident radiation of energy 21.2 eV and its comparison with theoretical calculations (right side). Black dots of the calcuiation are to be compared with hgh intensiaes in the experiment
141
Spectroscopic Approaches
Figure 8 Partial and total DOS of AuC%(001) measured in the (1 11) direction. Calibration on the DOS scale was made assuming 10 and 30 electrons/ceIl for Au and Cu, respectively
or
for two levels. C(n, 2, j ) and L(n‘, I’, j’), equation (3, or for one level and the OB (equation (6)) participating in the transition, respectively. In equation (G), N ( c ) denotes the probed OB densities of states. Mf-, is the matrix element of the transition probability; it is constant or varies slowly with energy depending on l(PflrlfPi)lwhere P,and Pfare the wave functions of the initial and final states. Therefore, in equation (3, the initial and final states are highly localized; in contrast, in equation (6), Pi is a localized state whereas Pfdescribes a hole in the 03.3.Spatial overlapping between the initial and final wave functions is required for a transition to take place, and this requirement implies that only the amplitude of Pfin the core hole region will give a significant contribution to the spectrum. Accordingly, XES has a local character. In addition, it is necessary that the radiative transition
Figure 9 Sketch of the pnnaple of X-ray emission. Panel a represents an X-ray transition between two core-levels. Panel b corresponds to an X-ray emission involving the occupied band
probability differs from 0, which is achieved provided the transitions fulfil dipolar selection rules, namely: AI=fl,Aj=0, f l
(7)
As a consequence, if a core hole with symmetry 1 is created in an element A, alone or in a compound, the local density-of-states with I f 1 symmetry around this element, denoted by N(k)’*’ will be probed by the XES technique, thus giving also a partial character to XES. Note that (i) transitions with j’ = 0 --j = 0 are not allowed; (ii) transitions to 1 f 1 states are favoured with respect to those to l - 1, therefore, from a p hole, states with d character will be probed with a higher
142
Bonding and Stability
probability than states with s character. Consequently, comparison of the experimental XES spectra with partial densities of states calculations is possible. More details can be found in many textbooks, as for instance Agarwal (19791, or in Bonnelle (1987). The shape of the distribution for a transition involving two inner levels is a Lorentzian curve whose FWHM is the sum of the FWHMs corresponding to the two levels involved in the transition. The shape of the emitted intensity distribution to which the OB contributes results from the convolution of the probed partial local DOS and the Lorentzian distribution L(n, 5 j ) . The initial hole can be created either with impinging electrons or with photons. Irradiation by electrons easily produces multiple interactions; hence, satellite emissions due to the X-ray transition in the multipleionized or excited system may also be observed in the spectra. The XES technique is straightforward, directly applicable to any kind of material: crystalline, amorphous, insulator, bulk, powder, etc. In addition, according to the conditions of the experimental setup it can inform the investigator either with reference to the bulk sample or to a thin layer just below its surface. OB of deep interfaces in solids may also be investigated with XES induced by electrons by tuning the energy of the incident beam so that it reaches the depth of the interface in question (Fargues et al.? 1985; Szasz and Kojnok, 1985). The total energy resolution in an experiment results from the natural width A q n , I, j ) of the inner level L(n, 1, j ) and the instrumental function. AE(n, I, j j varies from a few meV up to several eV according to the atomic number and considered level (Krause and Oliver, 1979); and it is generally the most important parameter in choosing the appropriate transitions to investigate. Despite the fact that no absolute DOS values are obtained, it makes sense to compare thc DOS of a given element in various materials; because, according to equation (6), any change in the shape and energy of the spectral distribution will give direct insight into modifications of the corresponding N(f>. An example is given in Figure 10, which shows the Mg 3p distribution in the pure metal and in Mg2CoHs (Belin et al., 1987). The feature in the low transition energy range, not present in the Mg 3p band in the lower curve, corresponds to additional states due to Mg-H bonding in the hydrogenated intermetalk. A relevant characteristic of XES is that the contributions of the various components to the OB of a solid can be investigated separately, each one obtained in its own transition energy scale. TOachieve
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X-ray transition energy (eV) Figure 10 Mg 3p distribubon of states in the pure metal (lower curve) and in NiMg2H, (upper curve) on the X-ray transition energy scale
a picture of the OB and have insight into the electronic interactions that are present, further adjustment of the various partial contributions on the energy scale is necessary. This can be realized on the binding-energy scale but requires knowing the Fermi energy EF for each individual X-ray transition energy scale. To do so, it i s necessary to determine the binding energy with respect to EF of the inner level participating in each Xray transition; this can be achieved thanks to complementary X-ray and (or) inner-level PES measurements. An example is shown in Figure I1 for Al~Cu2Fe.It presents the curves corresponding to the A1 3p, A1 3s-d, Cu 3d-4s and Fe 3d-4s contributions to the OB, respectively, as adjusted to the binding energy scale from the measurements of AI 2p3!2, Cu 2 p 3 p Fe 2p3p inner levels and the X-ray transikon AI Zp3p -+A1 Is. Each curve is normalized to its own maximum intensity. Note that as transition probabilities strongly favour d states, no actual view of the Cu and Fe 4s states is achieved. The overlap between the peaks for Fe 3d and AI 3p curves denotes a mixing of the corresponding states and therefore illustrates some hybridized, covalent character of the A1-Fe bond. The maximum of the Cu 3d peak is almost at a relative minimum of the A1 3s-d distribution curve. Here, this can be interpreted as a Fano-like interaction (Terakura, 1977) between the localized d states and the extended AI states which splits them into two bonding and non-bonding parts, located on each side of the Cu
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Binding energy (eV)
Figure 11 Al3s-d (dots), Al3p (solid tine), Cu 3d (stars) and Fe 3d (triangles) electronic distribution curves in OB of crystalline Al,Cu,Fe. The full vertical line at the ongm represents the F e r n level, which IS located within fO.1eV for A1 and f0.3eV for Cu and Fe respectively
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143
Approaches
3dmaximum (Belin et al.,1992). There is a decrease of intensity at EF of the various counterparts as compared to pure metallic elements, which indicates the opening of a small pseudo-gap at EF in agreement with the fact that this alloy is a Hume-Rothery intermetallic. Comparison between experimental spectra and partial DOSS is shown in Figure 12 (Trambly de Laissardikre ef al.,1995). The agreement is very good for the Cu and Fe states, but for Al 3p and 3d states there is a slight discrepancy in the energy range 4 eV below EF which is still a matter of investigation by theoreticians (Papaconstaiitopoulos, 1997). Note that the features towards low binding energies from the maximum in the experimental curves of panels a and b are satellite contributions to the main peak. The situation is less simple when the sample contains elements with open shells. The initial state of XES is then the same as the final state in PES. Therefore many features are observed on the emission spectral distribution curves, which arise from final state effects due to both ionized and excited configurations. Figure 13 displays the Ce 4f-3d emission spectrum of CeNiz. Structures due to transitions involving excited and ionized 3d94f1, 3dI04f0, 3d945-' configurations can be recognized. In this example, the occurrence in the spectrum of peaks and bumps (arising from peaks of smaller intensity) characteristic of both Ce3+ and Ce4+ established that the CeNi2 intermetallic is actually a mixed valence alloy (Sonder, 1990).
0.00
Binding energy (eV) Figure 12 Experimental electronic distribution curves (symbols) and calculated partial DOS'S (solid lines) for AI,Cu,Fe. From bottom to top, the panels correspond to Cu d, Fed, Alp and AI s-d states, respectively. The thick line of the upper panel IS for the A1 s states whereas the thin one is for d states
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Nmber of Steps Figure 13 Ce 3d4f emission spectrum of CeNi,. The two sets of peaks correspond to transitions involving 3dJI2and 3dsi2 inner levels, respectively. The bars show the features characteristic of Ce3+ whereas the arrows show those due to Ce4-i-
Bonding and Stability
144
2.3 C o r n ~ ~ e ~ n tofa PES r i ~ ~and XES Techniques
whereas Ru 5d states (triangles in XES curves) are near the EF.PES shows that the Cu states are domiiiant and also that the total DOS at EF is very low. XES establishes the low intensity at the EF, especially for the N states, and shows the interactions between the A1 and the Cu states on the one hand and between the AI and Ru states on the other hand. For Ru the energy resolution of XES spectroscopy is not very good, which makes the Ru spectrum broad. The high resistivity of quasicrystalline Al-Cu-Ru (around 1800 Q cm at room temperature (Berger et aZ., 1993)), is in line with the reduced density of the extended-like states, namely N 3 p , in the vicinity of EF which is about 20% of the intensity in fcc Al, and the marked pseudo-gap at EF as assessed from the energy distance of the AI VB edges from Ep. Another example is shown in Figure 15 for FeSi where the X P S and XES experimental results are
As PES provides a view of the total OB and XES gives the partial contributions, it may be interesting to combine both techniques for a better understanding of the electronic structure of a solid. This is exemplified in Figure 14, which presents the PES and XES OB spectra of icosahedral quasicrystalline Al-Cu-Ru. For such an intermetallic, no DOS calculations are available due to the lack of translational properties of the quasicrystalline atomic structure. Therefore, it is advantageous to investigate the electronic structure experimentally, Note that it is of particular interest to have a view of the AI (or Mg) states and of their interaction with the other components in such intermetallics, since the sp states are less localized in character than the d states and therefore are more sensitive to changes in chemical and topological environments. In addition, they can be principally involved in many physical and electronic properties; yet, due to cross-sections that noticeably favour d and f states, they cannot be recognized in PES spectra. Figure 14 shows as an example PES curves for A~~SCUZORUIS (top curve) and A&~~.sCUZSRU~~.~ (lower curve) icosahedral quasicrystals; taken from Nakamura and Mizutani (1994) and the XES curves for A16sCuzoRu15 from Belin-Ferri. et al. (1996). From both sets of measurements it appears that Cu 3d states (crosses in XES spectra) are in the middle of the OB
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Figure 14 PE5 (XPS) (two upper curves) and XES (four lower curves) for icosahedral Al-Cu-Ru plotted on the same energy scale with the vertical line at the origin showing the Fermi level. All measurements were earned out at room temperature
0.2 0.1
0.0
Energy (eV) Figure 15 Electronic structure of FeSi. Top panel: the XPS spectrum is the dotted line and the total DOS calculated with the LMTO method is the continuous line. Lower paiels: from top to bottom, the experimental Fe 3 d 4 , Fe 4p, Si 3s-dand Si 3p curves are the dotted and broken lies. The partial calculated DOS are solid lines for Fe 3d, Fe 4p, Si 3s and Si 3p, respectively, and the broken line is for Si 3d (Galakov et al., 1995)
Spectroscopic Approaches
compared to total and partial DOS calculations; the good agreement between the data validates the theoretical model (Galakov et al., 1995).
3. Investigation of Unoccupied States 3.1 X-ray Photoab~orpt~on Speetroseopy An incoming photon can deliver its energy to a core electron (n,l , j ) of a solid and promote it to a normally unoccupied level, provided the energy of the incident photon is equal or higher than the ionization threshold. This is schematized in Figure 16. Such a process leaves an inner hole in the core state. Therefore, photoabsorption spectroscopy (XAS) and XES can be considered to be complementary in that, whereas one spectroscopy refers to occupied states, the other concerns the unoccupied ones. Similar to XES, in the one-electron approximation, the energy distribution of a photoabsorption transition involving the unoccupied band (UB) results from the convolution between the energy distributions of the core-level and the conduction DOS respectively, weighted by the corresponding transition probabilities. The spectral energy distribution associated with the photoabsorption process is
.i)
~ ~ ~ - t l ! 2 ~ ( & R * 1, ~ ( ~ ,
(8)
Here also, the photoabsorption transition is expected to follow the dipole selection rules as expressed in
145
equation (7), and its probability depends upon the overlap between a final state, which may be of somewhat extended character, and a more localized initial one. This makes XAS both site and symmetry selective. Accordingly, the photoabsorption spectrum describes the sum of all the transitions from the core level towards continuum states of appropriate angular momentum. Since the matrix element of the transition probability is constant or varies very slowly with energy, XAS spectra are directly related to the unoccupied DOSS of the solid; but, similar to XES, no absolute values can be derived from the experiments. Here also, as for XES. the total energy resolution in an experiment results from the natural width AE(n, I, j ) of the inner level L(n, I, j ) and the instrumental function. If 10 is the intensity of the incident photon beam, and I, the intensity after transmission through a thickness x of the sample, I and 10are connected via the Beer-Lambert law:
I = Ioe-ltx
fi can be taken as the linear photoabsorption coefficient since this effect is largely dominant as compared to others such as the Compton and Thomson diffusions, Auger emission, etc. U , is a function of the photoabsorption cross-sections, CT, of the different constituents of the solid. Again, the variation of CT is proportional to both @i and @f, the initial and final wave functions. ‘@idescribes the initial state, here the ground state, and @f is the final state, namely the electron ejected into the UB. Measurements of I and 10 allow one to determine the variation of 1.1. As a result of the photoabsorption process, the core-level vacancy can be filled owing to the Auger process. Consequently a photocurrent, the so-called photoyield current Y, is associated with the electrons escaping from the sample. This current can be measured and gives rise to the so-called yield technique. The fraction of the photon intensity absorbed in the sample is (10- I ) / & where Z is the photon beam intensity at the depth x. Therefore, the photoyield cwrent Y can be written
Y = (Io - l ) / I o= y(1 - e-”)
(10)
where y is a constant. Because the penetration depth is much larger than the electron-escaping depth, Y can be considered to be ypx. Hence, Y depends on the mean-free-path of the escaping electrons, and the yield technique is basically surface-sensitive in contrast to the transmission technique, which is mainly related to the bulk material. According to the particular sample,
-
Figure 16 Sketch of the principle of X-ray photoabsorption
(9)
146
Bonding and Stability
the incident photon beam is totally absorbed through a thickness x that can vary from tens of nm to pm, However, the yield technique must be selected when films a few tens of nm thick, which are often required €or a good experimental accuracy in the transmission mode, are not available. TOsummarize, XAS allows one to investigate partial local densities of unoccupied states; and, therefore, comparison with theoretical partial DOSSmakes sense. As €or XES, further adjustment of an absolute energy scale is necessary to reveal a picture of the UB distribution; and again, measurements of inner-level binding energies allow one to adjust the various contributions on the binding energy scale. To exemplify, Figure 17a displays the unoccupied electronic distributions of Al p , Fe d-s and p as well as Cu d-s and p in Al7CuzFe (Sadoc et al., 1993); and Figure 17b shows the partid DOS calculations by Trambly de Laissardiere et al. (1995), broadened in order to account for the core-level life-time as well as instrumental broadenings. Similar to XES, qualitative changes in spectral shapes from pure elements to intermetallics or from one intermetallic to another one reflect differences in bonding due to modifications in charge transfer or hybridization. For instance, advantage has been taken of such a peculiarity to investigate mixed valence interrnetaifics and evaluate the valency rates. By combining both X A S and XES spectra, it is then possible to have a full view of the electronic distributions in a solid and a complete derivation of the electronic interactions. This is exemplified in Figure 18 which shows the experimental OB and UB in icosahedral quasicrystaliine AI-Pd-Mn. As the shape of the Mn UB d-like counterpart is similar to that in the pure metal (not shown in the figure here), this adjustment points out that localized states, Mn OB and UB states, essentially, are found on each side of EF.Accordingly, there is no significant charge transfer from Al to Mn states and only a small part of the A1 3p states are hybridized to Mn 3d states (actually 4s states are not seen due to transition probabilities that favour d states). The maxima of Mn and Pd UB states correspond to relative minima of UB AI p ; hence, this confirms the states are not mixed. Pure Al s OB states are found at about 6 eV below EF.Assuming the transition probabilities are constant in the investigated energy range, the AI p distribution is adjusted to be the same intensity at EF as its OB counterpart. The OB and U3 Al p-like sub-bands show a marked asymmetry with a minimum at EF which points out the formation of a pseudo-gap and a low intensity of the
0 -5 Binding energy eV
5
-10
Figure 17a Experimental empty states distributions in AI,Cu,Fe. Solid line: Fe d-s, crosses: Fe p , triangles: Cu d-s. diamonds: C u p , dots: AI p . All sub-bands are normalized to their own maxima. In this alloy, Fe d-s states are predominantly present at the Fernu level, mainly overlapping A1 p states, whereas Cu d-s states are found about 2eV above EF
-4.00
0.00
4.00
8.00
Binding energy (eV)
Figure 1% Theoretlcal partial DOS in A1,aFe frrambly de Laissardihre et al., 1995) broadened to account for the core-level lifk-.hmes involved in the XAS expenments and the instrumental functions. Fe d, Fe s, Cu d, Cu s, AI p , Fe p , and Cu p curves are shown. Note that in the calculations, the energies are counted opposite in sign to those in the measurements. Good agreement is found in the energy positions between the expenmental curves of Figure 17a and the calculations. Analysis of the shapes shows that empty Fe and Cu states are of mixed of d and s characters
147
Spectroscopic Approaches
12
4
8
0
-4
-8
Binding mergy (eV) Figure 18 OB and UB contributions in an icosahedral AI-Pd-Mn quasicrystal as obtained from XES and XAS expenments, respectively. Small dots: A1 3s-d, full line: A1 3p, diamonds: Pd dd-Ss, triangles: Mn 3 d 4 , large dots: Pd d-s, open dots: Mn d-s, broken line: AI p. Ail the curves are normalized to their maximum intensity except for the AI p distribution which. assuming the transiaon probabilities are constant, is adjusted to be the same intensity at EF as its OB counterpart
rather extended UB Al p counterpart above EF is observed. This is in line with the high resistivity of this intermetallic alloy (about 1000 f'l cm at room temperature at which the spectroscopic measurements are made) (Belin et aZ., 1994; Belin-Fed and Dubois, 1996). Note that XAS which refers to an energy range of a few tens of eV above the absorption edges is often labelled as XANES, namely X-ray absorption nearedge structure in contrast to EXAFS, extended X-ray absorption fine structures, which is concerned with energy ranges of a few hundreds of eV above the edges and mainly carries structural information. 3.2 Electron Energy Loss Spectroscopy A mono-energetic incident electron beam directed into a solid is slowed down because of collisions, either elastic or inelastic, with the core electrons. When the incident energy is high enough, ionizations and excitations of the electrons of the solid can be produced, and inner shell electrons can be promoted to unoccupied states of appropriate symmetry. Thus, electron energy loss spectroscopy (EELS) allows one to explore the distribution of unoccupied states (Figure
14). Note that as in XAS, there is a remaining core hole in the final state, therefore this spectroscopy is also site selective. The energy loss is measured with respect to the elastic peak in the reflection or the transmission modes for small scattering angles. The measurements give the fraction of the incident electron beam with energy E which is scattered into a solid angle dR with the energy from E1 to El+. If we denote by q the momentum transferred from the incident to the scattered beam, then the cross-section of EELS is given by: d2a/dQdE cx (l/q2)Im(--l/c)
(11)
1It) is the so-called energy loss function and E is the dielectric constant which is connected to the photoabsorption coefficient: For energies around lOeV, the loss function is mainly determined by the collective excitations of the valence electrons, whereas for higher energies core excitations are taken into account. Finally, in the independent particle approximation, and for small momentum transfers,
fin(-
148
Bonding and Stability
stie peak ero toss)
f ~
Energy Loss (ev)
Figure 19 Principle of electron energy loss spectroscopy. The energy losses are measured with respect to the elastic peak which is taken as the origin
Figure 20 EELS spectra describing AI s empty states in fcc A1 (upper curve) and in icosahedral quasicrystalline Al,,Cu,Ru,, (lower curve), respectively (Terauchi et al., 1996)
3.3 Bremsstrahlung Isochvomat Spectvoscopy
Consequently, EELS is subject to fulfilment of dipole selection rules. In the transmission mode, namely using particles of high incident energy, the spectra are equivalent to those measured using transmission photoabsorption, whereas for low energy excitations, the spectra obtained in the reflection mode are dominated by electron mean-free-path effects and therefore are essentially surface-sensitive, analogous to yield photoabsorption spectra. Note that when the incident electron energy is close to that of an absorption edge, extra features may appear on the spectra due to non-dipolar transitions. Note also that as for XAS, no absolute DOS values are achieved with EELS measurements, but comparisons between the same element in various samples is possible as the shapes of the spectral curves are related to the unoccupied DOSS (Figure 20). Features due to such energy losses are commonly observed in electron scanning transmission microscopy and are also found in XPS spectra where they generally give rise to broad peaks corresponding to the high binding energies of the main lines, so-called plasmon peaks. In UPS spectra, both surface and volume plasmons can be detected easily. Investigation of such plasmon features may provide information about the nature of the solid, in particular about the freeelectron-like character and number of oscillating electrons (Osterwalder et al., 1990).
An electron beam which penetrates a solid loses energy due to its interaction with the strong fields of the atoms. As a result, photons are emitted continuously up to a limit which corresponds to the very energy of the incident electron beam. This is the so-called Bremsstrahlung radiation (from the German word for braking radiation) which carries information on the solid itself. Its detection is therefore of high interest and gives rise to the Bremsstrahlung spectroscopies. There are two principal ways to detect the Bremsstrahlung radiation, as schematized in Figures 21a and b. In all cases, the incident electron is high in the continuum and is thus considered as a free electron. In
I
a
e-varies
b
Figure 21 Principle of Bremsstrahlung spectroscopy a: in the spectral mode and b: in the isochromate mode
Spectroscopic Approaches
process a, incoming electrons of constant energy are dumped into the unoccupied states and the photons emitted are scanned according to their energy. Because of energy conservation, their variation depicts the variation of the empty states. This is the 'spectral' mode. In process b, the detection is performed at constant photon energy by varying the energy of the incident electron beam; here also, the incident electrons populate the initially empty band, and the description of the variation of empty states is made in the 'isochromate' mode. The latter process is also often denoted as 'inverse photoemission' (IPES); hence, the spectral mode is generally labelled inappropriately as Bremsstrahlung isochromate spectroscopy (BIS). In any case, whatever the detection procedure is, these BIS andlor IPES spectroscopies describe the totality of the empty states and do not provide chemical selectivity. However, comparison with total DOS calculations is meaningful. In addition, Bremsstrahlung spectroscopies are surface-sensitive, since the mean-free-path of the electrons governs the depth sampled. Many studies have been dedicated to analysis of the role of transition matrix
149
elements and intensity distributions as well as manybody effects (Speier et al., 1985; Hoekstra et al., 1986; Sobczack and Auleytner, 1988; Speir et al., 1988). Experimental investigations have been carried out so far mainly at synchrotron facilities but also using home-made equipments. Two examples are shown, Figure 22 (Czyzyk et al., 1992) and Figure 23 (Qgawa et al., 3 993). In the latter, final-state effects due to Ce 4 . configurations can be recognized. r
.*r. P
-*
*.it
1
Figure 22 Bremsstrahlung isochromate spectrum of MoNi,. The upper curve is the raw experimental data, the dotted curve below is the experimental curve with the inelastic contribution to the background subtracted. The lowest solid curve is the calculated DOS. Peaks labelled A, C, D, E and features F, G, H correspond to both MOand Ni d states, M O and Ni p , Ni s, Ni p and to MO s states and MO and Ni p states, respectively
0
.
1
2
.
I -
1
4
.
1
.
1
.
6
I
ENERGY ABOVE EF {sv) Figure 23 Bremsstrahlung isochromate spectra of Ce(Pd,,Cu,.),. Multiplet structure arising from Ce f I and f configurations is observable whatever x . The second peak above EF IS due to both Ce and Pd X states
150
Bonding and Stability
1
-8
-6
-4
-2
0
2
4
Energy relative to E, (eV) c Figure 24 Principle of Bremsstrahluiig spectroscopy in the constant initial state inode
Another type of spectroscopy that involves Bremsstrahlung radiation is the constant initial state spectroscopy (CIS), in which the initial state is the one electron in the conduction fundamental state iband, and the final state is a core-level hole two electrons in the conduction band, as shown in Figure 24. Therefore, the observed spectra result from the autoconvolution of the empty DOS. In contrast to BIS, CIS can involve a deep inner level and so can be bulk-sensitive.
+
4. Conclusion
The various spectroscopic techniques introduced in this paper are only a few among those that can investigate DOSs of intermetallics. They have been chosen because they are straightforward. thus giving direct insight into the DOS, although not providing absolute DOS values. They are all complementary, each one revealing a special aspect of DOS. As far as occupied states are concerned, PES gives a total view of OB states modulated by cross-sections, but it is surface-sensitive and charging effects may occur for insulators and semiconductors. On the other hand, XES can investigate all partial local occupied electronic distributions in a solid whatever they may be, but XES is mainly related to the bulk (Figure 14). If one is interested in empty states descriptions, XAS and EELS provide partial local electronic distributions that may
Figure 25 Occupied and unoccupied densities of states in Y(Co,_&l,), investigatedwth X P S (left side of the figure) and BIS (right side of the figure), respectively. for different x concentrations. The vertical line at the origin is set at the Fermi level. and the curves are each normalized to the total area
be either bulk or surface-sensitive, whereas BIS techniques refer to total empty DOSs and are more likely applicable to the study of the surface. Note that as XAS is both site- and symmetry-selective, the combination of BIS and XAS techniques may give insight, for instance, into the role of the core-hole effects due to strongly correlated empty levels or to levels close to the Fermi level. It is also possible to combine PES and BIS techniques using the same instrument, therefore within the same accuracy, and have a view of total occupied and empty DOSs (Figwe 25) (Son et al., 1999). Similarly, in the same spectrometer, under the same experimental conditions, and hence with the same broadening, it is possible to analyse selected partial local occupied and empty DOSs that involve the same inner level from both XES and XAS measurements, provided films of suitable thickness are available for the photoabsorption experiments or the yield technique is used (Figure 18). All parameters that influence DOS, such as changes due to modifications in atomic structure or chemical environmentscan be investigated and characterized with all these spectroscopic techniques. Note that other spectroscopic techniques, not presented here, may also be complementary to one or more of the techniques described above. For instance, Nh4R or MBssbauer spectroscopies can be related to PES or XES measurements as they both give some view of the participation of states at EF. See, for
Spectroscopic Approaches
example, a recent study of the electronic structure of ion-beamprepared A31-,Fe, samples which combined Rutherford back-scattering, conversion electron Mossbauer and X-ray emission spectroscopies from which the metallic character of the compounds was ascertained (Traverse et al., 1996).
5. References Aebi, P., Kreutz, T. J., Ostenvalder, J., Fasel, R., Schwaller, P., and Sclilapbach, L. (1996). Phys. Rev. Lett., 76, 1150. Aganval, B. K. (1979). X-Ray Spectrosropy (Optical Series, S987, Springer Verlag, Berlin). Barr, T. L. (1993). Modem ESCA. The Prinnples and Practice of X-Ray Photoelectron Spectroscopy(CRC Press, Boca Raton). Belin, E., Gupta, M., Zoiliker, P., and Yvon, K. (1987). J. of Less Comm. Metats. 130, 267. Belin, E., Dmkhazi, Z., Sadoc, A., Calvayrac, Y., Klein, T., and Dubois, J. M. (1992). J. of P h y x Cond. Matter, 4,4459. Belin, E., Dankhazi, Z., Sadoc, A., and Dubois, J. M. (1994). J. of Phys.: Cond, Matter, 6. 8771. Belin-FerrB, E., Dankhazi, Z., Sadoc, A., Berger, C., Muller, H., and Kirchmayr, A. (1996). J. of Php.. Cond, Matter, 8, 3513.
Belin-Fed, E., and Dubois, J. M. (1996). .J. ofPhyS.. Cond. Matter, 8, L-717. Berger, C., Belin, E., and Mayou. D. (1993). Annales de Chimie, Fr., 18, 485. Bonnelle, C . (1987). Annual Report C, R. Soc. Chemistry of London, 201. Brown. D., Crapper, M. D., Bedwell, K. H., Butterfield M. T., Guilfoyle, S. J., Malins, A. E. R.. and Petty, M. (1997)., J. of Phys.: Cond. Matter, 9,9435. Brundle, C., R., and Baker, A. D. (1978). Electron Spectroscopy. Theory, Techniques and Applications (Academic Press, London). Cardona, M., and Ley, L. (1978 and 1979). “Photoemissionin Solids” in Topics tn Applied Physrcs, 26 and 27 (Spnnger Verlag, Berlin). Castro, G. R., Alvarez, J., Davila, M. E., Asencio, M. C., and Michel E. G. (1997). J. gf Phys.: Cond. Matter, 9, 1871, Czyzyk, M. T., Lawmczak-Jablonska. K., and Mobilio, S. (1992). Phys. Rev. B, 45, 1581. Fargues. D., Vergand, F., and Bonnelle, C. (1985). Surface Science, 163, 489. Galakov, V. R., Kunnaev, E. Z., Cherkaslicnko, V. M., Yarmoshenko, Yu. M., Shamin, S . N., Postikov, A. V., Uhlenbrock, St., Neumann, M., Lu, Z. W., Klein, B. M., and Shi Zhu-Pei (1995). J. ofPhys.. Cond. Matter, 7,5529. Hoekstra, H. J. W.M., Sperer, W., ZelIer, R., and Fuggle. J. C. (1986). Phys. Rev. B, 34,5177 Hiifner, S. (1995). PhotoeZectron Spectroscopy. Second Edition (Springer Verlag, Berlin). Krause, M. O., and Oliver, J. H. (1979). J Phys. Chern. Re5 Data, 8, 329.
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Mattheiss, L. F., and Hammann. D. R. (1993). Phys. Rev. 3. 47, 13114.
Mon, M., Matsuo, S., Ishmasa, T., Matsuura, T., Kamiyd, K., Inokuchi, H., and Matsukawa, T. (1991). J. ofPhys.. Cond. Matter, 3, 767. Nakamura, Y., and Mizutant, U. (1994). Mater. Scz. and Eng., A181-182, 790. Ogawa, S., Suga, S., Bocquet, A. E., Iga, F., Kasaya, M., Kasnya, T., and Fujimori, A. (1993). J. of Phys. Soc. of Japan, 62, 3575. Ostenvalder, J., Greber, T., Hiifner, S.. and Schlapbach, L. (1990). Phys. Rev. Lett.. 64,2883. Papaconstantopoulos, D. A. (1997). Private communication. Pilo, Th., Hayoz, J., Berger, H., Gnom, M.. Schlapbach, L., and Aebi, P. (1999a). Phys. Rev. k i t . , 83, 3494. Pilo, Th., Hayoz, J.. Aebi, P., and Schlapbach, L. (1999b). Physica B, 259-261, 1118. Sadoc, A., Belin. E., Dankhazl, Z., and Flank, A.-M. (1993). J. of Non-Cr”vst.Sal, 153 & 154, 338. Siegbahn, K., Nordling, C., Fahlman, A., Nordberg, R., Hamrin, K., Hedman, J., Johansson, G., Bergmark, T., Karlsson, S. E., Lindgren, I., and Lmdberg, B. (1967). Nova Acta Regiae Soc Sci. Ups, 4, 20. Siegbahn, K.. Nordling, C., Johansson. G., Nordberg, R,, Hedman, J., Hedh, P-F., Hamrm, K., Gblius, U., Bergmark, T., Werne, L. O., Manne. R., and Baer, Y. (1969). ESCA. Applied to Free Molerules (North Holland, Amsterdam). Sobczak, E., and Auleytner, J. (1988). Phys. Rev. B, 39.6251. Son, J.-Y., Konoshi, T., Mizokawa, T., Fujimorr, A.. Koui, K., and Goto, T. (1999). Phys. Rev. B, 60. 538. Sonder, A. (1990). Thbe de I‘tTniversitt5 Paris Vi, Paris, unpublished. Speier, W., Fuggle, J. C., Dwham, P., Zeller, R.$ BIake, R. J., and Sterne. P. (1988). J. Ph-vs. C. 21, 2621. Speier. W.. Zeller, R., and Fuggle, J. C. (1985). Phys. Rev. B. 32,3597
Stuck, A., Osterwalder, J., Greber, T., Hiifner, S., and Schlapbach. L. (1990). Phys. Rev. Letr., 65, 3029. S~asz,A., and Kojnok, J. (1985). Applied Surface Science, 24, 34,
Terauchi, M., Tanaka. M., Teal, A. P., Inoue, A., and Masumoto, T. (1996). Phil. Mag. Let., 74. 107 Terakura, K. (1977). J Phys F, 7, 1773. Tohyama, T., Ohta, Y ., and Shimizu, M. (1989). J of Phys.: Cond. Matter, 1, 1789. Trambly & Lassardi&re,G.. Dankhan, Z., Belin, E., Sadoc, A., Nguyen Manh, D., Mayou, D., Papaconstantopoulos, D. A., and Keegan, M. (1995). Phys. Rev. B, 51,4035. Traverse, A., Belin-FerrB, E., Dankhan, Z., Mendoza-ZBlis. L., Laborde. O., and Portier, R. (1996). J. of Phys.. Cond. Matter, 8, 3843. Yeh, J. J. (1993). Atonair Calculation of Photoionisation CrossSections and Asymmetry Parameters (Gordon and Breacli, New York). Yeh, J. J., and Lindau, 1. (1985). Al. Data Nucl. Data Tables, 32, 1.
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Chapter 8 Effects of Pressure on Stability and Properties Y. V. Levinsky Moscow Institute for Fine Chemical Technology, Moscow, Russia
During recent decades studies of effects of pressure on solids have been undertaken with exponential proliferation. There are at least four reasons promoting the specific interest. First of all, new high-vacuum or highpressure technologies have been developed; secondly, there is the opportunity for new materials with promising physical, chemical and mechanical properties; thirdly, investigations of processes under high pressure make a valuable contribution to further understanding of the quantum mechanical nature of the interactions in solid materials; and the last reason is a persistent improvement of experimental techniques in high vacuum and in particular under high pressure. Special attention is given to solid materials under pressures above 108 Pa. Surveying the thousands of entries in this area, the subject of intermetallic compounds has been given particular attention. Intermetallic studies, as a part of all inorganic investigations (pure elements, simple and complex oxides, halides, chalcogenides, phosphides, hydrides, borides, nitrides, carbides, etc.), have been increasing constantly. Thus, until 1990 the number of published intermetallic entries was about 2% (Tonkov, 1992) of all highpressure publications, whereas nowadays it has increased to 10-15%. And the reason is not a limit of simple substances to study but the constant discovery of new high-pressure phenomena in intermetallic compounds. Several aspects of the effects of high pressure on intermetallic compounds can be pointed out: Q
A thermodynamic one, i.e. phase transitions, shifts in phase-equilibrium compositions, different types of graphical representation of phase equilibrium.
Q
A kinetic one that focuses on the rate of transition to equilibrium, the stability of high-pressure phases and their decomposition under standard conditions. A structural one related to the mechanism of deformation of the lattice and the transformation of one crystal structure to another. A physical one that helps understanding of the quantum mechanical nature of intermetallic bonds, metal-superconductor transition, semiconductormetal transition, etc., changes of electrical, magnetic, optical, elastic and other properties. An applied one that outlines prospects for highpressure intermetallic phases useful in industry and technology; application of the obtained results in geology, astronomy, physics of the Earth; etc.
Thermodynamically it is convenient to examine a pressure/intermetallic (composition, structure) correlation, by analyzing an equation o f state that is of the general form: Q i d ~ l =0
(1)
where Q is the extensive parameter and pi the intensive parameter. If all the intensive parameters but temperature, chemical potentials and pressure are constant or their variations can be neglected, equation (1) yields SdT - Vdp -t
n,dpc,= 0
(2)
where S is the entropy, T, the temperature; V, the volume; p, the pressure; n, and p,, the mole fraction and chemical potential of the i-component. Thus, the analysis of the pressure effect on phase transitions and
Intermetallic Compounds: Vol. 3, Princ+les and Practice. Edited by J. H. Westbrook and R. L. Fleischer. 02002 John Wiley & Sons, Ltd.
154
Bonding and StahiZity
equilibrium compositions comes to a comparison of thermal (SdT), mechanical (Vdp) and chemical (Xn,dp.,) energy contributions in the total energy balance of the system. Experimental methods allow examination of equilibria in systems over a wide pressure range (from 10-* to 10l2 Pa) that by convention can be divided into high- and low-pressure intervals. Low pressure is that commensurable with the partial pressure of one of the elements of the intermetallic compound, whereas high pressure can be defined as the pressure under which the dT/dp value for the first type of phase transition can be found in experiments.The condition assumed above has a conditional character because, for different intermetallic compounds, boundaries between the assigned areas vary greatly. At low pressure it’s practically impossible to imagine an experiment where the equilibrium gas pressure above the intermetallic compound would be higher than the external one. Practically, for all observed intermetallics, the partial pressure of the most volatile component above the intermetallic compound is the main contribution to the total cquilibrlum pressure (ptotl), i.e. it can be assumed that pi =ptoti. Since = - RT lnp, the external pressure variations result in changing both the mechanical (ptotldv)and chemical (bqdni) energy components in the total energy balance. Calculationsshow that under low pressures the value of the mechanical component of the free energy can be disregarded, Thus the effect of external pressure on equilibrium will be observed only through the changing activity of the more volatile component of the intermetallic compound. The effect of external pressure is equivalent to changing the activity of tbe volatile component. The case can be simulated in the q u a s i ~ e q u i l i b r i ~ scheme when inert gases, non-reactive with the intermetallic compound, are introduced into the system. These conditions can be realized, for example, using a mixture of inert gases with a very low partial pressure of the volatile component of the intermetallic compound or by making use of a gas mixture that contains a small amount of the vapour of the element which is a component of the equilibrium of condensed phases (for example, oxygen in the mixtures Hz/H20, CO/C02; sulphur in the mixtures H2/H2SI etc.) or in isopiestic and electrolytic schemes. The examples stated above permit observation of intermetallic compounds under pressures much lower than those that can be produced by rarefaction of gas. Thus composition and properties of some chalcogenides have been examined under conditions that
simulate a pressure of IO-” Pa. Gas rarefaction of this magnitude has not been produced in experiments and on the whole makes no physical sense. The effect of high pressure on the equilibrium of condensed phases in intermetallic systems becomes perceptible typically at pressures above 108 Pa (Tonkov, 1992). In experiments the effect of pressure on equilibrium has been investigated at static pressures up to 5 x 10” Pa (Sung, 1997; Jayirnian, 1986; Hemley and Mao, 1997), whereas under dynamic conditions up to 10” Pa (Altshuler et al., 1999; Neinz and Yealoz, 1984; Kanel et al., 1996). Despite there being a wide range of pressures under which phase equilibria in binary and multicomponent systems have been observed, the principles of their graphical plotting are the same. It has been shown (Pelton and Schrnalzried, 1973; Pelton and Tliompson, 1975) that a graphical representation of equilibrium in a two-coordinate system coinpleteiy depends on whether intensive (qi)or extensive (Q,) parameters are the fixed parameters. Substitution of one parameter for another within the same group does not affect the pattern of the phase diagram. - Q2/& Since only three combinations q1- q2. 9% and Q1/&3 - Q2/Q3 (where Q d Q 3 and Q2/Q3 are the specific extensive properties conjugate to the intensive parameters (qland q2)are possible), there are three basic types of two-coordinate representation of phase diagrams. Figure 1 illustrates their salient features and conjugation. On the diagram of the first type (Figure la) the intensive properties ql and q2 are plotted along the axes, the value 40, is determined by the values of ql and q2, and the other (i- 3) intensive parameters must have constant values. For a binary system the constant value must belong to an intensive property. In Figure lathe two-phase equilibrium a 8 exists along a curve (line), whereas the three-phase equilibrium a + 8 y i s represented by a triple point. The second type of phase diagram is represented by Figure l b and Figure lc. At constant q4,qs . . ., the parameters q 1 and cp2 are plotted along the ordinate and the ratios Qz/Q3 and Ql/Qs are plotted along the abscissae, respectively. Each line representing a twophase equilibrium in Figure l a corresponds to a gap on the phase boundary outlining fields of two-phase equilibrium in Figure l b and Figure lc, and this is the fundamental difference in the topology of diagrams of the first and second types. Figure Id represents the third type of phase diagram with the coordinates Q I / Q ~and QZ/@. Each triple point in the diagram of the first type corresponds to a
+
+
Efects of Pressure on Stability and Properties
6-
w 4 7
-
Figure 1 Fundamental types of phase diagram representation (Pelton and Schmalmed, 1973; Pelton and Thompson, 1975)
triangle in the diagram of third type representing equilibrium of the three phases with constant extensive parameters; the latter are defined by the triangle angles. All the above-mentioned features of the three types of phase diagrams pertain equally to unary, binary, ternary and n-component systems as well as to the unlimited number of meaningful types of energy and, consequently, the same number of intensive parameters. If we examne the effect of pressure on equilibrium in systems with intermetallic compounds (with no external variable field of force), the intensive parameters are commonly the temperature, chemical potential and pressure. So three-dimensional, not two-dimensional, diagrams represent equilibrium in a binary system. Pelton and Thompson (1975) found that temperature, pressure and composition are the most convenient coordinates (i.e. P-T-X phase diagrams). Isobaric and isothermal cross-sections of
155
these diagrams belong to phase diagrams of the second type. Three-dimensional P-T-X phase diagrams of systems with intermetallic compounds are not common because of their rather complex representation. P-T diagrams, being projections of the three-phase equilibrium curves (lines) of the P-T-X diagrams on the P-T plane, are the most common and convenient representations, although they do not contain the compositions of the equilibrium phases. Extensive information on P-T diagrams, their construction methods and usage can be found in monographs by Vogel, 1959; Rhines, 1956; and Levinsky, 1990, 1997. Crucial points in these diagrams are coordinates of points of non-variant four-phase equilibria. The parameters of four-phase equilibria and phase compositions for those binary systems with intermetallic compounds that have been examined in detail are listed in Table 1* (Levinsky, 1997). It follows from Table 1 that thermodynamic characteristics of equilibrium transitions with intermetallic compounds have been investigated in more detail under low pressures than high ones. Cd-Sb (Aptecar et al., 1977) and Zn-Sb (Ponyatovsky and Belash, 1977) are examples of systems studied at high pressure. We will examine the effect of pressure. within the limits of 10-2-1010 Pa on the graphical representation of equilibria in the Cd-Sb system. Figures 2a-c give the isobaric cross-sections of the P-T-X Cd-Sb phase diagram (Aptecar et al., 1977) constructed on the basis of the experimentally obtained results. These results, as well as the data of pressure and equilibrium vapour content under low pressure (Borg, 1961), permitted construction of the P-T phase diagram of the system (Figure 3) (Levinsky, 1997). One can easily show that diagrams Figures 2a-c and 3 are not in contradiction and that the diagram of Figure 3 allows us to construct the isobaric and isothermal cross-sections with CdSb intermetallic compound (diagrams of the second type) within the limits of 10-2-1010 Pa and 200-700 "C correspondingly. Monographs (Levinsky, 1982, 1990, and 1997) report methods of graphical representation of this type of section for the Cd-Sb system and others.
*References to the orignal equilibnum studies are given in Levinsky, 1997. It is recognized that the phases shown in the table as taking part at equilibrium under the stated conditions of T and P, according to the referenced literature, are not always consistent with the accepted phases under standard '7 and P conditions as shown in the phase diagram literature. These are issues that must eventually be resolved.
156
Bonding and Stability
Table 1 The parameters of non-vanant four-phase equilibrium in binary systems with intermetallic compounds (Levinsky, 1997)
System 1
AI-Bd AI-Ba Al-Ba AI-Ba AI-Mg AI-Mg AI-Mg AI-Mg AI-Mg AS-CO AS-CO AS-CO AS-CO As-Cd As-Cd As-Cd As-Cd As-Cd As-Cd As-Cd ASK AS-K AS-K
AS-K AS-K AS-Pd As-Pd As-Pd As-Si As-% As-Si As-Zn As-Zn As-Zn As-Zn Au-Zn Au-Zn Au-Zn Au-Zn Au-Zn AU-ZII Au-Zn Ca-Hg Ca-Hg Ca-Hg Ca-Hg Ca-Hg Ca-Hg Ca-Hg Ca-Mg Ca-Mg Ca-Mg Ca-Pb Ca-Pb Ca-Pb Ca-Pb
Temperature (“C)
Phases, taking part at equilibrium (composition in parentheses in atomic %; L=liqmd, G=gas)
2
538 730 750 914 320 370 450 450 437 918 923 958 1014 465 465 595 595 610 62 1 620 386 386 530 584 53 1 780 610 728 797 977 1097 651 65 1 750 723 403 683 438 490 520 585 654 84 486 513 530 587 660 N39 517 445 370 638 968 1127 750
4 1 15 4 3x 10-2 5x10-‘ 0.9 -1 1.2 -0.3 -2 20 103 9x 1 . 3 ~104 1.2~104 1.7~10~ 5x104 1.3~10~ ~ x I O - ~ 3x 1 103 (?) 3x (?)
2X1O6 7.5 2 3x106 3x106 4x105 104 103 9x103 103 10 30 102 1.2~103 4 x 102 4.5x 102 1 7 x 10-* 16 6 2 20 4 0 - 3
1 0.2~5 3~10-~ 8x10-3 40 2 x 102 40
Ba, A1,Ba4, L, G Al,Ba4, AI5Ba3,L, G AI,Ba,, Al,,Ba,, L, G Al,,Ba,, Al,Ba, L, G P(38 Mg), ~(50 Mg), R (42 Mg), G P(38 Mg), $55 Mg), R (42 Mg), G a (18 Mg), P(38 Mg), L, G P(38 Mg), $45 Mg), L, G ~ ( 6 0Mg), 490 Mg), L, G CO, Co,As,, L, G Co,As,, Co,As, L, G Co3As,, Co,As, L, G CoAs, Co3As,, L, G d-Cd3AS2,d-Cd,As,, L, G d-Cd3As2, d-Cd,As,, CdAss, G P-Cd,As,, dr-Cd3AS2,CdAs,, G aN-Cd3As,, ,B-Cd3AS2,L, G P-Cd3AS2,CdAs,, L, G CdAs,, L, G CdAs,, As, L, G a-KAs,, P-KAs,, KAs, G a-KA%,,P-KAs,, P - K ~ A s G ~~, KAs, P-KAs, L, G K,As4, KAs, L, G K3As, K3As,, L, G As, As,Pd, L, G As,Pd, AsPd,, L, G AsPd,, A%Pd,, L, G As, SiAs,, L, G SiAs,, SiAs, L, G SiAs,, Si, L, G cu-Zn,As,, D-Zn,As,, L, G a-Zn,As,, P-Zn,As,, ZnAs,, G P-Zn,As,, ZnAs, L, G ZnAs,, As. L, G a(30 Zn), o1(28 Zn), ,B (37 Zn), G a( 42 Zn), P (28 Zn), L (45 Zn), G Zn, ~ ( 8 9Zn), L, G ~ ( 8 5Zn), y3 (83,5 Zn), L, G y(76 Zn), y2 (75 Zn), -r3 (78 Zn), G ~ ( 6 2 3zn), y3 (78 Zn), L. G P (57 zn), r(62,5 Zn), L, G CaHg, Ca,,Hg,,, L, G Ca,Hg, Ca, L, G C%W, Ca,Hg, L, G Ca,Hg,, Ca3Hg, L, G CaHg,, CaPg,, L, G CaHg, Ca,Hg,, L, G Hg, CaHg, L, G Mg, CaMg, L, G y-Ca, CaMh. L, G B-Ca, y-Ca, L, G CaPb, CaPb,, L, G Ca,Pb3 CaPb, L, G Ca,Pb, Ca,Pb3, L, G Ca, Ca,Pb, L, G continued
Effects of Pressure on Stability and Properties
157
Table 1 continued System 1
Ca-Si Ca-Si Ca-Si Ca-Si Ca-Zn Ca-Zn Ca-Zn Ca-Zn Ca-Zn Ca-Zn Ca-Zn Ca-Zn Ca-Zn Cd-Mg Cd-Pd Cd-Pd Cd-Pd Cd-Pt Cd-Pt Cd-Pt Cd-Pt Cd-Pt Cd-Sb Cd-Sb Cd-Sb CO-Mg CO-Mg Co-Zn Co-Zn Co-Zn Co-Zn CO-Zn CO-Zn Co-Zn CO-Zn Co-Zn Cr-Si Cr-Si Cr-Si Cs-Sb Cs-Sb Cs-Sb Cs-Sb Cs-Sb Cs-Sb Cu-Mg Cu-Mg Cu-Mg Fe-Zn Fe-Zn Fe-Zn Fe-Zn Ge-Mg Ge-Mg Ge-U Ge-U
Temperature (“C) 2 1030 1040 792 1268 394 391 414 439 420 638 642 690 669 650 320 ~490 660 314 670 710 730 770 290 445 3 10 635 970 -419 566 675 690 746 895 924 925 966 1305 1413 1380 473 417 404 553 459 487 485 552 725 425 530 782 560 636 696 -93 1 1071
Pressure Pal 3
0.2 0.4 10, -102-103 9x1W3 9 x 10-, 3~10-~ 0.1 10 9x102 8X1O2 2.5~ 102 4xld 15 10 ~ 3 0 30 15 2x104 - 2 . 5 ~ 104 - 2 . 5 ~ 104 - 2 . 7 ~104 1 1o2 3 x 102 2x 102 20 - 7 ~ - 5 ~103 -5~10~ 1 . 4 104 ~ -8X 104 N105 Nl05
-1.5 x 105 -5~10-* -0.3 -0.1 -3.5x 10-2
-0.2 -0.7 - 2 . 5 ~103 N2X 102 N8X 102 10 10 30 10 2 x loz 104 2 x 102 N2X1o2 3 -10-4 5 x IO-‘
Phases, taking part at equilibrium (composition in parentheses in atomc %; L=liquid, G=gas) 4 CaSi,, Si, L, G CaSi, CaSi,, L, G O-Ca, Ca,Si, L. G Ca,Si, CaSi, L, G Ca,Zn, Ca, L, G Ca,Zn,, Ca,Zn, L, G CaZn, Ca,Zn,, L, G CaZn, C a n , , L, G Zn, CaZn,,, L, G Ca,Zn,, CaZn,, L, G Ca,Zn,, CaZn,, L, G CaZn,, CaZn,,, L. G CaZn,,, CaZn,,, L, G 4 2 8 Mg), ,436 Mg),L, G Cd, $19 Pd), L, G ~ ( 1 7Pd), Y,(23 Pd), L, G P 4 4 Pd), 71 (20 Pd), L, G y(87 Cd), Cd, L, G 71 (76 Cd), ~ ( 8 Cd), 5 L, G y,(74 Cd), y2 (73 Cd), L. G F(69 Cd), 7 2 (73 Cd), L, G PI (51 Cd), E (65 Cd), L, G CdSb, Cd, L, G CdSb, Sb, L, G Cd, Sb, CdSb, L Mg, MgCo,, L, G MgCo,, CO, L, G Zn, y2 (92.8 Zn), L, G y2 (92 zn), y,(88.6 Zn), L, G yL(88 Zn), 6(89 Zn), L, G ~ ~ ( 8 7 Zn), . 4 6(88 Zn), $85.4 Zn), G 4 8 9 Zn), y(85 Zn), L, G PI (56.5 Zn), 1175.2 Zn), L, G Pi (50 Zn), PO0 Zn), L, G p,(47.9 Zn), p(49 Zn), a(36 Zn), G m(36 Zn), ,449 Zn), L, G Si, CrSi,, L, G CrSi, Cr,Si3, L, G CrSi,, CrSi, L, G Cs,Sb,, Cs, L, G CsSb,, Cs,Sb,, L, G CsSb, CsSb,, L, G Cs,Sb4, CsSb, L, G Cs2Sb. Cs,Sb,, L, G Cs,Sb, Cs,Sb, L, G Mg, CuMg, L, G Cu2Mg, CuMg, L, G Cu,Cy,Mg, L, G E (93 Zn), Zn, L, G 6 (96 Zn), E (93 Zn), L, G a(41 Zn), r(70 Zn), L, G r(75 Zn), 486 Zn), L, G Mg,Ge, Mg, L, G Mg,Ge. Ge. L, G Ge, UGe,, L, G U,Ge,, y-U, L, G continued
Bonding and Stability
15% Table 1 continued System 1
Temperature (“C) 2
Pressure @a) 3
Hg-Mg Hg-Mg Hg-Mg Hg-Mg Hg-Mg Hg-Mg Hg-Ni Hg-Pd Hg-Ti Hg-Ti Hg-U Hg-U Hg-U Hg-U Hg-U In-Sb K-Sb K-Sb K-Sb K-Sb K-Sb Mg-Ni Mg-Ni Mg-Ni Mg-Si Mg-Si Mn-Si Mn-Si Mn-Si Mn-Si Mn-Si Mn-Si Mn-Si Mn-Si Na-Sb Na-Sb Na-Sb Nb-Sn Ni-Zn Ni-Zn Ni-Zn Ni-Zn Ni-Zn Ni-Zn Pd-Zn Pd-Zn Pd-Zn Pd-Zn Pd-Zn Rb-Sb Rb-Sb Rb-Sb Rb-Sb Rb-Sb Rb-Sb Sb-Zn
170 558 560 519 508 453 232 238 300 300 455 669 725 773 735 492 -63 407 397 460 507 506 760 1097 637 950 1150 1155 1234 1070 1040 1060 1205 1155 -97 -435 400 2130 418.5 490 675 810 875 1040 425 565 780 845 530 37 398 418 456 515 439 400
- 3 ~102 - 3 ~10’
-
Phases, taking part at equilibrium (composition in parentheses in atomic %; L=liqmd, G=gas) 4
- 2 . 5 ~103 - 1 . 5 ~10, -6 6x 103 104 3x104 1.2~104 10’ - 5 ~ 2x 106 - 4 ~106 -107
0.1 -1.1 - 7 ~10-4 -8X w4 5 -10 16 1.3~10~
-103 1.5~10~ 0.12 0.5 2.5 3.5 2.5 4 60 30 -10-5
-1o-’ 3 x 10-4 20 80
-103 1.5~10~ 2.5~10~ -6104 -10 50 -103 (?) 4 0 3 (?) 30 w10-4 3~10-~ 4x10-3 -10-2 -10 50 - 7 ~109
-
InSb; Sb, L,-G K3Sb,K, L, G KSb,, Sb, L, G KSb,, KSb, L, G K,Sb, K,Sb4, L, G K5Sb4,KSb, L, G Mg, Mg,Ni, L, G Mg2Ni, MgNi,, L, G MgNi,, Ni, L, G Mg,Si. Mg, L, G Mg,Si, Si, L, G MnSi, 75-n, Si, L, G MnSi, Mn, 75 .Si, L, G Mn,Si,, MnSi, L, G Mn3Si,Mn&, L, G Mn,Si,, Mn,Si, L, G p-Mn, Mn,Si,, L, G 6-Mn, y-Mn, L, G p-Mn, y-Mn, L, G Na,Sb. Na, L, G Na,Sb, NaSb, L, G NaSb, Sb, L, G Nb,Sn, Nb, L, G fi(89 Zn}, Zn, L, G y(85 Zn), 6(89 Zn), L, G p, (51.8 Zn), p(50 Zn), L, G a(32 Zn), @,(45.3 Zn), p(47.3 Zn), G p(58.3 Zn), y(74 Zn), L, G n(38 Zn), p(50 Zn), L, G $85 Zn), Zn, L, G Pd46 zn), P’ (58 zn), Y (76 Zn), G (63 Zn), y(76 Zn), G (65 Zn), $76 Zn), L, G PI (56 Zn), y (76 Zn), PdZn,, G Rb,Sb, Rb, L, G RbSb, RbSb,, L, G RbSb,, Rb,Sb,, L, G Rb,Sb, Rb, L, G Rb,Sb,, RbSb, L, G Rb,Sb,, Rb,Sb4, L, G ZnSb, Zn, Sb, L continued
Eflects of Pressirre on Stability and Properties
159
Table 1 continued System
Temperature ("C>
1
2
Sb-Zn Sb-Zn Sb-Zn Sh-Zn Sb-Zn Sb-Zn Si-IJ Si-U Si- U Si-U Si-U Sn-U sn-U Sn-U Th-Zn Th-Zn Th-Zn Th-Zn Th-Zn Y -Zn Y -Zn Y-Zn Y-Zn Y-Zll Y-Zn Y-Zn Y-Zn Y -Zn Y-zn Y-Zn
--
460 430 -510
-530 -510 -540 1320 1570 1575 1510 -1610 1350 1380 1136 -419 1041 946 1045 996 420 630 750 685 1015 870 880
905 895 860 870
Phases, taking part at equilibrium (co~positionin parentheses in atoinic %; L =liquid, G =gas)
Pressure (Pa)
4
3
-2X 109 -lOW -5 x 10' -2x 108 2 x lox -2X 1oS N
~
10-3 X
1.5~10 4x10 1.5 x 10-' -0.3 -1 -1 -2X 10-? -10 -103 7.5x 103 1.1x 1OS 1 . 6 105 ~ -20 - 2 . 5 ~102 -3 x 10, - 6 ~10, 2x 104 ~ 5 x 1 0 ~ -4~10~ -3~10~ -4x 104 - 6 ~104 2 x 10,
ZiiSb, @-Zn,Sb,, Zn, L P-Zn,Sb,, J-Zn,Sb,, Zn, L ZnSb, P-Zn,Sb,, y-Zn,Sb,, L P-Zn,Sb,, y-Zn,Sb,, <-Zn,Sb,. L y-Zn,Sb,, q-Zn,Sb,, 5-Zn,Sb,, ,O-Zn,Sb, y-Zn,Sb,, q-Zn,Sb,, C-Zn,Sb,, L IJ,Si, L, Si, G U,Si,, USi, L, G U,Si,, USi, L, G USi,, US&,L, G USi,, U,Si,, L, G Sn,U, Sn,U3, L, C Sn,U,, Sn,IJ,, L, G Sn21J3,y - u , L, G Th,Zn,7, Zn, L, G Th,Zn, Q-Zn, L, G ThZn,, Th,Zn, L, G ThZn,, ThZn,, L, G Th2ZnI7,ThZn,, L, G YZn,,, Zn, L, G a-YZn,, P-YZn,, YZn,, G a-YZn,, P-YZn,, YZn, G YZn,,,Y,Zn,,, L, G P-YZn,, YZn, L, G YZn,, Y,?ZnSR, L, G Y13Zn58, Y,Zn,,, L, G VZn,, p-YZn,, L, G Y3Znll,YZn,, L, G Y2Zii17,YZn,, L, G YZn, Y, L, G
The sections of a P-T-X-binary phase diagram at constant concentration do not belong to any of the three types of phase diagrams discussed above, and do not contain information on equilibrium phases for reasons similar to those for polythermal sections of three-component systems at constant pressure. It follows from this that the widespread representations of the first type of phase transitions of intermetallic compounds in pressure-temperature coordinates generally assume that cornposition is variable and P-T binary diagrams with intermetallic compounds are diagrams of the f k s t type (Figure la), but with the requirement that the chemical potential of one of elements of the intermetallic compound is a constant. This condition has not been met in experiments, at least those the author has been acquainted with (an experiment obeying these require~entsis unlikely to be proposed). Consequently, all the published P-T diagrams of phase transitions for binary (and nioreover for multicomponent) intermetallic compounds
cannot be regarded in principle as the equilibrium ones. This is likely to be the reason for the frequently observed differences in interpretation of experimental P-T diagrams of intermetallic compounds. The variation of composition of intermetallic compounds in phase transitioiis of the first type under constant, and in particular under variable, pressure has been noted many times (Levinsky, 1974; Degtyareva el al., 1983; Degtyareva and Ponyatovsky, 1987). But most investigations of high pressure on structure and properties of intermetallic compounds are carried out in physical laboratories; and, as a rule, the phase compositions before and after applied pressure are not defined with the required accuracy of at least 0.01 at.%. The kinetics of phase transitions in such cases are quite complex, for they depend on both temperature and pressure. The rate of approach to equilibrium at rather high homologous temperatures, T/T,n,lt > 0.70.8, is high and depends weakly on pressure. Usually, it
Bonding and ~tability
160 Sb, mass. % 600 S0Q 400
300 200
6uu
5u0
400
300
Sb,at. %
takes several minutes to obtain equilibrium and the rate depends on the heating unit in the high pressure apparatus. A di~usion~ e c ~ a n i sismlikely under static pressures, whereas for dynamic pressure applications the rate of phase change corresponds to an explosive wave velocity and the velocity of sound (Altshuler et anel et al., 1994). In the latter case, the rnartensitic mechanism of transition is more likely (Alt$~uleret al., 1999; Bacanov, 1984). It will be noted that the structure and composition of the high-pressure phases produced at the same temperature and pressure, either in static or in dynamic pressure
Fi Isobaric section of the Cd-Sb System (Aptecar et al., 1977) (a) curve 1 - 1 ~ 1 0 ~2 ;- 1 0 ~ 1 0 Pa; ~ 3 - 1 9 ~ 1 0Pa; ~ 42 7 ~ 1 0Pa; ~ 5 - 3 5 ~ 1 0 Pa; ~ 6 - 3 6 ~ 1 0 ~Pa; (b) p< 108 Pa; (c) p = 10 Pa
application, are practicdly the same (Altshuler et al., 1999; Bacanov, 1986). At relatively low homolo~ouste~p$ratures,achieving equilibrium may take several hours. A hysteresis of the direct and reverse tran~i~ions is found quite often under these conditions; as the t e m p ~ ~ a t increases, ~re the hysteresis becomes smaller and fiiially disappears (Tonkov, 1992; Chupenko and Degtyareva, 1984). ~uenchingkinetics are c o ~ p l i ~ a t efor d in~~rmetallic cornpouiids that are in e~uilibriumat high temperature and high pressure and are then transferred to room temperat~re and standard pressure, as are the
Eflects of Pressure on Stability and Properticy
t--ra:L,G \
;taa
305
400
$05
600
70#
T,"C ure 3 P-T phase diagram of the Cd-Sb system in the range 200 to 700 "C and 10-2 to 6x109 Pa (Levinsky, 1997)
transitions of quenched and metastable phases into the equilibrium state. Quenching parameters quite often depend on both the cooling rate and time of pressure as well as on how both processes are correlated. Most experiments report that the high-pressure phases are preserved in the standard state. Metastable phases as a rule are slow to transform and can exist at room temperature and even lower temperatures and at standard pressure for a long time; heating to several hundred degrees Centigrade is required to bring the inetastable phases to equilibrium (Tonkov, 1992). The effect of high pressure on the crystal structures of intermetallic compounds becomes apparent during elastic compression (reduction of the specific volume) and fornnation of phases with new lattices. Elastic compression of intermetallic compounds is performed at high pressure and is a basis for calculating elastic constants and related phenomena. Lattice structures of intermetallic compounds stable only at the high pressure are different from those under normal conditions. Nevertheless, existing experimental results show some general trends (Degtyareva and Ponyatovs~y~ 1987). The basic effect is that as the pressure rises so does the density of the intermetallic phase, i.e. the number of atoms in a unit volume of the intermetallic compou~dincreases. Higher pressures increase the probability of crystal structures with larger numbers of external electrons per atorn. Seiniconductor-type compounds are transformed to
161
metallic ones. The above-stated phenomena have been found for phase transitions under high pressure in the following systems InAs, GaAs, InP (Bao et al., 1995/96); CoGe, ReGe (Larchev and Popova, 1982); Ti3Al (Sahu et al., 1997); AuGe (6-phase), AgGe (5phase) (Fujinaga et al., 1991); GaSb ( 1996; Malyushitskaya, 1994; Ilina, (Matsumara et al., 1997); BaSi2 (Imai et al., 1997; Imai and Hirano, 1995; Imai et al., et al., 1998); AlSb, CdsAs:!; CrAsz; InAs; MnAs; FeMnAs; Z113A.s~; CeCuzSi2; CoGe; VFeSb; GaSb; R SnSb (Tonkov, 1992). An assumption has been made ( Ponyatovsky, 1987; Tissen et al., 19 prediction of high-pressure phases in a homologous series of intermetalli~compounds. Application of high pressure causes the same changes in phase compositjon as does substitution of one element of the intermetallic compound by another heavier member of the same group. For example, there are three intermetallic phases ZnSb, Zn4Sb3, and Zn3Sb2 in the Zn-Sb system at atmos~heric pressure. When pressure i s increased, the isobaric cross-sections become less complicated, and at 3 CPa only the compound ZnSb is observed in the T-X phase d i a g r a ~ . of diagram but with a heavier element Cd fCd-Sb system) is characterized by the same pattern at atmospheric pressure (Pon.yatovsky and Belash, 1977). The systems of Pb-Sb and analogous examples. Under standard pressure the isobaric cross-section. of Pb-Sb eutectic, whereas in the system intermediate ephase. A similar phase is found in the Pb-Sb system under pressure 3 GPa. is similarly followed in the In-Sb and (Degtyareva and Ponyatovsky, 1987; De 1998). As the pressure increases, new phases near the eutectic composition at standard pressure can be fou in the Ag-Ge (Degtyareva et al., 1996), Fe-Mo(Mordovetz and Rachek, 19951, and In-Sb (Miiiomura et al., 1994; Asaumi et al., 1975; 1976) systems, Amorphous alloys that are affected by pressure are often crystallized under different conditions from those at st an~ardpressure. ~rystallizatio~ of amorphous alloys under pressure has been seen in the systems Nb-Si (Malyushitskaya, 1994); Nb-Ge (Iwasaki et a 1984); Al-Ge (De~tyarevaet al., 1~96);Fe-Mo(Mordovetz and Rachek, 1995); and In-Sb (Minomum et al., 1974; Asaumi et al., 1975; and Asaumi et al., 1976).
Bonding and Stability
162
Most examiimtions of high-pressure on the properties of intermetallic compounds have two main objectives: 1) expanding the theoretical knowledge of the quantum mechanical nature of the interaction forces and the electron structures of intermetallic compounds; 2) searching for new phases with extraordinary physical or mechanical properties. The first objective is achieved mostly through direct measurements of the properties of specimens under pressure; for the second purpose, the properties are examined under standard conditions on quenched, metastable phases. Basic research methods for specimens under pressure are X-ray-diffraction studies, measuring magnetic properties and measuring electrical resistance. X-ray-diffraction measurements convey information for crystal structure definition and also the basic data for calculation of the elastic constants, density, and energetic characteristics. Knowledge of magnetic (or electrical) properties vs. temperature (or pressure) extends our knowledge about the nature of, and allows prediction of, such phenomena as superconductivity, Kondo effect and Hall effect, shifting Curie or NCel points, etc. Tonkov's handbook (1992) contains a detailed survey of results in this field €or the period up to 1990; more recent results include those of Movshovich et al. (1996), Tomas et al. (1996), Tang et al. (1996), Watako et al. (1996), Gavriliuk et al. (1996), Lord et al. (1996), Cornelius et al. (19971, Thomasson et al. (1998), Kojama et al. (1998), Kobajashi et al. (1998), Thessicu et al. (1998), Hauser et al. (1998), and Koyama et al. (1999). No intermetallic phase generated by application of high pressure has yet been found to exhibit properties of such interest for industrial applications as to be comparable to the impact of diamond and cubic boron nitride. But more extensive investigation of new phases at high pressure, improving the experimental techniques, and constructing industrial apparatus for superhigh pressure and high temperature (Sung, 1997) allow us to predict that interesting new phases will be unveiled in the years to come.
1. References Altshuler, L. E.,Trunin, R. F., Urlin, V. D., Forto, V E., and Funtikov, A. I. (1999). Uspechi Fiz. Nauk., 169(3), 323 (Russ.). Aptecar I. Z., Belash, I. T., and Ponyatovsky, E. G. (1977). High Temp.-High Pressures, 9, 641.
Asaumi K., Shmomura, O., and Minomura, S. (1975). Rev. Phys. Chem. Japan, Spec. Issue, p. 3 1 1 . Asaumi K., Shimomura, O., and Minomura, S. (1976). J . Phys. Soc. Japan, 41, 1630. Bacanov, S. S. (1986). Uspechi Khzm.. 55(4), 579 (Russ.). Bao, Z . , Anderson, Y . R., and Schmidt, V. H. (1995/1996). High Temp.-High Pressures. 27/28, 383. Borg, R.J. (1961). Trans. AZME, 221, 242. Brazhkin, V V., Lyapin, A. G., Khvostantsev, L. G., Sidorov, V. A., Tsiok, 0. B., Baylits, S . C., Sapelkin, A. V., and Clark, S. M. (1996). Phys. Rev., 54(3), 1808. Chupenko, G. V., and Degtyareva, V. F. (1984). Fiz. Tverd. Tela (Leningrad), 26(4), 1210 (Russ.). Cornelius, A. L., Gangopadhyay, A. K., Schilling, J. S., and Assmus, W. (1997). Phys. Rev. B: Condensed Matter, 55(21), 14109. Degtyareva, V. F., Belash, 1. T., Chipenko, G. V., Ponyatovsky, E. G., and Raschupkin, V. I. (1983). Fiz. Tverd. Tela (Leningrad), 25( lO), 2968 (Russ.). Deglyareva, V. F., Porsch, F., Ponyatovskii, E. G., and Holzapfel, W. B. (1996). Phys. Rev. B: Condens. Matter, 53(13), 8337. Degtyareva, V. F., Winzenick, M., and Holzapfel, W. B. (1998). Phys. Rev. B: Condens. Matter, 57(9), 4975. Degtyareva, V. F., and Ponyatovskii, E. G. (1987). In VZijanze Vysokich Davlenii na veshtesrvo, A. N. Piljankevich, Kiev, Izd. Naukov Dumka, p. 20 (Russ.). Fujinaga, Y., Kusaba, K., Syono, Y., Iwasaki, H., and Kikegawa. T. (1991). J. Less-Common Met., 170(2), 277. Gavriliuk, A. G., Stepanov, G. N., Sidorov, V. A., and Irkaev, S. M. (1996). J. Appl. Phys., 79(5), 2609. Hauser, R., Bauer, E., and Gratz, E. (1998). Phys. Rev. B, 57(5), 2904. H e m , D. L., and Yealoz, R. (1984). J. Appl. Phys., 49, 3776. Hemley, R. J., and Mao, H. K. (1997). Encycl. Appl. Phys., 18, 555. Ilinn, M. A. (1987). Fiz. Nizk. Temp., 13, 201 (Russ.) (Sov. J. Low-Temp. Phys.), 13, 111. Imai, M., and Hir'mo, T. (1995). J. Alloys & Comp., 224, 111. Imai, M., Hirata, K., and Hirano. T. (1995). Physica C., 245, 12. Imai, M., Hirano, T.. Kikegawa, T., and Schmonura, 0. (1997). Phys. Rev. B, 55(1), 132. Iwasaki, H., Okajima, M., Kondo, S., Wang, W. K., and Toyota, N. (1984). Mater. Res. Soc. Symp. Proc., 22, 6770. Jayarman, A. (1986). Rev. Scr. Instrum., 57, 1013. Kanel, G. I., Rasorenov, S. V., Utkin, A. V., and Fortov, V. E. (1996). The Blast-Wave Processes in a Condensed Substance. Moscow, Yanus-k (Russ.). Kobayash, T., Miyazu, T., Takeshita, N., Shimizu, K., Amaya, K., Kitaoka, Y., and Onuki, Y. (1998). J Phys. Soc. Japan, 67(3), 996. Koyama, K., Goto, T., Fujii, H., Takeshta, N., Non, N., Fukuda, H., and Janssen, Y (1998). J. Phys. Soc Japan, 67(6), 1879
Efects of Pressure on Stability and Properties Koyama, K., Goto. T., Takeshi, K., and Ryunosuke, N. (1999). J. Ph-ys. Soc. Japan. 68(5), 1693. Larcliev, V. I., and Popova, S. V. (1982). J. Less-Common Metals, 87, 53. Levinsky, Yu. V. (1974). Zh. Fiz. Khim., 118, 1818 (Russ.). Levinsky, Yu. V. (1982). P-T-X Phase Diagrams of Binary Systems. Moscow, Izd. Metallurgija (Russ.). Levinsky, Yu. V. (1990). P-T-X Phase Diagrams of Binary Metallic Systems. Moscow, Izd. Metallurgija. vol. 1, vol. 2 (Russ.). Levmsky, Yu. V . (1997). Pressure Dependent Phase Diagrams of Binary Alloys, ASM-MSI, New York, vol. 1, vol. 2. Lord, J. S., Riedi, P. C., Tomka, G. J., Kapusta, Cz., and Buschov, K. H. (1996). Phys. Rev. B. Condens. Matter, 53(1), 283. Malyushitskaja, Z. V. (1994). Neorganicheskze Materiali, 30, 1360 (Russ.) (Znorg. Mat., 1994, 30, 1267). Matsumara, T., Kosaka, T., Tang, J., Matsumoto, T., Takahaslu, H., Mori, N., and Suzulu, T. (1997). Phys. Rev. Left., 78(6), 1138. Minomura, S., Shimomura, O., and Sakai, N. (1974). In Tetrahedr. Bond. Amorph. Semicond. Int. Conf: Yorktown Heights, New York, p. 234. Mordovetz, N. M., and Rachek. A. P. (1995). Ukr. Fiz. Zh, 40(3-4), 254 (Ukrain) 8241. Movshovich, R., Lawrence, J. M., Hundley, M. F., Neumeier, J., Thompson, J. D., Lacerda, A., and Fick, Z. (1996). Phys. Rev. B: Condens. Matter, 53(9), 5465: 1996, 53(3), 8241. Pelton, A. D., and Schmalzried. H. (1973). Metall. Trans., 3, 1393.
163
Pelton. A. D., and Thompson. W. T. (1975). Phase Diagrams. Progress zn Solid State Chemi,stry, 10, 119. Ponyatovsky, E. G. and Belash, I. T. (1977). High Temp.-High Pressures, 9(6), 645. Rhines, F. N. (1956). Phase Diagrams in Metallurgy: Their Development and Application. McGraw Hill, New York. Sahu, P. Ch., Candro Shekar, N.V.. Mohammed Yonsuf, and Govinda Rajan, K. (1997). Phys. Rev. Letr., 78, 1054. Sung, Chien-Moin (1997). High Temp.-High Pressures. 29(3), 253. Tang, J., Matsushita, A., Kitazawa, H., and Matsumoto, T. (1996). Physica E, 217(1-2), 97. Thessicu, C., Kamishima, K., Goto, T., and Lapertot, G. (1998). J. Phys. Soc. Japan, 67(10), 3605. Thornasson, Y., Okayama, V., Sheikon, I., Bnson, J -P., and Braithwaite, D. (1998). Solid State Conimun., 106(9), 631; 637. Tissen, V. G., Degtyareva, V. F., Nefedova. M. V.. Ponyatovskii, E. G., and Holzapfel, W. B. (1998). J Phys.: Condens. Matter, 10, 7303. Tomas, F.. Ayache, C., Fomine, I. A., Thornasson, J., and Geibei, C. (1996) J. Phys: Condens. Matter. 8(4), L51. Tonkov, E. Yn. (1992). High Pressure Phase Transformations - A Handbook, vols 1-2, Gordon and Breach, Philadelphia. Vogel, R. (1959). The Heterogeneous Equzlibria. Geest und Poztig, Leipug. Watako, Y., Ishii, T., Oomi, G., Takahashi. H., Mon. N., Thompson, J. D., Shero. J. S., Madru, D., and Fisk. Z. (1996). J. Phys. Soc. Japan, 65(1), 27.
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Chapter Magnetic Phase J. M. Cadogan School of Physics, The University of New South Wales, Sydney, Australia
1. Introduction A magnetic phase diagram shows the type of magnetic structure or magnetic ordering of a material as a function of parameters such as temperature, magnetic field, composition, pressure, etc. Most people will be familiar with the basic magnetic structures formed by intermetallic compounds, e.g. ferromagnet, antiferromagnet and ferrimagnet, and the reader is referred to Chapters 19 (Roth) and 40 (Kouvel) in Volume 1 of this series for discussions of the basic interactions and magnetic structures found in intermetallics. The reader i s also referred to the excellent summary of magnetism, magnetic structures and magnetic interactions in the Solid State Physics Source Book (Parker, 1988) for descriptions and definitions of magnetic phenomena. Examples of magnetic phase diagrams begin with Figure I , which will be discussed later. Each structure discussed in this chapter will be identified at its first mention with its ‘Strukturbericht’ type (where available), Pearson structure symbol, space group and space group number (#), based on the 1983 International X-Ray Tables. At its most fundamental level, the magnetic structure adopted by a compound is the result of energy minimization, and in this chapter I will discuss the magnetic structures found in intermetallic compounds, with an emphasis on intermetallics formed between rare-earth (R) and transition-metal (T) elements, in particular R-Fe-based compounds. There are two reasons for this emphasis; (1) such compounds have been studied extensively over the past 15 years due to their application as permanent magnet materials, with the tetragonal compound NdzFe14B (tP68, P42/mnm, #136) forming the basis for the world‘s strongest
permanent magnets and (2) unusually complex magnetic structures can arise in R-T intermetallic compounds as a result of the interaction between the localized 4f electrons of the R atom and the itinerant, non-localized 3d electrons of the T atom. Intermetallic compounds find numerous applications besides as permanent magnets and the reader is referred to the chapter by Stadelmaier and Reinsch (Chapter 14, Volume 2) of this series for a discussion of the practical applications o f magnetic materials. We refer the reader to the review article on the RzFe14B series of compounds by Herbst (1991) for an excellent summary of these principal interactions and the treatments thereof. Fornasini et al. in another chapter of this work, extensively review various rare-earth structures. Before considering the fundamental interactions which determine the magnetic structure of a compound and the associated magnetic phase diagrams it is instructive to consider briefly how one determines the nidgnetic structure of a compound. This will be followed by a discussion of some of the fundamental interactions (exchange, crystal-field) responsible for determining the magnetic ordering mode. Finally, I will illustrate various types of magnetic phase diagram with examples from a number of different intermetallic structures, once again with an emphasis on R-Fe based compounds.
2. Determination of Magnetic Structure
2.1 Neutron Diflraction Without a doubt neutron diffraction has made an inestimable contribution to the determination of
Intermetallic Compounds: Vol. 3 , Principles and Practice. Edited by J. H. Westbrook and R.L.Fleischer. 02002 John Wiley & Sons, Ltd.
magnetic structures in intemetallic compounds and it remains the most powerful meaiis of determining the detailed magnetic structure of a compound. The neutron interacts with the atoms in an interinetallic compound in two ways: (i) the nuclear interaction which gives rise to the nuclear scattering, used to d ~ t e ~ m i nthe e crystal structure (cell type, lattice parameters, space group, atomic positions etc.) and (iij the magnetic interaction of the neutron’s dipole moment with any magnetic moments 011 the atoms iii the crystal. The scattering produces peaks in the diffraction pattern according to the well-known Bragg formula
and the crystal structure is deterinined by (i) noting the syste~aticabsences of certain reflections (hkl) in a diffraction pattern obtained at temperatures above the magnetic ordering temperature so that the magiietic scattering is absent and (ii) fitting the relative intensities of the observed reflections. For exaiiiple, a body-centred cubic structure gives rise to reflections iller iiidices obey the condition w the magnetic ordering temperature, ~ d d i t i omagnetic ~ ~ ~ scattering arises from atomic planes along which there is some component of the ~ t o m i cmagnetic moment. In other words, those crystallographic planes which are perpendicular to the atomic magnetic moment do not contribute to the magnetic s c ~ ~ ~ t ~ rthe i n gscattering : intensity varies as cos2a where rx is tlie angle between the atomic magnetic moment and the crystal plane. Thus, one may often deduce intuitively the magnetic ordering direction of a crystal from a consideration of the presence or absence of any nzagnetic contribution to the nuclear scattered peaks in the ~nagneticallyordered temperature range. hirane (1959), the ability of neutron diffraction to determiiie the magnetic orderiizg direc, however, if one is studying tation arises from the supersition of non-identical reflections having the same one must consider scattering from a family of planes, each of which has the same interpla~arspacing and hence angle. The consequence of this av~ragingprocess is that one cannot determine the magnetic ordering direction at all for powder saniples of cubic crystals. For uniaxial crystals (tetragonal, hexagonal, rhombohedral) one can only determine the angle ( U ) between the magnetic moment and the unique (‘c’j axis; the azimuthal orientation (4) is indeterminate. For lower symmetry, e.g. orthorlioinbic, one may deterin~neboth 8 and #.
The first magnetic neutron diffraction pattern was obtained by Shull aiid mart (1949) from Pace-centred cubic MiiO (B1, cF8, F m h , fit225) and is shown in Figure 1. Below the magnetic ordering temperature of 122 K, extra peaks appeared in the pattern which could not be explained by the face-centred cubic crystal cell. In fact, the extra peaks corresponded to half-integer Miller indices and the ma gnetic structure was explained in terms of a magnetic unit cell which is obtained from the crystallographic cell by doubling the crystallographic cell along the three orthogonal directions a, b, c. This doubling of the crystal periodicity implies an antiferroniagnetic arrangement of neighbouring spins since a ferrornagnetic arrangement of moments would have identical magnetic and crystal cells and hence integer Miller indices. More exotic magnetic structure$ such as spirals, i n c ~ ~ m e n s u r a t e with the crystal lattice, give rise to peaks which may be indexed with Miller indices which are neither integer nor half-integer. An excellent accoirnt of the use of neutron diffraction to determine magnetic structures is that by
ossbauer spectroscopy is a local technique in the sense of providing a ineasurement of the local atomic magiietic moment, indirectly via the hyperfine field. Thus, one may estimate an atomic magnetic moment even in an antiferroinagiietic structure which would give a zero net niagnetizatioii when studied with a technique such as ~agnetoiiie try or thermogravimetry (in an applied magnetic field). The atomic magnetic inomeiit is only an estimate since one is actually measuring the liyperfine magnetic field at the nucleus produced by the atomic magnetic moment and there is, at times, coiisiderable uncertaiiity iii the conversion factor betweeii hyperfine field and atomic magnetic moineiit. The difficulty associated with preparing bulk magnetically aligned powder samples severely limits the ability of M~ssbauerspectroscopy to determine the magnetic ordering direction, but it is possible to observe the effects of changes in the ordering direction (spin-reorientations) via the associated change in magnetic liyperfine field resulting from the change in the orbital magnetic moinent and hence the orbital contribution to the hyperfine field. It is possible to carry out Mossbauer spectroscopy on single crystals but tlie crystal must be extremely thin to allow sufficient ~ a m ~ a - r atransmission. y
~ a ~ n ~Phase i i cDiagram
Figure P Neutron diffraction patterns of MnO obtained above and below the Ntel temperature (12% K). The top pattern, obtained in the a ~ ~ t ~ € e r r ~ ~ regime, a ~ i i e thas i c been indexed in terms of a magnetic cell whrch is o b t ~from i ~the ~ crystdlograpbic ~ cell b y doubling (Shull aizd Smart, 1949)
of the study of a magnetic crystal is that by Koon et aE. (1986) who studied the spin-reorientatio~in NdzFel4 (Figure 2). The ~ l e b s c h - ~ o r d a ncoefiicients which give the probabilities for t~ansitionsbetween nuclear levels show that the relative areas of the six lines in a magnetically split 57 Fe sextet are in the ratio
3:
~ 1 sin2(, . ~
1
4 sin20
+ cos26 :1:1:-----1 + cos28 : 3
where 8 is the angle between the hyperfine field (atomic magnetic moment) and the incident garnmaray direction. For a powder sample, this ratio reduces to the well-known 3 : 2 : 1 : 1 : 2 : 3 area ratio after powder averaging. The single crystal spectra shown in Figure 2 clearly demonstrate the tipping of the Fe magnetic ~ o r n e ~away t from the crystallographic c-axis. At room temperature, the atomic ~ a ~ ~~ eo t~ i eare ~~ atl is~ ~ ealong d the tetra
axis, corr~spondi~lg to 6 L=I 0" and g i ~ i na ~line ratio 3 : 0: 1 : 1 : 0 : 3. As the moments tip away from the caxis with decreasing ternperatu~e8 increases and the relative intensities of lines 2 and 5 in the spectrum increase. This spin-reorientation is ~ e t r i m e n t ato~ the use o f Nd2Fef4B as a p e r m a n e n ~ - ~ a g ~material et below 140 K. Spin-reorientations of the magnetization direction can also be detected by i ~ i e ~ the s ~temperature ~ ~ n ~ d ~ p e ~ d e n cofe the h ~ p e r field. ~~e contribution to the hyperfine field the spin component (p,) of the atomic magnetic moment but there is also a c o n t r i ~ ~ from ~ i o ~the ~ orbital c o ~ p o ~( pe L~) of t the ~ a ~ n ~~ t i oc ~The~ orbital moment depends on the orientation of the moment within a crystal structure, and ;i spinreorientation consequently produces a significant change in the hyperfine field:
~
Bonding and S ~ a ~ i 1 i ~ " v
action, one may detect spin~reorientations from the interplay of the electric and magnetic interactions in the total nuclear hyperfine Hami~tonian.For a site symmetry higher than ort~orhombic, the nuclear hyperfine Hamiltonian yields energy levels given by
[3cos2fl- 1][3m2- I(I+ l)] where fl is the angle between the hyperfine magnetic field and the principal Z-axis of the electric field gradient (EFG) whose largest component is VZZ,The first term in this equation is the eeman interaction of the nuclear magnetic moment with the hyperfine magnetic field. The second term represents the interaction between the electric q~adrupolemoment of the excited I = 3/2 state of 57Fe and the EFC, which is determined by the ch~rgesof the s u r r o L ~ ~ dlattice, i~g
4.2 K, with permissmn from Elsevier Science
where 01 and are constants, with opposite signs. In igure 3a we show the temperature dependence of the field at the 57Fe sites in hexagonal , P63/mmc, #194), as measured by ure also shows the hyperfine field at the crystallographic 4f Fe sites - the so-called 'dumb-beIl> sites. At room temperature, the Er3+ sub~atticeanisotropy is determined almost exclusively by the second~ordercrystal-field interaction. As the t e m p ~ r a is t ~reduced, ~ ~ ~ the higher-order (fourth and sixth) crystal-field terms at the Er3+ ion become stron.ger, relative to the second-order tern, and the ~r~+ moment rotates away from the room-temperature easy direction, The Fe atomic moment is therefore forced to rotate away from its preferred easy direction due to its exchange coupling with the Er3+ sublattice change in the orbital component of oment leads to an increase of the average hyperfine field at the 57Fenucleus of about 510%. A more detailed discussion of crystal-field effects i s given in the following section. In those cases where there is an electric quadrupole hyperfine interaction due to the surrounding charges in. the ~ ~ t t i c in e , addition to the ~ a g n e t i cdipole inter-
-0.1 5
0 F i g ~ 3r ~ (Top) The temperature dependence of the average 57Fehyperfine field and that at the 4f crystallographic site in Er,Fe,,C, (redrawn from Zhou et al. 1992), with permission from Elsevier Science; ( ~ o t t The o ~ te~perature ~ dependence of the ',Fe quadrupole splitting at the 12k crystal log rap hi^ site in Tni,Fe,,N,, (redrawn from Hu et u2. 1990b), reproduced with p ~ ~ ~ s s ~ o ~
169
Magnetic Phase Diagrams in addition to the electrons o f the host atom. Now, if it can be assumed that the EFG principal axis frame does not change direction with temperature, then any e in the physical orientation of the atomic magnetic moment will result in a change in 8 of the liyperfine magnetic field and therefore a change in the measured quadrupole split tin^ of the spectrum. In the extreiiic case of ail axis +-+plane ~ e o ~ ~ ~ there i ~ tis~a t i o ~ change in the experin2eiitally measured quadrupole splitting o f -2, being the extreme values of the second13 cos? 8 - 11 for order ~egendre polynomial O = O o - 90". In Figure 3b we show the measured quadru~olespiitting at the 12k Fe site in hexagonal ~ ~ fliP38, ~ ~~ ~ / ~ iy194), l l ~l as ~ ,~ ~ ~ ~by s ~1 l Hu et al. (1990b). The effect of the axis plane reorientation is clear. The reader is referred to onser (1975) for a detailed ossbauer spectroscopy and to the review on Nossbauer spectroscopy as applied to rareearth ~ e ~ ~ a magnets ~ e n t by ~ a d o (1996) ~ a ~ for further details.
4
~
~~
d
~
2
~
f-,
One may determine the easy direction of magnetization from ~eas u ~emen ts of the m ~ ~ n e t i z a t ~of o na single crystal as a ~ u n c of ~ iapplied ~ ~ ~ ~ a ~ n efield. t i c In practice, one orients the crystal using X-rays, fixes this orientation, then measures the magnetization along the various crystal directions. For ferromagnets one simply finds the direction along which the saturation magnetization is largest. In Figure 4 we show the results of a ~ i ~ ~ l ~i i- ~~ ~~ ~~ i §~study t t ~~ by l~ ~Cadogzln t i o ~er ~al. (1988) of the pe~anent-magnetmaterial Nd2Fel4 y do these data show clearly the tipping of the zation away from the crystal c-axis (the magnealong the 'easy direction' is 3% larger than that measured along the r-axis) but it is clear that drastic N
These so-called FO magnetization processes) are invaluable in the determination of crystal-field parameters and are the result of the complex interplay between the various energy terms in the anisotropy, whereby the magnetic structure adopts the minimum energy configuration. A detailed analysis of such processes has been given by Asti and Bolzoni (1980). actia
ethod to deternine the easy ation of a ~ e r r ~ m a g n e tor i~
~agnetizationcurves of single-crystal Nd,Fe,,B (Cadogan ei al., 1988). The canted magnetic structure of Nd,Fe,,B below the spin-reorientation tempera turc (140 I<>ts also shown, ca produced with p c r ~ i s ~ i oalfl 1OF
~
176)
Bondirtg and Stability
netic powder material is to disperse a finely or Nkl). Details of the pheiiomenolo~icaltreatment of powdered sample in an epoxy resin and allow the the exchange interaction as applied to mixture to set in an applied magnetic field. One can tallics may be found in the paper by Cadogan et al. then determine the easy ~agnetizationdirection from ( 1988). the cliffraction pattern by noting which (hld) peaks are The exchange interaction is dependent on the enhanced and which are reduced, or even absent, iiiteratoinic separation and is generally negative for n. This method relies on the short distances, leading to antiparallel coupling, and diff'raction is, in effect, positive for larger distances, leading to parallel layers of the powder and is co~~pling. Tlierc are a number of ways in which the not a bulk t e ~ ~ i ~due i ~ to u ethe limited penetration of magnetic structure of an iiitermetallic ciln be changed s mentioned with regard to the use of by c h a n g ~ ~the g inte~atoniicseparation, and thus the sbauer spectroscopy, it is cxtremely exchange Interaction. Such means include (i) atomic in fu'ull a~ignmeiitof the entire sample. substitution, which relies on differences in atomic radii, sim~~icity of this eth hod^ some care is necessary when (ii) application of hydrostatic pressure and (iii) absorpstudying antif~rr~iiiagnetic materials since the magtion of i~iterstitialeleinents such as H, N, 6 ,which leads netic susceptibi~~~y of an antiferromagnet in small to volume expansion. An example applied fields Is largest in the direction ~ e ~ ~ to e ~ interatomic ~ i ~ ~ separation i l ~ on ~ the exchan the axis along which the m o ~ e n t lie, s leading ofteii to hence the magnetic structure can be seen in the pseudoan incorrect idcntification of the casy direction of ternary system LaXV1-,Mn2Siz which is discussed in detail in section 4.5. The La3+ion is larger than Y3+and both ~ o s s b a u e rand n ~ ~d~ffraction t r ~ experime~ts ~ have been used to show that there is a conconiitant change in magnetic structure from f e r ~ o ~ a ~ ~atethe tic La end of the series to antiferromagnetic at the Y end. In passing, I would like to note that the magnetism of Mn and its intermetallics is notoriously complex and the e behaviour of tlie La,Y~-, n2Siz system is more enls in R-T iiitermetallics are in coinplicated than this simplc intera toinjc s ~ p ~ r a t i o ~ h the possible exceptioiis of Ce, argument would suggest. amiltonian dcscribing the magnetic There are interesting examples of magneti~structures which arise from the com~etition between different exchange terms. For example, if we consider 7 - l ~ o m 1= zrnrra-uion-ltr + 'Jfsrpm-arbii + K@\LI~ +R c ~ a chain of r n o i ~ e in ~ ~at crystal ~ structure and allow JI- 7 - l , ~ ~ ~ tion n ~ t~ ~~ ~ s ~ ~ ~i ~ ~ ~ ~ r ~ ~ only nearest-neig~bour (J1)l and next-nearest-~eigh~ bour ( J z ) exchange interactions, with different signs, where the various tesins are respectively (i) the intrathen it is possible to obtain a spiral atomic Coulomb interaction, (ii) the spin-orbit cou(Figure 51, such as in the case of pling, (iii) i ~ t ~ r ~ t magnetic o ~ i ~ c exchange coupling, approximation. Writing the excha (iv) the crystal field acting on the R3+ ion, (v) Heisenberg form ~agnetostrictiveeffects and (vi) any external effects e e ~ a ni~teractionof the moment with an externally applied magnetic field. The exchange and crystal-field terms are the dominant tions responsible for the magnetic behaviour of + nionient in a crystal.
"mean' field), and thc strcngth of this coupling may bc ed from the i n a ~ ~ e tordering ic temp~rature(Curie
it is straightforward to show that the exchange energy of a particular spin is E: = -J1(2 cos 4)- J2(2 cos 2 4 ) and the turn angle between adjacetit spins is simply 4 = c o s 1(-J1/4J2) (see Enz, 1960).
n addition to the ~ a g n e t i cexchange interaction, one must also take into account the magnetocrystalline anisotropy o f the R3) ion in an R-T intermetallic, which in some cases may be considerable, as illustrat~d
Magnetic Phase Diagrams
171
for hexagonal symmetry. The polar angles of the magnetic moment in the crystal axis frame are (0, 4)” The anisotropy energy terms K1, K2 etc. (which can be positive or negative and have quite ~ ~ ~ e rternperaent ture dependences) can be determined by fitting inagnetization curves obtained in applied magnetic field along the various directions in the crystal (torque measurements, Sucks~ith-Thompson etc.), The use of the K, anisotropy e fitting single-crystal inagnetization data, together with the relationship between these terms and the underlying crystal-field parameters &,,, can be found in the paper by Cadogan et al. (1988) and the reviews by Herbst (1991) and Franse and The case of XFtexch < 7 - l ~usually ~ applies to ionic compounds rather than to intermetal~i~s but does occur in R intermetallics which have very low magnetic ordering temperatures. The more complex case, when 7-tFlexcjz 7-lcF,requires that the full Harniltonian be diagonali~edand, in this case, no simple apprsximation can be made. As stated above, the main contribution to the magnetocrystalline anisotro tallics is the crystal-field electrons with surrounding and conduction electrons. The most common description of this tion is in terms of the point charge model which treats the interacinteraction between the tion as a simple C localized 4f electrons and a surrou~dinglattice of point charges. The interaction is then expressed in terms of a crystal-field Hamiltonian 7 - i ~ ~with : (Stevens, 1952) sp~n-operator equivale~ts ~ ~ ~ ( ~ which are polynomials in the angular moment~m operators, and crystal-field parameters energy terms whose m a g n i t ~ ~and ~ ss strength of the magiietocrystalline anisotropy and the symmetry of the crystal lattice PCM is a crude approximation nevertheless one may use the fo to great advantage under the protection of the crystal symmetry which the PCM, with all its i~perfections, ultimately must reflect! To begin with, the electrostatic potential at the 4f electrons (F$is written as a simple Coulomb summation over the neighbo~ringpoint charges (qj) at lattice positions (Rj)and then expanded in tei-ms of Legendre polynomials as N
*
Helical magnetic structur~o f Dy (schematic)
by the use of Nd@el& as the basis for the world’s strongest perinanent-~a~net material. The magnetocrystalline a n i s o t r ~ yi s a consequence of the crystalfield interaction acting on the R3+ion and the reader is directed to the review article by Hutchings (1964) for a complete description of the crystal-field interaction and its mathematical development in terms of spin operators. The exchange and crystal-field terms play the ~ o m i ~ arole n t in determin~n~ the magnetic properties of the R3+ ions in the crystal. In the situation where XFlexch > X C F , which is the case for R-T p e ~ a n e n t ~ m a g n materials, et the crystal field can be treated as a perturbation on the exchange interaction, and the anisotropy energy can be written in the classical form
for tetragonal symmetry, and E = K1sin20
+ rC, sin48 + K3 sin‘ 8 + K; sin‘ 8 cos 6d,
172
Bonding and St~~i~it”v
where cog is the angle between r;(0i, #J and Ri(Oj, #J). This may be rendered more tractable by using the spherical harinonic addition theorem to re-express Y ( r z )in terns of Tesseral harmonics and ~ nal l yin lar momentum operators J z , J2, J+ and J- of the 4f electron configuration, via the ~ i g n e r - E ~ k a rtheorem t (see, for example, Edmonds, 1957)).Finally, we arrive at the familiar form of the crystal-field Hanil1t onian describing the magnetocrystalline anisotropy o f the 4f shell:
n=O
m=O
For example, the dominant second-order diagonal operator is 0 2 0 = 3J5 - J 2 and the off-diagonal term Q& is Of;, r=: i ( J $ J!). The 7 - t ~ cannot ~; contain ternis of odd YI due to the inherent inversion symmetry of the problem; the anisotropy energy must be an even function of 0. Furthermore, if the quantization z-axis of XCF is a c-fold crystallographic rotation axis then XCF must contain terms of the form B,,,. The most general expression for 7 - l contains ~ ~ 27 terms in this expansion, but the crystal~o~raphic point symmetry of the atomic site in question reduces this to more manageable sizes. For example, in the case of hexa~onal sym~etry,such as in the R2Fel7 cornpounds with heavy R e l em e n~(and ~ SmCos), %er; takes the simple form
+
which is evidently more complex than the simpler form for the ThIVfnlz structure in which the R3+ point ~ tetragonal. syinmetry # / m is ~indeed To determine the magnetic structure adopted by a compound we must add the exchange interaction to the crystal field and, using standard notation, we therefore have
is an externally applied magnetic field and of the subl at t ~~e producing the is the m ag~et i zat i o~ exchiniige interaction. The exchange or molecular field or mean-field constant is A. The R3+ magnetizatio~is ~ ~ n{is the ~ number ) , density of R = ~ g ~ where R3+ moments and gJ is the Land6 g-factor. The equilibrium density matrix p i = (1/Z>exp ( - PEi) are the eigenvalues of where 1= ( l / k ~ Tand ) the 3t = 7i.exc/2+ 7 - t ~ ~ . The partition function , The ensemble av which leads to a iiig direction and to study spin-reorientations in the magnetization direction we need to study the angulardependent behaviour of the free energy of the system F(0, p) = - / t ~ T l n Z and the final magnetic configuration corresponds to the m i n ~ value ~ u of ~ F(0, q). We can separate the crystal-field parameters BE, into a 4f part and a lattice part: 4,m
in which the ‘diagonal terms’, i.e. with m = 0, determine the overall anisotropy (i.e. easy c-axis, cplane or inter~ediate)and the ‘0~“diagona~’ term with rn = 4 determines the in-plane anisotropy. Another efYect of the off-diagonal term in the ~ Y ~ isc Fto reduce the R3+ magnetic moment by crystal-field quenching. In the case of tetragonal symmetry, such as found at )~~ which have the R3+ site in the ~ ( F e , M coinpounds the ThMnlz structure (2)2b, tI26, 14/mmm, ##l39),we have 7 - 1 fI= ~ B~2 0 0 2 0
+ B&oi4 -k
$- B40040
.b)60060
+ &o&
At this point it is worth noting that 7 - t is~ determined ~ by the point symmetry of the site in question and nat the overall space symmetry. As an example we may whose overall crystal structure is ace group P42/mnm; but the Nd3+ site has the orthorhombic point symmetry mm, and the app~opriateXcF for the Nd3+ ions is
xci; = &O020
i60
3.B40040
+ & 2 0 i 2 + Bi40i4
+ B& o&+ B24o&+ B&jo&
=;
6,(
~
~
~
4
~
~
~
,
E
The Stevens (1952) constants & depend on the 4f electron configuration of the R3+ ion, whereas the crystal-fie~d lattice coe~cientsARm depend on the arrangement of charges in the surroundin are, to a first approximation, usually assumed to be ~onstantacross a series of compou~ds.Thus, within this f r a m e ~ o rthe ~ information on the sign of the crystal-field terms is contained within the 0, conn . example. Nd3+ stants for the R3+ ion in ~ u ~ s t i oFor has Oz .c: 0 whereas Tm3+ has 02 > 0 and one would therefore expect these ions to have opposing anisotropies (e.g. easy-axis vs- e a s y ~ p ~ in ~ nthe e ~absence of higher-order terms, The role of the sign of BEm in determining the easy direction of ma~netization may be illustrated simply by cons~derin~ the second-order operator term B20020= Bzo(3J; - J2).The corresponding energy is then ECF= ~ 2 0 ( 0 2 0 )= B20(3J; - J ( J + 1)) and we can consider the energies of two states, as shown in Figure 6 . The lJZl = J state, which corresponds to easy-axis ordering, has E ~ =FB20J(2J - 1) whereas the ~ J z = ] 0 state, which corresponds to easy-plane
173
Mugnetic Phase Diagrams m
**II R U I
.............................. e', .......'~*~*.........*.....".&...",.*. ................ I
I
..
m
*#?
Figure 6 The role of the second-order crystal-fieldterm in determining the magnetic ordermg direction: (left) easy-axis or (riglit) easy-plane
ordering, has EcF = -&0J(J f 1). Thus, 2320 > 0 favours easy-plane order and B20 < 0 favours easyaxis order. The relatively weak magnetocrystalline anisotropy of the Fe sublattice is not amenable to the above approach, due to the delocalized nature of the 36 electrons, so it it usually treated phenomenologically; and a siniple expression E, = K F sill28 for the anisotropy energy of the Fe sublattice is generally -T i~ter~eta11~cs7 where 0 is the nd tlie c-axis. In Nd2Fel4B, the Fe sublattice has axial anisotropy with lill ,-., 17 K/f.u. at room temperature.
As stated earlier, one may use the point charge model to great advantage provided one keeps in mind the crudity of this approximation. The symnietry will be correct but the magnitudes of the crystal field par~metersdeduced by the PCN summation should never be treated as 'cast in stone' - the signs of the calculated second-order terms are usually correct and it may be useful to consider relative magnitudes of . cannot terms within a given order, e.g. ( ~ 2 / B 2 0 )One deduce 0 priori values for the crystal-field parameters and the det~rmination of a set of Brim values appropriate to describe a magnetic structure remains an empirical exercise. There are numerous experiinental techniques which one may use to determine a set of crystal-field paramete~s,including single-crystal magnetization hyperfine interactions as f ( T ) heat capacity inelastic neutron scattering single-crys~alac-susceptibilit~
and the reader is referred to the review by for a discussion of these options.
s in
The R2Fel 4~compounds crysta~~ize in the tetragona~ Nd2Fel4B structure and, as mentioned earlier, are important as p e ~ a n e n t ~ m a g nmaterials. et The anisotropy of the Fe sublatttice is an easy-c axis. Above 140 K, the anisotropy of the R3+ sublattice is dictated by the second-order crystal-field term since the fourth- and sixth-order terms have more rapid temperature dependences and are only significant at lower temperatures. Those R3+ ions with I320 < 0 (Nd, Pr, Tb, Dy, €30) have easy-c-axis anisotropy whereas those R ions with B20 > 0 (Sm, Er, Tm) have easyplane anisotropy. As we have already mentioned, when Nd2Fel4B is cooled below 140 K, the hig~e~-order (fourth and sixth) crystal-field terms acting on the Nd3+ ions become important and the net magnetization tips away from the c-axis since these higher-order terms have opposite signs to the second-order term. In the early days of the R2Fel4B series much work was done on pseudo-ternary compounds in which two R elements were used, in an attempt to optiniize the per~anent-magnet properties. For example, it is known that Tb3+ has a significantly stronger crystalfield interaction, and hence anisotropy, than Nd3+ and partial substitution of Tb3+ for Nd3+ can be used to increase the overall anisotropy of the rare-earth sublattice. However, the Tb magnetic moment, being a heavy rare-earth, couples antiferro~a~netically to the Fe sublattice thereby reducing the overall ~agnetization,and one must t h e r ~ f o ~find e a compro-
inise between the increasing anisotropy and the decreasing magnetization when investigating the permanent-magnet potential of complex phases. A mixed system such as (NdYEr)2Fel4B(Figure 7) shows the effect of the competition between the negative secondorder crystal-field term of the Nd3+ and the positive tern of the Er3+. Thus, one obtains a transition from easy-c axis (& < 0) to easy-c plane (B20 > 0) as the Er content iiicreases (Cadogan and Li, 1992). ( ~ 12~ ,
The R(Fe,T) 12 compounds crystallize in the tetragonal ThMn12 structure (D2b, tI26, 14/mmm, #139) which ed in some detail in Chapter With the possible exception o f 12 reported by Cadieu et a/. 991), it has not been possible to prepare a binary 2 phase; a third element is needed to stabilize this 1112 structure. To date, the structure has been formed with T = Al, Si, Ti, V, Cr, MO, Mn, W, Nb or Ta: a high Fe content of around RFel1.3T0.7 has been obtained with Ta or N b as the stabilizing element. The anisotropy of the Fe su~latticeis easy-c axis, whereas that of the COsublattice in the isomorphous R(Co,T)]* compounds is easy plane. In general, R-sublatticc anisotropies are signi~cantlylarger than that of the Fe sublattice but in the R(Fe,T)12 compounds the two anisotropies are c o m p ~ r ~ b lThis e . near equality leads to a large number o f spin-reorientations being observed in these compounds. In Figure 8 we show
The competition between the axial anisotropy of R(Fe,T)lz and the planar anisotropy of R(Co,T)l? is illustrated in the phase diagrams (Figure 10) of the mixed series R(Fe,Co)llTi with R = Y, Dy, Gd, Ho, Tb and Er studied by Cheng et a/. (1990). As we shall see later, in section 4.6, the R(Fe,T)12 compounds provide viable permanent-magnet materials alternative to NdzFel4B after interstitial modification of their ma~neticbehaviour by the absorption of nitrogen or carbon. 17
The R2(Fe,M)17 compounds crystallize in either (i) the rhombohedral ThzZn17 structure (hR19, R h , #I 66)
for light R elements or (ii) the hexagonal Th2Nil7 structure (hP38, P63/mmc, #194) for heavy The anisotropy of the Fe sublatttice is easy-c axis. As mentioned in section 3. I , the exchange interaction between two moments depends critically on the separation of tlie moments. The effect of the application of hydrostatic pressure on the interatomic separation, exchange interaction and hence the magnetic structure of an intermetallic has been demonstrated in hexagonal Y2Fei7 by Nikitin ei al. (1991), who were able to produce a non-collin~ar helimagnetic structure starting from a collinear ferromagnet with increasing pressure (Figure 11).
The La(T,M)13 compounds form with the cubic NaZli13 structure (D23, cF112, F d c , #226) aizd this system has the highest transition~metalcontent of Et-T intermetallics, although the reduced anisotropy associated with the cubic symmetry probably precludes their use as p e r n i a n e n t - ~ a ~ ~materials. iet The only R-T binary with this structure is LaCol3, which is ferrornagnetic below 1290 I<. Fe-rich cornpounds in the range Fe1o.s-ll.s can be formed with stabilizing elements M = Si and A1 (Palstra et al., 1985). In Figure 12 we show the magnetic phase diagram of La(Fe1-x,Al.x)13 in which one observes antiferromagnetism at A1 contents in the range 0.08-0.14, ferroinagnetism for x in the range 0.14-0.38 and finally, mictomagnetisin for x in the range 0.38-0.54. (A mictomagnet is similar to a spin glass in that small groups of moments, coupled by direct exchange, are embedded in a spin-glass matrix phase. Early (pre-spin glass) work on mictoma~neticsystems employed a model involving a mixture of f e r r ~ m a ~ n ~ t i and sm antiferromagnetism, hence the name.)
The RT2X2 compounds (T = transition metals and X = Si, C e ) crystallize in the tetragonal ThCrzSi;! structure (D13, tIIO, 14/mmm, ##139) and have been discussed in great detail in the book by Leciejewicz (1994). These compounds are interesting because the only transition-nietal element known to be magnetic in this series is Mn. In those compounds with ~ i ~ n - ~ a g n eT,t i the c sublattice orders magnetically at low temperatures ( < 6 0 due to the indirect (RKKY) exchange intcractio etween R iraoments. In Figure 13 we show some of the possible ma
~ a g ~Phase ~ t Diagrams i ~
175
a
t
ure 7 Magnetic phase diagram of (Nd,Er),Fc,,B (Cadogan and Li, 1992). The letters a,b,c,d correspond to the magnetic structures shown below the phase diagram, reproduced with permiss~o~ from Elsevier Science
176
Bonding and ~ t u ~ i l ~ t y
Magnetization curves of single-crystal DyFe,,Ti (Hu et nl., 1990a)
Figure 9 Schematic experi~entalmagnetic phase diagrams of the RFe,,Ti series (Rzrare-earth) (HLI et al., 1989), reproduced with ~ e r ~ i s sofi ~1OP n
ordering modes of the R sub~atticein the compounds. It is clear that this series warrants to itself given the variety of magnetic order found in this series (ferromagiietic (F), antiferrom and various modulated structures best . general, though, we may terms of spin waves ( S ~ ) )In summarize the magnetic ordering in terms of the crystal-field interactions at the R3" ion, as detailed earlier. Thus, those R"+ ions with Stevens constant 82 < 0 (e.g. Tb, Dy the c-axis, whereas those R3" ions wi Tm) order perpendicular to the c-axis. As an aside, we note that the compounds with = Ce exhibit a wealth of properties such as heavy~fermionbehaviour due to the valence instability of the Ce ion. Unlike the remaining R ions, the Ce ion can empty its 4f shell by adopting a 4+ state rather than the usual 3+ state. The corresponding magnetic moment fluctuates between 2.54 fiB (Ce3+)and 0 fiB (Ce4+). The ma~neticorder of the Mn §u~latticein the RMn2X2 compounds (X = Si, Ge) comprises planes of Mn which are usually ferromagiietic. The overall magnetic structure of the compound depends critically on the interplanar separation. As mentioned in section. 3.1, short interatomic distances are associated with negative (antiferromagnetic~coupling whereas longer distances are associated with positive (ferromagnetic) coupling. The same applies with regird to the interplanar separation in RMnzX2 compounds. In
Magrzetic Phase Diagrams
174
~ ~ g u 12 r e Magnetic phase diagram o f La(Fe,Al),, (Palstra et al. 1985)
, Tb, Dy, No and Er) (Chciig et al., 1990) as conipiled by Szytula and Leciejewicz, 1994, reprinted with permission from CRC Press, Boca Raton, Florida
c
F
ure I1 Magnetic phase diagram of Y2Fe,, as a function of lattice co~pressionfrom applied pressure. PM, FM and HM represent paramagnetic, ferroinagnetic and helimagnetic structures, respectivdy (Nikitm et d., t991), reproduced with permission from Elsevier Science
Figure 14 we show the magnetic phase diagram of SniMnzGe:! as a function of applied pressure (Dumj et al., 1988). The transition from ferromagiietic order (F) to antiferromagnetic (AF) with increasing pressure, corresponding to Ia ttice contraction and hence decreasing interplanar separation, is clear. A similar effect in the S ~ ~ - ~ ~ (K ~ =~ n z ~ e z shown in Figure 15 where one se transition being driven by the replacement of Sm with R elements of different radii, leading to a change in the lattice parameter and, once again, the interplanar separation (Szytula, 1992). As shown in Figure 13, the magnetic structures formed in the R ~ ~ compounds 2 ~ z can be quite complex, with numerous different antiferromagnetic phases being formed. As an example, in Figure 16 we show the temperature-dependent magnetic phase diagram of TbNiZSiz as a function of magnetic field applied along the tetragonal c-axis ( 1991). One obtains ferromagnetic, antiferromagnetic and amplitude-modulated magnetism depending on the field and temperature. The distance dependence of the exchange interactions, which are responsible for the W magnetic order in this series, is demonstrated by the study of series ( ~ a , Y ) ~ n : ! S(Campbell i~ et al., 1999). is ferromagnetic (larger Mn- n se~aration)whereas YMn2 Sil is antiferroinagnetic (smaller separation). In Figure 17 we show the magnetic
178
Bonding and Stability
i~~~~ 13 ~ u ~ ~ of m the a ~different y types of magnetic order found in the RT,X, system (taken from Saytula and Leaejewicz, 19941, reproduced with permission from Elsevier Science
phase diagram of the mixed ( ~ a , ~ ) M n 2series, ~2 deduced from neutron diffra~tion and Mossbauer measurements carried out on (La,Y)MnzSiz samples doped with 0.5 wt.% of isotopically enriched 57Fe(the ossbauer isotope comprises only about 2% of
In Figure 18 we show a ‘universal curve’ for the Mn2X2 compounds (Szytula, 1992) in which the magnetic ordering temperature of the Mn sublattice is plotted as a fun~tionof intralayer separation. The critical distance marking the tra~sition~from antiferromagnetism to f e r r o ~ a ~ n eist ~2.85 s ~A, which agrees with the model of localization/delocalizationo f the 3d electrons proposed by ~ o o d e n o u ~(1h963). Similar eRects are seen in the Fe-based compounds RFel+Al,, where the critical Fe-Fe distance is 2.60 A ( ~ z y t u ~and a Leciejewicz, 1394).
In 1990, Coey and Sun showed that iiiterstitial ~odificationof the Rz(Fe,T)l? cornpounds leads to a doubling of the Curie temperature (T& and, perhaps more importantly, it can produce a change in the sign of the magnetocrystalline anisotropy. Thus, a compound such as SmzFe17, which is effectively useless as a permanent magnet material due both to its Tc being around RT and to its having an easy-plane anisotropy, leading to minimal coercivity, becomes a contender for p e ~ a n e n t - ~ a g napplications et after interstitial modification to Sm2Fe17Nm3 with a STc 700 K and §ubstantial coercivity due to its easy-axis anisotropy. This effect of interstitial modification is also observed in the (Fe,T)12 compounds with MdFe1ITiN, being a possible ~ e ~ ~ a n e ~ t - ~ i a g ~ N
Magrzetic Phase Diagram
Magnetic phase diagram of SmMn,Ge, as a function of applied pressure (Duraj et al., 1988). F = ferromagnetic, AF = antiferromagnetic aiid P= paramagnetic. The line segment in the range T < 105 K represents a transition to re-entrant ferro~~gnetism? reproduced with permission from Elsevier Science
material. In both the 2: 17 and 1 : 12 structures the interstitial N or C atom is situated arouard the R3+sites and causes a dramatic change in the crystal-field at the R3+ atom. One approach to modelling this effect is the bonding-charge model, proposed by Li and Cadogan (1992) and based on the work of Pauling (19601, in which one calculates the degree of electron transfer between the R and the N or C using electronegativity difPerences. Despite the fact that this is another example of a point charge model calculation, it has been quite successful in interpreting such experimental data as the m a g ~ e t i c ~ o r d ebehaviour, ri~~ anisotropyfield enhan~ementand change in m~gnetic-ordering direction. In Figure 19 we show the magnetic phase diagram of the GdZFel4B series as a function of €3 content, hang et al. (1988). (The 2:14:1 structure does not accommodate any significant a ~ o u n t sof N or C as interstitial elements, but one
179
Figure 15 Magiietic phase diagram of (Siii,R)Ikan,Ge, as a function of applied pressure (Szytula, 1992) The temp~rature T, marks the first-order ferro- to antiferro~ag~etic trans~tion and T, represents the transition to re-entrant f e r r o n ~ ~ ~ n e t i s ~ , reproduced with perniission from Elsevier Science
Figure 16 Magnetic phase diagram of TbNi,Si, (Blanc0 et al., 1991). Phases I and IV are a m p l i t ~ d e - ~ o d u l a ~phase e d , I1 is a simple a n t i f e r r o ~ a ~ i i(correspond~ng et to AFIII in Figure 13), phase 111 1s long-period coinmensurate and phase V is a complex magnetic phase, reproduced with permission from Elsevier Science
Bonding m d Stability
1450
7 Magnetic phase diagram of (La,Y)Mn,Si, as a function of temperature. F = ferromagnetic and AF = antiferr~magnetic,respectively. (Campbell et al. 1999). The magnetic structure notation is that of Venturini et al. (1993, in which Fmc = canted ferromagnetic, AFI = planar ~~ntiferroma~~ietic, AFI = axial antiferrQ~agnetic,AFmc = c a ~ t ~ a ndt i f e r r o ~ ~ ~ nand ~ t iF,,,,, c = a conical magnetic a r r a n g ~ ~ e nwhich t coexists with the canted magnetic structure, reproduced with permission of IOP
Figure 19 Magnetic phase diagram of Gd,Fe,,BH, (Zhang et al., 1988), reproduced with permission from Elsevier Science
\
La
I
can form a ternary R2Fe14C phase with most R elements.) The interesting point to note is the presence: of a spin-reorientation from axis to plane with increasing H content. Given that Cd3+ is an s-state ion and therefore any crystal-field effects will be extremely small, it seems the introduction of hydrogen alters the Fe sublattice anisotropy, even though the H atoms are preferentially located around the Gd3+ site.
I
One of the most complex ~ a g ~ e t phase ic dia~rams mapped out to date (if not the most complex) i s that of CeSb which, strictly speaking, is semi-metallic. Ce crystallizes in the cubic NaCl structure (Bl, cF8, Fm?m, #225), and its magnetic behaviour as a function of temperature and applied magnetic field was first studied in 1977 by Rossat-Mi~nodet al. The Dependence of the magnetic ordering t e ~ p e r a t ~ r e magnetic phase diagram of CeSb i s sh and ordering type of the RMn2X, c o ~ p o u n d son ~ntralay~r 20. Below the Nhel t ~ ~ p of ~16 ~ ~ ~ ~ r separation (Szytula, 1992). F = ferromagnetic, AF = applied magnetic field, CeSb exhibits five distinct antiferron~agnetic and P = paramagnetic, reproduced with p ~ r ~ s s i from o n Elsevier Science ~ a g n e t i cstructures which are all ~ o d u l a t e dwith
e
Magmiic Phuse Diagrams
P
I
T re 20 Magnetic phase diagram of CeSb ( ~ o s s a t " ~ i ~ ieti oal., d 1977). The notations F, FP, AFF, using I;=ferrotiia~iiet~c, AF = aniiferromagnetic and P =paramagnetic; so FP, for example, t-cpresents a strwture wlth both ferromagnetic and paramagnetic moments, as explained in the text, reproduced with permission from Elscvler Science
wave vectors [OQq]along the r-axis. The value of q varies discontinuous~ywith t e ~ p e r a t u r range $ to The peculiarity of this order i s that there are nonmagnetic Ce planes interspersed between mag~etic Ce planes in a t 0 JT 0 J a ~ r a n g e ~ e n t . These structures change in a complicated m a n ~ e r when one applies an external magnetic field and there are no fewer than 15 different nnagnetic structures known for CeSb, as a function of T and field. The u n ~ e r l y i nbasis ~ for this rich magnetic behaviour seems to be a hyb~dizationbetween the Sb p-boles and the Ce3+ 4f states. Xn a recent theoretical study of CeSb by Martiiiez et al. (1999) a frustrated Kondo lattice model has been proposed iizcorporatiag inter~ l a n a rexchan~einter~ctions ~ e ~ ~ neareste e n and next~nearest-neig~bours. The presence of the paramagiietic planes is tlieii explained in terins of frustration.
3.
-Fe-
The random addition of antiferroniagnetic exckaiige interwtions to leads to a loss o f P frustration. In extreme cases, foriiied with randoin isotropis: spin frcezing an neither a iiet magnetizatioii nor lower levels of frustration the acteristics of both extremes as long-ranged FM order
temperature Txy, followed by the
182
Bonding and Stability
re 21 Predicted magnetic phase d i a g r a ~of a system with a €rustration fraction f. PM, FM and SG are paratnagnet, ferromtagnet and spin-glass, respectively. (Thomson et d.,1992), reproduced with perinissioii of American Physical Society
F direct exchange, can be tuned via the composition as a consequence of the amorphous nature of the material. The magnetic phase diagram predicted for such a system using a Heisenberg model of nearest-neighbour iiateractions with a fraction o f the FM ‘bonds’ randomly replaced by AF exchange, is shown in Figure 21 (Thomson et al., 1992). The material phase diagram of the Fe-Zr binary system exhibits two deep eutectics at 24at.% Fe and 90.2at.’?/a Fe, which make it possible to prepare amorphous samples by rapid-q~en~hing techniques such as melt spinning. This system shows a wide range of beliaviour from superconductor to ferromagnet, depending 011 composition. At tlae Fe-rich end of the system the magnetic structure below TC comprises longitudinal ferrornagnetisni with transverse spin-glass order. At lower temperatures Fe-Zr undergoes a further transition to a state in which the spin-glass order in the transverse direction is frozen, without the ferromagnetic order (often referred to, erroneously, as a re-entrant spin-glass by imperfect analogy with superconductivity transitions). The two ramagnet (PM) 4 FM and ave been ineasured by a variety of tecliniques including Mossbauer spectroscopy, magneization and muon spill 1995; Ryan et al., 1998,
Figure 22 Magnetic phase diagram of amorphous Fe-Zr (Ryan et al., 2000) showing data obtained by (i) muoii spin relaxation, (ii) ac-susceptibility and (iii) “Fe Mossbauer spectroscopy. T, aiid T,, correspond to the transitions shown m Figure 21, reproduced with permission of American Physical Society
0I
%w#
t
I
I
I
tt
~ ~ ~ 23 u rMagnetic e phase diagram of amorphous Fe-Ru-Zr (Ryan rt al., 1998) showing data obtained by (i) acsusceptibility, (ii) neutron depolarization, (iii) magnetometry (Arrott plots) and (iv) 57FeMossbauer spectroscopy. T,, is the temperature at which a break in the temperatme dependence of the hyperfine field measured by Mlissbauer spectroscopy was observed. Thus, T,, corresponds to Txy in Figures 21 and 22, reproduced with permission from Elsevier Science
Magnetic Phase Diagrams
Y
I (1
61001
I
I
li I
183
field. Gignoux and chmitt (1995) have reviewed the effects of such fundamental interactions as crystal-field effects, quadrupolar interactions and bilinear exchan frustration in causing these t ~ a n s i t i o ~ ~ . In Figure 24 we show the single-crystal magnetization curves obtained on tetragonal DyGozSi:! where two field-induced ~ e t a m a ~ n ~transition$ tic c-axis are observed (Iwata et al., 1990) behaviour has becn observed in TmGa3 by d.(1987) where q u ~ d r u ~ o l ainteraction^ r are responsible for the etam magnet ism. ignoux and Schniitt (1995) have also coiisidered the state o f theoretical work on these processes and the ~greementbetween e ~ e r - i m ~ r o v iexperimental n~ and theoret~ca~ techniques.
clusio Magnetic phase diagram of DyCo,Si, (lwata et al., 1990), reproduced with permission from Elsevier Science
2000). In Figure 22 we show the magnetic phase diagram of a-Fe-2.3 which includes all these data. As the Fe concentration increases the two transitions approach each other, as expected from the spin-glass mean-~eld treatments described earlier (Figure 20). Eventually, the two transitions merge and thcre is a single magnetic transition from paramagnet directly to spin-glass. ~nfortu~iately, it has not proven possible to prepare fully amorphous samples with Fe concentrations beyond the critical concentration. However, by partially substit~tingRu for Fe up to 5 at.% Ru, Ryan et al. (1998) were able to study the cross-over froin FM to SG since the addition of nonmagnetic Ru leads to a rapid increase in frustration. In Figure 23 we show the magnetic phase diagram (zerofield) of ainorplzous a-Feg+xRuxZrio showing susce~tibility,magnetometry, neutron depolarization and Mossbauer data, which clearly map out the PM 4SG and PM -+ FM -+ FM + SG regimes with a critical Ru ~o~centration of 2.5 at.%.
In rare-earth intermetallic compounds in which only the R sublattice is magnetic, numerous types of metam~gnetictransitions have been found. use the most general sense of the word metamagnetic to refer to the breaking of an antiferromagnetic structure usually due to the application of a magnetic
The determination of the magnetic phase diagrams of rare-earth, transition-metal intermetallic compounds provides invaluable data which enable one to study such fundament~linteractions as fields, quadrupolar ordering, etc. understanding of the magnetic behaviour of those inter~etallicswhere the exchange int~ractionis larger than the crystal-field interaction, such as is the case wi tli permanent-magizet nia terial s. tallic compounds in which this criterion does not hold continue to provide a challenge to our understanding. Besides providing informalion on the fundamentals of the magnet~smof such i n t e ~ e t a l l ithe ~ ~deter~ina~ tion of magnetic phase dia~ramsi s also related to t potential application o f compouiids such as NdzFe14 as permanent magnets.
s Asti, G., and Bolzoni, F. (1980). .I. Itir~gn.M L ~ ~Mater., E. 29 Blanco, J. A., Cignoux, D., Schniitt, D., and Vettier, G. (1991). J. Magn. Magn. Mat Cadieu, F. J., Wegde, H., Rani aivarathna, A., and Chen, K. (1991). Appl. Phys. Cadogan, J. M. (1996). J . Phys. Cadogan, J. M., Cavlgan, J. P., (1988). J . Phys. F: ~ ~ tPhys a l Cadogan, J. M., and Li, H. S . (1992). J. ~ ~Magn, g ~ ~~ t e .r . ~ 110, L20. Campbell, S. J., Cadogan, J. M., Zhao, and Li, H. S. (1999). J. Phys.. Con& ~
Cheng, S. F.. Deniczyk, R. G., Laughlin, D. E., and Wallace, W. E. (1990). J, ~ a g n Mcl~n. . iwclter.,
87, L251-4.
Nikitm, S. A., Tishin, A. M., Kuz'iin, M. D., and Spiclikm, Yu. I. (1991). P h j ~Letr, . A, Palstra, T. M. M., ~ i e u w e n h u y ~ G., J., Mydosh, J. A., and Buschow, K. H. J. (1985). Phys, Riev. B, 3
University Press, Ithacca, New York. Ren, H., and Ryari, D. H. (1995). Phys. Rev.B, Rossat"Mignod, J. (1986). ~ e t h o o~f s~ x ~ e r i ~ e Physzcs, n~al Vol. 23, Academic Press, New York. Rossat-Mignod, J., Burlet, P., Villain, .J,, Bartholin, H., Wang, T. S., Florence, D., and Vogt, 0..(1977). Pbtys, Rev. B, 16, 440. Rotli, W. L. (1995). I ~ ~ ~ r Compounds: ~ e ~ ~ Vol. l l 1, ~ ~ Principles. Chapter 19 (eds, J. El. Westbrook, and R. L. Fleischer). Wiley, New York. Ryan, D. I-l. (1992). Recmt Progress in an do^ Magnets, Chapter 1 (ed. D. H. Ryaii). World Scientific, Singapore, pp. 1-40. Ryan, L). H., Tun, Z., and Cadogan, J. M. (1998). J . M4xgn. Magn. Mater., 177-1 Ryaii, D. H., Cadogan, J. M.$and van Lierap, J. (2000~.Pbtys. Rev. B, 66, 6816. Shirane, G. (1959). Actcl Cryst., 1 Hu, B. P.. Li, H. S., Suii, H., tawler. J. F., and Coey, J. M. D. Shull, C. C., and Smart, J. S. (19 lid State ~ o ~ ~76,~587. ~ n . , 995). In t e r ~ e ~ ~ l l i c Stadel~aier~ H. H., and Reinsc T. (1964). Solid Stafe ~ ~ y s i c16, s , 227. ~ o ~ p o Vol. u n 2, ~ ~Practice Iwata, N., Honda, K., Shigeoka, T., Hashimoto, Y., and Westbrook, atid R. L. Fleischer). Wiley, New York. Magn. Magn, Muter., 90-93, 63. Stevens, E(. W. H. (1952). Proc. Phys. Soc., ., Gallen, E., Das, B. N., Liou, S. H., ith, W., and Thompson, J. E. (1954) Proc. Xoy. Soc., ~ ~ ~ i iR. a n(1986). , J ~ ~ g Magn. n . 362. ouvel, J. S. (1995). I n t e r ~ e ~ a I l i C c o ~ p Vol. ~ ~ 1,~ n ~ ~ ~A. (1992). J. Alloys and Compo Szytula, A., and Leciejewicz, J. (1994). P ~ ~ n ~ i p Chapter l e * ~ , 40 (eds. J. €3. Westbrook, and R, L. Structures and Magne fic Pro~ertie.~of Rare Eurth Fleischer). Wiley, New York. I n ~ e r ~ n e t u l lCRC i ~ ~ , Press Inc., Boca Raton. and Cadogan, J. M. (1 992). Solid State Cornmun., Thornson, J. R., Cuo, H., and Grant, M. (1992). Venturini, G., Welter, R., (1995). J . Magn. Magn. Zhang, L, V., Pourarian, Magn. Magn. Mater., 7B,203. Zhou, R. J., Kapusta, Cz., Rosenberg, M., a K. H. J. (1992). J . Alloys and C o ~ ~ o 1~ ? i ~ , A ~ s t e r d a pp. ~ , 493-624. Jersey. p. 37. Enz, U. (1960). P~yszca, Franse, J. J. M., and Radwanskr, R. J. (1996). Rare-E(~rtl~ Iron ~ ~ r ~ ~ c l~ ?c ligen ~e tts Chapter , 2 (ed. J. M. D. Coey). Oxford, pp. 58-158. Schmitt, D, (1995). J. Alloys and 423. Topics in Applied Physics Volume 5: ectros~opy, ~~ringer"Verlag, Berlin, Heidel~erg. Goodenough, J. B. (1963). Mclgriefismand the Chemical Bond, Wiley, New York. Herbsl, J, F. (1991). Rev. Mod. Phys., Hu, B. P., Li, H. S., Gavigan, J. P., ancl . C o ? ~ ~Matter, e n ~ 1, ~ 755. ~ . D., and Gavigan, J. P. ~
Chapter 10 Calculation of
ase Diagrams
Department of Materials Science, University of Culifornia, Berke€ey, CA, USA
1. Introduction
A phase diagram is a graphical object indicating phase relationships in thermodynamic space. Usually, one coordinate axis represents temperature; the others may represent pressure, volume, concentrations of various components, and so on. Here, we shall be concerned only with temperature-concentration diagrams, for the sake of illustration limited mainly to binary (twocomponent) systems. Since more than one component will be considered, the relevant thermodynamic systems will be alloys, by definition, of either metallic, ceramic, or semiconductor materials, the emphasis being placed primarily on metallic alloys. Phase diagrams can be classified broadly into two main categories: experimentally and theoretically determined. The object of the present chapter is the theoretical determination, i.e. the calculution of phase diagrams, ultimately, their prediction. But a calculation of phase diagrams can mean different things: prototype, fitted, and first principles. Prototype diagrams are calculated under the assumption that energy parameters are known a priori, or given arbitrarily. Fitted diagrams are those whose energy parameters are fitted to known experimentally determined diagrams or to given empirical thermodynamic data. First principles diagrams are calculated on the basis of energy parameters calculated from essentially only the knowledge of the atomic numbers of the constituents, hence by actually solving the relevant Schrodinger equation. Such is the ‘Holy Grail’ of alloy theory, an objective not yet fully attained, although great strides have been made in that direction recently. Actually, theory enters as well in the experimental determination of phase diagrams, as these diagrams
indicate not merely the location in thermodynamicspace of existing phases, but must conform to rigorous rules of thermodynamic equilibrium (stable or metastable). The fundamentd rule of equality of chemical potentials indeed imposes severe constraints on the graphical representation of phase diagrams, while also permitting an extraordinary variety of forms and shapes of phase diagrams to exist, even for binary systems. That is one of the attractions of the study of phase diagrams, experimental or theoretical: their great topological diversity subject to strict thermodynamic constraints. In addition, phase diagrams provide essential information for the understanding and designing of materials, and so are of vital importance to materials scientists. For the theoretician, firstprinciples (or ab initio) calculations of phase diagrams provide enormous challenges, requiring the use of advanced techniques of quantum and statistical mechanics. The main portion of this chapter covers basic principles (Section 2), and is followed by one example of application to the AI-Li phase diagram (Section 3). A discussion (Section 4) summarizes the principal results and compares qualitativelythe various methods described in the main portion of the text. The reader will profit by also consulting chapters of Volume 1 of this series on IntermeialEic Compounds, Principles (Westbrook and Fleischer, 1995). In particular, additional information on mean-field methods applied to phase diagram construction (Section 2.2 of the present chapter) will be found in Chapter 5 of Volume 1 (Ellner and Predel, 1995), and more detailed treatments of electronic structure calculations (Section 2.5) will be found in Chapter 2 (Turchi, 1995) and Chapter 3 (Carlsson and Meschter, 1995) of Volume 1.
Intermetallic Compounds: Vol. 3, PrincipEes and Practice. Edited by J. H. Westbrook and R. L. Fleischer. 02002 John Wiley & Sons, Ltd.
I86
Bondiag and Sta~ility
he ther~odynamicsof phase equilibrium were laid ibbs over 100 years ago (Gibbs, 1875-1 878). s was strictly a ‘black box’ thermodynamics in the sense that each phase was considered as a uniform cont~nuumwhose internal structure did not have to be specified. If the %lack boxes’ were very small, then interfaces would have to be considered, which Gibbs 1 without having to describe their
provided in free energy~oncentrationspace by the coinrnon tangent rule, in binary systems, or cominon tangent hyperplane in multicomponent systems. A very complete account of multicomponent phase equilibrium and its graphical ~nterpretationcan be found iii the book by Palatnik and Landau (1964), and summarized in more readable form by Prince (1966). The reason that equation (1) leads to a common tangent construction rather than the simple search for the minima of free energy surfaces is that the equilibria represented by (1) are constrained minima, with coiistraint given by
lmholtz) free energy F (=I E - TA‘, perature and S is entropy), and
II
ZXI=:
I= 1
where 0 6 XI (of P, V, ir, say), even for the case of fluids or hydroally stressed solids, as considered here, are ally not known. Analytical functions have to be inv~nted’and their parameters obtained from experiment. ]If suitable free energy functions can be obtained, then correspon~ingphase diagrams can be constructed from the law of equality of chemical potentials. But what if the functions themselves are unreliable and/or the values of the parameters iiot determined over a region of thermodynamic space? Then to studying in detail the physics of the therinodyn~niicsystem under consideration, investigating its internal structure, and relating microscopic qua~titiesto ~acroscopicones by the techniques of statistical mechanics. This section will very briefly review some of the methods used, at various stages of the ‘~~lcu1ation’ of phase allow the elaboration of of which may be found in ~ ~ z review y ~ articles i ~ ~(de ontaine, 1979 and 1994), in a more extended version of the present article (de Fontaine, 1999), and in refe~encescited . A historical approach is given in the author’s Turnbull lecture (de Fontaine, 1996).
he conditioii of phase equilibrium is given by the set
(1) ~esignatiiigthe equality of chemical potentials (p) for c~~mpon1 e ~(== t 1 to n) in phases 01, p, . . . and A. ~ ~ n v e n i e ngra~hical t descrip~ionof equation (1) is
1
(2)
<1
designates the concentration of y the properties of the xjs, it follows that a convenient representation of concentration space for an YI-component system is that of a regular simplex in (n - 1)~dimensionalspace: a straight line segment of length 1 for binary systems, an equilateral triangle for ternaries (the so-called Gibbs triangle), a regular tetrahedron for ~ ~ a t e r n a r i e sand , so on (Prince, 1966; Paiatnik and Landau, 1964). The temperature axis is then constructed oithogoiial to the simplex. The phase ~ i a g r a m space thus has dimensions equal to the (non-indepeiident) number of components. Although heroic made in that direction (Cayron, 196 is clear that the full graphical representation of temperature-composition phase diagrams is practically impossible for anything beyond ternary systems, and awkward even beyond binaries. One then resorts to constructing two-dimensional sections, isotherins and isopliths (constant ratio of components). The variance f (or number of thermodynamic degrees of freedom) of a phase region where 4 ( 3 3) phases are in equilibrium is given by the fzimous Gibbs phase rule, derived from equations (1) and (Z), f = YI - @
+1
(at constant pressure)
(3)
It follows from this rule that when the number o f phases is equal to the number of components plus one, the equilibrium is invariant. Thus, at given pressure, there is only one, or a finite number of discrete temperatures at which y1 + 1 phases may coexist. Let us say that the set of y 1 + 1 phases in equilibrium is C == { E , p, . . ., A}. Then just above the invariant t e ~ p e r a t ~ rae ,particular subset of Z: will be found in the phase diagram, and just below, a different subset. lt is simpler to illustrate these concepts by a11 example. In isobaric binary systems, three coexisting
Calculatjon of Phase Diagrams phases constitute an invariant phase equilibrium, and only two topologically distinct cases are permitted: eutectic-type and peritectic-type, as illustrated in Figure 1. These diagrams represent schematically regions in teniper~ture~onceiitrationspace in a narrow temperature interval j list above and just below the three-phase coexistence line. Two-phase monovariant regions (.f= 1 in equation (3)) are represented by sets of horizontal (isothermal) lines, the tie-Zine‘~(or co-nodes), the extremities of which indicate the equilibrium concentrations of the coexisting phases at the temperature considered. In the eutectic case (Figure 1a), the high-temperature phase A (often the liquid phase) ceases to exist just below the invariant temperature, leaving only the (a+ /I) twophase equilibrium. In the peritectic case (Figure Ib), a new phase, p, makes its appearance along with one or the other type of two-phase material (a p) or (p A). It is seen from Figure 1 that, topologically speaking, these two cases are mirror images of each other, and there can be no other possibility. How the full phase diagram can be continued will be shown in Section 2.2 in the eutectic case calculated by means of ‘regular solution’ free energy curves. Ternary systems exhibit three topologically distinct possibilities: eutectic-type, peritectic-type and ‘intermediate’. In the ternary eutectic case, three 3-phase triangles come together to form a larger triangle at the invariant temperature, just below which the A phase disappears, leaving only the CI + p + y onov variant equilibrium. The peritectic case is, as in the binary case, its topological mirror image: the a + B + y triangle splits into three 3-phase triangles. In the ‘intermediate’case, the invariant is no longer a triangle but a quadrilateral; just above the invariant temperature, two triangles meet along one of the diagonals of the quadri~ateral,just below, it splits into two triangles along the other diagonal. For quaternary systems, the graphical representation is more difticult to describe, since the possible
+
+
187
invariant equilibria, of which there are four, eutectictype, peritectic-type, and two intermediate cases, involve the merging and splitting of tetrahedra along straight lines or planes of 4- or 5-vertex (invariant) figures (Prince, 1966; Cayron, 1960). For yet highercomponent systems, the full graphical r~presentationis just about hopeless (Cayron, 1960). The commercial firm Thermocalc (Jansson et al., 1993) does provide software which constructs two-dimensional sections through multidimensional phase diagrams, these diagrams themselves being constructed analytically by means of equation (1) applied to semi-empirical, multicomponent, free-energy functions. The reason for dwelling an the universal rules of invariant equilibria is that they play a fbdamental role in phase diagram determination. Regardless of the method employed, experimental or computational, prototype, fitted or ab initio, these rules must be respected, and often give a clue as to how certain features of the phase diagram must appear, rules which are not always respected even in published phase diagrams. They are, of course, respected in, for example, the three-volume compilation of evaluated experimentally determined binary phase diagrams, published by the American Society for Metals (Binary Alloy Phase D i a g r a ~ . ~1990). ,
The diagrams of Figure 1 are not even pro to types', they are schematic: the only requirements imposed is that they represent the basic types of phase equilibria in binary systems, and that the freeh~nd~drawn phase regions obey the phase rule. To be a little more quantitative, let us now look at the construction of a prototype binary eutectic diagram based on the simplest analytical free energy model, that of the regular solution. First, some useful general definitions. Consider some extensive thermodynamic quantity, such as energy, entropy, enthalpy, or free ener
F~~M 1 ~Binary e eutectic (a) and peritectic (b) topology near the three-phase invariant e q u i l i b r i ~ ~
188
Bonding and Stubility
For condensed matter, it is custoniary to equate the Gibbs and Helrnholtz free energies. That is not to say that equilibrium shall be calculated at constant volume, merely that the Gibbs free energy is evaluated at zero pressure; at reasonably small pressures, at or below the atmospheric, the internal state of condensed phases cbange very little with pressure. The total free energy of a binary solution AB for a given phase is then the sum of an ‘unmixed’ contribution, which is the concentration-weighted average of the free energy of the pure constituents A, I1, and a mixing term which takes into account the mutual interaction of the constituents. Therefore we have: (4)
the excess enthalpy depends quadra ticnlly on conceiitration. Then we have:
F*. = x(1 - X)W
(8)
where W is some generalized (concentration- and temperature-independent) interaction parameter. For the purpose of constructing a prototype binary phase diagram in the simplest way, based on the regular solution model for the solid (a) and liquid (A) phases, we write the pair of free energy expres$ions: J;f = x( 1 - X)W,
+ k B T [ xlog x + (1 - x) log( 1 - x)] (9a)
and
with F~lll X A F A
+ XBFB
(5)
The latter contribution, which we call the ‘linear term’ because suck is its dependence on concentration, contains thermodynaniic infor~ationpertaining only to the pure elements, The mixing term is the difficult one to calculate as it contains the important configurational energy and entropy of mixing contributions. The simplest mean field approximation regards Fn,,,as a slight deviation from the free energy of a completely random solution, i.e. one that would obtain for noninteracting particles (atoms, molecules). In the random case, the free energy is the ideal one, consisting oiily of the ideal free energy of mixing: F,d
(6)
-TSl,j
since the energy (or enthalpy) of mixing of noninteracting particles must vanish. The ideal configurational entropy of mixing per particle is given by the universal function
si, = - N k B ( X A
log X A f
xB log -“CB)
(7)
where N is the number of particles and k~ is Boltzinann’s constant. Expression (7) is easily geiieralized to multicomponent systems. What is left over in the general free energy is, by defi~ition,the excess term, in the mean-~eldempirical approximation taken to he a polynomial in concentration and temperature &(x, T ) . Here, since there is only one independent concentration because of equation (21, one writes x = xg, the concentration of the second constituent, and XA = 1 - x in the argument of F. In the regular solution model, the simplest formulation of the mean-field approximation, the simplifying assumption is also made that there is no t e ~ p e ~ a t udependence re of the excess entropy and that
These equations were arrived at by subtracting the linear term (equation (5)) of the solid from the free energy functions of both liquid and solid (hence the As in equation (gb)), and by dividing through by N, the number of particles. The lower-case letters symbols in equations (9a) and (9b) indicate that all extensive thermodynamic quantities have been normalized to a single particle. The (linear) A h term was considered to be temperature-inde~endent~and the As term was considered to be both temperature- and concentrationindependent, assuming that the entropies of melting of the two constituents were the same. Free energy curves for the solid only (equation (9b)) are shown at the top portion o f Figure 2 for a set of normalized temperatures (C= kB T/ ( w ( ) ,with wo 0. The locus of common tangency points gives the miscibility gap (MG) type of phase diagram shown at the bottom portion of Fi ure 2. Above the critical point ( t = O S ) , the two phases a and p are structurally indistinguishable. As and the constants a and b in A h = a 4bx were fixed so that the free energy curves of the soIid and liquid would intersect in a reasonable temperature interval. Within this interval, and above the eutectic (a -t- + A) temperature, common tangency involves both free energy curves, as shown in Figure 3: the full straight line segments are the equilibrium common tangents (filled circle contact points) between solid (flill curve) and liquid (dashed curve) free energies. For the liquid, we took I W RI< wo. The dashed common tangent (open circles) represents a metastable MG e ~ u i l i b r i uabove ~ the eutectic. Open square symbols in Figure 3 mark the intersections of the two free energy curves. The loci of these intersections on a phase diagram trace out the so-called To
Calculation of Phase Diagram
1813
0.0
-0.1
0% ion
0.b
i t
ility
kgT/lwl ~0.35
F ~ 3 ~Free ~energy ~ curves e for the solid (full line) and liquid (dashed line) according to equations (9a) and (9b)
0.6 0.
I--
0.1
indicated normalized t e ~ p e r a t u ~ and ~ s ) resulting miscibility gap
lines where the etast stable) d~sordered-state free energies are equal. Sets of both liquid and solid free energy curves are shown in Figure 4 for the same reduced temperatures ( t ) as were given in Figure 2. The phase diagram resulting from the locus of lowest common tangents (not shown) to curves such as those given in Figure 4, is shown in Figure 5. The melting points of pure A and B are respectively at reduced temperatures 0.47 and 0.43; the eutectic is at about 0.32.
This simple example suffices to demonstrate how phase diagrams can be generated by applying the equilibrium conditions given by equation (1) to model free energy functions. Of course, actual phase diagrams are mucl? more complicated, but the geiieral principles are always the same. Note that in these types of calculations the phase rule does not have to be imposed ‘externally’; it is built into the equilibrium conditions, indeed follows from. them. Thus, for example, the phase diagram o f Figure 5 clearly belongs to the eutecticclass illustrated schematicallyin Figure 1a. Peritectic systems are often encountered in cases where the difference of A and €3 melting temperatures is large with respect to the average normalized melting temperature t. The general procedure outlined above may, of course, be extended to mult~component systems. What if the interaction parameter W were negative? Physically, this means that unlike (A‘bonds’ are favored over the average of like (A-A, B-€3) ‘bonds’. The regular solution model cannot do justice to this case, so it i s necessary to introduce , ~ ~ ~ Z a ~ one t i c or ~ s more , of which will be preferentially occupied by a certain constituent. In a sense, this atomic ordering situation is not so unlike that of ~ ~ s ~ ~ f f ~ uillustrated t i ~ n , in Figure 3, where the two types of atoms separate out in two distinct regions of space: in the ordering case, the separation is between two i~iterpenetratingsublattices. Let there be two distinct
u
~
190
Bonding and Stability
Free energy curves, as in Figure 3, but at the iiidicated reduced temperatures
t,
generating the phase diagram of Figure 5
Calculation of Phase Diagrams
191
necessary to write Fx,as a pol~nomialof degree higher than the second in the relevant concentration variables, the temperature T also appearing, usually in low powers. The extension of the GBW method to include higher-degree polynomials in the excess free energy is the technique favored by the (see journal) group, a group devoted to the very useful task of collecting and assessing experimental t h e ~ o d y n a m i c data, and producing 0.25 calculated phase diagrams, agreeing as closely as possible with experimental evidence. In a sense, what 0.2 this group is doing is ‘ther~odynamicmodeling’, i.e. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 storing of thernio~yflami~data in the form of A ~~nc~n~ra~i~n B mathematical functions with known parameters. One Eutectic phase diagram generated from curves such may ask, if the phase diagram is already known, why as those of Figure 4 calculate it? The answer is that phase d i a g r a ~ shave often not been obtained in their entirety, even binary ones, and that calculated free energy functions allow sublattices, a and p (the same notation is purposely some e x t ~ ~ p o l ~ into ~ othe n u i i k i i o ~Also, ~~, ~ i i ~ w ~ i used as in the phase separation case). Tlie pertiiieiit free energies explicitly, allows one to extract many concentration variables are then (only the €3 concenother useful thermodynamic functions instead of only tration needs be specified) x“ and xp, wliich may be the phase diagram itself as a graphical object. Another each written as a linear combination of x, the overall useful, though uncertaiii aspect is the extrapolation of concentration of B, and q , an appropriate long-range known lower-dimensional diagrams into unknown order (LRO) parameter. In a binary ‘ordering’ system , o ~ ~ i with two s~iblattices~ there are now two i i i ~ e p ~ n d e n ~higher-dimensional ones. ~ i ~ ~ ~p l ~l ~~software can plot out two-dimensional sections through multicomposition variables: x and q. In general, there are one less order parameters than there are sublattices component systems. Such software is available introduced. When the ideal entropy, also containing commercially from Thermocalc (Jansson et al., 19931, linear combinations of x and q, multiplied by -7’is based in Stockholm. added on, we obtain so-called (generalized) GorskyIt is important to note, however, that the general~ p ~ g ~ (GSW) - ~ free i energies. ~ ~ ~ TQ ~ construct ~ ~ sa izatioiis just described - sublattices, Fouier ~ ~ a ~ s f ~ protQtype phase diagram, possibly featuring a variety polynomials - do not alter the degree of sophistication of ordered phases, it is now necessary to minimize of the approximation, which remains decidedly mean these free energy functions with respect to the LRQ field, that is, wliich replaces the averages of products parameter(s) at given x and T‘, then to construct (of concentrations) by products of averages. Such a common tangents. procedure can give rise to certain unacceptable Generalization to ordering is very important as it behavior of calculated diagrams, as explained in allows treatment of (ordered) compounds with extenSection 2.4. sive or narrow ranges of solubility. The CBW method is very convenient as it requires little in the way of computational machinery. When the GBW free energy is expanded to second order, then Fourier transThus far, the treatment has been restricted to a ‘black formed, it leads to the ‘method of Concentration box’ approach: each phase is coilsidered ns a themnowaves’, discussed in detail by Khachaturyan (1983), dynamic continuum, possibly in equilibrium with other with which it is convenient to study general properties phases. Even in the case of ordering, the approach is of ordering in solid solutions, particularly ordering still ~ f f c ~ o s c o peach i c , sublattice being also considered instabilities. However, to constructfitted phase diagrams as a thermodynamic continuum, possibly interacting which resemble those determined exper~ientally,it is with other sublattices. It is not often appreciated that, found that an excess free energy represented by a despite taking the crystal structure into ~ ~ n ~ i ~ e ~ ~ t quadratic form will not provide enough flexibility for in setting up the GBW model, the resulting free energy an adequate fit to theri~odynamicdata. It is then function still does not contain any geometrical 0.5
~~~~~~~
~~~~~~~
192
Bonding aPzd S ~ u ~ i l ~ ~ y
information: each sublattice could be located anyprocedure andlor using a ~ a m i l t o ~ ~based a n on where, and such things as coordination nuinbers can semi-enipirical potentials. To this we now turn: be readily incorporated in the effective iiiteractions W. deriving a variational method for the free energy, In fact, in the ‘mean-field ideal-entropy’ fomulawhich is at the heart of the cluster variation method tion, solids and liquids are treated in the same way: (CVM) (Kikuchi, 1951). termiiial solid solutions, compounds, liquids are The exact free energy F of a t~ermodynam~c system represented by similar ‘black-boxyfree energy curves, is given by and the lowest set of common tangents is constructed F = -kBTln at each temperature to generate the phase diagram. With such a simple technique available, which with partition function generally produces formally satisfactory results, why = e-E(state)/ksT (1 1) or several reasons: (I) the mean-field states overestimates the coiifigurational The sum over states in equation (1 1) may be partially entropy and enthalpy cont~b~itions, (2) the method decoupled (Ceder, 1993): often produces qualitatively incorrect results, particularly where ordering phenomena are concerned (de z + e-Ftat ( n ) l k ~ T (12) e (SRO) cannot Foutaine, 19’79), (3) s ~ o r t - r a n ~order {b) dyn be taken into account, (4) the CALPHAD method where cannot make the~odyiiamicpredictions based on ‘atornistics’. a much more elaborate ~ ~ c ~ o ~ c o ~ ~ ~ theory is re for the purpose of calculating ah irzitio phase diagrams. represents the sum of a replacive aiid a disp~u~ive To set up such a formalism, on the atomic scale, we energy. The former is the energy which results from the must define a reference lattice or structure, fcc, bcc, or rearrange~entsof types of atoms, still centered at their hcp, for example. The much more difficult case of associated lattice sites; this energy contributioii Iias liquids has not yet been worked out. Also, for also been called ‘ordering’, ‘ideal’, ‘~onfig~rational~, simplicity, we shall consider only binary alloys ‘chemical’. The displacive ener y is associated with static atomic displacernents. These displacements (A-B). At each lattice site (p), define a spin-like nfigurational operator bp equal to + l if atom of type themselves may produce volume effects (change in the volume of the unit cell), cel~~externaleffects is associated with it, -1 if B. At each site we also (change in shape of the unit cell at constant volume), attach a ( t ~ r e e - ~ ~ ~ e n s i ovector n a l ) up which describes and cell internal effects (relaxation of atoms inside the lacement (static or dynamic) of the atom from unit cell away from their ideal lattice positions) lattice site. For given configuration o (a boldfaced (r indicates a vector of No, = f l components, (Zunger, 1994). The sums over dynainical degrees of freedom may be replaced by Boltzmann factors o f the ven configuration in a supercell of N lattice sites), an appropriate ~amiltonian is then type Fdyn.(o) = ~ d ~ ~ ~ . (TSdyn.(~) b) to obtain finally a new partition function constructed, and the energy E is calculated at lir = P == 0 by quantum mechanical means. In grinci=;: e-*t4/ksT (14) ple, this program has to be carried out for a variety of In1 supercell configurations, lattice parameters and interwith ‘hybrid’ energy nal atomic displ~cements; then configurational averages are taken at given T and P to obtain exp~ctation values of appropriate t he~ odyna m i c functions, in particrtlar the free energy. Such calculaEven when considering the simplest case of leaving out tions must be repeated for all competing crystalline static displacive and dynai~icaleffects, and writing the phases, ordered or disordered, as a function of average replacive energy as a sum of nearest neighbor (nn) pair concentration x, and lowest tangents constructed at interactions, this lying ~ ~is i~possible ~ e tol ‘solve’ in various temperatures and (usually) at P = 0. As three dimensions, i.e. the suinmation in. the partition described, this task is an impossible one, so that rather function cannot be expressed in closed form. One must drastic a~~roximations must be introduced, such as then resort to Monte Carlo simulation or to variausing a variational principle to calculate the free tional solutions. To these several energies will correspond entropy contributious: particularly a energy instead of the correct partition function
+
z
Calc~lajionof Phase ~ ~ u g r a ~ s configurational entropy associated with the replacive energy, and a vibrational entropy associated with dynamical displacements. Let us consider the configuratio~alentropy. is to write the partition The idea of the C function, not as a sum o all possible configurations, but as a sum over selected cluster probabilities (x) for small groups of atoms occupying the sites of 1-, 2-, 3-, 4-, . . ., many-point clusters, such as pairs, triplets, q u a ~ r ~ p l .e .~ .~ of , lattice sites, for example. The transfoi~~~ion
z=
e-E(g)/kB’f’ + (4
cg( )e-E(x)/fcB = ceT
{XI
F(x)/!’
BT
{XI
(16 ) or number of ways the specified values There corresponds a configurational entropy
(17) hence a free energy F ( 5: E - TS),which is the one that appears in equation (16). The optimal variational free energy is then obtained by minimizing F ( x ) with respect to the selected set of cluster probabilities, and subject to c o ~ s i s t e n cconstraints. ~ The resulting F ( x * ) , with x* being the values of the cluster probabilities at the minimum of A?@), will be equal to or larger than the true free energy, hopefully close enough to the true free energy when an adequate set of clusters has been chosen. Kikuchi (1951) gave the first derivation of the g ( x ) factor for various cluster oices, followed by the more algebraic derivations of arker (1953) and Hijmans oer (1955). The simplest cluster approximation is of course that of the point, i.e. that of using only the lattice point as cluster. The symbolic formula for the complexion in this approximation is such that, inserted in the configurational entropy formula (equation (17)),it produces precisely the ideal entropy given, for binary systems, by the standard expression Thus the mean field entropy is identical to the C point a~prox~mation. To improve on the approximation, we need to go to higher clusters, pairs, triplets and so on. Of course, the result in^ entropy expressions will be quite a bit more complicated, but today, CVM entropy formulas can be derived ‘automatically’, for arbitrary lattices and cluster schemes, by computer codes based on group theory consi~erations.The choice of the proper cluster scheme to use is not a simple matter, although there now exist heuristic methods for selecting ‘good’ cluster
193
combinations (Finel, 1989; Vul and de Fontaine, 1993). The realization that config~rational entropy in disordered systems was really a many-body tbermodynamic expression led to the introduction of cluster es in free energy fLinctionals. variables led to the development of a very useful c l ~ s t e ~ algebra, to be described very briefly here (see the origiiial article (Sanchez et al., 1984), or various reviews (de Forrtaine, 1994, for e x a ~ p l e )for more details). The basic idea was to develop complete orthonormal sets of cluster ftinctions for expanding arbitrary functions of confi~urations,a sort of Fourier expansion for disordered systems. For s i ~ ~ ~ i cwe ~ty, shall look here only at binary systems, without explicitly considering sublattices. We shall see that the cluster algebra, applied to the replacive (or configurational) energy leads qujte ~ a t ~ r a l lto y a precise definition of effective cluster i ~ t e ~ ~ c t i o n s , similar to the pherromenol~gical w parameters of mean field equations (8) and (9). With such a rigorous definition available, it will be in principle possible to calculate those parameters from ‘first principles’, i.e. from the knowledge of only the atomic numbers of the constituents. Any function of configuration f ( o) can be expanded in a set of c l ~ s t ~ ~ . f ~ n cast ifollows o~s ( 1984): (18) CI
where the s u m ~ a t i o nis over all clusters of lattice points (‘a’ designating a cluster of fzcc points, of a certain geometrical type: tetrahedron, square, . . .), Fa are the expansion coefficients, and the “P, are suitably defined cluster functions. The cluster functions may be chosen in an infinity of ways but must form a complete set (Asta et al., 1991; Wolverton et al., 1991a; Sanchez, 1993). In the binary case, the cluster f u ~ c t ~ o may n s be chosen as products of o variables (= k l ) over the cluster sites. The sets may even be chosen ~ ~ t l ~ o n o r n i a l , in which case expansion (21) may be ‘inverted’ to yield the cluster coefficients
F; = PO
z=
J’(o)@CI(o)
(@as
f
(1%
(T
where the summation is now over all possible ZN configurations, and po is a suitable nor~alization factor. More general formulations have been given recently (Sanchez, 1993), but these simple formulas, (18) and (191, will suffice to illustrate the method. Note that the formal is^ i s exact and m o ~ e o v ~ r
194
Bonding and Stability
computationally useful, if series convergence is sufficiently rapid. In turn, this means that the burden and difficulty o f treating disordered systems can now be carried by the determination of the cluster coefficients Fa. An analogy may be useful here: in solving linear partial differential equations, for example, one generally does not ’solve’ directly for the unknown function, one instead describes it by its representation in a complete set of functions, and the burden of the work is then carried by the ~ e t e ~ i n a t i oof n the coefficients of the expansion. The most iniportant application of the clusterexpansion formalism is surely that of the calculation of the configurational energy of an alloy, though such theirnodynamic qtiantities as molar volume, vibrational entropy, elastic moduli and so on, as a function of configuration, can be obtained as well by this technique. In particular, application of equation (18) to the configurational energy E provides an exact expression for the expansion coefficients, called effective cluster interactions, or ECIs, V,. In the case of pair interactions (for lattice sites p and q, say), the effective pair i~teractionis given by
where ~!?IJ (I, 5 = A or E) IS the average energy of all configurations having atom of t.yp I at site p a i d J at y. ence it is seen that the If, parameters, those required by the Ising model thermodynamics, are by no means “pair potentials’, as they were often referred to in the past, but differences of energies, which can in fact be calculated. Generalizations of equation (20) can be obtained for multiplet interactions such as Vpqr as a function of AAA, AAB, etc., average energies, and so on. How does one then go about calculating the pair or cluster interactions in practice? One method makes use of the orthogonality property explicitly by calculating the average energies appearing in equation (20). To be sure, not all possible configurations (T are summed over, as required by equation (19), but a sampling is taken of say a few tens of configurations, selected at random around a given 13 pair, for instance, in a supercell of a few hundreds of atoms. Actually, there is a way to calculate directly the difference of average energies in equation (20) without having to take small differences of large numbers. Such a method i s called n~~ (DCA) the method of direct ~ o n ~ g z i r a t i oaveraging (Dreyssk et al., 1989; ~ o l v e r t o net al., 1991b, 1993; Wolverton and Zunger, 1994) It is unfortunately very computer intensive, and has been used thus far oiily in
the tight binding approximation of the ~amiltonian appearing in the Schrodinger equation. A convenient method of obtaining the ECls is that of the structure inversion method ( as the Connolly-Williams method from the names of those who originally proposed the idea (Connolly and Williams, 1983). It then turns out that the energy of a large-unit-cell structure can be obtained as a linear Combination of the energies of small-unit-cell structures, which are ~resum ab~y easy to compute, for instance by electronic structure calcu~ation.So what about electronic structure calculations? Section 2.5 gives a quick overview of standard techniques in the ‘alloy theory’ context, but before getting to that, let us already see the difference that the CVM makes, compared to the mean-field approximation, in the ~alculationof a prototype ‘ordering’ pkase diagram. 2.4
~
l
~
S
~
~
~
-
~
~
Thermodynamic quantities are macroscopic ones, actually expectation values of microscopic ones. Take the case of the energy; we need its expectation value ( E ) in cluster expanded form. For that we take the ensemble average of the general cluster expansion foimula (19) to obtain, per lattice point:
with correZatio~v a ~ ~ i adefined ~Z~~ by
the latter equality being valid for binary systems. The brackets indicate ensemble averages. The entropy, already an averaged quantity, is expressed in the CVM by means of cluster probabilities xor.These probabilities are related linearly to the correlation variables by means of the so-called configuration matrix (Sanchez and de Fontaine, 1978), the elements of which are most conveniently calculated by grouptheory computer codes. The required CVM free energy is obtained by combining energy (21) and entropy (17) contributions, and using Stirling’s approximation for the logarithm of the factorials appearing in the g(x) CVM expressions:
where the indices r and lr denote sequential ordering of the clusters used in the expansion, K being the order of
~
~
Calculation of’ Phase Diagrams
the largest cluster retained, and where the second summation is over all possible A/B configurations CQ of cluster k. The corre~at~ons c, are linearly independent variational parameters for the problem at hand, which means that the best choice for the correct free energy for tlie cluster appro~imation adopted is obtained by minimizing ( 3) with respect to the 5,. entropy expression are the socoefficients, which may be by a~propriategroup theory codes, as mentioned above. inimization of the free energy (23) leads to systems of simultaneous algebraic equations (sometimes as many as a few hundred) in the 5,. This task greatly limits the size of clusters that can he handled in practice. Note that, strictly speaking, the CVM is also a mean field formalisin but it does treat the ~ o r r e l a t i o ~(almost) s correctly for lattice distances included within the largest cluster considered in the ximation, and includes RO effects. Hence the is a ~ ~ l t i - s i mean te field model, whereas the MF is a siqgk-site model, the one we have referred to as the M F (ideal, regular solution, GBW, concentratioii wave, . . .) model. Of course the ‘point’ a p p r o x i ~ a t i o nor~ mean-field model, is very much simpler to handle than the ‘duster’ formalism. So how much is lost in terms of actual phase-diagram results in going from MF to CVN? That question was answered quite some time ago by exhibiting a very striking, yet siniple example, the case of ordering on the fcc lattice with only ~ r s t - n e i ~ h b o r eflective pair iiiteractions (de Fontaine, 1979). If one compares the calculated MF phase diagram constructed by the GBW mean field approxii~ation (Shockley, 1938), to that constructed by the CVM in tlie tetrahedron cluster approximation, it is seen that, even in a topological two diagrai~sare completely diflt‘erent: t diagram sliows a double second-order tra he central composition (XB = O S ) , whereas the CVM diagram shows three first-order transitions for the three ordered (L12-type ordered structure) and M phase diagram also shows two very small t~ree-phase regions which are actually peritectic-like, topologically, as in Figure 1b. There can be no doubt about which prototype diagram is correct, at least qualitatively: it is the CVM version, which in turn is very similar to the solid-state portion of the experimental Cu-Au phase diagram (Binary AZhy Phase ~ i a g ~ a ~1986; 7 z ~ in ~ ,this particular case, the first edition is to be preferred). The large discrepancy between the M F and CVM versions is mainly due to the fact that the basic ~eoinetricalfigure of the fcc
195
lattice is the nn equilateral triangle (and the associate ~ s t nn tetrahedron). Such a figure leads tca ~ where, as in this case, the first nn iiiteraction favors unlike atomic pairs. This reqL~ireme~t can be s a t ~ s ~ e d for two of the nil pairs making up the triangle, but the third pair must necessarily be a ‘like’ pair, hence the conflict. This frustration also lowers the transition temperature below what it would be in nonsystems. The cause of the problem with approach i s of course that it does not ‘kn the triangle figure and the frustr~tednature of its interdctions. Numerically also, the CVM contional entropy i s much more accurat~than the (MF), particularly if ~iigher-c~us~er approximations are used, accuracy being judged by ~ o m p a r i s o ~ with Monte Carlo simulations (Finel, 1999). The last sentence of this parag~aph begs the question: if the Monte Carlo ~ a l c u l a t i o ~are s the standard by which to judge CV results, why bother with clusters at all? Some resear~hers(see for example Wolverton and Zunger, 1995) ha to bother with the CVM at all. reasons not to rely entirely on comput~r~ i ~ u l a t i(1) o~: analytical methods are Ear less c o m ~ u t e r - ~ n t ~ and ~s~ve therefore much faster, (2) simulation methods are accurate but imprecise, analytical m e ~ ~ ~ are ods but inaccurate; that is to say that give results which are in principle correct but will be given to within a certain degree of ~ r e c i s i o whereas ~, the CVM will produce well-de~nedn u ~ b e r s(3) ~ if several competing phases are present, it is not often a simple matter to determine by simulati~nwhat phases are being examined, (4) c o ~ p ~ t a t i oofi i e ~ t r o ~ y hence free energy is not conveniently performed in simulation; simulation does not readily provide traceable free-energy curves, ( 5 ) ~ e t a s t a ~e~uilibria ~e can be calculated by cluster methods, not by the method. A technique which inay advantages of both cluster and suggested by Schlijper and mid (1989) but not used much since because of large storage r ~ ~ ~ r e n ion ei~t computers, a problem which is hardly restrictive ~ o ~ a ~ aThe y s .eth hod in question may be ~ a ~ a l e ~ hybrid one, as it combines aspects of both the C and MC simulation: the analytical free sion (23) is used, as in the classical cluster probabilities cCn, instead of bei minimization o f the free energy functional, are obtained by simply c o u n t i ~tlie ~ frequency of occurrence of the clusters of interest and inserting these values in foriiiulas such as (23). Avoidance o f the mini~izationstep, with its c o ~ v e r ~ e n cproblems, e is a
196
Bonding and Stability
big advantage of the hybrid method but, precisely because of its hybrid character, it is not as internally coiisistent as the ‘pure’ CVM. This undesirable feature was recently illustrated (Tepesch et al., 1998) for the case of ordering on the fcc lattice. In order to obtain correct phase equilibrium results, the authors found needed to be used, in int cluster combination. ver group-theory techiiiyues were wed to handle cluster algebra. The results agreed perfectly with , but entropies and free energies were given explicitly by an analytical expression, which is the great advantage of this combined MC/CVM procedure, in addition to the elimination of the minimization stage of the calculation. There are other benefits for using the cluster approach: the cluster expansion provides a rigorous formulation for the effective cluster interaction (ECI); see equation (20) and extensions thereof for multisite d multicomponent systems. That means for the replacive (or strictly configurational) energy can now be considered not only as fitting par~meters,but as quantities which can be rigorously calculated ab initio. Such atomistic computations are very difficult to perform, as they involve electronic structure calculations~ but much progress has been realized in recent years, as briefly summarized in the next section.
method. The methods also difYer by the approximations used to represent the potential that an electron sees in the crystal or niolecule. Pseudopotential methods define separate ‘potentials’ for s, p, d, . ., valence states, whereas other techniques are ‘allelectron’ methods. Finally let us note that planewave-basis methods (pseu~opotent~als,augment~d plane waves) are the most convenient ones to use whenever forces on atoms need to be calculated. This is an important consideration as correct cohesive energies require that total energies be minimized with respect to lattice ‘constants’ and possible local atomic displacements as well, best handled by Fourier techniques. There is not universal agreement concerning the definition of ‘first-principles’ calculations. To clarify the situation, let us define levels of ab itznitio character:
(a)lst Icw‘I: only the 2 values (atomic number) are needed to perform the electronic structure cnlculation, and electronic self-consistency is performed as part of the calculation via the density functional approach in the local density approximation. This is the most fundamental level. One can also use semi-empirical pseudopotentials the parameters of which may be fitted partially to experimental data. (b)2nd level: electronic structure calculations which do not feature electronic self-consistency. Then the Namiltonian must be expressed in terms of parameters which must be introduced ‘from the outside’. An example is the tight binding method ne of most important breakthroughs in condensed where indeed the Schrodinger equation is solved atter theory occurred in the mid-1960s with the d e v e l o ~ ~ e noft the (exact) density ~ u n c theory ~ ~ ~ ~ a(the ~ Hamiltonian is diagonalized, the eigenvalues suinnled up), and the TB parameters are calcuF) and its local density approximati~n(LDA) which lated separately from a level-one formulation. provided feasible means for performing large-scale (c) 3rd level: empirical potentials are obtained dielectronic structure calculations. It then took almost 20 rectly by fitting properties (cohesive, formation years for practical and reliable computer codes to be -energies, elastic constants, lattice parameters) to developed and implemented on. fast computers. Today experimentally measured ones or to those calcumany fully developed codes are readily accessible and lated by level-one methods. At level 3, the run quite well on work stations at least for moderate‘potentials’ can be derived in principle from size a~plications.The reader may consult Chapter 6 of electronic structure, but are in fact (partially) the first volume of ~ n t @ ~ ~ ? ~ Compounds e t ~ l l i c (Singh, obtained by fitting. No attempt is made to solve 1995) for information on density functional theory and the Schrodinger equation itself, Example of such references therein. approaches are the embedded atom method hat the various methods have in common is (EAM) and the tight binding method in the chrodinger equation (sometimes the second moment approximation. The ern bedded irac equation) in an electronically self-consistent atom technique is a very useful one at this level, manner. The methods differ from one another by the and is described in detail by Daw et al. (1993) and choice of basis functions used in solving the relevant by Voter rn Chapter 4 of Volume 1 of Interlinear differential equation: plane waves, muffin tin metallic Compounds (1995), for example. orbitals, or atoniic orbitals in the tight binding (TB)
(d)$th level: here the interatomic potentials are strictly enipirical and the total energy, for example, is obtained by sui~mingup pair energies. olec~i~ar dynamics ( ~ simu~ations ~ ) operate with 4th or 3rd level approaches, with the exception of the famous Car-Parrinello method forms ab i ~ i t niolecular ~Q dynamics, with level 1 approach. In the phase diagram context, the aim of the electronic structure calcul~tionsis to obtain reliable values for the effective cluster interactions, as exemplified by equation (20) for pairs, which are themselves central to the c a l c ~ l a t i oof~ c ~ i i ~ g u ~ a t i ofree n a energies, ~ as per equation (23), for example. ince the ECls are well to obtain precise defined o p ~ r a t i o n ~it~is~ possible y~ energy values for the V, by some form of ‘structure inversion’ or other method, combined with electronic structure calculations for which standard codes now exist. These various techniques are described in some detail elsewhere (de Fontaine, 1994), where original literature is also cited. Tlie ~ r o ~ for e ~doing ~ ~‘first-priiici~les e tlieriiiodynamics’ may thus be summarized as follows: Start with an CDA electronic structure method to obtain cohesive or formation energies of a certain number of ordered structures on a given lattice, then set up the appropriate system of linear equations and solve it to obtain the relevant EGIs V,. Or perform a DGA ver electronic structure inethod ake sure that convergencc is attained in the ECll co~~Litation§, then insert these interaction parameters in an appropriate CVM free energy, minimize with respect to the correlation variables, and thereby obtain the best estimate of the free energy of the phase in question, ordered or o ngeneral disorde~ed.A more complete ~ e s c r ~ ~oft ~the procedure is given at the end of the next section.
In the previous section the computation of ECls was disc~ssedas if the only contri~Litionto the energy were the strictly repiacive one, as defined in equations (13) and (15), yet it is clear from the latter equation that ECIs could in principle be calculated for the value of the combined function XP itself. But for now, let us still consider the ECfs limited to the replacive (or configurational, or Ising) energy, leaving for the next section a brief description of other contributions to the energy and free energy. 111 the present context, it is possible to break up the energy into different contributio~s.First
of all it is convenient to subtract off the linear term in the total energy, according to the definition of equation (4), applied here to E rather than E;, since we are going to c o ~ ~ i donly e r zero t e ~ ~ e r a t u~r e~ e c t s , i.e. ground state energies. In equation ( classical and M F notation was used, in the ‘cluster’ world of the physics c o i ~ m u n ~ it t yi s customary to use the notation ‘formation energy’ rather than ‘mixing energy’, but the two are exactly the samc, Also the symbol A will be used to emphasize the ‘difference’ nature of the forination energy; it is by d e ~ n i t i othe ~ total (replacive) encrgy minus the concentrationweighted average of the energies of the pure elements. Thus we have, for binary s y s t e ~ s ,
If the ‘linear’ term in equation (24) be taken as tlie reference state, then the f o ~ ~ ~ t ei noenr ~ ycan be plotted as a function of concentration for the hypothetical alloy A- as shown schei~atic~lly in Figure 6 (de Fontaine, 1994). Three (or compounds), of stoichiometry A3 and only those, are assumed to bc temperatures, in addition to the pure elements A and B. The broken line linking those five ~ t ~ “ ~ ~forms ~t~ires the so-called G O I P Z V ~hull X (heavy polygonal h e ) for the system in question. The heavy dashed curve r e ~ r ~ s e n t s schematically the formation energy of the com~letely disordered state, i.e. the mixing energy of the hypothetical random state, the one that would have been obtained by a perfect quench from a very hightemperature state, assuming that no melting has talccn place, The energy distance between the disordered energy of mixing and the convex hula i the ( z e r o - t e ~ p e ~ ~ t uor e~) ~ e r energy. i~g peting structures are identified, say the one whose ~ o ~ a t i oenergy n is indicated by an open square symbol in the figure, the energy di~erencebetween it a i d the one at tlie same stoichiometry (filled square) is by definition the st~ucturfflenergy. of energy d i a ~ r a such ~ s as that found for example in Chapter In~ermetall~c C o m ~ ~ (Perepezko, ~ ~ n ~ s 1995). All the zero-temperature energies illustrated in Figure 6 can in principle be calculated by cluster expaiision (CE) tecliniques, or, four the structures, by first~principles~ e t h o ~ § . energy of the random state can be obtained from equation (21) by replacing the correlation variable for cluster a by ncctimes the point correlatio~t l . Since the
198
~
o and ~tubility ~ ~
Schematic coilvex hull (full line) with equilibrium ground states (filled squares), energy of metastable state (open square), and f ~ ~ ~ a tenergy i o n of random state (dashed line); from cie Foiitaine (1994)
disordered state energy in Figure 6 is a continuous curve, it necessaril~follows that A and €3 must have the same structure and that the compounds shown can be considered as ordered ~Upers~rLictures,or ‘ddiccorations’, of the sanie parent structure, that of the elemental solids. ut which decorations do we choose to construct the convex hull, and can we be sure that a11 the lowesteiier~ystructures have been identified? Such questions are very difficult to answer in all generality; what is required is to ‘solve the ground state problem’. That expression can have various meanings: (a) among given s t r ~ ~ t u r eofs various stoichiometries, find the ones which lie on the true convex hull; (b) given a set of Cls, predict the ordered structures of the parent lattice (or ~tructure,such as hcp) which will lie on the convex hull; (c) given a maximum range of interactions adniissible~find all possible ordered ground states of the parent lattice and their domain of existence in ECI space. Problem (c) is by far the most difficult one. It can be attacked by methods of linear prograixniiiag: the requirement that the cluster concentration lie b e t ~ e e n0 and I provides a set of linear constraints (via the configuration matrix, mentioned earlier) in the correlation variables, which are represented in <-space by sets of hyperplanes. The convex polyhedral region which satisfies these constraints, i.e. the configuration polyhedron, has vertices which, in principle, have the ect 5-coordinates for the ground states sought. method can actually predict totally new ground states, which one might never have guessed at. The problem is that sometimes the vertex determination
i
~
~
produces [-coordinates which do not correspond to any coiistructible structures, i.e. such coordinates are internally inconsistent with the requi~ementthat the prediction will actually correspond to an actual decoration of tlie parcnt lattice. Another liniitatioii of the method is that, in order to produce a non-trivial set of ground states, large clusters must often be used, and then the dimensioiis of the 5-space become too large to handle, even with the help of group theorybased computer codes (Ceder et al., 1994). Readers interested in this problem can do no better than to consult the book by Ducastelle (1991), which also contains much useful information on the CVM, on electronic structure calculation (mostly TB-based), and on the generalized perturbation method for calculating EPIs from electronic structure calculations. Another very readable coverage of ground~stateproblems is that given by Inden and Pitsch (1991)’ who also cover the derivation of m u l t i c o m ~ o ~ eCVM ~ t equations. Accounts of the convex polyhedron method are also given in de Fontaine (1979, 1994). Problem (b) is more tractable since in this case the EGIs are assumed known, thereby determining the ‘objective function’ of the linear programming problem. It is then possible to discover the correspond~ng vertex of the configuration~lpolyhedron by use of the siinplex algorithm. Problem (a) does not necessitate the knowledge or even use of the ECIs: the potentially competitive ordered structures are guessed at (in the words of Zunger (1994), this amounts to ‘rounding up thc usual suspects’), and direct calculations determine which of those structures will lie on the convex hull. In that case, however, the real convex hull structures may be missed altogether. Finally, it is also possible to set up a relatively large supercell and to populate it successively by all possible decorations of A and atoms, then to calculate the energies of resulti structures by cluster expansion (Lu et al., 1991). There too, however, some optimal ordered $tructures may be missed, those whose unit cells will not fit exactly within the designated supercell, Let us close this section by sui~marizingthe general method of calculating a phase diagram by cluster methods. The solution o f the ground-state probleiii has res sum ably given. us the correct lowest e n e ~ ordered ~y structures for a given parent lattice, which in turn determines the sublattices to consider. For each ordered structure, write down the CV minimize it with respect to the config~~ation variables, then plot the resulting free energy curve. Now repeat these operations for another lattice, for which the required ordered states have been deter~ined. Of
course when comparing structures on one parent lattice with another, we must know the structural energies involved, for example the difference between pure A and pure in the fcc and bcc structures. Finally, as in the ‘classical’ case, construct the lowest common tangents to all free energies in presence, with the locus of common tangency points generating the required phase diagram, as illustrated for example in the MF approxii~at~on in Figure 4. The whole procedure is of course much more complicated than the classical or MF one, but consider what has in principle been accomplished: with only the knowledge of the atomic numbers of the constituents, we have calculated the (solid-state portion of the) phase diagram, and also such useful thermodynamic quantities as the long-range, short-range order, equilibrium lattice parameters, formation aiid structural energies, bulk modulus, and metastable phase boundaries as a function of temperature and concentration. Note that calculations at a series of volumes must be performed in order to obtain quantities such as the equilibrium volume and the bulk modulus. A summary of those binary and ternary systems for which the program has been at least partially c o m p l ~ t up e ~ to 1994 was givcn in table form in de Fontaine (1994). Up to now, only the strictly replacive (fsing) energy has been considered in calculating the ECfs. What about the other contributions, displacive and dynamic, which have been mentioned in previous sections? These have so far been left out of the picture for si~plicity,as indeed they often have been in early calculations. It is now becoming increasingly clear tliat those contri butions can be very large and, in case of large atomic misfit, perhaps dominant. The nk initio treatment of displacive interactions is a difficult topic, still being explored, so will be summarized only briefly here (next section).
In a 1994 review article, Ztmger explained his views of displacive effects and stated that the only investigators who had correctly treated the whole phenomena, at least the static ones, were members of his group. At the time, this claim was certainly valid, indicating that far too little attention had been paid to this topic. Today, other groups have followed his lead, but the situation is still far from settled, as displacenients, s dynamic, are diacult to treat. Let us adopt definitions and examine in more detail the term EdtsPl which appears in equations (13) and (15) of Section 2.3, We have, from equations (13), (15) and (24),
where Edlspl of equation (I 3) has been ~ r o k e nup into a volume dcformation (V ) contr~bution,a ‘cell external’ deformatioii (AEdef) and a ”cell Internal’ defor~ation(relax). The various t e r ~ ~ins e ~ ~ ~ t i o (25) are explained schematically on a simple s ~ u a r e lattice in Figure 7 (Morgan et al., 1998 u~~publislied): from pure A aiid pure on the same lattice but at their ~) equilibrium volumes (the refereiice state E I ~ we expand the smaller latticc parameter and contract that of the larger to a common intermediate parameter, assumed to be that of the h o ~ o ~ e ~ e o ~ s mixture, thus yielding the large contributi~nQEy,. Now allow the atoms to rearran~eat constant volume while r e ~ ~ i n i nsituated g on the sites of the averag lattice, thereby recovering e previous section under the ”Ilsingenergy’ was ~ o n t r i ~ ~ t ~ redistribution will lower th states, so that the lattice parameters will extend or contract (such as c/a relaxation), and the cell vary, at constant volunie, a c o ~ t r i b ~ t i odn AEdef in equation (25), but not indicated in Figure Finally, the atoms may be displaced from their positions on the ideal lattice, produc~nga contr~bution denoted as AErelax. Equation (25) also indicates the order in which the calculations should be perforined, given certain reasonable assumptions (Zunger, 1994; 1998 unpublished). Actually, the cycle should bc repeated until no signi~cant atomic d i s p l a ~ e ~ e n t s take place. Such an iterative procedure was carried out in a strictly ak initio electronic structure ~ ~ l c u l ~ ~ i o n and
DO23
in Al3Ti and
atomic displacements wcre small. For more coniplicated unit cells of lower s ~ m ~ e t ~ r yi i~i ~ n i i z ~ n total energy for all possible types of ~ ~ s p l a c e ~ e n t ~ would be a toa time-consuming process, so that actual atomic forces should be computed. For tliat, planewave electranic structure techniques are ~ r e ~ e r a b l e , such as given by F L 01- pseudopotent~al ~ ~ ~codes. Let us mention here the importance of calculating energies (or enthalpies) as a function of c/a, b/a ratios, . . . at constant cell volume. It is p o s s ~ ~ lby e , a so-called ‘Bain transforination’ to go coiititiuously from the fcc to the bcc structur~s,for example.
200
Borzdiag and Stability
re 7 Schematic ~ w o - d i m e i i s i oillustrati ~~~ Morgan et al. (1998, unpublished work at UC Berkeley)
important for calculating structural energies, essential for complete phase diagram calculations, but also for ascertaining ~ h e t ~ the e r higher-energy-structures are metastable with respect to the ground state, or actually unstable. In the latter case, it is not permissible to use e x ~ ~ a ~ o l a t i of o n phase boundaries (through extrapolation of empirical vibrational entropy functions) to obtain energy estimates of certain non-stable structures (Craievich et al., 1997).
utions a ~ ~ ~ a r in i nequation g (25); according to
Other more general ‘cell-external’ deformations have also been treated (Sob et al., 1997). Elastic interactions, resulting from local relaxations, are c~aracte~istically long range. Hence it is generally not feasible to use the type of cluster expansion described in Section 2.3, since very large clusters would be required in the expansion, and the number of correlation variables required would be too large to handle. One successful approach is that of Zunger
Calculation of Phase Diagrams
(Laks, 1992) who developed a k-space SIM with effective pair interactions calculated in Fourier space. A novelty of this approach is that the Fourier transforms feature a smoothing procedure, essential for obtaining reasonably rapid convergence; another is that of subtracting off the troublesome k = 0 term by means of a co~ic~ntration-dependent function. Previous Fourier-space treatments were based on second-order expansions of the relaxation energy in terns of atomic displacements and socalled ~ a ~ z fai rkc m~ (de Fontaine, 1979; Khachaturyan, 1983), wliich forces were calculated by heuristic means, or from the embedded atom method M) (Asta and Foiles, 1996). Another option for taking static dlsplacive effects into account is to use brute-force computer simulation techniques, such as molecular dynamics (MD), or molecular statics. The difficulty here is that firstprinciples electronic structure inet too slow to handle the millions of to reach e~uilibriumover a sufficiently large region of space. Hence, empirical potentials are required, such as those provided by the EAM (Daw et al., 1993). The vast literature that has grown up around these simulation techniques is too extensive to review here; furthermore, these methods are not particularly well suited to phase diagram calculations, mainly because the average frequency for ‘hopping’ (atomic interchange, or ‘replacement’) is very much slower than that for atomic vibrations. Nonetheless, simulation techniques do have an important role to play in dynamical effects, to which we now turn. 2. ~ero-temperature contributions were described in Sections 2.5, 2.6, and 2.7, and Section 2.4 dealt only with configurational free energy. As was explained, the latter can be dealt with by the cluster variation me~hod which basically features a cluster expansion of the configurational entropy, equation (23). But even there, there are difficulties: how does one handle long-range inter~ctions,for example those coming from relaxation interactions? Et has indeed been found that, in principle, all interactions needed in the energy expansion (21), must appear as clusters or subclusters of a ~ acluster ~appearing ~ in the~CVM configurational ~ l entropy. But, as mentioned before, the number of variables associated with large clusters increase exponentially with the number of points in the clusters: one faces a veritable ‘combinatorial explosion’. One approximate^ but none too reliable solution is to
20 1
(supertreat the long-pair interactions by the position, mean-field) model. A more fundamental question concerns the treatment of vibrational entropy, thermal expansion, and other excitations, such as electronic and magnetic ones. First, let us see how the static and dynamic ~ ~ s p ~ ~ c e mcan e n be t s entered in the CTd Several methods have been proposed; i (Kikuchi and Masuda-Jirido, 19971, the CVM free energy variables include continuous displacement$~ and summations are replaced by integrals. For computational reasons, though, the space is then made discrete, leading to separate cluster variables at each point of the fine-mesh lattice thus introduced. Practically, this is equivalent to treating a multiComponent system with as many ‘compo~~iits’ as there are discrete points considered about each atom. Only model systems have been treated thus far, mainly containing one (real) component. In another atomic positions are considered to be distributed about their static equilibrium Such is the ‘Gaussian CVM’ of Fine1 (1994), simpler, but somewhat less general than that of Masuda-Jindo (1997). Again, mostly dynamic displacements have been coiisidered thu perform cluster expansions of the framework (Asta et al., 1993a), in a ~ebye-~runeisen or of the average value of the logarithm of vibrational frequencies (Garbulsk~and Ceder, 19 of selected ordered structures. As for treating vibrational fre configurational one, it was sufficient to include a Delay for each of the phases present (Sanchez et al., 1991). However, Fultz and co-workers at Caltech have recently suggested (Anthony et al., 1993; Fultz et al., 1995; Nagel et al., 1995), based on e ~ p e r i ~ e n t a l evidence, that the vibrational entropy difference between ordered and disor~eredstates could be quite large, in some cases comparable to the configurational one. This was a surprising result, indeed, which perhaps could be explained away by the presence o f n u ~ e r o u ~ extended defects introduced in the method of preparation of the disordered phases, since in defective regions vibrational entropy would tend to be higher. Several quasi-harm~niccalculations were recently u~dertaken to test the experimental values obtained in the NiSAX system; one based on the Finnis-Sinclair (Ackland, 1994), and one based on E (Althoff, 1977, 1978). These studies gave results agreeing quite well with experimental values (Antliony, 1993; Fultz et al., 1995; Nagel cf al., 1995) and with 9
202
Bonding and Stability
handbook (Binary Alloy Phase Diagrams, 1990) is incorrect (a correction appeared in an addendum, reproducing the older version). Tlie CVM-fitted Al-Li phase diagram, including the metastable L12 phase region (dashed lines) and available experimental points, is shown in Figure 8b (Sigli and Sanchez, 1984). The Li-rich side of the %/a’two phase region is shown to lie very close to the A13Li ~toichiomet~y, along, as expected, with the highest disordering point, . A low-temperature nietastablemetastable miscibility gap (because it is a metastable feature of a metastable ~ q L i i l i b r i ~ ~) is~predicted to lie within the a/a’two-phase region. Note once again that the correct ordering behavior of the L12 structure by a first-order transition near xL, = 0.25 could not have hen could m to have perimental points by using the method of concentration waves, which is completeF model? The ans ly e~uivalentto the that these authors ntly left out the temperature portion of their calculated phase boundaries so as not to show the inevitable outcome of their calculation, which would have incorrectly produced a triple second-order transition at concentration 0.5. A first-principles calculation of this system was attempted by Sluiter et al. (1989, 1990), with both fccand bcc-based equilibria present. The tetrahedron approximation of the GVM was used and the EGIs escribed a comparison between ~ r ~ t ~ t ywere ~ eobtained by structure inversion from FLAPW (hill potcntial augmented plane wave) electronic approaches. What will structure calculations. The liquid free energy was be done in this section is to present an application of taken to be that of a sub-regular solution model with rious types of calculations to a real system, the fitted to experimental data. Later, the same -Li binary, in both Jirted and . ~ r s t ~ ~ ~ i n c ~parameters les AI-Li system was revisited by the same first author and s~~iei~es. other co-workers (Sluiter et al., 1996). This time the uniinum~lithiumalloys are strengthened by the LMTO-ASA (linear muffin tin orbital-atomic sphere able coherent A13Li phase of approximation) method was used to calculate the this phase is less stable than structures required for the SIM, and far more the two-phase mixture of an fcc Al-rich solid solution structures were used than previously. The calculated -based ordered structure AlLi (p), it formation energies of structures used in the inversion on the cxperimeiitally determined are indicated in Figure 9a, an application to a real diagram (Binary Alloy Phasc~Diusystem of techniques illustrated schematically in Figure ~~~~~, 1986, 1990). It would therefore be useful to 6. All fcc-based structures are shown as filled squares, late the %,/a’ metastable phase boundaries and bcc-based as diamonds, ‘interloper’ structures (those which are not manifestly derived from fcc or bcc), unrelaxed and relaxed, as triangles pointing down and up, respectively. The solid thin line is the fcc-only, and the dashed thin line the bcc-only convex hull. The heavy broken line represents the overall (fcc, bcc, interloper) convex hull, its vertices being the predicted note that the newer version of the AI-Li ground states for the Al-Li system. It is gratif~ingto rn in the second edition (1990) of the
each other, namely LAS,,~~ equal to about 0 . 2 k ~versus 0.2 to 0.3 k~ reported experimentally. Integrated thern~odynam~c ~uantitiesobtained from ~ A ~ - b a s e d calculations, such as the isobaric specific heat (C,), agree very well with available evidence for the L12 valev et al., 1974). Note that in the roaches, the d~sordered-~tate strucaxed (via molecular statics) and the leinperature-dependence o f the atomic volume (by minimization of the quasi-harmonic. vibrational free disordered state were fully taken into is one to make of this‘? If the empirical s are valid, and so are the experimental ones, that means that vibrational entropy, usually neglected in the past, can play an important role in diagram calculations and should be 1 more work is required to confirm both and theoretical results. Other contributing influences to be considered could e tkose of electronic and magnetic degrees of freef o ~ ~ ethe r , reader should consult the ertoii and Zunger (1995). For the latter, an example o f a ‘fitted’ phase diagram calculation with magnetic interactions was given by Dahmani et al. (I 985).
203
t
AI
ure 8a ALL1 phase diagram from the first edition of the phase diagram handbook (Binary Alloy Phase Diagrams, 1986)
AI-Li SYSTEM 1100
LIQUID
so0 n
5
w n: I3
700
L11: 4:
w a, c W
500
3OO 0.0
0.1
0.2
0.3
0.4
0,s
0.6
0.7
0.8
0.9
1.0
A T O N I C ~ O ~ C E ~ r ~ A rOFI OL Ni
b AI-LI phase diagram calculated from a GVM fit (full lines), L1, rnetastable phase regions (dashed lines) and corresponding e x p e ~ i ~ e n tdata a l (symbols); (Sigli and Sanchez, 1986)
Bonding and ~ ~ a ~ i l i ~ ~
204
-I
AI
Li
Conclentration Li
i~~~~9a Convex hull (heavy black line) and formation energies (symbols) used in first-principles calculation of ALL1 phase diagram; from (Sluiter et nl., 1996)
I
0
1
0.2
0.4
0.6 CLi
0.8
1
Li
igure 9b Solid-state portion of the A1-Li phase diagram (full lines) with metastable Ll, phase boundaries and metastablemetastable miscibility gap (dashed lines, Sluiter et al., 1996)
Calculation qf’ Phase Lliagmms see that the predicted (‘i.ounding up the usual suspects’) ground states are indeed the observed ones. The solid-state portion of the phase diagram, with free energies provided by the tetrahedron-octahedron CVM approximation, is shown in Figure 9b. The etas stable a/&’ (Ll2) phase boundaries, this time calculated completely from first principles, agree surprisingly well with those obtained by a tetrahedron CVM fit, as shown in Figure 8b. Even the metastable MG is reproduced. Setting aside the absence of the liquid phase, the ~rst~principles phase diagram (no empirical parameters or fits employed) differs from the experimentally observed one (Figure 8a) by the fact 32 ordered phase has too narrow a ty. However, the calculations predict such things as the lattice parameters, bulk moduli, degree of long- and short-range order as a function of temperature and concentration, and even the influence of pressure on the phase equilibria (Sluiter et al., 1996). The case study just presented is but one amo~gst many, but should give the reader an idea of some of the difficulties encountered while attempting to gather, represent, fit or calculate phase diagrams. Examples of other systems, up to 1994, are listed for instance in the author’s review article (de Fontaine, 1994, Table V, Section 17). See for example the work on noble metal alloys by Mohri and co-workers (Terakura et al., 1987; Mobri et al., 1988, 1991), that of Astti and co-workers on A1 alloys (Asta et al., 1992, 1993’0, 1995, 1997; Johnson and Asta, 1997) and Cd-Mg (Asta et al., 1993a), that of Sluiter, Turchi and co-workers on AI-Ni (Sluiter et al., 1992; Turchi et al., 1991a) and n (Turchi et al., 1991b), and various ternary systems. Recent entries in that category are works on Heusler-type alloys by McCoimack and others (1 996, 1997). For semiconductor-material systems, see the publications of the Zunger school, and for oxides those of Burton and of Ceder and co-workers, for example urton and Cohen, 1995; Tepesch et al., 1995; Ceder et al., 1995; Tepesch et al., 1996; Kohan and Ceder, 1996), In the oxide category, phase diagram studies of the High-T, superconductor YBCO (de Fontaine, 1987, 1989, 1990; Wille and de Fontai~e,1988; Ceder et al., 1991) are of special interest, as the calculated oxygen-orderi~gphase diagram was derived by the CVM before experimental results were available, and was found to agree reasonably well with available data. Applications of the methods discussed here are covered for the A1-Ni and Ni-Pt systems in the more extended version of the present article (de Fontaine, 1999). Material pertineiit to the topic at hand caii also be found in the proceedings of the joint NSFjCNRS
205
conference on alloy theory held in France in October 1996 (de Fontaine and Dreyssk, 1997).
ssio Knowledge of phase diagram is a ~ s o l u t ~ essential ~y in such fields as alloy development and alloy processing. Yet today, that knowledge is incomplete: the phase diagram compilations and assessments are fragmentary, often unreliable, sometimes incorrect. It is therefore useful to have theoretical models whose roles and degrees of sophistication differ widely depending on the aim of the calculation. The highest aim, of course, is that of predicting phase equilibria from the knowledge of the atomic number of the constituents, a true first-principles calculation. That goal is far from having been attained, but much progress is being realized. The difficulty is that so many different types o f atomic(e1ectronicinteractions need to be taken into account, and the calculati~ns are complicated and time consuming. Thus far, success along those lines belongs priniarily to such quantities as heats of formation; con~gurationaland vibrati~nal entropies are more difficult to compute, and as a result, prediction of transition temperatures are often considerably off. It is interesting to note that theorists look at alloy system free energies from two very different angles: in the felicitous words of Simon Moss (1978), ‘electronic structure specialists devote all their considerable talents to calculating internal energies, but regard configurational entropy as a piece of cake, whereas statistical mechanics types look upon calculations of confi~urat~onal entropy as worthy of a Nobel prize, but disniiss iaternal energy as another piece of cake’. Clearly, both contributions to the free energy, and many others, must be tackled with the same degree of sophistication, so must be investigated by universalists, rather than narrow specialists, hence the small number of practicing alloy theorists today, in a field which has tended to become highly polarized. Despite the often serious discre~ancies between calculated and experimentally determined phase diagrams, the dream of ah initio phase diagram calculations is we11 worth pursuing: how else may one ever attain a true Understanding of the various contributions to alloy free energies, electronic, vibrational, configurational, in a truly Qtomislic approach? The objective of designing directly from
206
Bonding and § t a b i ~ i t ~
the periodic table may not be as far off as currently believed by inany traditionalists. On the other hand, and for the time being, fitting procedures can produce very accurate results; indeed ‘with enough adjustable parameters, one can fit an elephant’. The exercise can be useful as such procedures may actually find inconsistencies in empirically derived phase diagrams, extrapolate into uncharted regions, or enable one to extract therinodynaniic functions, such as free energy, from experiment: calorimetry, X-ray diffraction, electron microscopy or other techiiiqiies, Still, one has to take care that the sta~tingtheoretical models make good physical sense. We have seen from the foregoing that Gorsky-BraggWilliams-type models, which produce acceptable results in the case of phase separation, cannot be used for order/disorder transformations, particularly in ‘frustrated’ cases as encountered in the fcc lattice, without adding some rather unphysical correction ut even in qualitatively favorable cases, the ropy expression of equations (7) and (9), for n regular, sub-regular, CALPWAD, ragg-~illiams, and concentration wave methods tends to overesti~atethe configurational entropy contribution, so that energy parameters backed out by fitting to experimental data will also ov~~estimate enthalpy and excess entropy parameters, in compensation It rnay be argued that ab i ~ i t i uatomistic methods are too complicated to be used with multicompoiient systems, so that only mean-field approaches are feasible. This rnay be true, and Thermocalc software, for example, can do a good job of plotting out sections through fitted inulticoniponent phase diagrams. The results are obviously only as good as the empirical parameters input to the codes, however, and there exists a lot of ~ncertaintywithin the large but still incomplete data bases presently available. Ideally, this drawback does not exist for first-principles calculations: the only inputs are known integers, the atomic numbers of the constituents! In tliis article, both approaches were presented, the empir~~ally driven mean-field, ~ h e n o m e ~ o l o ~ ione cal and the q ~ i a n t ~and m statistical mechanically driven atoniistic one. For now, both approaches must exist side by side, and it will be up to the user to decide which one to use. It is expected that ab irzitio methods will become increasingly useful in the case of intermetallic alloy systems, as such systems often feature e~ and ordered comordering on ~ f r u s ~ r a tlattices pounds which are readily amenable to electroiiic structure calcu~ations.
The author thanks Jeffrey Althoff and Dane Morgan for helpful comments ~once~ni ng an earlier version of the manuscript. This work was supported in part by the US Department of Energy, Ofice of Basic Energy s under contract Sciences, Division of ~ a t e r i a l Sciences NOS.DE-AC04-94AL85000.
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~
s
t appears that the human mind cannot arrive at siniplicity except by passing through the complex; it is like a mountain more or less elevated, whose heights must be overcome before the plain on the opposite base can be reached; and when rea ed, the level seems to be that of the plain left behind. when a simple solution to a problem is arrived at, and almost self-evident. 6
iscovery consists of seeing what everybody has seen and what nobody has thought.
If you do something once, people will call it an accident. f you do it twice, the third time and you’ve
The atomic-scale structure and properties of the free surfaces of metals and interinetallics have been intensively studied in recent years. The availability of new measurement techniques has improved the knowledge of surface structures substantially. Atomically clean surfaces can be prepared and modified, due to the availability of ultra-high vacuum techniques. Interfaces and free surfkces are of technological importance in the fields of catalysis, corrosion, oxidation and friction and wear. Surface structure and energy are important in fracture processes. Most interinetallics present brittle fracture behavior, wliere knowledge of the energy of the created surfaces IS essential in understanding and improving the fracture properties. The influence of interfaces and free surfaces on the ~ e c h a n i ~ abehavior l of inter~eta~licsis especially important in nanostructured materials. For the purpose of this review we define the surfiace as a region of space limited to a few atomic layers. Different terminations at the surface may affect the adsorption properties of various species. Many adsorbates can be deposited on a metallic surface, which influence the structure and properties of that surface. However, only clean surfaces of intermetallics will be discussed in this work. A general discussion of metal surfaces can be found for example in the book by Howe (199'7) or the review by van Hove (1993). It is well established that ordering in intermetallic bulk crystals has a great influence on the properties. The current interest in intermetallic compounds for high-temperature applications and fknctionai materials has led to a large effort in understanding ordering effects on bulk properties. However, the structure and
properties of surfaces do not necessarily reflect those of the corresponding bulk materials. which means a rearrangement o f atoms at the surface, may occur. Segregation of different atomic species at surfxes i s often related to these recoi~str~~ctions and can change the surface properties s i g n ~ ~ c a n tThe l~. ordering properties of surfaces are often diRcrent from those in the bulk. Also, the concentration of point defects may change due to the presence of free surfaces and interfaces (Aust et al., 1966, 1971). Experimental and theoretical methods of studying surface phenomena have been greatly irnpro recent years. Scanning tunneling microscopy allows direct irnaging of surf'itces with atomic tion, and even chemical contrast between different atom species has been achieved recently on some metallic and intermetallic surfaces. Surface ordering and disordering effects, therefore, can be s t u ~ i e d directly for the first time using ost experiniental characterization techniqucs yield information from the outermost surface area, which makes a careful extrapolation to the bulk ~ropertiesne~essary. The techniques for sui-face investigations will be described in the first part of this chapter. surface structures and their possible recoiistru~tions will be discussed. In section 4 the structures of s simple binary intermetallic compounds with B2(c and Ll~(cP4) structures will be reviewed. The influence of different constituent elements in isostructural compounds on surface structure and relaxation will be compared. Surface phase transitions and orderin~-disor~ering effects at surfaces will be treated in section 5. The surface transitions in a few intermetallic com~ouiids with a solid-state order-disorder tr~~nsition such as
~ ~ ~ ~ rCompounds: ~ e t ~Vol. i ~3, Principles ~ ~ c and Practice. Edited by J. H. Westbrook and R. L. Fleisclier. 0 2 0 0 2 John Wiley & Sons, Ltd.
Properties and Phenomenology
212
CU~AU have been studied thoroughly in the past. ection 6 deals with segregation properties, and in section 7 the properties of surfaces aiid some practical influences are considered.
xpesi erties
n important point for experimental techniques used surface science is achieving an extremely high surface sensitivity, to get information from only a few atomic layers of material. Van Hove (1999) e major techniques for structure e preparation is a critical step for surf'ace studies, since most surfaces are not stable in the clean and cry§tallographically ideal manner necessary for investigations. Most surface investigations, therefore, require preparation and storage of the specimens in ultrahigh vacuum (UHV) chambers at a base pressure close to 10-s pascal. Such environments allow even reactive surfaces to stay clean for hours. ~ r ~ p a r a t i oofn such surfaces is usually performed by a combination of annealing and sputtering with noble gas ions. However, preferential sputtering of one compoiient in a binary system can significantly change the surface coniposition from that of the bulk. For exaniple, A1 is preferentially sputtered in the B2(cP2) compounds FeAl and NiAl. Clean. surfaces of several brittle intermetallics can also be prepared directly by cleavage in vacuum (Heatherly et al., 2997).
iffraction techniques, inaiisly electron and X-ray ffraction, are widely applied to study the structure of bulk materials and surfaces. Low-energy electron diffraction (LEED) is one of the most successful techniques and has been applied in many dies of surfaces, see for exaniple the book by Van ove et al. (1986). Elastically diffracted electrons with energies in the 20-300 eV range are used to probe the surface structure. Since, in general, only elastically scattered electrons with a limited penetration depth iii the range of 1 nm, are recorded, LEED is a very surf~ce-sensitive technique. The diffraction patterns are displayed easily on a fluorescent screen and serve as a convenient monitor of the surface condition. Surfwe preparation procedures are usually controlled with this technique. The long-range-ordering parameter of intermetallic surfaces is determined from the intensity of the diffraction spots. Multiple scattering of electrons
complicates the interpretation of the experimental diffraction data. Therefore, the diffraction patterns of the entire multiple-scattering process are simulated for all plausible surface geometries, from which the surface which gives the best fit to the experimental results is chosen. X-ray diffraction is very useful in studying the structure of bulk materials. However, the long meanfree-paths of X-rays in solids makes them less sensitive for surface studies. Only grazing incidence or emergence techniques (with angles within a fraction of a degree) permit the desired surface sensitivity. These of course are challenging experimental tasks and extremely flat surfaces are necessary (Birgeneau and Horn, 1986), The sufficient photon flux required is often achieved only at synchroton radiation facilities. X-ray diffraction is particularly suitable for investigation of disordering phenomena such as surface roughening and phase transitions. Grazing-incidence X-ray scattering (GIXS) is based elow a critical angle, the X-rays are reflected out of the sample rather than into the sample. By varying the incident angle, it is possible to sample at different depths into the surface. X-ray diffraction at grazing incidence has better sensitivity at short distances parallel to the surface, thus in-plane strain measurements are possible directly and at various depths.
Field ion microscopy (FI ) is a well-established technique to study surfaces with atomic resolution. Nevertheless, the requirement to shape the specimen into a tip with a very small radius restricts its use to a few cases. A new development is the 3D atom probe FIM, "with which full three-dimensional atomic resolution with chemical contrast can be achieved. So, chemical mapping of 3D volumes is possible. A chaiinel plate is used as a detector for the fieldevaporated atoms, to get information as to where these atoms are evaporated from the tip. This, of course, is a very powerful tool to study segregation at interf.a e s or surfaces. Since the invention of the scanning tunneling microscope (STM) by Binnig and Rohrer, 1982, this technique became one of the most powerful and most frequently applied tools for surface scientists. The unique capability of visualizing atoms in direct space on a surface allows new insights into surface properties, which previously were accessible only by
Free S u ~ ~ S~t rcuec t ~ &and ~ e Properties theoretical simulation techniques. Steps, defects and atomic corrugations can now be studied directly. TM readily delivers geometrical data from surfaces, information about the chemical structure was obtained first of all on semiconductors with tunneling spectrsscopy (Tromp, 1989). For example, on a cleaved GaAs crystal either the Ga or As atoms can be made to appear in the STM image, by switching the bias voltage (Cox et al., 1990). On metals it appeared at first impossible to differentiate between different metallic species on surfaces, but recent results demonstrate atomic resolution with
213
chemical contrast on several metallic systems, see for example Schmid et al. (1993); Vargx and Schrnid (1999) and Sprunger et al. (1996). This, of course, offers the possibility of studying ordering and disordering effects on intermetallic surfaces with previously unattainable resolution. applied to an interrnetallic, an example STM image with ch surface is sliovvn in atoms appear at different gray levels and the amount of Pt/Rh concentration at the surface could be determined from the histogram. The difference in. the
Figure 1 STM image of Pt,,Rh,,(lll) with chemical contrast. The surface was annealed at 800°C after Ar sputtering. Thc histogram of the atom heights results m two separated peaks from which the concentrations caii be determined (from Hebenstreit et at., 1999), reproduced with permission
Properties and P ~ ~ e ~ o ~ ~ e ~ o l o g y
14
applied to study surface composition. A very high surface sensitivity is obtained with ion-beam techniques such as secondary ion mass spectrometsy (SIMS) and ion scattering s p ~ ~ t r o s ~ o(ISS). p y Static SIMS, which uses low ion intensitics for no~~estructive surface investigations, coupled with a time of flight (TOE;) mass spectrometer, is probably the most sensitive analytical technique. Ion scattering at low energies below l keV (LEiS) yields information from the top one or two atom layers. ~ ~ a t t e r with i n ~ alkali ions provides particularly good structural and compositional sensitivity, when monitored near the 180' scattering direction. This method is also called ALICISS, al~ali-ion-i~pact collision ion scattering spectrsscopy (Niehus and Comscz, 1984). Another scattering technique, NICISS (impact collision ion s ~ ~ t t e rspectroscopy in~ with neutral particle ~ e t e c t i ~ n ) was demonstrated to be very useful in studying surface structures (Niehus, 1991). These latter methods are parti~ular~yappro~riate in analyzing the surface composition in the very topmost layer and are very useful in studying the different possible surface t ~ ~ i n a t i o nof s inter~etallics. In high-energy ion ) ions can channel between rows scattering ( H ~ I S the
apparent height between h atoms depends on the tip condition. A maximum height difference of 25 pm was r ~ p o r t e ~ which , is much larger than the difference in atomic radii of Pt and Rh (Table 1). kerefore, the contrast cannot be explained purely etrically. The reason for the chemical contrast on surfaces is attributed to an adsorbate on er unstable tip conditions were reported by Schmid et al. (1993) as necessary to get tlie chemical ugh these images were obtained at room STM images can be tare, a ~ o ~ i c a l lresolved y obtained nowadays also at high te~peraturesup to 1200 "C and at low te~peraturesdown to a few elvin. This, of course, is very interesting for the study of phase tE.ansitions at surfaces.
number of techni~uesare capable of reflecting the emical composition at or near the surface. Scattering and electrons are the most Auger electron spectroscopy all, 1983), has been extensively
Periodic table for some metallic elements. The atomic radius and heat of vaporization are given for some metals (all data from Schulze, 1974) 1
0.143 nm 251 kJ/mol .
-
~
2
27
0.146 nm 66 kJ/mol
425 kJ/mol
3
0.125 nm
45
I
46
49
I
0.132 nrn 420 kJ/mol
0.137 nm 556 kJ/mol 77
81
I 0.136 nm 629 kJ/mol
I
Free ~ u ~ f Structure a ~ e and Properties of atoms in the crystal. efects or interfaces in the channeling direction repel the ions, which will be scattered strongly back out of the surface.
The physical properties of surfaces are, of course, essential for applications. Catalytic reactions for exaiiiple take place only at surfaces. The niagiietic properties of materials are largely influenced by surface or thin-film effects, as for example in the giant magnetoresistance (CMR) effect. Mcasurenieiits of the physical properties of surfaces are of great relevance for new developments. STM, as described above, was the first technique in the family of scanning probe microscopies (SPM) (Bonnell, 1993). The other scanning probe technique^ such as atomic force microscopy (AFM) or magnetic force microscopy (MEM) are especially useful for measurements in laboratory air (AFM) or to gain i~formation on material properties (MFM). Scanning probe microscopy is a very useful tool in this context as it allows m e ~ s ~ ~ ~ e mof e nthe t s magnetic and electric forces on a very local scale. A. combination of an AFM with a naiioiiidenter (NI-AFM) allows deterininations of the mechanical properties of very thin surface layers or close to interphases (Goken et al., 1999).
The theoretical re diction of surface structures and energies in atomistic siniulations is based on the iiiteratomic potentials, which in the simplest case is a pure pairwise potential. However, simple pairwise potentials fail to predict the structure of intermetallics accurately. More realistic potentials go beyond the pure pairwise description o f interaction and are called em~eddedatom potentials (Daw and Finnis-Sinclair potentials (Finnis and Sinclair, 1984). They all have the following form in the secondm o ~ e n a~proxii~ation t for the energy of an atom i at zero temperature:
where the first term represents a simple pairwise int~raction,that accounts for the repulsive interaction of the two ion cores. The second term is an attractive inaiiy-body potential that models the effect of electronic cohesion, also called the glue term. The square root
3t
functional form for the cohesive energy comes from the second-moment a p p r o x i m ~ t i oin~the t i g h t - ~ ~ n d ~ ~ ~ description. Potentials of this kind are very successfLi~ for inodelling most fcc metals aiid also many iiitermetallic compounds. Howevcr, they fail to predict tlie negative Cauchy pressure of certain cubic inetals (Pettifor and Aolsi, 1991), since they take no a~count of the angular forces in the total energy. Even more realistic inodels are three- and four-body potentials or tight-bind in^ models beyond the secondmoment approximation. Atomistic s i i ~ ~ ~ l aare ti~~s very successful iii calculating surface energies o f different structural models and iii predicting the relaxations of atoms in the topmost layers by niolecular statics at 0 K temperature. ~ynamicsand Moiite Carlo $imulations can be used to study segregation effects. In principle, the most accurate predictions are expected from ab-initio or ~ r s t - ~ r ~ ~ i cmethods. i~les ~ b - i n i t i o techniques have been used to calculate surface and cleavage energies of ilnaiiy ~nteri~etallic compounds. They are useful to study the surface electronic properties and to u n ~ e r s t a nsurface ~ rippling effects. However, they have not been appli~dto complex structures at interfixes in nietals, due to their high coi~putationalcosts.
A fair number of clean metal surfaces exhibit a bulk termination with only some minor relaxations of the surface atoms. This behavior is most p r o m i ~on~ ~ ~ metal surfaces with low Miller indices, such as fcc and bcc (100) and (1 11) surfwes or basal surfaces in hcp crystals. Clean (130) surfaces of the fcc m e ~ ~i lr si d i u ~ , platinum and gold are known to reconstruct to a (I x 2) surface in order to lower their surfwc energy by reconstruction rather than undergo a simple relaxation process (Niehus, 1984; g et al., 1983). The (1 x 2) reconstruction has a iig-row geometry, where rows of atoms from the ideal (110) surface are removed, thus forming very narrow (1 11) facets on the surf'ace. Surface structure and termination are more ambi uous in the case of lattices with more than one atom per primitive unit cell, such as the intermetallic compounds. Most of the crystallo~raphicorienta~ions imply a choice between two or more non~equivale~t terminations, depending on the exact depth at which the surface is cut. Even in pure metals, as for example on (10 1 surfaces in hcp cryst~ls, two d i ~ e r e n t ~ ~
terminated surfaces are expected from the bulk structure. Since the coinplexity of internietallic structures is very high, only simple binary systems will be discussed in this work. More examples on other systems may be found in the review by Vasiliev (1997). The surface structure of quasicrystals is er et al. (1999) and Shen et al. tructure of an AI5 (cP8) structure inharoy et al. (1986) and liquid metals are discussed by DiMasi et al. (2000). 4.1 Reconstruction and Terminations of
Some clean surfaces take on structures that differ substantially from the ones predicted from the bulk. uch surfaces are said to be reconstructed, as for example the well-known anid complicated (7 x 7) reconstruction of the Si(l11) surface, where a complex rearrangement of atonis in the several topmost layers is involved. In semiconductors the broken bonds at the surface, called dangling bonds, are directed out of the surface. Lowering of the surface energy occurs by re~ybridi~atioii~ that reduces the number of dangling iinpler reconstructions or ideal bulk terniiiias occur on most metals and intermetallics. ertheless, relaxations of atoms near the surface occur frequently, even on ideal, unreconstmctured surfaces. Since the surface atoms are located in an asymmetric environment, they are driven into new locations that correspond to minimum free energy. In the simplest case, only small displacements are needed to achieve the e~uilibr~um structure. However, relaxations have proven to be relatively large in intermetallic compounds.
t
The arr~ngementof atoms at the free surface is, in general, rather complex. Even if the surface is simply as in the bulk, which nieans it is unrecanstructed, the surface unit net is not necessarily a simple projection of the three-dimensional unit cell of the bulk onto the surface. Consider for example the (100) surface of an fcc metal, Figure 2 shows this situati~nwhere bolded filled circles denote atom positions in the top layer and gray circles the atom positions in the next layer. This surface has square symmetry, as expected from the four-fold symmetry. However, the surface is shown by the primitive square unit net s right in Figure 2. This kind of diflerence in description arises, of course, from the use of a noi~~primitive unit cell for the three-dimensional fcc bulk lattice. A convenient notation for surface structures~which is widely used, is that sug ested by Wood (1964). The notatjon defines the ratio of the lengths of the primitive translation vectors of the surface and substrate meshes, together with the rotation angle whicli is necessary to align both meshes. A structure having primitive translation vectors of length a' = p a and b' = gb with a rotation angle 0 is referred to as a (p x q)RB reconstruction. Figure 3 illustrates this notation for the (100) face of L12 ordered intermetallics, where two different surface t ~ ~ i n a t are i ~ ~ s possible. A Cu-Au layer on top of a Cu layer has a (J2 x J2) 45" reconstruction. This reconstruction is typically referred to as a c(2 x 2) reconstruction, where the index c denotes a centered unit mesh, The translational vectors of the centered unjt mesh are two times longer than the primitive translation vectors for the Cu layer. Note also, that already the primitive unit mesh has an atom in its centered position, since the surfxe mesh is built up of two penetrating simple
t
igure 2 (100) surface of a disordered fcc metal. A projection of the 3-D non-primitive unit mesh from the bulk is marked by dashed lines. The (1 x 1) unreconstructed primitive surface unit mesh IS shown on the right
Free ~u~~~~ Structure and Proper ties
2x7
Figure 3 Reconstruction of Llz (100) surface of Cu3Au. The primitjve surface mesh of a Cu layer is marked by continuous lines, the recoristructioa of the topmost AuCu layer dashed (primitive unit niesh) and dashdotted (ten tcred unit mesh)
compositioii Cu3Au, and 110 variations are expected at cubic lattices with different atomic species. Therefore, the surface. only the larger, rotated unit mesh is referred to as a The surface structures of two Llz ordered comcentered mesh. pounds have been examined in detail. The compound Next to structure differences of surfaces from the Wi3Al lias received ~ ~ n s i d ~ r a~b tl e~ e i i t becmsc io~ of binlk, one of the i ~ ~ ~ r features e ~ t ~of ~ordered i ~ its technolo~icali ~ ~ o r t a n case a ca~didatebase for inter~eta~lic surfaces is that they can have a different high-temperat~ire structural materials. The intrinsic termination, For exaniple (100) facets of the B2 brittleness of this compound in its polycrystalline form compound NiAl can have either a Ni- or Al-terminated is the major drawback. Alloying with boron im~roved surface. The number of possible t e ~ i n a t i o n scan be the fracture behavior considerably, due to its segregaobtained from the Miller indices (h, k , I ) in a simple tion to grain boundaries. Cu-Au alloys are a standard manner, For example, surfaces of B2 compounds t e bulk ~ ~and~ ~ whcre h + 12: I is even have one possible t e ~ i ~ ~ ~ a ~example i o n ~ of it binary ~ ~ ~ t i ~t l l~i ~swhose whereas all other surfaces have two possible terminasurface properties have been extensively studied. tions (Farkas and Ran, 1986). Cu-Au alloys have a negative mixing enthalpy and
-+
Figure 4 shows the structure of two i~termetallic compounds based on the fcc ~ t ~ u c ~the ~ r Llz(cP4) e, and the Llo(tP2) structures. The possible terminations o f low-index surfaces can be deduced from the structure. In the case of the ~lz(Cu3Au)structure three different orientations are considered. In the (100) and (1 10) orientations the ideal structure predicts alternating layers of pure Cu and 1:1 mixed Cu-Au layers. The ~oiicentrat~oi~s in the topmost surface layer, therefore are of great interest, In { 111) oriented crystals each plane in the bulk is o f stoichiometric
218
Properties and P ~ i e ~ o ~ ~ i J ~ o l o ~ y
form stable i n t e ~ e t a l l ~phases c at lower temperatures. e their bulk properties and structure have been es~ablislie~, it became a favorite phase for i~ivestigations of surface ordering and disordering 0th intermetallic phases, the tetragonal , phase are CuAu, klo and the cubic C U ~ A ULlz on the fcc struc~ure.The L1z structure in bulk ed by a discoiitinuous first-order transition at a temperature of 663 K from tlie ed fcc structure. The alloy systems Ni-Pt and re other e~ampleswith phase diagrams similar to that of Cu-Au; intermetallic pliases of the same struct~resare f ~ r m e din these systems. A lot of work has been done to clarify the questions of the surface structure and the termination of Cu3Au. Therefore we start with a discussion of it, 4.2.1 Cu3Am SurJiirC~s t is e x ~ e r i ~ e ~ t awell l l y established that the structure u (100) surface corresponds to an ideal bulk termination. LEED data froin Potter and Blakely (1975) showed the c(2 x 2) superstructure expected for the ideal t e ~ i ~ a t i oofnordered bulk (Figure 3). STM ehus and Achete (1993) showed that this surface i s unreactive to oxygen and nitrogen, and it t~ereforeis a model system for kinetic studies of surPxe phase transitions. The crystallographic structure of the oL~ter~iost layer is the same as that in the image of the surface er the surface layer
s found, with pure
detailed study of the te~perature dependence of he intensity of LEED superlattice reflections was evaluated as a function of temperature^ from e order parameter was determined. urface transition will be discussed later. in~estigated the (100) surface of 3Aii with STM and low-energy ion backscatter~~ig at room temperature. This study shows the first direct imaging of individual atoms on this e n t species, Cu and Au, could surface. The ~ i ~ ~ ratomic be ~~iscrimi~ated, although a direct identification in the was not ~ o s s see ~ Figure ~ ~ e 5.~ The NICISS data conceii~~a~ion in the surface layer 0 in tlie second layer. OnIy double were found on the surface with an
STM image of the CU~ALI (100) surface with atomic rcsolutlon. In thc lower right part both atom species are visible in the unit cell at different gray levels (from Niehus and Achete, 1993), reproduced with permiss~Qii
average step height of 0.39 nm, which is only 0.015 nrn larger than tlie bulk lattice parameter, Theoretical calculations by Wallace and Ackland (1 992) confirmed the experimental view and suggested that the stoichio~~trically mixed Cu-Au surface is energetically favored by about 0.3 J/iii2. Therefore, it could be excluded that small Cu-terminated areas exist on the surface. (1 10) surfwes of Cu3Au can exhibit the same possible terininatioiis as the (100) surface, either a pure Cu layer or a 50 at.(%Au,50 at.% Cu layer. As in. the case of the (100) surface, only mixed Au-Cu layers were found as surface terniinations (Morgenstern et al., 1995). LEED showed a investigations ( ~ ~ i ~ a etc al., h ~ 1989) r (2 x 1) diffraction pattern, which corresponds to an ideal bulk termination of the crystal. Further investigations by LEED and STM also revealed a possible (4 x 1) reco~$tructionafter slowly cooling the crystal. The surface composition was found to be again a mixed ALI-CU layer. An interpretation of the second possible rec~ns~ructionwith a detailed model of the surface struct~recan be found in Niehus (1995).
4.2.2 NE'& and
~~~~~
Ll2(cP4) ~ o ~ p o ~ n ~ ~
Next to C U ~ A Uthe , most intensively studied compound is probably Ni3A1. For the (100) surface the
Free Surface Structure and Properties
mixed layer termination is preferred rather than the other possible pure Ni termination (Sondericker et al., 1985). First-principles simulations ( 1986a) confirmed the experimental findings by calculating the cohesive energy, where the mixed layer termination was found to be more stable than the Ni term~nation.A mixed termination was also found for the (110) surface (Sondericker et al., 1986b). As expected from the bulk structure, a surface termination with stoichiometric composition was found on the (111) surface of Ni3A1. A small buckling of the topmost layer occurs 011 all low-index surfaces with the A1 atoms shifted slightly outward (Sondericker et al., 1986~). For the (100) surfaces of the compounds Pt3Ti and Pt3Sn the mixed surface termination was again found to be preferred, although later experiments on the Pt3Ti( 100) surface suggested a Pt termination (Atrei et al., 1992). In Pt3Ti a reconstruction was observed on the (1 11) surface with a pure Pt layer on top (Chen et al., 1993). In this compound the Pt termination may be favored because of the substantially different heats of vaporization of Pt and Ti. Though the top layer consists of pure Pt, buckling was observed in the top layer and stronger so in the second layer, with Ti atoms moved upwards and Pt a t o m moved downwards. The two top layers are contracted relative to the bulk. In Pt3Sn a buckling of Sn atoms out of the surface (Atrei et al., 1992) may be explained by the larger atomic radius of Sn compared to Pt.
The aluminide B2(cP2) compounds (for example: NiAl, FeAl, RuAl and CoA1) gained special attention because of their possible applications as high-temperature materials. Although their crystallographic structure is identical, the bulk and surface properties are quite different. The ordering energy seems to be a very important parameter with reference to their fracture mode and surface structure. NiAl possesses a very high ordering energy, whereas FeAl has a relatively low ordering energy. Compounds crystallizing in the B2 CsCl type ordered structure have bulk (100) planes with an A AB stacking sequence with alternating layers of all A atoms and all E3 atoms. So, for example in NiAl the (100) surface could have either a Ni or A1 termination. Figure 6 shows structural models for the low index surfaces. Results show that a non-bulk mixture or a reconstruction of the (100) surface can be excluded by the observation of (1 x 1)
219
unit cells. AI term~nationsappear to be favored on NiAl(100) surfaces (Davis and Noonan, 19813). The Al termination of the (100) surface was confirmed also by LEIS investigations ( ~ u l l i n s and Overbury, 1988), although a reconstruction of the surface was reported in this study after an annealing procedure between "90 K and 950 IS.The I5g.h ordering energy of NiAl fiwors a structure where each component is surrounded by the other species. A1 has a lower heat of vaporization than Ni, and a larger atomic radius (see Table 1) which may favor segregation of A1 to the surface and cause the AI termination of the NiAl (100) surface. A inore thorough discussion of the NiAl (100) surfzace can be found in the work of (1 10) surfaces in CO have a rectangular unit cell with a mixed stoichiometric composition. No different surface t e ~ i n a t i o n sare expected. The mixed surface termination was confirmed by a quaiititative LEED study (Davis and Noonan, 1987 and 1988). The outennost surface showed a large relaxation or rippled surface structure, which will be discussed in the next section. (1 11) surfaces of I32 compounds again are expected to show two different surface terminations. The relatively open structure of this surface consists of alternating layers of pure A or pu small interlayer spacing of 0.083 NiAI. Therefore, the structure of this surface is inore complex, and different explanations for the surface structure exist. Different possible terminations are expected to have different surface energies, and therefore one should be favored over the others. In contrast, LEED observations on the ( showed both possible terininati diRerent parts of the surface 1988). Noonan and Davis interprete~their investigation based on the assumption that the surface energies are comparable at finite temperatures and that no complete exclusion is to be expected. A model with two different terminations on different parts of the surface implies the existence of domain boundaries with rnonoatomic steps separating the areas with Ni and A1 t e ~ i n a t i o n s .As in the case of the (110) surface large relaxations were reported. STM and LEIS investigations by Niehus et al. (1990) revealed more details. The STM study showed large, flat Niterminated terraces with A1 in the second layer, separated by double atomic steps. No Al-terminated terraces were found on clean surfaces in this study. However, small amounts of oxygen cause the fomation of small triangular A1 domains on top of Niterminated terraces.
220
Properties and ~ ~ e n ~ ~ ~ n ~ l o g y
~ i 6 Struct~ral ~ u models ~ ~for the two topmost layers of low index surfaces of E32 (cP2) compounds. Dark circles are atoms A and light gray circles atoms B. Note the mixed ter~inationon the (110) surface
Relative to the iizv~sti~~tioiis on NiAl surfa'aces, i t is of interest to compare those results with measurements on other I32 compounds based on A1 such as FeAl, CoAl and uch less work has been performed on surface compounds. ~ r a u p n e et r al. (1995) and Hammer et al. (1998) investigated the structure i r ~low-index ~ ~ surfaces of arid s ~ ~ r ~b ~ ~ aa vti oof FeAl by AES and LEE . They found the (100) surface to be Al-terminated and unreconstructed, similar to the case of NiAl. Other surfaces, (1 10), (1 11), (210) and (310), showed no (1 x 1) diffraction pattern, thus indicating the absence of a bulk termination at the surface. ~ n c o ~ ~ e nsurface s ~ r aallays ~ ~ of FeAl2 were found on the (1 10) surface. In CoAl the (1 10) surface shows a bulk-like t e ~ i n a t i o nsimilar ~ to that on NiAl (110) (Hum et al.> 1996b). 1n contrast to nearly bulkterminated surfaces in NiAl and CoA1, FeAl shows significantly different surface structures which are also related to segregation effects and will be discussed in more detail in section 6.1.
Although surface reconstructions have not been observed frequently on i ~ i ~ e r ~ e t a l Isurface i ~ s , relax&tions are a quite common phenomenon. Atoms near the surface are located in very asymmetric environments. Therefore, the bulk positions may not correspond to the lowest energy state, thus driving the surface atoms into new positions of minimum free energy. ~ ~ l a x occur, a ~ ~both ~ ~per~endic~~lar s aizd parallel to the surfiice. Surface relaxations are studied experi~entally with LEED, and a best fit of the
~ i ~ r a ~ pattern t ~ o i iwith an ~ s ~surface ~ ~structure ~ i is~ sought. With such experimental techniques the relaxation of a few topmost layers can be determined. Atomistic simulations also yield detailed knowledge on the locations of atoms in each layer depending on the interatomic potentials used. Farkas (1995) reviewed different i ~ ~ ~ ~ s t i ~of a tthe i o surfatx ~ i s relaxation in the Ni-A1 system. The most striking relaxation process in many int~rmetallicsis a rippling of the surface, On surfaces with a mixed ter~inationthe plane of one atomic species is moved outward, whereas the plane of the other atoms is moved inward, thus producing a buckled surface structure. For example, an outward relaxation of A1 was found on all NiAl and Ni3Al surfaces. In. cases, where the interato~icpotentials can be approximated accurately as pairwise central potentials, the interplanar relaxation is always an expansion. The outermost surface layer is most strongly affected and expansions of several percent are c o ~ ~ m o(Allen n and de Wette, 1969). The magnitude of the expansion decays to zero within a few layers. Contractions, or inward relaxations, of the interplanar spacing also occur, and sometimes an oscillatory dependence of the lattice spacing was found near the surface. Contrdctions at the surface can be explained by a change in the interatomic potential and many open metal surfaces show an inward relaxation (Luth, 1993). A redistribution of electrons can cause such variations near the suiface, see Figure 7 (Finnit; and Heine, 1974). The electrons at the surface tend to smooth the initial boundaries of the Wi~ner-~eitz cell (A
d
22 I
Free SurJlzce Structure and Properties c
c w
together to push the A1 atoms out of the bulk. Surfaces with lower atom densities such as (1 10) surfaces in fccbased structures in general show larger r ~ 1 a x ~ t i ~ ~ than do close-packed (1 11) surfaces or (I 00) surfaces, which often have similar surface energies.
ce
Figure Schematic af electron smootliing 3 s a meclianism for an iiiward surFxe relaxation (from Lath, 1993)
CC indicated in Figure 7. The smoothing out of the charge density gives rise to the f o ~ a t i o nof a surface dipole layer. The positive ions follow this displacement as the result of electrostatic forces. Similar relaxations were found in several other compounds, as for example Cu3Au. Figure 8 shows a cross-sectional view of the relaxations near the (1 10) surface in Cu3Au, with the mixed 50% Cu 50% Au surface t e ~ i n a t i o n Au . atoms are moved outward in the top layer. Wallace and Ackland (1992) compared the relaxations in Ni3A1 and Cu3Au. In both cases the minority element, which has also the larger atomic radius is displaced outward with respect to the smaller atoms. They interpreted this result in terms of the atomic radius and interatomic potential. In Ni3Al Ni t i the o i imany-body term provides a. larger ~ o ~ t ~ i b ~to in the interatomic potentials. Therefore it is expected to reside closer to the bulk, where it might be expected to stabili~ethe surface more effectively. In contrast, Au provides a larger contribution to the interatomic potential in CusAu. In Cu3Au, atomic size and potential oppose one another, whereas in Ni3Al the effects of atomic size and potential work
A F
Layer 2
-
8 ~ r ~ ~view ~of the ~ relaxation ~ ~ of ~atomst in i the topmost layers of the Cu,Au (110) surface. Filled circles represent Au. All relaxations shown are highly exaggerated (from Wallace and Ackland, 19921, reproduced with per~ission ~~~~~~
Many bulk materials show phase transitions between different crystallographic structures. One might expect the surface to show the transition before the bulk material does because of decreased constraint and faster diffusion. However, in pure CO, for example, which undergoes a transition at 723 K from the hightemperature hcp structure to the low-temperature fcc structure, no deviation was found for the surface compared to the bulk. In contrast, the phenomenon of surface premelting has been found on pure metal surfaces, too. At least on some Pb surfaces premelting of a. few outermost surface layers was observed 100 K below the bulk melting temperature. In long-range ordered intermetallics a disordering phenomenon can occur at the surface before the bulk disorders. Phase transitions on alloy surfaces are often related to segregation; for a theoretical discussion based on the lattice gas model see (Teraoka, 1994). (See also chapters by Diniitrov in Vol. 1 on ordering and disordering processes and by Saboungi and Price in this volume on dynamic disorder.) 5.1
~~~~~~~
~ ~ f f s e
As in the case of bulk materials, surface phases are stable over a limited range of thermod~namicvariables such as temperature, coverage (in the case of adsorbates) or gas pressure. The range of tl~erniodynai~ic variables over whch a phase can exist at t h e ~ ~ o dynamic e q u i l i ~ r i ~citn i ~ be described in a phase diagram for the surface. The maxiinurn number of phases p that can coexist is given by Gibb’s phase rule. A useful classifica~ionof phase transit~onsis based on thermodynamic properties. Transitions are called of first order, if any of the first derivatives of Gibb’s free energy G is discontinuous. First-order transitions have discontinuous changes in V , S, chemical potential ,ugof coinponent i, aiid the surface energy ~ Since n the ~ e ~~ t ~ ~ Hl pisyalso ~ i ~ ~ o at~the~ ~ ~ 1). transition, a latent heat of transformation results in a transformation hysteresis. Every region o f the surface i s distinctly in one phase or the other. One example for
222
Properties and ~ ~ e ~ o ~ z e ~ ~ l o ~ y
such a transitio~is the well-st~diedfirst-order (1 x 1> to (7 x 7) transition on the Si( 1 11) surface (Osakabe et al., 1980). ~oexistingregions of (1 x 1) and (7 x 7) reconstructions are found near the transition temperature. In second-order phase transitions the first derivative of G changes continuously, but not the second-order derivatives. Thus, they have no latent heat of transformation and should not show any hysteretic behavior. The way in which ordering changes in the vicinity of a second-order surface transition can be described by a set of numbers called the critical exponents a, p, y, and v. These numbers do not depend on the actual interatomic potentials, rather they are based only on the symmetry properties of the surface. Rules for these critical exponents were developed by Landau and Lifshitz (1980) see also ottman (1981). Due to the variety of symmetries that can occur, there exist several sets of critkal exponents called universal it^ classes (Roelofs, 1996). Every second-order surface transition belongs to one universality class, through which its beliavior near the transition is completely determined. Each critical exponent predicts the variation of specific physical quantities near the critical transition temperature Tc.The te~peraturedependence of the long-range order parameter 11 for example is described by the critical exponent p.
The exponents y and v can be determined from accurate measurements of tlie diffraction-spot profiles as functions of temperature near the transition. Excellent agreement between theory and experiment is found for the surface phase transitions in pure metals (Unertl, 1993; Howe, 1997). For the (2 x 1) --$ ( I x 1> surface phase transition on the (110) surface in pure Au, theory predicts values for the critical exponent p, y, and v of 1/8, 7/4 and 1, respectively. From e~perimentalinvestigat~onsa value for /? of 0.13 wits found (Campuzano et al., 1985). Figure 9 shows the results of an investigation of the surface phase transitio~on the CusAu (100) surface in. comparison with the temperature dependence of the LRO parameter in the bulk. The LWO parameter y of the surface appears to be a continuous function of temp~rature; i.e. a second-order transition occurs instead of the first-order transitioii in the bulk, and the temperature dependence for the phase transition
Figure 9 Temperature dependence of the long-range order parameter for the bulk (triai~gles)(Feder et al., 1958) and surface (circles) (McRae and Malic, 1984) for the Cu3Au(100) surface. The dashed h e i s a fit to the data with ,O =0.23
can be described with equation (2). McRae and Malic (1984) conducted a detailed investigation on the (100) Cu3Au surface with LEED. They considered the exponential temperature dependence of the DebyeWaller factor for the beam intensities and obtained a critical exponent p of 0.23 and a surface phase transition temperature equal within error to the corresponding bulk transition t e ~ p ~ r a t u ifr emultiple scattering is neglected. The order-disorder transition at tlie surface was observed to occur reversibly; in short, none of the hysteresis was observed as would be expected for a discontinuou~transition. everth he less^ they also found weak indications for a partly discontinuous transition. A continuous order-disorder transition at the surface is equivalent to a wettingphase phenomenon at the (100) surface. The surface disorders prior to the bulk. The Cu3Au (100) surface therefore is an example where surface-induced disordering occurs. Though good agreement IS found in the literature on the chemical composition in the surface layers, i.e. 5Q%Au, 50%Cu in the topmost layer and pure Cu in the second layer, some discrepancies exist between different investigations on the nature of the surface t ~ a n s f o r m a t i ~These ~. dis~repa~ciesprobab~y are related to deviations from the stoichiometric composition. Rivers et al. (1995) studied in detail the orderdisorder transition in 3 at. % Au-rich Cu3Au crystals. In contrast to other investigations the order-disorder transformation at the surface occurs at a temperature 20 K above the bulk transition te~perature(644 K) of
Free Surface Structure and Properties this Au-rich composition, No changes in the surface composition were observed with Auger studies near the transition. Since the transition temperature is very close to that of stoichiometric CuliAu, Rivers et al. suggested that a surface layer of stoichiometric C U ~ A U is formed, which led to the increased surface transition temperature. On the (1 10) surface of C U ~ A the U surface transition froni the ordered (2 x 1) reconstructioii to the disordered (1 x 1') reconstruction occured at the same tem~eratureas in the bulk. In contrast to the (100) surface the transition was identified as first-order. McRae et al. (1990) found a significant hysteresis iii the long~range order parameter between cooling and heating cycles.
As well as disordering effects at surfaces of ordered crystals, the inverse: ordering at the free surface of alloys that are essentially disordered in bulk, can also occur. This effect was investigated in Ni-Pt alloys that are disordered in the bulk. Ni-Pt and Co-Pt are systems with phase diagrams similar to that of Au-Cu alloys. Ordered l;lz(cP4), Ni3Pt and CoPt3, and Llo(tP4), NiPt and CoPt, phases appear at lower temperatures. At higher teinperatures Ni and Pt form a coiitinuous series of solid solutions. Ni-Pt alloys gained special interest because of their use as catalytic materials. The surface structure, therefore, is of high interest for these materials. Pt-metal alloys have been extensively studied in the disordered state, see the review by Gauthier (1996). Single crystals of Ni9oPtlo showed an oscillatory Pt enrichment on (100) surfaces (Gauthier et al., 1990). Pt is enriched to a concentration of 24.3% in the topmost layer. The second layer is depleted in Pt to 6.4%. The LEED investigation showed no reconstruction of the surface. A siinilar oscillatory behavior was also found for the interlayer spacings. The topmost layer is expanded from the bulk, the second layer contracted, and the third again expanded. It is interesting to note that this behavior is in contrast to that of pure Ni and most other fcc metals, where a contraction of the topmost layer is found. However, it may be explained by the larger Pt atoms (see Table 1) segregating to the surface. STM investigations on Ni,Ptl-, (100) surfaces confirmed the Pt eiirichrnent of the surface for all investigated compositions (Hebenstreit et al., 1997). The STM study also revealed reconstructions on some surfaces. Strong Pt enrichment was also found on (1 11) surfaces, with a damped oscillatory composition profile. In
223
other words, each of these alloys developed a Pt-Mi sandwich-like structure with Pt on top. But the scgregatioii effect depends on the surface orieiitation and is reversed on (110) surfaces. The first ST investigation of the Ni~sPt25 (111) surface was conducted by Schmid et al. (1993) where the achieved chemical contrast was used to study ordering of Ni and Pt in the surface. Preferential sp~tteringand segregation cause an enrichment of Pt at the surface. The STM images show a short-range ordering eEect on the surface, Chains of up to seven Pt atoms appear in the STM image. Figure 10 shows the positions of atoiiis on the surface calculated with a Monte Carlo method, which results in positions very similar to those in the STM image. This structure is siinilar to an L1o ordered (111) surface, where alternating rows of Pt and Ni atoms are expected. Pt enrichment at the surface causes the formation of this ordering phenomenon at the surfice. The bulk with a 25% Pi composition cannot exhibit this structure. Therefore, a surfaceinduced ordering phenomenon was observed. Surhce-induced short-range ordering was also discovered on (1 11) and (1 10) surfaces of Co75Pt25 alloys, which are expected to behave very similar to Ni-Pt alloys (Gauthier, 1996 and Gautliier et al., 1998). An oscillatory segregation profile is observed, with Pt enrichment in the topmost layer. The surface slab
Figure 10 Atomic arrangement on the (1 1 1) surface of NiPt at 420 K calculated by Monte Carlo siinulations with embedded atom potentials (from Schmid et al., 1993)
stabilizes with a structure and composition quite similar to that of the L12 Co#t phase. Surfaceinduced ordering p~enomenawere also found in the Ag-Cu system, which presents a strong phase separation in the bulk (Meunier et al., 1999).
The composition of a free surface and layers next to the surfiice will generally differ subs~dntiallyfrom the composition in the bulk. Segregation in alloys has been investigated with a large effort. Farkas (1995) reviewed some basic s~gregationmodels applicable to segregation in solid solutions and ordered intermetallics. The ordering properties of intermetallics hinder the diffusion in these alloys. ~ ~ v e r t h e ~segregation ~ss, is also found in ordered compounds, which will be exclusively treated in the following.
Usually, surface segregation is inhibited by strong ordering forces in intermetallic compounds and consequently the surfaces o f these alloys are expected to be bulk terminated. ~~vertheless,in many weakly ordered compounds and especially those where ordering occurs only at lower temperatures, the surface com~ositionis changed largely by segregation. Some
alloys forming solid solutions in the bulls, where ordering effects at the surface are observed, were discussed in section 5.1 and 5.2. Segregation is also found in compounds with an ordered bulk (Heinz and Hammer, 1999). For example, segregation is important in Fe-A1 alloys of various chemical c o ~ ~ o s i t i o n s . Stoichiometric FeAl 2 compounds show strong segregation behavior, very different from that of NiAl, which has a much larger heat of formation. Hammer et aE. (1998) observed segreg~tiono f A1 to all low-index surfaces of FeAl. An in~oi~mensurate surface alloy of FeA12 was found on the (110) surface. Figure 11 shows segregation curves for several surfaces of FeAl. In all cases A1 segregates to the surface. Although the A1 segregation tendency seems to be more pronounced on open surfaces, the segregation sequence (111) > (310) > (100) > (110) can only be understood by considering the complex structure of these surfaces. An e ~ p ~ ~ n a tof i othe n d i ~ ~ r esnet ~ r ~ ~ a t~i o~nh ~ v i o r can be given based on the heat of formation in the broken-bond model (Sachtler, 1984). The broken-bond model predicts segregation of the element that has the lower heat of vaporization, since the heat of vaporization reflects the bond strength. The energy increase of two cleaved surfttces is minimized, if the surface is enriched by the element with the lower bond strength. In most Al-based B2 compounds A1 has the lower heat of vaporization and is expected to be the segregat~n~ element. In contrast the heats of formation of these
igure 11 Segregation curves obtained after quenching from high temperature for low index surfaces in FeA1. The different compositions of freshly sputtered surfaces at low temperatures are caused by the sputtering process. The near-surface concentration corresponding to bulk terminated surfaces is marked by open circles (froni ~ a ~et al., ~ 1998) e r
225
Free Surfizce Struct~reand Properties Surface reconstr~ctionsand term~nationsfor some B2 ordered compound§ Compound NiAl MiAl NiAl FeAl FeAI CoAl FeTi FeTi
Surface
Heat of formation
Reconstruction, termination
References
-58.9 kJ/mol
(I x l), A1 (1 x I), 5O%Ni 50%A1 ( l x l ) , Ni (1x1) A1 (3 x 3) A1 saturated, rich (I x l), 50% CO 50% A1 Fe-rich Ti-rich
Davis and Noonan, 1988 Davis and Noonan, 1987 and 1988 Nooiiaii and Davis, 1988 Graupner et al., 1995 Graupner et al., 1995 Blum et al., 1996'0 Felter et al., 1982 Felter et al., 1982
-25.1 kJ/mol -54.2 kJ/mol
compounds are rather different. For NiAl a heat of formation of 58.9 kJ/mol was reported (Table 2) which is considerably higher than that for FeAl with 25.1 kJ/ mol. Therefore, the driving force to lower the surface energy by segregation i s much stronger in FeAl than in NiA1. CoAl has a heat o f formation comparable to that of NiAl, a fact which is an excellent fit to the observation that similar surface structures are found on CoAl as on NiA1. A1 segregation to the surface was also proven to occur in the compound Fe3AI with the DO3 (cF16) structure (Voges et al., 1992). This occurs well below the bulk order-disorder transition temperature of 800 K. Tn this compound the heat of formation of -13 kJ/mol is even lower than in FeAl, which favors the segregation behavior. SiO
Surface diffusion along craGks or cavities can play the role of a short circuit for bulk diffusion and therefore can influence the high-temperature properties of inte~etallics. A comparison of free-surface and grain-boundary diffusion values gives a better understanding o f the diffusion mechanism. Surface diffusion in general is influenced sensitively by the environment and surface structure. Furthermore, surface diffusion is highly anisotropic. Thus multiple experiments are necessary to gain a thorough understanding of the basic mechaiiisin in intermetallic conipounds. Surface diffusion is studied from a microscopic atomic view with FIM and STN. However, the interaction between the STM tip or the conditions at the sharp tip in the FIM may influence the ~ e a s u r e ~ e n t s~acroscopic . investigations of surface diffusion are performed for example with gra~n-boundarygrooving experinients, which are widely applied to determine grain-bou~da~y energies and surface-diffusion coeEcients. The application of a n atomic force microscope (AFM), instead of convent~onallyused light microscopy allows analysis
of the profiles of rain-boundary grooves or surface undulations with much higher accuracy (Jin et al., 1999; Weber et al., 2000). Recently this technique has been applied to study the grain-bou~darygrooves in NiAl bicrystals (Rabkin et al., ~000). more work lias yet to be performed to study the surface diffusion properties of inte~etallics.
Interfaces and free surfaces have an important influence on the properties of intermetallic cornpounds, as for example m e c ~ a n ~ cproperties. ~l Corrosion and catalytic behavior are obviously dominated by the surface structure and composition of intermetallics. Segregation to free surfaces and interfaces can have a strong influence on the fracture behavior, for example in boron-doped NiJAl, where boron enrichment at the grain boundaries improves the fracture toughness considerably. S SS
The energy of a surface is closely related to the structure of the surf'ace. Surfaces tend to lower their surface energy by reconstructions and relaxations of the surface. Foiles (1987) computed the energies of (1 x 2) reconstructed and relaxed surfwes of many fcc metals using the embedded~atommethod and obtained the largest reduction in surface energy for Au and Pt, which show a (1 x 2) reconstruction. Nevertheless, reliable e x ~ e r i ~ e n t values al for surface energies are available only for a few simple surfaces (Porter and Easterling, 1992; Howe, 1997). Methods for surface-energy measuremen described for example in the book by (1973). Calculations of surface energies are widely made using known interatomic potentials. The surface energies of simple low-index surfaces can also be
calculated with current ab-iEitio calculations. A simple model to describe the surface energy for high-index s~irfacesis to a s s u ~ ea stepped surface ~onsistingof low-index facets. The energy of complex high index surfaces is then calculated as the SUM of all surface facets. Mutasa and Farkas (1998) recently compared simulated surface energies with the results from this simple model and showed that this method gives reasonable results for the compounds NiAl, FeAl and TiAl . For Cu3Au (loo), (1 10) and (1 11) surfxes Wallace and Ackland, 1992, computed surface energies of di~erentlytruncated and relaxed surfaces with FinnisSinclair many-body type potentials and molecular statics techniques. Their results for the surface energies are shown in Table 3. Clearly the mixed-composition Cu-Au surface terminations are energetically favored at zero temper~ture,in both the relaxed and unrelaxed states. These ca~culationscorrespond very well to the ex~erimentalob~ervationof a mixed Cu-Au termination. The close-packed (1 1I) surfaces have nearly the same energy as the open (100) surfaces. In pure fcc metals (111) surfaces would be expected to have substantially lower energies than (100) surfaces. In these calculations a buckled surface structure was also found for CusAu. The Au atoms with larger atomic radii are raised above the copper atoms on each of the three surfaces with the mixed termination. The importance of surface stresses recently became widely appreciated. For metals the sureace stress, which acts within the lateral surface plane, is normally of tensile nature. The surface stress determines the strain ~ ~ ~ e n d ofe nthec surface ~ energy. The influe~ice of surface eiiergy and surface stress is, for example, important in the g r o ~ t h~ e c ha ni s mof thin films, where coalescence of islands occurs (Nix and Clemens, 1999). Many experimental studies have also proven that the lattice constant of small particles is reduced from the bulk lattice constant (Mays et al., 1968; Salomons et d., 1988) due to surface stress, Surface stress can also influence the reconstruction of surfaces, as demonstrate^ by the (23 x J3) reconstruction
observed on Au (111) surfaces (Harten P t al., 1985). Needs et al, (1991) calculated the surface stresses and energies for some fcc metals. The surface stress i s always larger than the surface energy. For example, for A1 a surface energy of 0.06 eV/atoni and a surface stress of 0.078 eV/atom were found. The origin of the surface stress can be described in a simple manner. A t o m at the surface have a lower coordiiiatioii number and tend to iiicrease the charge density around the atoms by an inward relaxation. Since there is an electrostatic repulsion of the atoms, these relaxations are not able to reduce the surface energy to zero. Thus, the surface atoms still sit at a density lower than in the bulk. Therefore, the atoms tend to increase their density to the optimal value through a tension in the surface. Even though few data about the surface stress in intermetallics are available, it is expected that the surface stress makes an important contribution to the properties of fine-scaled materials, where large surface areas are present. 7.2
The details of surface structure, composition and energy are very important for the role of surfaces in the fracture process. ~ e ~ e r m i n a t i oof~ sthe surface energy should lead to a better ~~nderst an~iofngthe fracture process and the prediction of the preferred cleavage planes and fracture mode. Figure 12 for example shows (110) cleavage facets in NiAl imaged with an. AFM. The cleavage fracture in 2 aluminides was reviewed, for example, by Chang et al. (1992). A substantially different fracture behavior was found for NiAl and FeAl. In NiAl (110) cleavage is preferred, but sometimes cleavage on higher-index surfaces has been. reported. In FeAI cleavage occurs on (100) planes. Chang et al. proposed that the difference in the fracture mode can be explained by a broken-bond model. In those B2 aluminides having a low ordering energy such as FeAl, fracture i s suggested to occur on (100) planes. In materials with high ordering energy
Table 3 Relaxed and unrelaxed absolute-zero surface energies of ordered Cu3Au(from Wallace and Ackland (1992) Surface
y, unrelaxed (mJ/m2)
y, relaxed (niJ/in2j
(I00j Cu-Au terminated
896 1192 1051 1240 882
865 1171 1024 1173 863
(100) pure Cu terminated (1 10) Cu-Au terminated (1 10j pure Cu terminated (1 1I j Cu,Au
Free Surface Structure and Properties
227
Figure 12 Fracture surface of a NiAl single crystals. (110) cleavage facets are visible in the AFM scan (from Goken, 1999), reproduced with permission
(for example NiAI) with a relatively large charge transfer from A1 to Ni atoms, the surface charge could be balanced only on (1 10) planes. Ah-initio calculations by Fu and Yoo (1992) shed more light on this point. Their calculations suggested that a strongly directional d-bonding in FeAl is responsible for the high cleavage energy of this compound. The different termination of surfaces discussed so far often has no influence on the ideal cleavage energy determined by simulations. Cleavage in NiAl on (100) planes, which may have either a Ni or A1 termination, would always produce one Ni-terminated and one Al-terminated surface. The cleavage energies must be identical. Calculated cleavage energies for several compounds can be found in Yoo and Fu (1992). They included in their analysis a calculation of the anisotropic fracture toughness and considered also the shear stress on possible slip systems. Thus the preferred (110) cleavage plane in NiAl could be understood. 7.3 Mechanical Properties near Surfaces and Interfaces
With current nanoindentation methods the mechanical properties of very thin surface layers can be investigated. Figure 13 shows an AFM image, where the properties across a grain boundary in a NiAl bicrystal
were determined with extremely small indents. Only the indents performed with a maximum load of 300 pN show a significant increase in hardness at the boundary. Similar measurements at the free surfaces of cracks in NiAl (Kempf et al., 1998) also revealed only very slight deviations of the mechanical properties from the bulk properties at distances above 100 nm from the surface. On the other hand grainboundary hardening effects by solute atoms were observed in several compounds, for example AgMg, NiGa and NiAl (Westbrook and Wood, 1963; Seybolt and Westbrook, 1964). With nanoindentations it is also possible to probe the surface properties in a direction normal to the free surface. Then, even thinner layers near the surface are probed. Several effects contribute to the observed variations of the properties of surfaces in the nanometer range. The well-known indentation-size effect (ISE) increases the observed hardness close to the surfacc by the emission of geometrically necessary dislocations during indenting. Thin films on substrates show a larger hardness or strength than bulk materials (Nix, 1997). Nanoindentations on nearly all metals and intermetallics, as for example Ni3Al TiAl, Ti3Al and MoSSiBz, show a significant onset of yielding (pop-in) in the load-displacement curves (Goken and Kempf, 2001). Dislocation sources are activated first at a stress level close to the
228
Properties and Pdzeizomenology
3 Hardness across a grain boundary iri NiAl probed with nanoin~entation~. The AFM image (above) shows the impressions left from the indentations (from GCSken et al., 1999), reproduced with permission
theoretical shear strength level (Goken et al., 2000). Surface steps and ledges probably are preferred spots for dislocation emission and multiplication (Kiely et al., 1998). These effects are currently under investigation by several groups. The elastic properties near the surf~ceor of thin films seem to match inore or less the properties of the bulk. However, a thorough underof the plastic deformation properties at the surface is still lacking.
n most low-index surfaces of intermetallic alloys a bulk-like termination of the surface is observed.
Reconstruction (rearrangement of atoms at the surface) is not observed an many intermetallic alloys. In contrast, relaxation of atoms in the outermost surface layer and beneath the surface is a rather common phenomenon. Nevertheless, even some pure fcc metals such as Au show a reconstruction of the surface structure, i.e. a non-bulk ~ e r m ~ ~ aexists t ~ o nat the free surface. In intermetal~icsthe ordering energy of the compound may be high, for example in the B2 compounds NiAl or COAL These compo~ndstend to show a bulk-terminated surface since the driving force for a reconstruction is too low. llrr FeAl with a much lower heat of formation, Al. s e ~ r e ~ a t i oton the surface was observed and even reconstructions were reported on sonie surfaces. Ordered compounds can have different possible ~erminations,for example pure Alor pure N~-teri~inat~ons on the NiAl (100) surface. A1 terminations seem to be preferred, which may be understood by the relatively low heat of vaporization for Al. A rippled surface relaxation behavior was found on NiAl and other compounds with the larger A1 atonis moved outward from the bulk. In L12 compounds, for example Ni3Al and CugAu, the mixed surface termination seems to be preferred. A buckling of the ininority element A1 or Au out of the bulk could be predicted from a simple atomic-size argument. Nevertheless, the many-body term in the atomic potentials has a significant effect, which inay either reduce the surface buckling or enhance it. Surface phase transitions were i~vestigatedin detail experimentally and theoretically on. CU~AU, where a discontinuous bulk order-disorder transition occurs. Interestingly, the order-disorder transition in bulk is of first-order whereas the transition at the surface is of second-order. The ordering effects are related to segregation properties (Sanchea and Mora~-Lopez, 1985). Segregation can also influence the surface structure and inay induce a surface reconstruction, as observed in the Fe-A1 system. ~ e g r e g ~ t i oeffects n play a minor role in. conipounds with high ordering energy, for example NiAl. The structure of a free surface determines the properties at the surface. Surface energies were ~alculatedfor several compounds in the relaxed and unrelaxed states. Surface energy and surface stress are important quantities with regard to fracture and ~ ~ c r o s t r u c t u ~The e. anisotropy of surface energy in the fcc-based compound CugAu is significantly different from that in pure fcc metals. Ab-inim calculations of cleavage energies predict the fracture mode successfully. Although simulations and experiments are in relatively good agreement in determining and predicting the surface structure and
Free Surfbnce Structw'e and Pmperties relaxations, inore work has to be done on their influence on surface properties. Few iiivestigations in intermetallics are related to the properties at the surface, for example surface diRusion aiid tlze mechanical properties.
Allen, R. E., and de Wette, F. W. (1969). Phys. Rev., 179, 873. Atrei, A., Bardi, U., Roviadi, G., Torrini, M., and Zanazn, E. (1992). Phys. Rev. B, 46, 1649. Aust, K. T., Peat, A. J., and Westbrook, J. H. (1966). Acta Aust, K. T., and Westbrook, J. W. (1971). Act0 Me~all., 521. Binnig, G., and Rohrer, H. (1982). Helv. Phys. Acta, 55, 726. Binnig, G., Rohrer, H., Gerber, C., and Weibel, E. (1983). Sur$ Sci. Let{., 131, L379. Birgeneau, R. J., and Horn, P. M. (1986). Scrence, Blakely, J. M. (I 973). Introduction to the Properties of Crystal SugfiJces. Pergamon, Oxford. ehreiidt, D., and Niehus, H. (1996a). Surf:
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Color of a solid material i s usually encountered among dielectrics, semiconductors and insulators but not for ~ e ~with ~ lthes exception of old, silver and copper. But other colored ‘metals, do exist as illustrated by Figure 1 (see color plate section). Current definitions of an intermetallic compound are ~ m b i ~ L i oNesper ~s. (199 1) sug~estsd e ~ n ~ ninterg metallic phases as having two attributes, (a) being compounds of metallic constituents and (b) having metallic conductivity. This definition would exclude for example Go%:!, a metallic ~ ~ a t e r i aofl beautiful dark blue color. It is therefore preferablc to follow the ~ntroductorydefinition of Westbrook and Fleischer (1995) by considering in ad~ition to metal-metal coinpounds also metal-metalloid conipouiids which include silicides, for example. In many cases, these inter~etallic compounds imply a specific stoichiometric ratio between the components and may exhibit long- or short-range order. They might also be binary or i~ulticomponent;the decisive point is the metallic character of their electronic conductivity, which means that valence and conduction bands of the electronic structure overlap, at least in part. Their usually large electrical conductivity originates from rather mobile electronic states. For the nietallurgist, such c h a r ~ ~ ~ e r i s t iare c s typical for single element metals or disordered alloys which melt at a specific teniperature (elemental metals) or over a range of t e ~ ~ e r a t u r and e s compositions (solid solution alloys); however, interi~etal~ic c o ~ p o u n d in. s most cases solidify
congruently at a well-defined teniperature arid composition, and have in additioii a rather na~rowdomain of existence. Early applications of i i i t e ~ e t a ~ l iphases, c such ics mirrors of bronze, coatings for the d e c o r ~ t ~arts, v~ amalgam in dental medicine, and more recent uses as magnetic materials, superconductors, major constituents of superalloys for h i ~ ~ - t e ~ p e r aap~lications, tur~ and so forth, are well known (see e. 1977; SauthoR, 1995). owever, there is another, much less known, but distinctly visible, property of a certain class of ~ntermetallic ~ o ~ ~ o n~a ~ne l~y § , their apparent color. About 100 ~ ~ ~ ~ p oau ~ i~ d s o the 30 000 substances tabulated in Pearson’s ~ u ~ d (Villass and Calve blue NiAl, yellow dark blue CoSi:! Randin, 1994; ~teinemannet aE,, 1997). in ~hapterby Wolff on precious metal ~ntermet~ll~cs this volume.) These materials have metallic luster due to the strong coupling of photons in the range of visible light to c o ~ ~ u c t i ne lge c t r o ~ ~states, c and due to the absence of polarization of the reflected light. appearance and properties of such materials are ~~~c distinctly different from those of d i e l e ~ media. Colored i n t e ~ e t a l ~ ~might c s find a ~ ~ l i c ~ t i for o~is watches and jewelery if they could be properly molded and shaped. For this purpose the i n t e r ~ ~ t a l lniaterial ic must also possess suitable ~ecliaiiicalproperties, in particular they must be sufficiently ductile. For the engineer and jewelery maker it is necessa~yto know related data o f such a material. ~ ~ e r e ~ oatr tlie e , end of
i n ~ ~ r ~C ~ ot a~ l ~~ Vol. ~p ~3, ~ Priumpbs ~ ~ c and ~ Practice. ~ ~ Edited hy J. €3. Westbrook and R. L. Fleischer. @ZOO2 John Wiley & Sons, Ltd.
232
Properties. and P h e ~ o ~ e ~ ~ l ~ g y
our treatise we provide a compact section for applicaecause of the attractive properties of CoSi2 (concerning color as well as the standard mechanical properties), we have chosen this compound as an example, providing partially new calculated data for its electronic structure and optical properties, as well as elastic data and information about cleavage, com~ressionand ductility. Thc present chapter deals with the origin o f color in intermetallics and its relation to the electronic properties, bonding, and the crystal structure of colored intermetallic compounds. For a detailed discussion of many of the physical aspects of color of materials we refer the reader to the most recent book in this field (Tilley, 2000).
lee, 1956, 1921/1922), the great painter, describes color as ‘Gold is a fluctuation between deep te color o f extreme brightness, a er vibrates from dark to very bright and is also defined as a nioving value. Copper is a vibrato from red-orange to over-brightness. These metallic values of color are subtle pictorial agents’. Color, as an impression, is not easily accessible to an objective me~~surement, Most of the attributes used to describe the pressio ion of color such as brilliance, ness, saturation, Luster (see the appended ssary) cannot easily be cast into a definition of objective physical quantities, because they depend strongly on the physiology of the human eye and the stimulation to signal processing by the central nervous system. In fact, the human eye is more sensitive for green colors than for red and blue tints, and the a particular color varies with light wever, it is admitted that the spectral reflection power of a material is the reference and that a preferential reflection is perceived as a distinct color. From a physicist’s point of view, color of intermetallic compounds (which are not transparent to visible light) is connected with the reflectivity of the material. The relation between the perception of color and the p h ~ ~ ~ c a defined lly and measurable optical reflectivity is illustrated by the following examples of colored ‘metals’. For practical purposes, in particular for the jewelery maker, a color scheme was developed by the International Commission on Illumination (CIELAB), namely the so-called L*a*b* scheme, which has the
advantage of describing color in a mathematical way by the three coordinates meiztioned: L* stands far luniinance or brightness, a* and b* for the i~itensities of the color pairs red-green and blue-yellow. All these quantities can be measured by a spectrophotoxneter, which normally has a resol v~n~ power 5 to 10 times greater than the human eye. A more detailed description is found in the excellent article of Cretu and van der Lingen (1999) on colored gold alloys. Figure 2 shows reslnlts of optical reflectivity measurements for gold and the intermetallic conipound PdIn. In the infrared and longer wavelength range of visible light, gold reflects more than 95% of the e l o the ~ wavelength /z = 650 nm or at than 1.9 eV, the reflectivity falls off” rapidly with decreasing wavelength^ The yellow color of gold results from its low r~flectivity,or strong absorption of light for photon energies above 2.4 eV. In the case of Pdln, the absorption edge is shifted to lower energies, and the color of the compound then appears as purplish pink (Jan and Vishnubhatla, 1967; Cho, 1970). The corresponding ClELAB values are L* = 88, a* = + 5 , b* = +35 for Au, and L* =70, a* = 3-12, b* = +6 for PdIn. Other data are shown in Figure 3 representing reflectivities for Ni and the ter~etallicdisilicides NiSi2 and CoSiz; the CIELA values for CoSiz are L* == 66, a* = -2, b* = -7. In the case of Ni, the reflectivity decreases 1110x10tonically with increasing photon energy; thus this metal appears to be of a silvery white color. The curves for the silicides differ markedly because the reflectivity has a steep decrease below the visible range of the spectrum, followed by a peak at higher energies. The compound Nisi2 shows a niaximum at about 3 eV and an average reflectivity over the visible range of about 45% that gives this metal a bluish-gray hue. For CoSi2, tlic peak of the reflectivity is more pronounced and lies at lower energy. Also, the average reflectivity is only 35%’ therefore CoSiz appears to be of a dark blue color. y The optical properties of the H u i ~ e - ~ o t h e r€32 (cP2) aluminides NiAl, COAL and FeAl have been studied intensively during recent decades (Sambongi et al., 1966; Jacobi and Stahl, 1968; Schlemper and Thomas, 1994). The pronounced difference in color between blue NiAl and yellow CoAl is clearly represented by a distinct peak of‘ the reflectivity at 2.6eV for NiAl and for CoAl a shoulder of the reflectivity at lower energies which smoothly drops OR to a ininimuni at 3 eV. Special interest was attracted by the fact that these c o ~ p o u n ~exhibit s dramatic
Color and Q ~ t i c Properties ~l 100 I
100
233 I
1
1
I
I
I
1
I
80
80
s
8 i
5
6
50w U
u
U
w cc
-
20 -
"0
50
Y
. . A -
20
1
2 3 4 PHOTON ENERGY, eV
5
6
Figure 2 Reflectivity of Au and the intermetallic compound PdIn. The visible range and the color scale are Indicated. Two experimental curves are shown for PdIn (reproduced from Steinemaiiii et al., 1997)
changes of color for off-stoichiometry compositions within the existence range. The origin of all these color effects is well understood from an analysis of the electronic structure (Sclilemper and Thomas, 1994). Tlie relation between the electronic structure of intermetallic ~ompoundsand their colored appearance is explored in the next section.
Color is a consequence of the interaction of light with matter in the frt;quency range of visible light (tpproxinlate range of energy (R) 3.5-3.3 c=V or a range of wavelengths (I.) 827-376 nm; conversion factor is 2/01 (eV) = /2/1240nm). The interaction of metallic compounds with light in this frequency range is typically dominated by reflea;tion. Tlie incident photon can be described as a varying electromagnetic field. Entering the metallic material, the photon transfers its energy, inducing oscillations of the materia19selectron system. Due to axwell's laws, these oscillating electrons in turn emit electromagnetic waves, i.e. the reflected photons. In general, the frequency of incident and emitted photons i s the same. And indeed, most metallic compounds exhibit about equal reflectivity over the whole range of visible light and are therefore non-colored. A metallic material will appear to be colored, if over a certain range of frequencies of the visible spectrum light is absorbed rather than reflected. The selective absorption of a photon of a given frequency is caused by electrons in specific electronic states that are able to
0' 0
I
1
2 3 PHOTON ~
~
I
I
4 ~eV R
5
I 6
~ Y ,
Figure 3 Reflectivity of Ni and the two compounds Nisi2 and CoSiz. The visible range and the color scale are Indicated (reproduced from Steinernann et al., 1997)
accept the corresponding energy quanta to junip into an excited quantum state. The absorbed photoiis o f this frequency are then missing in the spectrum of the reflected light; what remains is the so-called complementary color. For example, if a compound has absorbed green light, it appears red. The electronic structure of i n t e r m ~ t ~compounds ll~~ and its interaction with photons can be studied and understood by means of quantum mechanical calculations, coinplemeiiting experimental measurements. Xn terms of quantum mechanics, the above qualitative picture of the interaction process can be put into a more precise formulation which enables calculation of reflectivity and absorption data from first principles, i.e. without introducing empirical parameters. In quantum mechanics, light is an electromagnetic wave, quantized in t e r m of energy packets, hv, with v being the frequency of the photon and h the Planck constant. The photon and its electromagnetic field interact with the electrons of the material. The response of the electronic structure of matter to the oscillating electromagnetic field as imposed by the photons is determined by the tensor of the complex dielectric fknction E ( W ) of the electron system. &(CO)
+
= ~ ( c o ) ic2(o)
(1)
Specifically, the imaginary part of the dielectric function ca (U-)) is directly related to transitions between different quantum states
234
Properties and Phenomenology
Equation (2) explicitly tells us (note the argument of the &function) that a photon intcracts with an electron (of mass 7 8 and charge e ) only if the photon's energy AUJ exactly equals the energy difference necessary to excite the electron from the occupied state with eigeiivalue Et, to, any available unoccupied state with eigenvalue E::
ACO = E: -
= hE
(3)
In the solid state a huge number of electron states, characterized by x-vcctors and band index n as quantum numbers, form quasi-continuous energy ands. The overall dielectric response is therefore given as a sun1 over all possible transitions between occupied Tates n' and unoc ied states y1 integrated over all ?z-vectors in the llouin zone (BZ). In addition, it i s required for an electron-photon interaction that the statc of angular nionientuin is changed by the transition, i.e. that the matrix elements
of the m o i ~ e n t uoperator ~ @ are non-zero, !Q$ denoting the wave f~nctionof the electronic state k , n. En the praxis of quantum nieclianical calculations, equation (2) can be directly evaluated, and the real part of the dielectric constant tensor is obtained from the ronig relations. The optical conductivity tensor 0 ' ' is related to the dielectric function by (5)
From the calculated dielectric function or conductivity tensor, the optical properties can be obtained by a few simple relations. The reflectivity is given as
R(w) =
I &&JE(W)-
1
and the absorption coefficient q is defined as 4 = 2k
cu
-
c
(7)
where k is the imaginary part of the complex refractive index and c is the velocity of light. upported by quantum mechanical modeling, it is possible to identify those features of the electronic structure causing the color of some intermetallic compounds. The required electronic structure is shown schema~ic~lly in Fi In order to achieve selective absorption within a narrow frequency rsmge and good reflectivity elsewhere, distinct and sharp peaks of the density of states
Figure 4 Sketch of electronic energy bands and photon absorption process in an intermetallic cornpound with a pseudogap
are required, separated by a pseudogap. A pseudogap is an energy range with only a few available quantum states, i.e. a valley in the density of states curve. The states below the pseudogap have to be occupied and the states above it should be empty excited states. In other words the Fermi energy separating occupied and unoccupied parts of the electronic structure has to reside inside the pseudogap. Photons with energies equal to, or greater than, the width of the pseudogap can be absorbed by the electron system by exciting electrons from occupied states below the pseudogap into excited states above the pseudogap, provided that the matrix elements for these tramitions are non-zero. These frequencies are then removed from the spectrum of reflected light, causing the intermetallic compound to exhibit the complementary color. As an example, Figure 5 shows the density of states of CoSi2 as calculated by a density-functional-theorybased approach (Hoheiiberg and Kohn, 1964; Kohn and Sham, 1965; Wimrner et al., 1981; Jansen and Freeman, 1984). The blue color of CoSi:! can already be understood by studying the density of states. The pseudogap separates two sharp peaks of the density of states, arising from occupied COd states and empty p states. The separation between these peaks is about 2eV and transitions are allowed, since the angular ~ o i ~ ~ n t changes u r n from I = 2 to l = 1 upon excitation. Therefore, photons with an energy of about 2 eV are absorbed by the electronic structure of CoSi2, removing photons of lower frequencies and thereby the
Color a ~ i dOptical Properties 6,
I
-
DOS of CoSi,
-
_---. CO d
-
I
...., ..., Si s “._I_.
-15
I
I
i
1
Si p
-1 0
-5
0
nergy
5
10
c eV 1
Calculated electroiiic density of states of CoSiz. Optical transitions creating the blue color of CO& are indicated by arrows
red colored light from the reflected spectrum. At higher energies, however, the density of states exhibits a second pseudogap at about 3-3.5 eV. Due to the small number of available excited states in this energy range, photons of higher frequencies are not absorbed and blue colors therefore dominate the spectrum of the reflected light. Some representative optical transitions involved are indicated by arrows in the band structure
15
10
5 n
235
of CoSi2 in. Figure 6. The band structure displays energy eigenvalues of the electron system along certain high symmetry directions in the Brillouin zone. Figure 7 shows the reflectivity curve as ~ ~ l c ~ i l afrom ~ e d the electronic structure. Indeed, the reflectivity shows a maximum at about 3 eV and a miniinurn below 2 eV as expected from the inspection of the density of states and band structure, thus reproducing the measured curve in Figure 3.
The bonding in metal disilicides i s well u n d e r ~ t o o ~ in terms of hybridization of transition metal d-orbitals and Si sp-like states (e.g. Pettifor, 1988). Above we showed that the position and width of a pseudogap are crucial for the optical properties of disilicides. They are also ‘good’ nietals as supported by measureiiients of transport properties (Amiotti et al., 1990; Ditchek, 1984; Hensel et al., 1984; ensel, 1986; Hirano and Kaise, 1990; Tiwari et al., 1993). The electrical conductivity at rooin temperature is about 6 x 104 (Ohm tin)-' for CoSi2, and 3 x 104 (Ohm cm>-’ for NiSiz, values which are comparable to lead. Because of the presence of the gap, holes dominate as charge carriers; in fact CoSi2 has only holes (one per unit cell) and NiSi2 has about 0.2 electrons and 0.3 holes per unit cell. The elastic scatteriiig lengths for these charge carriers are 13 and 6nm, for COS& and Nisi2 respectively, which are of the same order as the penetration depth of light, amounting to 17 nm for Nisi:!, a value also quoted for gold. One may ask, whether it is possible to formulate some principles and requirements for the appearance of colored intermetallic compounds. We believe so. First, the crystal s t ~ u c thas ~ i to ~ ~show h g h s y ~ ~ ~ ~ t r y , thus providing distinct features, i.e. sharp peaks and valleys in the density of states. iii particular, a pseudogap must exist, which enables a distinct onset of absorption bands. Strong covalent liybridi~ation 70
1
I
I
1
I
I
Reflectivity of CoSi, (calculated)
-10
-15 W
L
r
x
W K
Figure 6 Calculated electronic eiiergy bands for CoSiz. Representative optical transitions are indicated by arrows
I 0
I
I
I
I
I
2 3 4 Photon Energy [ eV ]
~ i g u r e7 Calculated reflectivity of CoSiz
I
5
6
236
Properties and ~ ~ e ~ ~ ~ e n ~ l o ~ y
may trigger distinct absorption bands with non-zero matrix elements. Siiice the Fermi level has to reside inside the pseudogap, the occupation pattern of the electronic struct~reis of particular importance. For binary intermetallic compounds this requires the involvement of transi~ion-i~et~l elements at the ends of the periods. In the following section we will try to provide some more specific guidelines on how to find colored ~ n t e r m e compounds. ~~~~~c
Following the discussion of the relationship between color and electronic structure of iiiterrnetallic compounds, we now try to relate color to crystal structure. Are there some rules for the appearance of color? It is an old chemist’s dream that a unique number can possibly be attributed to a specific element which also describes its unique behavior in molecules and compound materials, This idea is to some extent fulfilled by Pettifor’s structure maps (Pettifor and Podloucky, 1985, 1986; Pettifar, 1986, 1995), m a ppi ~ g crystal structures of binary compounds A,B, of any stoichiometry to a two-dimensio~~lmap of some ‘coordinates’ for elements A and B. For a particular stoichiometry A,$,, each point on such a twodirnensional map corresponds to a possible compound. The elements A and B are joined together along the xand y-axes, respectively, their sequence being determined by the ‘coordinates’. Existing compounds are marked on the map by a unique symbol for each crystal structure, For an appropriate choice of the atomic ‘coordinates’, well-ordered domains of crystal structures in the two-d~i~ensionalmap occur. In searching for a valid definition of these ‘coordinates’ it became obvious that the framework of classical parameters such as electronegativi~y,atomic size, and electrons per formula unit is not very suitable to generate the required well-defined mapping (Pettifor, 1986). However, the microscopic point of view in Pettifor’s scheme (Pettifor, 1988) is adequate: the local coordination, as determined by the nature of the quantum mechanical bond determines the ordering of atoms in the solid, and equally well the appearance of color. These ‘coordinates>are phenomenologicalparameters but can be justified from quantum mechanical principles for selected cornpou~ds(Beer and Pettifor, 1984; Pettifor and Podloucky, 1985, 1986). The concept af structure maps may help oiie to guess str:~cturesof yet unknown binary compounds, to find
hints for a structural phase transition or it might even ty of pseudo-binary urthermore, as we used to explore the appearance of colors of binary intermetallic compounds. maps for compounds of Figure 8 shows which could be cand~dates stoichiometry AB a for colored interm Table 1. Those domains where colored ~ompoundsmight occur axe l~igl~liglited, and the boundaries are marked by dashed lines. The cubic structure IS rather: frequent for inte~metallic compounds, aiid it dominates for the colored metals (with some known exceptions: violet Cu2Sb, a tetragonal pseudo-cubic compound, is discussed among other defect structures in Cu-Sb alloys by Bahn and Schubert (1949), or a number of minerals like bluish black, hexagonal pseu~o-cubicweissite Gul.9Te,violet, tetragonal rickardite Cu7Te5, or gray-yellow, orthorhombic pseudo-hexagonal dyscrasite Ag,Sb, a colorecl ~ u m ~ ~ o t hphase). e r y In fact, as outlined in Section 3, colored intermetallic compounds require a crystal structure of highest symmetry, which ensures a sufficiently simple electronic structure for distinct absorption bands of high intensity. A list of binary colored intermetallic compounds is provided in Table 1. Only two diflerent structure types occur: the bcc-based €32 (cP2) type for com~oundsof composition AB (left panel of Figure 8) a (cF12) type for composition A Figure 8). Component A is a late transition metal element of group 8-10 or a noble metal. and B is an element of groups 13 or 14 (with the exception of PdMg). It should be noted, that throughout the chapter the group notation of the periodic table is given in terns of the New IUPAC notation. The structure exhibits high coordination numbers typi of for metals, i.e. each A atom has an envi ~onm e~t eight B nearest neighbors arranged at the corners o f a cube and vice versa. In the Cl st cture each atom of type A is surrounded by eight nearest neighbors; however, each B atom has only four bonds to A atoms within the first coordinatio~shell. The typical configuration for metals maximi%in~the coordination number is thus combined with tetrahedral sp3 bonds typical for covalently bonded semiconductors. It i s therefore not a surprise to obtain a pseudogap in the electronic structure of CoSi2 and related Cl compounds. The high iiumber of valence electroiis of the late transition metal elements determine the appropriate location of the Fermi level inside the pseudogap, which mechanism provides absorption bands responsible for the color of these materials,
237
Color and Optical Properties
MA=
70
60 65 70 Tc Mn Fe Ru OsCo Rh Ir Ni Pt Pd Au Ag Cu M B AS CaF, ,c Sb Fe,C,o Bi
n
MB
B 85 Si Ge
CO%, h
MiAs, h HgNln, t FeSi, c
other
Sn
ao
Pb Ga AI
In Tl Be Zn 75 Cd Hg Mg
0
other
CU
Figure 8 Color maps: regions of high-symmetry structures 111 the AB (left) and AB2 (right) Pettifor structure maps (Pettifor, 1995). Mendeleev numbers (i.e. atomic Pettifor ‘coordinates’) and prototypes (c: cubic, t: tetragonal, 0: orthorhoinbic, fi: hexagonal) are shown. Limits for expected colored intermetallic coinpounds are indicated by dashed lines (reproduc~dfrom Steinemann et al.. 1997)
About one-third of the AB compounds of B2 structure within the highlighted region of Figure 8 are colored. The compounds PtGa and PdGa lying on the boundary crystallize in the B1 structure, which is a high-symmetry fcc-based structure with six nearest neighbors, but these compounds show no particular color because of the missing pseudogap. A further cubic compound on the boundary line, PtMg, is not a candidate for color because its I320 (cP8) structure (prototype FeSi), although cubic, is of lower symmetry. For compounds of stoichiometry AB2 eight out of 11 compounds of C1 structure within the highlighted region appear colorful. Other binary colored intermetallics with structures of lower symmetry are not found. However, the appearance of color for intermetallic compounds is not restricted to the short list of stoichiornetric binary compounds shown in Table 1. Due to the metallic coordination, B2 compounds exhibit a rather extended existence rail component can be substituted by a variety of related elements. As a matter of fact, by such substitutions color can be adapted and varied in a specified way, because the color effects are directly related to the valency of the added element, A well-known example is the spectrum of colors exhibited by NiAl within its
homogeneity region, ranging from yellow for Ni-rich samples (60%) to pink (55%), blue (50%) and gray (45%) with decreasing Ni contents. The appearance of colors in B2 aluminides was investigated, apply in^ the rules for Hume-Rotliery phases, by Jacobi and Stahl (1968) and later on by Schlemper and Thomas (1994). Another prominent example to be discussed is the red compound PdIn. Iridium can be replaced by isoelectronic A1 up to 100%. Even replacing 50% of In by A1 does not alter the color, and only substitution of loo%, resulting in PdAl, shifts the color from red to yellow. A similar change of color can also be achieved by increasing the Pd content of PdIn. Substitution of In by elements of higher valence like Sn and Sb enables a gradual colsr modification from red to yellow to silvery. On the other hand, elements of lower valence like Ag, Gu and Mg can be substitute^ for In up to 10% and the red color is thereby more and more intensified. Some of these compounds derived from Pdln are presented in Figure 1. Their outstanding properties, and the fact that considerable hardening is achievable by macroalloying and microalloying, make PdIn a rather interesting material for precious objects. For compounds of C1 structure the variability of color by substitution is quite limited, because these inpart-covalently-bonded materials have a rather limited
able 1 Colored binary intermeta~lic compounds: their structure types, compositions and colors €32 (cP2)
C1 (cF12)
Compoitnd
Color
Compound
Color
FcAl CoAl COG3 NiAl NiGa PdIn PdMg PdAl
(brown) yellow yellow blue bluish red yellow yellow
Nisi, PtAI, PtGa, Ptln, AuA1, ALlCa, AuIn,
dark blue gray blue yellow yellow yellow violet blue blue
range of existence. For instance, CoSi;! exists only for cobalt contents between 33.8 and 34.4% and ternary n, A1 and Ge are soluble only up to a few percent. This imposes limitations not only for the variability of color but also for ways to achieve ductil~zation. However, a whole class of ternary and quaternary oiiiids, structurally related to the C1 c o ~ p o u n d sexist, ~ ~ i may c h be denoted as Zintl phase derivatives, filled zinc blende structures, or simply AB2-derived compounds; and indeed, a considerable number of them are colored. The cry$tallo~raphicrelationships between the involved structures of cubic symmetry are described in Table 2 and the ~ o n s t ~ c ~ of i o the n ~ ~ r i vat i ves starting from the fcc lattice is illustrated by Figure 9 (in color plate section). The fcc lattice (Wyckoff positions a>provides octahedral sites ( ~ y c k o f fpositions b) and tetrahedral sites ( ~ y ~ positi~ns k o ~ c and d ) which can be occupied by different kinds of atoms. Occupation of all 6 positions or all c positions by atoms different from those 011 a positions yields the rock salt or the
zinc blende structure, respectively. The filled-up zinc blende structures of prototypes AdLiSi, CaF2, F3 are generated by occupation of 6, ns by atoms of different types as described in Table 2. Finally, filling all n and Et positions with atom type A and with atom type B results in the centered cubic, protgtype ' CsG above. A large variety o f elernents are able to build up c o ~ p o u n d sof the filled zinc blende struc~ure.As a typical occupation pattern, octahedra~lycoord~nateda positions are occupied by metal or of valence 3-5 ups 13-15: Sb, AI, Ga, In); tetrahedrally coordinat~d c and d positions are to some extent occupied by late transition metals or noble metals (groups 8-1 1: CO, Ni, Ru, Rh, Pd, Ir, Pt, Cu, Ag, Au), whereas metals of occupy b its well as c raphic datta of these terature (Zintl et al., 1937; Schuster, 1966; Pauly et al., 1968a,b; Schuster et al., 1969; Kistrup and Sch ter, 1972, 1974; ~ e e l ~ ~ i ~ 1978; Eberz et al., 1980; etersenn, 1981; ~ e t e r s e n ~ and Schuster, 1981; Eberz, 1983; ~ ~ h i ~ i d1985; t, Drews et al., 1986; Drews, 1989; Czybulka et al., 1990; Villars and Calvert, 1991). Whether compounds of the filled zinc blende structure are colored or not depends 01%s ~ ~ ~ c h i o ~ ~ t r y and the atom types involved, All known ternary and quaternary c o ~ p o u n dof s this type e ~ h i b i t i ncolor ~ are listed in Tables 3, 4 and 5. The binary boundary cases were listed earlier in Table I , Again, the ~ u e s t i ois~ whether there is a simple criterion which predicts the appearance of color for these compounds. It seems that a simple empirical counting scheme of valence electrons is applica~le,at least with some caution.
~~cht Pearson bcc and fcc structures and crystallogra~hicallyrelated itriictures, identified by S t r u ~ t u r ~ ~designation, symbol, and Wyckoff ~otationfor site occupatio~ Site occupation
St ~ ~ ~ ~ ~ ~ r b ~ r i c h t ~esign~tio~ Prototype
w CsCl NaTl BiF, CuHg,Ti AlLiSi CaF, ZnS N2-161 cu
Pearson symbol CE?
CP2 cF16 cF1 6 CA6 cF12 cF12 CF"3
c n cF4
Substance
P-AgCd PdIll CdLi PdLi,Sn PtLiMgSb PtMgSn CoSi, AuAl BiCe CdLi,
a
b
c
Ag or Cd on any site 41n 4Pd 4Pd 4Cd 4Li 4Li 4Sn 4Li 4Pd and 4Sb 4Mg 4Pt 4Sn 4Mg 4Pt 4Co 4Si 4Al 4.Au 4% 4Ce Cd and 3LI on site a
d
4111 4Cd 4Li 4Li 4Si
239
Color and Optical Properties T a ~ l3 ~ Group-1 1-based ternary colored intermetallic compounds of the Zintl type (derivatives of AB, structure). Table ordered according to noble metal component and increasing total number of valence electrons NVaPThe number of valence electrons is set at 1 for noble metal atoms, at 1 aiid 2 for alkaline and alkaline-earth inetal atoms, respectively, and at 3-5 for metals and metalloids, corresponding to the group number of the periodic table
Table 4 Group 8-, 9- and 10-based ternary colored intermetallic compounds of the Zintl type (derivatives of AB, structure). Table ordered according to transition inetal component and increasing total number of valence electrons NYal.The number of valence electrons per t~ansitionmetal atom i s set to zero (Ekman's rule) Compound
Golor
Compound
Color
CO Li, Ge
yellow-brown
6
Cu, Li Si Cu, Li Ge Cu Li, Ge Cu Li, Sn Cu Mg Sn c u Mg Sb
red-violet red-violet bright red dark violet blue-gray blue
7 7 8
Ni, Li Ge Ni, Li Sn Ni Li2 Si Ni Mg Sb Ni Mg Bi
brass-yellow yellow yellow-brown blue-violet blue-violet
5 5 6 7 7
Ag Li, A1 Ag Li, Ga Ag L1, In Ag Li, Sn Ag Li, Pb Ag, Li Sn
yellow-pink yellow gold-yellow dark red-violet blue-violet light blue
6 6 6 7 7 7
Ru LI Al, Ru Li Ga, Ru Li In,
yellow gray si1very
7 7 7
Au Li, Ga Au Li, In Au Mg Sn Au Li Sb ALILI, Sn Au Li, Pb Au Li,, AI, Au Li,, Ga, Au LI,, In, Au Mg Sb Au Li, Sb
green-yellow green-yellow red-violet red-violet pink violet blue blue gray gray bluish
6 6 7 7 7 7 7.3 7.5 7.6 8 8
RI1 Li, Ga Rh Li, In Rh Li Al, Rh Li Ga, Rh Li In,
light-yellow silvery yellow light blue silvery
5 5 7 7 7
Pd, Li Ge Pd, Li Sn Pd, Li Pb Pd Li, A1 Pd Li, Ga Pd LI, In Pd Li, Ge Pd Li, Sn Pd Li, Pb Pd Mg Sn Pd Li AI, Pd Li Ga, Pd Li In, Pd Li,Sb Pd Mg Sb Pd Mg, Sb Pd Mg, Sb
brown- yellow brown-yellow brown-yellow rose brass-yellow browi1-yellow yellow yellow brown- yellow brown-yellow violet silvery silvery brass-yellow violet light violet blue-gray
5 5 5 5 5 5 6 6 6 6 7 7 7 7
Ir Ir Ir Ir Ir
Li, Ca Li, In Li, Sn Li Al, Li Ga,
silvery silvery silvery red-violet light violet
5 5 6 7 7
Pt Pt Pt Pt Pt Pt Pt Pt Pt Pt
Li, AI Li, Ga Li, In Li, Sn Mg Sn Li AI, Li Ga, Li In, Li, Sb Mg Sb
bright-yellow bright- yellow brass-yellow yellow reddish-brown copper-red brown-pink pink brass-yellow violet
5 5 5 6 6 7 7 7 7
N"d
7 7 7
By such a scheme, 1 and 2 valence electrons are attributed to group 1 and 2 elements, e.g. Li and Mg, u ~ electrons to noble metals and and ( ~ g -~10)~ valence further to elements of groups 11 to 15, wherein ATgroup is the corresponding group number. In particular, for an intermetallic compound containing late transition metal elements such as Fe, CO,Ni, Ru, Rh, Pd, Ir, Pt, the number 0 is attributed according to Elsman's rule. Elcman (193 1) stated this rule as an extension of HumeRothery's electron concentration concept. Schlemper and Thomas (1994) have successfully applied Ekman's rule to determine the shift of optical absor~tionbands in transition metal alurninides. Applying the above counting scheme to all cornpouiids of the filled zinc blende type (the number of valence electrons for the colored compounds are listed in Tables 3-5) reveals the general rule that only those conipounds with valence electron numbers equal to or smaller than rn 7 exhibit color effects, as originally suggested by Eberz et al. (1980). As can be observed in Tables 3-5, this rule applies quite satisfactorily for most of the ternary and
NVd
7 8 9
7
Properties and P h ~ n ~ ~ ~ ~ ~ l ~ ~ y
240
Quaternary colored intermetallic compounds of the Zintl type (derivatives of AB, structure). Table ordered according to noble or transition metal cornponeiit and increasing total number of valence electrons Nynr as in Tables 3 and 4. Formulae that comprise partial occupations of WyckofF positions are included as found by chemical analysis and radiocrystallography Compound
Color
Pd Lt Mg Sn Pd Li Mg Sb
red-violet gray-blue
7 8
Pt LI,, Mg Sn l 3 L105 Mgo 5 Sb Pt Li h4g Sn Pt Li Mgo5Sb Pt Li,, Mg Sb Pt Li Mg Sb
dark red pink copper-red cupper-red dark blue-violet red-violet
6.5 6.5 7 7 7.5 8
Ir Li Mg Sn
gray-blue
7
Au Li Mg Sn
gray
7
NYd
quaternary Zintl-derived phases but also for the binary compounds of Table 1. For Sb~contai~ing phases and disilicides the range should be extended to valence electron numbers of up to 8. On the other hand, color effects may appear within a lower limit of x 5 for the valence electron number. It is further found that all four prototype structures, i.e. NaTl, BiF3, CuHg2Ti, AlLiSi, of the cF12 and cFl6 structure types occur among the ternary and quaternary compounds. Furthermore, there is a color trend from yellow to red, violet, and blue for an increasing number of valence electrons. There is some indication that isoelectronic i~aterialstend to show like colors. For instance, the violet compound AuAL2 is isoelectronic to quite a number of compounds like AgLizSn, AgLizPb, b, AuLizPb, AuLizSn, PdLiAlz, PtMgSb, whose color ranges between pink and violet. It should, however, be emphasized that Ekman’s rule until now lacks a satisfactory explanation from the point of view of electron theory, but is applied with some success on a purely empirical foundation. The color of intermetallic cornpounds does change with temperature. MuMawer (1 952) contributed a comprehensive study of this effect for (Cu, Ag, Au) - (Zn, Cd) /3-brasses. At low temperature (liquid nitrogen), these alloys are yellow, red and pale-gold, but appear pink, purple and violet at room temperature, At a p p r o x i ~ a t e 300 l ~ “C, their color changes to red for the common brass and gray for the other alloys. It is found that disordering is not the primary factor for the color change, but that a phase change,
e.g. the transformation of cubic P-AgCd to hexagonal results in the observed differences in appearance. The former compound has a salmon-pink color, the latter is silver-gray, i.e. i s non-colored. suggests connecting the loss of color with the Debye temperature On. In fact, OD is a measure for the onset of strong electron-lattice interactions. The thermal vibrations of the crystal lattice will change the energy levels of band electrons and ‘blur’ the band structure such as given in Figures 5 and 6 . The result is loss of color. A similar effect of ~attic~”e1ectron coupling might equally produce color changes under static mechanical strains. The variety of colors for Ziiitl phase derivatives might appear attractive for applications. However, there is a considerable obstacle, namely due to the large contents of Li, Mg, Al, the cornpounds are prone to corrosion, and yet another difficulty is brittleness. As a conclusion it appears, that applications of colored intermetallic compounds are limited. The following section will treat some of the questions related to applications.
c,
Knowledge about strength, ductility and toughness behavior is critically important for the engineer when shaping colored metals for precious objects. Several specific criteria may help to obtain information about these user properties. Again, we take as an example the dark-blue CoSi2 compound. Elastic properties are fundamental quantities which are insensitive to the processing and microstructure of a solid. This insensitivity makes the data useful to understand interactions among atoms, and it helps to clarify niicroscopic aspects of cohesion, such as yielding, dislocation interactions, and of fracture. Table 6 reports elastic property data for CoSiz, its ionic prototype (fluorite) Cap?, the metal CO and covalent Si. A first criterion by Pugh (1954) utilizes the relations between elastic and plastic properties of metals. It suggests that the ratio of bulk modulus K to shear modulus G is a measure of brittleness or of malleability. Then, a small value of K signifies easy decohesion and a large value of G characterizes high resistance against (shear) deformation, and vice versa. For cubic and hexagonal metals, the limit between brittleness and ductility lies at X/G x 2. Conteniplating Table 6, it is expected that the intermetallic
24 1
Color and Optical Properties
Table 6 Elastic moduli at 298 E; of CoSi,, CaF, (fluorite, ionic), CO(metal), Si (covalent). Columns ‘Poly’ and Single’ refer to experiments with polycrystals and single crystals; column ‘Calc’ lists ub initio data corresponding to 0 K. Subscnpt N refers Hill’s average. CoSi,
Bulk modulus (fo, GPa Shear modulus (GH),GPa Young’s niodulus (EH), GPa References PugWs ratio (K/G,,) Cauchy pressure (PJ, GPa Rice-Thomson criterion (Gb/yS)
Poly
Single
Calc
CaFz
CO
162 64 170 a,b,c 2.5
167 64 169 a,b,c 2.6 + 61 12
173 63 169 d 2.7
85 43 110 e 2.0 + 11
187 81 213 f 2.3 + 32
Si
98 67 I63 g 1.5 - 16
aGu6nin et al. (1990). bGiauque and Qberli (1992). bStemeinnnn (1994). “Yamaguchi et al. (1993). dStadler et aE. (1996). ‘HCIand Ruoff (1967). %andolt-Bornstein (1984). g ~ c S k i ~and i n Andreatch (1964).
compound Cos& has some inherent ductility, because K/G = 2.5 > 2. A second criterion, based on Cauchy’s pressure PC = c12 - c44, is related to the nature of bonding (Johnson, 1988). For central forces, PC amounts to zero. Electrostatic interactions are of this type, and in fact the ionic compound CaF2 has a small Cauchy pressure. The constant c12 represents a dilatation and c~ refers to pure shear. The negative value of PC in the case of Si is typical for strong directional bonding. For a metal on the other hand, the electron gas will not resist shear but will strongly oppose a volume change, and then PC becomes positive. CoSi2 has the signature of both the metallic and the covalent bonds, the local syminetry being octahedral for CO and tetrahedral for Si. A third criterion by Rice and Thomson (19741, relates the resistance to shear (that is Glbl, in which b is Burger’s vector) with the resistance to cleavage the surface or cleavage energy ys). If Glbj/y, < then a material behaves as ductile. For CoSiz, the [ lOO]l = a = 0.537 nm, equal to the lattice ~arameterof the und. No ~ e a s u r e ddata for ys exist, but a calc for the cleavage plane (110) yields a value of ys = 1.44 J/m2 per surface (Stadler et al., 1998; ~ogtenhuberand Podloucky, 1997). The resulting parameter Gb/y,y= 12 indicates brittleness, which is essentially caused by the large Burger’s vector of the nondisso~iateddislocation. Structure, bond strength, and anisotropy determine the active glide systems in crystals. Five independent systems are needed to accommodate deformation in a
polycrystalline aggregate. Only three glide systems exist in CoSiz (Yamaguchi et al., 1993; Anongba and ~teinemann,1993, 1994a,b, 19951, but this i s suflicient for the defomation of single crystals for which only two glide systems are needed. The compression tests of Figure 10 were done with single crystals in an orientation that can activate glide of the family of (001) planes. The rmation is limited at room temperature but extended above 100 “C. It is noted that (yield) shear stresses can be translated for axial stresses of polycrystalline materials when dividing by the Schrnid factor and multiplying by the Taylor factor of about 1.7. The resistance to compr~ssionof CO quite high, which means that CoSi2 is a hard material.
200c.
0
/4297K
10 SHEAR S T ~ A ~ 74 N,
20
igure 10 Compression tests with single crystals of CO%;!. Crystals are ariented along [ 1131 and the Schrnid factor is 0.27 for glide on basal planes. Deformation speed is 5 to 7 x 10-”s (reproduced from ~ t ~ i n e m a netn al., 1997)
242
Properties and Phenomenology
The fracture toughness of a sintered CoSi2 compound was measured by thee-point bending and by a Charpy test. The toughness values obtained were KIC == 3-4 and K z= ~ 7-8, respectively for the two tests. These are not particularly good values but are much higher than the purely elastic (or Griffithj toughness of KG = 0 . $ ~ M ~ a m 1 /It2 .must be concluded that the brittleness of CoSi2 is caused by the insufficient number of glide systems, but not by a lack of inherent ductility.
established. All the colored compounds crystallize almost exclusively in a high-symmetry cubic structure. Selective modification of colors by s~~bstituting ternary elements into ~ u ~ e - R o t h e rphases y is given as another example for the potential of color engineering. For a convenient overview, tables of compounds with their composition, color and valence electron numbers are provided. From an engineer’s point of view, the attractive colored appearance of metallic compounds must be combined with suitable m e c ~ ~ n i cproperties, al in order to enable processing of these materials in industrial appliczt‘ions.
The chapter focuses on the appearance of color for i n t e ~ i ~ 7 ~ tcompounds aZ~i~ which have distinctly different optical properties in comparison to ‘ s e ~ i c ~ n d ~and c~~r~s dieZ~ctrics.About 100 colored intermetallic compo~~nds exist. Apart from being attractive to look at, such hue a measure of the spectral energy materials might be applied for industrial purposes. The distribution of reflected light i2 is taken as a specific example apparent degree of emission of light throughout this chapter because of its beautiful or per unit area bluish-black appearance and its mechanical properties, brightness, creating possible applications in watchmaking. lightness, The definition of color is not unique. Scientists, luminance, engineers and artists have quite different schemes and or value understanding of color. A scientific definition can be the difference between the color pergiven in terms of reflection and absorption properties ceived and a neutral color perception 01which are based on the electronic structure of the of the same brilliance purity, material, whereas a technical definition for color is intensity, provided by the so-called L*a*b* scheme making use or deepness of luminance and intensities of color pairs. luster as perceived by the eye, the overall The origin of the optical properties of a particular impression of the refraction and com~oundlies in its electronic structure which comreAection of incident light from the prises the bonding characteristics of the solid material. solid surface Reflectivity spectra are therefore discussed in terms of tint a color diluted with white, having energy bands and densitie~of states. Indications and little inten~ity,but high brilliance requirements for the appearance of color o f an a color darkened with black, having intermetallic compound are formulated, namely: (a) little intensity, but low brilliance highly sym~etriccrystal structure and partially covalent bonding, both providing distinct features in the electronic structure such as sharp peaks in the densities of states and pseudo~aps;(b) an admixture of late transition or noble metals which places the Ferini energy suitably close to the pseudogap. We gratefully thank for support by the Austrian A further connection between crystal structure and Ministry of Science (grant nr. 651,45446), and the Center color is worked out. For binary compounds, Pettifor’s for Comput~tion~l Materials Science (CMSj in Vienna. structure maps turn out to be useful for locating possible compositions of colored compounds. For more complex compositions such as ternary or quaternary compoun~s (Zintl phase derivatives), a correlation between colors and the number of valence Amiotti, M., Borghesi, A., Giuzetti, G., and Navtz, F. (1990). Phys. Rev. B,42, 8939. electrons according to the so-called Ekman’s rule is
d Steinemann. S. G. (1993). Phys. Stat. Anongba, P. N.B., and Steinernann, S. G. (1994a). K S M A I ~ ~ " S t r e nof~ tMateriu~s h (eds H. Oikawa e i uL). The Japan Institute of Metals, Tokyo, 125. Anoiigba, P. N. B., and Steineiiiann, S. G. (1994b). ZCSMA i ( ~ - S t r e n ~oft hM a t e ~ i ~(eds l s H . Oikawa et al.). The Japan Institute of Metals, Tokyo, 431. d Steinernanii, S. 6. (1995). Acta Met.
edition of lectures 1921/1922, ~ ~ l i ~ v ~ ~ ~ c 19'79 Kohn, W.. and Sham, L. J. (1965). Ph*ys.Rev.
2161. Muldawer, L. (1962). Plzvs. Rev., 1 Nesper, R. (1 991). Angew. Chemie,
t. K. (1969). S c r ~ ~t e~t ~ i i . , eer, N., and Pettifor, D. G. (1984). Eiectronzc
of Cornplex Syxtenzs (eds P. Phanseau, and W. M. Pauly, H.. Weiss, A., and Witte, H. 6196%). ZeitschriJi T e ~ ~ c r n i a nPlenum, ). New York, 769. M e t u l l k ~ $ n59, ~ ~554. , Cho, S. J. (1970). Phys. Status Solidi, Petersen, A. (1989). Thesis, University of Cretu, G., and van der Liiigen, E. (1999). Gold B i ~ ~ ~3e ~ ~ n Petersenn, . A. v. (1981). Thesis. IJniversity 115. Petersenn, A. v., and Schuster, H.-U. Czybulka, A., Petersen, ~ r ~ ~ s t ~ l l ~ g156, r ~91. ~hie, ~ e s s - C o ~ ~ eo tna l s Pettifor, D. 6 . (1986). New Scienrisd, 29 May, 48. Ditchck, €3, M. (1984). J Pettifor, D. G. (1988). Mater. Sci. Technol., Drews, J. (1986). Thesis, University of Koln, Germany. Pettifor, D. G. (1995). I ~ t e r ~ e ~ ~ ~ l i ~ Drews, J., Eberz, U., and Schuster, H.-U. (1986). J of the VOL. I (eds J. H. Westbrook, and Less-Common M ~ t a l s , Chichester, England, 43 9. Eberz, U. (1983). Thesis, University of KGln, Gerxnany. Pettifor, D. G., and Podloucky, R. (1985). Phys. Rev. Letters, W.* and Schuster. H.-U. (1980). Z. 53, 1080. Peltifor, D. G., aiid Podloucky, R. (1986). J PhWys.C. ~ ~ Stale Phy,F., 19, 31 5. Pugh, S. F. (1954). Philos. Mug., dc Lausanne (in French), Randin, J.-P. (1994). Acfes PC; Gttkiiin, G., Ignat, M., and Thonias, 0.(1990). J Appi. Phys., Chronouniirie, Besaiiqon (France), 13 (in Frcixh). 68, 6515. Rice, J. R., and Thompsoii, R. (I Sarnbongi, T., Magiwara, R., and Yaniadaya, T. (1966). J . Phys. Soc. ~ a p a n21, , 923. Sautboff, G. (1995). Inter~etu~lic.s, VCH Verlag, Weinhet Schleinper, K., and Thomas, L. I(.(1994). Phys. Rev. B, 17082. Hohenberg, P., and Kohn, W (1964). Phys. Rev., 136, B864. Schnxdt, P. C. (1985). Z. Naturfom Jacobi, H., and Stahl, R. (1968). Nuturwis.~~l?.schafien, 55, 272 Schustcr, H. U. (1966). N a t z $ r ~ ~ s ~ ~ . , (in German). Schuster, H. U., Thiedeinann Jan, J.-P., and Vishnubatla, S. S. (1967). Carz. J. Phys., (1969). Zeitschrifi J: Anorg. 2505. Seelentag, W. (1978). Thesis, U Jansen, H. J. F., and Freeman, A. J. (1984). Phys. Rev. B, 38, Stadler, R., Wolf, W., Podloucky, R. 561. Furthmuller, J., and Hafner Johnson, R. A. (1988). Phys. Rev. B, 37, 3924. 1729. Kistrup, C.-J., and Schuster, H.-U. (1 972). Z. Nffturf~r'sc~izing, Stadler, R., Podloucky, R., Kresse, G., and Hafiier, J. (1998). 7b, 324. chuster, H.-U. (1974). Z . Anorg. Allg. Steinetnann. S. (1987). European Patent No. 0284699 (March 3 1). Klce, P (1956, 1921/1922) Bauhaus Lectures, original text Steinemann, S. (1990). United States of ~ n ~ e r i cPatent a ~n German: 'Gold 1st ern Hin-und-Her-Vibrieren von No. 491 1762 (March 27). sattem Gelb nach einem WeiB von fiberstarker Helle. Steincmann, S. (1994). .4ctes Sdme Corigrt;s EuropPen de Ein bewcglicls bestminter Wert. Silber vihricrt voii Chronom~trie,Besanqon (France), 7 (in French). Dunkel nach sehr Hell und ist ebenfalls beweglich St~inemann~ S. G., Anongb bestinimt. Kupfer ist ein Vibrato von Rotorange nach . El., and Podloucky, fiberhell. Die Metallwerte sind aparte bildnerische (1997). .I. Phase Equil., 1 Mittel'. In Paul Klee, Ilus bildnerische Denken, Benno Tilley, R. .I. I3. (2000). Colour ancl Optical Properties of' Schwabe & CO Verlag, ~aseI~Stuttgart 1956; Faksimile M ~ t ezuls, r Wiley Chichester, ~ n ~ ~ a i ~ d . a
)
l
24
~
~
0
~
and ~ ~ ~
., and Narayan, J. (1993). Phiios. Mag. 13,
10805. cstbrook, J. M. (1971). ~ e ~ Trans. a ~ A,~8 .
~
~i
e~ s
~
~
~
e
~
o
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~
Westbrook, 1. H., aiid Flcischer, R. L., eds. (1995). I ~ t e r ~ e ~ u l l i~co ~ p ( ~ u nvol. d s 1. Wiley, Chichester,
Zintl, E., Hardcr, A., and Haucke, W. (1937). Z. Phys. Chern.,
y
deconiposed into a sun1 of partial entropies associated with the different disordering processes: eking of a crystalline solid into a liquid is gener~~ly A S = AS, t- AS?. . . -5 A ought of as a disordering process from a state in long with the atomic structure chan which the atoms execute thermal motions about static place in this way, changes in the transport properties e ~ u i l i b r i usites ~ to one in which they all migrate randomly over the whole space occupied by the ~ a t e r i a ~Ln. a coniplex system, several d i ~ e r ~ i i t components of this di~orderinginay be distinguis~ed: these can include traiislational disorder of one subtransition or gradually over a temperature interval lattice, chemical disorder between two or more sublattices, orientatioi~aldisorder of molecules or between transitions. In this review we cover sonie aspects of ~ y ~ i a i ~ i c ~ l c o ~ ~ l eions, x or lattice melt in^ in one or two directions in the crystal. lien such a system is heated disorder in crystalline interim terms require some elaboration. towards the melting point, different disordering to processes set in until complete long-range disorder is disorder we exclude achieved in tlie liquid state (Ubbelohde, 1978), literature on order-disorder transforni~t~~iis in a ~ ~ althou~hsubstantial short- and i n t e ~ ~ e d i a t e ~ r a n g e imitrov in Vol. I), wliere the main interest lies in the ~tatistica~ and s t r ~ ~ t u raspects al of ersist well into the liquid state - see Singh (1995) in Vol. I of this treatise. Further the static disorder, as well as states of frozen disorder can be made as to whether a particular such as translational and o~ient~tioiial disordering process in the solid state occurs ~radually, crystals). We will also exclude vibrational d y n a ~ i c sas over an e ~ t ~ te~perature n ~ e ~ range, or suddenly, at a in phonons and phasons where the atanis return to phase transition. I f more than one process is associated static equilibrium positions. The only exception is that with a phase transition^ these transitions may occur at we will cover, in the last section, pre~ursorphases of a single temperature - the melting point (Figure la) some rnartensitic transi lions, since these bear some or a sequence of distinct temperatures resemblance to the phenomenon of nielting that proc ~ i l ~ i n a t i ning the melting point ( vides the backdrop to our present discussion. Tlie terinn 1997). In either case the entropy of melting may be ~ ~ excludes~ not only~ Z i ~ systems ~~ i ~ - ~covered Z ~~~~~~~~
~ ~ t e r ~ i o ~ ~t ~~ Vol. i o~ 3, u~ Principles ~~ ~d ~ and ~ Practice. Edited by J. €3.Westbrook and R. L. Fleischer 0 2 0 0 2 John Wiley & Sons, Ltd.
246
Properties and ~ l ~ e n o ~ e n ~ l o ~ y
igure P Schematic illustrations of thc melting process in which ditrt3rent disordering mechanisms set in (a) at the Same t e ~ p e r a t u ror~ (b) at a sequence of distinct temperatures (Reprinted froin Price, D. L. and Saboungi, M.-L., J. Phys.. ~ ~ ~ f f t9, t2707, ~ ~Copyright (1997), with permission from the Institute of Physics, VK)
h (1995) in Vol. 1 of this work s, which now include a wide range of amorphous alloys that can be quenched in bulk elt (covered by Greer in Vol. 1 of this chwarz in this volume), as well as quusici.ystalZiize compounds (covered by Kelton in Vol. 1 of this work). All these classes of material have their own complex and fascinating dynamical behavior that would take us too far from the priniary emphasis of this review. Finally, the term i ~ ~ e ~ ~ e t requires a Z Z i ~ some consideration since, as we shall see, materials formed from perfectly good metals may, in the compound, have properties more typical of semiconducting or even insulating materials. Some of the interesting types of behavior we shall encounter are more familiar in ionic and covalently bonded solids: the classic work on disorder in crystals arsonag age and Staveley, 1978) includes only scdt,s in the chapter on orientational disorder. In fact, some degree of strongly local or dire~tionalbonding appears to be essential for the kinds of disorder we are considering. From a structural point of view, this generally leads to a substantial degree of intermedia~e~~ange order, reflected in Bragg peaks at low scattering vectors in both ordered and disordered crystalline phases that transform into jirst sharp ~ ~~ e a in k ~the ~ ~liquidr (Price ef~ al., 1989). c Thus, we will include compounds not only of conventional nietallic elements with each other but also ones with metallic elements and hydrogen on the one hand
or with metallic elements and a Group IV (especially carbon), V or VI element on the other, which may exhibit a similar kind of behavior. Some of the most striking examples of this behavior are found in Zintl phases, compounds in which electron transfer coinbined with directional bonding of' the negative species leads to chemical behavior in these species characteristic of elements further to the right in the periodic table (van der Lugt, 1996). IFn addition to a fascinating collection of clusters and other local structures described elsewhere in this volume (Sevov, chapter 6), they exhibit dramatic changes in physical properties as the composition is varied over the intermetallic range. Compounds of alkali metals with lead, for example, behave as typical metals near the end members of the system but around the equiatomic compositions show a dramatic decrease in conductivity, with a positive temperature coefficient, typical of semiconductor behavior (Sabozrngi et al., 1990). As discussed later in this review, these phases often exhibit unusual kinds of dynamic disorder, with a subtle interplay between structure and transport as these diiferent kinds of disorder set in. Most of the experimental results presented in this review were obtained in scattering experiments, altliougli NMR has in certain cases provided useful complementary Furthermore the correla~ ~ information, ~ ~ tion between the microscopic information provided by scattering and resonance experiments, on the one hand, and the macroscopic thermodynamic and
~
lTj2iect.Y o j Mobile Species
transport properties on the other, are often illuminating. Since diffraction and inelastic neutron scattering ineasurements have provided much of the information on the structural and d ~ ~ a ~ iaspects c a l of disorder in intermetallic compounds, we will first in Section 2 give a brief review of these techniques. Those interested only in the experimental results and their significance may turn directly to Section 3, where we investigate some examples of the different types of disorder encountered, passing from translational disorder (hydrides, fast-ion phases) to orientational disorder (rotor phases) and thence to paddle-wheel phases and fullerenes, which exhibit both kinds of disorder. Finally ferroelastic phases exhibit a cooperative l i ~ u i ~ - disorder l~e in restricted directions or pkanes of the crystal.
catteriizg from disordered niaterials is invaluable for btaining two types of imcroscopic infor~ation:the a t o ~ ~ z~~t cr ~ c t uo rb ~t a~i ~ efrom ~ d i ~ r a ~ t i omeasuren ments, and the utomic dynamics, obtained from inelastic scattering measu~emeiits.A ~ z ~ ~ a cexperitio~ ment is designed to total s~atteringas a function of scatterin
(1) are the wave vectors of the incident ticks. These may be neutrons, X-rays or electrons - each has particular advantages and disadvantages. In the present work we present the formalism for neutron diffraction, but it can also be used for the other kinds of particles with rather minor modifications. In a diifraction experiment to fix the direction of priate collimators, det only the magnitude of one of the two, generally IQ. is evaluated from equation (1) under the on that the scattering is elastic, i.e. there is no energy exchange between the neutron and the sample, and so the incident and scattered neutrons have the same energy, and thus
(a)
(b)
Schematic illustration of (a) a iicutron diffraction and (b) an inelastic neutron scattering experiment
important, it can usually be taken care of by appropriate inela~ticity(or Tlaczek’) correcti~ns. After taking into account appropriate factors such as beam intensity, number of atoms in the sample, and detector efficiency, and making ~ o r r e c t i o ~for s absorption and multiple scattering iii the sample, the scattering intensity measured in tlie detector i s reduced to a fund~mentalquantity, the ~ z ~ ~ er r o~ ~ ~Y st- si~ ~ ~li o ~ per atom (Price and Skold, 1986).
where yla is the nuniber of atoms of type a in the sample ) is the partial structure factor for the atom pair (a, h). The structure factors are related to the structure in real space through a Fourier transform:
(2)
In practice this not quite correct since some of the scattering is inelastic, i.e. energy exchange does take place (see below). However, the experiments are usually designed to minimize this error and, if it i s
where gab(r) is the partial pair distribution function in real space for the atom pair (a, b) ~ ~ s h c r and ~ft
248
Properties uizd Phenomenology
angreth, 1 9 ~ 7 ) .The latter quantity has tlie direct physical interpretation that
is the average number of A atonis in a volume dr at a distance r from an a atom at the origin. In polycrystalline samples, isotropic structure factors derived from measL~renientson a powder can be defined by averaging all crystal orientatioiis. In a one-component system, the indices a, b disappear and only a single compound factor S ( and a single pair distribution function exist. In a system with more than one component, a full structural analysis requires a number of different measurements with different coefEicients in equation (3); in favorable cases, this may be accomplished with the use of isotope substitution. If only a single measuremen1 is performed, a weighted average of the partial structure factors is all that can be obtained. his can be defined as:
1 must be defined in tude and direction of both the design of the scattering apparatus. The intensity of this scattering process is reduced to a double ~ i ~ e r e ~c rt ~i ,~~ls - ~ e ~ t i o n ~
, E ) are the coherent and ~ ~ c o / ? e rpartial e ~ t scuttering ,functions (sometimes called dynamical structure factors) defined by:
We see here an additional complication arising from the mixture of colzerent scattering, which measures the correlated motions between pairs o f particles:
where
U
along with the corres~ondingneutron-weighted pair distr~butionfunction
In isotropic systems such as liquids and glasses, the structure factor and pair distribution function depend on the scalar variables and r, respectively. In polycrystalline samples, isotropic structure factors and pair distribution functions derived from ineasurements on a powder can be defined by averaging equations (6) and (8) over all crystal orientations.
and imoherent scattering which describes the correlatioiis in tlie positions of single particles at diEerent times:
The relative contributions of coherent and incoherent scattering will depend on the various elements and ost natural elements, as well stly coherent, whereas natural herent and natural lithium and silver, for example, are a mixture of both. These Pacts must be taken into account in the interpretation of the scattering data. Through the energy sum rules CD
The dynamics of' stystem can be measured in an ~ n e l ~ s~t ~ c ~~ ~ ~u texperiment t t e ~ r ~(Figure ~ ~ ~ 2(b)). ~ ~ In this case, the energy transfer given by
-00
(14)
(9) i s measured in addition to the scattering vector defined
in equation (I). To accomplish this, both the magni-
the scattering functions measured in an inelastic scattering experiment can be related to the structure factors measured in a diRraction measurement, which,
as discussed above, is designed to measure the total scattering integrated over all possible energy transfers. In a multicoi~ponentsystem, as in the difTraction case, several measL~re~ents, for example with separated isotopes, are needed to define the full set of partial scattering functions. 111 a single measurement, average scattering functions weighted by the concentration and scattering length of each elernent, analogous to equation (6), are obtained. owever, in many cases of practical interest, this may already contain much useful i n f o ~ a t i o n . In polycrystalline samples, isotropic scattering functions derived from measurements on a powder can again be defined by averaging over all crystal orientations. It is convenient to distinguish between four dynamical regimes of neutron scattering, illustrated schematically in Fi 3 (Price, 1997). Figure 3(a) shows a typical stru we treat Q as a scalar q either an isotropic s average or one with the values along a specific crystalline direction in the case of a crystalline system. S( Q ) shows delta-fu~ction-likeBragg peaks superimposed on a coiitinuous diffuse background: the first derives from the long-range crystallographic order (and would be absent in an isotropic system) while the second results from the various kinds of disorder the sample. We pick out a particular value of , and discuss the time development I(Q1, t ) of the correlations described by S(Q1). Figure 3(b) shows various time regimes that may appear in I(Q1, the corresponding features in S(Ql , urier transfori~ation.
t
3 Schcniatic illustration of dynamical regimes probed by inelastic neutron scattering: (a) stmctnre factor S(Q); (b) internrrediatc-scattering function I( (c) scattering function S(Q& The numbers denote the (1) recoil. (2) one-~honon, ( 3 ) quasielastic and (4) elastic scattering rcgimes. ~ ~ ~ from Pricc. D. L., Current Opimon in Lshiid State a d , 477, Copyright (1997) with permission from Elsevicr Science) ~~~~~~
1. The conceptually simplest scattering event is one that takes place as if the target nucleus i s independe~tof its neighbors. This is in fact what happens at short times, where I ( & , 2") falls off from its value at t = 0, generally with an approximately ~ a ~ s s i behavior. an In the limit of large (2, this recoil scafferingwill be the dominant contribution to S(Q1, E ) , consisting of a peak on the neutron energy-loss side ( E > 0) centered at the recoil energy ER =h2Q:/2M with a shape that reflects the momentum distribution of the system in its ground state. In particular, the variaiice in energy i s related to the mean kinetic energy K: (15) 2 , If there are vibrational processes, say with a frequency cop, I ( Q l , t ) will have an oscillatory part and Scoh(Ql,E ) will have scattering centered at
~
&&cop, generally referred to as ~ ~ ~ - p l z ~ ) scaffering. If the vibrational motion is liarmonic, this will have a delta-function form 5'1(Ql) 6( E Ifr: h q , ) . In crystalline materials the phonons can be labeled by the wave vector index j , so that measurements on single crystals can be made to identify these delta fu hence map out the phonoii dispersion 3. If there are relaxation processes in which the correlations decay at some characteristic rate a, say, S(Q1, E ) will have a b r o a d ~ n ec ~~ m ~ o n e n t
still centered at E = 0, generally called ~ ~ f f . s i e l a s t ~ carbons c (Winter et al., 19981, a class of alkali metalscatteririg EMS): in the case of an carbon compounds that we shall return to in Section is will have a Lorentzian 3.5. The most extensively studied mixed conductors are the silver chalcogeaides AgzS, Ag2Se and Ag2Te. These were first investigated in the nineteenth century by Hittorf?who observed the large jump in coi~ductiv~ . If there are structural correlations which exist ity at the cx --7\ /? phase transition (177 'C), which he interpreted as an increase in ionic conductivity; in facl for inlini tely long times (more precisely, times the effect is principally electronic, as established by t >fi/A.E where A E is the energy resolution of the e, along with their Wagner (1933). Ag2 experii~ent), for exainple in a solid where the copper counterparts, have in Fkct two disordered atoms execute thermal motions about fixed phases, /j and an fcc y phase from which they melt. , t ) will obviously The inter~ediate-tei~perature (8)disordered phase, ependent term. This shared with the non-electronically cotiducting, fast-ion will give a delta-function S,i(Qi)S(E) term in the conductors AgI and Ag3S1, has the bcc crystal scattering function, generally referred to as elastic structure shown in Figure 4. It is seen from the unit sc~t~eri~~. cell that there are 42 possible silver sites to which the In an actual coiidensed system, especially as the four silver ions in the unit cell can migrate. The low conaplexity increases, there will be coupling between 50 ineV per ion, activation energy for migration, the different types of motion and the simple forms means that the conduction process is almost liquid-like given above will be replaced by more complicated above the transition. Considerable activity, measuring evertheless, the distinction diffuse neutron and X-ray scattering in these phases, between the four dynamical regimes will generally be took place in the late l970s, driven in part by the meaningful. technological demand for advanced batteries and energy storage devices. A Fourier map of the silver rzeulrola
-
s of ses
The history of fast-ion conductors dates from Faraday's (1839) report of high ionic conductivity in bF2. Since then, many ionically conducting solids ve been identified, primarily high-temperature phases of ionic c o ~ p o u n d sin which the current is carried by unusually mobile monovalent cations or anions. A review of neutron scattering studies of their dynainical pro~ertieshas been given by Andersen et al. (1987), and a recent overview of fast-ion {or s ~ ~ e r i o ~ i c ~ conductors has been given by Agrawal and Gupta (1 999). A number of fast-ion iaternietallic compounds have also been identified, often called mixed conductors because both electrons and ions have high mobility. These ~ ~ t e r ipresent a ~ s an additional scientific interest erative mutual enhancement of the two components (Raniasesha, 1982), nit cell of the fast-ion (p) p 6b (octahedral) Ag' sites; as well as to their technological potential for use in Ag' sites; 0:24h (trian~ular)Ag+ sites (Reprinted from advanced battery electrodes. ost of these systems Andersen, N. H,, CLausen, K. N. and Kjems, J. K., ~ ~ a+ or Ag+ as the mobile ion, although Scufferthing,Methods of Experimental Physics Vol. 23, Ed. M. some divalent cases will be mentioned below. An Sltold a i d B. L. Prrce (Academic, NY), Part B, p. 187, importaiit class of Li+ conductors are the lithiated Copyright (1987) with perniission from Acadcinic Press)
~
251
Eflecls qf Mobile Sprcics
through. the 6b and 12d siles of the crystal structure shown in Figure 4. A simple model of a relaxation process in a solid is described by uncorrelated jumps o f a mobile atom to pz adjacent sites at distances with a mean residence time z between juiiips at each site (Ghudley and Elliot, 1961). In this case the half-wi~that h~lf-ma~imum of the scattering function in equation (1 6) is given by h I' El - exp(--i r2.z k=l
) =-
(17)
Broadening of this kind was observed in Q ~ e a s u r e ~ e i i ot sf Ag2S (Crier et d., 1984), reflectin a dynamic disorder on the time scale of the neutron experiments, 7-17 psec. Recent work on Ag2Se has been described by kazabi (19x3) and on Ag2Te by Keen an canonical case of an intermetallic conipound exhibiting fast-ion beh~vior.In the 1970s it was a material o f interest for the negative electrode in high-temperature, molten salt bat (Yao et al., 1971). It can be regar c o ~ p o u n d crystalli%ing in the structure, consisting of two inter~enetratingdiarnoiid lattices. Since this is a rather close-packed structure, Li diRusion relies on the relatively high ~oncentra~ion of mobile vacancy defects on the Li sublattice in the Lideficient side of the equiatoniic composition. Since silver and, even more so, both isotopes o f lithium have a substant~aldegree of ~ncoherencein their cross-sections, the distiiiction between coherent and incoherent scattering ment~onedinl must be taken into account. The i ~ c o ~ ~s cr ae~~t etr i n ~ *
Academic Press)
ion distribution in the (100) plane in the p phase of Ag2S at 325 "C, essentiall~~ ~in the ~sense of~ equation (5), is shown in Figure 5 (Cava et al., 1980). The result indicates an extremely delocalized Ag' ion d~strib~ition,with very ~ i g h - d e ~ s i tbands y passing
Np and unoccupied N , sites (Ander§en et al., 1987). If NI, << N,, the coherent scattering has a form similar to the incoherent:
~ ( ~ ) where SP( ) is a structure factor for an indi~idual particle taking the deforination of the s u r r o u n d i ~ ~ medium into account. On the other hand if Np >> N,,
252
Properties arzd P ~ z e ~ o ~ ~ e r z o ~ ~ g y
the coherent scattering 1s dominated by the motions of the vacasicies and we have (20)
conductor around 600 ture with silicon temperature it has a defect Lij I'orrning an fcc sublattice and distributed over tetrahedral and octahedral sites. An a/? i ~ molecular i ~ dynamics ~ ~ computer simulation (Wengert et al., 1996) shows that both cations are mobile, with the lithium having diffusion coe~cients 3-4 times those of the ma~nesium,and the diKusion taking place via vacancy migratioi~through directed jumps. To our knowledge, neutron scattering experiments have not yet been carried out.
by the (Brun et al., 19S1) found that the observed scattering could be described by the incoherent term, essentially equation (18) modified for encounter effects (Wolf, 1977), with the coherent tern broadened so much that it could not be seen above the background. s Ln addi~ionto ma~erialswith mobile Li4, Na4 and Disordered hydrides represent the other importnn t small number of fast-ion conductors class of solids in which diffusion occurs on a time scale have been observed. Mg3Bi2, which e that in liquids and are therefore her ch~lco~enides already ~ ~ ~ t i o n e ~do n ~ p a r a b lwith readily amenable to investigation with QENS. In view some unusual transport properties in the liquid (Xu et of their intrinsic interest for solid-state physics, and al., 1993b; Enderby and Collings, 1970), transforms at also because of their t e ~ h n o l o ~ i ~i ~ a lp o r t a i ~ cin e 703 "C from the l o w - t ~ ~ p e r a t uanti-La203 re structure energy storage, fwion technology and hydrogen to a B phase whose structure is not known but has been embrittlernent, metal fiydrides represent one of the arms et al. (1994) as a fast-ion early successes of neutron scattering ( ~ ~ r i n and ~er cond~ictiiigbcc phase. As in silver iodide and the Richter, 1987). The predo~inantlyincoherent scattersilver chalcogenides, cation motion appears to take ing cross-section of hydrogen was also an important place between the tetrahedral and tnangulrtr sites in factor in i n t e r ~ r e t i nthe ~ results obtained. the bcc lattice. A classic e ~ ~ e r i m e n t result nl is that of vior is found in the ternary Zintl Nelin (1967) on fcc palladium, reproduced in Figure 6. , which appears to be tt hst-ion
Widths of ~uasie~astic scattering in Pd-M (from Skold and Nelin, 1967). The solid lines represent fits of the ChudleyElliot model with the €4 atoms jumping between octahedral sites. The dashed line shows the poorer fit with the NI atoms jumping between tetrahedral sites (Reprinted from Skold, K. and Nelin, G., J . Phys. C h m . SoZ&ds 28, 2369, Copyright (1967) w t h per~issionfrom Elsevier Science)
253 It was found that the results could be nicely ~ ~ p l a ~ n e d ~ e q u a t i o(18-19)) ~~ for ween oc~ahed~al sites, vibration~lai~p~itudes ~ u r t ~ e r ~the o r iii e erstitial site could be obtained o f the ~ e b y ~ ~ ~factors ~ l l e r for bcc metals were more r e ~ n e ~ e nin t s the theory, for e ~ ~ the ~ p‘ ~ ~o ~e j~m lq ’e model in which the hy~rogenalternates between ‘mobile’ and ~immobile’ states ( ~ o t t et~ a/., ~ r ~979).V ~ n a d i uliy~ride ~ is a lzlt four ~ ~ ~o f iieutron i ~ es cs~ t t e r ~ n ~ tion 2.2 have been b r o ~ g h t into lay. For exaniple, a ~ o ~ b i n aof t ~recoil o ~ scatter in^ Lufr;mn et al., 1987) and vjbr~tion~L1 spectroe ~ ~ e l nefi al., ~ ~ 1989) ~ i has been used to dete~1inethe shape of the interstitia~potentia~weil in which the hydroge~atonis sit (Figure 7). For systems with higher hydrogen c o i ~ ~ ~ n t r aitt i ~ ~ n ~ has been possible to use both the incoherent scatter in^ ~ r o s s ~ s e c t i of o ~ hydrogen and the predomi~~ntly of d e ~ ~ ~to eobtain r i ~ ~ coherent scattering cross~sect~oi1 7 Potential af ~ ~ ~ ~ e r s NI t i tatoms ~ a l in the d~~l~rdered a more profound ~ n d ~ r s t a n d of in~ the dynamics. As ~ ~ discussed above, these often give ~ o ~ pkinds ~ ephase~ of V,H ~ deduced ~ ~€ramt inelastic ~ ~~ ~ ~u~ ~ r o~(from ~ e ~ ~ ~et ~al., e1987). l ~ The a solid n ~ curve ~ for tlzc exc~t~~tion o f in~orniation,At srnafl Q3the first can he related to energy (left and top axes) refers to the c direction in the crystal the s ~ ~ ~( ~ t /~ a c~~e i~~-’u~s i~oconstant n ~ ~D and ~ ~ while ~ thel dotted ~ curve refers to the a direction. The potential the second to the c ~ ~ ~ i (‘co~lective’~ cal d~ffusion (right and bottom axes) shown by the solid curve also refers to the c direction in the crystal and corresponds to the sum of constant Dch ( ~ ~ ~ i and ~ g Richter, e r 198’7; Hempelterms ~ ~ a d ~~a t~ i ~ and ~ hqrrartic e d ( ~d ~ ~ s ~in“ ~the ot~ ~~n~~~2 ~ ~Tlie 0 ~two . are co~nectedby the relation d i ~ p l(~ R ecp r~~ ~€ram ~~d ~~ ~ ~ p R.,eRichter, ~ ~D. a ~ aiid Price, D. L., Pkiys. Rev. Left, , 1016, Copyright (1987) with ~eri~~ssion from the A ~ e r j Physical c ~ Society) ~~~~~
n
where c is the liydroge~concentr~tionandf;. is a factor cracks that are larger than the inverse s~atteringvector ~ e s c r i ~ icorrelations n~ between s~~~cessive jumps. QENS ni~asureii~ents on rx-TaI-l were sizawzz to be of the neutron measurement, ther classes of alloy include the (cF24) Eaves phases such as consistent with equation (21) CO bmed with ( ~ studied ~ / ~ G15 ~ ~ determined by the Gorski relaxation method TriVzfl1.1 ( ~ k r i p oet~ al., 1998~and (Skripov et a l , 1999) al., 1984). A ~ o n s i ~ ~ ~ body a b l e of h i ~ h - r e s o l u ~ i Q ~ observed, one correspo ~ e a s u r e i ~ e has n t ~ been carried out on in~er~etallic hexagons formed by tetrahedral inter~tztialsites and alloys, m ~ of ~it driven ~ ~by ithe ~ ~ t e rin~ ~s ty d r o g e ~ ~ the other to jumps bet~veenthem. ~ ~ t r ~a tst e~~ ~~ ~~a ”j c tion ~ ~ a s u r e ~ e on n t sTi-Zr-Ni q~ts~crystals have storage materials such as LaNigzfh (see Ch. 21 of Val, 2 of this work by ~ c l ~ l a p b aet~al.). h Work up to found that hydrogen motions around 220 K are about 1987 was reviewed by ~ p and Richter ~ ~(19 n ~an order ~ of ~ a~g n i t ~ ifaster d e than in the ~ ~ ~ e s p o ~ i ~ p r ~ ~ ~the i ~dli ~e ~ u s ~c o ~n ~ s ~~ ~e n ~t by s u ~ a~p ~ ~~ o x j ~(Foster a n t et al., ~ ~ ~ 0 ) . should be related to the reaction rate co~stantKr for absorptio~or ~ ~ ~ o r pint ai powder o~ of grain size R: ~~~~
n’D Kr = R2
In practice the measured ~ e r i c ~ ~rate o n may be siowed by surfttce effects or speeded up by d i ~ ~ ~ s along ion
~ r y s t a c~os n ~ a i n~i~olecu1es i~~ or complex ions have 8x1 additional c o ~ p ~ e x i ct yo ~ ~ ~with r e dthose d i s c ~ ~ s e d up to now in that they possess o ~ ~ e n t ~ ~ as t i owell ~ aas l tra~islationaldegrees of freedom. They can t ~ e ~ e f Q r e
exhibit a variety o f types of orient~tiona~and translatio~a~ order, A ~ o ~ p r e l i e n s ~recent v e review spectra have the shape o f t h has been given by KI and he^ (1984). fu~cti~ ofnthe i n s t r u i ~ ~In~ the ~ t .a phase they show a They point out tha n-rotation coupling is ~ ~ ~ p ~ r ~o f ou ~ s ~i rt o~a od e~nand ~ db ~ ~ a d e compo~ed resent in all systems of tliis kind but is relatively more nents that can be well represented by a delta ftinction ~ r n p o r t ~ ~in n t ionic c o ~ ~ p o ~than n ~ in s ~ o ~ e c u ~ a and r single ~ o ~ e n t f~ ui ~a ~~ c t ~~ ~ ~s i~, ~ ~both ~ i v e ~ y crys~a~s since the ions are separ~tedby a lattice of broadene~ by the reso~~~tion f ~ n c ~ o The i~. cou~terioiiswhich wea~ensthe direct interactions ~ ~ ~ n c t i no tne n s ~ tpeaks ~ in the region of the ~ e t w e e ~~i e i g ~ i b o orie~i~~tions. ri~~~ We may expect iit, peaks at Q’ f A-I, but has a ~ i ~ n i ~ c a non-zero this to be even truer in those s e ~ i c o ~ i d u ~or t i n ~ value over the rest of the measured inter~etallic ~rystals~which exhibit o r ~ e n t a t ~ o ~ a lLaren t~ian-functionintensr ty has a n ~ ~the mobile electrons will degrees o f f r ~ ~ d owhere to the left of the Bragg peaks (Q screen the direct ~~ite~actions even further. starts to rise to large values at Two interrn~t~~llic compo~ndshave been identified dramatic rise in inten~i~y above 1 -5 in which ~~~~~~~~j~~~~~ as well as ~ ~ ~djsorder~ ~ of that , found ~ in~NaSn.~ The ~ ~ appears ~ ~ a sum of~ the two to N
-
n ~ i ~ b oefr ~ ~ ~ i sproperties ual arisii~g was a d o ~ t e din which ~ s units~ were~assumed b to~ from the fori~ationof tetrahed~alSni- or Phi- poly~ n ~ eindepe~ident, r ~ o ~ a n j ~u ~ between ~o ~~ s ~the four ions’). ~ r y s t ~structures l of these or~entat~ons found in the p crystal e ~ o ~ y a n i o nofs this type arra~~ged cm succession as one moves up the c ax a k c ~lattice, separa~edby a~kali-met~l ions, each of ~ a b o u n ~1991), i , Since these orientati~ns which is shared by two ~ o ~ y ~ n fi o ~ s spaced, two jump times, “ ~ tand zzlwere a s s u ~ e dfor ~ o e n i a ~1953), e ~ , In the ~ ~ ~ ~~ ~ t~ r~ o~ ~~a i~e tt t ie ornearest~ s~ and nr=xt-nel2rest-ne~gfibor jumps, ~ ~ s ~ e c t i v ~ ~ y f $lie l ~ q u si t ~ r o~n ~~first sharp d i ~ r a c t ~ opeaks n The quasie~astics ~ a t t e rspectra ~ ~ ~ c a l ~ ~ ~ fram ate~ are o ~ s e r v ~ ddue , to dense random p a c k ~ nof~ the this model showed both ~ ~ n ~ r and ~ b~r od~ ~e ~ ~e n e d ~ ~ofyanions( ~ e i j eet r ~al., 1989, 1990), The ~ ~ s o r ~ e r icompoiients ~i~ similar to the measured ones. The is a~sociated with dramatic changes in electrical i n t e ~ r a t ~inte~s~ties d of the two c o n ~ ~which ~ ~ ~ ~ t t r ~ ~ n $ ~~ropert~es. ort are inde~endentof the values of 71 and zzl are in The behavior o f CsPb is a prime example of an excellent ~ g r e e ~ ewith n t the measure orientatiotiaffy-disordered phase in an ii~ter~etallic over the diEerent runs ~ ~ i g 8). u ~ e only Phi- ~ o l y a n ~ o nr se o r ~ i~n~d et p ~ ~ i ~ edo ~ t not ly reproduc~ the first peak ~ o r e ~ ~i ~~ ~~ ~i o ~ atn~ e~ ~ i t cations must therefore be p in the dynamic disorder, apparently on a t ~ ~ e ~ s ~ a l e siniifar to that of the Phi- reo one line width i s observed iii the a phase. This behavior contrast as will be ~ ~ i ~ ~ in u s Section s e ~ a ~ ~ i rwhere, e The s t ~ ~ ~ ~ft u~ r~e t of ~ rthe s l o w ~ t e ~ ~ ~ e r @) p o l y a i i i ~ro~ations ~~ and cation n i o t i o ~a~ ~ ~ to~ a r the liquid were similar to those take place oii diEerent time scales. The d,c. electrical cond~~ctivity of CsPb rises s h a at~ the ~ j3-a ~ transition, indicatin~a s i ~ i ~ i ~ cdecrease a ~ i t in the gap in Q 1 A-1 that appeared to be a B(E) (Fortner et al.? 1995). It i n c ~ ~ slow~y ~ ~ e swith agg peaks with a diEuse, nont e ~ p ~ r ~int the ~ r xe phase, and drops ~ ~ ~at~theh t ~ y er c ~ y s t a ~ I pattern ~ n e at l ~ r ~ Q. point. The overt~ll~ isuggested ~ bytthe d ~~ E ~~ ~data, c t~ i ~melting ~~ More recently, cage structLires based a n a crystalliiie phase with e ~ t ~ ~ s idisorder, ve was ~ ~ ~ ~ e ~e l~es~ e un t ssuch ~ as ~ In~eand Tl have ~ been~repor ~ ~ ~ o n ~ r n by i ~ dii~e~astic neutron s ong and Corbett, 1993, 1994, nients carried out on the IN-6 s ~ e ~ t r o m e at ~ e the r 1995; Sevov, tliis volume). These have ~ o I y a ~ i oofn ~
higher wave vector decrease, p r e s u ~ a bon l ~~ccountof i n c r e ~ ~ idny~n a ~ i c ~disorder, l The ~i~~~~ str~ctul-~ shows a ~~ronoLinced 'first sliarp d ~ ~ r a c ~ peak' i # n at about I A-" typical o f liquids with large polyanions, and similar to that observe liquid KTI, CsTl and GsgT17 ed al., 1 ~ 9 ~ ? * The d i ~ ~ a c tresults i o ~ are s ~ i ~ ~ o rby t eqd~ ~ s i ~ l ~ s t i c
CsgT111 appears to be a rotor phase tei~peratures,while anothe~c o ~ p o ~ n ~ ~ shows no d y ~ ~ ~ ratation ~ ~ i c but a ~ seems liigldy disordered structure in the solid phase at all t ~ m p e r a ~ ~ studied. i ~ e s Tlie a ~ s e ~ cofe a change in crystal s t ~ u ~ ~a L ~~ ~~e ~ ~ the ~ aa ~~ ~ ~~ y~ of~i ~n a~ ~ dynai~icaldisorder in CsgTlll is in ~ i a r k ~contrast d to the belinvior observed in the I-JV CsPb discussed above and N 3.4. The r e ~ n ~ n i e noft the Corbett, 199.5) shows the Tl:, polyhe~ra~ ~ ~ iin ~ i t ~ a l ~ e r n a to~ientations ~ parallel to the c ( T 2 - ~ 2axis. ~ DTA. analysis showed an ind~cnt~un of a small thermal anomaly at 381 "C, but none at 294 "C where a transition is indicated in the ~ u b ~ i phase s h ~ d~ ~ a ~ r a ~ ~ ~ r u c t ufiitctors rc for (a> L o r ~ and ~ (bj ~ ~deltaa ~ ( ~ a s ~ ~ ~l ~9s ~ k ~owever, i ~, ~ . if there is a ~ i s o r ~ e ~ i ~ i ~u~i&tion peaks in the d ~ ~ ~ r ~solid e r ephase d of CsPb (880 K). t xn t ~ a n s ~ titi oappears ~ ~ to take place w i t ~ ua~change Circles: data: solid lines: resuits of the model described in the crystal s t r ~ ~ t u r e . text. The t c a ~ c u ~ structure ~ ~ e d factor in (€3) has been ~ r ~ a d e i ? e ~ with the ~ ~ ~ ~ ~ .Quresolutioa i ~ e n f~ ~a ~i ~~ c iR ~ ~~from ~~ r ~ ~ ~ e ~ Price, D. L. and ~ a b ~ uM,-L., ~ i ~ Phys. ~ " R ~ YB. 44, 7289, ~ o p ~ r(1991) i ~ ~wxtk t ~ ~ e r ~ i s sfrom i o n the American Physical ~ o ~ l e ~ ~ ~
e x t r e ~ ecases the traiistation-rotati013 c o u ~ ~ ~ ~ becomes so strong that the two degrees of Geedoin disorder together at the phase t r a n s i ~ ~ The # ~ "~ r i ~ e s the ~ r o u ~metal - ~ ~and I n example of this hehavior is found in ain the smallest p o ~ y a n ~to o ~ s analogous sulfates ~ ~ u n d e 1994 n ~ 8nd as high as '70, 74 and 78 in fullerene-like cages. These therein), where the motioii of the l i t h i u ~ions has phases bear the same relations hi^ to 1-111 diamondbeen given the p ~ ~ t ~ ~ ~ e s ~a Lof~ ~e ~~ ~e ~ ~ l e struct~~re Zintl phases (e.g. LiAl, NaPii, NaTI) that the migration. Recently similar behavior was found in ful~ere~es have to diamond. the i n t e ~ i e t compound ~ ~ l ~ ~ sodiu~-t~~i. The iso ordered solid and liquid phases of CsgTl11, NaSii has a complex melting behaviar, ~ x l ~ i b iin te~ ~ a and ~ ~a ~ K ~have 2 ~ been T ~~ s~udied ~ ~ ~by thel c ~ l ~ ~~ i ~data ~ e~t ~r ~ ~c o et u ial., i g1994) i shown in ~ ~ b et al. ~ ~~~ O ~~ These O ~) , g~ l i ia s ehave ~ ~ e l a t ~ v e ~ yFigure 10 along with that from CsPb. The ex1 spherical ~ o ~ ~ n i of o nthe s form Tliy, Tlii- and a two solid phases was first establi~~ed by ~ o ~ ~ b i ~ ~ofa 77:t i o naiid Ti;-, r e s ~ e c t ~ v eand ~ y ~are Rothery (1928) who did not, however, s Likely c a n ~ i d a t ~for s ~ y n ~ i c a d~sordered ll~ rotor about their nature.. The crystal struct~reat low igure 9 shows the structure factors in the tei~peratu~e ( ~ u l l and e ~ Yolk, r u o ~ - t ~ ~ p e r a t uand r e ~ i g ~ - t ~ n i ~ e rsolid a t ~ rand e in CsPb and the other Zintl corn liquid phases for CsgTlll (x1i.p. = 408 "C). Tlie with the alkali metals (except t e ~ i i ~ e r a att t ~ tern ~ e is in good a g r e e ~ e nwith ~ ray ~ i ~ r a c t results i o ~ (Dong and Col-bett, 199.5). the ~uth~rford-Appleton eating toward the meiting point, the crystal st~ucture Source (EIS) ( ~ a b ~ ~ ~ ~ ~ i does not cl~angebut the intensities of the peaks at 1995) exhibit Char~Gterist~ 111
256
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Structure factors S(Q) as a fu~unctionof wavc- vector Q for Cs,TI,, at room temperature (lower curve), 390 "C (middle curve) and 450 "C (uppcr crrrve). C~irvesare displaced s u c ~ ~ s ~ upward v e ~ y by 1 (from S~~~~~~~~eTt al., ~~~~) solid and liquid pl~ases.~ s p e c ~ ~remarkable, lly in view of tlie signi~cantincoherent scattering cross-section of Na, is the a~senceof o ~ s ~ r ~ ~diffuse a b l e elastic scatter~ngin the CI pliase, which is zero w i t ~ i nexperimenial error when averaged over all aiil;les except those c o r r e s ~ ~ n d to i n ~Q vahes near 1A-1 wliere there is considerable ragg scattering" The absence of s ~ g n ~ f i incoherent ~~nt elastic scattering indicates that tlie d y n a ~ i cdis~rderassociated with the Na+ ions is t r a n s l a t ~ ~ i ~rather ~ l , thaii o r i e n t ~ ~ i o ~in ~ a lnature. , The widths of the single Lorentzian fL~nction~ fitted s a f ~ ~ ~oft Q~ mo n ET chopper spectr whose width and intensity both increase considerably at higher Q. This component is not seen in the IRIS data at higher Q, beca~seit is too broad to show up within the IRIS window (A 0.4 meV). 0 1 2 the other barid the IRIS data show a much arrowe er component whose intensity
11, the ~ e a s widths ~ ~ of r the ~ 1~ IS data are seen to be in reas~~nablea ~ r e e n ~ ewith n ~ the ~ h ~ ~ ~ ~ ~ y - ~ l d ~ s t a ~ c1 eof 3.75 A ~ s i ~ i l ator ~~~~~~c~~ in the 6 crystal) and a ps. It i s therefore reasonable to associate this rrarrow ~ o ~ ~ o with ~ e the ~ i Ma" t ~ i ~ r a t ~and o nthe broad compone~twith the more rapid r e o r i ~ ~ ~ ~ of t ~ othe n s Sn2- pol yanions. The absence of s~gni ~cant elastic diEuse ~ ~ a t t eindicates ~i~g that these reorjent~~io~is are d ~ u s ~ 111 v en~t ure. Taken together, these results show that the a phase of NaSn is ~ y ~ a ~ i ~ o~r d e~r e dThe ~, ~ d y~n ~~~ ~ yi i c disorder consists of rapid r e o r ~ e ~ t a t i oonf ~the polyanions (fast rotor be1iavior) which enhance the slower cation migration (fast-ion ~ ~ ~ ~ d this ~ ~ ~ it~ i~ oa tis ~i o)n : schei~atica~ly illustr~tedin Figure 12. A l ~ h o u ~the h jump frequencies are different, the two processes must be stro13gly coupled since only one phase ~ ~ - a ~i s s ~ t observed prior to melting, ~ ~ 1 e c ~ ~ ~i rcaai ~ i s p ~ rint aSii is c o ~ p ~to e the d y n a atomic ~ ~ ~ d~ ~ s ~ ? r ~~e ~ * .~ ~of the~elec- ~ trical con~uc~ivity ~ ~ ~ ~ei al., r t 1995) n e show ~ a cfrop in two ~ ~ ~ p u agrees ~ e ~with t s the total s ~ ~ ~ t e r~ ~~ n d~ u ~ ~atithe y i t ~ t ~ ~ ~~ nr ~~ ~~ reflect~~ ~m ~a n~ measured in the diffraction detector and hence ing the additional scattering associated with the a c ~ ~ u n for t s the entire diRuse scattering. In Figure dynamic disorder; in contrast, any ionic ~ o m p o n e n ~
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at h ~ ~ of the ~ ntzian peaks for a-NaSn at A HET (40 m e Q the solid j u ~ ~ ~ d i ~niodet. u s i ~The n dotted and dashed lines joining the points m the upper curves arc a guide to the eye ~ ~ e ~from ~ P~ ~ n t e ~ M.-L. and Howells, W. S., Phys. Rev. B f 1995) with ~ ~ r ~ ~ sfrom s i othe n A ~ ~Physrcal ~ i Society c ~ ~
~
the alkali metals in the disordered phases of C24Rb and C24Cs with ~~~~. The i i i ~ ~ r ~ r e t awas t i oc~ ~ ~ ~ l i ~ by tlie fact that carbon is a coherent scatterer. Usin the simple ~ p ~ r o x ~ ~ i(aV~j ino~ny ~ 1958) ~d,
of the me~~sured conductivity must at the tran~ition.‘The large jump within the ct phase reflects a close c o ~ ~ ~between ~ ~ n ga t o ~ ~mi~ration c and electronic mobility, discussed in depth by Fortner et al. (1995). There appears to be little if any change in they e x t r a ~ ~ e ddiffirsion constants of the condu~ti~ity on melting. NaSn appears to translW5 cm2 s-l, much smaller than the vsrlues observed fomi to a crystal~ograph~c phase of lower symmetry, in the correspoiiding bulk liquids at this temperature apparently moiioclinic ( ichardsoii et al., 1996) at the and sL~ggestiveof a s u b s ~ ~ i i ~ i increased a~ly degree of disorde~iIi~ tran~ition~ an unusital example of lattice local correlation. symmetry lowering at such a transition, The most dramatic change in the c a r b o ~ - ~ ~ t a l A related phenomenon is proton diffusion m hydrogensystems came with the discovery o f C60t C?o and their bonded crystals by means of a ~ r o ~ t h ui~ech~nisrn s ~ o m ~ o uand n ~ alloys s in the M e 1980s. The crystaI~iIi~ al ii~volving a l t e r ~ a t i n ~ rotatio~al and t r a ~ i s ~ a t ~ o ~ phase of C60 itself undergoes an orientational dis4uiiips (Lechner CL al., 1993); however, this situation ordering tr~~iisitjon at 250 K, first studied with QE differs from the present case in that each mobile ion by Neumann et al. (1991). The doped alkali metal a t ~a~single center. site can be a ~ s o ~ iwith ~ ~ ~ ~ iqZiC6o., o u xn== dI > 3,~ 4 6, . e ~ h ~ bai range t of fascinating properties, including SuperconductiQity and ~~etal-~nsulator t r ~ n ~ i t i o nat s low ~ e ~ p e r ~ ~ i 3.5 The AI c60 cornp~und$have ~ i ~ h ~ t ephases ~ ~ ~ r a with the rocksalt struct~re,which exhibit s t r ~ c t L ~ ~ ~ ~~itercaiatio~i conipounds of alkali metals in graphite phase transitions oii cooling to orthorhornbic strucr e ~ r e ~ e an ~t w o ~ d i ~ e ~ i s ~ionnt a~~~ ~ e ~ asystem. llic tures with tiiiear p o ~ y ~chains e r of G ~ o These undergo disorder in^ transition^ in which the et al., 1993; Stephens el aE., 1994). layers of metal atoms behave essent~a~~y as 2d y n a ~ o~ rci ~ n t ~ ~ i odisorder, n a ~ ~ppareiitlyd e c ~ ~ ~ l e d Zabel et al. (1983) studied the diffusional motions of from the alkali metal motions (Christdes e~ aE,, 1992). ~~~~~~~~~
.3
32f ~ c o r n e sites ~ ) fully o c c ~ i ~and i e ~24e (hce center)
tiott model ( a $ s ~ ~ i a11 ng scatteriag to be incohere tfi, r e m ~ ~ k a bthe l y ~same jump time of 2.7 f 0 , 5 ps above and below tile is ordering transitio~~ ~ r i s t o ~ edl i al., n ~ 2 ~ ~ The 0 ~ . i~teyisityof the ~ ~ a t t e~ r~i e~ s~ u~~~~ ~ b l ~y ~ to o r t i ~ the iiumber of mobile ions, i n ~ r ~ a s~e s~ ~ b s t a nand ~~all~ seems to be closely c o r ~ e l ~ ~ twith e d the t e ~ r a g o i ~ ~ ~ dist~rtion of the cubic lattice, which must open
In this last section we address a type of dyiiarvric disorder which does not, like tbe o t ~ c ~o i~~ s~ ~ so de~e~ far, precede actual melting, ~ ~ s t it~ occurs a d near a phase trans~tion~ with an inten~itythat ~ecreaseson m o ~ away i ~ from ~ ~ the tra~sitionon both the highand ~ow~temperat~re sides, eve~th~less,it has features in c o ~ n wth ~ ~ the ~ i~~~t~~~p h e n o i ~ e i i ~ n that justify inclusion in the present review. Furthermore, orientational disorder in^ ~ransitio~s are o a ~ ~ o m p a ~ by i e dfer~oe1a~tic i ~ ~ t a ~ i l i t(i e~s y ~ ~ e n ~ and Michel, 1994). ~ e r r o e l ~ s t itra~sitions c by a ~oftening of ~~aasverse acoL~stjcmodes. ever, in contrast to conventioiial melting, longrder i s ~ e ~ e s ~ ~ b l i s h e d on cooling below the trai~~itio~i by a process of contin~~ous crysta~l~~ation ( arris et at,, 1993). They are classified by s y ~ ~ ~ e type t r y m, d ~ ~ e n on d i ~ ~ whether the acoustic i ~ s ~ a ~ i occurs l ~ t y at points ( m = 0), lilies ( m = 1) or planes (nz = 2) of reciprocal space (Cowley, 1976). A classic case is that of the alkali ~ i ~ane ~ cyanides, where the t ~ n s i t i o nis a c c o ~ i ~ p a by alignnient of the CNdipoles but with head-to-tail S c ~ ~ il~~strntion n ~ ~ tof ~~ a~d d I ~ ” ~ ~mrgrntion hee1 111 a-MaSn (from SnboLi~giet al., 1993) ~ R e ~ r i from ~ i t ~ ~disorder fluty, 1981). A typical case in a metallic alloy is that of I ~ J - ~ T(xI = ~ 0.16-0.31) alloys .-L.,Fortner, J., Howclls, W. S. and Price, D. L., 237, Copyright (1993), with permission from (Cunton and Saunders, 1974) where the elastic ~ ~~ ~~ Limited) 1g ~~ ~~ ~~ n1 ~ ~ - C J~ Z~) /tends modulus (C11 ~ to zero as the niar~ensiti~ traesitioii is approached from either the cubic or the tetragonal side. The best-known ferroelastic transitio~sin metallic While x = 4 appears to be the doping limit for the coinpotxnds such as heavier alkalis, values a s high as 12 have been found , 1966) and Nb3Sn with lithium and sodium. KohanoR et at. (1992) proposed on tbe basis of crb initio computer si~ulations dispersion relation A mP( that Li,,CbO should he a stable, symmetric cluster: this the [ l i O ] crystal direction and was subse~uentlysy~it~esized by ~ristofolin~ et ale rnents along [ 11Oj as the tram ( ~ 9 who 9 ~ also ~ n~easuredi t s crystal structure in both cubic to a s ~ ~ g ~dt il sy t ~ ~ ~tetragonal ed structure, is high- (fcc) and tow- ~ t e t ~ a g o i i atemperature ~) phases, approached from above. A somewhat unexpected In the fcc phase the Li4 ions reside in tlie octahedral result is that phonon s o f t e ~ ~ ~occurs n g not just in the voids of the f~~llerene structure, with 4’0 (center) and
Eflkc~so j Mobile Species
259
ure 13 Intensity of the QENS, after Debye-Waller correction, 111 Li,,C,, at 450 and 600 K. Thc continuous lines represent the th.eo~etica1fit to octahedral JUIII~S with. a jump time of 2.7f0.5 ps t~cprintedfrom Cristofolini, L., Facci, P., Fontana, M. P., Cicognani, C . and Dianoux, A. J., Phys. Rev. I3 61, 3404, Copyright (2000) with permission from the American Physical Society)
ion, although this is what drives the transition, but at large values of Q and also for along the [loo] direction. Furthermore the s phonons develop int 'central peak', i.e. scattering intensity centered at = 0, a phenomenon that is a coininoii feature of many ferroelastic and ferroelectric transitions that is not generally understood (Cowley, 1987).
The body of work reviewed, even though a limited selection of the large amount of re1ated studies in the literature, shows that most known types of dynamic disorder and disordering or partial melting transitions can occur in intermetallic systems, although they may be rarer than in ionically or molecularly bonded compounds. In fact, some degree of strongly local or directional bonding appears to be essential for the
a kinds of disorder we have c o ~ s i ~ e r e dFrom . structural point of view, this generally leads to a substantial degree of interniediate-range order, which survives into the disordered phases as well as into the liquid. Except in particular cases where there is a large cliange in the electron structure ([or example, melting of silicon, which takes it from a four-fold coordinated semiconductor to a six-coordinated liquid metal), the short-range structure does not change significantly either. Usually it is the long-ran changes: even though the disordere crystalline symmetry, in general it will be different from the ordered phase. In fact, often only the Brag peaks at low scattering vector, which c h a ~ a c ~ e ~the ize intermediate-range, remained well pronounced. The directional bonding may lead to a band gap at the Fermi energy when the intermeta~liccompound is formed, producing a serniconducting rather than a metallic system. In maiiy cases, however, this gap fills in, at least to some extent, at the disordering tra~sition.
Agr~iwal*R. C., and Gupta, R. K. (1991). J . Muter. Sci,, 3 1131. Andersen, N. H., Clausen, K. N,, and Kjerns, J. K. (1987). ~ ~ S ~ z a t ~~~ ~c t ~ h o~i d ~sof~ ~r , x p e~ r ~ ~~Physics e ~ i ~t ~ ~ ~ Vol. 23 (eds K. Sklild, and D, L. Price). Academic, Ncw York, Part €3, p. 187 A s ~ ~ r o fN. t , W., and Langreth, D. C . (I 967). PAYS. Rev., 1 685, ~ o w e W, ~ ~S, s(1994). ~ J. Phys.. tt, C. S. (1966). Phys. Rev., P 296.
Phonon dispe~~ion relation A cop long the tll0l crystal direction ~~splacementsalong [I 101 as the transition at 45IC is a ~ p r ~ ~ i cfrom h ~ dabove. The unit along the abscissa IS C where = Qv = <2x/a and a i s the lattice constant. Z. B. refers CO the zone boundary which is at = 0.5 (Reprinted from hir ran^, G, and Axe, J. D., Pkys. Rev. Lctk. 2'1, 1803, Copyrig~t(1941) with permission from the American Physlcal SO~~~tY)
Cava, R. J., Reidinger, F., andU'uensc~i,13. J, (1980). .I. Solid State Chem., 31, 49. ~ ~ i ~ i s t ~ C., d e sNeuniann, , D. A., Prassi~es,I<., Copley, J, R. D., Rush, 1. J.? Rossansky, M.J. and Haddon, R, C. (1992). Phys. Rcv., ~ l ~ ~ dC. ~ T., e yand , Etliot, R, J. (1961). Proc. Roy. Soc., 77, 353, Cowley, R, A. (1976). Pkiys, Rev. B, 13, 4877, Cowley, R. A. (1987). ~ e ~ t r oSn~ a t t e r ~ ~~g ,e t h of ~ ~ s (eds K. Skold, and D. L. ~ x ~ e r ~ Physics ~ e ~ Vol. ~ t 23 a ~ Price). A c ~ i ~ e ~New i c , York, Part C, y . 1. ~ristofoli~ii, L., Ricco, M., and De Rcnzi, R. (1999). P h y . Rev. B, 59,8343. Cristofolini, L., Facci, P., Fontana, M. P., Cico~nani~ G., and Dianoux, A. 3. (2000). Phys. Rev. B, 51, 3404. Dong, 2.-C., itlid COrbett, J. D, (L993). J . AWEY. Che~n.SOC., 115, 11299. Dong, Z.-C., and Corbett, J. D. (1994$,.I. Amer. Chem. Soc., 116, 3429. Dong, 2.-C., and Corbett, J. D. (1995). J , Sct., Enderby, J. E., and Collings, E. U'. (1970). J . ~ o ~ z ~ C ~ ~
~~~.~~~~
4, 161. Faraday, M. (1839). Article 1240, Taylor and Francis, L0ndon. .-L., and E n ~ ~J.r E.~ (3995). y ~ Phy.~. ~~~~~~~
This ~ r ~ mobile ~ ~electroils ~ ~or holes e s which, as we have seen, rimy interwt in ii cooperative fashion with the mobile ions, X t is this inter~laybetween iiiobife charge carriers, the n i o t i o ~of ~ ~ ~ iom n and ~ the ~ e t r a n ~ l a~~ n~ ~ c~~t ~ r o~l er ~ ~ t~i~~unt iao~of n scoinptex ictiis, that leads to the ~ ~ s ~ ~ divers~~y ~ a t i we n ~ encounter in these materials.
This work. was supported by the Ofice of ~ c i e ~ cUS e, rtiiient of Energy, under contract W-3 f-109-38 and by the ~ r ~ n CN ch
,I. P., and Dove, M. T. (1993). Pliys. Rev. Left,, ~ ~ ~ ~ eR. ~(2000). ~ ~Q a n n , Solid State ~ ~ ~ Clarendon, ~ ~ Oxford, ~ ~ UK. 1 ~ ) ~ ~ e ~ p ~ ~ R., ~ aRichter, i i n , D., and Pnce, D. L. (1987). P h y ~ . ~ e ~ p e l m a i i R., n , Price, 17). L., Reiter, G., and Richter, 2). ~ ~~ 9 ~~~ i ~. ~ t ~)~~ ~(ecls ¶ ~R.~~S, I oSilver, n s and e P. E. ~ Sokol). Plenum, Mew York, p. 213,
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Hume-Rotliery, W. (1928). J. Chern. Soc., 131, 947. Johnsoii, G. K., aiid Sabouiigi, M.-L. (1987). J . Clwm Plzys., and Hull, S. (1998). J . Phys.. Condens. Matt., 8217 KohanoC, J., Andrconi, W., and Parrinello, M. (1992). Clzem.
Saboungi, M.-L., Reijers, € T. I. J., Blander, M., and Johnson, G. K. (1988). J. Clienz. Phys.
wells, W. S., and Price, D. L. (1993). Nature, 365, 2.77 Saboungi, M.-L., Johnson, G. K., and Price, D. L. (1994). s Phase ~ r a n s ~ o r r n a t ~(eds un~ Statics and ~ y n a ~ t ocf ~Alloy , R., and Lamprecht, I. P E. A. Turchi, and A. Gonis), Plenum, New York, p. 195. T. (1979). Z. Phys. B, 3 Saboungi, M.-L., Price, D. L., and Corbett. J. D. (2000). 157. Private communication. Lunden, A. (1994). Solid State Iomcs, 6 Sevov, S. C., and Corbett. J. D. (1993). Sczence, Luty, F. (1981). l)~$cts zn I n s z ~ ~ ~ ~Crystals ting (eds V M. Shimojo, F., Okazaki, €3.(1993). J. Phys.. C ~ ~ n ~ ~ e n Turkevich, and K. K. Schvarts). Springer-Verlag, 3405. Heidelberg, p. 69. Shirane, 6 . . and Axe, J. D. (1971). Phy.s. Rev. Lett., 27, 1803. Lyndeii-Bell, K. M., and Michel, I<. HI. (1994). Rev. Mod Singh, R. N., and March, N. H. (1995). In~errnetallic Bhys., 66, 721. Compou~ds:Princ~lesand Practice (eds J. ET. Westbrook, Marsh, R. E., and Shoemaker, D. P. (1953). Acta Cr-vst., 6, and R. L. Fleischer). Volume 1 , Wiley, Chichester, UK I97 Skbld, TC. arid Nelin, G. (1967). J . Pktys. Chem. Solids, 2 Massalski, T. B. (ed.) (1990). Bitzury Alloy Phase Bmagrams, 2369. ASM Intl., vol. 1. Slcripov, A. V., Cook, J. C., Sibrrtsev, D. S,, Kannonik, C., Miiller, W., and Volk, M.(1977). Z. ~ a t ~ r f o r s c h3. , and Hempelinann, R. (1998). .I. Phys.: Condens. Matt., 1 Nesyer, R. (1988). Z . Krrstallogr., 182, 196. 1787. Neumann, D. A., Copley, J. R. D., Cappelletti, R. L., Skrtpov, A. V., Cook, J. C., K Kamitakahara, W. A., Lindstroin, R. M., Creegaii, IS. M., V. N. (1999). Phys. Rev. B, Cox, D. M., Romanow, W. J., Coustel, N., McCaulay, Springer, T., aiid Richter, D. Neutron Scatterrng, J. P., Jr, Maliszewsky, N. C., Fischer, J. E., and Smith, Methods of Experimental Physics Vol. 23 (eds M. Skold, A. B., I11 (1991). Phys. Rev. Lett., 67, 3808. and D. L. Price). Academic, New York, Part B, p. 131. Parsonage, N., aiid Staveley, L. A. I<. (1978). Disorder in Stephens, P. W., Bortel, G., Faigel, G., Tegze, M., Janossy. Cvystals, Clarcndon, Oxford. A., Pekker, S., Oszlanyi, G., and Forro, L. (1994). Nature, Potzel, U., Raab, R., Volkl, J., Wipf, H., Magerl, A., 370, 636. Salomon, D., aiid W o r t ~ a n G. , (1984). J. Less ~ u ~ ~ o n Ubbelohde, A. R. (1978). The ~ o l t e nState of ~ a t ~ e r , M d f i n g and Crystal Structure, Wiley, Chichester, UM. Opiiziori in Solid State and van der Lugt, W. (1996). J. Phys.. Condens. ~ ~ t t8,. 6115, , 8439. Verkerk, P., Xu, R.. Howells, W. S., de Wijs, 6. A., and van Susniaii, S. (1989). .I. Pliys. der Lugt, W. (1994). Price, D. L., Saboungi, M,-L., Vineyard, G. H . (1958). and White, R. (1991). Phys Wagner, K. (1933). Z . P Price, D. L., Sahomgr, M.-L., and Howells, W. S. (1995). Wengert, S., Nesper, R. (1996). Phys. Rev. Lett., 77, 5083. , M.-L. (1991). Phys. Rev. B, Winter, M., Beseiihard, J. O., Spahr, M. E., and Novak, P. 7289. (1998). Adv. Mater., 10, 725. Price, D. L., aiid Saboungi, M.-L. (1997). .I. P1zy.r.: CoIidem. Wolf, D. (1977). Sulid State Cbmrnuvi., Matter, 9, 2707 der Lugt, W. (1993a). J. Price, D. L.. and Skold, K. (1976). Neutrorz Scatterzn~, Methods of Experimental Physics Vol. 23 (eds K. Slcold, ., de Wijs, G. A., van der and D. L. Price). Academic, New York, Horst, F., and van der Lugt, W. (1993b). J Phys.. Ramaseslia, S. (1982). J Solid State Chevn., ond dens. Matt., 5, 9253. Reijers, H. T. J., Saboun~i,M.-L., Price, D. Yao, N. P., Heredy, L. A., and Saunders, R. C. (1971). J . J. W., Volin, K. J., aiid van der Lugt, W (1989). Plzys. ~ ~ e c ~ r ~ Soc.. ~ i z 118, e f ~1039. . Zabel, H., Magerl, A., Dianoux, A. J., and Reijers, H. T. J., Saboungi, M.-L., Price, D. L., and van der Phys. Rev. Lett., 90, 2094. Lugt, W. (1990). Phys. Rev. B, 41, 5661. Zhu, Q., Zhou, O., Fischer, J. E., McGhie, Richardson, J. W., Saboungi, M.-L.. and Price, D. L. (1996). W. .I., Strongin, R. M Ph-vs. Rev. Letters, 76, 1852. (1993). Phys. Rev. B,
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ac
Fast-moving charged particles are known to ~roduce t r d s of atomic disorder in an i n ~ ~ i ~ e nvariety se of dielectric solids - including crystals, glasses, and high polymers. The literature on such tracks and their uses is vast - estimated to consist of some 8000 journal papers as of 1998 (~leischer,1998). The fact that tracks can be prod~cedin a special variety of solids, as reviewed by Provost et al. (1995) and Barbu et ul. (1995) came as a distinct surprise (Fleischer, 1995) - the reason for which will be explained after a brief overview of the phenomena and nature of conven~ionaltracks, ~~~~~~~~~~
The easiest, most widely used technique for observing al which nuclear tracks in solids i s by c h e ~ ~ cetching, preferen~~~lly attacks the disordered regions and enlarges the ~ e s ~ l t i n~g ~ l-ep sr o ~ u c ~pn~ r~r n a n e ~ t , optieafly visible features in solids (Figure 1 gives exa~ples~ These etched tracks have a r e ~ i a r k a b l ~ diversity of uses - in science to study nuclear reactions, cosmic rays, the ages of minerals, the distributio~of certain elements in materials, and the history of extraterre~~~ial ~ a t e r i a and ~ ~ ;in ~echnologyfor such pur~osesas ~ i ~ ~e x e prl oa ~~a t i odosimetry ~~ of indoor f i ~ dsizes, radon, prod~~ction of filters of w e l ~ ~ s ~ e c ihole and inferring where thermal conditions in the earth were favorable for f o r ~ a t i o n(and later l~cation)of oil and natural gas, ~verviewsof the subject are given in three books (Fleischer et al., 1975; Durrani and Bull, 1987; ~ ~ e i s c h e19981, r ~ and other books describe the d ~ v ~in~ more ~ ~r e ~~ t ryi c ~topics: e ~ Spohr (1990)
rnicrotechnology, Wagner and van den radon and its uses. dating, and flic and ~ u r r a n(1997) i ~ t- king ~ a relar ~ ~ ~ t h ion u ~tracks g ~in ~ tively new o b s e ~ v ~(Barbu t ~ o ~ et al., 199.5) - have not yet been put to any of the uses just noted, the fact that so many ways exist of u t i l i ~ i ~other g tracks implies that there will be new outcomes from irradiated interiaetallics. Most importantly, tracks in c o i i d ~ c t i n ~ solids present a challenge to our under~t~nding o f how tracks are formed.
Now, consider what ~ a r t i c ~form e s tracks in solids and then how we best describe which of the a ~ e ~ ~ ~ a t particles that are available form tracks and which do not for in~ividua~ solids. And for those p r o j e c t ~ that ~~s can form tracks, at what particle speeds do they do so?
The charged particles that can produce tracks are atomic nuclei from which some or a11 of the e~ectrons have been stripped to produce ions. The simplest ions to work with in the laboratory come from radio~ctive l~s ~ ~ ~ r-ceither e s alpha p a r ~ ~ c (4 variety of heavy radioii~icl~des, fix example ~ i r a n i or ~n~ americium, or fission fragments from 2s2Cfor iiiduced fission of 2J5U (which gives a wide dist~ibutionof rather heavy projectiles, e x a ~ ~ p i ebeing s “OBa and 9 y ~ ~ Other ) . ions caxi now be accelera~edat a ~ i u ~ ~ of h ~ a ~ y - i omachines, n giving project~le~ with atomic 1 ~ ~ y d r o g eton 92 ~ ( u r a n i ~ ~ Prior ~ i i ~ .to n u ~ b e r from s
~ ~ ~~~~~~~n~~~~ ~ r Vol.~ 3, PriPaeipLs ~ t and~ Practice. ~ Edited ~ iby J. ~H. Westbrook and R. L. Fleiscber. 0 2 0 0 2 John Wiley & Sons, Ltd.
~
264
lgure 1 Tracks from fission €ragmeats in three classes of cfjelectnc materials: Left, Lexaii ~ o l y ~ ~ ~ a plastic; ~ o ~ceiiter, ~ ~ at e silicate glass; right, a crystalline. mineral - orthoclase, The shapes of the tracks are the results o f preferential etching and, in the case of orthodase, ~ ~ io f chemical ~ ~ attack t r ~ ~ ~
these machines becoming available, exposure to cosmic rays was the ~ e a n of s obtaining fast, very heavy nuclei (Frier et al., 1948; Fleischer ec al., 1967a; Fowler et aL, 1967, ~ ~The tracks ~ 0of interest ~ .here are from ions at ener~iesper unit mass of more than 100 keV. lower pro~ect~lesof such an energy as is used for ion ~ ~ p ~ a ~- perhags t a t ~ o1 ~keV per atomic mass unit - produce some atomic displacenients, but not tracks, and do their dainage by direct knock-ons of atoms, which is not the way tracks from fast ions form.
Figure 2. The ~ ~ ~ ~difference ~ ~ ~between t a tenergy ~ v ~ loss and primary ioni~ation is that the p r i ~ ~ r y ionization is localized at the core of the track - the region of the most i n ~ ~ ~ ~~ e h is respon~ c ~ ~ sible for the track contrast lu the electron ~ ~ i c ~ o s c ~ p e and for the ~ref~rential etching. Tlie energy loss, in contrast, includes energy deposited several nin from the core and thus includes irrelevant i n € o ~ a t i o n . The data in Figure 2 are for a plastic, Lexan polycar~onate. Filled circles denote ~ a r t ~ c ~that es made tracks, open circles those that did not. To satisfy the idea o f a threshold there is a horizontal dashed line, labeled 'Lexan', that cleanly s~pai~ates the two types of results and thus defines a critical ionization rate. 'T"u avoid confusion, data for other materiats are not given, y taking s a ~ ~ of ~ ae single s solid and b o ~ ~ a r d ~ n but g the ~ ~ r e s h o ~(as d sd a s ~ lines) e ~ are d r a ~ nin for separate pieces with different ions of different energies, other plastics and for minerals. Thus the figure shows many tests clarify the cunditions for the presence or also that solid detectors exist that have a variety of absence of tracks, Then the question becomes one o f sensitiv~tm~s, from which one can choose - d e ~ e ~ ~ i m i g finding a critical parameter that defines a t ~ r e s h o ~ d on the use to be served. Next we consider wby priimry above which tracks are formed and below which they ionizat~onis, after fum-ther thought, an approp~ia~e are not. The first thought was that the density o f parameter to control track f~rmation. d ~ ~ o senergy ~te~ (energy per unit path l e ~ g t hm~i g ~ t be a r e a s o ~ ~ bthr~sbold. le This idea failed the test of experi~ent, but a related q~antity- the primary ion~z~tiondensity ( ~ 2 u ~ b eofr electrons displaced Wide experience with nuclear tracks is consistent with from the narrow path of the ion per unit pat11 length:) their being formed by an ionization spike ~ e ~ ~ ~ ~ worked well (Fleischer et a/., 1967b), as displayed in ~~~~~~~~
265
Primary ionization as a ~ e a ~ ~ofithe r ei~itensit~ of track d~magein various n o ~ c o ~ d ~ c tsolids i n g IS p e n as a ~ ~ ~ i c t i o ~ o€ v ~~o ciand t y of energy per mass for various nticler. The damage increases with i ~ i c ~charge ~ a s(or ~ atomic ~ ~ ~u~~~~~ from hydrogen (M)to curiuni (Cin). It also increases as the particle slows down (untii it 1s going so slowly that it becomes less ionized and, and therefore less ionizing). The dashed horizontal lines give the tliresholds for track-recording materials that range front sensitive plastics at the bottom to mica and typical inineral ~ o n ~ t ~ ~ofumeteorites e ~ t s at the top. The ex^^^^^^^^^^ p ~ l €or ~ t ~ n ~ grven t ~ as open circles for zero ~ ~ ~ s t r a and t ~ ofilled i i circles for 100% ~ e ~ i s t r ~ t i o n accelerator tom in Lexan ~ o l y c a r b ~ are
~ ~ l e i ~ ~etlal., i e rlQSS), which is sketched in Figure 3. The idea is that the moving, positively charged particle ~ ~ With the model described in section 2.2 in ~ expels electroiis from atoms alon behind a narrow region packed with positively charged workers in this field were ~ ~ ~and ~evenr ~ ~i a zs e d~ ~ l~ic~ ions. These repel one another with. strong ~ o u l o ~ when ~ i ~the observations of tracks in i n ~ ~ r ~ e t a(and forces that by inutual repulsion eject tnany of the ions in certain metals) were reported ( from their normal sites - creating a high energy region Dunlop et al., 1993). As example of atomic disorder that is later c ~ e ~ i cetched a l ~ ~to show tracks of Pb and U ions in, display the track. This mechanism c m be regarded as a and NiTi. In these cases the tracks are viewed in sittr massive scaling up of the Varley (19S4) mechanism, in using electron inicroscopy, rather than by cheinical which two adjacent positive ions produce a lattice etching. Most o f the data on tracks in internietallics defect. Note, however, thnt if the ~ lec~ r ons return to (and, as we shall see, in metals) comes froni the group n e u t r a ~ ~the ~ eion spike before the ions have time to that includes A. Dunlop and . Lesueur, often with A. move, the electros~~tic repulsions are quashed, and Barbu, W. Dammak, and co-workers. no track f o ~ ~ a t i oisnexpected. Barbu et al. (199s) report that tracks are seen also in Thiis mater~a~s with good electronic c o n d ~ ~ t ~ ~ i t ~but iiot in AuCu3 or AlZr3. Thus, the list of BNi3, were not expected to allow track f ~ r ~ a t by ~ o this n i~tern~eta~lics in which the presence or absence of ~ e c h ~ n ~ This s m . inference is ~onsistentwith the fact t ~ ~ c k - f a~b ~r l~i ~is~y known n ~ Is not extensive. Yet, that metals and good s e ~ ~ ~ ~ ~ o ~ di o~ ~ r ~c fail ta o~rto~s y from these five c ~ i ~ p o u Barbu ~ d s et al. point out one form ion tracks. major ~ i ~ t that i ~ can ~ tbeimade, ~ ~ The two that do
266
w e 3 Track forma~ion by the ion explosion spike ~ e ~ ~ 1 ~ n Electrons i s m : are ejected from atoms by a ~ ~ o v i i i g charged particle. The r e n i a i n ~ positively ~~ charged region (a] IS unstable and the repulsive, e l e c t r o s ~ coulomb t ~ ~ ~ forces lead to atomic disorder (b)
not show tracks have relatively simple, ~ i g h ~ s y ~ i ~ e t r ~ crysta~struc~ures- cubic with only four atoms per unit Bright-field electron micrograph of NiZrz that was cell. an contrast, I?& and NiZr2 are respectively irradiate^ with 0.7 GeV lead ions to a dose of 10" (;;a) o r t h o r ~ o ~with b i ~ f 6 ato~s/celland tetragonal with along the beam ~ i ~ e c t i ofb) n ~view with ~~~~1~ tilted by e d d, i ~ e r ~ ~ i t lview ~ . iTi IS also c o ~ ~ p ~ c a tbut 20". From Barbu et aL(1995) with the p e r ~ i s ~of~ the o~ a s h ~ p e - ~ e alloy ~ ~ o( r~~ a y ~ and ~ a n ~ ~ t ~ rRescar& ~ a l sSociety noue, 1995) in which two phases can co-exist at room t ~ ~ ~ e r a 1-ua,r esimple, cubic form and a more di~lectricsolids, and its vaftte should be ~ o i i s i d e ~ e ~ . con~plicated~~iartensi~ic, monoclinic phase, The idea Using the same units as in Figure 2 for ~ o n ~ ~ ~ t ~ ~ thresholds for NiZr2 and NiTi are around 14.0, as conipared to 70 for the less sens~tiveof tlie niinerais~ Thus from this v ~ e w ~ the o ~t ~ r~et ~~h 3re o ~d~i s~ e ~ e n ~ by only a factor of about two. Two other i n t ~ r ~ e t a l l iNb&f c s ~ and V3Si, ~ h a n ~ e ~ s u ~ ~ r ~ o n d ~ properties ~ G t i n ~ strikingly as a result of internal fission fragment ~rrad~ation ( ~ l t l i o u ~tracks h I-tave not been seen from fission fragments in these materials, the result implied that 1 56 ketr/im niakes continuous damage was close to the level that would be ~ e ~ u i r e d . ones, In NiTi et al. (1998) have shown that the threshol~lies ~ ~ t w e eXe n at 32 keV~nmand Ta at 46 ~ ~ t r --~a nvery n ~similar value to that for NiZrZ3.1 These authors noted that these energy-~oss threshold^ or lie ~o~isider~b1y above values of about 1 k e V ~ nfor~ plastics and 3 to 6 ~ e ~for/ ~ inn e ~r a ~ s . ~ e ~ e t r ~pa~ticles t i n ~ may not register in solids for As ~ o i n t out e ~ earlier9~ ~ o w e primary v e ~ ~ i ~ n i z ~ t i o ~several reasons. The first and most decisive is when no gives a more ~ o ~ s i s t e ncriterion t for thresholds of charged particles can form tracks because of basic ~~~~~~~~
oxides - have shown tracks. And, more convinc~ngly, consider spiiiel ( ~ g A 1 which, ~ ~ ~because ) ~ it is an insulating material, was an unexpected non-recorder of fission tracks, Spine1now (Wiss and - making shown tracks of Bi ions from an ac~e~erator it clear that the issue was obtaining high enough i ~ ~ i % a t ilevels. o n Another spinel, ~ n ~ + a~ ~ ~a ~ O n e 4t Y3FesO12, and the oxide Fe304 magnet~te(Provost et al., 1995) are additional examples of insulators in which u n ~ s u a l ~l?i& y iun~~ation can ~ r o d tracks. ~ ~ c A~ third sort of reason for not observing tracks might be that tracks fade rapidly at the temperature where they are sought, even t h ~ u g hthey formed and then existed too briefly to be observed. The like~ihoodthat such cases exist is deinonstrated by the observation of Barbu et al. (1995) tliat the tracks which they could observe in ~~i~ s h o ~ t after l ~ i~radiation~ dis~~peare~ after a few months.
.Trac Given that one wants to u n ~ e ~ s t a nhow d tracks form in i n t ~ r ~ e t a l lci co ~ ~ ~ uitnwill d sbe~ h e l ~ to f ~know the c ~ r ~ also~ for~track ~ ~ so r~~ ~~in~ other ~~ t ~~ o ~ i conducting solids. As in Figure 4, except for ~ ~ i # n o NiTi ~ l i ~ irradiated at 90 K with 0.76 CeV Limiium to a dose of 5 x ~ m o ~ ~tracks # u sare seen at 300 K. (a) view along the beam direction; (b>mew with saiixpfe tilted by 27” From Barbu et of. (1993) with the permission of the ~ ~ t e r i ~ Research Society
~ ~
Again, as for i ~ t e ~ e t a l l ~most c s , of the work in this has been done by Dunlop, Lesueur, Barbu, l area s Danimak, and co-workers - and this work is summar-
ized by Barbu et al. (1995)- The only metal 111 which tracks have been seen at the time o f ~ r i t i this n ~ chapter physical principles. Xt is presently widely believed that is titaaiuni (see Figure 6), but there i s Information that the simple face~centeredpure metals Fall in tlZis class implies that several other metals, ~ n c l ~ d i nZr, g CO, Fe, (AI, Cu, Ni, , . .). A second is that particles that ionize and Be, are very close to track ~ o r ~when a tthey ~ are ~ ~ inteiisely enough may not yet have been used, i.e. the irradiated with the most heavily ionizing particles tliat threshold is ~ n u s u a l high. l ~ For exam~le,in the first are now available ~ A u d o u a ~etdal., 1990; Dunlop and few decades of part~cletrack etching the question as to Lesueur, 1993a,b; ainniak ef al., 1993, 1995, 1996; whether a material allowed track formation or not was Dunlop et al,, 1994). %xi fact, two of these metals - Zr resolved e~piricallyby b o ~ ~ b a r d iti ~with g the most (Dammak et al., 1995) and Fe ~ ~ a and~ ~ u ~n l o pa , k heavily i o n i ~ ~ nofg easily availab~eparticles - fission 1998) do show ~ r a ~ ~ - l features ike after irr~diation fragments - and then testing by transmission electron with fullererme (CO) molecules of 10 to 30 MeV. As m i c r o s c o ~or ~ etching. More recently at places like they enter solids, the ~ o m p o n e ~atoms t of such armstadt, Caen, and erkeley heavier projectiles projectiles itre rapidly ionized to their e q u i ~ i ~ r i u ~ have become available, up to Pb and U ions - particles charge (as shown by Lassen (1951) and Steiger (1963) that are about twice as massive as fission fragments e~uilib~ium is produced over distances o f ~enetration and more heavily charged. Since these more intensely of 2 to 20 pg/cm2, i.e. 2 to 25 nni in solids), so that they b e r slow down by ionization as though they were 40 ionizing particles have come into use, a n ~ ~ ~ of previously ‘iion-tracl~-registe~ing’, condttcting classes of separate atoins ~ ~ a u d ieti ial., 1994; T o i ~ ~ ~ ceth l ~ o materials - metals, i n t e ~ e ~ a l land i ~ s s~u ~ e ~ c o n d u ~ t i n1995). ~ Other metals, ~ n c l u dAg, i ~ ~Cu, Nb, Ni, Pd,
268
~ r ~images ~ ofht ~ t t~ i ithat ~i u ~was ~ ~irradiated ~ ~ with ~ 2.5 x 10" cnx2 of 2.2 GcV ~ r ~ ~ iions. i u (a) ~ i view ~ along the beam direction; (b) view with sample tilted by 10". From Darnmak et al. (1995) with the ~ e ~ ~ iQFsthe ~ ~i oa ~t ~Research ~ ~ l s Society
, show no hint of track form~tion~ ~ u n l ei o al., p ~ ~ t e r e s t i ~the g l ytrack phase is not the c o ~ m o nliighand, using fission fra~meiits~ AI, Au, and Zn can temperature bm cIZ structure, but the hexagonal form ( ~ a n i ~ ~eta al., k 1993, hP3, CO, hi~h~pressL~re be added to the no-tracks list ~~leisclier et al., 1975). 1996). The exception, is ~iiusualin two way^^ (1) It Using electrica~ resist~v~ty , has a c o i ~ p i i c a t erh~ behedral (hP2) structure, and sliowed that there was a rapid i (2) its density is decreased strikingly by d~sorder~ng~ duction for dE/dx values above about 40 keV/nm for In addition to crystalline metals, there are r, Fe, and most ~ a r k e d l yTi. And Dufour et al. two observations of tracks in amorphous metals (1993) showed a similar effect in Bi. Thus it is not ~ ~ r a u t ~ i i aeti ial., n 1993 and Dunlop et aZ., f997, 1998). ~ ~ l ~ that k e greater ~ y ioiii~~tioii levels from single ions 1x1 the first case ~ e 8the tracks ~ were~ made ~ ~ would ~ ~ @ ~t r u~ c in ke ~some or all of these metals for g . t h r e s h ~ ~ dw~~ which d i ~ p e or ~ ~isolated ~ d ~ l ~damage i ~- such ~ as e ~ visible by c h e ~ i c a e~ t c ~ ~ ~The reported to lie above 24 k e V / i ~and ~ thus is similar is i ~ e a s ~ by ~ erd~ ~ i s t ~-~isi large. ty to those in the other materials disctissed here, In The ~ h ~ e s ~for o l dtrack f o r ~ a t i oin~Ti is not well the second case, surface craters re o ~ s e ~ eon d d e ~ n e dIn terms of dE/dx it lies near 30 k e ~ / n mbut , with &160 irradiated foils of Ni3B after i~radiat~on ~ t ~ o nonly by a tower the primary ~ o ~ i ~ is~ bracketed ~ o l e c ~ lions a r at 30 iVeV and U ions at 800 MeV. The limit of 50 aad an upper value of f 70. In short, it may not be ~ i ~ e from ~ e the ~ tlevel iii the i ~ t e r ~ e t ~ ~ l i cpsr, o d ~ c t i oof~ surface pits and same effect as that observed by ~ tnearly a factor of two. a l t ~ itocould ~ ~be ~d i ~ e r eby where fission f r a ~ ate low ~ ~ angles ~ eject m ~ ~ e ~ a l The c o ~ m o na s ~ e c of t most of the metals in which from the surface and produce bulges from tracks just d a ~ ~ is g elarge (i.e. except Si) i s that they have below the surface. ~ l l o t r o ~forms. ~ c In short, the fact that a second, or third phase is available with little difference in free energy suggests a route to track production. In t i ~ there ~ ~ is de~nite ~ ~ ~vidence* L ~ ~ Tracks ~ have ~ been Aiiother gro-rrp of c ~ n ~ u c t imaterials n~ in wfikh shown to consist of a dif%erentphase from the room charged particle tracks can be p ~ o d ~ c eare d oxides t e m ~ e r ~ ~h ~ e xr ~e ~ o i iW2 ~ 1 alplia structLire, but
263 tlrat in some cases can be supe~conducti~g" Tracks in such materials can pose potent obstacles to motions of magnetic flux lines, and thus they can be useful in e~ihaiicing~ ~ g n e t properties. ic rovost et al. (1995) They show evidence of tracks in
~ o ~ ~ e m et o~ al.d e ions in "-1 23, with electron n ~ i c r o ~ ~ oobservatioiis pe b ~roject~les. ~ontinuuus tracks appear at dE/d.x values around 36 keV/nm and ionization levels at and above 150. In the same article Toulemonde et al. (1 994) describe eflFects of ion irradiations on supercon~uGtin~ properties. As in the case of intermetallics, prior work with fission ~ r ~ g ~(Fleischer ~ n t s et al., 1989) showed effects on supercon~uctivity from fission f r a ~ i ~ e n-t sthe most ionizing of which give a level of about 130, i.e. just below what is required for formation of continuous tracks in U-123. The effects of ~ r r a d i a t i oon ~ supercond~ictiv~ty has been a busy subject, but further d ~ ~ ~ ~liess outside s ~ o ~thei scope o f this work,
The main subject here is intermetallics. characteristics of the other conducting solids that allow track formation provide clues to factors that may enable tracks to form in these materials that have unusual track properties. First, a concise summary o f physical factors common to the condLt~ti~g track formers i s given, follow~dby some possible explanations. The models are s ~ e c u ~ a t at i v ~best, not well~ound~ co d n c ~ ~ ~(except ~ i ~ n perhaps s as viewed by the respective authors o f the p r u ~ o s a ~ sSome ~ . of the models overlap in part with one another.
Qne common factor among the three classes of materials of interest (iiitermetallics, metals, and oxide cand~ctars)is that the threshold in primary ionization (on the vertical scale of Figure 2) lies around 150 about double the value for the previously known least sensitive track detectors. In part this level defines their special character, but in part it was to be expected that if more int~iiselyionizing particles were to be found, then new detectors that have higher thresholds could be i ~ e n t i ~ e d~.e v e r t h ~ l for ~ s sa~ satis~actoryunderstanding o f these new detectors to be achieved, their t h r e s h ~ ~ must d s be e ~ p l a i ~ e d .
A second comi~onalityis in f w t a pair of properties. Both interrnetallics and oxides are ordered compounds - and hence sensitive to atomic interchanges that are of no i ~ ~ p o r ~ a n inc pure e metals. Alternate phases that are not too different in free energy is a second coninion factor, It has already been noted that the metals that either show tracks (Ti, Fe, and are inferred to be close to track ~ ~ ~ m(, a t ~ o ~ have ~ ~ ~ oe qt u r~ loi ~ ~rphases. i ~ ~ ~n A p a r a ~ l especufrt~ Lion about i ~ t e ~ ~ e t a ~isl ithat c s because there are so inany crystal structures in which a ~ a r t i c u f ~GOMr position might exist, the chances of 3 second phase being very close in energy to the e~uilibriumone are good. As a particle moves through, the locally intense gradients of ionization, heating, and pressure, might cause a phase change. It was noted that titanium does show such behavior.
There are two broad possibil~tiesfor track-fo~ation ~ ~ ~ h ~ ~ S 1 ~ S . 5.2.1 ~
~
e~~~k~ ~ ~
a
l
The jostling, ~ r i r n ~ ~ rfi-oin i l y ~0~1011ib ejection of electrons, but also from energy transfer to ions and
occasio~ialatomic interactions, creates mot~onsthat, new lattice positions~ a time that we equated to a a hot a ~ t h o not ~ ~ og r~i ~ ~ nr~ a~ l~y ~ soon ~ o produce ~ , ~ a ~ ~~iec~ea x a t ~time, o n i.e, abotrt s. That n ~ ~ region with a ~ r e c i ~ ~t teom~~se ~ ~ t grad~eiit. ure Can e ~ ~ c t i v eexcluded ly good condL~ctors. track format~onresult from this brief3 but violent A re^^^^^^: ~ ~ ~ v e v ~e ~ ~, m ef ~ al. ~(1986) ~ ~ e h e a t i ~ This ~ ? m e ~ h a n i is s ~a lon~-s~aiid~iig one (Seitz, correctly note that a more i i ~ ~ a n i ~ gtime f L ~for the 1949). Two recent papers have discussed track formaions IS that for them to gain adequate energy from ized track detectors tion in some of the n mutual repulsio~s. They estimated for three by t~ermalspikes, T et al. (1993) direct a time of ions (they were study in^ ~~~~~~~~) work by K, Izui attention to Si and Ge ~un~ublished 0.7 x s is required to gain energy that would o , and various metals and say that and S . ~ u r ~ n 1986) overcome the theoretica~shear s t r e ~ ~of t hthe solid (as realistic ca~culations need to be addressed to the ~ a t t i c e ~ ~ ~ time, l ~ x alW13 t i ~ s). ~ And thermal spike. The Toulenionde group (Wang et al., ions (considering the ~~ternietal~ic 1994) present such ca~cu~ations and (in the absense of NiZrz) 1 ~aIcu~ate about 4 x 10-l5 s for a motion by direct nieasurements on tracks) correlate them with each ion of half an ionic radius, by whnch time the ions the damage rates from irradiation, as inferred from each have an energy gain of 24 eV, which in an increases in electri~a~ resistivity. In addition, Szenes uiid~sturbedlattice is sufficient to part an ion or atom ~1995)considers a set of six oxides; he does c ~ l c u ~ ~into * a new site (see review by Howe, 19%). In an tisns based on the idea that, if the melting teniperature already disturbed lattice, disp1acements sliiould be is exceeded, disorder is quenched in; and finally he easier; and hence the time calculated is only an shows a good c o r ~ e l a t ~between o~ track di~meterand 'tpper limit. Thus a time of about 1Wi5 s should now . This result i s ~romising~ but interi~eta~l~csbe considered in t r a c ~ - ~ o r i ~models. at~o~ have not been considered, And alter~iativemodels The e v ~ l u a t i omade ~ earlier (Fleischer et ul., 1955) ~ itt is~ possible ~ ~ that other i ~ ~ that ~ ~metals e d failed to form t were not e ~ a l so~ that description^ fit these ~ ~ r ~ ~ cdata u l aequally r well. It a t o ~ r~e Ica x ~ t i ~times n were a factor of long. The discussion of times in the previous parsishould also be n u t ~ dthat thermal spikes have not been slxccessfid in making useful predictions for the great graph showed why the gap should be lowered by a factor of about 100, and the higher ioni~ationabove number o f more conventiona~ track detectors, as ~ i ~ ~byu~ ~ s es~ s~ceth~uE, e r (2965, 1975). ~ e ~ ~ e ~ ~ h e l ethat s s , of fission f ~ a g i ~ that e ~ t BOW ~ is ~ v a i l a bin ~~ in ~ ~ a ~ i t a t i vdiRerent ely materials d i ~ rnechane ~ ~ particles ~ ~ from heavy-ion accelerators supp~iesanother f x t o r of four or five - implying that it is borderline as isms may be ~ n v o l v e ~ * to wliether niettls should record particle tracks or not, The most telling evidence implies that the thermal a behavior which the observations in sections 3 and 4.1 spike is not the primary general cause of track fori~ation.The observation i s that primary ioni~ation~ document for materials that have metallic ond duct ion^ forz wakes: Another factor that is related to the rather than total energy loss rate or restricted energy revision required by laumiinzer et al.'s work has to loss rate, correlates with registration thresholds where do with other energ that is imparted ta the newly et al., 1967b; they have been measured (Fl~ische~ path by its created ions along a charged~partic~e~s Fleischer, 1980). direct coulomb interactions with them - a repulsion that gives each ion a radial impulse away from the 5.2.2 Ion path. The p o s ~ i b ~effect e was noted by ~ ~ e et al. ~ ~ c (1965) and i ~ d e ~ e n d e ~by t l yLesueur and Dunlop This mechanism, i l ~ ~ s t r ain t eFigure ~ 3, is also called on occasion a Coulomb spike, ~ o u l o i n b~xplosiQn, (1993). The former paper estimated energy transfers ~ ~ ~~ r~ ga ~y m to e na t Si atom of or ion spike. For good coiid~ictors from a f u ~ ~ ~ fission i o n i ~ ~ t i ospike, n about 1/30 eV - in short, a little above ambient we c ~ n c l ~ ~ dine dour o r ~ ~ i proposal ~ ~ a l (Fleisclcher csf thermal energies. From the i n c r e a ~ e~~ ~ ~ tbat u l s al., 1965) that such ~ ~ a ~ e ~would i a l snot forni tracks. are available from ~cc~lerated heavy tons, a few times ~e were no doubt in~uencedin ottr thinking by the the t l i e ~ ~energy al are available. Thus these inch~ul~~s lack of tracks from ~ssioi~-fragment ~rrad~atjons of a1 noise, and they can prowill not be lost in metals and the most c o ~ ~ u ~ tsemicon~uctors* ive The pagate as a wave. gh and Cilmaa ( 1 ~ and ~ ~ ) rea~oning given was that the re~axat~ontime for unlop ~ ~ 9 9 ~3 ) ~ ~ on ~the ~resenir ~ e e ~ ~ c t-rthe ~ ~time s to n e ~ t the ~ ions ~ ~that i ~had~ blance to a shock wave, One possible iiiipo~tan~e to been produced by the charged particle - needs to be this organized motion of ions is in assisting phase not less than the time for ionized atom to move into +
~~~~~~~~~
~~~~~
Ion Tr.acks changes that might be encouraged by high pressure or shear stresses in a ~ u l t i - a t o ~ iregion l ~ c - NiTi being an example of where shear tr~sforniatioiisoccur easily, and tracks are known to form. And, as noted earlier, where there lurk allotropic phases or hypothetical crystal structures that are just barely energetically unfavorable, these ‘organi~ed’deforniations may bring them into existence. Dunlop et al. (1991) and Lesueur and Dunlop (1993) consider the i~portanceof soft plzonon modes, wbxh they describe as encourag~ngdisplacive transfo~matlons. This behavior appears to be another aspect of the ion-wake ~ehavior. ~ ~ ~ ~ ~ ~~It iwould ~ be~ helpful t c ~ and ~ Z conve~ nient if there were simple e ~ ~ p i r ~~c agl ~of~merit e sthat would predict relative ease of track ~ o ~ n a t in i othe ~ various conducting solids considered here. For example, iii the case of insulating track detectors it was shown (~leischeret al., 1965) that threshol~sfor detection increased with the value of 5Eb4,wliere t is the ~ i e l e ~cu~stant, t r ~ ~ E Young’s modulus, and h the i ~ t e r a t o m idistance, ~ The cor~es~omi~ence of thresholds is not one to one, but it does divide the detectors properly into groups of similar ~ i a t e r i a ~ with s moiiotonically i ~ c r e a s i ntliresliolds ~ for track production. For intermetallics, only the values of lattice spacings are widely available; for cond~ctingsolids, it is not clear what to use for a dielectric constant (perhaps behavior at ultra-hig~i~ ~ e ~ u which e ~ ~ISc not y ~available). Values of Eb4 can be connpnred for nietafs in w h i ~damage l~ is easy (Ti, r, CO,Fe, and Be)+but this parameter does not correlate with damage production. Hence, this direction i s not f ~ ~ t f u l , The only useful correlation is that of Luzzi and Meshii (1987) for describing the ease of converting intermetallics from crystalline to amorphous. In their Table 7 they list two groups o f inter~etallics- those that electroiis can amorpliize and those they cannot. NiTi and NiZrZ can be disordered, and they are track recorders; AuCus and AlZr3, which have not fonned tracks, similarly are not disordered by electroil irr~diation.The statistics are not great, two structures roup, but this direction i s p r o ~ i s ~ ning that Luzzi and MesGi’s list suggests a dozen other ~ n t e ~ e ~ d l lthat i c s are likely track formers, and 15 others that are unlikely cand~dates,Among compounds that ‘were not made amorphous’ are several that (on the basis of crystal complexity) might be expected to allow track f o ~ ~ z a t i othe n ~fact that they did not is merely a State~~ent that in the p a r t i c u ~ ~ r experim~~ reported, ~s they stayed ~r~stalline* In fact, s , Banerjee et n17, one of the r ~ f e r e ~ c eedx ~ e r i ~ e i i tby
27 1
(1984), showed that for irradiation at 200 (tT10, Bla) did in k c t become an~orphoL~s. Of the 12 c o ~ ~ p o u n d that s can be made a ~ o r p ~ o u s by electron irradiation, 11 are of lower thau cubic symmetry, and 10 have more than four atoms per unit cell. The rei~aiiiinginter~etal~ic is Cu structure - but it is notewo~hyin that it exists as an equilibrium phase only between 715 ”@ and 935 “6, hence disorde~ingniay be easy. that C ~ ~ c ~xper~mentally Z ~ ~ ~ it~has~been ~ show~i : charged particles create damage tracks in some ~ n t e ~ ~ ~ ~and ~ ~not ~ l in l i cothers, s in at least three metals and are close to track ~ o r ~ a t i oinnothers, aiid in s u ~ e ~ c ~ n d u c tthat o r s have been studied. ~ the oxide : ~ec~nsideration of the free electron ~ e n s ~ tand y r e ~ a ~ a t i otime n ~ ~ p l that i e ~the usual ion explosion spike model is s ~ i ~ c ~ to e n~t x ~ l a itrack ii forniation from projectile^ that exceed ion f r a ~ ~ e n in ts ~o~iizing power. ~ r y s t a ~that s can be disordered or caused to change phase are ~ a r t i c u l ~ rsusceptible ly to track forniation.
This chapter i s devoted primarily to d o c ~ ~ ~ n eand ~tin~ understanding track f o r ~ a t i o nin i n t e ~ e t a ~and ~i~s allied materials that might aid in. learning about the behavior of solids in general and i n t e r ~ e ~ ~ linl i c ~ particular. ~ o ~ e vsince e r ~particle tracks in solids have many uses iiz science aiid techiio~o~y, it is of interest to ask whether tlzere are pros~ec~ive appl~ca tioas o f tracks in intermetallics. Since neither alpha particles nor fission ~ r a g ~ e n t s make tracks in intermetallic compounds (or the other conductors) uses for radon ineasure~ents~ alpha or fission ~~appimig, fission track dating, and d o s ~ ~ ~ e t r y are not available. The unique feature of i i ~ t e i ~ ~ e t a l l ~ c s is their insensi~ivity,and thus they would be effective in recording a few? very rare events from inteiisely ionizing particles in the midst of a background of less ionizing particles. Hence, searches of tlie cosmic rays for slow, heavy nuclei or h ~ o t ~ i e t i c aother l particles are scientific possibilities. Two routes may be considered, One is to synthesize sheet material for exposure to present-day cosmic rays. A second is to locate and examine one of the good many natrxral inter~etalliccompounds (De~ries,1995) that may have been exposed over geological time - just as nieteoritic minerals have recorded ancient cosmic rays (Fleischer et al., T967a). DeVries notes that iron meteorites contain two ~ ~ ~ i ~n t edK ~a ~ ~~ a l~~ ~
~ a n i ~ a H., k , Dunlop, A., Lesueur, D.*Brunelle, A., Dellai(Llo, tP4) and F i3 (Llz, cP4); these might be Negra, S., aiid Lc Beyec, Y. (1995). ~ ~ Rev. 2 Lett., ~ 7~ ~ ~ useful provided they do record particle tracks. FeNi E 135. ( t e t r ~ t a e ~ because ~ t e ~ ~ it is of lower s y ~ ~ e t risy ,the nd Lesueur, D. (1996) Nuct. more likely ~ ~ i ~ ~The ~ ~ chance a t e of .tracks ~ o r i ~ i ~ ~ in FeNi is enhanced by the fact that FeNi is disordered to a ~~ce-cent ere^ solid solution by lieating above about 300 "C ( ~ l i ~ ~ ~eti al., b e1979). r ~ ~ DeVrres, R.C . (1995). In I n ~ e r ~~ ~ ~o ~ ~~ -l ~~~ri ~i o ~ ~~ ~ l~ ~ A potential ~racticaluse is iii making filters, which arzd Practice (eds J. H. Westbrook, and R.L. Fhschcr). might be doiie by irradiation across thin sheets aiid Wiley, Chichester, vol. 1, leischer et d, 1964). ~ i i t e ~ e t afilters ~ l ~ c ~ u € o C., ~ rALido~a~d, ~ A., F., Dural, J., Girard, ~ ~ ihave ~ special l ~ t ~ r # ~ ~- for r t example ~ ~ s u ~ ~ i s ~ a l ~ yJ. P., Hairre, A., Lev M,, Palmier, E., and sistanee or h j g h - ~ e ~ ~ ~ ~ e r a t ~u ~o~ u ~ ~ RA[.~ (1993 o n ~J. ~Ph-ys. ~ ,~ ~ ~~~t~~~~5, d s t ~ ~ ~AlRu t ~ rise a ~ ~ t ~ r i a l 4573,
otE9 this voltirne). As yet, it is iiot known whether tracks can be made in any 2 structures, however.
Dm1op, A,, Legrand, P., Lesueur, D,, Loreiizelli,N., Morillo, J., Barbu, A,, and BouEarcl, S. (1391). ~ ~ ~ ~ Lc3tx-,, ~ ~ h . ~ ' s . 765. r, D.> and ~ a r ~ A. u ,(1993). f . Nuct.
unlap for lielpfml correspondeiice and her ~ ~ i ~ for n ds e~ ~ ~ lthe y photos i n ~ for this ~~a~ter.
Dunlop, A., Henry. J., and J ~ ~ s k ~ C. ~ ~(1998)~ w ~ ~ z, *c ~ ,
Ces lanzat, E., Boflard, S., Jousset, J, C,, , Dunlop, A., Lesueur, D., Fuclzs, G., er, J., and Thorn&,L. (1990). Phys. Rev. ~
e C. aP., Fieischer, ~ ~ R. L,, S w a r ~ P,~S., ~ and Hart, N,R., Jr. (1965). J. ~~~~~. Phys." 37,2218. ., arid Averback, R. S.
axnd Lesueur, B, (1995). A., Hardoitin Duparc, A., Jaskier G., and Lor~nzelli~ N.(1998). Nucl. ~ n s ~Meth., r ~ ~ . 354. anerjee, S., Urban, K., arid Willtens. M. (1984) Acts Metall.,
Dunlop, A., and Lesueur, D. (199323). Rnd. ~ ~ ~~ ec f ~t c~t , s~ ~ ~126, 123. r ~ ~ ~ ~ , A., and Lesucur, D. (i993b). ~ ~ t e r SCL i a ~~r~~~~ ~ ~ 9, 553. ,S., and Bull, R. K, (i987). Sokid State ~ ~Track ~ ~ Detection, Pergamon, Oxford. Fleischer, R, L. (1980). In Prog-, iiz ~ ~ Sci., ~ ~ ~ ~ ~ Anniversary Volume (eds J. W, Christian, P. Haasen, and T. B. ~ ~ a ~ Pergamon, a ~ s ~ ~ j ~ . Ffeischer, R, L. (19%). M R S &I, Fleischer?R. L. (1998). ~ r to ~ ~ ~ ~ s in. Scwice and ~ e e h S ~p s~~ ~~ ~ ~ o r ~-New V~e York. r~~ ~~ ~ , F ~ e ~ s c ~R. e r ,L., Price, P B., and Symes, E. M. ( ~ ~ 6 4 ) * B., and Walker, R. M. (1965). J. B., Walker, R.M., M~urette,M., and Morgain, 6. (1967a). .I; ~ e o ~ lRm., ~ ~ 72, s . 355. er, R. M., and Hubbard, E. L.
Fleischer, R, L., Price, P. B., and Walker, R. NI. (1975). Baradin, K., ~ ~ ~ n eA., ~ l Ghabot, e, M., Della-Negra, S., m cl^^^ ~ ~ a c IN l ~ Ss o ~ ~Unw. ~ s of ~ ~ a ~ ~ ~ o Press, rnia ~ e ~ a u.Iw .~ ,~ a r a., ~ ~ ~~ k~~ n, ~P., s oLen Beyec, , Y,, Berkeley. 3~11ebaud,A., Fallavier, M., Remilfieux, J., Poizat, Lay, K. W., and ~ L ~ ~ o r s k y ~ and Thomas, 3. P (1994). ~ ~~ ~ ~ ~Me& s ~ ~ r ~ ~ FJcischcr, ~ ~ . R. r L-, Hart, . 13. F; E. (1989). Phys. Re 341. Flciscber, R. L,, Field, , and €31-iant, C. t. ( ~ 9 9 ~ ~ . B ~ ~ l l o R., u ~ and ~ , Cilman, J. J. (1966). J. Appl. Phys., 37, ~ e t a l l ~ Trims., r ~ ~ c ~ ~ 2283. Fowier, P. H., A ~ ~ ~R,i A., ~ sCowen, , V. G., and Kidd, J. M. C ~ a m b c r ~ A., d , Laugier, J., and Penissoxi, J. M. (1979). J. (1967). M ~ ~ ~ ~ e~t ~ % samMater.,~ 10, 139. ~ ~ ~ ~ c Proc. Roy. So Fowler, P. H., Clapham, V M.. Cowcn, V. Dammak, 15.. Barbu, A., Dtrtilop, A,, LC~LICW, D., and and Moses, R. T. (1970). Proc. Roy. Soc., Loreazelli, N. (1993). Phil. Mag. Lett., 67, 253.
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Szenes, G. (1995). P h j ~ . Frier, P S., Lofgren, E. J., Ney, E. P., Oppenheimer, Fa, Bradt, H. L., and Peters, B. (1948). Plzys. Rev., Tomaschko, Ch., Brand Howe, L. M. (1995). In I ~ t e r ~ ~ ~ ~ tCompounds aLlic Volt, H. (1995). NucL and Practice (eds J. H. Westbrook and R. L. Fleischer). To~lemonde,M., Paurni Wiley, Chichester, vol. I, p. 791. Efeects and 0eject.r in Ilk, R., and Durrani, S. (1997). Rado;k,va ~ e a s u r ~ ~ ebyn t . ~ Toulemonde, M., Bouf-Tard, S., and Studer, F. (1994). Nucl. Etched Track Detectors, World Scientific, Singapore. ~ l a ~ ~ u n zSe. , rHou, , M.-I>., and Schumacher, 6 . (1986). Trautmann, C., Andler, S., Bruchle, W., Kiiorr, T. G. (1964). J. App1. phys., 35, 2753. Lasscn, N. 0. (1951). Dan. Mat. Fys. ~ e d d . 26 , (no. 5), 3. op, A. (1993). Rad Efects Defects i, M. (1987). Res ~ e c h a n i c a , Provost, J., Simon, Gh., Hervieu, M., Groult, D., Hardy, V., Studer, F., and Toulenioiide, M. (1995). M R S Bull., (12), 22. 1949). Disc. ~ ~ r Soc., a d ~ ~ ~ ~ (I 990). Track ~ ~ n d a ~ ~ n ~ ~ s c e ~ ~ a n~e ~o ~z ~l is c ~ t iVieweg, a n s . Braunschwei~. Steiger, N. H. (1963). Lawrence Xrxd. Lab. Report UCRL10888, UC-34 Physics, June 26, 26 pages.
lemonde, M. (1993). Rad. ~ ~ e cand t s 207. Varley, J. H. 0. (1954). ~ ~ t u r e , Wagner, G. A., and Van den Haute, P (1992). Fi.~s~on-Tracl~ Dating. Enlre, Stuttgart. Wang, Z. G., Dufour, Ch., Palmier, E., (I 994). J. Phys. Candens~d~ ~ a ~ t ~ r , Wayrnan, C. M., and Inoue, ?A. R. P, (1995). In I n t e r ~ e ~ ~ ~ l i ~ C o ~ p o i -~ Pn r~~ ~ c i ~and l ~ s Practice (eds J. H, Westbrook, and R. L. Fleischer). Wiley, Chichester, vol. 1, p. 827. Wiss, T., aiid Mntzke, 14j. (1999). ~adi~~tio;k,va ~ea~si~rei~e;k,vats, 31, 507
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structures or the same type of atoms in the e ~ e s~ruc~ure are further apart, which may ~ m ~vacancy ~cieiitificactivities in the field of ordered inte~~~etallicsmi~ration. For defect studies in ordered i i i t e r ~ e t ~ ~ l l such as the Ti-AI, Ni-A1 OF Fe-AI s y s t ~ i ~ arise s from pounds, which date back to the early work of basic research interest^ in these ~ ~ n s ay srt e~~ ~and ~s defects their potentia~for technical applications ~ e ~ t b r o o k and ~ Taylor (1937), a variety of constit~~tional such as the vacancies YEand Yp on fke two s u b l a t ~ ~ ~ ~ 1993; ~ e s t b r o oand ~ Fleischer, 1995; Deevi and cx and fl as we11 as the antisite atoms Ap and B, are to Sikka, 1996; A ~ p ef ~ lal., 2000; ~ a r o l i a2000~ ~ as be considered in inte~etalliccom~ounds.In ~artic~1ar, l ~ g h t ~ w e materials ~~ht with promising high-temperain AI-rich B2-NiA1 high concentrations of vacancies on ture properties (Yamaguchi and Umakoshi, 1990) and the Ni sublattice are found. V a c a ~ ~ i eon s both corrosion resistance. Stimulated by the growing intersublattices are required for ~tabili%ati~n of the la est far teclinical app~ication,research on intermetallic structure in some cases, as, e.g. in the case of Blcornpolxnds also comprises studies on novel alloys as, (Anderson et nl., 1957; Terauchi et al., 1978; Valeeva et e.g. MO-based silicides ( h i et al., 2000) and transition-metal Laves phase compounds (Liu et al., 2000). al., 2001). For the vacancies in i n t e ~ e t a l l ci ~o ~ ~ o ~ two nds In basic research, order-disorder (see e.g. chapter by different types have to be ~ i s t ~ i i g u i s ~Besides e~. Diinitrov in Volume 1 and Calin, 1994) and diffusiori processes (Larikov cliapter in Volume 1 and Mehrer, comcoi~stitutionalv a c a ~ c i ~ ins ordered ~ n t e r ~ e t ~ ~ llic 1996), which are also related to the t e c ~ ~ i ~relevant all~ pounds which are necessary in some cases to creep resi~~dnce p ~ e n o m e n( ~ a u ~ hf o893; ~ , and^ c o ~ ~ p e ~ s afor t e o ~ - ~ t u i ~ ~ i ico o~ i~ ~t r~~~c s oif t ~ o ~ et al,, 1999), are of i ~ p o r ~ i ~The c e .~ n d ~ r s t a ~of d i ~ gthe i n t e ~ ~ e t a lc~oi cm p o ~ nto~ ~ ~ a i the ~ ordered ~ a i ~ these processes requires a profound k n o ~ ~ e dofg ~ structure thermal vacaiici~salso exist, T t h e r ~ a ~ lformed .y defects in ~ n t e i ~ i ~ t a lcompounds, Iic tion of the const~tutionalvacancies can which is the subject of this chapter. the con cent ratio^ of the thermal vacancies as, e.g. in It will be shown below that crystaf structure appears the case of Al-rich NiAl c o ~ p o u n d sfor whrch several. to play a role in thermal vacancy formation. A nuniber atomic percent of constitutional vacancies have been of binary i ~ ~ t e r ~ e t acrystallize ~ l i ~ s in a close-packed reported (Bradley and Taylor, 1937).A clear ~ i s t i n ~ t i o ~ or nearly close-packed structure such as Llz(cP4) has to be made, however, between ~ o ~ ~ t ~ t u t i o n a l (?&AI), D019(kzPS)(Ti3Al) and Llo(tP4) (TiAl) or in vacancies and quenched-in or remnant vacancies, the bcc-type structures which can remain in the lattice of an i ~ t e r ~ e ~ a ~ ~ i (cFl6) (FQAI, Fe$%) structures the compound due to their low mobility and which can also sublattices of the majo yield fairly high concentratio~sthat then have signifiinterco~nected~earest-ne~g~bor sites of the same type cant csrssequences €orthe ~ n e c h a n iproperties ~~1 (Ckmg of atoms, a ~ituationthat fmors vac an^^ jumps on th' et al., 1993; Pike e~ al., 1997). For details on tlie sublattice, whereas the minority atoms in the A3 of r e m ~ a nvt a c a ~ c see ~e~ s e ~ t i 3.2, o ~ In the case o
ion
*
*
type iiite~~metallic coni~oundssuch as NiAl and FeAl can be derived from the d ~ p e n d e n cof~ CV on the the concent~atio~ of thermal vacancies V, on the pressure p tr~nsition- eta^ sublattice has been predicted (Fu et al., 1993; ~ a h et~al.,~ 1999) e to exceed that 01%the A1 (4) sub~~tttice which r e ~ e n t ~has y been ~ e ~ o ~ i s t r a t ~ ~ From the pressure d e p e ~ ~ e n cofe the e q ~ ~ l i b r a t i o ~ rate, the v a c ~ n ~ c ~ g ~volume ~ can t bei deduced ~ ~
local co~~position (see Scliaefer and B a ~ u r a ~ ~ e r g e n ~ 1997). A review of the literature on defects in €32-type which is the volume change during a difibsive jump. iiitermetallic c o ~ ~ o ~ t was i d s given by Cliang and ~ ~ u (1982) ~ ~ withndatan available at the time (three ~i~ ear in a 1998 MRS s y m p o s ~ on es i ~ t e i ~ e ~ d l In l ~ this ~ s . ~eview ) the data on CoGa and ~ i (see~Figure a 4) obtained by measuring techr-riques For s t ~ d y ti h~ ~ ~ eaql ~ ~ l ~ atomic b r ~ udefects ~ in s ~ ~ c i ffor i c v~cancyd ~ t e c t i oshould ~ be particular^ y solids, several r e q u ~ r e ~ ~ ehave i ~ t sto be ~ ~ l l i l by l ~ the d empliasi~ed.Iiz the present overview we will mainly detection t e ~ ~ ~ ~ ~ q u e : deal with vacancies in thermal equilibrium. For this ~ u r ~ the o s~~h ~ r m o d ~ nand a ~ ~iiietics ~ i ~ s of t h e ~ a l (i) high s ~ e c i ~ c ifor t ~ 7a particular type of defect (ii) high sensitivity e ~ ~ i l i ~ r i uvacancies ni are summarized briefly. By (iii) a p ~ l ~ ~ a bati high ~ ~ t temperatures, y and ~ i i ~ ~ ~of~the r variation ~ ~ e nof~the s thermal equirs that i ~ fast ~ e ~ ~ i ~ i b r a T e (iv) short ~ e ~ st i ~ e so I ~ ~ rv~a uc i~~~~ ~~ ~c i~ ~ n tCv~ with ~ t ti eomn~ e r a t ~ processes of the thermal defect c # n c e n t ~ a t i o ~ after rapid t e ~ p e ~ changes ~ ~ ~ ucan ~ be e ~ e a s ~ in order to study the f o r ~ a t i o nand migr~ttionof the same type o f atomic defects S i ~ ~ l t ~ n e ~ ~ s I y the egective vacancy formation entlzalpy HF can be If we restrict ourselves to m e a s ~ ~ r itne~c ~ ~ n i ~ ~ ~ derived, where 3; denotes the efTective vacancyq uleft~ ~ which fullill criterion (i), only a few t ~ c ~ i are ~ ~ r ~ aentropy t i ~ and n k,, o l t ~ ~ n nconstant. ’s of these t ~ c ~ n ~ may q L ~ exhibit ~ s d i ~ ~ ~ l in ties and some From the ~ i ~ e ~ d e ~~ qe ~ ~i ~ i~b nof r at the t i omean ~ f u l ~ i l i nthe ~ residual criteria (ii) to fiv) as discussed in vxancy ~ o n c e n ~ r a G(i) ~ i o ~ after fast temperature the ~olIowing~ c h a n ~ at ~ shigh t e ~ ~ ~ r a t u r ~ ~ is specific to the ositron Ii~etitiz~ spec~ro~copy i ~~n ~ c a n c defects y ~ ~ ~ ~ e detectio~of the ~ ~ r i i i a tof due to the ch~~racteristi~ increase in the lifetime o f a positron when trapped in a vacancy, A with the vacancy diffusivity di~erentia~jon of k-acancies ctn the two sublattices of binary inter~etallicalloys is, however, hardly feasible because only minor di~erencesof their positron lifetimes are ~ r ~ d ~ c ttheoretically ed ( ~ i r ~ s k oetv al., ~ 1995), A specific i d e n t i ~ ~ a t i o ~ the ~ ~ e c t ~v v e~ c m ~ ~~~ ~ r a yte ~ n to~ ~ a ~ p y is of these d i ~ e r e i types i ~ of vacansies is, ~ o ~ e v e ~ , ~ ~ d for ~ the ~ ecase d of a regular distrib~tionof feasible by e ~ i p ~the ~ ~oincident ~ i n ~ i~eas~ir~nzent vacaiicy sources or sinks. Here, C, and Cv denote the of the ~osit~on-electro~i ~ n n i h i l ~ ~ t iphoton on line equilibrium vacancy c o n c ~ n t ~ ~ t i oati i the s initial and (see Section 3.4). final tenzper~tures T, and T f , respectively, d the The positron trapping rate vacancy jump distance, z the coordination number, ebye ~ ~ e ~ u e n2i$fc ythe ~ vacancy niigratioii a quantity c h a r a c t ~ r i ~the ~ nsource/s~nk ~ ~ion ~ ~ n ~ iand t y 1,/ t e the ~ h a r a c t e ~ i ~et~i cu i ~ i ~ r arate, of thermal v~c~tncy c o ~ c e n t r a t CV ~ ~can ~ s be detern a d d i t i ~ i i~~ ~ ~ ~ a c tpar~meter e r ~ ~ t of ~ cthermal mined making use of the time ~ o i i s t a n tTO ~ and ~ o n VF which v a c ~ n c i ei s~the vacancy f o ~ ~ t volume
HY
detectioii limit for vacancy c~ncen~rations but the z1 and the in tens it^ I1 = I - 10 derived from the ~echniquei s not so sensitive to v a c ~ concen~ ~ y positron lifetime spectra. If the specific positron trations below o t i i ~ e - d e ~ e n ~studies e s ~ t of t ~ a ~ p i nrate g cr is considered to be t e ~ ~ e r a t u r e the defect equi~ibr on used for i ~ v e s t i g ~ t i ~ ~ ~~idependent~ then the vaca~icyforii~~tion enth~tlpy defect niig~ationby this t e c h ~ i i ~are ~ ~ltnown e to ffF, c‘clll be d e ~ n e das an effective ~uantityby the the authors. tei~perature va~iation of Cv as ~ ~ e a s ~ rby ed (c) ~ i g h - p ~ e c i s ~ neutron o~i, d i ~ r ~ c t i o tn e c h ~ ~ ~ u ~ positron lifetime spect~oscopyaccording to equa(Kogachi t?f al., 3996) may be useful fur detect in^ tion (6). For a theoretical understanding p ay er vacancies aiid antisite atoms s p e c i ~ c a ~on ~ ythe and F$ilinle, 1997; Fiihnle et al., 1999) of the particular sublattices, They are, however, limited experimental value of the conco~itantformain sensitivity and no ti~e-dependentdefect equition of the entire ensemble of thermal defects has to be taken into ~ccountin order to ~ ~ ~ c uthe l ~ ~ t e libration studies have been reported. tempe~atu~e variation of the vacancy co~centratio~ ($)A t~me-dependentlen th change, A& ( K , Tf), of a s~ecimen ( t i ~ e - ~ i ~ e r e n t i~aill a t o m e t r ~is~ in analogy to the ex~er~mental p~ocedure.In this expected due to the e q ~ i ~ i b r a ~process ion of the regard the recently reported opinion (the chapter by thermal defect con~en~rations after fast temde Novion in ~ o l u 3) ~ that e positron annihilation perature changes between the initial and final expe~iment~ are ina equate to yield the vacancy tempe~at~~res T, and Tf and can yield direct f o r m a t ~ oe ~n ~ h a is ~ i~isleadin~. p~ and on i~iformationon the defect f o r ~ ~ t ~ Fur the direct study of the eRective ~ i i g r a t i o ~ dies by a length pr ~nthalpy of the therm~llyformed vacaiicies, i n v e ~ t i ~ ~ tati ohigh n ~ te~iperaturesin the vicinity of with the speciineizl were thermal e q u ~ ~ i bafter ~ i ufast ~ ~ te~iiperatu~e changes p~rforniedearlier on CoGa (van ~ ~aiid dei ~ are d e s ~ r a in ~ ~order e to avoid ~1iai~ges of the defect ~ i r a ~1981). d ~ ,~ c c o r d to ~ nits~time dependen~e (Figure 1) the ~ e change ~ AE(t, ~ T,,t Tf) ~ due to pattern due to q ~ e n ~ ~ ia~~ gi n.guse of the timedi~erentia~ niea~urin~ tec ique both q ~ ~ ~ n t ~ t ~ e sthe , defect ~quilibrationprocess may be s e p a r ~ t ~ ~ H$ and H v , can be measured ~ n d e p e ~ d e ~ t l y from the instantaneous a ~ i h a r ~ lattice o ~ ~ expanc o ~and s (3) by the teniper~~ according to e ~ ~ a t i (2) sion AI‘, and may be of particular interest for the lure vari~tionsof the ai~p~itude and o f the time investigation of defects if p ~ ~ i t r ostud n depende~ceof the the defect concentrainapplicable, In the s i ~ case ~ ~ of~ ae tion, resp~ctiv~ly. ts of this type were distrib~tionof defect ~ourcesor siiaks the time perfornied by posit atioii techn~queson a ~ependenceof the s p e c i ~ e nlength time scale of some tens of mi~liseco~ds in Au chmid, 1989) and on the scale of ~ ~ ~ set crtl., l ~ i~ 9~ ~ For b~ ) . thermal vacancy studies irn ~ n t e r n i ~ t ac~o~~i c~ ~ o u n d s by means of posit~on”~ifetinie spect~osco~y the with measuring techn~quesand the specinien reparation l* = I*(TJ 3- M’ (7bl ere described earlier ~ ~ c h a eetf ~al.,~ 1990; r o s s ~ a n net al., 1994; ~ ~ r s c eth d., u ~1995b). after a fast teni~eraturechange i s @veil in a ~ ~ l o g ~ ~1thoL~ the ~ h~ositron-lifet~~~e spectroscopy has to equation (2) by an e x p ~ n e n twhere ~ ~ l the time substantial~yc o n t r i b ~ ~to t ethe ~ investigatio~of the constant f~ contains Dv. From its t ~ ~ p e r a t ~ i ~ properties of thermal vacancies in i n t e ~ ~ e t a ~ l i ~dependence the vacaiic~~ i i g r a ~e ~ ot ~ ~ aH l ~v y ~ ~ (see b ~ ~ this t~e c~~ n ~ i q uis~i~~ a p ~~~ i~c ”, can be~ ~ e t e ~ ~d i in n eanalogy d s to equations (2) and able in the presence of high co~centratjonsof (3)- The q u ~ ~ t i tI0yfT,) deiiotes the ~ ~ u i l i b r a t ~ ~ ~ o n s ~ i ~ u tori o~~~~~le ~ c l i e~d - i~n ~ ~( >~10-3), i c i e state ~ at r,, when only saturatiun trapping occurs, as, e.g. in From the temperature v ~ r ~ a t i oofnthe l e ~ ~clian th a d u r a ~ ~ e r g e3997) n ~ or in quasic~ystals( ~ ~ 7 ~ r s cobl nl., ~ ~ ~1904, n i 199%). he di~erentialt h e ~ expansion ~ a ~ ( ~ i ~ ~ i i arid ons aluffi, 1960) technique, which is capable of ~ ~ e a s ~ ~absolute r i n g coii~entratioiisof vacancies, vacant lattice sites, indrzced, e.g. by theriii~tlly-for~~e~ can o v e r ~ o mthis ~ difficulty. There is no upper the effective v~c‘an~y formatj~s~ e n t ~ H~c lcan ~ be ~ ~~
gure IL ~ ~ ~ eof m the ~ t i ~t ~~~ e~ - ds i length ~ e r ~change ~ i ~ iQE~ ~ Sketch of the ex~erimentalset-up for the time(Tl,Tr,t ) due to the equil~b~at~on process of the thermal defect d i ~ e r e ~ ~ t i alength l change ~ e ~ ~ s ~ r e ~after e n t sfast c ~ n e ~ ~ ~ aafter t i o ant e ~ ~ e r a t ~change i r e from T, to Ti. The Two mirror planes are prepared on ure spon~aneouslength change Qk’ due to the a ~ h ~ ~ rlattice ~ o n ~ ct ~ ~ p e ~ a t changes. ~ x ~ a ~ t iss iindicated, o~~ reproduced with p e ~ ~ ~ from s ~ ~ o nthe specimen front platie and the ledge plane in order to measure the length change by the reflexions of the two laser Elsevier Science beams. The s p e c ~ e nand the ~ ~ ~ s ~ a ~ ~ efurnace - ~ e aare ted suspended in an evac~ated c ~ a ~ b ereproduced r~ with permission from Elsevier Science
derived; here BY 1s the change in the atomic volume Y due to the atomic relaxation in the vicinity of the va~~n~y. (Schaefer et al. l999a). ~ p e c i m ~ nwith s co~~ositions The ~ ~ ~ e c t - i n d uti~e~dependeiit ~ed length change Fe55Af45 and EPJi47A153., as an~lyzedby EDX (energy may be s~bs~dntia~ly more complex than is sketched dispersive analysis of X-ray spectr~sco~y), were here, because of more complex source/sisk structures prepared by co-melting the ~gh-purityc o ~ p o n e ~ t s or the s i ~ u l t a ~ ~ formatjo~~ o~s of ~ ~ ~ ttypes i ~ ofl e in a water-cooled Cu crucible and s u b s e q ~ homa~~t defects as, e.g. vacan~iesand antisite atoms on the genization by zone-m~lting* From these rods cy~i~drical s ~ e ~ i ~with e ~ ia s rin~-shape~ ledge (see various s u b ~ a ~ t i of c ~isn t e r ~ ~ e ~compounds ~ l ~ i c which Figure 2) were spark-cut. also may c o ~ t r i ~to~ the t e length change due to their using this high~y s y ~ n i e t r ishape, ~ ~ ~ e ~ s ur t~~ rib~a t i o~~due s to rel~xat~on volLmes (Fiihnle and Meyer, 1998). s ~ e ~ i m ebendi~g n d~iring~emperatur~ changes are It should be poiiited out, that in the case of such a eli~ii~ated. After etching the specimen with a mixture ~ e f e c t - i n ~ ~ dc ~ e d~ a y change ed of a s~ecimenproperty, o f 2 parts of conc~ntratedHN03 aixd 5 parts of 36% two types of e~~erinients inay be pe~furmed. As two parallel p ~ a n ethe ~ ~front plane and the d e s c r i ~ eabove, ~ after a single t e n i ~ e r a ~ uc~~e~ ~ i g eHCI, , ledge plane (see Figure 21, were polished to a high the time ~ e p e n d e of ~ ~the e response may be observed, ~ i t ~of. a t w o - ~ e alaser Byi menm ~ ~ ~ t e r n ~ t ~the v ~same l y , ~ ~ ~ f o ~ m is a tai ov~~i i ~from ~ ~ l e optiezl ~ e ~ e ~ ~ ~e~i inte~fero~eter, the variation of the s p e ~ ~~~easuring e x ~ e r i ~ ~ ewith n t speriodic t e m ~ e ~ ~ tchanges u r e and the length (20 mm) can be tested directly to an ac~LIracyof phase shift observed for the response function, Specific s atomic defect heat m e a ~ u r e ~dewing ~ ~ s~ ~ g h ~ f r e t~e ~~p~e ~ ~nt cL yt r eabout 20 nni which c o ~ e s ~ o ttoi ~an of about 3 x IQv6 in the case of the o s c i ~ l ~ t ~were o ~ s reported r ~ ~ e n t l (y ~ ~ ~ f t m a ~ h econcentration r, g~neratio~i of vacancy type defects. The specimen 19971, teiiiper~turewas ~ o ~ i i t by ~ rtliree e~chro~e~-~~lu~ For thermal defect studies in interi~~tal~jcs by t ~ e r ~ o ~ oy ~i e~ ~I ~eaisn pical ~ t ~ ~ ~ ~ ~r a~ ta ~d ~i ~r en ~ h i ~ ~ - ~ r ~ c i st i o~n~, ~ ~ d ~ ~~ei r~ ~a tnu tmi eatan l~ yincre, of less than 20 K at 1300 over the ~ e a s u rlength i~~ mental ~ ~ c h ~ laser ~ s in~erferomete~ o n was employed. on the specimen and a temperature eqLiilib~~ti~n means of this contact-free technique, making use time of 200 s after a te~peraturechange; this prese~itly a two-beam laser interferometer (see Figure 21, limits the time range of the l e ~ ~ ~ t h ~ cstudies. ~ange ~ ~ a ~ u r e m eup n t to s li~ghtemperat~resare feasible as For studying defects in intermetallic conipounds demonstrat~din the cases of Fe~~Al45 and Ni47A15~ perturbed angular c o r r e l ~ ~ t i(PAC) o~ ~ ~ ~ ~ s u ~ e ~ e chaefer et al., 1999a,b;Calin, 1999) with an accuracy were also used ( ~ o ~et~al.,i ~ 1997). s in ~ ~ o defect ~ i c~ o n c e ~ t ~ a t iofo nabout 3 x
T h e ~ Defects ~ a ~ and ~
rac I
3.2 Thermal vacancy formation in intermetallic compounds was studied recently by positron lifetime spectroscopy (Wurschuin et al., 1995b; Schaefer and Badura-Gergen, 1997; Schaefer et al., 1990; Brossinaiin et al., 1994; ~ u m m e r l eet al., 1995; VVGrschum et al., adura-~ergenand S c ~ ~ e f e1997; r , Schaefer et al., 1999a). From these studies three main features are evident (see Figure 3): -
At ambient temperature no constitutional vacancy concentration higher than 10-6 was found in nominally stoichiol~etric Ni3Al, TiAl, Ti3Al, Fe3Al, and Fe3Si. This i s concluded from the short positron lifetimes in these coinpounds measured at a ~ b i e ~ t - t e m p e r a t u(see ~ e Wiirschurn et al., 1996a; Scliaefer and Badura-Gergen, 1997) which ai-e similar to the free positron lifetimes in pure metals with similar valence electron densities and
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~
~
u
,
~
i
~
~
279
negligible vacancy concentratio~s(see et al., 1996b). This conclusion is ~ d d i t i o ~ a l ~ y corroborated by the appearance of an S-shaped increase of the mean positron lifetime at elevated temperatures, which - as in the case of pure metals - is ascribed to the trapping of positrons at therma~lyformed vacancies. Positron trapping at thermal vacancies begins in the close-packed intermetallics such as Ni3 Ti3Al (see Figure 3) at mtich hi than in the bcc-type compounds FeAl Fe$%. This indicates lower thermal vacancy concentrations and higher effective HF values in the former case. In NiAl (Figure 3) the high positron lil'etinie that is almost independent of te~peratureis attributed to positron saturation t r a ~ p i n g at i ~ i ~ o b i l e vacancies (see below) or coiistitutional vacancies which obscure the te~perature-de~endent thermal vacancy f o r ~ a t i ~ In n . this case, other t e c ~ n i ~ u e s such as tiiii~~differe~tial theriiisrl expansion studies after temperature changes (see below) can supply specific ~nformation.
igure 3 Temperature variation of the mean positron lifetime 5 due to thermal vacancy f o ~ a t i o in n Ni74 1Alzs 9. Ni76 sA1235 (Badura-Gergen and Sckaefer, 1997), Ti48 SA151 5 (Brossmann et nE., 1994), Ti65 6A1344, Ti77 ,A122 9 ( ~ u r s c h et u ~al., 1996a), Fe75Si25, Fe79Si21 (Kiimmerle ef al., 1995), Fe6lA139, Fe63A177 (Wiirschum et al., 199%) and Ni50A150 (Schaefer and BaduraGergcn, 1997). The close-packed structures are denoted by open symbols and the bcc-type structures by filled symbols. Roundedoff co~pos~tions are glveii in the figure, reproduced with permission from Elsevier Science
The te~peraturevariation of the positron tra~ping rate (Figure 4), which can be derived froni the positron lifetii~e spectra according to equation (6), yields high or low values of the effective vacancy forination entlialpies H c for close-packed or more op~n-structL~red bcc-type compounds, respectively (see Table 1). These results can be understood by nearestneighbor (nn) bond models or ~ ~ cal~ulations ~ e r ~ a d ~ i r ~ ~ ~1997). ~ r gIne n ~ ~ 1, see b ~ c~~ a eef and the simplest picture this may be according to nn bond adura and Schaefer, 19931, ascribed to a and a higher fraction of higher c o o r d i n ~ t i o~~1~~~~ ~ tra~sition~metal bonds to be broken when a vacancy on the t r a n s i ~ ~ o n ~ ~sublattice etal is formed in closepacked AJB compounds in contrast to the more o ~up o~~ n~dThis s~. ~picturee, o p e n ~ ~bcc-type ~ r ~B2~ c ~ however, is ~ ~ s u ~for9 c ie.g. e ~~ ~2 - ~ iwhere ~ l , the e x ~ e ~ m e n t ~ ~ ~ l y - d e t e vacancy ~ m i n e dformation enthalpy (1.5 eV) exceeds the low value (0.93 eV) derived from theory for the ~ r a ~ s i t ~ ~sublattice. ~ - ~ n ~1x1t f~ l f ~
c ~ l c L ~ ~ a tof i o ~the s vac~ncyf o ~ ~ i ~ ~~ i iot ihi~ l ~in ies Ni3A1, Fe3A1, FeAl, and NiAl (see Table 1) the H t values for the t r a n ~ i t ~ o n - ~ esub~attices ta~ are, however, o t ~ e ~ w i sin e uod ~ ~ ~ withr the ~ ~ ~ e x p e ~ i m e ~ t adetermined l~~ values, whereas the WF values for the At ~ ~ ~ b ~ a are t t icc ea ~~ ~ ~tol be a i~iuch ~ e ~ higher than on the transition metal s~blattices.This ~ i ~ predicts thermal vacancy f~ ~ r ~~ a~ t ~ oe ~f one the ~ ~ ~ ~ , t r ~ ~ s i t ~s ou ~b -~ ~a (Fu ~ t~et~~af., ~~ 1993) e ~ as demonstrated recently in the case of B2-FeAl by the coin~identlymeasured ~ u p ~ l ebroadening r of the p o s ~ t ~ o ~ - e ~a~ ~c tir ~ ni ~ photon ~ ~ a ~line ~ o~n ~ ~ l ~ e r 2000; ~ ~ l lete al., r 2001b) (see Section 3.4). When we discuss prefere~~tia~ formation of vacancies on one sublattice of an ordered intermetallic cornpo uiid as d e t ~ c ~ se dp e c i ~ ~by ~ ~p loy~ i t r o~ ~~ n ~ h i l a t i o ~ spec~roscopy,we imply that sim~ltaneousl~ antisite atoms are created to maintain stoichiornetric cornposition in analogy to triple defect formation in B2 * ~ ~ ~ ~r u~ ~ ~ ~~ a~s~i~l e~r~ 1968)~v s s~ ~For , c ~ n i p ~ ~ swith on
Arrhenius ~e~resentation of the positron t ~ a p p i nrate ~ CTC,{ l e f t - ~ a no ~ d i ~ ascale) t e of Ti3A1, P-Ti3Al ( ~ ~ ret s c al., 1996~1,TiA1 ( ~ ~ o s s et~ al., a ~19941, n Nip41 (Badura-Cergcn, 19951, Cu3A~1( ~ ~ m and ~ Shim, ~ u 1996) c ~(measured above the disordering t c ~ p ~ r a t ~re), i r e AI, Ni, Fe (Schaefer, 19871, FqAI (Schaefer et al., 19901, Fe3Si (Kummerle et al., 1995), Feh1Af39~Fe63A€;f?~ W ~ r ets uk., ~ 1935b), h ~ ~CuslZn49 ~ (Shim, 1988) and of the thermal vacancy concentration Cv from ~ ~ 19761, a ~ and ~ ~ i ~ r e r ~ nthennal tial expansion studies ( r ~ g ~ t - ~ aordinate nd scale) of Fe31A149 (Kerl et al., 19991, C o ~ (Berner, ~ i s ( ~ a s~ ~ Ia e 2968). ~~s ~~, Note the high vacancy c o n c e n ~ ~ a ~ ifor o n ~Fe,,Al,,, Ni,,Ga,, and Co,,Ga,, d e t e r ~ i by i~~~ d ~ ~ e r~ ~x ~~ at nistudies. ~~ i ~ nThe actual C, values were deduced by the present authors from the data grven 111 the rcferenms cited, For the vacancy comcentratton in Ni47A153 (Schaefer et al., 1999b) the value Cv = 3AIjlo was uscd. The abscissa IS n o r n ~ ~ to ~ ~the ~~ e de ~ t t~e n~ g~ ~ r a tTitI* ~ r For e s further details see {Schae~erand ~ a d ~ r ~ - C ~1997) rgen~
~
28 1
Thermal Defects and Diflusion
Xe P Effective vacancy formation enthalpies HF derived from cCv(T) according to equation (1) with a te~peratureindependent CT value; vacancy equilibrium concentrations CVat Ti,4/2 (half the inelling temperature TM);self-~iff~~sion or foreign diffusion activation enthalpies Qsy ; and eRectivc vacaiicy- ration enthalpies H v and self-diffusion or foreign atoni difksioii activation enthalpics, Qsu. The values for Cv(at TM/Z)and 25'; are taken from differe~itialthermal expans~oiidata on FeAl and Fe3Si (Kerl et al., 1999) or from positron lifetime data for the other compounds a s s u ~ i n gc = 4 x 1014s-l- Thc o-values are derived from a comparison of the positron trapping rates (Fig. 1) and a€diffe~ent~a~ thcrmal expansion data (Kerl e t id., 1999). Values for the vacancy formation volumc, VF, and the vacancy migration volume, V y , are given for Fc,Al,,. For further references for the present data see Schaefer and Badura-Gergen, 1997
H{ (ev) TM
C o ~ ~ o u n d Structure
(IC)
exp.
theor.
CV (at TM/2) 25'; (w7) (k,)
V ~ ~ : 1 . 8") 7 0.014 V~1.2.651' 0.083 0.21 Vpe:1.25 ') 240 100
FetxA139
B2
1660
MiAl
B2
1911
0.98 1.0 a) 1.5 a)
QsD
(ev)
4.9
Ni 3.15
0.7
Ti 3.03 Ti 3.1 Fe 2.44
5 3.7 3.7
Fe 1.65 Ge 3.25 Fe 2.76
Ni 3.01
EI,M(eV exp.
theor,
@
vy
(a) (a)
CT
(10'5 s-I)
0.M
3.6
1.7 2.14 S ) 1.5 a)
1.7 [ ) , j )4.6 'l
1.3
1.8 a) 2.1
")Schaefer et al., 1999b "Fu and Painter, 1997 ')Mayer and Fahnle, 1997
~ F etUal., 1993 ')Wurschum et al., 1995b fkentziiiger and Schober, 2000 69Fahnle et al., 1999 ~ ) ~ i s hand i i Farkas, ~ 1997 '1 Muller et al., 2001b /)Wolff et al., 1997a
experiments the entire defect ensemble has to be taken into account when theoretical studies are performed. When the thermal vacancy concentration 1s high (see Figure 4) and the vacancy binding energy is high (0.38eV predicted for FeAl (Fiihnle et al., 1999) divacancies may contribute to the defect pattern (Wiirschurn et al., 199513). An association of thermal vacancies to form divaccancies is indicated by ix relatively high vacancy formation volume of 1.42 R (s2 is the mean atomic volume) (Wolff et al., 1997a; iiller et al., 2001b) and by a large vacaiicy migration volume of about 4.6 SZ (Muller, 2000~~ ~ l l ete al., r 2001b) derived for €32-FeAI from positron annihjlation under pressure (see below). With the nn bond energies derived from the concentration dependence of thermal vacancy formation, an estimate of the thermal concentration of antisite atoms - iieglecting tlie forniation entropies can be given. This yields values that in Ni&l, TiA1, and FeAl are higher than the thermal vacancy concentrations (Badura and Schaefer, 1993; Schaefer and ~ a d u r a ~ ~ e r1997). ~ e n The ~ specific studies of
thermal vacancies by positron annihilation spectroscopy and tiiiie-differential dilato~etry (see next section) reported here, were p e ~ f o r at ~ tee~m ~ e r a t u r ~ s well below the critical temperature TCfor disordering, so that the data are characteristic for the nearly fully ordered state. The differential thermal expansion studies of Kerl et al. (1999) on FeA1, which are extended to high temperatures, yield indications of temperat~re-dependentchanges of the vacancy formation enthalpy which may be due to disordering or structural transformations. Calculations of the teniperature variation of the vacancy formation enthalpy with the order parameter were performed for y-TiAl (Badura and Schaefer, 1993) as well as for Ni3A1, NiA1, and FeAl (Badura-Gergen, 1995). Thermal vacancy formation 8s a function o f composition has been studied in the cases of Ni3AX (BaduraGergen and Scliaefer, 1997), €32-FeAl ( ~ ~ r s c et h u ~ al. 1995b; Schaefer and Bad~ra-Ger~en, 1997; al., 1999) and Fe$%(Kiimmerle et al., 1995; Kerl et al,, 1999) and can be understood in terms o f nn bond models with bond energies independe~tof compo~i~ion
282
~
~
f
~
~
equation (2)) were derived from the temperature variation of the time constant f~ ~ e t e r ~ by ~ ~i nt t~i ~ g the e~uil~bration process by an exponential (see Figure 6). The low value o f the pre-expo~ential factor compared to the Debye frequency can be attributed to a total number of vacancy jumps of about for the e ~ u i ~ ~ b r a tprocess ion of the va~ancyc o n c e ~ t r ~ t i o ~ which may yield a ~easonabledensity of sottrees or f ~ u n dfor sinks. A high value of H y was ~ddit~onally the nex~-~earest ~ ~ i g l i b o(100) r vacancy jumps in ~ ca~cu~ations (Fiilinle ~ ~et al,, ~1999) ~ FeAl by ~ (see Table I). 353 40 50 0 The vaca~cy~migration process i s closely related to the recent discussion of the p r i ~ ~processes ~ y of Vacancy formahon eiithalpies in F e 4 compounds self-diffusion in intermetallic compounds, Studies of as a function of the composition as measured by positron ~ l Sepiof, ~ ~ ~ lifetime ~ ~ e c t ( ~~~~s~~~~ o ~ c ~et d., ~ ~f995b, EII ~ c ~ a e F e r the Fe jump vector in FeAl ~ V o and ~ a ~ ~ ~ ~studies a t ia v ie ~at ithe~ atomic ~ d i f f ~ ~ i oonn Shirat et al., 1989), or by ~ i ~ e r e ~ thermal tial ~ ~ ~(A Ho ~ and ~ Dodd, s ~1978,o 0 Kerl i ~et at., 1999). The e r al., 1998), and tlie the two s u ~ ~ ~ t t i c~ e~s e h r et full line is ~ ~ ~ l cinuterms l ~ of t ~a nn ~ bond mode1 (Badttrae ~ t r e ~ elow ~ yvacancy co~ice~itratio~ expected on the Gergen, 1995) by II fit to positron lifetime data ~ ~ u r s c et ~un~ AI sublattice from ca~culations(Mayer and ai.,1995b), ~ e p ~ o ~ with u ~ e~ de r m ~ s from ~ ~ o Ekevier n Science FZhnIe, 1997; Fahnfe et at., 1999) favor the picture that the Fe diffusion occurs by simultaneous jumps of two neighboring atoms giving rise to a ~esu~ting jump to a next-nearest neighbor (100) site or a third~~iear~st neighbor (11 I} site without a measurable occupancy density ~easurementsafter ~ u e n c ~ ~ i n gtime of the AI sublattice by v a c ~ n c i ~ ~ . As conclude^ from the ~ o ~ ~ a rofi H s oy for ~ pure bcc iron (< 1.3 eV Schaefer et al., 1977) to that of ~~~~~~~~~
If
and ~~~~~i~~ can be deduced (see Table I). These values are higher than those for pure metals as, e.g. for s-l (Schaefer, 2987)). vac~nciesin Af (a-= 4 x The ~ i ~ r a t oi fothermal ~~ vacancies at high ternperatures was successfuIly investigated recently by of the e q ~ l i b r ~ t i oprocess n positron l i f e ~ i ~studies e of tlieriiial vacancies after temperature changes at high ~ r ~ c het u al., ~ 1995b). By this ~ r o ~ e ~the u r ~e i g r a t i ~ofn thernzal vacancies, which are i ~ e n ~ i by ~ etheir d pasitran l ~ ~ e t ~ can i ~ ebe s ,studied ~~ ~~ o~~f q~ u ~e ~ ~ losses l ~ i ~or ~ ~ ~ ~ a e v c o t eEects clu~~ering in earlier ~ x ~ e r i m e ~n tS~e i d m and ~ ~Baluffi, ~ ~ z ~ z a1972; n ~ ~ h n and o %no, 1978). 1 a high value H v = 1.7 eV (see Table I) and a ~ ~ e - e x ~ ofactor ~ e n1/t~,o ~ i ~=~1.9 x 108 s-' (see
~ 2 - ~ e 6 ~(1.7 A IeV ~ ~~ ~ r s c h u et n i al., 1995b) the vacancy migration enthalpy tends to increase with ~ h values and high decreasiiig Fe content. ~ i high > 1, the removal of thermal vacancies ratios ~~~/~~ beconies difficult due to easy forination of thermal vacancies at relatively tow temperatures where the vaca~cymigration is slow. This appears to be the case in B2-Ni52A148 where positron s a t u ~ ~ t i otnr a ~ p ~ n g at remnant vacancies occurs at ambient temperature y ~ o n ~a n~~ ~e a i~ n(1.5 ~g ex 1 0 ~ s) at peratures (685 K) and positron lifetime n i e a s ~ r e ~ e n(t s~ ~ ~ s c aiid ~ u Schaefer, n i 1997; Zhang et al., 2001) a time constant t~ < 6.2 x 106s for the removal of vacancies could be estimated. Ths yields, together with the pre-exponential factor of h al., u l ~ ~ E , Q 5 x 10-9 s found for FeA1 ( ~ ~ ~ s c et 199Sb), a value H y = 2.1 eV, This is in good agreement with recent molecular dynaiunzcs studies (see Table 1, Mishin and Farkas, 1997) and with further lengthvacancy studies in NiAl by time~di~erential ~hang~ after s fast ~ ~ ~ ~ ~ ~which ~ will a tbe ~ discussed in the next section. A c o i ~ with ~ ~ respect ~ t to the ~ i ~ r a t of io~ i should be made. Here, according to the values given in Table 1, a value Ny =: QSD=0 ~ is anticipated ~ ~ (QSa e is the ~ activation enthalpy for self diffusion). From this an i s o c l ~ r o nannea~ing ~~ of non-eqL~ilibriunivacancies by long-range m i ~ r a t i oi s~ ~expected in a conventional i s o c ~ ~ r o en ~~l p e ~ ~ on e nat I h time scale at about 35OK; this behavior in fact is observed after lowt e i ~ p ~ r a t electron ~re i r r a ~ i a t ~(see o ~ Figure ?), thus co~firmiiigthe low value of El? in Fe3Si. ~~~~~~~
As ~ugge~ted above, length-changen i e a ~ ~ r e ~ eafter nts fast t e ~ ~ e r a t uchanges re should enable specific studies of t h ~ r ~ ~ ~ ~ -f odremf aet c~ ~ o~. The time-depende~tisothermal contraction o f a Fe55Al45 specimen, after cooling from high temperatures to various slightly lower temperatures is shown iiz Figure 8. The accelerat~onof the e ~ ~ l i ~ r a tprocess ion with an increase of the final t e ~ ~ ~ e r(Figure ~ t u r8%) ~ is clearly visible. For a reasoi~ab~e fit of the time d ~ ~ ~ e n d e of n c the e i~othermalcontraction o f Fe55Al45 in Figure 8 two su~erim~osed e x ~ o n e ~ t i a lare s required. From the l temperature variations of the time constants t ~ and t ~ 2 attributed , to the c o n ~ ~ i b ~ ~with i o nthe s higher or
~ i ~ 7u Isochronal-annealing r ~ (fa 30 rnin) dete~~ination of the mean positron lifetime T in Fe;% after irr~diatioi3with r e electrons o f energy F , = 2.5 M ~ Vand dose #e = s 1 0 ~ ~ e-jrn2, reproduced with permission from Elsevier Science I=
the smaller amplitudes, respective~y(see ~ i ~ u9), r ethe a c t ~ ~ ~ tparai~eters ion = (1,s k0.2) e\l and t& = 4 . 105 s-‘; HE”= (0.6 f0.1) eV and tg& = 0.83 ~~7~
(9a) (9b)
are derived (see equation^ (31, (7)), The data of equation (gal are identified with the vacancy migration ~9arameters (see Table 1j which. were s ~ e c i ~ ~ ~ l l y determined from equilibration studies by positron lifetime s ~ e ~ t r o ~ c~o ~~ y~ r s et~ al., h u1995b) i ~ oy1 FeAl. This coincidence in the case of FeAl dernonstrates that thermal vacancies in 2 ~ ~ t e r ~ e t a can llic~ be studied by sensitive lengt~-chaiige~ieasurements. The second process in tlie lengtli-cliange studies on Fe5sAlit5 (Figure 9) is characteri~ed by a weak temperature dependence that requires further discus~ ~Figure ~ s Wa sion. It should be xioted that the ~ s o t h e rin niay need an even more complex description because of the initial ~ n c u ~ a t ~behavior, on w h i ~ hm i ~ i ~~t ~ ~ ~ a t characteristics of a nucleation and growth process (Rieux and Goux, 1969). The te~iperatu~evariation of the ~ ~ (Al,l /lo) and ( ~ l ~ 2of/ the l ~ length ~ change ofFes5A14~ as derived from two-ex~o~ential fits to the data in Figure 8b are presented in Figure 10 together with the coi~ceiitrat~on of v a c a ~~a~~~~ ~ sites as derived from positron-lifetime spectroscopy (Wiirschum et al., 1995bj and the cr-value given in Table 1, The ~ e ~ ~ i
84
P
Time dependence of the i ~ o t h e I ~ acontract~o~ 1 Al of a FessAl45 s p e ~ ~ I i after i e ~ fast cooling from the initial tei~peratureT, to the fiiial te~~perature T f ,a) variation of the ~ q u ~ l ~ ~ r rate a t i owith i ~ Tf and b) variation of the a ~ p l i t u of ~ ethe 1 the process with the l~ngth-c~iange with the initiai temperature 7;where the time scale i s normalized to the relaxation time t ~ of higher amplitzide. The different values of Tfcan be neglected in the evaluation of the amplitudes. The gray lines denote model fits to the e x ~ ~ r j m edata ~ t a (see ~ text), reproduced with ~ e ~ ~from i ~IEIsevier ~ ~ Science o n
of the ~~~~~/~~~ data at high temperatures (Figure 10) can be e x ~ ~ a by ~ ~defect e d losses during cooting, if the vacancy ~igrationen~halpyof equation (9a) is used. From the length-change amplitudes of Fe55A145in ~ ~ the preigure 10, the activation e n t ~ a l p iand ~ ~ ~ o ~~ ~ ~~ i ~t i ~t l ~ ~ s
N~= * (1.0 ] s0.1) eV and 111-A 6 + s".'/kB 4.3;
v
A
HF+* = (0.9 f0.1) eTT and ln-
=t
Pp
4
P I
-5
(104
v,+ SF-'/kB = 2.7 v
1Ob)
s i ~ ~ to~ ithe~ ~ vacancy r f o ~ a t ~ oentha~~ies n determined specifically by posi~ron-lifetiiiie spectroscopy ( ~ u r s c h u met aE., 1995b) are derived (see equation @)>,The results given in e ~ u a t ~ o n(10%) s and (lob) f ~ t h e r i i i ~d ~e e~ o ~ ~ t that i ~ aboth ~ e processes originate from thermal va~aiicyformat~un,where high annih~lati~n for thermal vacancies in Fe3A1 (Franz e1: f ~ r ~ ~ a ~e ni tor on ~ ~ eSF s > 3ka are derived when a/., 1995). A higher value of AF'/Y= 1.42 (WolfT h V / V = 0.53 (see below) is assumed. From a comOZ., 199%) was derived from the h i g h ~ t e ~ p e r a t ~ r ~ parison of the present data with the positron ~ ~ e s s udr e p e ~ d e nof~posi~ron ~ anni~ilationv ~ ~ a ~ ~ ann~hilationdata ~ ~ u r s et~ al., l ~1995b) u ~ on B2studies on B2-FeAt wlzich was a t t r i ~ u tto~ ~the FeA1, we can ~ o ~ c l uthat ~ e the f o r m a ~ i ~and n of some of the vacant lattice sites to ~ i ~ r ~ of ~ i~ u n ~ vacancies ~ can ~ be ~ s ~ ~ c~~ ~ c aaass~ciation l ~ yl ~iv~cancies. detected by t i ~ e - d i ~ e ~ el en nt ~g ~t ~l - c ~ studies, ~n~e Studies of thermal vacancies by ~ i ~ e ~ d ~ ~ e ~ e n From the c ~ ~ p a r i s oofn the total length change ge may be partic~~l~r1y ( ~ Z s * -+ and the c ~ ~ ~ e i C\I ~ ~ofr vacant ~ t i ~ i ~~e n ~ t h - ~ h a ni~~asurenients 2-NiAI, where s p studies ~ are ~ ~ lattice sites in BZ-FeAf (Figure 10) the volume of e c ~ n ~ t i t ~vacan~~~nat the vacant lattice sites can be d ~ t e to ~ be ~ n scarce ~ ~ and where i m ~ o b i ~and cies obscure the detection of thermal vacancies by AV/ V = 0.53. A value o f A Y / Y = 0.7 for this range means of specific pQsitron"a~nihi1atio~ studies due to was derived from the pressu~~~dependent positron ~~~~~~~~
f 0" 0.
0.3
t ature ~ ~ r ~ a t i oofn St ange 11 Isotlierni~~ ~ € ~ e - ~ ~ ~ ~length e r e nchange t ~ a l Al(t> 1 and A l s ~ (after /~~ 1 or in B~-NLQAI~~ after cooling or heating the specimen to Tf, A145 derived from tw 1 fits reproduced with petmission from Elsevier Science to the tmie differential length changes after temperature changes (Figure8b) and of the concentration CV (0) of vacant lattice sites d e t c ~ ~ i ~ €rom i e d the positron t r a p ~ ~ n ~ rates aC'vfll) iit Fe61A13~ ( ~ u r s c et~ ial.,~ ~1995bj ~ (see Figure4) making use of t7 = 1.3 x 1Oiss-' (see Table I). The deviation at 1 g h ternper~~tur~s of the lengtl~-cl~~nge and amplitude^ from an Arrhenius behavior IS due to vacancy AY fosses on cooling (an increase from the present cooling rate of ln - ~~/~~ = 4.8 (f2b) t Kis IS ~ e ~ i r a reproduced b ~ e ~ ~ with peimrssioti from Elsevier Science ~~~~~~
v+
saturation of ~ositront ~ ~ p p i n g~ .e n ~ t h - ~ mea~an~ on ~ ~ - ~ arei shown ~ ~ in. A Figure i ~l l. ~ In s~reineii~s this case eq~ilibrationexperiments upon cooling as well as upon heating (Figure 11) could be performed. Froin these data on NiAl it is evident that, with about time constants as in B2-FeAl the same eqLii1ibratio~~ (Figure 9j, the a ~ p l i t ~ of ~ dthe e length change is much srnaller than in FeA1 which indicates a lower ratio ~~/~~ and a higher value in the case of ~ i 4 7 A The ~ e ~ ~ g ~ h ~ c~l ~ s a~ nt gh ee~ieasured r~s for Ni47A153 ~ ~ c h ~eti al., e f 1999a) ~ ~ are well described by a single exponenti~land from the teiii~eratu~e variation of the rate c ~ n s t l~/ ~t ~(see t Figu~e12) fur the first time a vacancy ~ig r atio nentlialpy with the high value
This NF value for N i 4 ~ A lis~ ~higher than in eFe61AJ39 and c ~ the earlier ~ ~ ~~n - j e c t~deduced ~~re s from the lengtli~c~i~nge data in Fi~LIre11. fn additio~, a ~el at i velhigh ~ v a c a n c y - f o ~entropy ~ ~ ~ ~as~ ~in other inte~netallics(see Table 1) is observed. The
-
~ ~ 'Ia4 ~ ~ .. 'cn
Y
& -r. 2-
l0"
'I
0.8
and with tbe ~ r e ~ e x ~ o nfactor en~~~l ~~~~~~
1.O
I .2
1 / T [ I a3K"I]
1.4
12 ~ e r n ~ e r V ~ ~a u~ r ~~O~f the t ~ ~~ n
t .Ei ~ rate
l / a in B2-Ni~7A153deter~inedfrom ~ ~ p o n ~ ~fits t i to a lthe isotherms, equation (7j, in Figure I I after cooling ( in f32-NiAI could be determined. These values are heating (U) the s p e c ~ ~ eIn n . addition, the reaction rates (0) similar to those in the case of B2-FeA1. for clustering o f remnant vacancies in NiS2Al48 after lowFrom tlie l e ~ ~ t h - ~ h a ndata g e of Ni47Al53 tlie t c ~ ~ e ~ ~long-term t ~ i r e anneal in^ (Zhang et at., 2001) as t e ~ ~ ~ evar~ation ~ ~ t u of~ the e ~ e i ~ ~ h ~-~ ~ i ~ ~p lai t nL ~ ~~ e ~te ~ ~by t ep do s ~ t ~ o ~ ~~s p ~~ c ~ e~(see o sFigure ~~ o ~~14) ~ are~
3
~ (see ~Figure~ 13) was / derived ~ yielding ~ the values
plotted
~
e
286 N A ,i,I Ta=660 K
z -m
7
10"
m
10"
0.8
0.9
1.0
observat~o~~ that the present e ~ p e r i ~ e n tHF a l value for the time ~ e ~ e n d of e ~the c ~ p u s i t r o n ~ t r a ~ rate ~i~i~ ~ i 4 7 is~ higher l ~ ~ than ~redictedtheoreti~~lly (see ETCV after a fast t e ~ ~ e r change ~ ~ ~ when i ~ a e pressureTable 1) may raise the question as to how many nt p o s ~ t ~ o ~ - ~ rrate a p ~ ~ ~is g antisite atoms are fomed or whether a t e ~ ~ e r a ~ u r ie~ d e ~ e n ~ especific assumed (see Figure 16). The curves in Figure lija dependeiice of the c o n s t ~ t ~ t i o vacancy n~l concentraare characterized by a two-stage ~ ~ process. ~ tion inay c ~ n t r i ~ ~ ~ ~ . In the l o n g t e ~ main ~ process it is e v ~ ~ that e ~the t final to the high ratio of ~~/~~ in NiAl discussed r i u ~ co~cent~ation CV is reduced and v a c a ~ c ~cap1 e ~ be removed only by ~ o n ~ - t e r e~ ~ u i ~ ~ bvacan~y l o w ~ t e ~ ~ e iimea r ~ ~ ling, u r ~As shown recently for y p o s i ~ ~ olifetime n s ~ e c ~ ~ ~after s c ~specipy men ~ ~ ~ p a r a ~m i oo n o, v a ~ a ~ i care ~ ~ savailable as conciuded from the positron lifetime z = (179 rrfI: 2) ps (Z1iang et d, 2UOl). They become mobile during longterm a n ~ ~ ~and l i fomi ~ g clusters of more than 20 cooling ~ ~ c as ~e v i~~ e ncc eby ~~ thee ~ ~~ p e a r a nofc a~ tong intet moled cell wall vacuum positron lifetime (see Figure 14).
n
32 ~
In a d ~ ~ ttoi othe~ ~ n ~ hofav a~~ ~~ n € ~ c yo ~~ ns~ a tand io~ ~ g ~ a t derived i o ~ from temper~ture~de~endent studies, specific defect data on the formation volume V;, which has been ~ t ~ d i ebriefly d earlier (Emrick 1980; ickman et al., 1975; Franz et al., 1995; Wolff et ., 1997a), or the migration volume V v (Emrick, 19&l)of vacancies can be deduced from the pressure ra~ure dependence of h i g ~ ~ ~ e i ~ ~ e pos~tron-l~fe~ime ~ e a s ~ e m e nAn t ~appropriate . h i ~ ~ ~ t e m p e ~presatu~e a /J-Ti90Al6V4 alloy and been described recently 001b) (see Figure 15). Schematic drawing of the experimental setup for The eEect of pressure on the e ~ u i ~ i ~ r ~oft ithe o i ~ positron lifetime n ~ ~ a sas ~a function ~ r ~ of~pressure ~ ~ tand temperature (Muller, 2000) thermal defect concentrat~onCV may be reflected in
-0.56
10"
-0. h
-. -0.60 .c-I" T-
e i;z
2 P
-0.62
-0.64
Q
50
100
150
0
0.05
0.10
200
t Eh1
(a)
Figure I6 (a) Isotlicrmal equilibration with tiine ofthe thermal vacancy concentration CVof F~6~A139 at the temperature T3as a function of hydrostatic pressure p after rapid cooling from the initial temperature 770 K. The figure shows the model curves of two s ~ p ~ r i m p o expon~ntials s~d fitted to the experimental data, (b) pressure dependence of the time co~istaiit1~ af the long-term process for deducing the vacancy migration volume @ (Muller, 2000; Miiller et al., 2001b)
that the equil~brationprocess i s sigiii~cantlyslowed down when pressures up to 0.1 1 GPa are applied. From this behavior a rather high vacancy forination volume V g = 1.7 R similar to the volume reported recently (Wolff et al., 1997a) can be deduced and may be assigned to divacaiicy formation. Furthermore, from the pressure dependence of the equilibration time (see Figure 16b) a vacancy migratioii volume of V v = (4.6 k 1.1) f2 is available for the first time. This turns out to be surprisingly high. Much lower values of about 0.15 R were reported from electrical resistivity annealing experimeats after quenching of pure Au (Enirick, 1961). Effective migratioii volumes higher than this and closer to the present value are conjectured from the pressure dependence of Fe self-diKusion (SD) in FeAl (Eggersmann, 1998; Eggersmann and Mehrer, 1999) which report a lower limit value YsD = YF Y y N 1.6R for the activation of self-diffusion as well as from the pressure dependence of Fe foreign diffusion (FD) in pure A1 yielding YFD = 2.9 R (Kummel et al., 1996). A high vacancy-migration volume, i.e. a relatively strong lattice expansion in the saddle-point configuration of the vacancy jump compared to the vacancy on a lattice site, inay originate from a complex jump mechanism in which a number of atoms are involved for locally maintaining the ordered structure. A high activation volume may be supported by the model of a complex diffusion 2-FeAl ~Fahnleet al., 1999); here, in a correlated process, Fe and A1 atoms are suggested to exchange positioiis by siiiiultaneous jumps in the first step of a modified s i x - j u ~ pcycle.
+
3.
aE
The above detailed compilation demonstrates that data on tlie enthalpies and activation volumes for the formation and the migratxon of thermal vacancies are now available for intermetallic compounds and in particular for B2-FeAl. However, the long-standing question is on which sublattice, the transition nietal sublattice or the A1 sublattice, the formation of thermal vacancies occurs. This quest~oncan now be answered by experiment. To do this, we made use of coincident measurements of tlie Doppler broadening of the 511 keV positron-electron-annihilation photon line (coincident Doppler broadening technique) (Miiller, 2000; Muller et al., 2001b). By this technique the electron momenta up to the high values characteristic of core electrons can be detected. This allows for a chemical differentiation of the atonis in the vicinity of the positron annihilation site (Alatalo et al., 1995). In the case of a positron trapped in a vacancy, the atomic environment (and therefore the sublattice on which the vacancy is located) can be specifically identified. In Figure 17 coincident Doppler broaden in^ spectra of FeslA139 normalized to pure defect-free A1 are shown. The momenta of electrons giving rise to Doppler shifts above 514 keV are characteri~ticfor core electrons (Alatalo et al., 1995). The spectrum of FeblA139 measured with the equilibrium vacancy concentration at 610 IS, where due to a low vacancy concentration only partial positron trapping at vacancies occurs (T,,,, = 147 ps), is between tlie spectra of pure Fe and pure Al, because the ~artially
288 ~acanciesin se~iconductorshave been studied recently s p e ~ ~ c ~by~ l the ~ y coincident DOp13lt2r broadening tec~niquein Sic ~ ~ef al.,~20Ola)l ~ and other ~ o n i ~ soe ~ i~~ o~ ndd ~ c(t ~ 9l r~~ teta at. l ~ 1995; Saarinen et al., 1996). In SIC the vacancies on the C or the Si sublattices were directly id~iiti~ed. For this purpose vacancies were selectively generated on the one or the other sublat~iceby low- or l i i ~ ~ - e n e ~ g y electron irradiation. The vacancies on the different sublattices then were s p ~ i ~ c a l lidenti~ed y by coincident Dopgler broa~eningspectroscopy (Miiller et at., 2001a).
3
$ 2
i
51 1
cili 3
555
517
519
E [keV]
ure 27 ~ o i n c i ~ ~ ~nieasurcd tly ~opple~-bro~~~~~d spectra of the p o s i ~ ~ o n - ~ l ~~~nt n~~o~n~ l a t iphoton oii ~ i o ~ i ~tol purc i ~ eA1~(Mkfiiller ef al., 2001b). For details see
compound can drastically change the mechanical pro~erties (see e.g, Fleischer, 1993a,b; Pike et al., 1998). Ternary interi~etalliccompounds may be of delocalized positrons give rise to aniiihilation with particular interest because of high mechanical creep Fe, as well as with Al, core electrons. After a ~ ~ ~ e ~ ~l ei ~ s ~g s at ~ ~e~eva~ed n ~ e ~ e n i p e r ~ t ~as ~ r ed se m o n s t r ~ t e ~ at 770 K a positron lifetime of zv == (185 f 2)ps was for ~ 2 - ~ i ~~ F ~e ~~'1993). ~ ~~ This lt ~strengthenh~ o ~ ~ observed which i s due to positron s a t u ~ ~ t~i o r ~~ p p i n ~ing . may be affected by the ~ r o ~ e ~ tof i e st h e ~ ~ ~ l The ~ o ~ ~ l e ~ ~ ~~ r~ oe ca t d~~eue m ~a seu ~r efor ~ this v ~ ~ a n c i for e s ~which ~ r a c ~ i c ~ l ldata are availabl~. case is s u ~ s t a ~ t i ashifted ~ l y towards A1 (see Figure 17) Recent ~ ~ e a s ~ r e m eshow nts engel and Schaefer, whicli is clear evidence that the thermal vacancies are 2001), that in ~ i 4 alloys ~ ample F ~v a c a~ i ~ ~~~ formed on the Fe sublattice, In this case, positron concentratioi~sare present at anibieiit tempe~dtures annihil~tionwith high-momentu~ electrons occurs so that positron saturation trapping occurs (positron p r e d o ~ i n a n t ~with y core electroils of the A1 atoms that lifetime T 185~s);this ~ e c ~ therefore i ~ ~ ~ is ine neighbor the Fe vacancy in the ordered a~c~ sensitive to the detection of t h e r m a ~ ~ v a cformation st ~ ~ t ~ ~ r e . at high t ~ ~ p e r a t u rA~ high s . concen~ationaf vacanThe obse~va~ion that the e l e c t I . o ~ i ~ ~ o mdistrie~tu~~ bution at 770 K does not coincide with that of pure AI. can be unders~oudby the deviation of the Fe~lAIsg composition from stoic~~iometry' This gives rise to the al., 1999). In this s i t ~ ~ t i othe n merits of the time~ ~ ~ p e ~ i rofa iFe ~ catoms e in the n e a r e s t - n e i ~ ~ shell ~or d ~ f f e r e ~ i d~ i a~~~ ~ t o ~ meect h~n i ~after u ~ f&st t e n i ~ e r ~ ~ of the Fe v ~ c a i i which c ~ ~ may be even more i ~ ~ o r t a n t changes (as d ~ s c r i ~above) ~ d c m be e ~ ~ ~ o y e d ~ when the short-range order around the vacancy i~h~temperature dilaton~etr~ data are shown in deviates from that of the long-range ordered crystal. Figure 18. The fast initid s~~rii~king of the specimen In a d ~ i ~ i othe n , positron wave function may extend to due to the t e ~ ~ e r a t u r e ~ d e p e n ~lattice e n t anharthe n~xt"nearestvacancy neighbors where Fe atoms ~~onicities is clea~ly sep~rated from the del aye^ dominate. isothermal shrinking originating from the ~ ~ u i l i b r ~ t i o n Vacancy f ~ r ~ ~ aon t ~the o nFe sublattice in FeAl has of the thermal vacancy concent~ation(Figure 18a). been ~ u ~ g from e s ~~ ~ ~~ n~ c i~d eo ~~t ~b rl oea dre ~ i n ~ The tempe~~ture variation of the eq u ~ l i ~ r ~ t time ion studies after quenching ~ ~ o m i e setk ial., 1999) but has a l sthe constants derived from fits of e x p o ~ e ~ ~ t ito now been ~ e i ~ i o n s t r ~directly t e d under thermal equilii s o t h e r ~ a~~~ d ~ u r e i ~is e~i i~~ s~ s ine ~~~ g~ ue18b r ed ~~i~~~c o n d i ~ ~ Ito ~~ ~~.r t h e r m has~ rbeen ~ su~~~sted ~ i ~ l dai re~atively n~ high vacancy ration ~ n t ~ ~ a l c ~ ~ c ~ ~ a t(F~linle i o n s et al., 1999). Mote by ~~~~~~i~~~ of H y = (1.40 IO,1>eV (low v a c ~ ~ c y~ o b i l ~ t y ) again that aiitisite defects must be s i m ~ l ~ ~ n e o u s l yt o ~ ~ t h ewith r a ~ r e - ~ x p o ~ ~ e nFactor tial l / i f ~= ,~ created to i ~ a i n t athe i ~ ~overall ~ o ~ p o s i t i o n . 3 x 105 s-I for thermal vacancies. From the relatively text
289
IV
1
-1
(a) Time-depeiident length change A1 of the N i ~ o ~ e , o specimen ~ l ~ o after fast cooliiig from 1023 K to 723 K. The initial shr~nkingof the specimen due to the lattice aii~iarmon~c~ty, concomitant with the temperature change, can clearly be separated from the tim~~~ependeiit shrinkage caused by the equilibration of the thermal vacancy conccntratton. (b) Temperature dependence of the reciprocal time constant t ' ~as a function f tlie reciprocal equilibration temperature Tf (Arrhenius plot). The 1023 K, Cl 973 IS, V 923 K initial te~iper~tures T, were chosen as follows: A I073 K,
low amplitude of the time-dependent length change in ~ i ~ ~ ~ e ~a low * Aconcentration l ~ * , of thermal vacancies can be estimated which, together with the low vacancy mobility, could explain tlie high creep resistance o f ~ i 4 ~ ~ e at l o elevated ~ l ~ ~ temperatures (Sauthoff, 1993).
esses for
all
The self-di~~sivities D in ordered internietallic compounds have been discussed in the framework of various models (see Mehrer, 1996 and Chapters 23 and 32 by deNovion and by Larikov iii Volunie 1). The tem~eraturevariations of the diffusiviti~splotted in Figure 19 on a scale normalized to TM diger by many orders of magnitude for different compounds. The main features may be understood by the characteristics of t ~ e r malvacancies: - In close-packed structures the transition-metal
diffusivities
L)
are as low as in pure metals, or
lower, due to a low thermal-vacancy c o n c e i i t ~ ~ ~ i ~ n te CV (a high H: value) and an i ~ t e r ~ e d i avacancy diffusivity (i nt e~~edi atHe v value). 2 compounds the In the open-structured diffusivities are also low but for different reasons: H; is low and H v is high (see Table l), In the case of inany pure metals the vacancy-mediated tracer difhsivity is governed by the re~ationship
a* ==f.v*Cv
(13)
where v accounts for the vacancy jump frequency and J' is the te~perature-illdependentcor~~l at i on factor. The activation enthalpies are then related by
In the case of B2-FeA1 the experimental values of the activation enthalpies (see Table 1) fit together pe~fectly~ c ~ o r d i ntog equation (14); this ~ehavior also occurs for the most recent data on €32-NiAl by Divinski et al. (2000). Thus in these interinet~llic alloys a simple v a c a n c ~ ~ ~ ~ e d i aprocess ted may govern the transition-metal diffusivity~in fact without significant temperature dependence of the correlation factor. Here it should be mentioned
t
I
1.5
A ~ ~ ~ d e ~~ ua ofs~ the~ s en i ~~ - ~ i ~ u sNi-Ni3Al iv~~~~ (H s ~ ~ c 1971 o c ~A ~ ~ - ~ (Larikov i ~ A ~er al., 19811, Ni-NilGe ~ o ~ et ~al., k1997), a Ge-Ni3Gc onak aka et al., L997), Ti-TiA1 (Mroll et a).,19921, Ti-Ti3AI ( R ~ s i nand ~ Merzig, 1995), ALP CL~~A (disorde~ed) U (Bena et al., 1965), Co-CoCa, Ga-CoGa (Stolwijk et al., 19801, Fe-FeAl ( ~ ~ ~ e r s et ~ aal., n n1997, Eggcrsmann and re^, ZOOO), AI-FeRl (Larikov et al., 1981>,Ni-NiAl (Divinslci et al., 2000), Fe-FeA1 (Tokci et a?., 199Q AlFe3Al (Larikov et al., t981), Fe-Fe&, Ge-@c3Si, ~ e - F e ~ , § (Cudc i ~ y and Mehrer, 1997), and Ce-MoSi, l.,Ge-MoSi, 11 (1.and 11 to the tetragonal axis) (Salainon et al., 2001) as well as the sel~-di~usi~ities AI-AI (Dais et al., 19971, Fe-Fe (Lubbeh~~scii and Mehrer, 1990), Ni-Ni (Maier p t nl., 1976). Ti-aTi (Koppers et al., 19971, and TI-PTi (Cerold and Nerzig, 1997) in the pure metals, The Au ~ ~ ~ in ~Cu3Au s ~(Bencl o et n ul., 1965) IS ~ e ~ § ~ iinr ettic d d i s ~ ~ ~ phase, c ~ c dThe abscissa is ~ o ~ a l i toz the e ~~ e l ~ j n g t ~ ~ i ~ e ~ ~T‘, t u r e s )$
that a c o ~ i ~ r e h e n ~study ~ v e of f-I,M as a functi~nof the ~ o ~ ~ o s i tof i oFeAl n would be of interest, This o nis valid for study could test how far ~ ~ u a t ~(14) various compositions as Qs” increases (Mehrer et nd., 1998) aad H c decreases (see Figure 5) with ~ n ~ r e a s ~AIn gcontent. - The Fe tracer ~ i ~ ~ i ~ observed i v i ~ i in e ~D03-Fe3Si (see
coiit~ntori~inatesfrom a decrease of the t ~ ~ e v~c~ncy ~ ~ c ~ n t r a t Cv i o n~ ~ u ~ ~ et ~ al., i e 1995). r l e The Si or Ge ~ i ~ ~ s i y iin~ Fe$% i e s which are inuch lower than the Fe diffusi~iti~s ( ~ e ~ r e1996) r , (see Figure 19 and Table 11, may arise from a lower thermal v ~ ~ a n ~once~tration cy and a longer vacancy jump distance with a higher vacancy ~ i g ~ a t i o n enthalpy H v on the Si sublattice.
~
ehrer, 1996) are much higher than in B2FeAl (Figure 15), due to both a high concentr~t~on and a high diffusivity of thernial vacancies. Again, the a ~ t i v ~ t i o~~ithaipies n HF and H y (see above) fit QsD (see Table 1) a c c o r ~ i nto~ e q ~ ~ t i o(14), n indicating a conventional vacancy-mediated As demonstrated recently, thermally formed atomic appear to play an i ~ ~ o r t arole i i ~in the kigtn1 the Fe s u ~ ~ a t t~i i~~~u. s i o n ~defects l ~ i ~ u psr ~~c oe s01~~ temperature ~ e c h a n ~p rco~~ ~e ~ t i eofs i n t ~ r ~ e t a ~ l i c jumps of Fe atoms on the Fe sublattices in sto~chiometr~cFe$% were also inferred by alloys, e.g. in the case of the y i e ~ d - ~ t r eanomaly ~s in ~ ~ Acr ~~ o f the ~ Ejssbataer ~ ~ ~ (Sepiol e slid ~ rF o e where ~ ~ xi1 ~ incrmse ~~ yieXd~stress with ~ n c ~ ~ a sti en ~g ~ e r a ~isu robserved e at 800 K ~ ~ e ~ r Vogl, 1993). Tlie decrease of 6)* with increasing Fe
nietry, and using theoretical studies. vacancy formation in intemetallic coinpounds obtained from pos~tron-lifetime ~pectroscopy yield high effective~formationenthalpies HF in ~ l o s e ~ p ~ c k e d structures, and low values in bcc-type ~ t ~ ~ ~ t u r e s , results that can be well understood theoretic~lly.The vac~n~y~migratioi~ e n t h ~ ~ p ~ha at high t e ~ ~ e r a t ~for r e sB the e~uilibrat~on process a As d e ~ o ~ s t r a t ehere d in a with the shear modulus G and characteri~i~ig the FeAl, the thermal f o ~ ~ a t i oand n ~iigrationof defects strength of the hardening. From a fit of equation (1.5) also be sensitively investigated by ~ii~e-~ifferent~al can to the increase of A(r between 700 K aiid 850 K a length-change studies after t e ~ ~ e r a tchanges ~ r e in the vacancy-formation enthalpy of 0.96 eV, very similar to vicinity of the equilibration t~m~eratures.From the value derived by positron lifetime spectroscopy (see pos~troii-iifetj~~ie measurements under pressure after Table 1) was derived, fast temperature changes, the a c t i v ~ t i ovolumes ~ for It furthermore was shown that, after fast heattng the formation (V: = 1.7 SZ) and, for the first time, for from lower temperatu~es,the yield-stress anomaly at the migration. = 4.6 12) of vac~ncieswere derived, 855 I< emerges as a function of time (see Schaefer et nl,, In B2-FeAl, formation of thermal vacancies is experi1997) and, from an exp~~iential fit to these kinetics, a men tally demonstrated time constant t E = 220 s is derived that fits the vacancy co~ncidentmeasuremen m i ~ a data ~ o in~ Figure 9, From the coi~icidenceof ton tine. First the tenipe~ture dependence and tinie-depei~dent the positron-e~ectron-a studies on the ternary c o ~ ~ o ~~ n~d ~ * yield ~ e ~ * kinetics of Acr (see Schaefer et al,, 1997) with the low mob~lities and low ~ ~ n ~ e n t of ~ ~t~ermal ~ ~ o n s ~ ~ c a ~ ~i coy~ a t i oaiid n ~ i ~ r a t ~kinetics on studied vacancies that may give rise to tlie high creep ~ p e c i ~ c aby ~ l ypositrons ~ ~ u r s c l i uet~al., n f995b), we resistance. The present vacancy data can explain the conclude that the high~teiiiperatureme~haiiicalprowide variation of the transition~ni~ta~ self-di~usivities 2-FeA1 are strongly influenced by thermal in intermetallic compounds. For vacancy formation. At present this streiigtlieniiig is temperature mechanical properties are closely linked discussed in terms of an interact~onbetween thermally to the d ~ (111) ~ dis/ 2 ~ formation of thermat defects, as ~ v i ~ e n c eby formed vacancies with pairs of ~ the temperature variation of the yield stress ~ n o ~ a l ~ l o c ~ ~ t i o ~separated is~ by an antiphase boundaiy, and its time d ~ p e ~ d e nafter c e fast heat~Iig. g~idlngon a (1 to) plane. The e~ico~nter of a vacancy with one of the dislocati~nsgives rise to climb, so that the disordered tube generated by the motion of the d~slocation~ cannot be restored by the second dislocation. This tubular disordering exerts a drag on the dislocation, i.e. it gives rise to the increase in yield We thank X. Y. Zhang for his comments aiid stress. ~ ~ o k e f a l v i ~for ~ ~ technical gy help. The ~ n a ~ c ~ ~ support of Deutsche Forschuiigsgemeinschaft (Projects Scha 428/17-1,2,3) is appreciated.
and Baker, 1998), (see also Schaefer et al., 1997). This increase can be specifically ascribed to strengthening via the interaction of thermally formed vacancies with dislocat~onsin analogy to the hardening of after quenching (see Ceorge and Baker, 1998; Schaefer et al., 1997) where the ~ n c r ~ a in s e yield stress Acr IS correlated to the vaca~cyconce~tration&ii by
(P'y
compounds, and, in Atomic defects in inter~~etallic particular thermal vacaiicies and constit~i~iona~ vacancies, play an i ~ p o r t a n trole for the understanding o f diffusion processes, o r ~ e r - ~ i s o ~ dtransitions, er plastic d e ~ ~ i ~ aetc. t ~ ~o un b s ~ ~ progress i i t i ~ ~has been achieved recently in s t ~ d y i n the ~ the~iodynaniicsand kiiietics of t ~ e r m vacancies ~~ by employ~ngtechniques specific to vacancy detection, for example positron~nnihilationspectroscopy and time"differentia1 dilato-
292
Properties and Phenomenology
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Mehrer, H, (1996). Z. ~ e t a l l k ~ . , ni, J., Gas, P., and Beke, D. L. (€998). Riasing, J., and Herzig, Chr. (1 995). Acru Mater,, 46, 4821, 561. Valeeva, A. A., Rempel, A. A, Miiller, M, A., Reichle, E;. J., Saar~nen,K., Laine, T., Skog, K., Nakinen, J., ~ a u t ~ ~ a l - v i , Tang, G., Spren~el,W. haefer, E-E. (2001). P., ~ a k e n n ~K., ~ s Uusrmaa, , P., Salokatve, A., and Pessa. PIfysica S t a t ~soli^^ ~ (b) M. (1996). Plzys, Rev. Left,, 77,3407 J, (198t). Phil. M&., van Qmnien, A. H., and de Sadananda, K., Feng, G. A@, 387. (1999). ~ a l : ~Sci. p " Eng. Vogl, C., and Sepiol, B, (1 9941, Acta Me~all.~ f ~ t e r , Snlamon, M., Xto, K., wds~lewsk~, R. J,, Butler, s, R., and Ranlon, .T. E. (1968). J. Eversh nd Mehrer, €3. (200l), Defect aizd 1 3 1 8 . Apple Phys., 38, 4234. F ~ p ~ 523.~ ~ e ~ t b r oJ.o €3. ~ , (1993). Xn S ~ r ~ c f ~~p a~l ~ ~ r(eds~ R.e t ~ ~ S a ~ ~ h ~ ~ ,. In ~ ~ ~ aiz2s Ui r a~ e~ r Allays e~ (eds B. . Warrendale, p. I. Frxltz, W. Caha, and D. Gupta). TMS, W ~ ~ e n d a ~ e ~ Darolia et ~ 1 , ) TMS, Westbrook, J. H., and Fleisclier, R. L., (eds) ~ 1 9 9 ~ ~ ~ p. 205. ~ ~ ~ t e ~ ~ Ce ~ ~a l l ~i-c~ ~ r ~ ~ ~m~d ~ ~ ~ ~~ ~~~ ~~l ts~ Sclia~fer,€%.-E.(1987). P ~ ~Stat. ~ s Sat. . (a), 10 Vol. 1 + 2, Wiley, Chichester. Schaefer, H.-E., Wurschun~~ R., gob, M.,Zak, T., Yu, W. Z,, WoIR, J., Broska, A., Franz, M., ICiilzler B., and Hehenkainp, Eckert, W., and Banhart, F. (1990). Phys. Rev., B41, Tb. (1997a). Mater. Sci. ~ Q ~ ~ ~ , 1 1869. WdT, J., Franz, M., Broska, A., Schaefer, H.-E., Maier, K., Weller, M., Herlach, D., Seegel-, A., and Diehl, 1. (1977). Srr. Metall., 81, 803. (1 997b). Defecl: and DiZ"Forum, ~chaefer,&E., Damson, B., WelSer, M., ~ ~ ~R., ~~ r ~c ~ B., sh Urban h ~ o ~~ , Oeorge, E. P. (1997), Ph.y,s. Stat. Sol. ( a ) , Schaefer, K-E., Frenner, M., and ~ u r s ~ R, h ~(1999a~. i ~ ~ u r s c ~ i u nR., i , Trocv. T,, and Grrtshko, B, (1995a). Phys. In tepB~ ~ t ~ l l 7~ ,c2.77. s, Rev., B52, 6411. ~ c h a e ~ eW.-E., r ~ Frenner, K., aiid ~ i i r ~ R, e ~(199%). ~ z W ~ r s c h ~ mR., , Grupp, Ch., and ~ c h K-E. ~ e(1995b), ~ ~ ~ ~ Phys. Rev, Left., 75, 97. d u r ~ - ~ e r ~K. e n (1997). , Detect ar2.d W u r ~ c ~ R., ~ mKiiinrnerk, , E. A., 3 a ~ ~ ~ aK.,- Seeg~r, ~ e ~ ~ ~ ~ A., Herzig, Chr., and Schwfer, €3.-E. (1996a). J. ~ p ~ l . chmid, G. (1989). J. Phys. Cond. ~h.y.s.,80, 724. ~ a ~ f e 1, r ,SA 49, W ~ r ~ c R., h ~ Badura-Gergen, ~ ~ , K., Kiani~e~le. E. A., ~ e ~ d ~ a CO. n nN,, , and ball^. R. W. (1965). Phys. Rev., C., and Schaefer, €%.-E.(399Sb). Phys. Rev., ~ 1 1824. ~ ~ , 9, Seplol, B,, and Vogl, G. (1993). P~JAS. Rev. Letit,, 71, 731. W , R., and Sc~aefer~H,-E. (1997). Matcr. Sci. Simmons, R. O.,and Ballufi, R. W. (1960), Phys. Rev., 117, Forum, 255-257, 81. 1. Y a m a ~ c kM., I ~ and Shirai, U.~ 1 9 9 ~In) .~ h y s ~~c ~e l t u ~ ~ ~ Shirai, Y . (1988). Ball. Jap Inst. Met., ~ Shirk, Y., Seeger, A,, and Schaefer, %-E. ( ~ ~ 8 9In) .~ a s i t ~ a ~ and ~ r ~ ~of ~~ ~s t .e rs ~ ~~~~a ~~~ l i~c(eds~ N. ~S, o S t o ~ oand ~ , V. K. Sikka), Chapman and Half, New York, ~ ~ ~ ~ (eds ~ i L.~ Cj O~o r~~ lf~ ~j nos -~~ et aal.'). n ~ ~World a~~ p. 3. ScientiEc, Singapore, p. 419. ., and Umakoshr, Y, ( 1 9 ~ ~ P) .r g r . ~ a ~ c r ,and Mullett, L. D. (1999). Phil.
H.-E. (2001). Defect
U M Difl ~
Zhang, X. Y., Sprengel, W., and Schaefer, €3.-E.(2001). To be published,
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~ ~ i s a t i s f yase the ~ past discourse may have made you nk me with the d o ~ t r ~ of ~ ethe s ~ ~ ~~~o~~ ~ the i s ~ ~~~~~~t~and the p ~ ~ n ~ i 1 p can ~ e syet ~ so little d i s ~ ~ ~ e r what to i l . ~ ~ u i in es~ that ~ p e ~ ~ h ~ Ithe Z ce~ ~ ~ ~ io rf i ~ s others have scarce been more U my QWIZ have been to myself,
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While iiiodeling the te~peratureand stress dependence allows one to extrapolate creep data, it obscures the roles of short-range aiid long-range order, the nature Generally inelastic deforniation at constant uniaxial of the crystal lattice, alloying, aiid iiiicrostructure, all stress is perceived as creep, since tlvs is the way a of which contri~uteto i ~ p ~ o v e m e no tf creep resismateria~is characteri~edin the laboratory and the tance. It is hard to ignore the p resulting data used for design purposes. However, in a improving creep resistance with alloy broader sense any time-dependent inelastic deforma~ i c r o s t r ~ c t u r a~l o d ~ ~ c a t of i o the n ~ three p ~ i n c i p ~ l tion, such as stress relaxation at constant strain or a study of strai~i-ratesensitiv~tyare also ~ ~ ~ i i f e s t a t i o n sintermet allic intermetallic-based phase nickel-base superalloys ( of creep. 1998; Cetel and Duhf, 1988), e ~our t current underThis chapter is an ~ ~ s e s s mof s t ~ i i ~ iofn ~creep ~ e h a ~ i oofr in~ern~eta~lics and and Marlsson, 1997; Lupinc et al,, 1997). See also the inter€~etall~c-based ~ L i l t ~ ~ h aalloys. se The principal objective is to coiiipare creep behavior of i n t e ~ e t ~ l l i c s chapters in V o l u ~ 2e by with ordered struct~res, to that of diso~der~d kiu and Pope ~ ~ i ~ ~ ~ j " and Huang and Chesnti ~ ~ a ~ and e rbring ~ ~forth. ~ sany ~ ~ i ~ i q uaspects e that spite of no systematic pattern o f change in stress contribute to the enlianceflient of creep resistance. exponent or activation energy, This question has rece~vedsome atten~~on, and it kas Outside the conventional fo~iison ~ i n i m u mcreep been concluded that the same constitutive equation rate, impressive progress has been Underapplies to internietallics as to conventioiial metallic o Chen er stand~ngthe primary creep behaQi~r systems ( ~ ~ u t 1991, ~ o 1993; ~ , Jung et al., 1987). The al., 1998: Nemker et al., 1997; eddoes et al., 1997; implied n o n ~ ~ n i ~ u e of n e intermetal~ic$ s~ appears to et d,, 1997, 1998; and ~ u d et ~al., n199?), ~ and ~ ~ be a result of our preoccupation with the temperanickel-base superalloys (Caroa et al., 1388; Bollock ture dependence (a~parentactivation energy) and and Argon, 1992). ft is critical to note that even though stress de~endence(stress exponent) of creep rate, high priinary creep has little inipact on creep mechanrather than the ~ r o ~ o r t i o n a ~ iconstant ty (preisms of steady-state creep, as we now ~ ~ ~ d e r s ~ita n d , e ~ ~ o n e n t ifactor), al which connects these paranieters inhibits the e n ~ ~ i e e rai n~~ ~ l ~of ~ ~a ~ . the~~ ~t ti e or iIn (Larikov et al., 1981; Appel and Wa~iier,1998). To terms of absolute a ~ c u ~ u ~ a of t ~ strain o n at a given some degree the role of inter~etall~cs is better ~ e alloying time, the effects of n ~ c r o $ t r u c t ~and discerned using the difhision coeEcient as a more additions on the kinetics and d ~ a n i i of ~ s~ i s ~ ~ c a t ~ o n fundamental paraniete~. motion are critical but d i ~ c L ~tol tasse~s~ ~ a ~ t i t ~ t i v e l This line of inquiry forces one to re~teratethat creep and hence to i ~ e i ~ t ithe f y role of i n t ~ r ~ e t ~P ~e r~~ ~ acpss. is a p ~ e ~ o i i i e ~por inn i a r i ~of ~ en~~neering interest; of it may be more ~eaningfulto assess the use~ulnes~ wherein ~ i n i m i ~ i nthe g creep rate and strain at a given. l i csecond s phases, rather than as parts of time, in an absolute sense, is of paramount i~portance' i ~ t e ~ e t ~ l as eticr
I ~ ~ e ~ ~ i t Cl t ~ ~ l i c~ Vol. 3, Principles ~ and ~ Pracfictl. ~ Edited by ~ J, €3. Westbrook n and ~ R. L. ~ Fbs&er. ~ 02 0 0 2 John Wiley & Sons, Ltd.
298
~ e ~ l ~ ~Properties n i c a ~
a monoliths recogn~~ing the critical role of semicoherent or coherent interfaces as dislocation harriers. To ~nderscorethe role of interme~~l~ics in creeplimited sit ~ ~ a t ~ owe n s ,will conclude the ~nt~odLiction with a rev~ewof the ~ p p l i ~ a t i oofnintermetallic~.Then to set the stage in s u p ~ o rof t the theme outlined in the preceding para~raphs,we consider the measuremelit and analysis of creep behavior in some depth in ~ e c t ~2.o ~This i i s ~ o ~ l by o a~ ~~i s ec ~~s s i oofn factors ~ n ~ u e n c icreep n ~ resistance of inter~etallics and intermeta~lic-basedsystems in Section 3. roughou out tIGs cliapter we have atte~iipted to bring Corth an ~ ~ ~ d e rc lo iy~im~o~~ a l using ~ t y detailed discussion of more mature ~ ~ s t e ~ s .
1.1.1 Creep , ~
re F ~ ~ i l and ~ r e~ ~
~
~
i ~ ~ ~ ~ ~ i o n ~ ~ ~ ~
Although creep rupture is one of the most commoiily recognized failure modes, d~mensionali n s t a b i ~ and i~~ distortion due to creep are e ~ u ~ coininon ~ly issues ~ ~ e ~ compon~nt t i ~ g ~ u r a ~ j ~ iand t y perfo~~ance. While creep rupture failure niay be of primary interest in ~ ~ ~ ~ G a t ii no vi ios l ~ rotating i ~ ~ parts, h e i ~ d i nand ~ d ~ ~ t o r ~ of i o nthin wall sections can become a critical aspect of design for static components subjected to severe temperature gradients,
I . I .Z Role in
~~~~~~~
~~~~~~~~~~a~ F ~
~~~~~
~
~
g
Creep behavior ofcoatin~s,also plays a pivotal role in. ~of coated ~ ~ systems (Duhl, 1989; Boone and Sullivan, 2973). Here the d i ~ e r e n t i in ~ l both tlierinal expansion and creep resistance of the coat~ngand subst~atelead to re~idual stresses upon thermal cycling, and eventually to failure. However, with the emphasis on c o ~ t ~ ~ g oxidation and co~rosionresistance of c o a ~ ~ as ~i~s~ well as coating appl~cat~on technology, marginal attention is paid to coating creep resistance.
lead in^ to t h e ~ 3 ~a e~c h a n i cfailure ~l (
a ~ ~ a ifew n ~~ x c ~ p t ~ ~~~~g o n s and C ~ u ~ ~19981, re, i n ~ e ~ in ~ s creep t behavior of the vast ma~orityof i n t ~ ~ e t a l lisi ~ s driven by aerospace and industrial gasations (Nabarro and de Villiers, 1995, hile ~e~atively high-stress and short~time e s ttong-time creep creep is of ~ ~ ~in ~the~ former, behavior is of interest in the latter case. However, because o f s t I ~ ~ ~ safety e n t and p e r f o r ~ a n cissues ~ a ~ s o ~ i ~ with t e d the a e ~ o s p a cindustry, ~ it leads in 1.13 Stress ~ e l ~ ~ Notch a ~ i ~o e~h ~~ ~ am! i o ~ , terms of advanced material development. But we are Creep/Fatigue ~ n ~ e ~ ~ ~ t i o ~ w ~ t ~ an e interesting ~ ~ ~ n period ~ where some of the ~ 0 t ~ h " r ~ i p tbehavior ure and the role of dwell time on a~vanced,~irectionallysolidified, single-crys~~l nickelare portan ant aspects o f how f ~ t i ~ u e - ~ i ~ i t ~ d base ~ ~ ~ etechnologies r ~ l ~ are o being ~ ~ r a ~ ~ s fto e ~ r efatigue ~ components can fkil in practice. In both cases creep or as turbine. This is likely to bring forth s~ress-relaxationhe~aviorplay a critical role. Gener1on.g~tiinecreep issues in conju~~ction with large ally, study of these aspects is assunied to be in the ~ o ~ p ~ n e iiat n t sfaced hitherto. It is i ~ i ~ ~ o r t aton t domain of meclianics (Tilly, 1972; Gallerneau, 1999), e, not only that the typical superalloy is 60% hut there is clear evidence to suggest that intrinsic sed intermetal~icby volume but that several material behavior plays a very i~~iportant role. It has metallic c o a t ~ ~systems g also derive their excellent been shown that two specii~en~ of the nicl~e~-base from nickel and ~ l a t i n ~alurniii~ ~ ~ i d a t j ore~ist~nce ii superalloy IN 100, with differing heat-treat~~ent condi~ ~ ~i n t ee~ ~ i~e t a l~~Xfi sufficient ~ s~. s progress e ~ is made tions, can have sig~i~cantly different ~ o t c h ~ r u ~ t ~ r e in refractory-metal-based systems, the future presence lives despite yielding identical smooth ~re~p-rupture of i n t e r ~ e t a lsificides l~~ in both the base niateriaf and lives (Law and ~ l a c k b ~ 1980). ~ i ~ , Swh studies of potential c o a t ~ n ~iss inescapable" fii the case of monolit~icinterine~allicsare n a t ~ i r ~limited ~ i y (Lupinc titan~um alloys, we are already on our way to et a/., 1991). c ~ - ~ i A ~ - b a ssystenis. ed (See at.) Even if the creep behav~or of ~ n t e r ~ e t a l l were i ~ s not any better than that of I . P .4 ~ r o c e ~ ~ s i ~ g disordered alloys, the inherently better oxidation ~ u p e ~ p ~ a sf t~i cr ~ i and n g di~usionbon~ingare used ~e~istance of aluminides and silicides forces one to and investigated (Schuh and Dunand, 1998) as an learn to live with them. ~ h a u g hnot always recognized alternate forming processes. Creep plays an ~ ~ ~ o r t a i i t and used directly in tl-ie design process, creep behavxor role in these processes, but in. an opposite sense. of these materials manifests itself in various failure Nevertheless, correlatio~sb e ~ ~ e ~ e ni i ~ r ~ s ~ ~ uand cture ~Odes* *
299
Creep mechanical behavior would provide additional insight. However, this aspect is beyond the scope of this chapter, and will not be discussed further.
alysis Generally creep behavior is assessed in uniaxial tension and a plot of strain vs. time is generated at various te~peraturesand stresses. Often in industria~practice no strain history is recorded, and the material is assessed solely 011 the basis of its rupture life. For brittle intermetallics, in the early stage of development, compressive creep, or bend creep is used to assess the potential of material. By and large, at high teiiiperatures where creep is primarily diffusion controlled, the creep rates in compression and tension do not differ. However, in highly textured, coarse or columnar grain, and single crystal materials, diKerences in creep rate at lower temperatures can be significant in some orientauhl, 1988). Besides constant stress experiments, stress relaxation and constant strain-rate experiments (Dudzinski et al., 1997), can provide invaluable insight into material characteristics, but few such experiments are carried out. In its most general form, tensile creep behavior may be schematically represented by a strain versus time curve, such as the one presented in Figure 1. The early incubation period, where no measurable creep occurs, is followed by a rapid rise in creep strain or the period of primary creep. To better delineate the primary creep region, creep results are often plotted as strain-rate
versus strain. High primary creep ( > 1%) rarely seems to occur in wrought and fine-grained nzaterial. Generally, high primary creep i s associated with a relatively low density of mobile dislocations, and it i s shown to be sensitive to heat treatment in i~~iltiphase alloys. As shall be discussed later, this aspect has not received s u ~ c i e nattention. t Much of the focus in the literature has been on the second stage of creep or the minimum creep rate.
Et has been well accepted that minimum creep rate can be related to stress and temperature by the relation, i = A exp(-Q,/RT)s”
(1)
where, i is the strain rate, Qc is the apparent activation energy for creep; Tis the temperature in K.; R is the gas constant; and A and n are constants. ( the equation to be dimensionally true, s should be replaced by ( a / E )where E is the elastic inod~ilus,or by (a/oo), where 0-0 is a reference state. This omission, however, does not impact the follo~ingdiscussion.) This relationship seeins to be as much valid for monolithic and multiphase intermetallics as it is for pure metals and disordered solid solutions. Thus it would appear that intermetallics play no special role. This may be so because high-temperature materials of interest occupy the power law creep region with reference to Ashby’s ‘deformation mechanism maps’ (Ashby, 1973).In this region, the power law relationship with a stress exponent of 3 may be phenomenologically
In
igure 1 Most general form of h i ~ ~ - t e ~ p e r ~ tensile t u r e , creep behavior
justi~ed~ i t h o u reference t to any specific dislocation ~ e c h ~ as~ follows. n ~ s ~
t "?.' pbv; but since U QC cr; and p o( cr2$ i 01 g3 (2) where p is the dislocation density, k. is the vector, and L, is the dislocation velocity. Zf dis climb were c o ~ ~ s i d ethe r e ~r a t e - ~ i ~ i t ~step, n g a higher ess e x ~ ~ n eof n t3.5 or 4.5 might be ratio~ia~i~ed. See e ~( 1 9r~for ~ t)~urther ~ discussion. ~ ~ ~ e e r ~ ~ and an~ ~lternatively~ the validity of equation (1) may be nothing more than a recoii~rmationof the usefulness orn, or the more popularly used raiiieter P, for represent~ng creep data for all metallic (Evans and ~ i ~ s h i€993), r ~ , and i ~ t e r ~ e t ~ l 1 i c , ( ~ t o ~ 199S), o ~ , y-TiB1 ( ~ u p i n c et al., 1997), and NiAl (Noebe and ~ a l s t o n ,1997) systems. ~ n d e equation e~~ (1) forms the physical basis for these ~ a r a ~ ~ ~ The t e~,arson-~iller ~s. parameter P is expressed as,
stress can then be g e ~ ~ r aast in ~~, consider the scenarios where we want to increase or decrease the creep rate by two orders of ~ ~ ~ ~ i t L ~ d changing either A, uz or (2, one at a t h e . ~ i ~ i l a rin ~y, Figure 2(b) we can plot stress for fixed strain rate or time to 2% creep vs. 1 of temperature, and
pure tiickel, to I ~ to the ~ most~ creep~ r e ~, i ~ t ~ ~ advanced single-c peraf loys. As the plots in s ~ g ~ ethe s t i~~ ~ ~ r o v einm ~ n ~ creep resistance from pure nickel to an advanced sLiperalloycan be achieved,either by c h a n ~ i n ~ the pre~~x~oneiitial factor A by orders of ~ a ~ n i t u d ~ , by c ~ a n ~ ~Q nby g -50 kJ,hnol or by ~ ~ i P$ by ~ ~ ~ 30%. Note that, deterio~~tion or e n h ~ n c e ~ine creep ~~t ~esistance,achieved with variation in any of the parai~eters,yields curves so pardel to each other that any c o ~ b i i ~ a t i of o i ~change in the three parameters can account for the change in creep behavior~ P = ?-(fog t 4-C) validity o f the empirical (3 depending on the stat~st~cal data. Since Q and n can be ind~pendentlyde~erni~ned, where T i s ab~olutetemperature^ t: i s rupture life or these values are r e ~ ~ r but t e the ~ value of A , which time to fixed strain and 1 M 1/i and C i s a constant for , must chaillge by nn order of i ~ a ~ n i t ~isd e~eiierally a wide variety of ~ i ~ t e r i a l s . ignored. This is so even though the ~ a r a ~ Ae ~ e ~ arsoi~-~iller paraiiiet~rin equation entails, the pre-ex~onentialDo ('art of the d i ~ ~ s ~ o (3) is a r e ~ e x ~ r of ~ an s ~~ ~ r r o~ e~n i u s ~ t re~at~onsh~p ype c o e ~ c ~ as e nwell ~ ~as ~islo~atioii mob~lity,and microbetween time and te~peratureas in equation (1). The structural parameters, which greatly infiuence the successful ~ p p ~ ~ ~oft the i o Earsoii-Miller n parameter absolute sate of creep. A s a m ~ l i of n ~these parameters would seem to su~gesteither that equation (1) is very for a wide variety of i n t e r ~ e t a l ~systems ~C studied in robust, of: that the three para~etersA, &, and pz are recent years indi~atesno rational pattern in the value as i i ~ ~ e p e as n ~wee think. ~ ~ ~ ~x~erimentally, while of YE or in the a c t ~ ~ ~ tenergy, i o n as far as the absolute n t ~ y ~ level of creep resi~tanceof alloys is c~nGerne~. nd M, can be d e t e r ~ i n ie n~ ~ e ~ e ~ i ~Ae cannot. eed, row^ and ~ s h (1980) ~ y have shown that A The first question i s this: can an order of ~ a ~ ~ ~ can vary from less than I to more than IQi5. Such R chaiige occur in A with variation in crystal s t r ~ c t ~ r e s ~ variztion has been reported by b ay as hi et al. (2991) order in^* and a l l o ~ i ~ofginte~metal~ics? Based on the for Ni,(Al, X), simply with stoichiometry. In many Russian compilation (Larikov et al., 198I , Chapter 4) ~ ~ t e r ~ aasl ns increases , A increases also. A~cordingto of d ~ ~ u s i oinnordered alloys, the answer seems to be rown and A s h b ~f1980), A and n are a ~ p r o ~ ~ m a t e l ya ~ r ~ a t i v fet. is known, that while the Rctivat~o~ related by o n be a'~~o~imate1y 36T~ e~iergyfor s e l f ~ d i ~ u s ~can c a l / ~ i o l e where - ~ ~ M is for ~ e l ~ jthe ~ gvalue ? of the p r e - e x p ~ n ~ n tfirae~q ~ ~ e nfactor ~ y Do falls in the range of 0.05 to ~,0cm3~sec. For e x a ~ ~ lthe e, where C and IT' are constant^^ dependence of volunie self~di~usion in aTO~ i n ~ e r ~ t the a n dsensitivity o ~ e q ~ ~(1)t to i othese ~ and Nb is described by the followiiig rehtions. this experiment. Xiimgine a basep a ~ ~ e t e rconsider s, a line alloy with 100 hr to 2% creep, or approx~mate~y ~ ~ ~ icreep i ~rateu of~ 7 ix 1OeS sec-] at 1200 K and 200 MPa. This is a close a ~ ~ r o x i ~ a tto i othe n behavior l y nickel~ba~e of ~~1~~ - one of the c o ~ ~ o n used ed superalloys with 55% ~ ~ 3 ~ l - b a sprecipitates* Further zssurne that for such an alloy, M, = 3.5 and Q = 3 ~ ~ J / m Ao ~plot . of n i i n i creep ~ ~ rate vs..
Creep
30 1
I,
Fi~ure2 Sensitivity of equation (1) to changes in pre~exponentialfactor A , stress exponeiit E , and apparent activation energy Q for (a) two orders of magnitude change in strain rate at constant stress, or (b) for a 200K changc in temperature capability at c o ~ s ~ acreep n t strength
302 These values clearly suggest that Do is affected by the creep occurred at intermediate t e ~ ~ e r a t ~(760 r e s"C) d i ~ ~ r ~b~tween n c e the c~ose-p~cked (fcc) vs. open (bcc) only, and the o r i e ~ t ~ i t ~ o~np e n ~ eof~ pi cr ei ~ ~ creep ry str~cture?and that even in pure metals, tlze presuggested that it was associate^ with s i ~ g ~ edefor~s~i~ t exponential factor can vary by -10. We a u g ~ e n this ased on further an~lysis~ Paslay PC al. {~970), a r ~ u ~ ~ ~L~rther e i i t in Section 3, with a d i s ~ ~ ~ s sof i ohow n asserted that the ~ r i ~ creep a ~ yrate for a va~ietyof degree of ordering, s t o ~ c ~ i ~ i i ~ and e t r yalloy , in^ addiorie~ita~ion~ can be best represented by e n ~ p ~ a s ithe ~in~ tions influence Do, and hence D, of single-phase s in preference to (1 1I)( 110) ~ n t ~ r ~ ~ e t aIndeed l l i ~ s . ~ c c o r d i nto ~ ~ ~ u t (199 h oI),~ f971), however, s ~ o w that e~ the diKusion coefficient is the niost i ~ p o r parat ~ ~ ~ ~ occurred in coarse-graine~~ meter; and Ilie creep rate i s best correlated with and directional~y~ ~ l i d i ~c oe ldu ~ n a ~ - g r amaterial, ~n di~~si~ o no e ~ c ~ errsang n t s the orn e~uation,which is and that while ~ r i n ~ a rcreep y strain d e ~ r e ~ s ewith s similar to equation (I), for dislocation creep, where C decreasing stress, the time to complete p r i ~ ~ a rcreep y is the shear ~ o d u ~ u ~ . increases with decreasing stress. Add~~~onally, they also claimed that primary creep strain IS su~pressedby the c.. = ~ ( ~ ~ ~ ~ / ~ (9)~ )in~rod~ictio~i ~ ~ / ~ ) ~ z of a ~ ~ i e - s c as ~u e~ ~ t r ~ ~upon c t ~ shock ~re Tn contrast to diEusion ~ ~ i e c h a i i i s however, ~~s, it is difiicult to isolate the ~iifluence of slip geometry, than a decade later, Caron et ad. (1988) d ~ ~ ~ o c a~ehavior, t j o ~ ~ and ~crostructuralp a r a ~ ~ t e r s that the ~ehaviorwas even more complex than on tlie pre"ex~o1ientia~ factor A, in the framework of previously envisioned. As seproduced in Figure 3, iheir e q ~ ~ t i o (I) n s and (9)* in any reliable manner, Nonestudy of three major or~entatioiisof' a sing~e~~rystal theless, the ~ o n ~ i i i ~rote n t o f these para~etersin alfoy d e ~ o ~ i s t r ~ t botli e d i ~ ~ u b a tperiod ~ o ~ and rmproviag creep resistance in real applications is a function of orientation and y' e ~ p i ~ i c a ~l ~i ~yd e n i a ~Thus, l e . though largely a valid ntly Kakehi ( 2 0 0 ~Iias ~ corroborated these findings and has shown that p r i ~ a r ycreep model, e ~ u a t ~ o n(I) s and (9) are a poor guide for istance of two-phase systems of' is affected by cooling sates, which influence tlie fine fore we return to these aspects in precipitate structure. Primary creep was also observed of ~ ~ creep ~- a ~to be a~ €unction r of major y (Shah and Cetel, 1996) and ~ e ~ t i o3, nhowever, a discussio~~ minor (Shah and Duhl, 1988>, alloying additions to hitherto ignored aspect of creep behavior - is in order. single-crystalsuperalloys.However, based on extensive analysis of the ( 100) o r ~ e n t es ~i ~ g l e ~ ~sL~~era1loy rys~~~ ( ~ 0 1 atid 1 ~ ~~ r ~g o ~~ 9, 9 ~~o)n c f ~ d ethat d No universal, physical model exists to describe primary primary creep following initial incubation WilS a result creep, which is the most strLzcture-sensitive part of creep of ~ ~ j ~t i ha 1 e r misfit ~ ~ ~s t r e s ~ ~ b se t ~ the ~ e7 ~and y' e s~ ~ ~n rg~i ~ a creep ry ~ etiorm, In ~ an ~on ~ ~ ~~ esense, phases, and that it was related to any workbecomes an issue of concern, when 1-2% creep strain hardening or recovery processes, In contrast, Miura is a c ~ ~ ~ u ~ina at efew d hours, in spite of' a sixstained et ak. (1991) argue that in singte phase ~ ~ - ~XIvi ~ ~ s~ea~y-staie creep stage and ~ ~ n d r e dofs hours of the initial s~~nioidal behavior is a reflection of the creeprupture life. Parcametrically, primary creep is yield-point behavior observed under constant tensile d e s c ~ b eas~~ ~ d r a dcreep, e-~ strain-rate testing. Again in co~itrastto Pollock and i e n tKear a i d Argon (1992), an in ~ ~ r e e ~ ~with Piearcey (1967), hu et at. (1998a), studying ~ m ~ ~nn tg~ ~ e t a f l iand c s , inter~eta~lic-based alloys, Ni.,(Al,Ta) in various orientations, concluded octahethe inc~batioi~ period and ~ r i ~ a creep r y phenomena dral slip to be r e s p o ~ s i bfor ~ ~p ~ ~ creep, ~ r while y have been s p o r a d ~ ~ astudied ~ ~ y in Ni,Al, and twoe ~secondary creep. Further c~zbe-crossslip c o n t r i b ~ t to phase cast s L i ~ e ~ d l ~but o y ~recently ~ have received Zhu et al. (1998b) conclude that the blocking OS edge c o ~ ~ s i d a~te~ition e ~ a ~ ~ in ~ y ~ ~ I These ~ 1 . studies are o n ~ their climb ~ i ~ l o c ~ t i obyn sforest d ~ s l ~ c a t ~causes ~ r i e reviewed ~y in the following. and the termination of primary creep. ~~~~~~
~
l and ~~ ~ ~~ ~y ~ ~ ~ ~ t a2.2.2 k ~k ~ c~ ~~ ~ ~
1x1 tlie earliest work on ~ ~ n ~ l e - c r ysuperalloys sta~ (Kear iearcey, l 9 ~ ~it)was , observed that high primary
t a
~~
i
~ ~
~
The same tlieme recurs with binary ~ ~ L i d ~ i nets kat., i 1997) and a~loyedy - T N ~ ~ ete al., o 1997). ~ r i n i a ~
Creep creep in y-TiAl is observed to be a sensitive function of alloy composition, heat treatment, and microstructure. In contrast to superalloys, however, lamellar refinement leads to a reduction in primary creep in y-TiAl; and Rong et al. (1998), showed that pre-straining increased the primary creep strain as additional twinning was introduced. We return to this aspect in some more detail in Section 3. Study of orthorhombic Ti-23Al-27Nb also shows a strong dependence on the primary creep microstructure. In this coinplex system, aging treatments, which induce the precipitation of additional phases, reduce the prima~ycreep strain ( oehler et al., 1997). These observations are opposite to the effect of fine y’ precipivates in superalloys. Nonetheless, following the hypothesis put forth by Pollock and Argon (1992) this commonality points to a potential correlation between misfit strain and primary creep. A common theme between these two classes of materials seeins to be a low density of mobile dislocations initially causing an incubation period, arid eventually bursting into rapid ~ultiplication,leading
303
to high primary creep. restraining or microstrLLctura1 changes which can sniooth out this transition seems to lower the primary creep, but the opposite can occur instead if dislocations are inhibited. It may be rationalized that variously solute atmospheres, misfit strains between the two phases, transition in slip behavior, or dynamic change in microstructure ( aiid Hall, 1991), may all interfere with a smooth transition to steady-state creep. Load-drop experiments, which allow one to measure the extent of reversible strain, provide a good insight into detailed niechanisms.
Generally, creep properties are measured in ambient environments, and for a given ~ a t e r i a are l expected to be reproducible. However, those dealing with a large amount of creep data for well-characterized alloys know that consistent biases in results occur from test location to test location. This aspect has not been systematically addressed so as to isolate environmental
Creep strain (%)
1
(a)
Q
2d0
Figure 3 Effect of y’ size oil creep bebavior at 760°C and 750MPa of CMSX-2 single crystals for the three main orientations: (a) [OOl], (b) [I 111 and (c) [Oll]. Froin Caron et al. (1988)
factors, such as humidity, and and C1 content in air; but the effect of these factors cannot be ignored. In the extreme, it is known that creep properties are severely degraded in low oxygen and sulfur environments. See tidies of superalloys by Seib (2000), and tlow (1985). ~nfortunately,while environmental effects on creep sorely deserve more attention, they are beyond the scope of this review.
3.1.1 Role of Sl@ Gametry
Even though creep resi~tanceis measured by uiiiaxial strain rate at a given stress, usually the deformation takes place on a number of slip systems. In a truly random fine-grained, polycrystalline material, this is a moot point, as it is ave~agedout and may be qu~ntified by the Taylor factor. In single crystals, however, it is fair to consider to what degree each slip system experiences a signific~ntresolved shear stress, and thus contributes shear strain to the total tensile creep strain, is largely a function of geometry. Unfavorably oriented slip systems will be less stressed, and conseq~entlycontribute less strain. In the early stages of creep with a low total strain, the contrib~~tion from each slip system may be assumed to be linearly additive
(Shah and Cetel, 1996). Thus, ignoring intera~tions, steady-state axial strain rate iii may be expressed as,
for all possible families of slip systems, where ap,k are Schniid factors for thejth slip direction on a lcth slip plane, within a family of slip system, ~ i t h i na given family of slip systems, it is reasonable to assume that the proportionality constant Aj/<would be a constant. A good match between predicted and observed creep anisotro~yfor a disordered, solid~so~ution-~~rdened nickel-base alloy (Hastelloy-X) single crystal, vindicates the validity of this relationship. Such a material with fcc structure is known to deform predo~inantly by octahedral (111)(110) slip. Purely based on a consideration of Schmid Pdctors and number of participating octahedral slip systems, a factor of -8Xdecrease in minimum creep rate in the { 111) direction compared to the (100) direction is predicted and observed. See Table 1 for further details. As further d e ~ i ~ n s t r a t eind Table 1, similar arguments can be made to rationalize the 50 times lower creep rate in the ‘hard’ (100) orientation compared to the ‘soft’ { 111) orientation in binary MiAl (~itabjianet al., 1999), where (100) is observed to be the predominant slip direction. The terms ‘hard’ and ‘soft’ are used qualitatively to describe very low and
able 1 Assessment of creep anisotropy based on strain-rate partitioning over operative slip systems
lip systems
Axial Orientatioii (111)
{ 100)
Proportionality factor
Creep ailisotropy
Exaniple
Min, creep rate along (100) Min. creep rate along (1 1I)
No. of Schmid No. of Schmid systems factor systems factor
FCC/L 12 (1 11}(1l0)
8
0.4083
6
0.2722
A cd
-8 (Octahedral slip only, Acd = 0)
Hastelloy-X Shah and Cetel(1996)
CO01} (110)
0
0.0000
3
0.4714
Acd
-2 (Cube slip participation A,d = 2A&)
Typical Superalloy Ni,(AI, Ta) Shah and Cetel(1996)
B2 (001} (001)
0
0.0000
6
0.3333
A,
(1 10}(001)
0
0.0000
3
0,4714
Ad,
1/50 (predominantly (001) dislocations A,, = Adc = 100 Acd = 100Add)
~001}(110) {ll0](110)
0 4
0.0000 0.5000
3 0
0.4714 0.0000
Add
A cd
-
-1 (both (001) and (110) diSloCatiOns A,, = Ad, Acd = Add)
NiAl Kitabjian (1 999)
Ni-47.5A1-2.5Ti Kitabjian (1 999)
Creep high resolved shear stresses on the operative slip systems. In Table 1, equation (11) has been applied to assess the extent of creep anisotropy, which is arbitrarily defined as the ratio of minimum creep rates in (100) to (111) directions. Note from Table 1 that in contrast to simple systems
additional slip systenis intervene. Specifically these are cube slip-(111) (100) in the case of y’ and y/y’ alloys, and (001) (110) and (1 10) (110) slip systems in the case of NiAl. Generally, increased numbers of slip systeins lead to a decrease in creep an~sotropywith a wider dispersion of strain. Of course the extent of decrease in anisotropy is dependent on the relative ease of glide of various families of slip systems, wliich can be defined in terns of a ratio of proportionality constants A j k , as has been done in Table 1. The interaction between the two slip systems is a function of degree of order, alloying additions, and oreover, because of the extended nature of superdislocatian core structure (complex SF and APB), ease of dislocation cross-slip is facilitated or in~ibited,dependin on the orientation and direction of creep stress - that is, tensile or compressive - at intermediate te~peratures (Pope and Ezz, 1984). Recently a dislocation dynamic based model has en developed to capture these interactions by rehrn and Glatzel, 1998, but we are far from predicting the behavior n priori. Not surprisi~glythe model converges to equation (11), when slip interactions are dropped. Though not fully developed, the models allow one to qualitatively rationalize the trend in creep anisotropy with various alloying additions (Shah aiid Cetel, 1996). In some high~molybdenu~ alloys, where MO is known to partition only to the y-matrix, the creep anisotropy factor, defined as a ratio of creep resistance of (1 1 1)/
1400 F 100KS1
305
(100) orientations, can be as high as in Figure 4 (Dalal et nl., qualitatively resembles that of discussed earlier is compositio equivalent to the y-matrix, and shows very high creep anisotropy. Of course, in light of the fact that that the creep anisotropy i s also affected by the ~recipitatesize as shown in Figure 3, the p~enomenaare obviously complex and should not be oversimplified. Nonetheless, if irnproveme~tin creep resistance were the only objective, it is clear that a (111) oriented single crystal of nickel-base y’or y/y‘ would be at least a factor of2X inore creep creep-resistant than (100). analytical interest in rnodeling the nature of creep anisotropy for predicting the multiaxial of notches in single crystal superalloys ( 2000), its value in discerning the basic dis~ocation structure and alloying effect cannot be overlooked. Similar studies of creep as a function of orientation for highly alloyed and two-phase ~iAl-based single crystals are limited (Noebe and Mechanical properties of sucli alloys have been primarily investigated near the (100) orientation (Darolia and Walston, 1997; Garg et al., 1998). Creep anisotropy studies of other intermetallic single crystals are lacking, perhaps due to processin di~culties.Especially the behavior is anticipated t be very interesting in non-cubic intermetallics, such as orthorhombic Ti,AlNb and i,, with their lower symmetry. The lower s y m ~ e t r yshould present even greater opportunities to orient the active slip systems with reference to the principal stress direction and enhance creep resistance in some ‘hard’ orientations. Note that creep anisatropy studies of polysynthetically twinned (PST) crystals of y-TiAl do not fit the framework of the preceding discussion. As discussed later, a highly aligned lamellar rn~~rostructure aiid perhaps other Factors play more dominant roles than
2000 F 2 0 K 5 f
1800°F/36 KSI
0
TIME (HOURS)
TIME (HOURS)
‘0
100
200 TIME
300
400
500
(HOURS)
Orientation dependence of creep bchavior of SC IN-6-7 (Ni- 13.5Mo-6.1MI-6.8Alwt.%) single crystal superalloy. From Dalal et al. (1984)
orientation of slip systenis in ST crystals (Parthsarthy et al., 2000).
3.1.2 Grain Texlure
Ideally, creep anisotropy is expected to manifest itself if there is a strong grain texture. For example in the simplest case, directionally solidified { 100) oriented columnar-grain superalloys such as Mar M200 and MO02, practically behave like ( 100)-oriented e crystals. It is interesting to note that rapidly solidified and recrystallized, high-Mo superalloys were initially claimed to have high modulus and superior creep resistance (Cox and van Reutl], 1980). Subsequently it was t is covered that both characteristics were owing to a strong (111) fiber texture, and similar
when the grain size is much finer than the thickness of the specimen, it is reasonable to assume a random orien~atioii.In such a case, the anisotropic behavior of individual grains inay be ignored, as it is averaged out, and can be accouiited for by the Taylor factor. The real challenge arises when the grain size becomes compamble to the section size of the specimen or the component: There, unless the grain orientation is accounted for, a wide scatter in creep behavior may uch has been the case with transverse -grained materials and creep properties of col bicrystals of superalloys d O’Hara, 1996; Shah and Cetel, 2000). As sh igure 5, scatter in the erties of (100) oriented columiiar M200 may be attributed to a grain orientation ranging from dist~ibutionin at for (100) oriented columnar800 T--775 750
i
CE
-i IQ000
igure 5 Comparison of stress versus rupture life at 1400 “F for Mar M200 1- Hf for single crystal and columnar-grained (CC) material. From Shah and Cetel (2000)
grain material, any direction in the transverse plane can only be those lyin in the (100) plane. Note also that in Figure 5 , scatte in the data extends from being equivalent to the poor creep resistance of (110) orientated single crystals, to the superior creep resistance of (100) oriented single crystals. The dominant effect of grain orientation on creep behavior is well supported by a detailed study of DS IN738LC uested et al., 1988). Using electron back s~attering patterns to assess creep strains, they clearly demonstrate that cracking and/or cavitation in transversely oriented grains occur most clearly when. the adjacent crystals exhibit evidence of different levels of creep strains owing to different orientations. The problem is exacerbated by significant lattice rotation in the large grains with high creep strain. In the preceding discussion the roles of grain boundary sliding, environmental effects, enhanced grain boundary diffusion, and grain boundary segregation effects, were deliberately ignored to e i ~ p h a s i zthe ~ role of plastic anisotropy and resulting strain incompatibility, However, again McLean and Strang (1984) and Quested et al. (1987) have shown that while grain boundary segregation of low melting elements such as Bi, Sb, Se, and Te reduce creep-rupture life and fracture elongation, the failure occurs only along the grain boundaries normal to the stress axis. Moreover study of Bi-doped Mar MO02 shows that degradation is more severe in equiaxed material than in transverse columnar grain inaterial, and it is always owing to adjoining grains with large differences in creep strengths. In much of the p~~blishedliterature on grain-size effects, the preceding viewpoint is ignored because of a lack of data and knowledge of creep anisotropy, and an inevitable but perhaps ‘distracting’ variation in grain boundary microstructure. Obviously, creep behavior of polycrystalliae intermet~llic-based alloys must be controlled by both intergrann~~lar and transgran~~ar bebavior and ~nteractionsthereof, However, with increasing availability of modern tools such as orientation imaging microscopy (OM) to determine grain texture and strain condition, paying due attention to the transgranular behavior is very fruitful, as has been demonstrated by Quested et al. (1987, 1988).
Global spending of upwards of tens of millions of dollars over the last 30 years on improving the creep resistance of nickel-base superalloys is a testimony to the highly empirical nature of our understanding of the effect of alloying. It is not an exag~erationto say that
307
Creep Dii3bsion coefficient, D, and activation energy, (2, for A1 and Ti, and for ~ i ~ ( A 1 . T ~ ~o~pound _
_
_
Values at 1000 “C Q for A1 D for Ti kJ/mol cm2/sec
cm2/sec
Do for Al cm2/sec
1.7 x 10-I’ 8 . 2 10-j2 ~
6.6 x 10-4 6 . 6 10-4 ~
185.0 211.0
__
__
-
D for Al
Do for Ti crn2/sec
Q for Ti kJ/rnol
-
__
~
Ni,AI Ni,(AI,,Tio2) NiWO 6%) 4) Ni,(Alo,Ti,,) Ni3(Alo4Tio6)
3.1 x 1 x 10-’ 2.9 x 10-12 3.1 x
many of these eflorts were focused on creep strength, because the impact of the gain in low-teniperature strength has been modest compared to the influence of enhanced temperature capability as measured by creep strength. While all this is true in a broader perspective, it i s deceptively simple to characterize the alloying trend as merely increasing additions of refractory elements, especially Ti, Ta, MO, W, and Re. See Erickson (1995) for a compilation of recent developmen ts in single-crystal superalloy compositions. The phenomenology of dislocations and the effects of alloying in L1 intermetallics and Ni-based superalloys has been reviewed by Westbrook (1996), who also defines some of tlie unsolved problems that impede continued development of these materials. Exploration of the creep behavior of inte~etallics also shows the refractory elements to be potent creep strengtheners. Comparison of minimum creep rates of binary and ternary alloyed intermetallics based on FeAl, y-TiAl, Ni,Al, NiAl, Cr,Si, and MoSi, in Table 3, clearly shows that the minimum creep rate can be decreased by orders of magnitude by alloying with any of the refractory metals. Interestingly, note the major effect of the addition of Ir in NiAl by Chiba et al. (1998). However, in-depth alloying studies of various intermetallic-based systems such as y-TiAl and NiAl abundantly show that the latitude of alloying is limited. In ordered intermetallic systems, away from terminal solid solutions, the complexity of phase fields and limited off-stoichiometry of the ordered structure constrain the addition of alloying elements. Nevertheless, in appro~matelya decade - a relatively short time - very modest amounts of alloying additions to MiAl have brought the creep resistance of the singlecrystal alloys AFN-12 and AFN-20 to levels comparable to those of superalloys ( arolia and Walston, 1997).
Whether alloying elements improve creep resistance by solid-solution strengthening or order strengthening is a
242.8 228.1
-
-
__
-
2 . 3 ~10-” 2.1 x 10-l2
1 . 9 10-6 ~ 1.1 x 10-‘
145.3 139 4
7.85 x 10
3.3 x 10-6
137.3
l2
matter of site occupancy. In either case a decrease in diffusivity leads to to an increase in creep resistance. In disordered structures, there is little choice but to characterize the effect of alloying additions as solution strengthening, until a tendency for short-range order (SRO) or clustering is discerned by more sophi~ticated techniques. For example, till the advent of transmission electron microscopy, or the application of neutron diffraction, sluggish ordering of Ni2Cr was referred to as the K-effect in Ni-Cr solid solutions. Since then, both theoretical studies (de Fontaine, 1975), and sketchy data on binary phase diagrams do suggest similar clustering tendencies in many NiNi7C06)aiid refractory-metal solid solutions. Interestingly, often when such clustering tendencies lead to a non-cubic structure within a cubic solid solution, e.g. Ni,Cr in Ni-Cr, a domain structure is formed. It may be argued, though, that in inany of the Ni-X binary systems cited above, the order-disorder transformation temperatures are known to be relatively low, and the influence of SRO on the high high-teinperat~recreep behavior may be questionable. However, in practice we are dealing with multicomponent solid solutions, where the theoretical understanding of short-range order is complex, and einpirical data are limited. Indeed, an atom-probe study of coniponent superalloys does show a correlation be improvements in creep resistance and the presence clusters in the y-solid-solutio (Blavette et al., 1988). ~nfortunate~y, 111 a two-phase system it is difficult to completely isolate the solidsolution hardening effects of alloying additions from other aspects of microstructure, sucli as the matrixprecipitate interface and lattice misfit; but given that an improvement in creep resistance is achieved with additions in a wide variety of the second generation of single-crystal superalloys (Broomfield et al., 1998; Cetel and Duhl, 1988), and in the nickel-base eutectic alloys (Lernkey and Machlin, 1985) with different niicrostructure, suggests something more fundamental to the Ni-Re solid solution. Un~uestionably, while our 9
understanding of such clustering beliavior in multicomponent alloys is poor, the authors believe that such tendencies must in~uencethe long-term iiistabilities of nickel-based solid solutions to the formation of undesirable topologically closed-packed pliases. Interestingly, it nized that in two-phase nickel-base superalloys, the high-~emperaturephase-instability of the solid-solution hardened matrix and high creep resistance go hand in hand. This aspect is further discussed in the next section with reference to stacking fa~iltenergy and electron-vacancy number. The ~lusteringtendency is not limited to terminal solid uper-ordering can occur within an ordered well. An example of such a clustering of G-phase (Ni,,Hf6Si7), tendency i s the p~ecipit~ition kave even a trace amount of Si again, the clustering ratures only, and its -temperature creep is considered to be solid~sol~~tion strengt~ening, as the phase dissolves. The critical point is that, without the knowledge about the cl~steringtendency, it may be difficult to understand why some intermediate solid-solution compositions may show optimun creep resistance. In wellc~aracterizedordered intermetallics, a description of site occupancy is useful, but without a quantitative characterization of the degree of ordering, it may be treated as sublattice solution strengt~ening. 11 discuss this with reference to the Ni,(Al, Ti) ,where it has been shown that the occurrence o f slowest diffusion around 12.5 at.% Ti correlates well with the highest degree of orderin
~nfortunate~y, the pre-exponentia~ parameter A' is found to be about 4 x 1Ol2, instead of unity, and so equation (12) must be regarded as an empirical law without an ade~uatetlieoretical foundation (Mabarro and de Villiers, 19951, p.76. h se~i-theoretical,the preceding correlation allows one to u~derstandwhy most unstable nickelbase superalloys with a solid-solution-hardened yinatrix and an electron vacancy number of N v w 2.5, tend to be the most creep resistant. ~ ~ l c u l a t i oofn the electron vacancy number, Nv, or (10 ininus the number of d electrons), for the y-matrix is traditionally used to assess the stability the composition to the formation of TCP phases ( cker, 1970). A ~hysicsbased model suggests that NV can be related to the g fault energy in transition metals as shown in 6 (Papon ei al., 1979). Very simply, Figure 6 is an attempt to predict the stable crystal structure using a single atomic p~rameter.The two curves represent results of different calculatio~s.The point of interest in Figure 6, is the intersection of the two curves around NV 2.5. Clearly the physics suggests that in solidsolution alloys of transition metals, stacking fault energy is lowest around Nv 2.5, and that is the condition at which the FCC structure starts becoming unstable with respect to other close-packed str~ctures. Essentiall~,if creep resistance is enhanced with low stacking fault energy (SFE), phase instability is inevitable when the SFE approaches zero. Similar fundament a1 physics-based rationali~ationshave not been developed for other less mature systems, but exploitation of phase instability in developing creepresistmt pTiAl is ~ r o ~ i s i n g . N
N
3.2. I. 1 Stack~ngFault From the point of view of dislocation inechanics, improve men^ in creep resistance with alloying may be rationalized in terms of lowering the stacking fault energy in solid solutions with closed-packed disordered structure and ~ o ~ p l e x - s t a c ~ i n ~ - fand a u l tanti~hasey in ordered structures. Low fault extended dislocation-core structures, which inhibit cross-slip and dislocation climb, and thereby slow down the recovery. ~ n ~ e ~e od h a m e dand n (1974) have shown that for many pure metals and ~ u - b a s solid e ~ solutions, creep rate can be correlated to the third power of the stacking fault energy y as
i =~
'
(
~
/
~
~
)
3
(
~
~
~ (12) ~ /
3.2.2.1 Degree of Ordering ~ i ~ u s i obehavior, n which strongly controls creep resistance, is further affected by the degree of ordering in ordered structures. For example Ni,Al (with the closed packed L1, structure) has a first order orderdisorder rans sit ion based on the nearest neighbor (Br agg-W illiam) approximation, whereas NiA1 (wi112 a tructure) has a second . If the respective me assumed to be the order-disorder transition temperatures, the variations of degree of o temperature can be compared, as in 1F basis, it may be argued that ~ i f f u s i o nmobility ~l at the same absolute temperature is likely to be higher in ~ NiAl ~ ~ than 4 ) in Ni,Al. Such a kinetic extrapolati~nbased
309
Creep
ure 6 Theoretical plots of stack~iig-faultenergy versus d-band clectron- or electron-vacancy n u ~ b e r( N v ) (Papon et al., 3979). The solid-solution-hardened y-matrix in mast cre~p~resistant nickel-base superalloys has an NV o f approxiniately 2.5
on thermodyna~icparameters, however, is not well accepted, even though it is known that in C u ~ n ( ~ 2 ) aker, 1995), a large increase in creep rate occurs upon disordering, and that in Fe,Ai (StoloE, 199S), a low order-disorder transition temperature limits the high-temperature creep resistance. Though not rigorous, such thinking allows one to rationalize as to why the creep resistance of ~iA1"basedcoatings with open structure is lower than substrate superalloys containing Ni,Al, with their close-packed structure. 3 2 2 . 2 Effect of ~ t o i c h i o m ~ ~ r y
In ordered i n ~ e r ~ e t a ~ ~the i c s degree , of ordering is further influenced by composition relative to stoichiometry. The situation is even more complex in ternary and ~ u l t i c o ~ ~ o n eordered nt i nt ~ r ~ e t a l l i cwhere s ideally more than one ordering parameter i s necessary to describe site occupancy. However, a loss of order does not nec~ssarilylead to an increase in di~usivity and a loss of creep resistance as one deviates from the ~ ~ ~ ~ cc ~~~ ~~ ~ ~ o In ~s i fact ~ t i oethe ~~ . variations r i c in diffus~vityand creep resistance are functions of crystal struct~reand b o n ~ i ncharacte~istics ~ of the elements. We shall discuss these issues with specific reference to N&A1(and superalloys) with Llz (cP4) structure and NiAl and s i ~ i l ian~t ~ ~ e t a l l i with cs
concentration on either side of the stoichio~etric composition. Three representative results o f their study for Ta- V-, and CO- modified Ni,Ai, are presented in Figure 8 (a), (b) and (c), respectively. Behavior of binary and Ti-ii~odifie~ Ni3Al, are similar to that of Ni,(Al, Ta), but occur at progressively higher creep rates. The results show a sharp isc continuity in creep rate at the stoichiomet~iccomp~sition.Also note that, while the rate of variation of creep rate with constant for Ni,(Al, V), it is weak for Ni,(AI, Ta), ~ lthe , ~ i " r i c hside of the very strong for ( ~ i , ~ o ) ,on stoichiometry. Though the reason for this behavior in the latter two cases i s not well un reasonable to assume that both V and 1
a. a.
l?0.5 CD
.E 0.4 e 0.3 0 Q)
0.2
0.1
a Ni3(A1,X) and ~ ~ ~ ~ r a ~ a yexhaustive, s In l an coinpre~$ive-cree~ study of binary Ni,Ai, and ternary nzodifications with 5 ajo addition of Ti, Ta, V, and CO, Wayashi ef al. (1991) have shown that steady-state creep rates in all cases decrease with increasing nickel
Figure 7 Comparison of degree of ordering in NiAZ vs. Ni,AI, assuming the order/disorder transition occurs near the melting point
Mechimical Propertics
310
1x10*
WO-'
f
I
i -
1x10'
a
\r
v)
M,(AI,T$) ,150MPe
1x10-'
0 1123K
I MO-'
78 75 74 M Concentratton / nt%
13
77
500 [
78 75 Td NI Concentration / sf%
1x10-' 77
73
A
1223K
a
1123~
76 75 74 M Concentration / at%
I
I
\
0N b i A i V i 0 (Ni.CoJ,Al 0
%AI
0
3
8 0 0
A
Q
%
.-
NI Concentration /
51%
Ni Concentralion / at%
Figure 8 Effect of stoichiometry on the compressive steady-state creep rate of (a) Ni,(Al,Ta), (b) Ni,(Al,V), and (c) (Ni,Co),Al, from Hayashi et al. (1991), reproduced with permission of the Materiafs Research Society. Analyzed variation with stoichiometry in (d) stress exponent, (e) activation energy, and Q pre-exponential factor, for all binary and ternary Ni,Al material. evaluated by the authors
311
Creep
strong occupants of A1 and Ni sites respectively, as assumed. Analysis of the data show that while the stress exponent (- 3) does not vary with alloying additions or with deviation from stoichionietry (Figure 8(d)), the activation energy iiicreases with increasiiig creep resistance, ranging from 150-500 kJ/mol (Figure 8(e)). ~nfort~inately, as shown in Figure S(f), the latter is also accompanied by orders of magnitude variation - 10-6 to 107- in the pre-exponential factor of the power-law relationship described by equation (l)! Once again, this brings forth the inadequacy of using oiily the stress exponent and activatioii energy while ignoring the pre-e~ponential factor as a guide to developing creep-resistant alloys. At least one fundamental basis for the variation in the pre-exponential factor has been succinctly demonstrated by a diffusion study of Ni,(Al,Ti) by Larikov et al. (1981). In a teriiary intermetallic, both the site occupancy of the third element and the degree of ordering, influence di~usivity.As listed in Table 2, while both activation energy and Do go through maxim^ around ~ i ~ ( A l ~ ~for T D,,, i ~ ~the ) , inverse is true for DT,. As shown in Figure 9, this composition corresponds to maximum ordering as measured by Xray diffraction, and it also coincides with the miniinum in the diffusion mobility of nickel. It is interesting to note that the apparent activation energy of ~ 4 0 kJ/mol 0 from Figure 8(e) for creep of stoichiometric Ni,(Al,,8 T&), is significantly higher than -211 kJ/mol determined by diffusion experiments in Table 2. However, also note that the variation in the pre-exponential factor with stoichiometry, derived from the creep experiments in Figure 8(f), i s also higher than the variation derived from the diffusion experiments for Ti additions. Clearly diffusion can account for some variation in the pre-exponential factor but it is difficult
to isolate the diffusion contribution from other aspects such as anti-phase boundary (APB) energy (Flinn, 1960), unless careful creep and diffusion experinients are done for the same material. In any case, isolating all the contributions is inherently impossible, as the more creep-resistant nickel-rich stoichiometry leads the ~ ~ a t e r i ainto l a two-phase field more akin to nickel-base superalloys. Here the contribution of the two-phase m~crostructure formed by spinoidal type decoi~positionis major. There is little evidence that the creep resistance or the two-phase alloy can be exceeded by its constituent single phase ordered i n t e ~ e t a l l i c(Shah and 1987). NiAl and other B2 ~ ~ t e r ~ e t a For l l i ~intermetallic ~~ compounds with B2 structures, diffusional behavior mirrors the variation af constitutional vacancy concentration with alloy deviation from stoichio~etry. However, the behavior of constitutional vacancy concentration is strongly dependent on the pair of elements forming a specific €32 compound. The important point is that both activation energy and the pre-exponential factor Do can vary with offstoichiometry, as shown in Figure 10 for But in the case of CoGa(B2), both Do and CO and Ga increase slowly with increasing Ga concentration (Baker, 1995). Once again it is clear that a knowledge of crystal structure, activation energy and stress exponent alone cannot capture the whole picture. Differing atomic boiiding between different elements affects the diffusion mechanisms of the two species (correlated or unco~related),and may lead to different levels of creep resistance. In fact, as shown in Figure 11 (Jung et al., 1987) for stoichiometric (Fe,Ni)Al, the max~mum in creep
able 3 ERect of ternary refractory element addition on ~ i n i creep ~ u ratcs ~ of several binary inter~etallics Alloy
("0)
Fe-28 A1 Fe-28 AI- 1.5W Ti-52.3 A1 Ti-40Al-7.5Ta Ni-24.1 A1 Ni-19.1 A1-5Ta Ni-50 A1 ~i-lOlr-5OAl Cr-23Si Cr-20.3Si-34.1Mo MO-66.6Si MO-69Si-12.6Re
Temperature
Stress
873 K
200 MPa
I255 K
100 M P n
1223K
100MPa
1373K
100MPa
1473K
100MPa
1673K
103MPa
Min. creep rate
Source
2.4 x 10-6 s-' Zhang et al. (1 998) 4.4 x 10-"-' 1.0 x 10-6 s-' Valencia et al. (1990) 2.7 x 10-6 s-' 1 . 6 10-6s-' ~ Hayashi et al. (1991) 1.3 1 0 - 7 ~ 1
312
~ ~ ~ c h a ~Properties ical t 70
4
1 60
I50 I 40
130 1
120
1
from Elsevier Science (a) ~ ~ r i a t i oinn intensity ratio of fundamental I, and superlattice I X-ray diffraction lines and (b) s e l f - d i ~ ~ s ~ o n compared to a simple creep test, these are difficult coefficient of Ni, AI, and Ti, with Ti content in Ni,(AI,Ti) parameters to assess experimentally. ~ u r t h e r ~ o r e , (Larikov et al., 1981) these ~ a r a ~ ~ tdo e rnot s capture the role of dislocation-
resistance at 10 at.% Fe coincides with the minimum in interdiffusion coefficient.~nfortLinatelyin this case we have no i n f o r ~ a t i oon~ the degree of ordering, but it is reasonable to assume that it must be a maximum around 10 at.% Fe. According to Sauthoff (1991), it i s not uncommon to observe a higher apparent activation energy for creep than for diffusion, especially at higher teniperatures, and this difference may be attributed to the temperature dependence of the pre-exponential factor. To avoid this discrepancy, the diffusion coefficient is considered the most important parameter; and, as shown in Figure 12, the creep resistance of binary and ternary 2 aluminides can be correlated with difhsion coefficients. The straight line through the data corresponds to the Dorn equation for dis1ocatio~creep, similar to equation (l),
The plot in Figure 12 provides a rational explanation softer FeAl to NiAl improves the creep resistance. It is clear that determination of the ordering parameter or site occupancy and diffusion coefficient can throw more light on the role of ordering. However,
core structure and microstructLire in two-phase intermetallic alloys. Undoubtedly, a lack of cohesive ~nderstanding o f diffusion and dislocation core structure, in terms of atomic bonding in ordered intermetallics, buries the special role of i ~ t e ~ i e t a ~ l ~ c s within the apparently successful applicatio~of the ~arametricequation.
Among the two-phase alloy systems developed with useful high-temperature creep resistance, ~recipitation~ hardened nic~e~-basesuperalloys, precipitationhardened NiAl-based alloys, eutectic NiAl-based alloys, and ~amellary-TiAl are most notab1e.I We can certainly add two-phase Nb- E-Ti-Si-based alloys (Bewlay et al., 1996, and the chapter by and can also add steel to this list, if we consider Fe$ as an inte~etallic. However, we shall limit our discussion to the foriner two as ~recipitatio~-harde~ied system. systems, and y-TiAl as a 1am~llar"stren~thened 'Naka and Khan in their chapter review design of alloys that are similar to pre~ipitation~hardened Ni-based superalloys.
313
Creep 1
.-c I
0
1
i~~~~ IZ (a) Creep r e s i s t ~ n(at~ ~i = I O - ~s-'> and (b) estimated mterdiffusion coefficient L? as iz function of the iron content for stoichiome~ric(Fe, Ni)Al at various temperatures. From Jung et al. (39871, r ~ ~ r o with ~ ~ p~~ rc~ i~s sdi oonf the ~ a t ~ r ~Research als Society
3.3.1 ~~~~~~~~~~~n ~
~
~
~
d
~
~
i
~
~
~
3.3.1. I ~ ~ c ~ ~ l - perall ~ a salloys e d
iz
In comparison to the d e v e l o ~ ~ ~ of e n ts t r e n g t h e ~ i ~ ~c m e c ~ a n i theories s~ for ~ ~ d e r s t a n d~i in~~h - s ~ r a i n ~ r a t e tensile or compressive strengths, rnodeling of creep beliavior of precipitation-hardend systems is sparse aid not well recognized~In any case, in a series of two pnpers, Carry and ~ ~ r (1977, ~ d 1978) e ~ have ~ e s c r ~ ~ e d the essential elements of creep behavior of precipitat ~ o ~ " h a r superall~ys. d e ~ ~ ~ ~ o w ~ vbefore e r ~ we discuss the conceptual model, a ~ e s c r i ~ t o~foancotigle of wellv) accepted empirical correlations, is in order. ClJ L E~pirically,as shown. in Figure 13 irkin in and Kancheev, 19671, it is known that creep resistance is maxiinized when the € ~ r ~ c ~ ~ ~ i t (7'-y) a ~ ~ lattice - ~ a t r ~ x br L misfit is nearly zero. Since then ~ ~ ~ attempts e ~ o U ~ s have been made to model and r n e a ~ ~the r e misfit, but the issue is fraught with ~ ~ ~ bofl ee ~~ p s~ r i ~ e n ~ ~ ~ ~ e t ~ ~ b ~~l iet ay .s u r lattice ~ n ~ misfit at a given temperature of interest for creep ~ ~ € o ~ ~ ainvolves t i o n hight ~ ~ p e r a t u rX-ray e diffraction, which is a non-trivial eradeavur, Nonetheless, it is generally well accepted that ilzost o ~ t i ~ ~ s%~e~d e r ~with l ~ stable o ~ sc ~ b o ~ ~ a ~ p~~~ig~ i tt ~r ~t ec t ~must r e s have close-to-zero misfit. Secondly, as ~ l ~ in ~ Figure w ~ i 14 ~ ~ ~l ~~ ~iti is ~l ?, , also wet1 known that creep r e s ~ $ t a is ~ c~~ i a ~at ~ ~ i ~ e ~
10"7s"'
\
n CO
If3
m
I
some inter~ediateprecipitate size. As-solutioned and rapidly cooled superalloys with very fine y' size are known to display high yield strength at lower te~peratures~ but poor creep resistance at higher t e ~ p e r a t ~ i ~On e s .tke other extreme, overaged alloys with very coarse preci~itates t r ~ c t ~ have r e low yield strength and are also known to be weaker in creep. 0th of*these results, as well as n L ~ ~ e r o transmisus sion e l ~ c t ~ ~o i~~i ~ ~ o sobservations ~ o p i c of dislocation beliavior d ~ ~ r creep, i n ~ are consistent with a simple
model as follows. In general, much of the ~ i ~ l o c a t i o n glide tinder creep cond~tionsis limited to the disordered y - ~ a t r with i ~ ~screw dislocations bowing out between the precipitates, leaving edge dislocations in the y-y' interf'stces. This is well i l ~ u s t ~ ~ byt ~TEM d micrographs presented in Figure 2 5. The ordered y' p~ecipitateis d i ~ c ~tol shear t because of the formation of antiphase boundaries that require superdislocations, However, if the precipitates are small, the dislocation^ can bypass the ~ r e ~ i ~ iby ~~tes climb. Inhibition of dislo~dtionglide i s a h a r d e ~ i ~ ~ process, and dislocat~o~ cliiftb is a r e c o process, ~ ~ ~ ~ and a balance ~ e t ~ ~ the e e two n may result in steadystate creep. In this respect the large p~ecipit~tes can delay recovery (soften~~g), by requiring a tonger time for the dislocation climb, which occurs via the y-y' interface. Since d i s l o ~ a t i o ~ climb is a d i ~ u s i o ~ ~ controlled process, any significant y-y' misfit (positive i s vexpected to speed the recovery and or i i e ~ ~ t ~ e~ enhance creep rate. If the y' ~ r e c i ~ i t a size t e i s very large, the climb process may be delayed, but at a constant volume fraction of tlie ~recipitatesthe matrix c h a n ~ e ~~si d e nr ~ ~ u i r lower i n ~ stress to glide the screw d~sloca~ions, thus e n h a n ~the i ~ strain ~ rate. Indeed, though, as shown by Pearson et at. (19801, creep resistance cafl be ~igni~cantly improved if the y' precipitate is elongated (y' rafting), without much change in tlie interparticle spacing, and thereby s~gni~cantly slowing down the climb process. Such a structure may na~u~ally form early in the creep process because of large y-y' misfit or can be d e ~ i b e r a t e ~ ~ p r e ~ o ~ eunder d stress. Climb of inter~ace edge dislocatio~sis the principal con troll in^ ~ e c h a n i s ~ ~ ,
creep
3 15
< 0.01 I - . QB-~ Z ~ igure IS (a) initial precipitate structure before crccp tcstlng of a single-crystal superalloy N ~ - ~ C ~ - ~ M ~ - " I ' F ~ - S A Q.01C(b) Edge d ~ s l ~ networks ~ a ~ ~1x1othe~y")~' interface after 2.58 hrs and 1.7% strain of a (103) oriented sample, creep tested at 850 ~ ~ MPs./ From ~ Carry ~ andQ Strudel (1978), reproduced with ~ e ~ ~ i shm s i oElsevim ~ ~ Sclence
and slowing this step - either by lower in^ di~L~sion via all~yin~ low , interph~semis-tit, or elongated structure - all tend to improve creep resistance. As s u ~ i ~ a r i 2 ebyd Carry and ~ t r ude(1978), l for the clinxh ~ e c h a n i ~ to m he c ~ ~ n t r o l l the ~ ~ ishear g ~ stress must be below it critical stress, z,, given by the Orowan spacing L in relationsh~pin terns of the interp~~rt~cle this equation,
on those whose sole objective is the d e v ~ ~ o p ~ of ent
creep-~esjstantalloys. One would assume that, since cutting y' is a difficult process, ~ingle-phasey' should be more creep r ~ ~ ~ s t ~ n t . ~ o ~ e ~ine spite r , of a long sustaine~eflbrt in tliis direction, there is no evidence that sucli i s the case. Xi1 fact Shah and Duht. (1987) have shown tbat even with a highly alloyed 1'' c o ~ p o s ~ tei ~~ ~~ i, v a to ~ eoiie ~ tin a coinplex supera2loy, the creep resistance of the superz,= 2 Gb/L (14) alloy cannot be ~ x c e e d e ~ . studyiiig creep behavior o Above zc, strain would proceed by glide of dislocations noted that even a small volume fraction of Ni solidthat bow out and leave Loops around particles, thereby solution phase enhanced creep resistance. As discussed raising the internal stress of' the material. before, all this is ~onsiste~it with the fkct that creep stra~ningcould take place by climb of dislocations resistance improves with increasing Ni concent rat i ~~ around the particles. One of the theoretical difficulties on either side of stoichiometry (see Figure 8). Yet, it is with this model i s that when interface and pipe an enigma, that while y' ~ r e c ~ p i ~can ~ t inhibit ~s d i ~ ~ s i oare n conside~~d to be c o n t r o l ~ i ~the g ~ stress dislocat~oii~ o t i o iii i ~the weaker ~ ~ ~ i ~and~ the ~ t yr ~ x , expoiiei~tis expected to he around 1 based on the welly' interface caii slow down dislocation climb, tlie single accepted Nczbarro model for grain boundary creep, but s ~ n ~ l e ~ ~y'hcannot a s e slow down the creep process any stress exponent is in the range of 3 4 . better. One potential e x ~ l ~ ~ n a tmay ~ o n be that a trudel ~ l ~ and 7 ~ nxmy ) others have dislocation-free ordered phase is produced through a suggested that this must be rationalized by assuming solid-state reaction. It is known t h t the t h e o r ~ ~ i c ~ l an internal stress gi in tw~-pl~ase materials, such that the egective stress 6, is defi~edas strength can be achieve^ in w hi ske~~, o w i n ~to their d~s~ocation-free nature. It is possible that any presence 6, = (Ta - 6i (15) of a disordered y-tnatrrx allows the ordered phase to be th~reby~ ~ ~ c l any u ~plastic i n ~strain The a r g u t ~ eworks ~ ~ i i i a t ~ ~ ~ a t ~ cin a l lbyr i ~ g ~ n g dislo~ati~~i-free, contribution from the large volume fraction of y', down the stress exponent in equation (1)? and is in~ conceptually appealing, but it lacks a wel~~defined except at higlier stress where dislocations o r i g i n a t i ~ the~ y'~ ~h r e ~ ~ ~ ~ ~ physical origin. ~ x ~ e metkods ~ ~ ehaven been ~ ~ the ~ y-matrix can shear t h ~ o ~ Alternat~v~ly~ it may also be a r ~ ~ that e ~ the , most suggested to ~ e t e r ~ i nthe e internal stress, creep-resistant Ni-rich y' with tlie lowest difrustvlty methods fail to provide Q priori guidance. cannot exist as a single phase w i t ~outthe presence of i ~ g basis, such a r g ~ e n tare s lost with no g ~ ~ i dphysical
i-rich ~ i s o ~ d e r ey.d onetheies~the pivotal role of the y-y' interfa in ~ ~ ~ r creep o v resistance i ~ ~
th. As we shall discuss with reference to c o ~ p o s i t e stlie ~ coherent nature of this y-f interface i s ~ ~ ~ the h most ~ ~ ~ p si ~ attribute n ~of the ~ nickel~ ~ base s ~ p e ~ a I ~ o ~ s .
~
t
d that many refractory elements, r, Nb, and Ta, have l~mitedsolid NiAl, and c o ~ ~ e ~are~effective e ~ t l ~ ~ r e ~ i ~ i t a t istren~theners, on as two-phase fields are attained even at low conceiitratios (Noebe and arolia and ~ a l s t o n ,199'7; Liu and e 16 Weak beam image taken using g = 002 r ~ ~ e c ~ i o n of NiAI-2Hf aged at I173 K for 100h and crept to 28% at work on two-phase NiAl1073K under a compressive stress of 35OMP'a show^^^ ements, systenmtic eEorts d e f o r i ~ a t i o n ~ i ~ d ~dislocations, ced Precipitates are rotated have been made to u ~ d e r s t athe ~ ~creep behavior of d ~ creep r ~ ~~ f ~o ~ ~From ~ a tOh-ishi ~ o ~ er', nl. (19971, reproduced with permission from Elsevier Science
aNiAl(C14-Laves phase) The most c r e e ~ - r e s i ~ t ~ ~ ~ i t d AFN-20 also rely on. of l o w - t e m ~ e r ~ t ~ prere
to note that ~ ~ p ~reci~itation ~ ~ s eis an. ~inantic~p~ted ~ o n s ~ ~of~ trace e ~ camotrnts e of Si from the ceramic shell molds used for casting. ~ o n e t ~ e l e sthe s , benefit of p r e c ~ ~ i t ~ t hi oan~ ~ ~ n i n T IS well d e ~ o ~ s ~ r ~ t e d ~ r o c e s s eto ~ be free of rders of m a g n i t ~ ~ e i ~ ~ r o v ein~creep ~ ~ i t wrth fine ~ r e c ~ ~ ~ ~ ~ t ~ o ~ Figure 16, is apparen ~l ethat of the scale of the ~ i i c r o ~ ~is rc o~n ~i ~ta ~r ~rbto s u ~ e ~ ~inl Figure ~ o ~ s15, Indeed, the ~ i c ~ ~ s is t r ~ ~ ~ ~ r e of l o w - v ~ ~ ~ ~ e -sraperfrac~~~~ alloy, ~ b v j the ~ ~analogy ~ ~ ~ y cannot be taken too far. since the matrix in the present case is an ordered ~ n t ~ r ~ eNiA1, ~ ~ l and l i ~ the a ~ ~ ~ r e ~ i p iitself t ~ t is~ a t e r ~ inte~nieta~lic.
7 ~ a r i a tof~ stram ~ ~ i rate with the ~ ~ ~stress ~ ifore d binary ~NiAI and MiAl-2Hf con t a~i i ~ i nfinc ~ ~ ~2 , - ~ i ~ ~A ~ ~ ~ precipitates. The previously reported data o f binary N S f In precipitation- and dispersion-ham-deledtwo-phase are plotted for comparison. From Oh-ishi et ul. (1997), o i ~ Elsevier ~ ~ i e ~ c ~ ~ a t ~ r i athe l s ~ e f o ~phase, ~ ~ i ~g o ~ ~ called o ~ the l y ~eproducedwith ~ e r ~ i s s ifrom
3J.2
~~~@~~~~
~
~
r
~
Creep
3 17
urgers vector ~ r o v i d ~ a sscale factor matrix, is general~ycontinuous^ and the niicrostructure acing. owe^^^^ note also Il can be t ~ ~ ~ast largely e d i s o ~ ~ ow~~i ~c t~hthe e r~ a t e r ~ a ~ be insen~itiveto L for L > l pm. ~ n t ~ nstr s~c is po~ycrysta~l~ne or siiigIe crystal. Thus creep behavior only results when the scale of the ~icrostructureis is well understood in terms of the scale of the sufficiently fine to influence dislocat microstructure and the orientation of the single crystal the same way as interparticle spaci owever, in y-TiAl, the deformiiig y superailoys i s in equation (14). Lac a single grain or a lamella within a this aspect has stimu~atedthe simplistic iiotion of grain flanked by a2 lamella in polycrystai~inematerial, composites to appear very ~ t t r a c ~ i vtame e and a or the entire la~el1ars t r ~ c ~ ucan r e be aligne~tfiroughout the body in a po~y"synt~etica11yt ~ ~ n ( ~~ i ~e T~ )but in vain. Only composite ap~roachesmore akin to dispersion harde~iing have met with some success le crystal. The d e ~ o r ~ a t i oisnno longer contiiiuous (Sadananda et al., 1993). t h r o ~ ~ g l i othe ~ t grain but is continuous within each lamella extending across the entire grain. The dominant role of anisotrop~cor highly aligned lamellar micro3.3.3 Composites structures 1s we21 d e i ~ o n s ~ r ~ ~ int ePST d crystals by ~ a ~ t h s a r a t hety al. (2000~~ Their results clearly show fn the zeal to improve the fracture t o ~ g ~ n eof s sbrittle that ~ a~ r e ~ ~ep s ~ ~ is~i ~~ nc c~ e~e when v e ~the ~ ~ i~t s es ~ m ~~ ~~ ~p man^ ~ e t ~i ~i ~ i n t~e ~ ~ e t a i ~ori c~§ e c a of lamella are oriented parallel to the stress axis. Though different composite approaches have been explored strongly dominated by microstructural alignment for a number of inter~etallicsystems. A variety of compared to precipitation~hardeningsystems, the effect reinforce~entshave been considered, i n c l u d i ~parti~ of a fine-scale ~icrostructure on creep behavior is culates, platelets, fibers, and whiskers. identical. Limiting defoi~ationto the narrow channels Petrovic (1995) for MoSi,, Bowman of the d e f o r m ~ nphase ~ improves creep resistance~This ~ r ~ et nal. (1992) ~ a for ~ Ni,Al, and ous to the i ~ ~ r o v e iin~ creep e ~ i ~ ~ ~ i s t a of n c e (1993) for r ~ f ~ a c t oir ~ y t e r ~ i e t aftl is ~ a~ ~ s~~a rthat ~ nbyt et ~ ~ ~ p e r a ~upon l o y s~ ~ ~ f tof i ny'g precipit~~~es and large no s i g ~ ~ i ~ c iniproveinent airt in creep s t r ~ ~ g t ~ al., 1980). has been achieved with the c ~ m ~ o s iappro~ch. te Since the two-phase y structure can be produced The broader scenario i s best reflected by twin studies through solid-state rea n in polycrystalline y-TiA1, a of y-TiAl by Rosler et al. (1990) and Valencia 01 al. variety of microstructures can be produced through (1990) and by a study of based coinposites by judicious process~nga ~ dheat t r e a t ~ e n ~For s ~ the ~ a d a ~ a et n ~al.a (1993). first case, a Ti,AtC purpose of disc~ssionhere, creep behaviors of duplex platelet dispersed coiap (DP), fully l ~ ~ ~ e ~l c~rao rs t r u c ~ ~ rwith e s narruw observed that while platelets give rise to a ~ r o n o u ~ c ~ d spa~ing(FEn) and those fully lamella^ with wide strengthen~~g effect at room temperature, the same spacing (FLw) are coinpared in Figure 18. The data was not maintained under creep conditions at high are from Beddoes et al. (1997) and Ghen et aE. (1999), temperature. The loss of strengthening was attributed for binary ~-TiAl(Ti-48 %Al). The correspond in^ to diffusional transport along the particle-matr~xintermicrostructLires are presented in Figures 19(a)(b), and face. There is no surprise if this behavior resembles a (c). It is obvious tfrat a fully lamellar structure with fine textbook case of Coble creep in f i ~ e - ~ r a ~nia~eri~f n~d ~ n ~ e ~s ~~ a a~ ~eand~ planar n ~ grain bound~ries at low t e ~ ~ e ~ ~ ~ u r ~ s ~ enhan~escreep resistan~es i ~ n ~ ~ cmore a n t than ~ ~ can Similar loss in creep re~is~ance for ~ i ~ - ~ ~ r ~ i c ~ be achieved with wide lamellae and interlocked grains. reinforced MoSi, was observed by Sadaiianda ei d. It is iiiteresting to note, however, that creep behavior (1993), but was attributed to attendant grain size of material with wide lamellae approaches that of reduction with increasing particle population, inhibitmaterial with a duplex ~ i ~ r o s t r ~ i c t uItr eis. tempting to ing grain growth. As shown in Figure 20, up to 20 vol. % conclude that the l a ~ e l l amo~phology ~ may not be Sic, creep rate is higher compared to ~ ~ r e i n ~ o r ~ r i t 1 ~ and a l ~ perhaps ~ i ~creep l ~resista~ce r could be ~ ~ ~ ~ MoSi2.~ i creep e rates appear to he s i ~ n ~lower a ~ ~ ~ e vif ean d extremely fine, duplex ~ ~ ~ c r ~ s t r ~ c twith u r e 40vol.% Sic, the creep bel~dv~oiof all r e i ~ ~ ~ ~ could be produced. The creep deformation is shown to and unrein€orced i ~ a t e r i a ~as~ p e a rto ~ c~nverge at be controlled by dislocation glide, with finer lamella higher stresses. Sadananda et al. (1993) have proposed requiring a higher Orowan stress rC to bow a modified shear lag theory to account for these dislocations between interfaces with spacing L, as observations, and have shown that increasin~the aspect shown by equation (14). ratio of rei~orcementis beneficial.
earson on
In the second study, of Ta ~ber-reinforcedy-TiAl, as presented in Figure 21, Valencia et a/. (1990) showed that, althou~hTe2 w a s added to ~ r o d ~ ~fibers c e on ~ o k i ~ ~ ~ c athe tion i ~~ ~ ~ ~ o inv creep ~ ~ ~resistance ~ e n t could not be attri~utedto the fibers, but was due to solid-solution alloying with Ta. This study i s reminis14 ?2 cent of the major t ~ r ia~ d ~ ev~ e l ot ~ i ndirection~1ly~ 10 eutectic systems, back s ~ nickel-base ~ ~ ~ i in the ~ ~ 8 1960s ~2nd 1970s ~ ~ ~ 3990). o Besides d tke ~ cost ~ of ~ ~ 6 ~ ~ o d u c ~ ~i ioi c~k,e ~ - ~ aeutectic se alloys could not $ 4 compete with the ~ ~ e~ ~r e ~ v ~ ik of o~~single~~ e ~ t 2 U crystal nickel-based alloys, because there was no clear 0 $00 200 300 400 500 600 700 ~ ~ ~ ~that e nwc ~e ~ l ~ ~h l ii g~ ~h~ -dcarbide ~~ ~ fibers l ~ ~ ~ ~ were ~ b s o l u t en~e~~ s ~ for a ~ iy n i ~ r creep o ~ ~rews~ ~ tance. Creep bchavior of dirpfex (DP), and wide (FLw) Given that we still do not fully understand the impact and narrow (FLn) fully lamellar y-TiAl (Ti-48%A1) at 760 "C/ t ~ t r~~l l o y i ~ ~ ~ 4 0 Data ~ arc ~ from ~ Beddoes . et at. ( 1 9 ~ ~r)e, p r o d ~ i ~ ~of~ subtle changes in ~ i ~ ~ o s t r u cand with ~ e ~ ~from i TMS s ~ C in ~~I ~~u n i c aand t ~ Chea ~ ~ i et al. behavior of two-phase s ~ ~ ~ r a ~l il ~~l ~ bse,2 alloys, sed (I 9991, reproduced with pcrizissiou of Elsevier Science and or of y-TiAI, it is naive to think that ~ r t i ~ c i ~ l l y
~ i ~ r ~ s ~ r u c ~ofL(a) I r duplex cs (DP), (b) wide fully lamellar, aad (c) liarrow fully tamefiat. y-%Al. From Beddoes et al. (19971, reproduced with permission from TMS ~ o ~ ~ n ~ c a tand i o Chen n s ct al. (1999), reproduced with perinrssron of Elsevier Science
Creep
3 L9
igum 20 Creep rate of SiC-partide-reinforced MoSi, matrix cornposrtes with different volume fractions of SiG phase (Sadaiianda et al., 1993)
When the grain size is coarse ( ~ 3 or~ is ~ ~ adding strong articulates or fibers will necessarily lead ~, a ~ i s o t ~ ~ e the e r o s ~ - s e c t j ~creep It eise ~a b u ~ ~ ~ a n t l yc o n ~ ~ a r a b lto to i n i ~ r o v e ~ e iiii i t creep ~ e s ~ s t a ~ appears to dominate the average creep behavior. clear that unless the scale of the microst~~~cture IS fine Also, in this case intergranular failure can occur enough to influence dislocation glide and climb, no because of environ~enta~interactj ons. When the intrinsic improvement in creep resistance occurs. If the grain size is fine, the increased area of grain boundaries scale of the microstructure is too coarse, the creep s c e i~ ~ ~n r ~ aQ . ~ ~ ~ ~ e s ~ s t ~ of n cthe e d e f o ~ i matrix ~ g d ~ ~ ~the~creep ~ ~ t~ e ~s ~the ~ behavior of the system. In such cases, the overall creep resistance is no better than that given by a rule of 3.4.1 &&ct ojGrain Size mixtures. ~nfortunately,even if this were attractive, the inevitable i~troductiono f additional incoherent Studies of a wide variety o f ~ ~ t e r ~ e t a l l iand cs ~ ~ s ~inter~eta~lic-b~sed interfaces would provide rapid diff~sionp a t ~ w and alloys show that c r ~ ~ ~ - r ~ s i s t ~ escalate the creep d e ~ o r m a ~ ~ oThe n . situation IS decreases as grain size decreases. exacerbated when composites are arti~eial~y made, as studies of MoSi:, by §adananda et al. (1993), of opposed to being produced in situ. Furthermore, creep nickel-base superalloys by Bain et al. (1988), and of ~esistanceis unlikely to be helped, if the matrix/ Fe,A1 as cited by Stoloff (1998). accord^^^ to r e ~ n ~ o r e e ~ e~nt~e rmust f ~ cbe~made weak to improve al.dff993), these results may be best ~ a d ~ ~ eta ~ a fracture t o ~ i g ~ ~ e s s . rationalized by using a creep ~ o d e for l d ~ ~ u s ~ o n ~ mechanisms expressed as i = A(l/d,Y e ~ p ( - ~ ~ / ~ ~ ) (36) ~ F ?
~ 2e i ~ t As noted earlier, the effect o f grain ~ o ~ i n d ISa best ~ ~ e ~ where, d is the graiii size, and grain size ~ ~ ~ o pi is for ~ a b ~ r r ~ - ~ e r creep r i n gand 3 for Coble creep. The r ~ t i ~ ~ ~ lini terms z e d o f two factors based on grain size.
320
stress e~ponentE , is 1 for both processes. A simple c~~lculation shows that because of an inverse power law ~ e p ~ ~ i d e0n11cgrain e size, the creep rate is decreased by an order of mapitLKk up to cl grain size of 300 pm, but than that the rate of change te that in e~uation(171, ( l / d ) is not dimensi , unless it is implicitly a s s ~ that ~ e the ~ grain size is n o r ~ a l i ~ etod f pm a ~ ~ r o x i ~~quivalen~ a ~ e ~ y to a typical ~ e a s L ~of r esome t ~ ~ ~ ~ o ~ at ~r a~ ~c~Note te ~t ethat ~ ~a. in~ all the work s ranged from 30 to 4QOprn. s in this range are g~nerallynot ~ p ~ ~ i ~ ~but ~ i oaret i very s a t t ~ ~ ~ cfor t ~ vfat~~Lte-l~ni~ted e applicat~~ns that require a d ~ ~ u a creep te ~ e ~ ~ s such ~ a nas~ t eu ~r ~ i ~ and ~ ~ d shaft a ~ p l i c ~ ~ i o n s . ~ x c e ~ t i o to i i ~grain-size depeidence have been observed t y ~ i c ~ in l y systems with poor creep resis~ s e Fetance, In t ~ ~ - p h AI-rich et al. (1995) have observed no eep strength of ~ e A l ~ - F e ~and A l ~FeA13-Fe,A15. mitarly, T a ~ a h ~ and s h ~~ i ~ (1~99 1) w also a observed 1x0 effect on grain size in Al-rich single-phase y-TiAl. winan (1992) reported no di~erence in creep NiAl. istance o f (1 00) ori$nted or polycrystal~~~e ese ~ ~may be ~~a t ~ o ~~ aoail the i ~ basis e~~ that t in weak ~clteria~s, the ~ i ~ ~ in~ diffusioii e n ~ chare acte~isticsatid hence the creep c o ~ t r ~ b ~from t ~ o nthe
grain ~ o ~ ~ n ~ and a ~ ithe e s Bulk niaterid can insigni~ca~t.
Ix
In material with close-packed st~uctures,d i ~ ~ L ~ ~ ~ o n alang grain b o ~ n d a r ~ ecan s be s i ~ n i ~ c a ~ faster t~y v 19Sl), ~speci~lly for than iii the bulk ~ ~ a r i l ~etoal., f 0" grain b ~ ~withn~ ~ ~s o r ~ e n rt ag~r~~ i oa ~t than ~~~ rs ~ (Turnbull and ~ o ~ 1954). ~ aThis n limit ~ seems to coincide well with the e ~ ~ ~o ~r ~i~ r~v aat i~othat ns creep ~ ~ ~ eand n ~ d utc h~ i l i~t ~r ~ ~ i ~drop ~ in t osingle ~ ~ l y crystal sLipera~~o~s with high-angle-boundary-type ~ s ~ with t ~ i ~ ~ r i e ~>~10" ~tion defects 1996; Shah and Cetel, 2000). Tole grain boundari~scan be ~ ~ n p r o with v e ~the ~ d ~ i toi"i o ~ ~ minor elements such as C , , Zr and Hf, as is typically done in equiaxed or co~umn~r-grain sL~~e~alloys. While identifying the exact role .of these popularly referred to 'grain boundary s t r e n g t ~ ~ n ielements n~' is a complex issue ~ ~ c and~ Strang, e a 1984), ~ it is apparent, based on the above facts, that these elements must mitigate e n y i ~ o ~ i ~ de ~$ i~t ~~ ~l d aoft ~grain o n boundaries. Once $ ~ ebehsd~ e n ~ ~ r o ~ ~d e~gn~t~adla tisi ~~n~ p p r ~ creep vior is ~ d o ~ i no a t ~by d d~ ~ ~ o ~ ~~ ~i an t~i oo ~n p a ~ i ~ i ~ ~ t across grain boundaries. The role of creep a n i s ~ t ~ ~ ~ y was discussed in this context in ~ e c t i ~3.1.2, n There
the nature of ordering not only alters the ~ctivation energy but also has a significant influence on the preexponential factor as well. of the change in a preexponential factor may be tured by a n a l y z ~ nthe ~ and incorpo~atin~ creep data in terms of di~L~sivity model. that as part of the const i t ~t i v~ ~ e a s u r e m ~ofn ~d i ~ ~ s i may ~ i ~ not y be e ~ s y * f ~ n d a ~ e n t ~ lthe l y ,theoretical or experimental Creep behavior of inte etalfics or alloys based on mination of the iiature of ordering in ~ ~ ~ ~ ~ t i c o n i p o n e ~ intermetallics, follows t same constitutive relationalloys xs even more complex. s such, the c ~ e ~ ~ l o ~ ~ ship as other metals and alloys, which 1s g of an optimum alloy c o ~ i ~ o s i t i with o ~ , the lowest expressed as di ~~usi v~t y highest creep resistance, still remains and Xii that largely an e x p e r i ~ ~ n t ea l~~ p ~ ~ exercise. cal context, the general trend for a c ~ e v ~high i i ~ creep This behavior, however, does not imply that the resistance with the addition o f refractory elements such ordered nature of ~ ~ ~ t e r r n e ~plays ~ l ~ ino c s special role as Ta, MO, W, and to interi~etallicsand interp resistance o f the alloys. On the ~erstandabl~? the most useful ~~etallic-based alloys i in-depth literature review, and a approach. Undoubtedly, ftirther r e f i n ~ ~ e niiit this sensitivity analysis of the constitutive relationship process will occur with a d v ~ n c e ~ e ~ini t di~raction s that an iiiter-relationbetween the ~arameter and imag~ngtechni~ues. ship between A , PI, and scures the origin of the ~reep-res~stance en~ia~cement owing to planar core factors which lead to se in creep rate in an lure of dislocations in alloys with low SFE or absolute sense. Essentially, neither the determination energy is well reco nized. Indeed, in the limited of the apparent activation energy, ~ h tthe in at ion of the stress e x ~ o n eP~I ,~provides , suffic~en~ case of superalloys we also have some i ~ i ~ iinto re~atio~iship between $FE, pli~~se-~iistability and elecinsight into the role of tlie factors coiit~-ibzttingto tron vacancy number, but there is no absolute way to i~iiprove~ent in creep r e s i s t ~ n cSuch ~ ~ factors remain iiiclude this in the c~nst i t ut i v~ relatio~~s~p* buried in the p~e~expoiientia~ para~~ieter A which is has been made in under~ neither ~ ~ ~ s twith a n temperature, t nor i n ~ e p e ~ ~of ~ e n t ~ o n s i d e r a b lprogress standing and ~ o ~ of ethe ~a n i is o t~~ ~ pnature ~~ c of the stress exponent, sLi~niary~ the constitutive creep behavior in single ~rystals. In sin~le-phase model equation for cr serves well for interpolating materials as well as two-phase materials with almost and extrapolatiiig creep data, but provides 110 mechanisotropic ~ i c ~ o s t r ~ c t L Icreep r e ~ anisotropy can be istic iiisight into the I‘actors cont ~ ol l i n~ creep rate, and rnodefed using the ~onstitL~ti~e equation hence fails to ~ l ~ ~ c i dthe a t erole o f interi~etallic~~ with the geometry of the slip systems. ~ i i I ~the~ well-accepted e ~onst~t~~ model t ~ v efor clear that orientation of the aligned tw steady-state creep rate, no universal relationship has structure in ‘single ~rystals’can d o ~ i ~ a the t e creep been proposed for nzodeling primary creep, as this anisotropy, as it does in fully lamellar initial, transitory creep behavior is very sensitive to y-TiAl, and superalloys with prerafted y’ precipitates, material processing history and microstrtict~r~. In any e ~ ~ n ~ s o t ~ino p y ~pplicationo f this ~ n o w ~ e dof~creep case, this aspect is receivin~the needed ~ t t e ~ t i oas ii c o ~ i j ~ n with ~ t ~advances o~ in o p t ~ c a~~ ~ a teclini~ i i i ~ high p r i ~ a creep r ~ strain is r e ~ ~ ~ n i 2toe hinder d the ques is likely to improve our ~ n d e r s t a n ~ ~ofn gthe ~ ~ p ~ ~ cofa the t ~ ~o n~ ~ ~~ ~t ~Li A ~ l r- b~alloys. ~ ns e ~d A low creep behavior of polycrystalline mate~ials, density of mobile ~is l~ cat i ons due to a variety of Based on experience with two-p reasons appears to be a c o ~ ~ oorigin n for high sztperalloys, NiAl-based alloys and y primary creep in many materials. abu~idantly clear that intrinsic creep resist~~nceis It may be concluded that the ~iaxii~ization of the o ~ affected only when the scale of micr~structureis Riie degree of order~ng,which leads to n ~ i n i i ~ i z a t iof enough to i n ~ ~ ~ e dn~c sel o c a t ~glide o ~ or cliiab ~ i e c ~ a ~ d i ~ u s i ~ i taty an o p t ~ m u ci ~o ~ p o ~ i t ~ofo nan alloyed isms. Thus, attempts to improve creep resistance with i n t e ~ ~ ~ e t awill ~ l i cminimize , the steady-state creep rate, composite a p p r o ~ ~ h erarely s seem to succeed, espeIn a sense, the effect of deviat~onfrom the stoichiocially at higher stresses where creep ~ ~ f o ~ a t isi o n metric c o ~ p o s i t i o ~ ,which is cry$tal-structLire expected to be doiniiiated by dislocation motion. depe~ide~it, may be considered 111 the same manner. ~omparisons of the precipitation-hardened alloys With reference to a coIistitutive model, it is clear that
appears to be no paral~elto this kind o f behavior in other intermetallic systenis, but that may be more a reflection of tlieir early stage o f developnient.
Ij
with c o ~ p o s ~s y~set e ~ s ,~ ~ d o u ~ t e point d l y to the Poflock, R. D. Kissinger, R. R,~ ~ o ~ mXI.a A. n ,Green, M, McLean, S. Olson, and 5. J. Schirra). TMS, Warrcndale, critical rote of the interface in controlling creep PA., pp. 515-524. t ~ ~ ~ a v~ ~h oi lrethe . coherent or s e ~ i - c o ~ e r e ninterBeddoes, J., Zhao, L., Au, P., D u d ~ ~D.,~ and s ~ ~ face formed by soli~~state reactions generally helps to ~ r i a n t a ~ ~ f.~(1997) o ~ i , S r v ~ ~ r ~ ~ ~ a l 1997 ~ ~ t (eds e ~ ~ ~ t a i n ~ i b recovery ~t and eiihance creep resistance in the M eNstthal, R. Darolia, C. T. Lm, P, N I ~ ~D.t M ~ ~ l~ ~, ~ ~ ~ former; i ~ i v ~ r ~ a~iicoIi~reiit bIy interfaces resulting from R. Wagner, and M. ~ a i ~ ~ ~ The u c hMiner~tls, i ~ . Metals & ~ r t i ~ c icomposite al processes provide rapid diffusion Materials Society, pp. 109- 118. paths and enhance creep rate in the latter. Bewlay, B. P., Jackson, M. R., and Lipsitt, 1% A. (1996). Otrr ~ ~ d ~ r s oft ~the~ role ~ i of n ~s ~ ~ o r t ~ r a i i ~~~ ~ and ~er. ~~ v1 A (Physical ~ ~ ~ . ~ ~e t a . l ~ and u r ~ ~ ~ ~ d ofe i ~ ~ n~ ~t ~ ~in ~i n~ ~~ ~l r l othe i v ~creep ~ s~ ~ A, no, 12, 3 ~ ~ ~ - ~ 8 ~ 8 r ~ s i s t a ~ will c e come from a study of well-~~aracteri~ed Blavette, D., Caron, P., and T. Khan (1988). S i ~ ~ ~IQ&'~ ~ ~ l o (eds D. N. Duhl, G. Maxrer, S. Antolovich, C . L-und, and microstructures resulting from controlled processing S . Reichman). TMS, W~~rrendnle, PA, pp. 305-314. such as d ~ I : e c t ~ ~s noal~~ ~ i ~ cand a t ~controlled o~ coola ~ Miracle, , ing in solid-state ~ ~ o ~ e s~ s r ~ ~ . ~of advances l ~ ~Boehler, ~ C. J., t ~ a~ ~ ~ o~B. dS.,~a Sre ,e t h a r ~ ~V., in ~ ~ ~ r ~ and c t ~~ o na ~ e cg ~ i i~~~ ~ ~~~ ~~ ~the ~e~us ~d j D.~ B.,g and Wheeler, R. (I 997). ~ S ~ r ~ ~r n~ rl ~~ ~~rr. ~a ~i e ~ a ~ ~ 1997 (eds M. Natlral, R. Darolia. C. T. Liu, P. ~ ~ ~ rD.t ~ n , advent of o r i ~ ~i ~~i ~t a ~ ii n~ g~i c~~ ~o s ~ o ~i sy Miracle, R.Wagner, and M. ~ ~ ~ a gThe u Minerafs, ~ h ~ ~ . likely to shed more light on the funda~entalplastic Metals & Materials Society, pp. 795-804, processes and the nature of creep anisotropy in single Boone, D. H., and Sullivan, C. P. (1973). ASTM STP 520, i n ~creep crystals, arid i t s pivotal role in c o ~ t r ~ l l the ~ m e r ~ c aSociety n for Testing and Materials, pp.40 1-4 t 5. ~ e hoI: ~of ~ po ijycrystalline i ~ ~ t e r i a l s ~ o ~ r n ~a. a nR., (1992j. Mat. Ress Soc. symp, Proc., ~~~~~~
a
155, §
We are in~ebtedto Dr. Chi Law, Dr, Davjd ~ ~ o Dr. w ,
B r o o n ~ ~ e R. ~ d ,W., Ford, D. A,, Bhangu, J. K.* Thornas, M. C,, Fraster, D. J., ~ u r k h o l ~ e P. r , S., Hnrris, M., Errckson, C. I_., and Wahl, 3, B. (1998). J. Er2g. jbr Gas Turb. and POW.,220, 595-608. ~ r o w n A. , M., amid Ashby, M -F, (1980~.~ ~ Met.,r 1 ~ p 1297-1 302, Caron, P., Ohtaa,V., Nakagawa, Y. Gh,Khan, 3'. (1988). S ~ p ~ 1988 ~ ~ (eds l ~D. ~ N.} Duhl, ~ ~ 6. ~ ~aL~~er. S. A ~ t o l o ~ i c6. ~ ~Luiid, , and S. Reichman). TMS, Warrendale, PA,, pp. 21 5-224. ~ ~ c h ~ ni i ~oo r ~~ a t~iservices o i~i ~ for their timely help Carry, C., and Strudcl, 3. L, (1977). Acta ~~~~~~.~ in literatur~search. Carry, C., and Strudel, J, L. (1978). Acra M ~ ~ ~ ~ i . ~ Cetei, A., and Duhl, D. N. ~ 1 9 ~~ ~ ~j . ~ e1988 r (eds a D. ~ N. ~ ~ ~ s Duhl, G. Maurer, S. Antolovich, 6 . Lund, and ees S. Reichman). The ~ ~ ~ ~ l l u r Society, g ~ c a lW a r r e ~ i d ~ ~ ~ ~ PA., pp, 235-244, a. Beddoes, , ~ ~~ l ~oJ., ~.and ~ ~,Zhm,~ L. ~ Allen, J. M., and w hit low, C . A, (1985). ,I. ~ ~ ~ ~ Chen, ~ n W. ~R., ~e r ~r ~ ~~ t.~I ( 1999). r ~ ~ ~ ~7, 171-178. r ~ ~ t a ~ ~ ~ ~ ~ , Power., Tram. @'ASME> Chiba, A., Ono, T., Li, X. C., and T n k ~ ~ ~ sS.~ (1998). lr, Appel, F., and Wagner, R. (1998). Mut. Sc. arzd Engv., ~ Y I t e v ~ e ~ a ~6,~ i35-42 c,s, 187-268. Ashby, M. E;, ( I 973), P r ~ ? of ~the ~TTtzird ~ ~~ n t~~ ~n ~ ~ t ~i ~Cottrell, )~ n a i A. €3. (1964). T ~ e o r ~ t ~ Sr u~l r . u r ~~ ~e~ a~ ~a l l ~ ~ Camelot Press, London, pp. 195-198. ~ ~ ~ OYIa the~ S t er . ~ a~~ tof~~i ~~~u ~ ~ e Cox, A. R. and van Reuth, E. C. (1980). ~ ~ ~~~~~~~~~ t a ~ ~ ~ C a ~ b r i d g eThe j , Institute o f Metals, Vol June 1980, 238-243. Baixz, E(. R., Cambone, M. L,, Myzak, J. M Dalal, R. P., Thomas, C. R.. and Dardi, L. E. (I9845. M. C. (1988). s u ~ e r ~ €988 l ~ ~ (eds ~ ~ sD. N. Duhl, Superalloys 1984 (eds M. Gell, C. S. Kortocicb, R. €3. C. Maurer, S. Antolovich, C. Lund, and S. ~ r ~ c ~ xW z ~ B. l ~ ,Kent, and J. F ~ ~ d a v ~ TMS, ch~. ~ e ~ c ~ i 1988, ~ a n~~S~ ~ , W~~rrendale, PA, pp. 13-22 ~ a ~ r e n d a lFA., c . pp. 185-193. Baker, I, (19535). Mat, Sct. Eag. A, 1 Darolia, R., and Walston, W S , (1997). ~ r r ~ ~ r ~ v a Basoalto, EI. C,, Ghosh, R, N., Ardakani, M. G., Shollock, r ~ t e r . ~ ~ ~ e (eds ~ a ~ M. ~ i cN , s ~ t ~R. a ~ Darolia, , 6. T. Liu, P. B. A., and M c L ~ a M. n ~ (2000). S ~ p e ~ ~2000 l ~ (eds o ~ T. ~ NI. ~s
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Uamagucbi). The Papon, A. M., Sinion, J. P., Guyot, P., aiid Des~onqueres, Minerals, Metals Cci Materrals Society, pp. 147-156. M. C. (1979). Phil. Mug. B, 39(4) P a r t ~ a ~ ~ ~T.a A., t h ~S, u b ~ ~ ~ a n ~ a ~ , ratta, M. G., and Diniidulc, D. M. (2000). A 541-551, 0). Tmns. Paslay, P R., Wells, C, H., arid Leverant, 6. ~ ~ s e f fSockt.y r e ~ S y r v l p ~ ~P' sr ~a ~c ~ e ~ ~ ~81, ~ n263-275. ~~s, Kakehi, Koji (2000). Mater. Sci. a d Evlg., A27 764. Kear, B. H., and Piearcey, €3. J. (1967). T r ~ ~a ~ s~.Met, ~ Soc. ~ e Pearson, D. D., L c d e y , F. Ca., and nf'.41A4E*239, 1209-1215. S ~ p e ~9~~ ~ ~(eds~ J. l K.~Tien, ~ ~A. ~ T, L. ~ Wlodek, ~ i ~ a b j i Pa ~H., , Garg, A., Noebe, nd Nix, w. D. Morrow ITf, M. Ge12, mid G. E. Maurer). Anieri (1999). Met. a d ~~~- ~ ~ uA ,n , ~ ~ -600. Society for Metals, Metals Park, OH, Larikav, L. N., Geichenko, V. V., chenko, V. M. Petrovic, J, (1995). Mat. Sei. and E E ~A, . (1 98 1). Dgfusion Procemes in OrcJered Alloys, Amcrind Pollock, T., and Argon, A. (1992). Rcia Publishing, New Delhi, India. NO. 1, 1-30. Law, C., and Blackburn, M. (1980). S~6perullays1980 (eds J. K. Pope. D. P. and Ezz, S. S. (1984). frzt. ~ ~ t ~ l , ~ ~ ~ v ~ e ~ Tien, A. T. L. Wlodek, H. Morrow 111, M. Gell, and 6.E, 167. Maurer). American Society for Metals, Metals Park, OH, Quested, P. N., Hcndersori, P J., and McLcari, M. (1987). pp. 651-661. Proc. qf the Third I ~ ~ e r ~ ~~ o~ i~ ~ f~onenCreep ar ~ ~nnd~ ~ ~ ~ Lemkey, F. D., and Machliii. I. (1985) Eutectic super~~loy ~ r f f ~of t~ un ~~i v~l e e r ~~nc g~ i e r i aaid l s ~ t r u c t ~ ~pp. ~ 279,s, coi~pos~tions and articles, Patent No.: US 4543235 Patent 294. A s s ~ ~ ~ e e Wiiitcd ~ § ) : Techn~log~cs Corp., Patent Date Quested, P. N,, Hetiderson, P J., and McLean, M. (1988). Filed: Filed date 22 Sep 1982, ~ublicatioiiDate: 24 Sep Arm ~ e ~ ~36,~2743-2752. l . , 1985 p v. Rong, T. S., Jorxes, I. P., and S ~ R. E. ~~~ 9 9 8Acta. ) *~ ~ Leverant, G. R., and Duhl, L),N. (1971), Met. Trms., ~ ~4 ~ ~~ 4507-451 1 ? ~~ ~7. r . ~ 908. RGsler, J., Valeiiei~~ J. Is,Lcvi, C. C., Evans, A. ~ 3and .~ Lnu, C. T. and Horton, Jr,, J. A. (1995). Mat. Set. avld Egr., Mehrablali, R. (1990). Mat. Res. Soc. Symp. Proc., A ~ ~ 170-178. 2, 241-248. Lundstroin, D., and Kirlsson, B. (1 997). Structzn.rr1 Ross, E. W., and O'Hara, K. S. (1996). Super € ~ ~ ~ e r ~1997 2 ~(eds ~ aM. I ~Nathal, ~ c ~ R. Darolia, C . T. Liu, R. D. Kissmger, D. J. Deye, D. L. Anton, A ~~~~~
324
Mechanical Properties
Nathal, T. M. Pollock, and D. A. Woodford). TMS, Warrendab, PA.. pp. 19-25. Rowe, R. G., and Hall, E. L. (1991). Mat. Res. Soc. Symp. Proc., 213, pp. 449-454. Sadananda, K., Feng, C. R., Jones, H. W.,and Petrovic, J. J. (1993). Structurnl Intermetallics1993 (eds R. Darolia, J. J. Lewandowski. C. T. LIU,P. L. Martin, D. B. Miracle, and M. V Nathal), TMS, Warrendale, PA., pp. 809-818. Sauthoff, G . (1991). Proceedings qf ~nternationa~ Symposium on h t m e t a l i i c Compoundr, Sendai, Japan (ed. Osamu Izumi). The Japan Institute of Metals, pp.371-378. Sauthoff, G. (1993). In LX@ion zra Ordered A&ys (eds B. Fultz, R. W. Cahn, and D. Gupta). TMS, Warrendale, PA. pp. 205-222. Schuh, C., and Dunand, D. C. (1998). Acta Mater. 46, 56635675. Seib, David C . (2000). S u p e d l ~ j r2000 (eds T. M. Pollock, R. D. Kissinger, R. R. Bowman, K. A. Green. M. McLean, S. Olson, and J. J. Schirrir). TMS, Warrendale, PA., pp. 535-544. Senba, IEiroyukt, and Igarashi, Masaaki (1997). Structural lntermetullics 1997 (eds M . Nathal, R. Darolia, C. T. Liu, P. Martin, D. Miracle, R. Wagner, and M. Yamaguchi). The Minerals, Metals & Matenals Society, pp. 595.604. Seo, D., Bieler, T., and Larsen, D. (1997). Structural htemetallics. 1997 (eds M. Nathal, R. Darolia, C. T. Lm, P. Martin, D. Miracle, R. Wagner, and M. Yamaguchi). TMS, Warrendale, PA, pp. 137-146. Seo, D. Y, Beiler, T. R.. An, S. U.,and Larsen, D, E. (1998). Metal!. Mater. Tram A, 29A, 89-98. Shah, D. M., and Anton. D. L. (1993). Structural Intermetallics I993 (eds R. Darolia, J. J. Lewandowslu, C. T. Liu, P. L, Martin. D. B. Miracle, and M. V. Natlial). TMS, Warrendale, PA., pp. 755-764. Shah, D, M., and Anton, D. L. (1991). Mut. Res. Soc. Symp. Proc., Materials Research Society, 213, 63-68. Shah, D. M., and Cetel, A. (1996). Superalloys 1996 (eds R. D. Kissinger, D. J. Deye, D. L. Anton, A. D. Cetel, M. V. Nathal, T. M. Poilock, and D. A. Woodford). TMS, Warrendale, PA., pp. 693-702.
Shah, D. M., and Cetel, A. (2000). Supera1loy.s 2000 (eds T. M. Pollock, R. D. Kissinger, R. R. Bowman, K. A. Green, M. McLean, S. Olson, and J. J. Schirra). TMS, Warrendale, PA., pp. 295-304. Shah, D. M., and Duhl, D. N. (1987). MRS Proceedings Vol. 81 (eds N. S. Stoloff, C. C. Koch, C. T. Liu, and 0. Izumi), pp.411-417. Shah, D. M., and Duhl, D. N. (1988). Superalloys 1988 (eds D. N. Duhl, G. Maurer, S. Antolovich, C . Lund, and S. Reichtnan). TMS, Warrendale, PA., pp. 693-702. Stoloff, N. S. (1998). Mut. Sct. and Eng. A, A258, pp. 1-14. Takahashi, T., and Oikawa, H. (1991). Proceedings of International Symposium on intermetallic Compounds, Sendai, Japan (ed. 0. Izumi). The Japan institute of Metals, pp. 513-517. TiHy, G. (1972). J. of Strain Anal., 7, No. 1 , 61-68. Turnbull, D., and Hoffman, R. (1954). Acta Met., 2, 419. Valencia, J. J., Lofvander, J. P.A., Rosler, J., Levi, C. G., and Mehrabian, R. (1990). Mat. Res. Soc. Symp. Proc., 194, 89-96. Weertman, J., and Weertman, J. R. (1983). ‘Mechanical properties, strongly temperature-dependent’ in Physical Metallurgy, 3rd edition (eds R. W. Cahn, and P. Haasen), pp. 1309-1340. Westbrook, J. H. (1996). Superalloys (Ni-base) and dislocations - an introductlon, in Dislocatioras in Solids, Chapter 48 (eds F R. N. Nabarro, and M. S. Duesbery). Elsevier Science. Woodford, D. A. (1990). JOM, 42(11), 50-55. Zang, Z., and Couture, A. (1998). Scrlpta Mater., 39(1), 4553. Zeumer, B. and Sauthoff, G. (1998). Intermetullics, 6, 451460. Zhang, Zhonghua, Sun, Yangshan, and Shen, Gtianglun (1998). Scrlpta Mater.. 38(1), 21-25. Zhu. W., Fort, D., Jones, I. P.. and Smallman, R. E. (1998a). Acta Mater., &(Ill, 3873-3881. Zhu, W., Fort, D., Jones, I. P.,and Smallman, R. E. (1998b). Phil. Mag. Letters, 77(6), 307-313.
oxygen content at high ten~peratures.The s i g n i ~ c ~ ~ n c e of environ~ienta~~y i n d ~ i c ee~i ~ b ~ t ~ l e m ewill i i t be discussed in detail in a later section.
This chapter is concern~d with the respoiise of iiiter~e~dllic coilnpounds to cyclic defori~atio~i. The ~ r o ~ r e s s i oofn fatigue d a ~ ~ during g e the early stages as is the in~uenceof of cyclic loading is descri~ed~ numerous e x p e ~ i ~ ~ and ~ n~t a~ t~~~r variables ~al on fktigue life and crack growth rates. The vast majority The fatigue response of any material i s a fimction of of the fatigue literature describes experiments under both material ~ r o ~ eand r t ~~x ~~ ~~ r ~ conditions. ~ e i i t ~ l stres~-c~iitrolle~ loading, and this i s reflected in the For example, yield strengt~affects ~~i gh-cycl fatigue ~ data reviewed in this chapter. life, while ~ ~ c t i ~ii ~t y~ u e n lco~ws - c ~ cf ~a~t ~ fife. ~ ~ e The earliest studies of fatigue bchavior of inter~ i c r o s t r ~ fkctors c t ~ ~(grain ~ ~ size, ~r~~~~~~of pre~ e t a ~ ~s li i~o w s ~ ~that long-range order can cipitates) tend to agect fatigue response indirectly, s i ~ i ~ i ~ c a naffect t l y ~ ~ g h - fatigue c y ~ ~fives ~ of Fe-Go-V through their egects on ~ t r ~ n g and th ~~ict~~ity. ttner et at’., 1946). Eater, high-cycle fatigue com~osites, ever, in the case of inter~etallic-~atrix e carried out ~ ~ ~ ~onather two i ~systems: y volume fraction of reinforcement, interface strength Ni3A1 (Doherty et at., 3975; Fuchs and Stoloff, 1987) sand o r i e n t ~ ~ ~ ofo$np e c ~ ~ e relative ns to the remforceand Fe3Al (Fuchs and StofoR, 1988). Data for these iiient ~xi s~axesplay s i ~ n i ~ c a nrotes t in ~~t~~~~ s ~ s t ~ ngene i s rat^^ prior to 1987 can be found in the behavior. External variables differ in their impact review of Stoloff et nl. (1987). Since those investigations were reviewed there have been many studies o f d e p ~ ~ dupon i ~ gthe teni~eratureor other c o n ~ i t ~ oof ~is fatigue behavioi. in al~iiiinidesand silicides reported, test, The ratio of ~ i ~ i m ~ to i ~m a x cyclic ~ stress ~ u ~ with most of the data r e v i ~ w ein~ several ~ ~ b l i ~ a t i o n s(R ratio) is ~ a r t i c u l ~i ~m~ ~y o ~ in t ~c n~ ~ ack-~ru~t~ guchi and ~ ~ a ~ o 1990; s h ~ Stolog~ , 1994a,b; expe~iments,while f ~ e ~ ~ e is n cim~ortant y only wlien 1997). In general, the fatigue b e h a ~ i ~ofr ~ ~ v j r ofactors i ~ ~ or creep ~ e ~ r~o ~c ~~c~o n~t re~sb ~to te intern~etallicsis i ~ t e r i ~ ~ d ito a t that e of conv~ntio~ial fatigue damage. At low t e m ~ e ~ d t ~oE creep ~ ecourse, s, structural metals and cerainics. F is less likely to be a factor. The physical size of prere brittle systems (NiAI, TiAl and existing cracks also is im~ortant,~ s ~ ~in ~the~case a ~ l y high c r a c ~ - ~ r o rates ~ t h and big1 of crack-growth studies. ‘Short’ or ‘small’ cracks tend 0nents ~ o i ~ ~ toa more ~ e dductile i ~ ~ e r ~ e tsuch a ~ as l ~ ~ sto grow much more r a ~than i foiig ~ ~cracks, ~ and often 14- B. Perhaps the single factor niost cannot be described by the ~ a r ~ s - ~ r ~(1863) oga~ characteristic of the fatigue behavior of many interrelationship between crac~~growth rate and stress~ ~ ~ is ~ their ~ significant l f i d~ e p~~ n ~ e n upon c~ i n ~ e ~ sfactor i t ~ range. Finally, surface ~ ~ i ~ dmust i ~ i o ~ environ~entalconditions, including especially h m i d be considered, as f’atigue resistance falls wrth incre~s~ng ity level and hydrogen content at low tei~iperatu~es and surface roughness. ~nfort ~nat el y, the latter variable
Mechatdcal Properties
326
seems to have been studied only in TiAl alloys (Jones and Eylon, 1999).
3. Evolution of Fatigue Damage Damage during cyclic loading evolves from a characteristic defect structure accompanying the development of slip bands, to surface roughening and ultimately the development of fatigue cracks. This process has been widely studied in metallic materials, but little information has been reported for intermetallics. Deformation substructures of fatigued Ti3AI consist of walls of tangled edge dislocations that arise from edge dipoles produced by cross-slip of 2/3{ 1120)screw dislocations (Kerans, 1984). Hsiung and Stoloff (1990, 1992, 1994) have reported observlng dislocation dipoles and vacancy agglomerations in single crystals of Ni,AI that precede the development of surface intrusions and extrusions. Point-defect clusters are continuously generated as cyclic plastic strain is applied. Fatigue damage is then initiated by formation of microvoids at persistent slip band (PSI$)/ matrix interfaces, as shown in Figure 1 (Hsiung and tolofK, 1990). It was shown also that the defect structure was affected by the external environment, with damage developing more rapidly in air than in vacuum. Later, Smith et al. (1992) and Kallingal et al. (1995) compared the development of dislocation substructures in Ni,Al polycrystals and NiAl single crystals, showing that extrusions and intrusions also preceded crack development in NiAl, A detailed analysis of dislocation substructures in these intemetallics, produced by cyclic loading, showed that a high density of dislocation loops and dipoles was formed, see Figure 2. Kallingal (1996) also showed that low-energy, misfitrelieving =rays of dislocations formed. It was shown that low-energy cell structures and veining patterns could be simulated by using a method originally developed by Kratochvil and Libovicky (1986). Cyclic hardening in NiAl single crystals at room temperature was shown to result from dislocation interactions, point-defect formation and the growth of dipole arrays (Kallingal et al., 1995). Cyclic hardening and fracture behavior of polysynthetically twinned TiAl crystals (in which all lamellae are oriented alike without any grain boundaries) have been studied by Umakoshi and co-workers (1995, 1996, 1998). Strain-controlled cyclic hardening and fatigue life were both strongiy dependent on temperature and orientation, see Figure 3 (Umakoshi
Figure 1 Scanning electron micrograph showing formation of surface damage at PSB/matnx interfaces m single crystal Ni,Al (S. A.=stress axis) (from Hsiung and Stoloff, 19903, reproduced with permission from Elsevier Science
et al., 1998), but independent of V and Nb alloying additions. The angle cp is between the loading axis and the lamellar boundaries along a (110) zone in the y phase. Study of dislocation structures during cycling revealed numerous deformation twins and a high density of 1/2[110] dislocations within the y phase but not in the a, phase for crystals oriented with v, = 0". In contrast, specimenscycled with v, = 45"revealed slip and twinning along (1 11) planes in the y phase, parallel to the lamellar boundaries. Vanadium additions decreased the stacking fault energy of y, allowing easy formation of twins. The latter produce substantial residual stresses and coarse surface steps which act as nucleation sites for microcracks. In this fashion vanadium reduces fatigue life (Yasuda et al., 1997). This is in contrast to monotonic deformation, where the forniation of twins promotes higher ductility. Studies of fatigue damage mechanisms and their relation to monotonic deformation properties have been reported by Campbell et al. (1999), Worth et al. (1997), and Chan and Shih (1997) for TiAl polycrystals of different microstructures. These studies have largely comprised observations of the development of cracks as related to the underlying microstructure. Dislocations of 1/2(110) type and twins of 1/6(112) type are seen, but no deformation-induced cell structures are observed (Srivatsan et al., 1995). It is generally agreed from these studies that the superior fatigue crackgrowth resistance of lamellar microstructures results from intrinsic toughening inechanisins such as increased toughness under localized yielding. As a
327
2
B
are 3 Relation between stress a ~ ~ l ~and t u number ~ e of cycles to failure iri ~ o l y s y n t ~ ~ t i ctwinned ~ l l y (PST) TiAl si~lgk crystals at various temperatures: a) 0" orientatioit b) 45" orientation (from Uniakoshi et al., 1998), r e p ~ o ~ u c ewith d permission of TMS and ASM € ~ t e r ~ i ~ s.t p. i ois~an ~ ~ .~ o ~ ~ llow o upoint s ~ y
328
Mechmical Properties
result, crack-growth rates for different microstruct~res correlate well with fracture toughness: higher toughness leads to lower crack-growth rates. The evolution of damage under cyclic loading also lnas been studied at room temperature in CoTi single crystals, which display the sB2 structure (Behgozin et al., 1997), see Figure 4. Cyclic hardening is gradual, and reaches saturation after more than 103cycles at a strain range of 0.1%. A large iiuinber of dipoles and small loops were produced by the motion of dislocations containing jogs, as in the case of Ni,Al single crystals (Hsiung and Stoloff, 1992). Activation of secondary dislocations in addition to the motion of primary ( I 10)(loo} dislocations accelerates cyclic hardening and shortens fatigue lives. Dislocation interscctioi~son primary and secondary planes induce the formation of pileups with strongly concentrated residual stress fields, resulting in the initiation and propagation of niicrocracks.
CF) and low-cycle (LCF) fatigue properties of TiAl have been extensively reported. As in the case of fatigue-crack growth (FCG) studies, limited data indicate tliat a lamellar microstructure is more desirable than a duplex structure for improved CF lives, for an alloy tested at 760°C (Huang and Chesnutt, 1995). Another TiAl alloy tested at elevated t e ~ ~ e r ~ t u showed res s o ~ e w h a tcontradictory behavior, in that a lamellar structure provided better
fatigued at various strains, normalized by the maximum stress at the first cycle (from Behgozin et al., 1997), reproduced with p e ~ i s s i oof~The Iron and Steel Institute of Japan
fatigue resistance than a duplex structure at 8OO"C, with the opposite result noted at 600°C Chesnutt, 1995). Additional evidence for t efTects of a lamellar structure has been provided by Trail and Bowen (1995), who have studied the room beliavior of a gamma alloy temperature, R = 0.1 co~taining2 mass% ~ a t i g u elives were affected by microstructure, re stresses and surface roughness. Fdly lamellar structures were superior to partially lamellar structures; and residual tensile stresses, as well as microcracking introduced by electrodischarge niachining, reduced fatigue lives. On balance, taken together with behavior to be described below, the l a ~ e l l astructure ~ is preferred for fatigue resistance. The HCF behavior of nearly stoichioi~etricTiAl has been studied between room temperature and 900°C (Sastry and Lipsitt, 1977a,b). The ratio of fatigue strength at 106 cycles to the ultimate tensile strength was in the range 0.5-4.8, which compares favorably to the ratio for nickel-base superalloys of 0.3-0.4 in the range 700-800 "C (Sastry and Lipsitt, 1977b). Larsen et aE. (1994) and Ku (1994) have reported einforced TiAl (XD) that the HCF properties of T are excellent. Smooth and notched fatigue strengths at room temperature and at 537 "C and 649 "C are a high percentage of their smooth-bar yield strength, and in some cases actually exceed the yield strength, in contrast to nickel-base superalloys and other precipitation-hardened structural alloys, which display much lower ratios of fatigue strength to yield strength (Stolog, 1993). The superior HCF resistance of the XD alloys was attributed by Larsen et aE. (1994) to strain aging caused by interstitial boron, and in the case of notched samples to the superposition of strain aging and notch-strengthening effects.
Limited HCF data at 650°C have been reported for two a2 alloys and a composite reinforced with SCS-6 S i c fibers (Larsen et aE., 1990). When tested in the longitudinal orientation, HCF lives are increased relative to the base alloy, but are inferior to those of Ni-base IN-100; transverse properties of the composite are very poor. These results are fully consistent with those for FCG of the same composites, as will be shown later. Later work by Wang et al. (1998) on a hybrid SCS-SjTi 6-4/Ti 25-10 composite showed that an experimental S-N curve could be simulated by a computer code that also has been applied to crack-
329
Fatigue
The lives of powder-extru 8 . 5YO ~AI- 7.8 Y0Cr-0.8%22-0. extended, relative to tests in (Gordon et aE., 1994). ydrogen also degrades the lowtemperature HCF resistance o f this alloy ( 1992). in spite of tlii similar alloy, IC-221 than the nickel-ba shown in Figure 5 this type of alloy are affected by pores resulting from solidification of castings; higher cooling rates from the inelt promote fewer pores and iiiiproved fatigue resistance. Low-cycle fatigue data other intermetallics are very sparse. and Unni (1991) have reported the dependence of life on strain amplitude for the polycrystalline alloy IC-218. see Figure 6. The transition fatigue life, N,, defined as the LCF life where elastic and plastic strains are equal, is an important factor in gas-turbine disc life. Nt for this alloy is about 3700 cycles, which i s reasonably close to the value for ferrous alloys of the same
growth data. This work also showed that optimum life was achieved with 25 vol.% fibers and that the presence of the ductile Ti 6Al-4V around the fibers accounted for improved properties.
Surprisingly little is known about the HCF resistance of this class of alloys, and most of the data were published prior to 1987 (Doherty et al., 1975; Stoloff et al., 1987). Fatigue life in stress~controlle~ tests of an alloyed Ni,A1 was shown to be independent of temperature below 800 "C, which correlates well with the t ~ m p e r a t ~ r ei n d ~ p e n ~ e n c of e the microyield strength (Doherty et al., 1975). Other important ftlctors governing the HCF resistance of Ni,Al and its alloys are the composition and the test environment. It i s well known that alloys containing 25a% (13.3 mass %) or more of A1 are brittle when tested in air at room temperature. Consequently, fatigue resistance is expected to be poor in this co~positionrange.
Nominal compositions of nickel alurninides Alloy
Element: weight % (atomic %) Ni
IC-50 IC-218 IC-221
Al
Cr
B
0.02 (0.10) 88.1 (77.9) 11.3 (21.7) 82.9 (74.8) 8.5 (16.7) 7.8 (7.9) 0.02 (0.10) 82.0 (74.2) 8.5 (16.7) 7.8 (7.9) 0.02 (0.10)
f
Zr 0.6 (0.3) 0.8 (0.46) 1.7 (0.99)
Figure 5 Comparison of the fatigue life (NE)of IN 71 3C with an Ni,Al alloy, IC221N1, tested at 650°C In air at a maximum stress of 85 ksl and with stress ratio R = 0.05. IC-221M test bars were produced by investment casting at PCC-Oregon and PCC-Airfoil. See Table I for compositions (from Gieseke and Sikka, 1992), reproduced with permission from Elsevier Science
2 18 compared fmorably 1 alloys such as Ti-6A1-4V steel, especially at high strain n and ~ n n i 3991). , This observation is c o n ~ i s t ~ with ~ t the high ducti~ityand good resistance displayed by TC 218. ve ~tudiedthe i n ~ L ~ e of ~ cboron e
~ ~ ~ e a to r e~dci1itate d crack nu~leation,but fracture stage were similar in the of fatigue cracking in has been carried out by hang et al. ( 1 ~ ~Stage 7 ~ .E cracking simultaneously on
I
tram ~
~
two or more (111) planes and c l e ~ v a ~ f rea c t u ~were ~ observed under cyclic tensile loading. An orieiitationdependent threshold for fatigue cracking from a notch root was noted. s
Very little has been reported on stres~~controlled lives of an alloy etermined at three elevated temperatures, see Figure 7 ( 1994). Very high ratios of fatigue limit (at 107cycles) to yield strength were obtained~e ~ ~ e c iina c~ol ~~~ a r i s o n to nickel-base superalloys such as Astroloy ( ~ s o ~ o t o toloff>1990) (also shown in Figure 7) and Udirnet 700. The higher emhmince ratios of may arise from rapid cyclic har~ening,w h i c ~in , turn, delays crack initiation. In the case of NiA1, however, the high notch sen$itivity at low t e i ~ ~ e r ~ t ushou~d res lead to rapid pro~agation to failure. Noebe et al. (1995) have reported strain produced NiAl alloys at 100 Zr a~ditionsprolong life at low strain amplitudes, see Figure 8. On increasing the strain range for the
Io4
~vs. r le ~ ~i r sto ~~ lfailure s ~ for ~ Mi,A1 e alloy IC-218 (from Gordon and Unni, 1991)
o5
33 1
Fatigue
igure 7 High-cycle lives of P/M Astroloy, Ni,Al+ B and NiAl+ 0.28%Fe normali%edfor yield stress (from ~ a t s etual., ~ 1994)
0.
Fatigue life versus total strain range for P/M NiAl alloys at 1OOOK (from Naebe et al., 1995), reproduced with permission of the Materials Research Society
NiAl+Zr alloy from 0.38% to 0.40%, a drastic reduction in life was noted, due to rapid exliaustion of its already limited tensile ductility. For this reason, no data points are shown in Figure 8 for strain ranges above 0.38%. Fatigue lives of Wf-doped, (1 00) oriented, single crystals, tested at 9 8 0 T , are similar to those of Rent: 80, a nickel-base s u ~ ~ r a l l owith y comparable creep resistance, as shown in Figure 9 ( The behuvior of NiAl appeared to be independent of surface co~dition,i ~ d i c aatlack ~ ~ of ~ notch. sens~tivity
This is in contrast to the situation at room temperature, where notch ~ensitivityis hi
S
4.5.1 Fe,A/ AZluys
HCF experiments on Fe& alloys have shown a complex dependence upon temperature and composition (Fuchs tolofT, 1988). Typical data for Fe-28.7 a%Al are shown in Figwe 10. A h . ~ p # s ~ ~ i e ~ 23.7 ~ ~ a%Al etrie
Mechanicac!Properties
332
5
igure 9 The high-cycle fatigue behavior of a Hf-containing NiAl single-crystal alloy compared to that of R e d 80 (from Wright et al., 1992)
alloy is less fatigue resistant at 25 "C than a 28.7 a%Al alloy, but there is a reversal in resistance at 500°C. This may arise from an aging effect, since a two-phase, coherent, alpha + DO, structure develops in the 23.7 a%Al alloy at the higher temperature, while the other alloy remains single phase. At 25 "C, on the other hand, the presence of superlattice dislocations in the higher AI content alloy probably delays crack initiation, thereby prolonging Fatigue life. HCF data for two Fe,Al alloys are compared to data for quenched (disordered) and slow cooled ( 2 ordered) FeCo2%V, see Figure 11 (~oettneret al., 1966, Fuchs and StoloE, 1987; see also Yamagucbi arid Umakoshi, rdering increases fatigue live for the 0, version of Fe-28.7aYoAl provides longer lives than the quenched (partially B2 ordered) condition. These data show clearly the effects of g on fatigue behavior. ntly, Cieseke et al. (1997) have reported a size effect on HCF life for alloy FA-129 (see Table 2 for compositions of Fe-A1 alloys described in this chapter) at 600"C, apparently as a conse~uenceof differing yield stresses. As tliicltness increased from 12.7mm to 16.5mm, yield stress decreased, thereby reducing life. This is one of the few reports in the literature of the effects of processing 011 fatigue behavior.
4.5.2 FeAl Alloys
om~temperaturecrack-growth properties of Fe%AI have been reported by Castagna and Stoloff life data have iiot been reported. owever, the crack-growth data for Fe-35a%Al are
~igure10 ERects of temperature and type of long-range order (€32vs. DO,) on high-cycle ~ ~ t ~ of gu Fe,Al e polycrysta~s (from Fuchs and Stoloff, 1988). reproduced with p e r ~ s s i o n froin Elsevier Science
siinilar to those for an Fe,Al alloy (FA-129) in tlie 332 condition. The e~~vated-temperature Fatigue strengt~of stressrelieved FeAl was found to decrease sharply between 400 and 750"C, as shown in Figure 12 (Jaske et al., 1998). Life was controlled by a co~binationof fatigue cracking and cyclic creep. In another study, Vasuda et al. (1999) reported a peak in cycles to hilure of Fe48 a%Al at about 400 "C when cycled at d o = 150MPa, see Figure 13. There was no direct corres~ondence between the fatigue strength and the temperature dependence of yield strength. ~ n o ~ a l o strengthenus ing at an intermediate temperature does not necessarily result in increased fatigue life. It was concluded that the to-and-fro motion of (100) dislocations during cyclic defor~ationat high temperatLires induces the formation of excess vacancies and/or cavities, resulting in a decrease in fatigue life.
The only stress-life data for niobium aluminides have been provided by Srivatsan et al. (1996) and Soboyejo et al. (1999) for a ~ b - l 2 ~ A 1 - ~ 4 T i ~alloy, l . 5 ~ as 0 shown in Figure 14. The latter is one of a class of ductile, low density I32 alloys developed for possible structural applications. The endurance limit correspoiiding to a cyclic stress range at which the fatigue life is 107 cycles was about half of the ultimate tensile strength, as is the case for many steels. Crack initiation
333
Fatzgue
11 Coinparison of fatigue resistance of Fe-28.7a%A1 with ordered and disordered FeCo-V at room ~~mperature (from. er et al., 1966; Fuchs and Stoloff, 1988), reproduced with pemission of TMS and ASM ~ n t e r ~ ~ t i o i ~ a ~
Co~positionsof Fe-A1 alloys, a%
FAP-Y Fe A1 Cr Zr C MO
Nb Y Grain size (pm)
FA-129 Fe-35%A1 Ternary
1%Zr-C
65.0 35.0
65.95 28.0
77.07 16.12 5.44
66.12 28.08 5.04
0.11
--
0.13 1.07
0.20
-
0.5 1
0.06 42
-
67.0 28.0
O.5%Zr-C 0.5%Zr 66.45 28.0
66.5 28.0
-
__ __ __
-
385
*Partially recrystallized.
was associated with. slip-band initiation and slip-band interactions/intersections.
loading conditions, crack growth. is usually very rapid, with unusually high stress exponents, up to 100 or inore, in contrast to 3-4 for ordinary structural alloys, as noted in the Paris-Erdogan (1963) equation:
Much attention has been directed towards the fracture bekavior of intermetallic compounds under rnonotonic loading. It i s well known that most interinetallics of interest for structural applications are relatively brittle at low and intermediate temperatures, although in many cases brittleness is the result of an environmental effect (Stoloff and Liu, 1994). ~imilarly,under cyclic
where a is the crack length, N is tbe number of cycles, AK is the stress-intensity range during each cycle; C and rn are experimental constants. Again, the test environment can play a major role, especially in the case of alu~inidesand silicides. However, the study of crack-growth resistance under cyclic loading conditions has lagged investigations of monotonic bebavior.
da/dN= ChK"
(1)
5.f .1 TiAl Alkoys
Elevated temperature fatiguc resistance of stressrelieved FeAl (from Jaslce et al., 1998), reproduced with ~ e r ~ i s sfrom i o ~ Elsevier Science
t e ~ ~ p e r ~int ~anr eFe-48aY~Alalloy cycled at AG = 150 MPa (after Uasuda et al., 19991, reproduced with permission from Elsevier Science
nly in the case of a few intermetallic systems has a comprehensive study of factors in~L~encing crack growth been carried out evious reviews of fatigue beliavior in intermetall have demonstrated just the literature (Stoloff, 1996; there is now an appreciable m alui~inides, some Fe,Al se composites of differing morpliologies. ~nfortunately,data for other intermetallic systems remain scattered and there is insufficient uiiderstaiidin~ of cyclic deformation phenomena in most inter~etallics.
In the case of g a ~ TiAl ~ aa b y s , the best combination of mechanical properties i s obtained in the two-phase region centered around 48 a% Al. ~nfortunately, crack-growth expo~entsare extremely high. Therefore, once initiated, cracks grow extremely rapidly. A wide range of crack-growth exponents, from 8.2 to 56.2, is obtained with different test conditions for a Tin-2Nb alloy, but in all cases the exponents are higher r conventional structural materials (James wen, 1992). Under such conditions, flat S-N cur also are to be expected, so that knowledge and control of stresses is extremely important. High values of the exponent are typical of many brittle ceramcs and intermetallics. For these alloys, high growth rates have been attributed to lowenergy fracture niodes such as cleavage of gamma grains at room te~peratureand trans~ranulardecohesion of the gamma and alpha-two phases at 700 or 80Q"G. It was concluded that inicrostructures with a large proportion of gamma grains have much poorer fatigue properties lamellar gamma/alpha-two alloys (Venkateswar et al., 1995~).Some of the difference between and elevate^ teiii~erature FCC results in Ti-48 a%Al have been attributed to the effects of oxide-induced crack closure at the higher temperatures (Soboyejo et al., 1991). Gampbell et al. (1999) show that for the various inicrostructures (single-phase gamma, duplex and lamellar) the crackgrowth resistance and fracture toughness rank in the same order, see Figure 15. The superior FGC resistance of ~amellarniicrostrLictures IS attributed to enhanced crack- tip shielding arising from crack closure and also have shown a bridging. Campbell et al. (199 deleterious correlation between C ~hresholda i d the percent of equiaxed gamma diRerent TiAl microstructures. C report that a ~ne-grainedTiAl alloy showed a higher tensile ductility but lower fracture toughness and crack-growth resistance when compared to a largegrained material. These workers also reported that sniall cracks in fine-grained lamellar material propagated at K (stress intensity factor) levels below the large-crack threshold reported in the literatu~efor a coarser grained alloy of similar, but not identical, Composition, see Figure 16. Additions of chromium or niobium to binary TiA1 refine the grain size but have no effect on crack-growth resistance at room temperature (Gnaiiamoorthy el al., 1996). Tlie anomalous effects of temperature on crack growth in TiAl alloys
7
400
1
1
Effect of maxiinurn axial stress on high-cycle fatigue life of ~b-12.5Al-41Ti-l.5Moalloy (from Srivatsan et al., 1996), reproduced with p e r ~ ~ s s i oof n The Minerals, Metals and Matcrials Society
Figure 15 Fatigue crack-growth rates for thr~~ugh-thickness long cracks and small surface cracks in duplex and fully lamellar microstructu~esof TiA1 (from Camgbell et al., 1999), reproduced with permission of TMS and ASM International
are discussed extensively by ~ c ~ e l v et e yal. (1997), see below. The superior performance o f lamellar microstructures under both cyclic and rnonotonic loading has as shown in Figure 17, For both microstructures, longbeen attributed to extrinsic shielding from crack crack data can be corrected for the influence of deflection, microcrack nucleation alzead of the crack shielding, in which case long- and short-crack data tip and resultant bridging by lamellar colonies in the coincide. Chan and Shih (1998) have reported in depth crack wake, similar to the behavior of aligned on the ineans by which small cracks grow into large composites (Gnanamoorthy et al., 1996). ones iii a TiAl sheet alloy. Small (relative to the relevant microstructural unit 10 size) crack behavior is important to study because o f potential problems in designing structures based upon long-crack data. Long cracks are defined as having plastic zone sizes sufficiently small to meet the criterion for small-scale yielding while being large compared to the basic microstructural unit (grain size or lamella size). Many structural alloys display much more rapid crack growth when small cracks are present compared to long-crack data. In fact, sniall cracks in a fine-grained, fully lamellar TiAl alloy do not exhibit a growth threshold, but they propagate at rates consistent with extrapolation of long-crack data for the same microstructure, as 1 was shown in Figure 16 (Chan and Shih, 1997). Later work showed, however, that sinall surhce cracks in a fine lamellar microstructure grow faster 10'2 1 than long cracks at the same stress-inteiisity levels; this behavior was ascribed by Campbell et al. (1996) to restricted coiitributioiis from crack closure and Figure 16 Summary of fatigue crack-growth data of large and small cracks in fine-grained, fully lamellar Ti-47A1-2Nbbridgin~ d ~ t eto the limited wake associated with 2Cr-0.2B and c~niparisoii with large-crack data for two small cracks. Camp~eliet al. (1999) clearly demoncoarse- grained lamellar alloys, Ti-47Al-2.hNb-2CCr -t V) and strate the much larger differences in sinall and long Ti-48Al-2Nb-2Cr (from Chan and Shih, 1997), reproduced crack behavior in lamellar and duplex m i ~ r o s t r u c t ~ ~ ~ e swith , permission of TMS and ASM I n t e r ~ ~ t i o n a l I
w e 17 Effect of ~icrostructureon fatigue-crack growth resistance of TiAl (from Campbell et al., 1999), reproduced with permission of Thc Minerals, Metals and Materi~ilsSociety
When TiAl is reinforced with ductile particles (20 vol.% Ti-Nb), FCG resistance is soiiietimes reduced, see Figure 18, and in other cases increased, depending upon the orientation of the faces of the pancake-shaped particles relative to the crack plane ao et al., 1994, 1995a). Specifically, fatigue resistance is enhanced only when the particle
faces are oriented normal to the crack plane. Figure 18 shows also that R ratio is a fixtor in that only for R = 0.1 does reinforced material behave similarly to unreinforced TiAl. The degradation of fatigue resistance with ductile particles, seen also with MoSi, (Soboyejo et al., 1993), is attributed to one or more of several factors: the absence of crack bridging, the influence of the ductile reinforcements in decreasing the crack opening displacement (COD) under cyclic loading, and the accumulation and partition in^ of inelastic strains. In replotting the data of Figure 18, Sadananda and Vasudevaii ( I 995) showed that the threshold is a function of Kmaxas well as 21. Only one study of the effect of brittle reinforce~ents on crack growth of TiAl has been reported; XD T i ~ l + 7 v ~ T ihas ~ , a threshold of 7 ( ~ u m a r ,1994), which is slightly higher than for the TiAl alloy shown in Figure 18. McKelvey et al. (1997) have commented on the a n o ~ a l o u st e ~ ~ e r a t udependence re of FCG behavior of TiAl alloys. Near-threshold growth rates are lower at 800°C aiid higher at 600°C conipared to room temperatu~e.Correspondingly¶ thresho~dsare highest at 800 "C and lowest at 600 "C, with 25 "C behavior in bctwecn. Since the effect is lcss striking in vacuum compared to air, environmental e ~ b ~ i t t l e m e may n t be at least partially responsible for the anomalous
0-'
Influence of load ratio, R, on the cyclic fatigue crack-growth behavior in y-TiAl composite reinforced with 20 v% Ti-Nb particles in the edge (C-R) orientation (from Venkateswara Rao et al., 19941, reproduced with periiiissiovp from Elsevier Science
Fatigue
337
temperature behavior. abru et al. (1997) have shown rates for a nearly fully lai~ellarTiirllloy are lower in high vacuum ( < 5 x 10-4 Pa) than in air, see Figure 19. This embrittling effect was attributed to hydrogen released from water vapor in the air, similar to the environmental e~brittlementdisplayed by iron alurninides. 5.1.2 ~ r t h o ~ h To i ~~ ~A il Alloys ~~ b
This class of alloys has higher tensile strength at temperatures to 760°C as well as comparable fracture toughness and ductility relative to Ti,Al alloys. A recent study (Wang and Yang, 1997) of the cyclic deformation of an orthorhombic composite strengthCS-6 SiC fibers reported the development of matrix fatigue cracks from damaged fibers and fiber/ matrix interfkces near free edges. An integraied computer code was developed to simulate the evolution of fatigue damage, the deg~adationof mechan~cal properties and the ~istributionof fatigue lives. The siniulation was based on a modified J-integral approach in which the progressive damage to fibers was incorporated. In general, the predictions agreed well with the expci-imental results. Tliis technique also has been applied to composites based on Ti-6Al-4V and Ti,Al (Wang et al., 1998). 5.1.3 Ti3Al Alloys
As in the case of TiAl alloys, microstructure plays a major role in fatigue crack-growth resistance of Ti,Al alloys (Aswath and Suresh, 1989; Soboyejo, 1992). A coarse ~ i d r n a n s t ~ t tstructure ~n provides better FCC resistance than does an equiaxed or alpha-two structure in a idm mans tat ten matrix. Roorn-ternperature FCG rates in Ti-2~Al-llNbare strongly affected by heat treatment, with the lowest rates at room temperature obtained with an inhomo weave' structure (Aswath and Suresh, 1989). Growth rates increase sharply with test temperature, with rates at 800°C 100-200 times greater than at room t e i ~ p e r a t ~ r This e . increase in growth rate is accompanied by a change in fracture mode from transgranular cleavage to a tra~sgran~ilar ductile mode at 800 "C, but oxidation at the higher temperature may also contribute to the difference. Davidson (1991) has sliown that the iiiitiatioii and coalescence of microcrac~sare important factors in FCC in Ti-24Al-11Nb. These microcracks are assumed to form in brittle zones ahead of the crack tip. Soboyejo et al. (1989) havc shown that the linkage of
Figure 19 Effect of environment on fatigue crack growth of Ti-48AI-2Mn-2Nb (from Mabru ef al., 1999)
these microcracks can occur below uncracked ligaments even when contact does not occur between the crack tips at the surface. There i s a general tendency for fatigue cracks to grow along brittle phases in these alloys (Aswath et al., 1990). This results in a tortuous path for crack growth, no matter what heat t r e a t ~ e n t is used (Aswath and Suresh,l~89~. Finally, it should be noted that the FCG resistance of similar to that of ill-annealed utilized of the commercial titanium alloys, and to Ti48 a%Al, except that the latter has the highest fatigue threshold (Soboyejo et aE., 1993). Several studies of crack growth in Ti,Al alloys have provided evidence for an envir~~nI~ient~1 influence. There is an effect of frequency on growth rates in lab air as well as in 10-5 torr vacuum for a Ti-24Al-l lNb alloy tested at 649 "C (Parida and Nicholas, 1992). Cracks grow much mor in this alloy as well as i al., 1995). Similar obs temperatures in the range between 650 and 800°C (Aswath and Suresh, 1989; enton et al., 1992; Balsone et al., 1990). There is a significant effect of frequency on growth rates in this alloy; lowering of frequency from 100 Hz to 0.01 €32 causes growth rates to increase by a
factor of 10. In general, growth rates in a, alloys increase owever, transversely oriented fibers result in with moist environments, lower test frequencies, tlie highest growth rate of all, increased hold times and increased test temperatures room and elevated temperature essels et al., 1989; Venkaturaman, 1987). Limited work has been done on small crack 5.2 S L alloys (Davidson et al., 1991; d Larsen, 1992; ~avichandran, 5.2.1 Fe3Al Alloys ). Small cracks in super a2 grow at a slightly higher rate than in the nickel-base superalloy Astroloy, The fatigue belzavior of iron aluminides has been 10-100 times slower than in 7075 A1 extensively studied, over a range of al~iminumcontents et al., 1991). Small cracks in Ti-24AIfrom 16-35 ao/o (Castagna, 1994; Castagna and evelop arbitrary shapes that are affected by 1992; Alveii aiid StolofF, 1996). Effects or ternary microstructure and texture ( avichandran, 1995). solutes, microstru~~ure,te~perature and R ratio These shapes, in turn, affect crack-growth rates. With ( ~ i n i m u mto ~ a x i m u mstress intensity) have been a basketweave inicrostructure, as well as with two other studied under both aggressive (i.e. moist) and inert (i.e. microstructures, (a, and a, + fi), small- and long-crack dry) environments. Most of the work has been carried data correlate well when crack closure is accounted for. out on compositions that exhibit Fe,& type order, owever, small cracl~-growthrates were always higher although some work bas been done on the FeA1 alloy than those for long cracks for an aligned colony struccontaining 35aY0Al. We review here the most recent ture; the latter behavior was ~~ttributed to the nonfindings, e ~ ~ h a s i z ithe n ~ effects of Cr and Zr continuum nature of crack growth in that microstrucadditions and environment on crack-growth behavior. ture. Data for crack growth at tlie surface for the four The Fe-AI alloys studied, a11 of wliich were produced struct~i~es are shown in Figure 20. are by the Oak ~ i d g eNational ~ a b o r a t o ~OR^^) y baps the single factor most likely to in~uencethe listed in Table 2. Note that some alloys are partially growth resistance of titanium aluminides is the llized so as to i ~ ~ x i mtensile i ~ e ductility. Allo use of fibrous reinforcements. A continuous SCS-6 S i c (17a%Al) is disordered, Fe-35a%Al is a fibe~-reinforc~dTi-244.1- 11Nb alloy ( l o n ~ i t u d i ~ a ~ i n t e r ~ e t a ~ ~and i c all of the other alloys orientation) is Far more resistant to crack growth ordered Fe,Al type, tested in either the fully ordered than is nickel-base superalloy I -100 (Larsen et al., DO, conditioii or in the partially disordered
igure 20 A comparison of crack-growth rates of Ti-24Ai-llNb. ~ ~ a v i ~ l i1995) a n ~ ~ ~ ~ ,
and large cracks in four microstructures
Fatigue
339
well as the 0.5 a%Zr-C alloy (Alven, 1997). These data condition. All tests were run at a frequency of 20 have been utilized to formulate a model of enviroiiand an R ratio of 0.5; atmospheres varied betw niental enibrittleinenl, in which the r~te"1iiiiiti~g step is laboratory air, oxygen gas and hydrogen gas, as well as transport of hydr~genre~easedon contact mo~eratev a ~ u u It ~ ,has been shown in ~ u ~ e r ~ udislocation s of water vapor with a clean aluminLi~-richsurface investigations (see StoloK and Liu, 1994 for an (Castagna et al., 1993). extensive review) that under monotonic loading iron Fractographic examination showed that dimpled and nickel a~uminidesare embrittled both by atomic rupture is present in all e n v i r o n ~ e ~ tfor s the hydrogen and by the dissociation of water vapor into containing alloys, except hydrogen and oxygen. The latter effect is particularly hydrogen (Alven, 1997). pernicious, since embrittle~entmay occur even under ternary alloy predomin very low partial pressures of moisture. environments. Dimpled rup lure is oiily evident in A summary of FCG data for the Fe,Al alloys listed in Table 2 appears ure 21 (StolofI and Alven, 1996). The highest rates are e~hibitedby tlie disordered FAP-U while the lowest rates are 2 ordered 0.5%Zr-C alloy. Work on ratlares (Tortorelli, film formation at elevate alloy FA-129 has shown that FCG rates are lower in affects trapping of 1997). It is possible, also, the B2 than the DO, condition, and that there i s little difference between rates for fully and partially recrystallized ~icrostructures(Castagna, 1994). The effects of environ~entare decidedly different for ordered conditions, as shown in 5.2.2 FeAl rllloj)s 1994). Note that there is a much gen gas (1 atm.) on s~ow-~oo1ed~The earliest report of fatigue data for Fe DO, material than in the quenched, partially by Alven and StoloE for Fe-35a%Al; data arc ordered condition. Oxygen gas is considered to be as included in Figure 21. T inert as high vacuum for iron aluminides (Stoloff and e~brittlingeffect of 1 atm. Liu, 1994). pared to either oxygen or air environments, see Figure Frequency efTects are significant for Fe,Al alloys 23 (Castagna and Stoloff, 1995). tested in air, as i s typical under conditions of have reported FCG data for a e n v i r o n ~ e ~ embritt~ement ta~ (Matuszyk et aE., 1990). containing 1wt. O h iianometri~-si~e Y2O3particles and Crack-growth rates increase sharply as frequency is prepared with two inicrostructures by either hipping or lowered, for alloy FA-129 (Castagna et aE., 1993) as extrusion. As in the case of Fe,Al alloys reported
3
Fatigue c ~ a c k ~ g r odata w ~ for ~ several Fe-AI alloys. See Table 2 for compositions (from Stoloff and Alven, 1996)
~ ~ c h ~ nProperties i c ~ l
340
Effect of long-range order on fatigue crack-growth of Fe,Al alloy FA-129 at 25 "C (from Castagna, 1994)
above, the crack-growth resistance was higher in high vacuum than in air, The difference in growth rates for the two environments could not be explained by closure ~rguments.Table 3 coinpares these data to na and Stoloff (1995) for Fe,Al alloys. ote that the thresliold values obtained for the HIP
FeAl were much lower than for the more ductile Fe,Al alloys, perhaps due to closure effects in the latter. Further testing by Tonneau et al. (1998) showed that dissociation of water vapor in air, thereby releasing hydrogen, is responsible for higher crack-growth rates in air than in high vacuum or in oxygen. O xyge~seems to
1
E ~ b r i t t ~ i nefFect g of hydrogen on fatigue crack growth of Fe-35a%Al at 25 "C (from Gastagna and Stoloff, 1995)
34 1
Fatigue able 3 Fatigue crack-growth data for iron aluminides (from Castagiia and StoloE, 1995 and TonneaLi et al., 1998)
HIP-FeAl HIP-FeAI HIP-FeA1 HIP-FeAl FA-129 (B2) FA-129 (B2) Fe-35%A1 (B2) Fe-AI-Cr-Zr-C (B2) Fe-AI-Cr-Zr-C (B2)
Air, 25°C Low vacuum, 25°C High vacuum, 25 "C 0,, 25°C Air, 25 "C O,, 25 "C Air, 25 "C Air, 25°C 0,, 25°C
prevent moisture-induced embrittle~entby reducing the number of adsoprtion sites for water vapor at the crack tip. It should be noted, however, that oxygen does little to prevent moisture-induced enhancement of FCG rates in TiAl alloys under similar experimental conditions, suggesting that there is no universal mechanism of embrittiement in a ~ u ~ i n i d of e s di~erenttypes.
5.3.1 Nip41
In spite of the overwhelming interest in the mechanical behavior of nickel aluininides, little has been published in the past five years on their fatigue behavior. However, for the sake of completeness, we include here a brief summary of what is known about the crack-growth behavior of these aluminides. It has been known for some time that crack-growth rates in Ni,Al alloys are lower than for many superalloys, and that rates of growth increase with increasing temperature (StolofT et al., 1987). Detailed studies of an alloy designated 1C-221 (see Table 1 for cornposition) showed that environmental effects are very important, in that oxygen accelerates crackgrowth at elevated temperatures (Matuszyk et al., 1990). Creep processes also contribute to growth rates at temperatures above 700 "C. Crack-growth rates increase with decreasing frequency in both vacuum and air for this alloy at 800 "C,but the rates always are higher in air. Intergranular fracture occurs in air at all test frequencies, while transgranular fracture is noted in vacuuin. Secondary cracking i s enhanced at lower frequencies, s~ggestingthat diffusion of oxygen contributes to their initiation. 5.3.2 NiAl There is surprisingly little information in the literature about the fatigue crack-growth behavior of NiAl
9. I 12.5 13.7 14.3 23.9 (22) 24.1 23.4 42.3
8.0 5.6 7.2 5.2 6.9 3.0 -
4.7 4.8 6.3 5.5 14.5 20.0 16.3 18.1 18.6
alloys. Flores and Dauskardt (1997) have reported a very high Paris exponent, yy2 = 34, for NiA1-0.25a%Fe single crystals, see Figure 24, as would be expected for a brittle material. This observation suggests that fatigue life under stress-controlled conditions will be extremely sensitive to the applied cyclic stress level. Also, the very low thres~oldof about be eliminated entirely by applying p sive overloads. This effect was first shown for aluminurn and steels by Topper and Yu (1985). The fatigue crack-growth behavior of a NiAl-9% aligned eutectic is strongly dependent on Kmaxand less dependent on 6 K (Wong et al., 1998). There appears to be an R-independent fatigue threshold of about 6MParn112 in the range studied: -0.3<X,<0.35. In this system the ductile MO fibers did not provide a ~~dck-bridging enhancement of fatigue resistance, in contrast ta the beneficial effects of the fibers on 104 rrq
a,
U
G
3%
i
W 1
Fatigue crack-growth data for NiAl + Fe single crystals, showing high Paris exponent (from Flores and Dauskardt, 1997), reproduced with peimssion from Elsevier Science
342
~ e c l ~ a n Proper ~ ~ a lties
monotonic toughness. Similar behavior has been noted in ~b-particle~reinforced MoSi,.
The fracture and Fatigue behavxor of Nb,Al and several composite alloys with Nb particles liave been reported by ~ u r u g e s let~ al. (1992, 1993), DiPasquale et al. (1995) and Hanada et al. (1995). These have generally shown the characteristic hi h crack-growth exponents associated with brittle materials. A study of FGG in a ~ b ~ ~ in-sifu ~ , Acoinposite l showed cracli-growth rates that were much lower than for the unreinforced iiitermetallic, although not nearly as low as for pure esh et al., 1993). Crackrowth rates in 18ao/oA1 alloy, also an z n - ~ i t ~ to those of lamellar TiAl 6w%Al) as well as Nb,Al and Nb (from Murugesh et al., alloys (Davidson and Anton, 1993). Aging of a hot1993), reproduced with permission from Elsevier Scieiice
increasing toughness, cornpared to fibers or layered reinforcements. In fact, coarse laminates with Nb produce drainatic improvements in moiiotonic and cyclic crack-growth resistance of Nb,Al (Bloyer et al., 1997). The effect of laminate orientation is more significant for fatigue crack growth than for monotonic toughness. ~ncreasingthe layer thickness improves both fracture toughness and fatigue crack-growth resistance. The toughness and fatigue threshold values for Nb15ao/o~1-10%~T~ and ~b~15ao/~A~-250/oTi alloys in which Nb,Al precipitates of unknown volume fraction are dispersed in a B2 matrix have been reported asquale et al., 1995). The fatigue threshold of the er alloy was only 3 MPam1I2, compared to a fracture toughness of about 20 MPa rn1/2. Data for l-lO%Ta it^ composites show an i~provernentover Nk,Al, but FCG exponents are y high and cracks in Nb still grow more slowly nada et al., 1995). Recent work shows, Figure 26, that ductile, predominantly I32 Nb-Al-Ti alloys containing 40 or 41a%Ti have comparable or better FCG n mill-annealed Ti-6A1-4V and monoasquale et al., 1996; Ye et al., 1999). The improved crack-growth resistance afforded by high levels o f titanium a to be related to improved fracture toughness. ent toughening, slip band formation at crack tips and crack-tip blunting are believed to account for improved toughness (Ye et al., 1999).
5.5.1 ~~~i~
Several investigations of fatigue crack-growth resistance of MoSi, and its composites with Nb or Sic particles have been published. Soboyejo et al. (1993) reported that at room temperature, stable crackgrowth occurs at AK values as low as 1.'7MParn1/2. The crack-growth exponent, m, was 14, consistent with the high values reported for other brittle intermetal~ics. The same study revealed that the fatigue resistance was lowered by the ad~itionof ~ O V O ~ . ~Nb / O particles, even though the rnonotonic fracture resistance was increased slightly by the particles. This work was important in that it de~onstratedthat improvements in fracture toughness by the use of ductile particles do not necessarily lead to improved fatigue crack-growth resistance. Crack bridging IS observed under rnonotonic conditions but not under cyciic loading. It has been shown by the same group that crack-growth rates increase with increasin N b fiber diameter, aiid that growth rates with 75Opin diameter fibers are 100 times greater than for laiiiinated composites reinforced with 200pm thick Nb lamellae (Soboyejo et al., 1996). The varying effects of different microstructures was attributed to differences in reinforceme~tspacing and cracktip blunting by the Nb fibers. The latter results in much lower Paris exponents for the composites, coi~paredto unreinforced MoSi,. Iii the near- threshold regime, the laminates had similar crack-growth resistance to the particulate
Fatigue
343
. .
1
U
1
Fatigue crack-growth data for Nb-Al-Ti alloys coinpared with data for other engineering materials; (a) as-cast 10Ti, 25Ti and 40Ti alloys, (b) cast and heat-treated l0Ti alloy, (c) cast and heat-treated 25Ti alloy, and (d) cast and hcat-treated 4073 alloy (from ~ i ~ a ~ q ueta al., l e 1996 and Ye et al., 1999), reproduced with perinission from Elsevier Science
344
~ e c ~ ~ aProperties ~ i c a ~
reinforced material. Interestingly, the crack-growth resistance of pure Nb, a weak but ductile metal, IS n i ~ c hgreater than that of any of the composites. By way of contrast, composites with fibers and laminates provide higher monotonic toughnesses than for monolithic MoSi,. Another recent finding is that a wire mesh b reinforceiiient provides much lower crack-growth b particles, see Figure 27 (Badrinarayanan ct al., 1996). A similar effect was noted by the same group on monotonic fracture resistance. Increasing load ratios from 0.10 to 0.70 results in much higher growth rates and reduced fatigue tliresliolds; sucli behavior is characteristic of other metals and ceramics, but the data for this system are much more sensitive to Kmaxthan for metals. A modified Paris power law relation which includes the effects of both AK and Kmax has been established: da/dN = C'K;,, Are"
i, with
~her~s
(2)
ere G' is a scaling constant which is independent of ax, K and R, while y1 and p are e x p e r i ~ e n t a ~ constants, determined to be 13.2 and 7.5, respectively, adrinarayanan e f al., 1996). The oved properties of the wire mesh-reinforced i, have been attributed to extensive crack deflecron at the interface between the matrix and the reinforcements, interface debonding, and frictional sliding between mating crack-face asperities. Therefore, increased crack-tip shielding is believed to result from crack deflection and roughness-induced crack closure. Another feature of the fatigue crack-growth resistance of the composites is that stable crack growth readily occurred, while stable crack growth is very difficult to obtain in monolithic MoSi,. Therefore, a mixed result is obtained with these and other ductilecomposites (e.g. T i ~ l - ( T i , ~ b ) ) ao et al., 1994, 1995a), in that tmce is increased under nionotonic loading for all reinforcement morphologies, but is creased under cyclic loading of part~cle-reinforced oSi, except insofar as stable crack-growth is more readily achievable in the composites. Finally, wire mesh is the most effective reinforcement under both monotonic and cyclic loading, while unidirectional wire reinforcements are intermediate in their effectiveness. In s u ~ i ~ a r fatigue y, crack-growth resistance of oSi,-Nb composites is intermediate between that of many cerainics and unreinforced intermetallics and of most ductile metals. everal studies of crack growth at room and elevated temperatures have been shed for MoSi, and its composites with Sic. a from two sources *
10-6
7 Variation in cyclic fatigue-crack growth rates, dal d N , as a function of the nominal (applied) stress-intensity - K,,,), at R = 0.1 for MoSi, reinforced range, AK (= KmaX with 20 vol.% Nb in the form of high aspect-ratio wire mesh (Nb,/MoSi,) and as spherical particles (Nb /MoSi,) (from Badriiiarayanan et d.,1996), reproduced witi pcimissiaii oT TMS and ASM International
(Soboyejo et al., 1993; amamurty et al., 1994), plotted in Figure 28, sho that cracks grow at very low AK values and progress rapidly in ~ o n o l i t h i c specimens at both 25'C and 1200°C. Creep and environmental effects dominate at the high temperature (Sadananda et al., 1999). Much slower crack growth was noted in the composite because of crack deflections at the matrix-reinfo~cement interfaces. Cracks followed an intergranular path at high temperature, and growth was facilitated by oxygen diffusion through the grain boundaries. It has been shown that the fatigue resistance of ( composites at elevated temperat~rescan be improved by addition of 2w%C ( R a m a ~ u r t y et al., 1994). Previous work had shown a similar improvement in fracture toughness with carbon additions (Maloy et al., 1991). Both eEects seem to result from the prevention of formation of silica during processing as well as during exposure to air and the formation of a ternary Nowotny phase that coiitributes to toughening. The presence of carbon increased the threshold for fatigue crackgrowth initiation and contributed to lowering crackgrowth rates. Further, carbon reduced the incidence of cavitation at crack tips in the composite samples.
345
Fatigue
crack with the layer interfaces may promote crack-tip shielding by debonding, crack-tip blunting and crack bridging. Preliminary data indicated that crack-growth rates were higher than those in ~ e t a ~but s , slower than those in other brittle materials.
0
8 u
n O
0
0
CO
D
0
0
5.5.2 Nb5Si3 a
0 Q 28C
Crack-growth data for MoSiz aid MoSi,-Sic composites (from Soboyejo et al., 1993 and R a ~ a i ~ u r et ty al., 1994; see also Sadananda et al., 1999), reproduced wlth perinission from Elsevier Science
Later work by Lu et al. (1996) reported fatigue crack-growth data for MoSi, composites reinforced with Zr0, particles and Sic whiskers or particles. Fatigue crack-growtli parameters, shown in Table 4, revealed very high crack-growth exponents at 1200 "C for monolithic MoSi, and two of the composites; however, composites with Sic particles displayed exponents more typical of those of metals, in the range 3.8-6.0 at 1200 and 1300 "C. Stable crack growth at 1200°C occurs only within a narrow range of AK values, between 0.9 and 1.4MPai~1'1~. The very high growth rates noted in whisker-reinforced material was attribuied to viscous flow of amorphous glassy phases at the grain boundaries superimposed on mechanical fatigue damage. The fatigue and fracture behavior of layered MO%,/ Nb-15A1-40Ti coniposites with different Nb alloy thicknesses has been reported by Ye et al. (1996). Stable crack. growth was achieved at room temperature with 500pm thick layers, unlike monolithic MoSi,. It was suggested that the interactions of the advancing
Only recently have FCP data for reported. (Zinnser and L e w a ~ ~ o w s 1997). In the former work, a Nb prepared as an in-situ composite, c solid solution in equilibriu~wit metallic. Crack-growth experiments carried out at R ratios of 0.1 and 0.4 showed that crack-growth for two composites were higher than for a 1.24a%Si alloy which is equivalent to the matrix composition. Although the fdtigue behavior of singlephase Nb,Si, was not studied, the of 2 MPam1i2reported for this mat 1992) suggests that stable crack gr
appeared that the increase in growth rates for the Composites relative to Nb were proportional to the volume fraction of intermetallic, although differences in micros~ructuremade this comparison d i ~ c u l t As . crack growth proceeded from the ear-thr~shold region to overload, there was an increasing proportion of cleaved primary Nb observed, suggesting an important role for Kmax in the fatigue behavior. Paris-law slopes of 2 to 5 were observed for the composite, in contrast to much higher values, in the range 30 to 100, reported for a variety of i ~ t e ~ e t a l l i c s toughened with Nb or Nb alloys. It should be noted that the size and distribution of Nb particles or fibers has a major influence on fatigue response, with the best results seen when a Nb mesh is utilized as the
Fatigue crack-growth parameters for MoSi, and coniposites, v = 10 Hz, R = 0.2 (from Lu et al., 1996 and Rarnamurty et al., 1993) Materials nionoll~hicMoSi, MoSi, + 20 vol.% Sic, MoSi, + 20 vol.0/0 TZ2Y* MoSl, + 20 vol. 94 Sic, MoS1, -+ 20 vol.% Sic, MoSi, + 20 vol. % Sic,
C {min/cycle)x (MPa4m)-
9.1 x 10-G 2.3 x 1W6 1.8 x 10-l' 3.3 x 10-9 2.3 x 10-7 1.8 x 10-6
*MoSiQ,+ 20 vol.% ZrQ,, stabiliz~dwith 2mole% Y,O,
rn
AK Range (MPaJm)
Temperature "C
32.1 155.6 40.8 3.9 6.0 3.8
0.9-1.4 0.98-1.3 1.Cl.3 4.1-8.0 2.1-4.7 4.67.0
1200 1200 1200 1200 1300 I300
adrinarayanan et al., 1996). nother iiiteresting finding for the composite was a glier threshold than previously noted for silicide matrices, although the thresliold was not as high as for i solid solution which corresponds to the coniposition of the tough phase in the in-xitzk oom t e ~ p e ~ a t u rcrack e growth rates for Nb-Si composites have been compared with those for two E. (1997). The threshold -Si alloys than for other is exponents are lower, apparently as a consequence of the good fatigue characteristics o f the metallic constituents in these systems. Further, toughness is insensitive to temperature up to 500*6, and the thermal expansion ~ i s ~ a t c ~~~et sw e em~tallic n and i n t e ~ e t a l l i cphases isystem are small (Bewlay, 1996).Therefore, mposites appear to be promising for hightemperature structural applications.
The Fatigue results survey d in this review were (with one exception, for NiAl) determined under stress
control. It is well known that under such loading conditions strength is more important than ductility in determiiiing lives or rates of crack growth. Therefore, one of the most direct means of increasing fatigue life or reducing crack-growth rates is to increase the flow stress of the material, provided that no new low-energy fracture modes are introduced. In general, trends seen in HCF tests are expected to ofYer insight into FCG behavior as well. It has been shown, for example, that the test enviroiiment affects both behavior of the nickel and iron alumi manner (Stoloff and Liu, 1994), with hydrogen detrimental and oxygen beneficial. A study of lowcycle fatigue of B2 Fe-42a%A1 also shows that moisture-induced embrittlement can be prevented by deformation in an oxygen environment or by coating with a protective film ~ ~ a n and e s ~ i ~ ~1997). l a , the major fatigue studies of recent years have focused upon FCG beliavior, the remainder of this discussion will be devoted to a summary of FCG observations. A suininary of crack-growth data for most of the alloy systems described in this chapter appears in Table 5 (Stoloff, 1997). While there has been considerable efYort devoted to o ~ t a i fatigue ~ i ~ data ~ for TiAl alloys, Fe,Al alloys and MoSi, composites, there still remains a serious lack of comprehensive data for most
Fatigue crack-growth parameters for structural interrnetallics (Stoloff, 1997)
Alloy
Ti 48AL Ti-47.3A1-2.3Nb- 1..5Cr-0.4V(d) Ti-47.3Al-2.3Nb- I . SCr-0.4V(l) iAl-20 vol.%TiNb Ni,Al + I3 + Hf Fe-28Al-5Cr-0.5 Fe-28Al-5Cr-0.5 Fe-28A1-5Cr 0.5 Fe-28Al-5Cr(€32) Nb,Al Mb, AI/Nb Nb- 18Al-I 0Ta MoSi,-20 vol.%Nb, MoSi2-20v o l . a / u ~ b ~ ~ ~ ~ o , ~ ) S i ~ - 3vol.%SiCp 0 TiAZ TiAl-20 ~ o l . ~ / ~ T i N h Ti-47.3AI-2.3Nb-1.5Cr-0.4V(l) Ti-47.3Al-2.3Nb-If5Cr-0.4V(d) T i - 4 $ A l - 2 ~ n ~ 2(as ~ bcast)
Temp. (“C,
Frequency (Hz)
25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 1200 800 800 800 800 700
-
“Depends on orientation, heat treatment, **Crack growth across eloiigated grains.
R
25 25 20 20 20 20 20 25 25
0. 1 0.1 0.1 0.1 0.1 0.5 0.5 0.5 0.5 0.1 0.1
20 25 25 25 10 25 25 25 25
0.1 0.1 0.1 0.1 0.2 0. 1 0.1 0. I 0.1
25 25 __
A&, (MPa 5 6.5 10 7 5.5 5 20 14.5 13.5 18 16.9 0.6 3 4 4-7-5* 1.7 2 7.2 4.1 5.5 4.9 12 8
(MPa III~’~) m 8 7.5 20 22 8 9.6 60 29.9 19.8 60 26.4 1 4 5 30 3 3 8.5 9 9 8 18 12
50 15”
6.9 11.2
14 14 3.9 6.3 6.9 10
Fatigue
intermetallics. This is particularly striking for NiAl, for which numerous fracture studies have been published, but for which most of the published Eatigue data are under strain-controlled conditiolls (Noebe et al., 1995; Noebe and Lerch, 1992, 1993). What appear to be the only published crack-growth data for NiAl appear in Figure 24. In order for intermetal~ics or their composites to be seriously considered as commercial materials, more effort needs to be placed upon obtaining databases that include both stress- and strain-controlled fatigue data. However, certain guidelines are available to judge the fatigue resistance of these materials. Unless high ductilities and fracture toughnesses are achieved, FCG exponents will be high and thresholds will be low. Environmental effects are a serious problem; hydrogen introduced directly or by breakdown of water vagor causes severe ~ ~ b r i t t l e m e n t of iron aluminides under both cyclic and nionotoriic conditions (Stoloff and Liu, 1994; Takasugi, 1993). Similarly, NiJ.1, TiAl and Ti,A1 alloys are sensitive to these environments.Therefore, hydrogen contact must be avoided to determine intrinsic FCG rates. Oxygen also causes problems with Ti,Al (Wessels et al., 1989) atuszyk et al., 1990) at elevated temperatures. While oxygen prevents hydrogeninduced embrittlemeiit in iron aluminides, there seems to be no similar beneficial effect in TiAl. The effects of hydrogen aiid oxygen on FCG in other alloy systems has not been studied. Nevertheless, the use of ductile Nb r e i n f o r c e ~ e ~ ttos improve toughizes~of silicides can be expected to lead to serious probleins in both monotoiiic and cyclic properties. This is because of the strong afinity of b and other group Va metals of the periodic table for 0th oxygen and nitrogen and the poor oxidation resistance o f Nb, Furthermore, Nb is readily embrittled by hydrogen (Hardie and Mc~ntyre,1973). The role of microstructure in HGF and FCG has been studied extensively only in titanium aluminides. For TiAl alloys lamellar structures clearly are superior in their HCF and FCC resistaizce to all other microstructures. There is contradictory evidence for the role of grain size in crack growth, but in general grain-size effects on fatigue properties are not expected except through resulting changes in flow ever, the distribution of strengthen in^ phases will be a significant factor. This is clearly the case with composites, wliere it has been shown repeatedly that ductile particles niay actually increase FCG rates while fibers and lamellae can be effective in reducing FCG rates. Orientation effects are significant when non-spherical reinforcements are used
347
et al., 1994). Clearly, much more to clarify the differing effects of second phases on monotonic and cyclic properties. This nec~ssitates the study of crack-sh~eldin~ phenomena, as has been extensively done to date only for some TiAl and MoSi2 systems. Small cracks also grow at rates that are de microstruc~ure,as in the case of Ti 1995), adding another variable to the experimental 1% atrix . Apart from microstrLictura1 and environi~ental control, there are additional variables that can influence HCF and FGG resistance. These include frequency, temperature and R rat general, FCG rates increase and re, decreasing frequency and ver, anoma~suste~perature i~creasingR ratio has been seen in TiAl alloys. Frequency effects are most likely to be observed when an aggressive environment is present or when creep can occur during the fatigue cycle. The influence of R ratio is a result of its effect on crack closure; increasiiig X reduces the likelihood of a crack closin while unloading occurs. The result of this is that the ful~ applied stress-intensity range is felt at the crack tip. The significance of Kmaxhas been discussed authors (Sadananda and ~ a s L ~ d e v a1995; n~ nanan et al., 1996) and this Factor also needs to be considered in dealing with intermetallics, as with other brittle materials. Zn short, the status of our knowledge of fatigue processes in intermetallics remains uiisatisfactory if these materials are to be used in structural applications. When comparing the fatigue behavior of interme tallics and conventional alloys intended for structural applications one finds many si~ilarities. Crack initiation and growth i~echanis~ns are basically the same in both classes of alloys, but the presence 01 long-range order in the i n t e r ~ e t a l l i ~suppresses s slip processes at a crack tip. As a conse~uence,in most intermetallics, it is more difficult than in disordered alloys to initiate cracks under cyclic Isa in an increase in high-cycle fatigue life. difficulty 111 inducing dislocation motion at a crack tip results in stresses not readily relaxed by slip and in a consequent increase of crack-growt~ rates. This is especially apparent in the inore brittle intermetalli~s: TiAl, NiAl, MoSi,. The crack-growth response of the brittle intermetallics, therefore, closely resembles that of ceramics and is a significant impediment to commercialization, especially in critical a~plicatioiis such as aerospace.
348
Mechanical Properties
We close the chapter with a brief summary of research that needs to be done to improve our un~ers~anding of the cyclic behavior of intermetallics. ch more attention should be devoted to mechans of fatig~~e-crackinitiation and growth. location interactions leading to persistent slip ands and extr~sion-intrusion formation have only been reported for NiAl and Ni,Al, in marked contrast to the many such studies on pure metals aiid conventional alloys. The relationship between slip processes at various temperatures and fatigue-crack nucleation ancl growth remains unknown in most interi~etallicsystems. The role of environment in ~ a t i ~processes ~ e also needs further study; i ~ - s i t ~ observations of crack-tip phenomena in the scanning electron microscope are desirable. The influence of surface coatings and surface tr~atmentssuch as shotpeening has not been reported, in spite of their potential importance in commercial applications. levated temperature fatigue properties are lacking , with the exception of TiAl and nately, there i s no alternative to further extensive experi~~ental studies to fill in the gaps in our knowledge of cyclic phenomena in inter~etallic ~~mpo~~n~s.
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~ e ~ ~ i a n iProperties cul
Sastry, S. M. L., and Lipsitt, H. A. (1977a). m et all. Trans., A8, 299. Sastry, S. M. L., and Lipsitt, H. A. (1977b). Acta ~ e t u l l . ,
. (1996). Oak Ridge Natioiial Laboratory, unpublished.
Tonneau, A,, Henaff, G., Gerland, M., and Petit, J. (1998). 1985). Intl. J . Fatigue, 7 , 159. Tortorelli, P. (1997). Oak Ridge Nationai Lab, unpubl Trail, S. J. and Bowen, P. (1995). Mater. Sri. Eng., A19 427. Tsutsurni, M., Takano, S., Kitamura, T., and Ohtani, R.
H. Y., and Nakano, T. (1995). Mater a, H. Y., and Nakano, T. (1996).
~enkateswaraRao, K. T., Odette, G. R., and Ritchie, R. 0. (1994). Acsa Metull., Venkateswara Rao, I<. T., and Ritchie, R. 0, (199%). In Fatigue and Fracture of Ordered I n t e r ~ e t u ~ ~I1i c(eds ~ s T. S. Srivatsan, W. 0. Soboyejo, and R. 0. Ritchte). TMS, ~ ~ ~ r e ~ i dPA, a l 327. e, Soboyejo, W. O., DiPasquale, J., Ye, F., Mercer, C., V~nkatesw~ra Rao, I<. T., Kin, U-W., and Ritchie, R. 0. Srivatsan T. S. and Konitzer, D. G. (1999). Metall. (19958). Scripta ~ e ~ a l l3. , Trans., Venkateswara Rao, K. T., Kini, Y. W., Muhlstein C. G,, and Srivatsan, angwood, M., and Soboyejo, W. 0. Ritchie, R. 0. (1995~). Mater. S n . Eng., A19 (I 995). and Fracture of Ordered I n t e r ~ e ~ a l l i c ~ e n k a t u r a m ~ nS., (1987). A F W A L ~ T ~ - 8 ~ - 4 1 Air 0 3 , Force ~ ~ 1 II0 (eds ~ sW. 0 . Soboyejo, T. S. Srivatsan, and R. 0. Materials Lab, Wright Patterson Air Force Base, , Warrendale, PA., 117. Wang, P. C., and Yang, J.-M. (1997). Mater. Sci. Erg Snvatsan, T. S., DiPasquale, J., and Soboyejo, W. 0. (1996). 101. In D e f o r ~ a ~ i oand n ~ ~ a c t ~ofi rOrdered e I ~ ~ e r ~ e t a i l iIII c,s Wang, P. C., Her, Y. C., and Yang, J.-M. (1998). Mater. Sci. (eds W. 0. Soboyejo, T. S. Srivatsan, and H. L. Fraser). TMS, Warrendale, PA., 483. Wesseis, J . F., Marquardt B. J., and Krueger, D. D. (1989). Stoloff, N. S. (3992). In U r d e r e ~I n t e r ~ e ~ a ~ l-i cPhysical ~s Presented at TMS- AIM^ Svmp.on Creep and Fracture of M~rallurg9and Mec~anical~ e ~ a v i o(eds r C. T. Liu, R. W. ~itaniA u ~l ~ ~ i n ~TMS, ~ e s IndianapoSis, . IN. Cahn, and G. Sauthoff). Kluwer, Dordrecht, Netherlands, Worth. I3. D., Larsen, J. M., Ba 257. (1 997). Metoll. Mciter. Tram Stoloff, N. S. (1993). In Critical Issues i n the D e v e l o ~ i ~ e nof t Wright, P. K., Maurer, E;. High Ternper~ture~ ~ t ~ r i (eds a l s N. S. Stoloff, D. J. Unpubl~s~ed research, General Electric Aircraft Engines, Duquette, and A. F. Giamei), TMS, Warrendale, PA, 367 Ciiicmnati, OH, see also D. 23. Miracle and R. Darolia Stoloit; N. S. (1996a). In P ~ 9 ~ s~i e~tuu ~f l u r and ~ y Processing rme tallic ~ o ~ p o u n d sPr i n c ~ ~ l e and s uf I ~ t e r ~ e t a ~Cl ioc m ~ o ~(eds ~ i ~N.s S. StolofY, and V K. (eds J. H. ~ ~ s t b r o o kand , R. L. Sikka). Chapman and I-Tall, New York, 126. Chichester, England, 53. Stoloff, M.S. (1996b). In Structural Interrnetallics 1997, Proc. Umakoshi, Y, (1990). Prog, Marer. Sci., Second Intl. Sytnp. on S t r u c ~ u Ir ~~ t~e~r ~ e t a l l(eds i ~ s M. V. Nathal et al.) Seven Springs, PA, TMS, ~ a r r e n d a ~PA, e, no, T., Nakazawa, J., and Urnakoshi, Y 33. (1997). J / s f ~r~ternatiunal, 37(12), 1210. Stoloff, N. S. (1997). ISIJ Irzternat~o~al, 37(12), 1197. Yasuda, H. Y., Behgozin, A., and Umakoshi, Y (1999). ., Fuchs, G. E., Kuruvilla, A. K., and Choe, S . J. ( 1987). In High ~ e ~ ~ e r a t Ordered ure I ~ t e r ~ e t a l lAlloys ic Ye, F., Lederich, R. J., and Soboyejo. W. 0. (1996). In N. S. Stoloff, C. T. Lm, and C. C. Koch). MRS ~ e f o r r n ~ i ~ arzd ~ o n Fracture oj Ordered In~errnetal~~c 1, 247. ~ a t e r ~ III a l (eds ~ W. 0. Soboyejo, T. S. Srivat~an,and Sto S., and Alven, D. A, (1996). In Proc. Symp. on H. L. Fraser). TMS, Warrendale PA., 457. COrros ion- Def ~ r ~ioii~ aIntf erac t ions. Mice, France Sept . Ye, F., Farkas, D., and Soboyejo, W. 0. (1999). M~rter.Sci. 24-26, Abstract TV OR 23. Stoloff, N, S., and Liu, C. T. (1994). Inter~etallics, Zhang, G. P.,Wang, Z. G ., and Wu, S . W. (1997). Takdsugi, T. (1993). In Cvifical Issues in the D ~ ~ v e l o ~qf~ e n t ~ e t u lMater. ~. Trans., J. (1998). Metall. Mater. High Te~iperati4r~ ~ a t e r i ~ ~ 1(eds . s N. S. StoloK D. J. Duquette, and A. F Giainei). TMS, ~arrendale,PA, 399
.Int Although priinary mechanisms of solid solution hardening are known in dilute metal alloys, the mechanisms in inter~etallicc o ~ p o u n d sare only beginning to be established. The availability of such knowledge for high-temperature intermetallics is intended to aid the logical development of useful ordered structural alloys. In this chapter some basic results in solid solution hardening of intermetallic compounds are sunimarized. It is concluded that, within our limited current ~no~vledge, hardeniiig is consistent with that caused by standard types of elastic interactions between point defects and moving dislocations. owever, major gaps in our knowledge exist, and they obstruct adequate quantitative tests. Major sotirces of uncertainty that are discussed are (1) identificat~onof the atomic nature of the defects in individtial cases, (2) deciding what temperature for testing is best to maximize and clarify the effects that are sought, and (3) how to deal with superimposed effects of more than a single type of defect. A step toward uiidei-sta~idingsolution hardening in inte~~etallics is to test whether the same elastic interactions between solute atoms and dislocations dominate as have been identified in dilute alloys of pure metals, but with the effective solute concentration
increased in intermetallics by the substitutions or vacancies that are created by deviations from stoichionietry. Such evaluations have now been done in B2(cP2) structures for the alloy and Ti in AlCo (Fleischer, 199 and Ti in AlRu (Fleischer, C1S(cF24) Laves structures for (Fleischer, 1992) - the last using data by Livingston et al. (1989).
re
Note that solutes can affect a variety of mechanical properties by various secondary alterations that they make in the crystal structure. They can precipitate new phases; they affect phase ecluilibria, solubility limits, and phase distrib~tionsin alloys with more than one phase, profoundly altering strength and ductility; they can pair with other solutes, and efyectively remove them from solution; or solute can pair to form dipole defects that have basic interactions with dislocations. Only the latter (basic interactions of solute with dislocations) are the subject of the main text of this chapter. For example Huang and ~ h e s t n u t t(1995) detail the effects of solutes 111 TiAl - fracture toughness, phases present and their distribution, creep, yield stress, and plastic strain to fracture. These are all vital quantities to consider in designing a useful structural material, but the complexity of the structures and the "Derived from the author's article 'Issues in understa~di~g diverse roles of alloying elements and of stoichiometry solid solution hardening of inter~etallics,' in ~ t r u c t u r f f l confuse any attempt at a scientific test of the I ~ t e i edited ~ ~ by ~ R. t ~Darolia, ~ ~ J. ~ J.~ Lewandowski, ~ ~ iiiechanical role of solutes. Similarly the work of C. T. Liu, P. L. Martin, D. B. Miracle, and M . V. Nathal, The Darolia et al. (1992) shows striking effects of Fe, Ga, PA Minerals, Metals & Materials Society, Warreiisb~~rg~ 1993, pp. 691-698, by per~issionof TMS. and MO on the yield strength and ductility of NiAl. ~ n ~ e ~C ~o ~ pt ~a Vol. ul ~~3 ~, ~Principles s ~~ and Practice. Edited by J. €3. Westbrook and R. L. Fleischer. @2002 John Wiley & Sons, Ltd.
352
~ e c h ~ n ~ Properties ca?
However, the non-i~onotonic nature of the effects makes clear that some secondary effect is present - a likely possibility being that the substitutional solutes are acting to remove the (s~aller)amounts of an interstitial solute, or solutes. Thus initial additions reduce strength and increase ductility. Unfortunately little is known in inte~etallicsabout the mechanical effects of interstitials and, again, from these (important) experiments it is diEcult to derive any fundamental information on solute-dislocation interactions. The best hint of a significant role on interstitials comes from the hardening of NiAl by carbon (Cotton et aE., 1993) at a rate (increase in yield strength per unit solute concentration) 3G, where G i s the shear modulus. Such rates signify dipoles (Fleischer, 1962), and were seen also for (Cotton et al., 1993) and for ishirna et aE., 1986c; Cotton et aE., - suggesting that they too produce dipoles. ver, C, Hf and Zr also have major effects on stic moduli (Lin and Zhang, 1993), so that the conclusions just reached must be regarded as tentative. Other types of interactions - again somewhat indiraffect solid solution hardening were iduk (1991) who suggests that solutes in Ni3A1iinportaiitly affect the stacking fault energy of sup~r-disiocations, thereby altering the difficulty of cross-slip, and hence affecting strength, work hardening, and ductility. This variation (for an ordered structure) of the Suzuki effect (Suzuki, 1952) in metal systems IS of a more fundamental nature. However, as noted elsewhere, since in Ni,Al conventional elastic interactions appear able to explain the hardening ( ~ i s h i m aet al., 1986a), it unlikely that the cross-slip effect is of primary importance. To further clarify what is not attempted here, hight ~ ~ p e r ~ effects ~ u r eOS solutes are often intermingled with the ‘imomalous? increase in strength seen in several intermetallics. Until that eEect is adequately unders~ood, it will be difficult to separate superimposed effects. The simplest ideas of solute ~ardeningare most nearly valid at low temperae - as long as brittle failure does not intervene. nce the discussion here will mostly address observations at relatively low temperatures.
ve~~i
S
ardening of ~ r y ~ t aby l ssolute atoms can be caused by a variety of niechanis~s,For randoml~located solute atoms there are two classes of solute, those that produce large hardeiiing per atom (‘rapid hardeners’)
and those that produce lesser (‘gradual’) hardening (Fleischer, 1962). Rapid hardening i s usually caused by atoms - either interstitial or substitutional - that produce large, asymmetrical strains, and therefore have large shear strains and strong interactions with screw as well as edge dislocations. ~ubstitutional solution hardening, such as is of interest here, 1s generally of the gradual hardening type, most often ascribed to one or both of two mechanisms. In the first of these, atoim that alter the lattice parameter b have effectively a different size from the matrix atonis (Mott and Nabarro, 1940) and will produce hardening that increases with the size misfit ~b(=
d(ln b)/dc),
(1)
where c is the concentration of solute. In the second mechaiiis~?atoms that alter the shear modulus G can be regarded as tiny inclusions of different moduli (Ciussard, 1950), which should produce hardening that increases with cG(= d(1n G)/dc).
Hardening in Cu and Ag alloys correlates better with EG than with E,,. and thus was concluded to be the more important factor for those metals (Fleischer, 1961). However, for quan~itativecompleten~ssit is necessary to consider both effects and appropriately sum them to calculate the hardening and to determine the relative effects of size difference and modulus difference (Fleischer, 1963a). In different s y s t e ~ sa variety of summing rules have been used, as is summarized elsewhere (Fleischer, 1987). Ty~icallyin dilute alloys o f metals, ~ardeningis by an amount Gc3’2c14x,where E is the appropriate, weighted sum of cl, and eG and a 700 (Fleischer, 1964).The value of a varies inversely with the volume per unit cell and with the slip vector; it therefore is likely to be smaller for an ordered compound than for the same structure disordered. N
The view followed here was originated by Westbrook (19651, but was not tested quantitatively: ~ingie~phase alloys that are off stoichiometry have inherelit (con~o~~~ defects - ei~hervacancies or A or or A sites - that lead to hardeiiin~on both sides of stoichiometry at low temperature; at high teniperature the same defects increase the diffusion rates and soften the material, so that it then is strongest at the stoichiometric composition (Westbrook, 1965). Direct measureinents of diffusion rates also support this idea
strongly; see the data tabulated by Hagel (1967). Thus one unique aspect of soficl solution hardening of intermetallic compounds is the inherent presence of superimposed effects of ordinary solute additions and those of constitutional solute. In order to determine whether deviations from stoichiometry are ~ c c o m ~ o d a t eby d vacancies or by substitutioiis of one type of atom on the other sublattice, knowledge of the density and lattice parameter as a function of stoichiometry is pertinent, as Figure 1 illustrates (Hagel and Westbrook, 1962). Vacancies will lower the density, while the effect of substitutions is to approximate a rule of mixtures. The data in Figure 1 make it clear that for cases where adequate ofT-stoichioinetry can exist, the alternative defects considered can be readily identified. For example, 2% to 3% on either side of stoichioinetry would have beeii adequate to determine the slopes on either side of stoichiometry from the data in Figure 1.
Although a number of measurements of hardness vs. composition implied that constitutional defects do produce hardening at temperatures that are less than half of the melting temperature, yield-stress results such as those of Wood and Westbrook (1962) are more
definitive and were the best early indicator of effects. Their data, plotted in Figure 2, follow a squai-e-rootof-the-concentration relation, which i s the most frequently observed behavior in solution hardening (Fleischer, 1963b). This behavior i s regarded as strong evidence that the expected constitut~~nal defects do produce conventional solution hardening.
The literature on solution hardening of ixiter~etallicsis limited, so that few studies exist in which data were adequate to test the existing solution hardening models. Prior literature is listed by Fleischer (1993a,c). The striking, definitive exception is a pair of studies on Mi,Al and Ni by Misliima and coworkers (1986a,b). They showed in the Ll,(c structure Ni,Al that hardening followed a function of c,, and cG for the various solutes just a s would be expected if superimposed size and modulus interactions controlled the solution hardening. Even more important is tliat (as shown in Figure 3) solutes in Ni (inany of them the same solutes) caused hardening that followed the same function almost q~antitatively.Not only do these results imply that conventional elastic interactions control the solution hardeniiig in
\ \
Pigure 1 Lattice parameter and density measurements allow constitutlonal defects to be identified. From Hagel and Wcstbrook (1961)
354
ure 2 Flow stress of AgMg vs. square root of the expected concentration of substitL~tiona1defects (Ag on Mg sites or Mg a n Ag sites). Replotted data of Wood aiid Westbrook (1962). The liiicanty IS consistent with the expectation that point-defect hardening i s occurring
but the fact that the results are nearly identical to those i implies that there are no extra major sources of solid solution hardening that are due to the ordered structure of Ni,Al at room temperature. Thus, for the LI2 structure the initial qL~estioii appears to be answered (i.e. conventional hardening occurs). We therefore turn to other structures - B2(cP2) and C 15(cF24).
The work to be summarized addressed three issues Are the primary effects similar in nature and magnitude to those identified previously? What point defects are formed‘? What eflects are seen from cases where there are simultaneously two or more types of defects? uperimposed defects occur in the general case where there are ternary solute atoms and constitutional defects ~~acaiicies or substituted major-constituent atoms on a ‘wrong’ sublattice), Both vacancies and wrong sublattice subs~itutions can act as ordinary solute in altering elastic moduli and lattice parameters and producing elastic iiiteractions with dislocations.
Measureinents of density p and lattice paraineter b determine the unit cell occupancy number N,. In AlCo aiid AlRu, vacancies result from excess A1 in binary alloys - one vacancy per excess A1 atom in AlCo, fewer than one in Al leisclier, 1993~).Using the formula N , = p Nob3/ where c, is the concentration of atoms of er mole M,, and No is Avogadro’s number, results such as those in Figure 4 are derived. The figure shows that for AlCo, excess CO is mostly in A1 sites, but some vacancies are also produced. Substitutions of ternary elements occasionally produce vacancies also, so that in such cases three or four types of defects inay contribute to hardening. The ductilizing element boron (somewhat surprisin i s inferred to reside in substitutional sites in A. (Fleischer, 1993e), where its addition lowers the shear modulus, does not produce precipitates, yet does not alter the lattice parameter. i n the C15 (cF24) structure the lattice parameter data in Figure 5 show that in Cr,Zr each compoiienl can substitute for the other. Hf can replace Zr, and MO replaces Cr (Fleischer, 1992). Here the defect structure is simpler than in AlCo, but relevant mechanical testing is more difficult.
The nature of hardening can be tested ~~alitatively by whether the magnitude is typical of what a given mechanism is known to cause in other systems and quantitatively if the strengths of the interactions with specific atomic defects are known. Interpretation will naturally be simpler in cases where only a single type of defect is present - whether constitutional or thirdelement substitutions. Hardening in binary AlCo alloys is consistent in magnitude and relative effects wlth conventional size and modulus interactions with vacancies and CO substitutions, and the same i s true for Al-rich 8 2 alloys. The effects of ternary solutes are of the expected average magnitude but they do not correlate well with the observed c,,’s and gG5s in AlCo. The presence of multiple types of point defects that need better characterization is a suggested explanation (Fleischer 1993b) . Figure 6 illustrates the situation in binary AlCo single-phase alioys (Fleischer, l993b). At the ‘low’ temperature of 750°C - 0.53 of the melting temperature - (Figure 6, top) the defects that were documented in Figure 4 produce hardening on either side of stoichiometry. ‘Low’ is as close to as possible,
--1
I I
I I
P
I
I
8
F i 3 ~ a r d~e n i n~gper unit ~ solute concentration as a function of combined interactions from size effects "a( = cb) and elastic ~ o d u l u eG. s The data on the left arc for Ni,Al; those on the right are for Ni (Mishima er al., 1986a.b). Solid dots are given for transition-metal elements
0.050
0.025
C (AI-ri~h)
0
0.025
0.050
0.075
0.1 00
0.1 25
C (Go-rich)
Cell occupancy for binary AlCo B2 alloys calculated froin their density and lattice paramcter. Each excess AI sltoin produces a vacant lattice site on the CO sublattice. Excess CO substitutes for A1 but produces increasing but lesser vacancy coiic~ntra~ions (Fleischer, 1993a)
Mec.hclnical Properties
356
In contrast, Cr2Zr (another C15 c o ~ p o u n d )could only be tested in compression to 950 "C (0.63Tm)due to equipment li~itations,so that except for one sainple with Zr in Cr sites, samples were brittle (Fleischer, 1992). Nevertheless, within the scatter, and consistent with microhardness tests at 950"C, there was hardening from solute and constitutional defects that was consistent with the hardening relation noted earlier for metal alloys, but with a somewhat lower value of a which is expected for intermetallics, since unit cells and slip vectors are larger, Although the results described (I) show solution hardening in intermetallics and in the simpler cases (2) fit the models that have been used to describe metal alloys, full understanding of effects awaits solution of several problems to be considered next.
/ 7.23
7.22
7.21
r
7.20
HI for Zr
inary Cr-Rich
719'
''"0
I
I
'
3.0
I
I
I
I
6.0
I
9.0
CO~CE~TRA~IO~ (ATOMI C %)
Lattice parameter data versus composition as a function of off-stoichiometry and solute additions for Cr,Zr alloys (Fleischer, 1992)
but above, the ductile-to~brittletransition (T&),so that plastic flow can occur. In spite of most of the samples b e ~ ~ v i n~lastically, g tlie two that are highest in CO were brittle, giving therefore only lower limits on the flow stress (as indicated by upward arrows). At the higher tei~peratureof 950"C, which is 0.64 of the melting temperature T,, the constitutional defects are presumably mobile and therefore weaken the alloys, as shown by Figure 6 (bottoi~),The ratios of the liar~eningper (unit concentr~tion)1'2are consistent with the measured q,'s and gG's. The Laves phases are difficult to test in a meaningfu~ way, at least when they have high T,, since plasticity mostly occurs at T- 0.8Tm or above. For the relatively 15(cF24) type-compound Cu2Mg ~ivingstonet al. succeeded in showing effects of four solute species by testing at 0.86T~,~(650 "C). The results were shown to be consistent with summed size and m o ~ u l u s effects (Fleischer, 1992), subject to the inference that valence difference is a surrogate for the dulus effect, as it is in dilute copper alloys eischer, I963a).
There are diverse obstacles to being able to test solid solution hardening effects rigorously in intermetallics. They cluster under topics o f deciding on nie~ningful testing temperatures and procedures, identify in^ the number aiid nature of defects, and modeling how to superimpose the effects of more than one type of point defect.
Figure 6 and the discussion of it noted one of the dilemmas of selecting a temperature where interpretable tests can be run. As high temperature is approached, solution hardening ceases at a temperature at which hardening is replaced by softening if defects aid d i ~ u s i o As ~ . temperature is lowered, most intermetallics become brittle, and as a consequence the more variable fracture stresses of brittle materials may mask the effects sought. It would appear that a reasonable protocol would be to lower the temperature to a small increment AT above Tbdin order to measure stresses for plastic flow - which are what most existing theories predict. A further complicatio~that is evident in Figure 6 (top) is that Tbdmay vary with composition. Does one pick a single t ~ m p e r a t ~ ~as r ewas , done in Figure 6, or should each composition be tested as a function of l' and the stress at a fixed Tb,+AT used? Another related questioii i s how one infers what the flow stress would be at absolute zero t e ~ p e r a t u r e ~ where most theories apply most directly. If TbdIS low, a meaiiingful extrapolation may be reasonably straightforward. However, as noted, T,, for some
357
0.
0.1
0
15 1
0.5
0.3
0.4
0.
OLUTE C O ~ ~ E ~ T ~ A T I O ~ ) ” ~
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ure 6 Flow stress in compression versus ofr-stoichioinetry in AlCo B2 iiitermetallics at 750°C (top) and 950°C (bottom) (Fleischer, 1993b)
358
~ e c ~ ~Properties ~ i c ~ l
inter~eta~lics may be at a high homo~ogoustemperature with a small temperature interval between Tbdand TD,where TDis the temperature above which increased diffusion causes point defects to weaken alloys. A different, but useful workin assumption would be that the stress at Tbd+ AT is nearly the low-temperature value desired, except that the elastic modulus would need to be adjusted to its value at T=0.
efect identification in i~termet~llics is a major problem. It will become clear that the general case where both solutes and con~titutional defects are present is experimentally unresolvable at this time. omewhat less complex are the cases of binary intermetallics when only constitu present. Figure 7 shows some po in a nearly equiatomic intemetallic. Excess atoms of each type ~ ~ g substitute h t in the other sublattice, reside interstitially, or be compensated by vacancies in r sublattice - six distinct possibilities. , Al~-formulaaluminides only two types of constitutional defects are known - X atoms in A1 sites, and X-lattice vacancies for excess AI (Chang and n, 1982). In other B2 alloys such as AgMg, ions occur on both sides of stoichiometry. In
stress dipoles of many varieties, one of which is sketched. Stress dipoles, examples of which appear in Figures 7 and 8, are known to produce major hardening in metals and ceramics (Fleischer, 1962), but cases have not beeii clearly documented in intermetallics. The existence of vacancy pairs has been described in FeAl (Wurschum et al., 19951, and the differences in hardening brought about by thermal treatments (Nsgpal and Baker, 1990) may be from that source. One conclusion is clear. Only for the simplest situations are we likely in the iiear future to be able to infer what defect is present and what its elastic strength is. ~easurementssuch as are given in F i ~ u r 4e will continue to help in this process. In some cases
0
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S ATOM IN L SITE
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0 both substitutions and vacancies, some of which may are retained by rapid Efect was shown by in their Figure 17. wever, Figure 4 is discrepant with their interpretation of compiled results in that the vacancy concentration increases with. deviation from stoichiometry rather than decreases. Ternary substitutions in binary intermetallics have been made, with complicated cell occupancy numbers r e s ~ l ~ i nin g ,both AlCo and AlRu (Fleischer, 1993a,c). In many cases vacancies are produced simultaneously with the ternary substitutions. In such cases, it is not known which sublattice the vacancies occupy or whether they are in both. A few defect configurations that can be imagined appear in Figure 8. The foreign (F) ternary atom may substitute in either sublattice (or both), may lie in one of several interstitial positions, may lead to vacancies osite or the same sublattice - at least nine s. Finally, defects may interact to form
0 0 0 L ATOM I~TERSTITIAL
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F i ~ 7~ Possible r ~ defects in a binary AB intermetallic. S and L are the smaller and larger atoms
Solution and Defect Hardenirtg
0 0
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L = LARGE ATOMS S=S M A ~ ~ A T O ~ ~
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359
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REQUIRES VACANCY IN SAME SUB LATTICE
REQUIRES VACANCY IN OTHER SUB LATTICE
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SOFT F A T O ~ ~ ATTRACT
Some possible defects lrom ternary solute In an AB lntermetallic
defects can be further characterized by electron channeling measurements in electron microscopy ( A ~ C ~ Eliterally ~ I , Atom Location by CHanneling Enhanced Mfcroanalyses), but this inethod i s insensitive to vacancies.
rich compositions of AlCo iiiay be one example of where two types of point defects are present; dipole formation - if incomplete - is another; solute that substitutes on inore than one sublattice is a third.
It is evidently likely that in any real case both constitutional defects aiid ternary (or higher-order) solute are present - perhaps niultiple types of defects. How do their effects combine'? Gypen and Deruyttere (1977) and Pike et d.(1997) have made a beginning of a theory, but no organized, definitive experimental test has been reported. The early predecessor theory is given by Koppenaal and Kuhlman-Wilsdorf (1964). We don't need greater complexity, but we must note a further complication: In measuring effects on lattice parameter and elastic modulus, it is difficult to infer values for individual defects if more than oiie species is present. Where the individual defects can be separately produced in different samples, their effects on b and on 6; can be measured; but where they are structurally associated, the separation is not accessible. The Co-
Existing experiments in relatively simple cases of ORstoichiometry aiid of teriiary substitutions in binary alloys are consistent with the primary strengthening coming from the familiar elastic forces between point defects and moving dislocations due to size and modulus interactions. These statements apply to data on Ni,Al (LlJ, Cu,Mg (C15), Cr,Zr (&115),AlCo ( and AlRu (B2). The conclusion should not be taken as applyiiig necessarily to properties and testing ranges that have not been examined. Other properties of order or of dislocation dissociation into partials may play a role, but they have not yet been demonstrated. In many cases multiple types of point defects are present, and adequate definition of their separate abundances and effects is lacking. complications aiid uncertainties that need to be resolved have been identified.
Mechanical Proper ties
360
The author i s pleased to acknowledge the General esearch and Development Center for its hospitality during the original writing of this inanuscript.
Gypen, L. A., and Deruyttere, A. (1977). .J. Marer. Sci., 1 1028-1 033. Hagel, W. C. (1967). ~ n ~ e r ~ e t Ca ~o ~~i c~ o ~Chapter n ~ ~ s20, , 377-404 (ed. J. H. Westbrook). Wiley, New York. Westbrook, J. H . (1961). Trans. AIM& Chesnutt, J. C. (1995). Inter~etallic C a ~ p # -~Principles ~ ~ s and Practice (eds J. H. Westbrook, and R. L. FIeischer). Wiley, Chichester, UK,
efereiices -WilsdorC D. (1964). Appl. Chang, Y. A., and Neumann, J. P (1982). Pro$. Solid St,
. D.%and Kaufman, M. J. (1993). In Struct~ral ~ f a t e r ~ (eds ~ ~ l ~R.s Darolia, et al.). TMS, Warrenclale, PA, p. 513. Darolia, R., Lahrman, D. F., and Field, R. D. (1992). Scripfa Diniiduk, D. (1991). ,J. dc. Physique, 3 (no.l), 1025. Crussard, C. (1950). M2taux et Corrosion, 25, 205-226. Fleischer, R. L. (1961). idcta Met., 9, 996-1000. Fleischer, R. L. (1962). Acta Met., 10, 835-842. Flcischcr, R. L. (1963a). Acts Met., 11, 203-209. Fleischer, R. L., and Hibbard, W. R. (1963b). NPL Con$ On ~ e l a t i ~Bemeen n Structure and Properties of Metals, 0, London, p. 261-297. Fleischer, R, L. (1964). Chapter TV in The ~ t r ~ ~ gof ~ ~ e ~ f f D. ~ sPeckner, , Ed., R e ~ n h o l93-140. ~, Fleischer, R. L. (1987). Scripfa Met., 21, 1083-1085. Fleischer, R. L (1992). ScriJltu Metall. Mater., 29, 799-804. Fleischer, R. L (1993a). J. Matericds Res., 8, 49-58. Fleischer, R. L (1993b). 3. ~ ~ t e r zRes., a ~ .8,~ 59-67. Fleischer, R. L Fleischer, R. L Fleischer, R. L
In S t r ~ c ~~a ~t ~r r~i (eds a~ ~ s R. Darolia, et d.).TMS, Warrendale, PA, p.445. Livingstoii, J. D., Hall. E. L., and Koch, E. F. (1989). Mater. Res, Soc. Syrnp. Proc., 133, 243. Mishima, Y., Ochiai, S . , Hamed, N., Yodogawa, M., and Suzuki, T. (1986a). T ~ a n sJapan . Ins Mishima, Y., Ochiai, S., Hamed, N., Suzuki, T. (1986b). Trans. ,Japan Ins Mishima, Y . , Ochiai, S., Yodogawa, (1986~).Traits. Japan Inst. ~ @ ~ a27, I s 41. , Mott, N.F., and Nabarro, F. R. N.(1940). Proc. Pkys. Soc., 2, 86-89. Nagpal, P., and Baker, I. (1990). Metall. Trans., A., and LIU, 6. T. (1997). ~ e ~ 2 j ~ ~ orts Res. Insd. ~ o h o Ubziv., ~ ~ ~ i 455. Westbrook, J. EI. (1965). High Strength Materids, 29, 724760. Wood, D. L., and Westbrook, J. €3. (1962). Trans. A M E , 224, 1024-1037. p, C., and Schaefer, H.-E. (1995). Phys.
The theoretical and experimental basis for the phenomenon in metals and alloys of increasing flow stress with plastic straining~ termed strain hardening, has had a glorious history (Basinski and 1974; Hirsch, 1964; Hon966, 1975, 1982; Kocks et lsdorf, 1962, 1966, 1985; Mecking, 1977, 1981; Mecking and Estrin, 1987; Mecking and Kocks, 1981; Mughrabi, 1975; Nabarro, et al., 1964; ~ o ~ l and e t ~Kocks, 1994; Seeger et ctl., 1957; Sevillano, 1993; Taylor, 1938). A great deal of experimental and theoretical insight into the nature of strain l i a ~ d e n i nof ~ crystal~ine materials has been gained over the past 50 years. Unforttznately, a concise, quantitative theory capable of describing all the aspects of work hardening in single and polycrystall~ne materials, whether disordered or intermetallics, for all crystal symmetries remains elusive. This review is aimed at the phenomenon of strain hardening in ordered intermetallic c o ~ p o u n d s .It is not intended to be an overview of work hardening in single- and polycrystalline materials in general, therefore the reader is encouraged to refer to the articles and reviews cited above. The strain-hardening behavisr of i n t e ~ e t a l l i cis~ quite complex, given the broad array of plastic
deformation processes possible over the range o f crystal structures encountered in these systems. details on dislocations in specific intermetallic syst the reader inay wish to refer to a number of recent reviews (Appel and Wa 1993; Banerjee, 1995; Miracle, 1993; Nabarro al., 1993; Pope and Ezz, 1984; Sauthoff, 1989; Sikka et al., 1993; Suzuki et al., 1989; ~ e y s s i ~ and re 1995; Yamaguchi and Umakoshi, 1990; Yoo et al., 1988, 1990). As will be discussed in more detail in following sections, the und~r§~anding of h~rdening processes in inte~ietallicsis rapidly evolving due to numerous recent deformation, electron niicroscopy and dislocation-m~delingstudi~s.~ o n t i n u ad~ances e~ in the u n ~ e r s t a n d ~ of i ~ gdisloc~tionsin the hardening processes is very important, since intermetallics tend to fail in a brittle manner in tension only after a limited amount of plastic deformation accu~ulates.Also for this reason, strain liardening in ordered intermetall~cs must generally be studied under compressive §training conditions. To assess the unique characteristics of interme tallics, it is useful to contrast their strain-hardening behavior with that of disordered inetals and alloys. Accordin a brief summary of strain hardening in sing1e-crystal and golycrystalline disordered materials is first presented. Thereafter the unique features of the strainhardening behavior of ordered intermetal~ics are
I ~ ~ ~ ~ r n eCompoundc t u ~ l ~ c Vol. 3 , Principles arzd Practice. Edited by J. €3. Westbrook and R. L. Fleischer. @ZOO2 John Wiley & Sons, Ltd.
reviewed from the point of view of macroscopic phenomenology and microscopic dislocation processes.
atevials
hear-stress/sl~ear-straincurves (the shear stress and strain resolved on the most active slip system) for tive disordered metal single crystals, includCu, and Fe, are shown in Figure 1. All curves entations such that the resolved shear stress will be thc highest 011 a single slip systeni for the duration of most of the deformation imposed. Given this type of loading, the majority of slip in fcc and hcp metals is known to occur on the primary slip system. his occurs although the applied stress, due to strain s u ~ c i e n that t the critical resolved is exceeded on a secoiidary, less ip system. This process, known as latent hardening, raises the resolved flow stress for shear on all slip systems of a given type when the flow any system is increased by strain hardtaneous slip on several systems will occur if the crystal is oriented such that the resolved shear stresses 011 two or more systems are equal. Wnlike fcc and hcp-type metals, bcc metals typically exhibit slip on two or more planes which share the direction of niaximum stress rather than on a single plane from the start of deformation (called 'pencil glide'). The shear-stress/sliear~stsaiii response of singlecrystal hcp Mg, Figure I, displays a constant low hardening rate that is sustained up to fracture. Note that the hardeniiig rate, 8, is defined as the slope of the resolved shear s t ~ e s s - s t r acurve, ~~ 8 = dz/dy. The single-crystal Cu, which is fcc, exhibits three stages of ilsdorf, 1966; Rollett and age I , termed "easy glide', is characterized by a low linrdening rate, of similar magnitude to that of the Mg. Stage 2, which exhibits a high and a ~ p ~ o ~ ~ i i iconstant ~ ~ t e l yhardening rate, is termed the 'linear hardening' stage. Finally, Stage 3 is the region of the s~ngle-crystalresponse in which the hardening decreases, due to stress-assisted dynamic recovery. itional stages of hardening may also be present at and Haasen, 1993; llett and Kocks, 1994); these are not discussed here, as they are not as relevant to mtermetallic compounds. Finally, in contrast to fcc and hcp materials, the bcc Fe crystal in Figure l exhibits a strain-hardening rate which continuously decreases as deformation proceeds, as is typical for many bcc materials.
The three stages of hardening in fcc crystals, shown in Figure 1 for CL^, also correspond to stages of dislocation substructure developineiit (Nabarro et al., 1964; Rollett and Kocks, 1994). These are worth briefly reviewing, as substructure development in intermetallics is typically very different. During Stage 1 the dislocation density increases, but with ~ i n i ~ a l dislocation entanglement. The strain-hardening rate is low and has been related to the elastic interactions of edge dislocation dipoles and multipoles. Accordingly, the rate of hardening in Stage 1 is insensitive to temperature due to few dislocation intersections and minimal need for thermally assisted processes for continued glide. During Stage 2 deformation there is continued dislocation n~Liltiplicationand storage and activation of secondary slip systems. H~rdeningarises from longrange elastic interactions as well as from ShQrter-ran~e entanglements that begin to develop due to dislocation intersections. Mobile dislocations that glide into sessile entanglements cluster in tlieir vicinity. The degree of clustering increases with increasing dislocation density (and therefore with increasing stress). The tangled clusters eventually evolve to more closed cell structures. This stage of deforniation is characterized by a high, nearly constant strain~harden~ngrate which correlates with increasing hardness. As the cells become fully developed, with high densities of dislocations within their walls and much lower densities in their interiors, Stage 3 cominetices.
n
-0
10
50 in, 5%
Figure 1 Shear-slresslshear-strain curves of disordered metallic single crystals of Fe, Cu, and Mg
Hardening continues during Stage 3, but with a hardening rate, due to the onset of dynamic rocesses. There are several possible dynamic recovery ~ e c h a n ~ s m (Nabarro, s 19891, including cross-slip, cancellation of dislocations in cell walls via glide encounters with dislocations of opposite sign, climb by core diffusion and climb induced by vacancies created during plastic deformation. If these local processes result iii the removal of sessile obstacles, there may also be a subsequent glide collapse of dislocations that previously accumulated due to the presence o f the sessile barrier (Prinz and Argon, 1980). Although less often addressed, hardening in bcc metals and alloys is different compared to fcc-type materials. The entire shear-stress/shear-strain curve o f single-crystal Fe resembles the decreasing strain-hardening rate representative o f Stage 3 deformation in fcc crystals. In spite of the non-planar screw dislocation core structures (Christian, 1983; Mitchell et al., 1963), cross-slip is observed from the initial stages of deformation in bcc single crystals, unlike fcc crystals where widely dissociated partial dislocations limit -slip and dislocatio accumulation processes neville et al., 1988; u h l i ~ a n n ~ ~ i ~ s d1966; orf, tt and ICoclss, 1994). To generalize the flow behavior of rnetallics as function of strain rate and te~perature,Figure shows a scheniatic of the characteristic strain-har ening behavior of polycrystalline fcc, bcc, and hcp metals and their alloys. igh-purity fcc metals in an annealed condition, such as Cu, Ni, AI, and Ag, exhibit nearly strain-rate independent yielding behavior, while their post-yield strain hardeniiig is strongly rate dependent, as shown in Figure 2a. This strong rate dependency of strain hardening in fcc metals i s due to the sLippression of dynamic recovery processes with
increasing strain rate and/or decreasing the temperature. Alloying fcc metals or testing bcc or hcp metals above their intrinsic lattice ~ e s i s t a n cor~ ' dominated regime, as schei~aticallysho 26, i s known to produce an increased dependency of the yield strength on rate and temperature while retaining a divergent strain harden in^ ~esponse. strain-hardening response of bcc metals (Fe, Tn, MO, Nb) (Clien and hcp metals and alloys Kocks, 1975) i s represen streiigtlis of bcc and licp metals and alloys display a strong temperature and strain-rat their high lattice resistance (Chen In this class of metals, strain-hard yielding are nearly invariant as a function of strain rate; i.e. the stress-strain curves are all nearly pa~dllel in slope although offset 111 their initial yields. The variatioii in the dependency of the yield and strainhardening responses of metals, whether disordered or in the current case of intermetallics, forms the basis for development of advanced constitutive models. The bulls of the infori~ationon strain hardeniiig in internietallics is available for polycry~tallineforms of material in Compression. U tiliztrltion o f compression testing, in contrast to tensioii, allows in-depth study of the Work-hardeninE response of the various alu~inides without the preinature termination of the stress-strain response due to intersectio with the failure envelope (George and Raker, 1998; irnura et al., 1994; al., 1993; Yainaguchi and Inui, 1993). As will he shown in the next section, the Strain~hnrde~iinE response of polycrystalline intermetallics differs substantially from the general behavior of disordered metals and alloys shown in Figure 2 in two distinct ways. The first is tlie influence of crystallogra~l~ic order on the
in igure 2 Schematic representations of the influence of temperature and strain rate on the yield and strain-hardenmg response oT: pure fcc inetiils such as Ni, Al, Cu, b) fcc alloys such 8 s 304 stainless steel and/or bcc or hcp metals at higher t e ~ p ~ r 8 t u r eand s , c) bcc aiid hcp metals at lower temperature and/or high strain rate
a> anncalcd
364
Mectzanicd Properties
strain-hardening behavior for a fixed composition, which leads to high inherent hardening. The second is the propensity for high strain-hardening rates to be sustained up to large Bow-stress values. While knowledge of the mechanisms is still incomplete, the role of the ordered crystal structures and the dislocation processes associated with these qualitative differences in intermetallic strain-hardening behavior will be reviewed.
3. Strain Hardening in I A number of cli~racteristi~s of ordered compounds, conipared to their disordered counterparts, have the potential to substantially influence flow and hardening behavior, including: urgers vectors of dislocations in interinetallic coinpounds are typically greater in magnitude compared to their disordered counterparts. This may result in a high intrinsic lattice resistance to dislocation glide and/or increase the probability of dislocation dissociation or decomposition, A high degree o f elastic anisotropy may influence the decomposition andlor glide characteristics of these dislocations, The energy of faults such as antiphase boundaries and complex stacking fiiults may vary widely and have a high degree of variation on different slip planes,
e
Multiple types of slip systems may operate during the course of deformation at a fixed temperature, Slip inode transitions rnay occur as a function of temperature, Ordering usually decreases the diffusivity of the individual species within the compound; this in turn rnay influence static and dynamic recovery processes, Variations i n the degree of ordering may exist.
These properties ot intermetallic compounds and their influence on hardening will be briefly highlighted to the degree that they have been considered in investigations of the flow behavior of various ordered materials. Exaiglples of systems where these features strongly influence the hardening behavior will be given in the following sections.
As first pointed out by Cottrell(1953), the existence o f order should influence the deformation, since dislocation glide in the superlattice is likely to occur via pairs of dislocations coupled by an antiphase boundary. While increasing the degree of order in an intermetallic a s initial ~ flow stress, in may either increase or ~ e c ~ e the most systems an ordered alloy will exhibit a iiiuch higher rate of strain hardening, compared to its disordered counterpart (Flinn, 1960; Stoloff and Davies, 1966; Vidoz et al., 1963). An illustration of the effect of order on strain hardening is shown in Figure 3 for the case of CuJAusingle crystals tested in
igure 3 Strcss-strain rcsponse of ordered aiid disordered Cu,A-u single crystals quasi-statically deformed at room temperature and 77K (Jin and Gray 111, 1995)
Strain ~ a ~ d e ~ i n g
both an ordered and disordered state. The strainhardening rate for the disordered Cu,Au single crystal is signi~cantly lower than that displayed for the ordered Cu3Au at both temperatLires during quasistatic deforniation: 50 aluiiit strain for the disordered versus 565 MPa Cu3Au. Ordering t r a n s f o ~ a t materials also result in such enhancements in work hardening (Hosoda et al., 2000). Ordering also substantially reduces the temp~raturedependence of the stress-strain response of Cu,Au. Decreasing the temperature from ambient to 77 K for quasi-static loading IS seen to increase the flow strength of disordered C~i3Auby -40% while the ordered material increases its flow stress by -20% for the same decrease in temperature. ~icrostrLictura1examination of deformed Cu,Au samples in both states of order has shown fine slip and uniforinly distributed dislocations in fully ordered Cu3Auand coarse, planar slip accompanied by inhomogeneously distributed dislocations in the disordered state (Jin and Gray 111, 1995). It has been suggested that these differences in slip distribution and accompanying differences in hard~ningrate may arise due to retention of local order on the slip plane for fully ordered alloys and d ~ s r ~ ~ tof i oany n local order present on the slip plane in the disordered variant of the material. This progressive destruction o f the local order would promote further flow localization and concentration of sLibsequent glide on the same slip plane, resulting in coarse slip (Flinn, 1940), for a disordered alloy. Clearly a coinplete understand~iigof the influence of order on st~ain-hardeningbehavior requires information not only on the macroscopic aspects of flow, but also on the character of dislocations gliding on a given slip system and their ability to cross-slip, climb and interact with one another and other structural features. As with disordered materials, it IS most straightforward to first consider the slip systems and hardening behavior of i n t e ~ e t a l l single ~ c crystals.
-
3. The shear-stress/shear-straincurves for single-crystal ordered intermetallics are difficult to widely assess due to the lack of con~~rehensive studies on large-strain single-crystal deforniation behavior. Nevertheless, the limited sin~le-crystal studies on inter~etalliccompounds of several different crystal structures, including Ni,A1 (L12), poly thetically twinned (PST) TiAl (L1,) and NiAI ) reveal significantly different
365
hardening behaviors, compared to disordered materials, Figure 4. An obvious difference is the absence of Stage 1 hardening in any of the compounds shown in Figure 4, even for orientations where only a single-slip system IS operating (§hi et al., 1999a), Figure 4(b), This absence of Stage 1 hardening is also apparent for FePt 2) single c r y s ~ ~(l s~ ~ ~ ~ets al., u g i 1998). A coi~parisonof the shearstress/sliear-straiii curves in Figure 4, relative to Figure 1, suggests that the response of intei~etallicsingle crystals is similar to that of a bcc metal. While the stress necessary to iniliate dislocation glide is often similarly high in the bcc and intermet~lliccases, due to a relatively high Peierls stress (or perhaps interstitial impurities), the strain-hardening responses thereafter usually bear little in common. Followin in the intermetallic crystals the strain hardening is characterized by nearly linear hardening that can continue until strain localization, cracking and fracture intervene. This essentially linear train-hardening behavior is observed under both quasi-static and high strain-rate loading cond as shown in Figure 4c for (100) and (1 10) NiAl, aloy and Gray-111, 1995; Maloy et al., 1995) d d under i~u~ti-slip conditions. These differences in the early stages of hardening in single crystals of ordered compounds suggest that the intrinsic inobility of dislocations is limited compared to that observed in fcc and hcp c Figure 5 shows the substru~ture stages of deformation on a single ( system at room temperature. The substructure contains a fairly high density of p r i s ~ a t i cloops, with longer segments of dislocations that contain superjogs created as a result of frequent, double cross-slip of screw segments, wbich have a much higher mobility than the edge segments in this system (Caillard et al., 1999; Field et al., 1991; ~essersc1itmidtet al., 1997; Sfii et al., 1999). Interestingly, cross-slip occurs easily, in spite of the elastic-anisotropy-driven stability of the screw orientation under no applied stress (Loretto and Wasilewski, 1971). The prismatic loop debris is a result of the drag of inter~ediate~~ieight jogs on the screw segments. In spite of the fact that these dislocations with conipact core structLires (Ternes et al., 1995) initially glide with ease, their mobility is quickly reduced by their tendency for cross-slip, The general tendency for the mobility of dislocations to be limited by cross-slip processes appears to be a of deformation in many intermetallics. ple of this is shown for TiAl in Figure 6, where a/2[110] screw dislocations are repeatedly p i ~ n e dalong their
00 500
100
length (Ott, 1998). The progressive ii~mobili~ation of screw dislocations by such pinning processes would serve to suppress cross-slip induced dynamic recovery processes. In fact, the high liardening rates present in many internietallic systems have been attributed to a general lack of dynamic recovery processes (Gray 111 and ~ m b u r y , 1993). Another important point for the specific example of NiAl is the greater degree of spreading o f the core structure o f the (100) dislocations with deviations from esserschmidt et a/., 1997). This that changes in dislocatioii mohility and the resultant hardening could be expected from relatively minor shifts away from the stoichio-
n
formation of cube-oriented crystals o f NiAl, an orientation which activates non-( 100) type slip systerns, also provides an interesting perspective on the unique characteristics of hardening in iiiteri~etallics (Kim and Gibala, 1991; ~ r i ~ i v a s aetn al., 1997, 1998). In this orientation, a(111) dislocation motion is associated with flow stresses that are approximately three times higher than in non-cube-oriented crystals. However, as temperatures are increased, there is a stoichiometry-dependent decrease of flow stress that is associated with a transition in the dominant operative slip system. Associated with this transition i s the decomposition of the a ( 111) type dislocations into a( l10>+ a(001) type dislocations. Although the
106
0
0.
0
(a) Shear-stresslshear-stra~ncurves of [001] single crystals of Ni,A1-0.223 at 298 and 8C)OK after Heredia and Pope and binary PST-TiAl (orielitation B) tested in vacuum after Y a i ~ a g u ~ (b) h i ~[223] NiAl oriented for single slip (Shi et al., 1999a); aiid (c) multi-slip (100) aiid (1 10) NiAl (Takasugi et al., 1990; Whang et d,, 1998) stress-strain data for quasistatic and high-strain rate loading
of Weak bean? ~ ~ c r o g ~ aofp hthe su~s~rL~cture NiAl following room-temperature deformation of a 12231 oriented single crystal oriented for single slip. Alf dislocations are 1100) tvne. Microeranh courtesv of X. Shi \
I
.‘A
U
I
Strain ~ u r ~ e n i ~ g
i~~~~ 6 Ordinary a/2[110] dislocatioiis in Ti-4~Al-2Cr-2~b after 0.5% plastic strain at 760°C at a strain rate of 2 x lW4/s
inotion of the a(110) type dislocations is responsible for subsequent straining at higher temperatures, highresolution traiisiiission electron nlicroscopy studies suggest that they are constrained by local climb caused by decomposition of their edge components (Srinivasaii et al., 1998). Because motion of the edge components would require the operation of local di~usionalprocesses, deviations from stoichiornetry that influence the vacancy content of the material would be expected to influence the hardening and recovery characteristics of the MiAl crystal in this orientation. The dorniiiant presence of edge components following deforination is also observed 111 other intermetallic single crystals, such as CoSi, (Ito et al.,
1992), suggesting that harden in^ associated with a high instrinsic resistance to the motion of edge dislocatioiis is not uiicoiixnon in intermetallic systems. Other substructural features unique to ordered systems that may influence strain hardening are anti-phase boundary (APB) tubes (Sun, 1994; Vidoz and which have been considered in detail for L1:, type systems (Hazzeldiiie aiid Hirsch, 1987; Schoeck, 1969; Shi et al., 1996) and faulted dipoles that contain superlattice intrinsic or extrinsic stacklng Faults (Viguier and Heinker, 1996). Compreheiisive studies documenting substructure evolution along with quantitative nieasuremeiits of changes in dislocation density (or twin density) with
365
~ ~ c h a ~ iProperties cal
stress, are essent~alinput to work-hardening models, but are presently lacking. Nevertheless, studies conducted on iiitermetallic single crystals to date clearly suggest different directions for the development of hardening theories, coinpared to disordered nnaterials. Given that intrinsic limitations on the motioii of either components correlate with high rates of is clear that mechanisms of immobilization and the associated storage rate of dislocations must be accounted for in a comprehensive theory. A e lies in developing better capabilities for predicting dislocation core structures and mobilities and integration of these key aspects of deformation into multi-scale models that quantitatively predict the onset of yielding and the rate of hardening for any given system in its single-crystal form. Finally, there are a number of additional considerations for hardening in polycrystalline intermetallics; these are addressed in the remaining sect~ons.
ver the past 10 years a greater amount of inforniatioii on the hardening response of polycrystalline interme tallics has accumulated, particularly for aluminidetype intermetallics, due to their potential for structural app~ications~ Y a ~ a g u and c ~ iUmakoshi, 1990). Variations in te~nperatLir~~ composition, microstructure, environmental effects. stress-state effects, and strain rate have been broadly utilized to probe the deformation behavior, including the rate dependency of yield and work hardening. Qf particular interest has been the contribution of work-hardening phenomena to the aiiornalous increase in the flow stress with temperature, present in a wide variety of intermetallic compounds. A survey o f the literature (Gray 111, 1996) on tem~erature, strain rate and work-harden~~g effects on the flow of Fe, Ni- and Ti-alurninides yields a significant number of experimental studies: (Albert and
uk, 1993; Kitano and , 1994; Lee et al., 1995; Gray III, 1995, 1996; Maloy et uE., 1995; Mendiratta et al., 1993; et d., 1992; Palm et al., 1997; Shih et al., 1993; and Gray 111, 1992; Sizek and Gray-
3611, 1993; Viguier et al., 1995a; Yoshimi and Hanada, 1993; Yoshiini et ul., 1995). Models for the deformation response of some of these aluiainides have also been developed, with particular emphasis on the anomalous rise of flow stress with temperature (Busso and M c ~ l i i i t o c ~1996; , Ezz and Hirsch, 1995; George and Baker, 1998; and Sun, 1993; Viguier et A comparison of the work-hardening response of Ti-, Ni-, and Fe-alu~iinidesusing com~ressiondata for five intermetallic aluminides (Gray 111, 19961, is shown in Figures 4 and 7. In-depth details of the composition, processing, heat-treatments, and final microstructures have been presented previously for Gray 111, 1995; Maloy et al., 1995), Ni,A1 (Sizek and Gray 111, 1992, 1993), Ti,AI (Albert and Gray 1997, Gray I11 et al., 1993, 1996), TjAl (Gray TIE, 1991; Gray I11 and Enibury, 1993; Jin et al., Maloy and Gray 111, 1995, 19961, Fe,Al ( 19931, and FeAl (Gray 111, 1995). The coinpressive true-stress true-strain beliavior of NI&, NiAl, Fe&, Fe-40,414). 1€3, Ti-24A1-1 ZNb, aad Ti-48A1-2Cr-2Nb all depend on both the applied strain rate, which ranged from 0.001 to 7500 s-', and the test temperature, which was varied between 77 and 1273I< (Gray H I 9 1996). Examination of the individual stressstrain responses of the aluminides as a function of strain rate and teinperature reveals some striking similarities and some distinct di~erences.These can be seen in Figure 7a and 7b for quasi-static and dynamic loading, respectively. The quasi-sta tic yield stresses of ail the polycrystalline aluminides at both strain rates span a relatively narrow range from 250 to a. The work-hardening behaviors o f the Ni-, Fe-, and Ti-aluminides all exhibit: 1) considerably higher hardening rates than that typical for their disordered polycrystalline base metals, and 2) remarkably sustained lineal- hardening behavior, in particttlar for the Fe-4OAl-0.1B, NiAl, Ni,Al, and Ti-45A1-2Gr2Nb compounds, over a wide range of temperatures. The average work-hardening rates for the aluminides are summarized in Table 1. The remarkable linear tage 2 stress-strain behavior , NiAl and Ti-48A1-2Gr"2~bpersists to true strains in excess of 0.20. In some instances, s ~ ~ h as for Ti-48A1-2Cr-2Nb, sequential reloading with relubrication can be used to strain aluminides in compression to flow stresses >2GPa prior to failure by non-crystallographic shear (Gray 111 and Embury, 1993). These stress levels are equivalent to -E/lO (where E is Young's modulus), which is an inipressive flow stress for any material to stably support.
369
2
ure 7 Stress-strain response for polycrystalliiie aluminides at 29s K, a) quasi-statically, and b) d y n a ~ i c ~ ~ l y
Overall, the stable high rate of work h a r d e ~ i ~ g exhibited by inany polycrystalline intermetallics, with hardening rates often >>p/lOO (where p = shear modulus) and absolute flow stresses > 1500MPa, is consistent with the suppression of dynamic recovery processes (Gray IIX aiid Embury, 1993). Althougli there has been very limited study of the sub~tructureof
inter~e~allics following higher strain deformat~oii,the available evidence suggests a lower tendency for the formation of the cell structures that are characteristic of Stage 3 d e f o r ~ a ~ in i o~~i s o r d e r ~crystals, d where dynamic recovery processes become operative. An. example of this is shown for Ti-48A1-2Cr-2Nb in Figure 8, where a fairly u ~ i f o r i~istribu~ioii ~ of
370
MeclznnicmI Properties
Figure 9 Polycrystalline RuAl after 7%) cornpresswe strain at room temperature. Su~struc~ure consists o f a mixture of { 110) and (I 00) dislocations
Bright field TEM inicrograph of (101} supe~dis~ocationswith g = (002) in Ti-48-2-2 after deformation at 900°C and strain rate of 2000/s (after Maloy and Gray, 1996)
superdislocations is present after a compressive strain of 16%. Other examples of materials that show a limited tendency for cell fori~ationinclude orthoranerjee, 1997), L1, nl., 1995) and C15 Cr,Nb (Takasugi et
al., 1995). One interesting exception is exhibits a marked tendency for dislo at compressive strains as Low as 7%, Figure 9. In this (110) high melting point C O ~ ~ Q L (100) E K ~ and , dislocations on (1 XO] planes are observed within the tangled substructures (Lu and Pollock, 1999); if. is worth noting tliat slip on the { I l O ] plane with this urgers vectors provides five independent slip systems. As ~ i g ~ l i g h t e by d the original analyses of Taylor (Taylor, 193&), five independent slip systems are needed for uiiiform deformation of ~olycrystals.~nfortunately,many intermetalli~slack a sufficient number of slip systems at low temperatures.
~ u m ~ a of r yrate sensitivity and w o r ~ - h a r d e ~ ~response ng of intermetallics studied at 298 K
Material
~ o r l ~ - h a r d e nrate i n ~ t) at ~ i t 0.001 s-l [ ~ ~ a / ustrain]
Ti
Fc Ni Superalloy NiAl [100] NiAl [310] Cu,Au
Ni& Fe-40Al-0.1B Fe,Al RuAl Ti-48A~-2Cr-2~b Ti-24Al- 11 Nb
I000 I000 3000 2400 4000 2900 565 5 500 6600 1000 6000 ~ 5 0 ~ 0 0 0 1800
Quasi-static" Stage-2 ratio of p at 25C
Work-hardening rate at 2000 s-' [ ~ ~ a / u nstrain] it 2400
1600 5000
4000 3 560 530 8000 6500 6500 4500 3600
"Nori~aliziiigthe quasi-static work-~~rdening rate t3 (column 1) with the Taylor factor, M , equals 8/M2
Strain-rate sensitivity, m (1/1n> 67 (0.015) 20 (0.05) 100 (0.01) low 41 (0.024) (0.08 5)
low low 21 (0.047)
217 (0.0046) 35 (0.029)
~ o d i f i e dTaylor-type analyses have been performed via finite-element-based crystal plasticity models for deformation in such intermetallics (for example, for NiAl, which has only three independent systems (Ahzi, 1999)). It is apparent that stress levels within the polycrystalli~ieaggre~atewill be elevated due to this lack of sufficient iiidepeiident slip systems (Parks and choenfeld et al., 1995). However, a quantitative assessment of tlie coiitributioii of this constraint to overall wor~-har~ening rates has not yet been consi~eredin detail for any system. During compression testing of niany of the aluminides shown in Figures 4 and 7, microcrac~ingat the scale of the grain size often occurred at strains far below those which Liltini~~tely result in catastrophic failure. This suggests that the characteristically hi hardening rates in inte~ietallics(and the corresponding high stresses) contribute to the early onset of fracture in tensioii. Apparently damage evolution in compression within most aluminides does not significantly alter the stable, high rate of work hardening typical of these materials. The rate sensitivities, ‘WE’(= d l i i ~ / d l n ~for ) , these aluminides were calculated using the flow stress values at a plastic strain of -2% (t strain-rate change data with bar data, without the comp dure of directly measuring rate sensitivity). Tlie rate sensitivities and work-hardening rates available are 1976). Overall, the Fe-, Ni-, d exhibit a wider range of strain-rate sensitivities than their high-purity disordered base metals. The relatively hi sensitivities suggest low activation volumes for deformation (short-range barriers to dislocation glide) in some, but not all, inte~metallicsat low temperat~res. This wide range of behavior is perhaps not surprising given the variety of deforination modes arid the potential array of dislocation core dissociation and decomposition phe~omena in these intei-rnetallics (Veyssiere and Douin, 1994). One notable exception with regard to rate sensitivities is Ni3Al, which displays an extremely low dependence of its yield strength on strain rate at 298IL consistent with a low Peierls barrier for dislocation motion ( izek and Gray 111, 1993). This very low rate-dependence at 298 I( (Sizek and Gray TIT, 1993), along with the anomalous dependence of flow stress on temperature, has been the focus of a great number of experiments and widely contested inechaiiistic models for the rate-limiting flow plienomena in Ni,AI. These are reviewed in d e t d elsewhere
emlcer et al., 1992; Ezz, 1984; Veyssikre strain-rate effects on have played a pivotal role as delimiters for ~ i ~ e r e n t i a t ing new defect model des interesting exception is sensitivity characteristic compound also has an apparently high tougbness in its polycrystalline form and contains s tions of both (100) and (110) type substructure along with a tendency of cell-type structures after large-strain compressive Fleischer and Zabala, 1990; Lu an Because of the wide variation in sli occur within a single class of c cannot easily be predicted.
the hardening behavior, detailed s y s t e ~ ~ tstudies ic are lacking. Comparison of the w o r ~ - h a r ~ e n i n various aluminides as a function of temperature at high rate reveals that the rate of strain hardening is predo~inantlyi~variaiit~ again exception of Ni3AI and to some extent Ti-4 2Nb. In the majority of the aluniinide data p suminarized (Gray 111, 1996), increasing strain rate and/or temperature at high rate was seen only to shift the hardeniiig curves up or down; the nearly invariant hardening rates result in a family of parallel curves. The observation of a pronounced increase in yield and flow stress with decreasing teiiiperatLire and/or increasing strain rate is typical for bcc, Figure 2, and lower symmetry crystal structures and has often been explained by a high Peierls stress 1975), or in some cases due to interstitial impurities. For the case been shown that the interstitial impur material has a significant influence on the flow
rate also prevalent. iiot only influenced also by deformatio in this volume fo increasing strain rate and/or decreasing temperature, the propensity for twin formation in TiAl i s seen increase. Increasin~a ~ o u n t of $ ~ e f o ~ ~ a ttiwoi n~ n i
372
~ e & h u ~ ~Properties cul
are seen to correlate with an increased rate of work hardening (Gray 111 1994; Maloy and Gray HI, 1996). In addition to twinning, long planar arrays of straight < 101 > superdislocat~ons are observed following high-strain-rate t restraining at elevated temperatures as seen in Figure 8. th of these modes of deformation result in a h rate of defect storage and inhibit dynamic recovery, thus producing a high work-hardening rate (Maloy aiid Gray-111, 1996). See the chapter on twinn~ngby Yoo. s mentione~previously, one interesting feature present iii many ordered intermetallics (but absent in their disordered cou~terparts) is the anomalous i n c r ~ ~ in s e the flow stress as a function of increasing temperature. This was first observed in Ni,AI by Flinii (Flinii, 1960)- and was foreshadowed by the hothardness experi~ents of ~ e s t b r o o k (1957). The presence of this behavior for the Ni, Fe, and Tialuminides is shown in Figure 10. The low-strain flow stresses of Ni,Al, Ti-4$Al~2Cr-Z~b, and Fe-4OA1-0.1B all exhibit an anomalous increase in stress level with increasing temperature at high strain rate. The anomalous increase in. flow stress in Fe-40A1-0.1B with increasi~igte~~perature above 600K is preceded by a proiiounced decrease in flow strength upon increasiiig temperature from low temperature. This U-shaped flow stress behavior with temperature is consistent
with the constitutive response of Fe-40Al-0.1 48A1-2Cr-2Nb being dominated by the Peierl low temperature aiid then involving one or more additional hardening mechanisms upon increasing temperature. One of the earliest models of the anomalous tem~erature dependence of the flow stress in systems was proposed by Kear and Wilsdorf ( and Wilsdorf, 1962).They suggested that the increase in flow stress with temperature occurred due to t h ~ r i ~ a l l y activated cross-slip of APB-coupled a/2(110) dislocations from the (1 11) plane, where they are mobile, to the (100) plane where they are immobilized and contribute to hardening (and thus the anomalous increase in the flow stress). Subsequent discussion of this mechanism, more recent experimeiital observations and other cross-slip inspired models are reviewed by Nabarro and de Villiers (1995). Whether a KearWilsdorf mechanism, another cross-slip pinning ~ ~ c ~ (Baker ~ n and i sNagpal, ~ 1993; Hirsch and Sun, 1993; Yoshimi and Hanada, 1993) or vacancyinduced hardening (George and Baker, 1998) is responsible for the anomalous temperatur~d e p ~ ~ d e n c e remains a subject of current debate. Not all iiitermetallics display the anomalous hardening and increase in flow stress at intermediate temperatures. For example, MiA1, Ti-24Al-1I Nb, and
Plot of flow stresses at fixed plastic strains versus temperature for various intermetallics at high strain rate
Struin ~ ~ r d e n ~ n ~
display a decrease in their high strain rate Bow s with increasing temperature, Figure 10. This behavior is also more typical of disordered metals and alloys where fall-off in the yield strength of a material is commensurate with the decrease in shear modulus with increasing temperature. The one unique feature in the current observations of the anomalous yield increase with temperature is the lack of a downturn in yield at very high temperatures. At conventional nturn is well documented (Anton, 1994; e, 1994; Yarnaguchi and Inui, 1994). Unlike the usual fall-off in yield with temperature for samples tested at quasi-static rates at high temperatures, due to the activation of additional slip systems, such as cube slip in Ni,Al, or climb-related processes in FeAl (Baker, 1995), high strain rate loading is observed to prevent this high-temperature deformation mode change in the aluminides exhibiting anomalous yielding. Up to the temperatures attained to date in split-Hopkinso~-bar testing, the high strain-rate yield strengths of Ni,A1 (Sizek and Gray 111, 1993), Fe40Al-0.1B (Gray 111, 1995), and Ti-48A1-2Cr-2Nb ~ ~ a l and o y Gray TIT, 1996) have not been observed to decrease at high ternperatures, However, it is expected that a downturn would be encountered as the melting point is approached. Of the aluminides in Figure 10 that display the anoinalous increase in yield strength with temperature at high strain rate, the overall magnitude of the temperature effect on yielding and post-yield flow stresses is most evident in Fe-40Al-0.lEQ. Previous studies have documented this phenomenon in FeA1, in articular in the work of Yoshirni and Hanada (1993) r et al. (1995a,b), ker (1995), Klein and 94), aiid Yoshiini a Hanada (1993). Fe-39 rigle crystals have been observed to display a 200 MPa from nearly constant yield stress of ambient temperature to 600 I<, followed by a positive ure dependence with a peak at a temperature when tested at a strain rate of 1.7 x 10-4 sit (Yosliirni and I-lanada, 1993). The anomalous slip transition in FeAl in that study was related to the decompositio~of (111) ~islocat~ons, while a change in slip vector from the (111) to (001) type occurs d the peak temperature 1993). It has recently been alous yielding phenomenon in Fe-40Al i s perhaps linked to vacancy hardening To summarize, inte~metallicsdisplay an amazingly diverse range of work-hardening beliaviors and characteristics as a ftnnction of loading conditions, whether
373
they are in single- or polycrystalline form. This depth of response makes generalizations about the physical mechanisms and processes controlling w o r k - ~ ~ r ~ e n i n behavior in intermetallics, and the odel ling of these processes, problematic. While sustained ‘Stage 2’ hardening is often observed for a number of intermetallics to relatively large strains, substructural observations show that the processes controlling this hardening vary between intermetallics with difTererrt crystal structures. Continued work i s required to provide the basis of more generalized models describing the micromechanisms controlling plasticity in intermetallics, particularly for polycrystalline intermetallics. Such models will necessarily be multi-scale in nature to provide an accurate description of intermetallic hardening, spanning from modeliiig the dislocation core up to c a l c ~ l a t i nthe ~ contributions of long-range barriers such as grain boundaries. Future utilization of structural iiiterinetallics in engineered applications will require a ~ r ~ d i c tunderiv~ standing of the yielding, strain hardeiiing, and damage evolution behavior.
Based on this brief review of the strain-hardeniii behavior of single aiid polycrystalline intermetallics, a number of general observations can be made: e Interinetallics, when tested in compression so that
fracture processes are suppressed, typically sustain very high strain-hardening rates to high flow stresses. e A comparison of the work-hardening rates of the various a l ~ r ~ i ~ i as d e as f~nctionof strain rate or temperature often reveals an invariant rate of strain hardening, similar to the response of pure bcc metals. The exceptions to this behavior are low Peierls-stress intermetallics, such as Cu,Au or and systems that deform in part by twiiining, such as TiAl. The high rates of strain harden in^ often observed for intermetallics are due to a ?qgh rate of storage of dislocations coupled with a general lack of dynamic recovery processes. High rates of dislocation storage may arise due to: a) a low tendency for cross-slip that results in a generally low rate of dynamic recovery or b) high rates of storage of screw dislocations that readily cross-slip, but are subject to cross-slip pinning processes that also create debris, or c) accurnLilation of a high content of
344
~ e c h ~Properties n i ~ ~ ~
dislocation^ that are relatively immobile due to a high Pejerls barrier, point-defect pinning andlor a complex core structure. Studies of the deformation and strain-hardening response of intermetallics can provide insight into the details of defect generation and storage processes in ordered i ~ t e ~ e t ~ lconipounds. lic In addition, they are relevant to many operational and nianufkturing questions concerning engineering utili~ationof intermetallics.
The authors are grateful to J. Schneibel of ORNL, R. rolia and C. Austin of General Electric and ischer for materials used in the studies presente
ert Carpenter 11 f ~ assistance r with niechanical testing. The work of 6.71. Gray 111 was performed he auspices of the US Department of Energy. ollock would like to acknowledge the experiE.A. Ott and D.C. Lu BES grant DE-FG020 0 E 1 ~ ~ ~ 8For 2 0the preparation of this manuscript
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Dislocations exist in both conventional intermetallic crystals aiid iiitermetallic quasicrystals (QCs), especially in deformed specimens. Figure l shows densely distributed dislocation lines in a Al-Pd-Mn single icosahedral quasicrystal C) bent at 720°C. Studies of dislocations in QCs h drawn extensive attention because of their importance, not only to structure investigation, but also to understanding many physical and mechanical properties of QCs. Since plastic deforination of single QCs occurs mainly via dislocation glide, studies of Burgers vectors of dislocations and dislocation arrangements in differently pretreated aiid deformed QCs are very iinportant for understanding the microi~eclianis~ of plastic deformation of QCs. As described by Keltoii (1995) in Chapter 20, Vol. 1 of this series, a quasiperiodic lattice may be described as a projection froin a N-dimeiisional (ND) liypercubic lattice onto a 3D physical subspace that has an irrational orientation with respect to the original lattice. N = 6 for IQCs, and N = 5 for decagonal quasicrystals (DQCs), octagonal quasicrystals, dodecagonal quasicrystals and pentagonal quasicrystals. Therefore, Burgers vectors = [BI, B2, . . ., B N ] of dislocations, displacement vectors W and reciprocal vectors G = [Gl, G2, . . ., GN] in a QC are all vectors with N components. This unique character of QCs complicates the experimental determination of rs vectors and elasticity theory of dislocations in compared with those of dislocations in convenIn the present chapter, we will describe the Volterra process of a dis~ocationin Cs, methods of experi-
mental determination of Burgers vectors of dislocations in QCs, linear elasticity theory of calculation of the elastic field arouiid a dislocation in a QC, as well as some experimental results about Burgers vectors of dislocations, slip systeins and dislocation reactions in QCs. Finally, we will explore dislocation niechaiiisms for high-temperature plastic deforination of QCs.
and Trebin (1989), Klernan and leinan (1995), Yu et al. (1997), Y (1998) and Diiig et d.(1998) discussed the Volterra process, a constr~ction method for dislocations in QCs. The Volterra process for dislocations in coiiventional crystals consists of four steps: (1) Cut the crystal along an arbitrary surface (which i s bounded by the dislocation line L, forming two lips C1 and Cz. (2) Displace these two lips relatively one to the other by a urgers vector of the dislocation line. (3) Fill the space between 61 and C2 with perfect crystal matter or re ove extra matter; (4) Glue the lips together. Because is a lattice vector, this process restores the lattice everywhere outside the dislocation line L except for the continuously field around the dislocation line L. stress fields around the pletely defined by the line and the elastic properties of the crystal, but are
/nfPrmefallic Cornpocdv: Vol. 3, Principles Lmd Practice. Edited by J. II.Westbroolc arid R. L. Fleischer. @ZOO2 John Wiley 6t Sons, Ltd.
380
~ e c h a n i ~Properties ~L
d re 1 Densely d i s t r i ~ u t edislocation ~ lines in Al-Pd-Mn icosahedral single quasicrystal bcnt at 720 "C
independent of the special choice of 2'2. Such a Volterra process can not be performed in QCs themselves because tr~~nslation s y ~ ~ e t isr ylost. Since a Burgers vector of a dislocation in Cs is a translatioii vector in
haded strip S is the projection window that has an irrational orientation with respect to the the lattice points lying within this d onto the physical subspace PI1 to form the QC. The Volterra process constructing a dislocation line Lil with a consists of the following steps (see Figure 2): dislocation line Lit, described by a in physical subspace Pll into a -location byperline L in ND hyperspace. L is a direct sum of 5 ,11 and the perpendicular subspace PL:
Schematic d i a g r a ~describing the Volterra process in ND hyperspace constructing a dislocation line Lll in 3 0 physical (parallel) subspace PI1 with R ND Burgers vector The vertical line represents the (N - 3)D pe~endicular subspace PL. The l D dislocation line Lll in physical subspace, designated by a filled circle i s lifted into ND space forming a (N - 2)D hyperliiie L, The 2D cutting surface Cl1 and the corresponding two lips CI and Cl are lifted into (N-l)D hypersurface t: and two hyperlips CI and Cz. The shaded strip S is the projection window, that has an irrational orientation with respect to the ND hyperspace. All the lattice points lying within this window are projected onto the physical subspace PI! to form the QC
vector of the dislocation line ,511. This ND Burgers sists of a p~ionon-type physical and a phason-type ~erpendicular
(2) Feuerbacher et al. (1997) introduced a strain {=I a c c o ~ ~ n o d a t parameter io~
L = L" @ P-'
hyperspace along an arbitrary surface C which is bounded by n hyperline L, forming two (N- 1)D and C2. The projections of the rsurface t: and two (N- l)D hyperlips 221 and 2'22 onto tlie physical subspace
vector, this process restores the N D lattice everywhere outside the dislocation byperline L except for the continuously di~tributedstrain field around the dislocation line L. Notice the displacement vectors are ND vectors (11) consisting of phonontype physical compone~tsu(d) and phason-type perpendicular components vv(rl1):
(3)
Dislocations ir2 Quasicrystnls
38 1
where the phason type dis~lacementsw(r11) lie in the perpendicular subspace PL and cause some lattice points to move into the strip S and some other lattice points to move out from the strip Project all the lattice points lying within the strip S onto physical subspace Plf, forming a quasiperiodic lattice co~itainingthe dislocation line LII. must be emphasized that: The displacement field is a function of the position vector d in the physical subspace Pi' around the dislocation line defined by the line I;//position, and the elastic properties of the QC, but is independent of the special choice of C .
cutting surface Ell, and this dislocation is not a perfect, but a partial o erfect dislocation. he displacement field , after traversal of a c C surrounding l;ll in Pll:
(P")
=
(4)
Figure 3 Schematic diagram of defocused convergeiit-bea~ electron diffraction. The crossover C of the ~onvcrgentincident beam is deviated from the specimen (Sp) by a distaiice Af (defocus). Thus the diffraction pattern (EDP) at tlie back focal plane of the objective leiise (Obj) contains both diffraction and real-space information of the illuminated region
2.2.1 Defocused CBED D e t e ~ ~ ~ n a qf t~on Vectors of D ~ s l o ~ a t in i~n~~
Figure 3 shows a schematic diagram of a defocused CBED. A conical incident electron beam with a half angle 0.4"-1 .O" converges at the crossover C which deviates from the specimen (Sp) by a distance Af (defocus). Thus a circular region of the specimen is illuminated by the incident beam. If the illuminated There are three methods of experimental detennination of Burgers vectors of dislocations in quasicrystals: (1) Defocused convergent-beam electron diffraction (CBED) method. By this method all the inforination about a Burgers vector, including its direction, sense and magnitude, can be determined. This method is appropriate for isolated inclined dislocation lines. (2) Diffraction contrast method. Usually only the direcurgers vector may be determined by this method. If coiiiplemented by computer simulation of the contrast images of a dislocation, full information about a Burgers vector inay be obtained, This method is appropriate for inclined dislocation lines whose density niay be higher. (3) High-resolution lattice fringe method. This method is appropriate for nearly end-on dislocation lines. When there are two neighboring zone axes with a small angle for high-resolution imaging, full infoimatioi-z about a Burgers vector may be obtained.
ion of the displacement field around the dislocation DlD2. For diffe nated points, the displacement vectors incident directions are different, resulting diffracted and transmitted intensities, and one observes a correspoiiding contrast In (l-zkl) diffracted and (000) transmitted disks as shown in Figure 3 where the points D1 and D2 in the specimen have their corresponding points D1' and D2' in the (000) transmitted disk and points D1" and diffracted disk. Therefore, a defocused contains both diffraction and real-space the illuminated region. As described and reviewed recently by tioii line along tlie direction U with a Burgers it and twist of the briglit diffracted disk and their
correspond in^ dark de~cientfringes in the t r ~ ~ s ~ ~ i t t e d
physical components and
~ e t e r i ~ i i i iby ~ dthe inner er-order reflection.
if G is a weak
ED pattern taken from a perfect an A170,Pd,, 2Mn,, IQC. Indices G, o f rcflection numbered as I = 1, 2, . . ., 17 are listed i n Table 1
modulus of the value the criterion may be expressed as follows: If a weak higher-order reflection fringe corresponding to a ~ ~ $ i o ~ ~line t i oofn a will split into In1 -+ 1 brandies with In\ nodes wheii
of reflection fringes G , 111 Figures 4 and values for a dislocation line shown in Figure S(a) ineasurcd froin thc &focus CBED pattern sliown in Figure 5(b) (111: not i n t ~ r ~ ~ ~ t ~ d ~ M,
= rl.
linearly i n d ~ p e ~ ~ N e nrec~procal t vectors GE2,. . ., G 2 ~(1E= 1, 2, . . ., N ) whose fringes interct the dislocation line. The indices G, of the fringes may be obtained by computer simulation of the '
1 2 3
4
s
6
a
7
6 1 1 -3 -4 -3 3
11
and the values
32 13 14 J5
17
from a perferct region ol' an A170,4Pd2i~zMn, IQC. The bright. circular disk of 0.6" radius is the transmitted disk and each bright fringe ~ ~ ~ ase 1 ~2, e. . d., 17 1s a niain reflection fringe in the respective diffraction disk.
2 2 -4 -6 -4
8 -4
-8 -4 4 6 I I) 5
-3 -5 -2 3 7
--I
-3
-12 6 -2 -3 5 1
-6
-4
-4 4 2 -6 4 2 2 4 -2 8 -4 -4 -6 2 -3 3 1 -3 3 -1 2 2
-5 5
-7
-1
5
1
-1
-3
1
2
2 4 -6 -10 -8 12 8 1
3
-6 8 2 -6
1
0 nl -2 ni -2 (1
nr
E 111
high temperature. hen the d e f o ~ u s ~incident d beam illuminates this dislocation liiie, one obtains ii defo-
side of the dislo~ationline twists opposite direction and hence we ~ i ~ ~ l a toifothis n ~ ~ twe~deduced ~ r all n the indices of the reflections appearing in Figure 4 as listed in Table 1. age of a clislocation line deformed plastically at
not intersect the dislocation line, hence they do not split and we cannot btain the correspondiiig experimental values of Gi,= nj for i = 4, 6, 12 and 14. AIL
Ddocutions in euasicrystuh
383
1994b; Feng et al., 1995; selecting ( N - 1) linearly al., 1994b; Wang, 2000). (i = 1, 2 . . . N - 1) under independent reflections ast of the dislocat~onis which the diffraction c iiivisible or weak, then we have (6)
e2
LGN-1.1
Figwe 5 (a) Contrast magc of c?. dislocatmi linc i n an Al,, Pd,, Mn, IQC deformed plastically at lt~gh-teiii1-’el-ature. (b) Defocused CBED pattern takcn front the dislocation line shown in Figure 5(a). Indices Gtl of reflection fringes the G, . B = n, valucs are listed in Tablc 1
the information is listed in the last columii of Table I. There are many possibilities of selecting six linearly from the nine experimental values lving for any select arne Burgers vector =(1/2)[~3~~2~].
2.2.2 Burgers Vectors qf ~ i s l o ~ a t in i ~ QCs ~~s Determined by a Contrast Experiment ~ e c h n i ~ ~ e
ED technique described above is appropriate for isolated dislocatioii lines. Iii case of densely distributed dislocations, especially dislocation dipoles and small dislocation loops, one may use a contrast experiment technique (Feng and Wang,
GN-1.2
...
eN
* * *
GN-1,N
where fi is a coefficient dependent on the niodulus and , G, thejth component o f sign of the Burgers v the reciprocal vector eJ tlieBth unit vector of an orthonormal system. sing properties of the deterniinaiit one caii confirm that the vec equation (7) satisfies equation (6) 1994b). The technique of matching the c o i ~ p u t e ~ ~ s i m u l a t e ~ dislocation coiitrast images to e~perimentalelectron micrographs (Head et al., 1 vectors of dislocations was al. (1994b) identified the dislocation by using both d ing techiiiq ues. By matching c o n i p ~ t ~ r - s i m ~ ~ l a t e ~ contrast images to experimeiita loops were identified in Al-Si1991) atld Al-Pd-Mn IQC (W By coin bining defocused techniques we successfully identi~eda dissociation of exteiided dislocations of the forin 1/2[ 1?OO? I] --3. i,qi31111] 1/4[iiii31] with a sLacking f a ~ l t between these two partial dislocations (Feng et aE., 1995).
+
2.2.3 Burgers Vector Determination by the High- Resoht ion LLIt tice Frmge Method As pointed out by Yang et aE. (1998), in a highresolution lattice friiige iinage obtained from an inverse Fourier transform by selecting the reciprocal E , there are Inz,/extra dislocation with a Burgers vec Thus we can es from high-resolution lattice fringe images of a disloca Fourier transform by selecting a w we will discuss how to deter ni. Figure 6 shows s c ~ e ~ ~ t an i c edge a ~ ~ ~
384
~ e c ~ i a i t i Properties ca~
image there are only four linearly indepenTherefore, we need at least two HRTEM images with the dislocation line being nearly end-on. Owing to the high symmetry of the icosahedral point group, we can choose a dislocation with a line nearly along a three-fold axis and get its images at this three-fold axis and also at a neighboring pseudo-two-fol~ axis. Since the angle between these two axes i s only 10.8", the dislocation may remain almost end-on for both eases. At last, selecting any six linearly independent j, and the experimentally determiiied i t i into equation (9,one can solv . ., BG of the 6D Burgers vector the dislocation line. ecently, Yang et al. (2000) determined experimen== [-2, 0, 3, - 2, 3, 01 in a n quasicrystal by the highresolution, lattice-fringe technique described above.
...-.....
........*
I
ic diagram showing the definition of the an edge dislocation with a line direction U
By using the defocused CBED technique and other
dislocation with an extra half-plane. According to the University (Wang and Dai, 1993; Wang ez al., 1994a; Feiig and Wang, 19948; Ding et ul., 1998; Wang, 2000) d e t e ~ i n e da series vectors of dislocation Cu25,5Fe, lines in and in Al,oCo,sNi,s s c ~ u n g s z e n t ~ Ju u~ enfeld et al., 1995; ~ e u e r b a c ~ eetr al., 1997; Urban ex al., 1999) determined a series of Burgers vectors of dislocation lines in annealed and h i g l ~ - t e ~ p ~ r a t uplastical re AITOPdzl Mn, IQCs. The deter~ined tors are listed in Table 2 where the superlattice constants a % 1.3 nni for the fkce-ceiitered AI-Cu-Fe and AI-Pdrelated to the periodic of dislocations in Al-Co-Ni DQC. In Table 2 we also ) images. In their lattice
d 5 in Yang et al., 1998), obtained by inverse Fourier transform in each figure by selecting 15 difTerent reciprocal vectors Gl with i = 1, 2, , . ., 15, extra fringes are clearly seen. We find the 30 lattice fringe images are all in excellent reement with the sign criterion expressed above.
1997) defined as the ratio of the modulus o f the perpendicular phason to the modulus of the p of a high dimensional a dislocation in a QC. Notice that usually the urgers vectors in IQCs possess rather large 5 values ranging from z3 to 2' (z = (1 + &)/2) indicating a large phason component of the strain field around a dislocatlon line. According
385
Dislocations in Quasicrys tals ~ x ~ e r i n i ~ n t adete~mined lly Burgers vectors
32
DQC DQC DQC DQC DQC DQC
= (~00000) 4 = (-00000) = ~00000)
I I 1
0.4 = (10000_0) D,1 = ( 0 1 0 ~ ~ 0 ) 0.2 = (0111 10)
I1 II
0,2 0,3
BJ, 234, B5, B,5]of dislocations in ~uasicrystals
Al-Pd-Mn, Al-Cu-Fe Al-Pd-Mn, AI-Cu-Fe AI-Pd-MIi Al-Pd-Mn Al-Cu-Fe Al-Pd-Mn AI-Pd-Mn Al-Pd-Mn Al-Cu-Fe Al-Pd-Mn
0.296 0.183 0.1 13 0.070 0.215 0.10% 0.174 0.067 0.513 0.098
= (1/4)(515151) 0.1
= [ B I ,3 2 ,
I
to the statistics provided by osenfeld et al. (3995), Feuerbacher ef al. (1997) a Urban et al. (1999), about 90% of the dislocations investigated are perfect dislocations and show two-fold urgers vectors, i.e. their directions in the physical su pace are parallel to a two-fold axis of the IQC. Slip-plane normals PI of an
five-fold axis. Less frequently, two-fold and three-fold slip planes were also observed. Thes densely packed planes of an A1-Pdincreasing plastic strain from 0% to 1% the frequency of occurrence of dislocations with higher accommodation ratio ( increases. For example, while the frequencies of occurrence of dislocations with I; == 2 3 , z5 and 27 are 34%, 60% and 6% respectively for the specimens annealed at 760'6, they become 094, 64% and 36% respectively for the specimens compressed at '760 'C to a strain of 170.They remain almost constant when plastic strain increases still fbrther.
0.20 0.40 0.60 0.80 0.19 0.30
0 0 0
Al-Co-Ni Al-Go-Ni AI-Co-Ni
0 1iz. 1 p
correspond to trans~ations,distortions and rearrangements of unit cell (Levine et al., 1985; 1986). In the higher-dime ND displaceme~tvector (equation (3)). Then we have
where V = ejV, with V, = a/ax, = ai being a differential operator relative to the position vector IP// = (XI, x2, x3). can be decomposed into symmetric and antlsymmetric parts. The antisymnietric part describes a rigid rotation that does not change the elastic energy. Since there is an energy cost associated with the a n t i s y ~ e t r i c derivative of w, the elastic en components of the gradient of Thus, the elastic energy depends only on the following strm1s:
It is easy to verify the com~atibi~ity e ~ u ~ t i o( n al., 1993, 1994):
s have two types of elastic hydroone is the phonon variable u and the other is the phason variable w. Moreover, the excitations analogous to dislocations do top0 as well. Phonons, phasons and dislocations exist
where ejJlcis the alternator symbol. ~ u r t h e ~ m ~the re? elastic energy density can be expanded in terms of the Taylor series in the vicinity of Ezj= 0 and wlJ= 0 to the second order:
MechanicaI Properties
384
T, there is another stress tensor H with components Hz, along the x, direction in PI- acting on the surface orthogonai to the xJ direction in PI/. If n is the outward unit vector normal to an element surface, then we have
(17)
t, = Tlpj h, = H@,
As Lubensky et aE. (1985) pointed out, in the case of QCs the theorem of‘ momentLlm possesses the form
-1 d
p(ir+w)dV=
df.v
J .v
where V i s an arbitrary volume in PI! and S is the boundary surface of V. Application of Gauss’ theorem to equation (18) leads to two equations of motion
where
+ g , = pi+,
C$TzJ+J1 = pii,
(19)
and two static equilibrium equations are quadratic elastic constants in the classical elasticity theory with C I J k l= c k l I J = Cji,cr c i j l k . We Call denote all Crilrfby a symmetric matrix [C]. Similarly, =z1
(13) are elastic constants of the phason field with fir!&/ = which can also be decoded by a symmetric matrix
are the elastic constants associated with the phonoiiiously, Rllkl = RJlfcl,RijkE= R/iiik3 f fi)kEEjI R b k l $ Riilj-w e denote and ER’] with [R’]= [RIT.These four matrices compose a matrix [C, I(,RI:
i.),T,,+JI = 0
(20)
The theorem of angular momeiituni associated with the phonon field has the forin dY=
s,.
rli x f d Y +
Hence, by Gauss’ theorem and equation (19) we obtain T,\ = 1;i
(22)
This means that the phonon stress tensor is symmetric. ) transform differently under different representations of the point group (niore precisely, the former transforms like a vector, but the latter d the product represenlations, contain any vector represent~tions.This implies that for the phason field there is no equation aiialogous to (21), from which it follows that, generally, HIJ
ing et al., 1994: Yaiig et d.,1993). With these notations, we can write the elastic energy in a compact form:
+
h’&YiJ g, = 0
# HJI
(23)
By an argument like that given in classical elasticity theory we obtain
Substituting equation (1 1) into the above equations gives the generalized The m o v e ~ ~ of n t a t o ~ through s a barrier, ~eading to a rearrangement of the unit cell, needs some forces. Thus, besides the conventional body force density f and surface force density i n Pll, a generalized body force density g and surface force density h in P-Lshould be introduced in calculating the elasticity of QCs. Similarly, in addition to the conventional stress tensor
Tzj
HLJ
= c i j k ~ ~ k+l Rijkl =~
~
+~
“fJ/Cl
wkl
“h~ I
which can be expressed in matrix forni
(25) ,
~
/
~
i
387
Dislocations in Quasicrystals Substituting equation (25) into (20) gives the nonhomogeneous partial differential equations satisfied by U and w: Czjk/@%uk
Rklya&%uk
+ Rzlkla,alWk +.6 = + KzJk/qalwk f gz =
(27)
3.2 Elastic Constants of Various Laue Classes of QCs The number of independent components and their explicit forms in the elastic constant tensors can be calculated with the aid of group representation theory. From group theory one knows that the number of independent tensor components is equal to the number of times that the identity representation is contained in this tensor representation, i.e.
r = rs+ r, + r7
(30)
+
It follows that a vector in PI1 transforms under r5 rl, whereas a vector in PL transforms under r7. The tensor characters for the elastic constants Cjjkl, KijkI and Ro/clcan be derived as follows:
x(e)
x(a)
x(a2)
21 21
3+2& 3+28 -6-4&
1 1
36
x(a3)
3-2d 3-2& -6+4&
0
x(m4) x(P) x(@) 5 5 4
5
3 0
5 3 0 (31)
From equation (28) it follows that the numbers nc, nK, and n~ of independent elastic constants Cijkl, Kijkj and Rijkl are
nK=4,
n,=5,
nR= 1
(32)
To determine their explicit forms we should notice that the transformation properties of Cijkl, Kijkr and Rijki follow directly from those of Eij (T'j) and Wij (Hij). If we find the precise components of Ei, (Tij) and Wjj (Hij) that transform under the same constituent representation, we can construct all the invariants formed by their c.ombinations and then establish the independent components of Cijkl, Kukl and Rijkr. For the phonon field six symmetric components of El, transform under
w, + r,)x (r,+ r,)is= 2r1+ rs+ rs
(33)
where {. . .}s denotes the symmetric product representation. This means that E11 E22 and E33 form two ID subspaces (the identity representation 1 ) . They are two linear invariants. E11 - E22 and 2El2 form one 2D subspace (r6) giving one quadratic invariant (scalar product)
+
- 0 1 0 0 0 0 0 1 0 0
o o o
r(E)=
1
o
- 1 0 0 0 0 - 0 0 0 0 10 0 00 - 1 0 o o -1 o o 0 - 1 0 0 0 0 0 0 0 1
-1 0
r(p)=
0
0
(E11 - E22HEll = (E,, -E&
- EZ?)+ (2E12)W12)
+ 4E:2
and E23 form another 2 0 subspace another quadratic invariant
.E13
(34) (r5) giving
E73 + E:3
(35)
Thus, there are a total of five quadratic invariants due to the phonon field (Ell
+ E2d2>E L , (El1 + E22)E33, E:, + Et3,
EllE22
- E:2
(36)
Among them the first three are products of two linear invariants: Ell E22 and E33. From equation (36) it can be see that the non-vamshing components are
+
388
~ e c I ~ u EProperties i~~1
K= IK1 K. K2 0 0 0
which can be written in the matrix form
\o
Kl 0 0 0 0
0 0 0 K4 0 0 K1 + & + K , 0 0 0 rc, 0
0
(44) where the double indices labeling the phason strains are arranged in the order 1I, 22,23,12,13,21. Finally iiotice that the pairs (E11 - E22, ~ E Q and ) (Wl1 W22, W ~-I W12)transform acco~dingto the same representation (r6).This means that there exists an invariaiit
+
(Ell
where the subscript 5 stands for the number of independent components. The correspondences between iiidex pairs and single indices are, as usual, ( j j ) = 11 22
i = l
2
33 23 31 3 4 5
12 6
(39)
iniilarly, for the phason field six coniponents of Wij transforni under
I - ?T22 and W21 t FVl2 form two different ID subspaces (r3 and r4) giving two quadratic iiivariants
w21 - 'c.1/12) and (T'T/139 W2.3) pairs (kV11 form two different 2 subspaces (r'6 and ]r7) giving two other quadratic iiivariants W k 9
Thus, there are a total o f four quadratic invariants due to the phason field. They are listed in equations (41) on-vanishing components are
The correspo~di~g matrix form i s
- E22)(Wll
+ W22) + 2EIdW21 - w;,)
(45)
coupling El, to Wif.Non-vanishing components are Rl,,,
= RI122 = -R2211 = 4 2 2 2 2 = RI221 = R212r - - R m = -R2112 = R
(W
with the matrix form
R=
0 0 0 0
0 0 0 0
0 0 0 0 0 0 0 - R
0 0 0 O
0 0 0 R ,
I
(47)
Therefore, it can be seen that there are 10 quadratic iiivariaiits and hence 10 independent second-order elastic constants for 8~~ s y ~ m e t r yAmong . them five components (nc = 5) are due to the pbonon field, four constants (IZK = 4 ) due to the pfnas~nfield, aiid one constant ( E R = 1) associated with the ~honon-phason coupling. The results coincide with those given in equation (32). Table 3 gives all the point groups of2D QCs. They are divided into 18 Laue classes which belong to 10 systems. 111 the same way, we can determine the numbers of the independent components and the explicit forms of the elastic consta~tsof various Laue classes of QCs. All the results are listed in Tables 4 aiid 5.
In this subsection we apply the generalized elasticity theory to the case of icosahedral QCs. Elastic constants of icosaliedral QCs have been discussed by several authors. The elastic constants depend 011 the choice of the coordinate system. Unfortunately, a
389
Dislocations in Quasicrystals Table 3 Systems, Law classes, point groups and numbers of independent elastic constants €or 2D QCs
__
No. of Laue classes
Systems
-
Orthor~omblc Tetragonal Tr1gonal Hexagonal Pentagonal Decagonal Octagonal Dodecagonal
groups
- - -
Nc
NK
21 13 13 9 7 6 7 6 5 5 5 5 5 5 5 5 5 5
21
--
1,
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Triclinic Monoclinic
POlllt
NR
____
._ -.
i
2, in, 2/m 12, 1111, 12/m 2rnn1, 222,mmrn, mm2 4, 4/1n 4mm, 422, 4%2, 4/mmm 3, 3 3rn,-32, 3m 6, 62 6/m (Iiiim, 622, 6752, 6/inmm 5, 5 5m,52, 5m 10, 10,10/m lOmm, 1022,-10m2, 10/rnmm 8, 8, 8jni Smrn, 822L8m2, 8 / ~ m m 12, 12,12/m 12111m, 1222, 12rn2, 12/mmm
13 12 8
7 5 7 5 5 4 5 4 3 3 5
4 5 4
Sun?
36 20 18 10 10 5 12 6 8 4 6 3
78 46 43
27 24 16 26 17 18
1 0
33 16 12 10 9 12 10 10
0
9
2 1 2
particular choice for the coordinate system 1s somewhat arbitrary, and at least two choices appear in the literature. A coordinate system can be chosen with the z axis pointing to a vertex of an icosahedron (Levine ak, 1985; Ding et al., 1992). Another coordinate system has the x, y and z axes parallel to the three twofold axes of an icosahedron (Lubensky et al., 1985; Jaric, 1985). Here we use the former coordinate system to express elasticity tensors, i.e. its y and z axes are parallel to two- and five-fold axes, respectively. The corresponding elastic conslants ;we given in Table 5. In this case the generalized Hooke’s law is given as follows: T,, = 1 2 0 T’22
= A8
T’,, = A8
+ 2 , ~ E , l+ R(31~1+ 82~2+ + 2pE27 + Piz(Ol~1
+ + 83~1)
8 3 ~ 3 &3tl.’1)
8 2 ~ 2 8 3 ~ 3
+ 2pE3, - 2R8,w3
+ +
T73 = 2,~E23 R(82w3 - 8 2 ~ ~ 8 11 ~ 2 =) T32 = 2@31 R ( & w ~- $w, 8 1 ~ 3 = ) ‘Ti,
+
+
Tlz = 2,~1E12 R(alw2 - 83 W? - 8 2 ~ 1 = ) T21 = R(E11 -E22 +2E31)+251;alw1 +K2(dlw3 + a , ~ l ) H22 = R ( E 1 1 - ~ 2 , - 2 ~ , , ) + K ] a ~ ~ ~ + K 2 ( a-a,w,) ~W1 f& = X(E1, 4- E22 - 2&) (K; K2)03w3 ff23 = -2RE12 (Kj - K2)83~~2K2(82~l- i 3 j ~ 2 ) ff3l = 2RE31 &(a1 w1 - a,w,> (Kl 1Y3 f f 1 2 = -2R(E23 E , ~ ) rqa2w, ~ ~ ( 0 ~ 1 . 1 )a21.1J3) ~ .ff,2 = 2RE23 ( K , - K~)&IV,- K2(82~1 31~2) ff13 = R(E,1 - E22) K2(a11~1 8 2 ~ 2 ) ( K , - K 2 ) a 3 ~ , ff2, = 2R(E12 - E23) - K 2 ( 8 3 ~ 7 82~3) KID,PV~ (48)
+ + + + + +
+
+
+
+
+
lasrtic
&)a,
+ + + + +
In order to find out the elastic fields induced by dislocations in QCs, we nmst solve the inhomogeneous partial differential equations (27) with given boundary conditions as people have done in the elasticity theory of dislocations in crystals. In the derivation. that
Mech ~ n i Pvuprties c ~ ~
390
Elastic ~ o n s ~ a nof t s 2D QCs with noncrystailographic sy~~metries
All 2D QCs with nonc~ystai~ograplllc syrnrnetries have the same phonon elastic constants (CtJk()listed below:
Laue class 12
All the same as above except for Kc, = Rz = R3 = R5 = 0 ( 2 jlX l, 1X1). All the same as above except for rCr, = R2 = R4 = Rc,-- 0 (211x2, ypz d_ x2). Laue class 13 K6 = Kl = R3 = .& = Rs = S6 = 0 Laue class 14 Kfj = K7 = R2 = R3 = R4 = 115 = jP6 = 0
Laue class 15 Phason field Ktjlc/
Laue class 11 (Thc numbers of Laue classes i s the same as in Table 3) Phason field K,j/cl 11
22
23
12
13
21
11 22 23 12 13 21
11
22
23
12
13
KI
0 0
K5 -K5
0 0 0 0
0
K2 K1 0
K5
-K5
0
0 -K5
K2
K5
where C = K1
K
4 0
0
0
C 0
0
K
4
21
Kj
-& 0 K3
0
K3
0
c
12
13
21
112
0 0 0 0
-R2
+ Kz -I-K3
Phonoa-phason coupling R i j k l
11 22 33 23 31 12
Phonon-p~asoncoupling Rljk/ 11
23
22
13
12
21
11
22
23
RI
RI -RI 0 0 0
0 0 0 0 0 0
-R1 0 0 0 R2
R2
-R2
0 0 0
-R1
0 0
R2
0 0 0
RI
Laue class 16 Kj = R2 = 0 Laue class 17 The same phason elastic constant as Laue class 15, but no constants associated with the pl~onon-phasoncoupling Law class 18 The same phason elastic constant as Laue class 16, but no constants associated with the phonon-phason coupling
follows we assume a QC (body 7) to be an infinite, homogeneous and free body. Thus, the boundary condition T,,11, = .ElzIn, = 0
(50)
According to the eigenstrain method (Mura, 1987), a subdomain 7’ in the body z i s subjected to eigenstrains E ; and Wc during the Volterra process. The actual strains in domain z, E,J arid WzI,are the sum o f the eigenstrains E: and W; and the elastic strains E;j and W’iI, i.e. --j.
00.
Et/ I= Eij +El:’
Wit
Wi,
and EllJ by the generalized Wooke’s law equation (25), we obtain
+ “v;
(51)
Since the elastic strain fields E;i and W ; induced by the dislocation are related to the internal stress field Tij
Tij
= cyklEkl
$- R i j k t w k l
€$zj
= RI,It$&
+ Kijkl wkf - ~kitjEk*I- K j k l wz,
- CijkEE?l
.+. Rzjklw?E
(52)
Substituting equation (52) into equation (20) and considering ji = gL= 0, we have ~
i
j
Rt,I,+%’k
k
3-~R ~ ~l k l~~ l ~~ l= w~k~~~~~~1~~~ k $- ~ ~ wfl, k (53) -I- ~ ~ k = 4c/,ja/-Gl ~ ~ 4-~ K,lx ,14w;, ~ ~
By comparing equation (53) with equation (27) one can see that the contribution of E$Land W & to the equilibrium equations is similar to that o f two body forces X,and YE:
~ ~
~ k
39 1
Dislocutions in Quasicrystals
Table 5 Elastic constants of lQCs (the coordinate system is chosen with the y and z axes parallel to two- and five-fold axes of the icosahedron) Phonon-phason coupling
22
33
23
31
12
~ t - 2 ~a
a a
0 0
0 0
0 0
p o o
o p o
o o p
11 11 22 33 23 31 12
a a
i+2p
i
a+q
0 0 0
0 0 0
o
o
0 0
o
33
23
31
12
32
13
21
R R R - R - R R
O
O
O
O
R
O
11
11 22 33 23 31 12
o
22
Rijkt
0 0 0 0 - R O 0 0 - 2 R 0 0 0 0 0 0 0 0 0 0 0 - R R O - R R - R O 0 R 0 0 0 0 0 0 0 - R O - K O 0 R
Phason field K&
11
22 33 23 31
12 32 13 21
11
22
33
23
31
12
32
13
21
K] 0 0 0 K2 0 0 IG 0
0 plii
0 0 KI +K2 0 0 0 0 0 0
0 0 0
K2
--kfi
0 0 0 Ic, 0
0 0 0 0 0
K2 Ic,
0 0 0
0 0 0 0 I(1 - Ic, 0
-K2
0 0 -K2 0 0 K2
0
K1
- K2
0 K2 0 0 --K2
0 0 KI - K2 0 0 0 0
-112
-K2 0 0
K1 - K2 0 -K2
o
0 0 -K2
0 K1
if we define A@@, Vcr and
Upon Fourier transformation equation (53) beconies
M,kgk
RLkG/c
R& 3. N t k W k =
2,
r,
(55)
and
where an overbar represents the Fourier transfori of a function, i.e.
.m> =
where
+f(k)exp(ik.x)d
where
Equation (59) is a set of inliomogeneous algebraic equations, the solution of which can be expressed in terms of Green’s functions as
and
where
2, = -iCi,,lk,&:L F, = -iRk,ljk&l
- iRIJklk, Wll - iKrJklkj@f,
163) (58)
Equation (55) can be written in a compact forin (59)
Mecltan ical Properties
392
When we transform equation (62) from Fourier space back to coordinate space, we find the general expressions for the elastic ~~splacement fields induced by Cs (Ding et al., 1994, 1995~): w
)Zfl (x’)dx’
(65 )
-#
42.1 The ~ e n e r ~ l i z a t iof’ o ~ ~ ~ h e l b ~ 3~ ’ ~s t h o d (Diigg et al., 1995a)
From the generalized elasticity theory of described in the preceding section, we know tha linear partial differential equatio phonon and phason displace~~ents follows (we assume J;: and gi in equation (27) to be zero):
with Green functions
~ u b s t i t u t i n equations ~ (54) and (60) into (65) and ~ntegratingby parts, we have
where we choose a dislocation coordinate system in which the .U;? axis is along the straight dislocation line in physical space. it should be noted that the elastic constant tensors ClJkl, KIJkland R,/,I in equation (68) are all referred to the dislocation coordinate system and the subscripts with small letters (i, k ) take the values 1, 2 or 3, while the capital letters (J, L ) take tlie values 1 or 2. Using
vqx) = 6 ~ ~ ~+~~ ~( -x3)w , ~ ( x )
(69)
(see equation (60)) and setting
q’
6r($cTj,c,
+
(’i-3Ri/kl)
+ CSP-~(~~)R/~*~, +
@-34jkl)
(70) The following are noteworthy: (1) The body forces X, and YL(equation (54)) both act at the point x’ in Pi’, but the directions of X,and Y, are along the axes in PI1 and P’, respectively. (2) Gap(. - x’) represents the a component of the displacernents at the position x in PI1 produced by a m i t point body force along the fl direction actiiig at the point x: in PI. (3) The elastic constants in the dislocation coordinate system are not, in general, the same as those in the conventional coordinate system of QCs, and accordingly a coordinate transformation must be performed.
Equation (68) can be written in a compact form (7 1) According to Eshelby et al. (1953), equation (71) has solutions of the type
vqx) = A’If(q)
q = XI +pxz
(72)
where p is an undeteriiiined parameter which we will find below. If we substitute equation (72) into (71) and introduce a inatrix with the elenients
then we obtain a set of linear algebraic equations for A as given by
As we know besides the Green’s function method given in section 4.1, there are other methods in the case of ordinary crystals, such as Eshelby’s method 953; Hirth and Lother, 1968) and troll, 1958, 1962; Bacon et al., 1978), which may have an advantage over the Green’s method for some actual calculations, in the following, e will generalize these two methods to the case of Cs and give some general expressioiis for the elastic fields of straight dislocation lines.
a@AP
0
(74)
It follows that the parameter p in equation (72) i s determined by the condition de;ltla”Pl = 0
(75)
which is an algebraic equation for p . energy is always positive and the coefficients are all real, the roots p(n) of equation (75) are necessarily coinplex occurring in conjugate pairs. Following the analogous
Disloca Eiopzs in &uasicrystals procedure proposed by Eshelby et al. (1953), the displaceinents induced by an infimte straight dislocation line parallel to the x3 axis can be expressed in the form AI-'(n)D(n)In
,4
(76)
where Re means that only the real part is to be taken, the sign of 2ni is taken to be the same as the sign of the imaginary part of p(n). The constants D(M)are determined by the following equations:
r
6
393
Since the elastic energy (equation (16)) is positive, i.e.
the symmetric matrix
is always positive-definite. The elements of [C, K, RI are none other than the terns in ~ q ~ a t i o(70). n It follows that there exists a real, non-zero vector a in PI1 and a real, non-zero vector P = + P~ such that
1
where b@are the components of the Burgers vector the dislocation. Furthermore, if we introduce the symbol
M; = "Fl,+ 6:-"Hg,
(78)
the generalized Hoake's law (equation (27)) can be written as
Ad; = ~ ~ ~ ~ , ~ ' ( x ) (79) By the same method as Foreman (1955) used, the elastic energy per unit length of the dislocation can be easily obtained as
4.2.2 The Generalization of Stroh's Method (Ding et al., 1995b)
The anisotropic elasticity theory of dislocations in crystals developed by Stroh (1958, 1962) has played ail i ~ p o r t a npart t in the theory of defects in solids. Bacon et al. provided an overview on the Stroh theory in their review article (1 978) in which the orthogonality, completeness and invariance relations for the Stroh eigenvectors, and the integral formalism were derived in considerable detail. In what follows, we shall extend the 6D formalism o f Stroh to a higher-dimensional one and then give an integral representation of the elastic fields induced by dislocations in QCs, which may be more suitable for numerical calculations. For definiteness we consider icosahedral QCs.
This means that the matrix
is positive-definite. This result guarantees the existence of an inverse matrix ( a a - ' . Moreover, if we again define another non-zero vector in PI,then it is easy to prove that the permutation s y ~ ~ e t ~ofi the e s elastic tensor indices (see equations (12--14}) assure tliat
(ad)"I-'= ( d ~ ) B a
(85)
We assume that a QC is infinite, hoiiiogeneous, anisotropic and a free body. Let mutually orthogonal unit vector parallel to a straight dislocation line. Let x denote the position vector from the origin to a point in N.In the present case, U and vv, induced by i n ~ n i t estraight dislocation lines parallel to t , are independent of the
displacement field solution of the form V q X ) = AI-'f((n)= APf(
where AB is a 6D constant complex vector, p i s a complex constant andf is an analytical function of its a r ~ i ~ e n t s . Using the expressions ~n equations (69-71), and substituting equation (86) into equation (69), we obtain
+
+
+
{ ( m n ~ ) " ~ ~ ( m ~ ) (tzm)"'] ~I-' p 2 ( p z ~ ~ ~=P0~ A(87) '~ The set of equations (87) has non-zero solutions for AB only if the determinant o f the coefficient matrix vanislies:
ce the above e q ~ a t ~ oi sn a polynomial with real ~ c i e i i t sthe , 12 roots (p = 1, 2, , . ., 12) occur in coniplex conjugate pairs uppose p p ( p = 1, 2, . . ., 6) is equal to the roots with a positive imaginary part, and then Ygf6 = p;, I f we define another vector as
LE
p= 1
y= 1
(34)
+
L; = --[inm)"P ~ l l ( n n ~ aPP J A y where 8 is the aiigle between the basis plane ( ') in the plane normal to a new basis plane ( Additionally,
or equivalently
the n ~ r ~ ~ l ~ z acondition tion
(95)
should be satisfied, which ensures uniqueness for A; and ~ i r ~ ~ e r ~theo fo~lowing re, conjugate relations hold: IJ/L+b
I_
1';
=
;'+6
L;+6
( p = 1, 2 . . . 6 )
$.
Furlhei-niore, we can define three 6 x 6 real matrices and give integral representations of them:
= (LE)*
(91)
t shodd be noted that the sum rule is not available any subscript in equations now on sunii~ationover repeated
the position vector x, then Therefore, in a polar coordinate system we have
+
taken for ,LL = 1, 2 . . .6, - for y using the definition equation (89), equation (87) can be r ~ ~ r i t t easn where
is
with s",L
=
[;*.I
1. Using equations (89) and (96), equation (92) can be expressed in ternis o f Sap and
~ l t i ~ l y equ~tion in~ (98) by mP and nP, respectively, we have
and ~ntegratingthis equation yields the r~presentationof the displacement field 8 1 v q r , 0) = -b"(-Sfl" In r + 4 0 ' " Su[(n~)-~]~idO 2n; ~ r t h ~ ) g o ~ ~ c~o~~l ~i t~y~, e t e iand i e s sinvariance are still and pkL,i.e. valid for A;,
(1009
An uncomplicated calculation on the Fourier transeaiiwhile9inserting equation (98) into equation (199), ) of the Green's functions gives the the resulting stress field is bp following results for k3 = 0: M," = B"P { - ~ ~+s~ ~ ~ [ "( ~ ~ ~ ) - ' ~ ~ ~ ' [ 4 ~ ~ ~ " J I 2nr ~
+ (.m)'Asi"]}
(101)
Consider a straight dislocation line with Burgers vector = (bl , bi, bi, hf , b i ) parallel to the periodic direction. In this case the dislocati~ncoordinate system is with the conventional QC coordinate system. along the periodic direction (x3 axis) without corresponding phason components, the phonon displacement field corresponding to b[ is the same as that in any transversely isotropic co~itinu~m. Hence we need only consider the elastic displacement field induced by the (hl, b!, 0, h f , h i ) . In this case V"(x)(in equation (60)) is dependent of x3, i.e. V" = vol(.xl, xz). For = (bl, 0, 0, bf, 0) the subdomain z' consists of an infinite s e ~ i p l a ~(x'~ e < 0, xk = 0, - 00 e x i < 00). The eigenstrains can be obtained as *
irac delta function and H( -x), the Heaviside step function. Substituti~gequations (66) and (103) into (67), we have
9
exp[i(klx,
+ k2x2)]dkldk2
k3-0
(lo4)
the other G a b = 0 where k2 = k: ki C = (C66K1 - R2#C,1K, - R 2 ) (106)
+
Substituting equation (105) into (104) and carryiii the Fourier integrals (Yao et al., 19971, we can find the
396
Mechanical Proper ties
expressions of the displacement field for h f , 0). Moreover, the expressions corres = (0, b!, 0, 0, b i ) can be obtained by rotating our coordinate system by n/2 co~nterclockwise in the physical space and by 3774'2 m the complenieiitary space. Finally, the expressions for the elastic displacement fields duced by the dislocations with Burgers vector = (h!, b!, 0, hi". h i ) (Ding et al., 1994, 1995c) are *
+
where r2 = .xy xz and ro is the radius of the dislocation core. If a straight dislocation line t lies in the quasiperiodic plane, say, it i s perpendicular to a two-fold symmetry axis, we can choose a dislocation coordinate system (q,x2, x3) such that the x3 axis is along the positive direction of and the x2 axis is along the periodic axis. This system can be obtained from the c o ~ v e n t i o ~system ~l (xi, xi, xi) by the subscript transformation: 1' -+ 1, 2' --+ --3? 3' + 2. After this transformation we find that non-vanis~ing elastic co~stantsin the dislocation ~oordinatesystem are
From equations (71), (72) and (108) it can be seen that equation (74) in this case consists of five equations which are divided into two sets ofequations: one set for A ' , A2 and A4 given by (C1,
+ C44p2)A' + (C13 + C44)pA2+ RA4 = 0 + C44)pAt + ( C M + C33p2)AZ= 0 (109) RA1 + (Kl + K4p2)A4 = 0
(Cl3
wit11 P(4 = P ( l ) , P(2>, p(4), p(7), p(8) and P ( W , and the other set for A' and A6 given by
(C,, RA3
+ C44p2)A3+ RA6 = 0 + (K; + K4p2)AB= 0
(1 10)
with p(n) = p(3),p(6),p(9) and p( 12). ~orrespondin~ly, equation (75) consists of two independent algebraic equations for p :
397
D is10 cat ions in Q uusicrystals
+ 2K4Rh$]tan-“/-”>
2C44K4 X I
and
For simplicity, we consider a dislocation with 0, b!!,0, h i ) , In this case the only equations we have to solve are (110) and (112). Equation (112) has two pairs ate roots (p(3), p(9)) and ( ~ ( 6 ) ~ p(12)). Suppose the roots with a positive imaginary part to be, say, p(3) and p(6) given as (1 16) Elastic displacenlent fields induced by dislocations in QCs with other symmetries have been discussed by a number of authors (Yang et al., 1995; Li and Fan, 1998). where Of
~ubstitutingequation (1 13) into equation (110) and putting ~ ~ ( =3 ~) ~ ( =6 1,) we have 2C44R
A6(3)= c44 K1
- c66K4
- s2
2CMR
A4(6) = c44 Kl
- cfi6K4
+ s2
Substituting equations (113) and (114) into (77) and noting h3 = hi, b6 = b i , we have
Finally, combining equations (60), (72) (76), (1 13), (1 14) and (115) all together, we find the displacement fields induced by a dislocation with (Ding et al., 199%) are as follows:
Quasicrystals are all brittle with a high Vickers hardness between 800 and 1000 at room temperature. Upon heating, the hardness decreases and the plasticity increases. It was found that above about 600°C Al-Cu-Fe IQC becomes ductile (Bresson and Gratias, 1993), and above about 700°C AI-Pd-Mn 1QC does also (Inoue et al., 1994). In the fo~1owingwe will cite some experimental results of compression deformation of Pd,,,, Mn,,, icosahedral single ~uasicrys~a1s, carried out by the Juelich QC research group, summarized by Feuerbacher et aE. (1997) and Urban et nE. (1999). Figure 7 shows true-stress versus true-strain curves at 760 “C and 800°C and at a strain rate of lowss-l. Both curves show the same features. After the elastic deformation stage there is an initial hardening stage YM with a very high hardening rate. Then a maximum stress is reached at M, followed by a pronounced yield drop and a continuous softening. Neither saturation nor secondary hardening observed up to strain h the maximum stress values of more than 20% c~~~~~~ and the flow stress cflow decrease with increasing the temperature T, as s u ~ ~ a r i z in e dFigure 8. Figure 8
described in section 3, the most frequently occurring dislocations in defor ed Al-Pd-Nn TQC are those with ers vector of c = r5 corresponding to .183 nm. The correspond in^ activation areas = AlAx) range from about 0.87nm2 to , which are about two orders of magnitude larger than the area per atom. As discussed by Urban et al. (19991, AI-Pd- n IQC can be described by an arrangement of Mackay-type clusters of a diameter 0.9 nm. Thus the obstacles, which are thernially circumvented or cut by the gliding dislocations, are not singular atoms, but ackay-type clusters.
b
0
igure 7 True-stress versus true-strain curves of AI,, Pd,, Mn, IQC at 760°C and 800°C and at a strain rate of j*-9 ;-I
shows the t e ~ ~ p e r a t udependence r~ of the maximum stress a-max, which decreases from about '750 activation volume V', which is defined as
modulus of the physical component of the Burgers vector of the ~lidingdi~location,and A x i s the distance swept by a dislocation segment of length Al during thermal activation. Hence V'/lbll I = AlAx represents area of the obstacles therma~lycircumt by the gliding dislocations and is called the activation area. The temperature dependence of Y can in good a ~ ~ r o x i ~ a t i be o n described by Pa). As determined by Rosenfeld ct al. (1995) and Feuerbacher et al. (1997) and
most cases as isolated lines, while in ~ i g ~ ~ t e m ~ e r a t u r e deformed AI-Pd-Mn IQCs usually more or less dense dislocation networks are observed. This i s the result of various dislocation reaction processes taking place in the course of plastic deformation. Therefore, by investigatmg one of the most lrequently observed ~ r r a n g e ~ ~of n tthe s networks - a triple node formed by three dislocation line segments - information on the reaction processes a n be obtained. Wang et al. (1998a) dis d possible dislocation reactions in face-centered s from the geometric and energetic points of view. Feng et al. (1995), W'nng et al. (1998a), and Wang (2000) provided some experimental examples of the reactioi~sby i~entifyingthe Burgers vectors of dislocations in triple node arrangement. These are 1/2[OiOlZ2](f = 2 7
+ 1/2[022iOl]~<= 2 )
= 1/2[032023](<= T 7 )
1/2[03?023](C == 2 7 )
+ 1/~[0Z2iOl](C= 6)
= 1/2[OlOiZZ](~ = T 5 )
i / 2 [ i o i i i o ] ( ~= =
of the stress-stram curves of At,, Pd,, ,Mn, icosaliedral single yuasicrystal compressed at a strain rate 10-5 s-* (after Feuerbacher et al., 1997)
(irnax
(120)
+ 1/2[121Zoo](<= 2 )
= i / z ~ o Z i o i z l (--~ ?)
and
(1 19)
+ ~ / ~ [ ~ i i i o =o ~T (~ f )
= 1/2[i0iiio](f = 2)
i / ~ [ i 0 0 2 i ~ ]= (f
(1 18)
+ i / ~ ~ i i i i o o ]=( fr3)
i/2[0122101(< = 2 )
1/2[01Z2io~(f= 2 5 )
(1 17)
(121)
in Q u a s i c ~ ~ ~ t u / ~
Among these dislocation reactions, reactions (1 17)(120) and (122) lead to a reacted product with different { ratios coinpared with the reacting disloc~tions. Therefore, it i s reasonable to suppose that the dislocation reactions give rise to an increase in C at an early stage of plastic deformation, and subsequently a dynamic e~uilibrium between the increase and decrease in the strain-accommodation parameter < is reached. The reaction (122) forms an extended dislocation consisting of two partial dislocations with a stacking fault in between. ere the partial dislocations with Burgers vectors of 1/4[1iil-?I] and 1/4[131iil] a five-fold type with I III = 0 . 1 7 4 1 ~and ~ I / = T ~ see , Table 2. es of'
In order to understand the iniportant role played by dislocations in plastic d e f o ~ ~ t i o nit, is crucial to observe the microstructures in differently deformed QCs. 111 the following we summarize the results observed by transmission electron microscopy.
and Feuerbacher et al. (1997) observed dislocation motion directly by an m-situ straining experiment in a high-voltage transinission electron niicroscope. The motion was viscous with a velocity ran 0.12 prn s-l to 1.2 pins-' , i.e. neither jumps nor local pinning of the dislocation line were observed. The moving dislocations left behind a contrast of the slip trace, which in some cases was observed to disappe~r after some time. The dislocations liad a proiiouiiced tendency to follow each other on the sanie slip trace. No examples of demobilization of ~ n ~ v i nd gis locations by interaction processes of any kind were observed. QLiantitative measurements of carried out by Wollgarten et al. (19 (19951, Feuerbacher et nE. (1 997), a differently deformed and aiineale IQCs revealed that: Dislocation density is d i ~ e r e n t for annealed specimens compressed to different plastic deformations epipl. For example, while the dislocatio~ density in an annealed specinieii is 8 x 107cm-', the dislocation densities of spec~~nens deformed at 730°C at a strain rate of 1W5s-' to 0.5%, 1.5%, 3.8%, 5.2%0, 8.2%, and 11% are 3 x 109~ m - ~ 8.8, x 109~ m - ~ 11,x 109~ m - ~12,x log 9.4 x 109 and 6.3 x 109~ m - res~, pectively. Namely, dislocation deiisity increases at the beginning of the deformatio~and increases further when the stress drops steeply after the maximum stress. The dislocation density reaches a maximum value at a plastic strain tpl 5-6%, and then decreases conti~uouslyuntil it reaches half of the inaximuin value (for the specimen 2i 11%). Wlth Dislocation density decreases with i n c ~ e a s i n ~ deformation temperature. For example, when specimens were deformed to a plastic strain 1% at a strain rate of 1 0 - ~s-l at various ~~1 temperatures, dislocation densities in the specimen deformed at 695"C, 730"C, 790"C, arid 820°C were 9 x 109 6 x log cmP2, 0 . 7 5 ~ 109 and 0.3 x 109 respectively. Dislocation density decreases during annealing. For example, when annealing a specimen with a dislocation density of 12 x log at 730 ('C for 13 rnin, 45 min, and 90 min, the dislocation density decreases to 7.7 x 109~ i i i - ~4.9 , x 109 and 4.8 x 109 respectively. This experiment indicates that the measured dislocation density in the unloaded specimen is lower than that in the stressed specimen, because the time period from I
Wang et u2. (1993) and Yan and Wang (1993) deformed an A17@ CO,,Ni, decagonal polyquasicrystal by hot impact and observed the microstructures of the deformed samples. In most of the regions they observed either densely distributed stacking faults or densely distr~buteddislocations. The fault plane was perpendicular to the 10-fold axis and the displacement vector lay in the fault plane and was parallel to a two-fold axis any dislocations possessed a Burgers vector parallel to the 10-fold axis. On the basis of this observation they proposed tlie following mic ism of ~i~h-temperature plastic deformation whose 10-fold ams is a periodic direction. In t ed by dislocation motion. the moving dislocation is d axis, the situation is the same as in coiiventional crystals, and densely distributed dislocations are observed, When the Burgers vector of the gliding dislocation i s a higher dimensional vector with its physical comp parallel to a quasiperiodic direction, for example, axis, the region slipped by a moving dislocation becomes a stacking fault region. The Juelich QC research group systematically studied the dislocation nisni o f plastic deformation in A17@., Fdzl.oMn, Wollgarte~et al. (1995)
,
399
400
Mechanical Properties
unloading to quenching a specimen is usually longer than 2min. As summarized by Urban et a/. (1999), ~~lthough a number of plastic d e f o ~ a t i o nexperiments were carried out on Al-Cu-Fe IQCs, no evidence had been found for a dislocation mechanism in this inaterid. However, Wang et a/. (2000) have recently observed densely distributed dislocation lines in hot-impacted Al,, Gu,, Fe,, IQC. All the experimental observations described above indicate that dislocation motion is the predominant process mediating the liigh-temperature plastic deformation of quasicrystals, at least for Al,, CU,~,,Fe,, Cs and Al,,Co,5Ni,, DQC.
,
5.3.2 tacki in^ ~ a ~ lTt ~, ~and i n C ~ y ~ t a l lPhases i~e in Dejormed QCs
ensely distributed stacking faults were observed in hot-impacted and rapidly cooled Al,, CO,,Nil, DQC ang et id., 1993 and Van and Wang, 1993), A170,4Pd21.2Mn8.4 IQC (Wang et id., 1998b; Urban et al., 1999; ~ a n etg al., 2000) and Alb2Cuz5.5 XQC ( ~ a n get al., 2000). Contrast and trace analysis revealed that the fault planes are ail parallel to one of the slip planes, are usually dense atomic . The displacement vector in the fault plane and is the physical component of one of the Burgers vectors of the dislocations. However, stacking faults in ~~igh-temperat~~re deformed and slowly cooled Al,o,4PdZ1.,Mns ZQC were only occasionally observed ( ~ ~ etnal.,g ~998b).They are not conventional planar defects but extended into wavily bounded walls of about 2.5-10 nm thickness. The apparent displacement vector o f each stacking fault, determined by a contrast extinction experiment, is parallel to the fault plane nornial. In order to clarify why stacking faults are only occasionally observed in high~~emperatL~re deformed and slowly cooled Al-Pd-Mn amples, Yang et al. (2000) carried out an in-situ observation of the hot-impacted and rapidly quenched sample, in which densely distributed stacking fault contrasts were observed. Up to a temperature of about 650°C, no remarkable change of the contrast could be observed. Further increasing the temperature to 700°C leads to an increased blurring of the fringe contrast. Within approximatel~5 min the fringe contrast completely disappeared. The positions of the bounding dislocations o f these staclciiig faults did not change compared to the initial state, and the contrast of the bounding
dislocations became sharper. This ir?-situ observation revealed that the stacking F~ulksformed during hot impact of Al-Pd-Mn IQC may be annealed out without any motion of the bounding partial dislocations. All these experimental observations reveal that a inoviiig dislocation in Cs leaves behind a stacking fault with a displaceme vector, which is equal to the physical component of the urgers vector of the gliding dislocation. This stacking fault is not a conventional planar defect but a wavy wall. Owing to the intense diffusion at high temperature, it broadens along the lateral direction, inducing an apparent displacement along the normal direction. of the stacking fault, and ~ n a l l ydisappears. The situation for AI-Cu-Fe IQG is complicated. In addition to stacking faults and dislocation lines, twins (Shield et a/,, 1993; Shield and Kramer, 1994) and shear-induced, one-dimensionally periodic lamellae (Shield and Kramer, 19973) were observed. Based on these observations, Shield and Kramer (1994, 1997a) suggested mechanical twinning and martensite-type shear inechaiiisnis in the high-temperature deformation. In addition, Shield and XCramer (1997b) suggested also a grain boundary mechanism, and Bresson and Gratias (1993) emphasized that atomic diffusion is the major cause of deformation. 5.3.3 Pha.son Strain Fields in Plas~ica//yD
Franz et ul. (1999) demonstrated that phason strain fields in plastically deformed quasicrystals can be quantitat~velycharacterized by means of selected area electron diffraction in a transmission electroil microscope by using iinaging plates. They found that niovlng dislocations may introduce phason strain into the regions free of dislocations in quasicrystals. The inteiisity of the phason strain varies with position in a given specimen and increases with increasing amount of plastic deforniation.
Based on the experimental obsewations reviewed above and discussions described by Feuerbaclier et aE. (1997), Wang et al. (1998a, 1998b) and Urban et aE. (1999), we conclude thdt the elevated temperature plastic deformaFe,,, and tion of quasicrystals, at least for A~,,CU~~., IQCs, and Al,, Go ,,Nil DQC is PdZ1 mediated by thermally-activated dislocation motion. The phonon component of a dislocation on a densely
,.
,
401
~ ~ s l ~ c ~in t Quasicrystals i o ~ s packed plane of a QC may glide under applied stress leaving behind a stacking fault. Owing to the strong intermetallic bonds in clusters in a QC and large stacking fault energies, the critical stress for dislocation movement i s very high. Hence ahnost all the QCs are brittle at room temperature. At high temperature, thermal activation helps moving dislocations to circumvent or cut these clusters in the course of plastic deformation. The stacking fault left by a moving dislocation broadens and then disappears due to intense di~usionat high temperature. There are three points that must be emphasized: (1) Dislocation motion in QCs is not an equilibrium niotioii, in which the static equilibriuni structure of the dislocation is maintained at all times. (2)The obstacles to dislocation motion are clusters with a high density. Thus a large activation area and a viscous motion are observed expe~mental~y. (3) Dislocation motion at high temperature is dependent on atoinic diffusion, which leads to the recovery of the phason strain. However, it is controlled, not by difhsion, but by localized obstacles (Feuerb~cher et al., 1997; Urban. et al., 1999). There are two competing processes in the course of the plastic deformation of QCs: strain hardening and disorder softening. Owing to the high structural symlnetry, plastic deforlna~-ion in f QCs is usually enhances the ‘lip carried Out by strai~-hardenin~ process, so that we observed an initial hardening stage VM with a very high hardening rate. On the other hand, the strain accomn~odationpara11 I of the moving dislocations become larger during the early stage of deformation and reach the values of 2 5 - r7. Hence the phason-type strain left behind by the moving dislocations is rather strong and its recovery is insufficient. This causes a disordering aiid hence a softeiiing of the obstacles to dislocation motion, leading to a decrease of the flow stress with increasing plastic strain, as observed experimentally. Based on these concepts, Schall (1998) tried to calculate the stress-strain curve and obtained a good consisten.cy with experimental curves. In the preseiit work we stressed dislocation motion as one importa~tmicromechanism for high-temperature plastic d e f o ~ a t i o nof quasicrystals. Of course other mechanisms, such as diffusional creep, grain boundary sliding, twinning, and marteiisite-type shear may also contribute to the hi~h-temperatureplastic deformation of quasicrystals.
s was supported by the National Natural undation of China.
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“-3
z.*
Eshelbi, J. D., Read, W. T., and Shockley, W. (1953). Acta metal^., 1, 251. Feng, J. L., and Wang, R, H. (1994a). Convergcnt-beam electron diffraction study of the Burgers vectors of dislocations in icosahedral quasicrystals. Phil. Mag., A69, 98 1-994. Feng, J. L., and Wang, R. H. (1994b). Burgers vcctor determination for quasi-crystalline dislocations by the diffraction contrast technique. J. Phys.. C~ndens.~ ~ f t e ~ , 6, 6437-6446. Feiig, J. L., Wang, R. H., and Dai, M. X. (1995). Observation and analysis of extended dislocations in ail Al-Pd-Mn icosahedral quasicrystal by trasmission electron mcroscopy. J. Mater Res., 10, 2742-2748. Feuerbacher, M., Metznnacher, C., Wollgartcn, M., Urban, K., Baufeld, B., Bartsch, M., and ~ e sse r sc h i ~ i d tU. , (1997). The plasticity of icosaliedral quasicrystals. Mater.
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Hirth J. P., and Eother J. (1968), Theory o j Dtslocations, McGraw-Hill, New York. Hu, C. Z., Ding, D. H., and Yang, W. 6 .(1993). rlcfa I'hys. Sin. (Overseas Edition) 2, 42-47 Hu, C . Z., Dirag, D. H., and Yang, W. G. (1993). 3. Wzkhan Umv.(Nat. Sci. Edition) 3, 21-28 (in Chinese). . H.. Yang, W. C., and Ding, D. H. (1996). Actu Cryst., 8 5 2 , 251-256. ,, and Masumoto, T, (1994). Mater. , 850. Cryst., 842, 261 -271. Jam, M. V. (1985). Pkrys, Rev. Lett., 55, 407-610. Kelton, K . F. (1995). In ~ n t e r ~ e t ~Cl ~oi ~c p ~ u Vol. ~ ~ s1,: P ~ z ~ e z ~(eds l e . ~J. H. Westbrook, and R. L. Fleischer). Wiley, pp. 453-491. IClenian, M. (1995). Czech. J. Phys., 45, 935, omniers~C. (1991). Actn Met. Mat., 39, 287. Levine. D., Lubensly, T. C., Ostlund, S., Ramaswamy. Steinbardt, P. J., and Toner, J. (1985). P h y . Rev, Lett., 1520-1523. Levi~ie,D., and Steinliitrdt, P. 1. (1984). Pl7.y~.Rev. Left., 53, 2477-2480. Li, X, F., and Fan, T. Y. (1998). Chin. Phys. Lett., 15. 278. Lubensky, T. C. (1 988). Introduction to Quasrcrystuls (ed M. V. Jaric). Academic Press, Boston, p p 199-280. amy, S., and Toner, J. (1985). Plzys. clzutiics ofdejeects in solids,Martinus Mijhoff Publ., Dordrecht. . H., Ding, D. H., and Lei, 3 . L. (1997). J. Plys.. Condcns. Mufter. 9, 859 872. Rosenfeld, R., Feuerbacher, M., Baufeld, B., Bartsch, M., anke, G., Beyss, M., Messerschm~dt, (1995). Study of plastically deformed Mn cpsicrystals by transmission electron microscopy. PhiE. Mag. Lett., 72, 37.5-384. Schall, P. (1998). Diploma thesis, RWTH Aachen. S1iield, J. E., Krarner. M. J., and McCallum, R. W. (1993). J. Mater. Res., 8, 1199. Shield, J. E., and Kramer, M. J. (1994). Plzil. Mag. Lett., 69, 115. Shield, J. E., and ICrmer, M. J. (1997a). J . Mater. Res.. 12, 300. Shield, 3. E., and Kramer, M. J. (1997b). J. Mater. Res., 1 2043.
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Wang, R. H. (2000). Micron, 31. 475. Wang, R. H., and Dai, M. X. (1993). Burgers vector of dislocations in an icosahedral Cu,, Fe,, quasicrystal determined by means of conver~ent-bea~electron digraction . Phys . Rev ,, Wang, R. H., Feng, J. L., Yan, U. F., and Dai, M. X. (1994~). Convergent-beam electron diffraction determination of the ors of dislocations in quasicrystals. Mrxfcr. Sci. 151, 323-334. Wang, euerbacher, M., Wollgarten, M., and Urban, K. (I 998a) Dislocation reactioiis in icosahedral AI-Pd-Mn quasicrystals. P M . Mag., APf7, 523-540. Wang, R. H., Feuerbacher, M., Yang, W. G., and Urban, K . (1 998b). Stacking faults in high-temperature-deforrned AlPd-Mn icosahedral quasicrystals. Yhil. Mug., A?$, 273284. Wang, R. H., Yang, W. C., Gui, J . N., and Urban, K. (2000). Dislocation mcchanrscn of hi defor~ation of Al-Cu-Fe and quasicrystals. Maler. Sri. E~zg.A , Wang, 2. G., Wang, R. H., and Transmission-eleceron-i~icr~~scopystudies of small dislocat~on loops in Al,, Si, Mn,,, icosahedral phase. Phys. Rev. Lett., 66, 2124-2127. Wang, Z. G., Wang, R. M., and Feng, J. L. (1994b). Dynamical siinulations of dif'fraction contrast images of straight dislocations in icosahedral quasicrystals. Phil. Mo.~.,A70, 577-590. Wang, 2;. G., Dar, M. X., and Wang, R. H. (1994~).Phil. Mag. Lett., 69, 291-296. Wen, J. Q., Wang, R. H., and Lu, G. H. (1989). Distortion of the zeroth-order Laue-zo in a silicon crystal. Acta Wollgarten, M., Beyss, M. Koster, U. (1993). Phys. Rev.Lett., 71, 549. Yan, Y. F.>and Wang, R. (1993). Phil. Mug. Lett., 67, 51. Yang, W C., Wang, R. El., Ding, D. ET. and Hu, C. Z., y theory of cubic qwsicrystals.
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The phenomenon of twinniiig in crystalline solids has been a subject of scientific research thr 20th century, mostly by mineralogists crystallographers in the first-half and and electron inicroscopists in the second-half. the past few decades, it has been recognized by ~ a t e r i a l s scientists and solid-state physicists that twiiining plays important roles in high-temperature intermeta~licc o ~ p o u n d s ferroelas, tic sliape memory alloys, ferroelectric sensors and actuators, ferromagnetic high-eiier~y~densitymaterials, high T, superconducting oxide compounds, as well as in a niultitude of ele c materials such as compou~idse~iconductors. n the past decade, two symposium proceedings and Wuttig, 1994; ande, 1999) were ~ublished" whicli cover all types of twins in the so-called advanced materials including intermetallic compounds. Whe recent review articles by ~hristian and (1995) and by ~andershaeve(1998) are on defor~ation twinning, and mechanical twinning in semiconductors, respectively. ~ollowingFriedel(1926), a twin may be defined as a portion o f a crystalline body which has undergone a 'tra~isformation' in such a way that the crystal structure of the resulting product is identical with that of the parent, but oriented diKerently according to well-defined relationships. In accordance with their twins may be classified into three different urgers, 1945): (a) growth twins, (b) transformt-tlioii twins, and (c) defbrmation twins. Growth twins are those formed by a solidification process from a liquid or vapor phase, and f o r i ~ a l ~these y belong to a
special kind of grain b o u ~ d ~ ~ ~ ri ae ~ s .s ~ o r n i ~ ttwin^ io~i ate tran$~orniatio~, an may result during they are further div of a niarteiis~t~c tr within a new crystal struct~~re ~ u r i nthe~ t r ~ n s f o r ~ l a eformation twin~ingor ~ e ~ ~ a n i c a l a shear defon11ation process caused applied stress, and i s one of the two (slip is the otlier) o f plastic d e ~ o r ~ ao t i ~ ~ solids at an ambient t e i ~ ~ e i - araiige t ~ r ~where defor-
cold-work and aIinealin~of polycrystals. s far as the r ~ ~ a t i o nbet s~~~ t w ~ n n i n and ~ i ~ e c ~ a bn e~~ ~ vl i oinr i n t e r ~ e t ~ l l i ~ compounds is concerned, xt i s worth ~ e ~ i t isomc o ~ ~ ~ i ~ general notions often stated in e~ei~entary text~ooks twinning occurs p i - e d ~ ~ ~ i n a n t i y
404
Mechanical Properlies
need to be modified. t will also be shown that transformation twins and growth twins play important bchavior of intermetallic alloys. ves (1952) has been often cited as pred~cting that loiig-range ordered alloys of cubic be incapable of ‘true-twinning’ o be d e ~ n e din the next section) Its in the literature are in support of this prediction, e.g. ahn and Col1 (1941) and ki and Fisher (1943). In some ordered s of bcc~basedstructures, ine~asticdeformation can occur due to the proftise ‘pseudo-
are readily available, such as heterophase interfaces and/or grain boundaries, and (b) the degree of chemical ordering (7’ as conipared to fccy) and/or solute segregation to the interfaces can lower the intrinsic stacking-fault energy of an alloy and hence provide a surmountable energy-barrier for twinning. The tension/co~pression asymmetry observed in a creep-deformed Ni-based superalloy is attrib~tedto the unidirectio~ialityof itie twin system ( which may be an important factor in plastic instability and creep-fracture initiation of this important engineering allay system based on Ni& (Anton, Ch. 1 in Vol. 2). en, 1979) and NiTi (Goo er al., The i ~ p o r t a n c eof the role twi~ning plays in physical properties and mechanical beliavior of interng of these intermetallics, the restoring forces stemming from the ‘pseudo-twins’ nietallics has been further demonstrated in those of cause them to untwin or detwin and give rise to the sonon-cubic fcc-based str~ctures,viz. the Ll, (tP4) and r and the related shape(tIS) types. In CuAu-I (El,)-type alloys, such as Inoue, Ch. 35 iii Vol. 1; 8, Fe-Pt, and CO-Pt alloys, the A1 (cubic) +Ll, ragonal) transformation is accoi~panied by the suka and lien, 1999). formation of a po~ysyntheticallytwinned (P bic structure, L1, (cP4) ture (a repeated twi d below, Clialcraborty ttendant to the at the so-called ‘superresult of the strain atomic ordering re inode occurred in fully 1942; Vlasova et al., 1972). A significant enhancement ordered alloys, whilst the usual fcc twinning mode was of magnetic properties of polytwinned ferroma~netsis observed in disordered and partially ordered alloys. In cons id ere^ to be possible through better under~tand~ng Ti) y’ phdse of the Ll, s t r u c t ~ rat~ elevated of the relationship between the PST i~icrostructu~e atures, ~ i c r o t w i n n i nof ~ the true-twin mode and the mechanism of coercivity (Zhang and was observed to initiate from the y/y’ interfaces under a 1992). In the Ti-A1 system, the fact that a variety of c r e ~ ~ ~ d e f o r m a t icondition on uimier and Strudel, two-phase ~icrostructu s consisti~gof y (Ll,) phase ar er al., 1970). The experimenta~results and a2 phase of the 0,9 (hP8) structure can be ~emonstratetwo important points: (a) contrary to the conventio~alw i s d o ~ twinning , in ordered i n t e r ~ ~ t a l - obtained because of the presence of 01 phase (hcp solidsolution) of the A3 (hP2) structure at high temperalics can occur at ~ i t e~~ ~ he r a t u r and e s low strain rates tures was discussed in the review by Kuaiig and if hetero~~neous ~ucleationsites for twin formation
~ r y ~ ~ a l l o ~ r aelements p h i c and parameters of ~
~
i
~
n
i
~
~
Twirt n irzg and ~ The roles of trans~ormation ic~ostructure-propertyrelationshi~sand of deformation twinning in i~eclianical
discussed recent
eical Be ~ havio r~
~
a
~
~
405
(or K i ) planes. U! is the ~iiterplanarspaein
ucture have been review articles,
e pLi~ose of this chapter is to present a comprehensive review of research highlights aiid depicted in Figure 1, the result 1s a s~ipercellof the uiiresolved issues on the roles of twinning in deformatwinned lattice with the base tion and fracture of intermetallic c o ~ p o u n ~Special s. liile -rC, and q r are fixe emphasis is placed on material that was not covered in by (180"2211/) to the earlier volumes (1995). pecific terminolo~yused in respectively. The twinning shear IS g = 2 cot$ = this chapter regard in^ crystal structure, aiid genesis of twins is ev I/@* The four orientation relationships of the classical In Section 3, experii~entaldata reflection in theory are: (i) are s u ~ m a r i ~ eaccordin d to the crystal classes. The ql, (iii) reflection in the plane normal to q l , and (iv) current status of our understand in^ o 180" rotation about the direction norinal to K,. The iiieclianisnis of twin formation i s reviewed require~entfor a crystal superlattice to be uncli~nged 4. The next two sections, 5 and 6, discuss th and ductility of i n t e ~ ~ e t a l ~ i cby the shear leads to the condition that either K , and q2 both have rational, low-index elements (type I twin), or ts of teiiiperature, microome of the key issues are l o ~ - i n e~l ~ m x e i ~(type ts which suggests specific s are rational, the twin is directions of future research. twins observed in metals aiid alloys are of the coi~poundtype. ~ ~ ~ e ~ ~ando t - r ~~ ~e ~~ tin ~ ~ai i ~~ ~ ii ~~ ~ g pound of the L1, structure are shown in and 2(b), respectively, and In general, a true twin niay be defined as a twinned portion of a crystalline body which has a crystal structure (including the state of chemical order) ~denticalwith that of the parent matrix. The orieiitaq values should be lialved i lion relatio~shipsbetween the true twin and the matrix representing the primary twin s can be specified using the classical theory of the CompreEicnsive ~ r ~ oC the ~ c t~ y ~ s ~ ~e~ ~ ~ of o g r~incompleke ~ ~ ~p ~ y~ twin unless atomic s h u ~ i n g( qr 2) of those atoms indicated by the strokes on the circular symbols possible t w i n ~ i nmodes ~ in sup~rlattice structures based on fcc and bcc structures were given by follows. In the co~plementarytwin s Aruiiachalam and Sargent (197 1 Cliristian and also called a .wper-twiR (Chalcrabo g i s twice as large as in the pseu ~ a L i ~ h l (1989), in and 6 0 0 (1994). atomic s ~ i L ~ is ~ inecessary n~ (q = 2). ments and parameters for other cubic L2, types), tetragonal (L1, and O,, type) structures 1 and 2. We are concerned only with compound twin modes which give small twiniiiiig~shearvalues, g < 2/2. the acute angle between q l and q2 (or q i ) or between In this chapter, unless ~ e n t i o n e d oth~rwise, the )?
406
ure 2 Crystallographic elcnients of (a) pseudo-twinning, $ = 70.53", and (b) complementary anti-twinning, $?, = 54.74", in an A,B compound of the L1, structure
able 1 Crystallo~raphicelements and parameters of twin modes in cubic ordered structures Structure type
Twin type
P (Primary); C (Complenientary)
K,
KZ
yI1
yI2
S
(I
g
Twinning und ~ e c h u n i c a Behavior l
407
Crystallographic elements and parameters of twin modes in tetragonal and hexagonal ordered structures. based on disordered unit-cell dimensions
A=
c/a 1s
P (Primary); C (Complem~ntary)
Miller-Bravais indices in an ordered crystal structure are referred to the crystal structure of the corresponding disordered state (fcc for Ll,, Ll,, and DO,,; bcc for B2, DO3, and L2,; and hcp for DOl9). The nuiiierical value of e is simply 2/3 for the twin modes in cubic str~ctures(Table 1). In contrast, the nLi~~erica1 value of c! in the primary (K,, ql) twin systenis of non-cubic crystal structures depends on the axial ratio, 1,= c/a, as given in Table 2. On a primary twin plane of K, = (1 11) in the tetragonal cases (L1, and O,, structure types in Table ), one of the three twinning shear vectors, = [112]/6, creates true-twinning or order-twinning and the others, [?11]/6 and [121]/6, lead to pseudotwinning (e.g. see Figures 8 and 12 by Yamaguchi and Umakoshi, 1990; or Figure 1 in Yoo et al., 1994b). It is this true-twinning mode with relatively low values of'g and q that ont tributes signi~cantlyto the plastic deformation of Ll, and DO,, alloys. In the cubic and tetragonal structures (Tables 1 and 2), primary twin systems and conjugate (reciprocal) twin systems are crystallographically equivalent, i.e. {Ki,> = {K'J and (qJ = (q2).In all other twin modes, they are not. Furtheri~ore,the conjugate deformation mode, (K,, q,), to the co~plementary twin (antitwinning) mode is found to be the secondary slip system at low and intermediate temperatures, which becomes the primary slip system at high t~mperatures, in all the ordered alloys for which the information on deformation modes xs available (Yoo, 1989). Table 3 summarizes these conjugate re~atio~sliips between the complementary twin (anti-twinning) systems and the slip systems at elevated temperatures in various superlattice structures.
Table 3 Slip-twin conjug~te re ~ ~ t ~ o n s h i m p s ordered superlattice structures between c o mp l e i ~ e n ~ ~twin ry (antitwin~iiig)system of (K,,- q,) and the slip system of (K2,q2)
Structure type
Complementary twin
i'c;
rll
Active slip (hkl)
fuvw] g
A simple criterioii for twinning results from geonietrical consideration^ that a twinni~gmode needs to have a small shear strain, g, and either no atomic sliufling (qg 2) or a simple shuffling mechanism represented by a small value of q when q> 2. Formally, these two parameters, g and q, are related, respectively, to energetic and kinetic aspects of deformation twinning. For a given c l ~ s e - p a c ~plane ~ d in a non-cubic crystal structure, there exist a unique set of translation and rotation operations for crysta~lograpliicalydistinct interfaces. For instance, y / y interfac~swithin a ? + a z lamellar doinain of a y-TiAl based alloy exhibit three orientation relatioiiships (Feng ei al., 1990; Inui et al., 1992; Yang and Wu, 1992). The f o ~ r t hkind of
orientation relationship mentioned above 6' %Ivesa truetwin with the rotation angle of 0 = 180", a pseudo-twin (8 = 60"), and a rotational boundary (0 = 120"). Interfacial energies of these three types in TiAl were given ao et nl. (1994), and Yoo and Fu (1~98b). In the classical nucleation theory of twin formation, the most important physical parameter is the specific inter~~cial ener rlattice intrinsic/extr~nsic
orn fir~t-prii~ci~les calcuntermetallic compounds
scopy ( techiiique~.A couple of examples are shown es 3 and 4. Figure 3 shows a lattice image picture of a true-twin taken in a deformed Ti54at.%Al (hereafter, ~ ~ - 5 4 Aspeci l) al. (1994). Figure 4(a) shows a typical a y/y lamellar ~ o u n d a r y of the ( B = 180") taken along the [1T0] direction of a TiAl PST crystal by Inui et al. (1993), and a true-twin boundary in anothe ift by the transla, 1997) js shown in
There are two types of dislocation describe a twin embedded in the matrix
or atomic structures of twin/matrix interfaces can be electron microchar~cterizedby using hjg~-resolutio~
Lattice image ~R~~ picture of a twin in Ti-54A1 (from Couret et al., 1994, reproduced with p ~ r ~ i s s i ofrom n The Minerals, Metals and Materials Society). M is the matrix and T 1s the twin
09
Schematic illustratioiis aiid HREM images of y/y lainellar boundaries in a TiAl PST crystal, (a) the true-twin type (from Inui et al., 1991) and (b) the true-twin type with an APB type translation (from Sicgl rt al., 1997)
twin formed by dis~ocationswith (Frank aiid Stroll, 1952; allel to q2 gliding on lough, 1957). Alternat ly, disclination models for winning are sometimes useful to describe certain aspects of twinning phenomena (~rmstromi~, 1965; Romanov and Vladirov, 1992), such as a case of twin(M~llneret al., 1994; M~llnerand ta of ~ransmission electron microscopy (TEM) indicate that an incoherent twin boundary consists of steps and/or ledges on the CT interface, where each step is a twin or glissile-type twinning dislocation as Frank (1951) originally proposed. Figures 5 and 6 are shown as typical exam~les. Low- and high-i~agnification H ~ E Mimages from y-TiAl shown iii Figures 5(a) and 5(b) confirm that tapering of a twin l a ~ e l l ais due to the presence of steps (Singh and Howe, 1992). Figure 6 shows a bright field in situ TEM image of a twin tip in Ti-54AI under g (from right to left) at a very low ouret et et al., 1994). Each sequence (I, 2, and 3) indicates a set of three Shockley partial dislocations, and the gradual decrease in the interspacings of these partials (especially of the first 15 partials at the left in a thcker region of the foil) confirms the validity of a dislocation pile-up model of deformation twiiis in y-TiAl. This dislocation pile-up ler (1992%) to alnalyze the dual twin dislocations of a in TiAl. The results of
n u m e ~ ~analyses ~l indicate that twin nuc~eation is difficult, but twin propagation is rehtively easy. Using an in situ strain in^ TE al. (1997) investigated deform migration in a fully lamellar two-phase TiAl alloy at room temperature. The results showed that only the interfacial dislocations in tw for slip along the mobile, suggesting that the a& interface is higher than (0 = lSOO) or pseudo-twin IS = 60") interface at room temperature. The junction between a coherent ii~coherent{121} twin boundary in a yinvestigated using (1996). The straight iiicoherent (122 ) boundary perpendicular to the coherent (111) ~oundarycan be produced either by a shear process in the y phase or as a result of the a--+? t ~ a n s f o i ~ i a t ~ oThe n . niobility o f such an incoherent twiii boundary is believed to be intrinsically low, but can also be hampered by solute segregation. The topological theory of interfac~aldefects was proposed by Pond (1989) who showed that ad~issible interfacial defects are characterized by combinations of symmetry operations froin each of the two adjacent crystals. In their recent H interfaces in T i - 4 4 ~ l - ~ Z r (1999) found no lattice misfit dislocations, but a variety of interfacial steps. The Burgers vectors deter~inedfor
image d e ~ ~ o n s t r ~the t i i tapering i~ of a twin lamella due to the presence of steps 111 yarea showing multiple-pl~nesteps at the twin interface marked by arrows (from Singh and Howe. 1992, reproduced with permission of Taylor & Francis)
image of a twin tip iri Ti-54A1(from Gouret et al., 1994, reproduced with ~ ~ ~ i ~ i sfrom s i oThe n ocrcty). The letter X points out an iniperfectio~iin the sequence (1, 2, and 3) or partial
clislocati ons
aisaz e2: al., 1997) were t mapping metliod by
step and di~locationc ~ a r a c t ~The r . spIi and dislocation components yields a s tion of interface flux for d i ~ u ~ i o n a ~ transport ~ s s o c i a t ewith ~ the motion and interaction defects has been treated formally nd (1998). That the presence of' a ( I 11) / 3 Frank partial dislocation at a twin bo~~ndary in a l u ~ ~ i np~oduces ~m a step that can move by c ~ ~ was concluded from th dlin et al. (1997) and
b
(1999). This is an important finding in that it provides a dislocation i~echaiiism whereby twin growth can occur by non-conservati~e thermally activated processes, which is consistent with the role of Frank partials in twin nucleation in y-TiAl scussed recently by oo (1997) and Yoo and ishinuma (I 997, 1999). se
In accordance with their genesis, twins niay be classi~ed into four different kinds: growtli twins, annealing (recrystall~~ation)twins, transformation twins, and deforination (i~echanical)twins. All of these kinds have been observed in intermetallic compounds. Interfaces created by growth twins in an ch the order-disorder han the melting point boundaries in it. A 113) type in Ni,Al is , Ch. 24 in Vol. 1). In the compounds (T,K T1J, e.g. in Vol. l), annealing twins are also possible because ‘cold working’ in the disordered state ( T > T,) i s easier than in the ordered state (T
atom-by-atom correspondence between positions in the parent phase and the twin, not only for those cases with 4>2, but also for the cases of intrinsic anti-site defects and/or vacancies, sL~bstitLitioiia1solutes, and interstitials trapped in different positions. Whilst we d~stinguish t r u e - t ~ i n n i n and ~ pseudo-twinn~ng for ideal superlattice structures in the belief that this distinction inay also be important in real materials (Christian and Laughlin, 1989), one must keep in mind possible roles of intr~nsicand extrinsic point defects in deformation twinning of ~ u l t i c ~ n i p o n eintermetall~c nt alloys at elevated te~peratures.
atio
3.1 fcc-
res
3.1.1 L1, (cP4) ~ 0 ~ ~ 0 ~ n ~ s
~ e f o r ~ a t i otwin~ing n was reported to occur under shock loading in Cu,Au ( ikkola and Gohen, 1966) and Ni3A1 (Gray, 1994). In the latter, the operative twinning mode is assumed to be of the complei~entary anti-twinning type (Albert and Gray, 1995). This true twin .in the Llz structure can be regarded as an array of SISFs on consecutive K , = (111) twin pia TEM microstructures of shock-deformed Ni,Al (e.g. Figure 2 of Ilcebuchi et al., Ni,Al+B (Albert and Gray, 1994) show a dispersed distribution of stac~ing-faultfringes that are indicative Transformation-induced twinning in interinetallic o f individual S than ‘microtwins’.A similar superlattice compouiids was reviewed by Yamaguchi et distribution of observed by TEM investigaal. (1994) and a general theory of transformation tion of defornie e (Takeuchi et al., 1973). twinning kinetics during ordering reactions was given Emission of extended SISFs from a crack tip has by Khachaturyan et al. (1994). Since pseudo-twinning been reported in Ni,Al (Yoo et al., 1994a) and in intermetallic compounds, as (Co,Ni),Ti (Liu et al., 1988), where the former was q ~ a s i - t ~ i i i n i n(Cahn, g ~ 1992) or of stoichio~etriccoinposition and the latter had a Goaxtoii (1994, 1995), is a special 23Ti-3Ni composition. case of stress-iiiduced mart~nsitic transformation, The term ‘microtwins’ may be reserved for those ongoing debates on unresolved issues (e.g. mixed twins whose thickness (D)is on the order o f 7000 characteristics of ‘diffusional-disp~acive traiisforniainterplanar lattice spacings ( D w 7 x 1O3 d, where eneous nL~cleatioiisites, etc.) recorded 3d.;;r;0.4nm for Ni,Al) and the term ‘macrotwins’ in a number of‘ inonographs on displacive t r a n s f o ~ a - inay be used otherwise. Accordingly, twins of t~~ickness tions apply here as well (Tanner and Wuttig, 1990; on the order of several lattice spacings (Da7d) may be Cahn, 1992; Christian et al., 1995). called ‘nanotwins’, but these must be thicker than 3d so ~ ~ c o r d i ntog the strict de~nitionby Cahn (1977), that the twin orientation based on the stacking true-twi~ningas defined in Section A B ~ can ) be ascertained in the deformation in most loys except completely random structure. A geonzetrical method of det substitutional alloys. y a homogeneous lattice strain, thickness of a nanotwin under an in situ T real intermetallic alloys with long-range order lose an was given by Gomjou et al. (1988).
awasaki (1966) showed actual examples of TEM icrographs in which overlapping of distinct stacking faults sometimes shows contrast similar to those of thin twins or nanotwin~. Whether the twins observed in Gu3Au ( ~ i k k o l and a Cohen, 1966; Chakraborty and Stark, 1975) are of the ~seudo-twin type, or the true-twin type was not resolved unanibiguoLisly. The rotation (or tilt) of the angles of $ = 70.5" and =[i01] or [101] can be determined by measuring the deviation of marker lines drawn on pre-polished surfaces, which gives an estimate of the magnitude of a twin shear after deformation, but this is obviously very difficult to obtain when microtwins are very thin.
The relationshi~sbetween twinning and mechanical and other L1, alloys were discussed ew papers (Yoo, 1998a; Yoo and ~ a ~ a g u c h2~00). i , The twinning shear associated with system shown in Figure 7(a) was in y-TiAl (Shechtuian et af., 1974). ar as a f u n c ~ i oof~ the axial ratio (A = c/a), as given in Table 1 is plotted in Figure 8 for the primary and ~ Q m p l e ~ e n t atwin r y systems and also f o r ~ a t i o ntwin system with
unit twin dislocation for the primary twinning is ]/6, and that of the a~ti~twinning case is = [ii2]/3 as shown in Figure 7(b). Wher ent twin boundary energies for the two cases are the same and calculated to be rather low, rT = 5 0 - 6 ~ i ~ ~for / ~ TiAl 2 (Fu and Yoo, 1991; ~ o o d ~ a et r daZ., 1992), tlie twinning shear oi" the former is about one-half of that for the latter (gp= g&) wlien it zz 1. Figure 7(c) shows that the primary and its conjugate twin systems are crystallographically equivalent. Under an a ~ ~ r o p r i a internal te stress field, therefore, te pair niay give rise to a pure shear strain, on1 an algebraic average of two simple cated by the dashed parallelograms in Figure 7(c). In contrast, the slip-twin conjugate relationship of (OOl)[l 2 and (111) [ii2]/3 is s ~ e ~ c h eind ~ i g u r e cause of the large niagnitude of twinnin (gc> 1.2 for it< Ll)? deformation by the complementary or anti-twinning mode is not 1i~elyto occur unless it is needed at a site
U2
Ib I
ldl
ure 7 Twinnin~ in the Ll, s t r u c ~ ~ r e(a) : primary t ~ w i ~ ~ nsystem, i n ~ ~ (b) co~plementary ~ an t i ~ t w i n n i n ~ ) system, (c) crystaliograp~i~ally equivalent conjugate twin systems, and (d) non-equivalent twin-slip conjugate system
where a large amount of strain i n ~ o ~ ~ a t i bmust i ~ tbe y relieved, such as at a twin-twin intersection or a crack tip, In addition to finding the direct role of twinning partial dislocations in plastic deforniation of y-TiAl, Singh and Howe (1992) attr~butedthe formation of a three-plane (9R) deformatio~-induce~ structure parallel to pre-existing twin interfaces to an ~ ~ t i - t w i n n ~ n g shear operation an every third plane CAB). This result, together with the oh accommodation shear by basal (00 1)[11 twin-twin intersections of type-1 (don cozonal direction) at high t e ~ ~ e r a t ~ r e s al., 1993; Sun et al., 1993), gives an indirect evidence of the slip-twin conjugate re~ationshi~ (Table 3). However, Abe et al. (1937) coiiciuded from their analyses with tlie aid of image simulation that the ~~~
AuCd MnPt
Nblr
AgTi
1.6
I.2
0.8 0.4 0
95
1
1.05
7.1
re 8 Variation of thc twiiining shear wlth the axial ratio in LI, c o m ~ o ~ n d s
structure was caused by overaiid not by the hen an (001) pi01 1~ode-Icrack is s ~ b ~ ~ ctot ean d uniaxial tension along the [0011 direction, crack-tip blunting by two symmetric tension twins of the co~plemeiitary (antitwinnin~) type is ~eometrica~lyand energetically
the so-called 'c-domains') is formed are known to deform plastically by twinning. investigation of deformed CuAn-I, Syutlrina ovleva (196'7) observed prominent bands of deformat~on which changed direction at the domain boundaries and Pashley ei al. (1969) interpreted then1 as s concluded from their inant deforn~ation U-]I at room temperature was { 111) deformation twinning and not uAu-I alloy o f coarse grains ( 5 to
10 pm) without the lamellar structure (colonies of cdomains), Greeiiberg et al. (1 999) observed microtwins in the temperature range -96°C to 3 primary { I l l ) (113) twinning i s reported to be the major deforination mode in FePt from room temperature to 600 "C (Gao and ~ h a 1994). n ~ In~ FeFd, while defor~ationtwinning was the secondary mode of deformation under tension, profuse twinning was observed after cold rolling (Rao and SoEa, 1997). In two-phase TiAl alloys, deformation twins originate froin various interfacial boundaries. Figure 9(a) represents the twinned microstructure typically observed after high tei~peratured e f ~ r ~ a t i o(Appel n and Wagner, 1994). The propagation of the twins i s essentially limited by the widths of y-lamellae. The twins are generally very thin (D< 50 nin), as documented in Figure 9(b) by the frequency distri~utionof their thickness. Tlie mean thickness of deformation twins lies in the 15-20nrn range. There have been many reports of ~ ~ ~ t -3: ~ o r ~ observations of twin intersections in y-TiAlalloys, e.g. Singli and Howe (1992), Wa (1993), Appel et al. (1993), Chaturvedi (1993), Sriram et al. (1994), Loubradou er d.(19951, Jin et G I ~(1995), . Hsi
0,16 0,12 II h
9 0,08 2 0,04 0 0
20
40
60
igure 9 Deformation twins in Ti-4881-2Cr alloy (a) deformed at 800 "C to failure at sf = 10.2%; foil orie~tat~on [loll, and (b) frequency d~stribL~tionof twin thickness. N, = 884 is the total numbers of twins investigated (from Appel and Wagner, 1994, rcproduced with ~ e r ~ i s s i ofrom ii The Minerals, Metals and Materials Society)
414
~ e c ~ ~ a n Properties ~cal
Figure 1 Q Temperature dependence of the apparent CRSS for twinning observed in y-TiAI single crystals (after Kisbida et al., 1996)
Inui et al. (1997), and hang et a/. (1999). As ~ e n t i o n e dabove, there are two types of twin-twin type-TI in reference to the = [lOT] directions, respectively. These studies revealed a variety of localized deformation processes (subsidiary twins, basal or cube slip, nanotwins, formation of 9R structure, etc.), but no clear evidence of microcrack initiation. In single crystals of Ti-54A1 and Ti-56A1 under co~pressive~ ~ ~ ~ i aloading, x i a l twinning was observed at the ~ 0 0 1orientation ~ and high temperatures ida et al., 1996; Inui et al., 1997). A plot of the vs. temperature (Figure 10) shows a transition of the defor~ationmode from superlattice slip to defoi~ationtwinning at about 750°C. At the [OOl] orientation and room temperature, Mahapatra et al. (1995) reported that d e ~ o r ~ ~ t iino n23-51AI single crystals occurred ~ r i ~ d r i l by y twinning, but an increase in the A2 content to 54 at.% resulted in deformation primarily by slip.
The primary (1 1I) [112] twinning of the true-twin type in Ni,V was first observed by Vanderschaeve and Deformation in this alloy arrazin (1977) using proceeds mainly by p lion of stacking faults and twinning due to the rela tiveiy low stacking-fault energy about 22 i n ~ ~ m (~a~derschaeve 2 and Escaig, 1978). cause of the Al--+DO,, transformation at T,= 1045 "C, domains in the shape of elongated prisins b o u n d e ~by ( 110) transfo~ation-twinplanes inay be
formed. Thus, inechanical properties of this alloy are affected by interactions of { 111) slip dislocations and deformation twins with the (1 10) twin boundaries. Zigzag propagation of deformation ~ ~ c r o t w i across ns the domain boun~aries observed by TEM (Vanderschaeve and Escaig, 1983) was attribBted to crossslip of partial ~ i s l o c a t i o ~via s the stair-rod mode (Fleischer, 1959). eformation twinning in A13Tj was reviewed by Uaniaguchi and Umakoshi (1990), and Yoo et al. (1991). The Fact that (111) (112) true twinning is the major deformation mode in A1,Ti at elevated temperatures (20-800 "C) was established following the compression study of single crystals by ~ a m a ~ u c h i (1986) and Uaniaguchi et al. (1987) and the TEM analyses of deformed polycrystals by Vasudevan et al. (19898). Twins were often observed to propagate from one side of the sing1e-cryst~~lsample to the other accompanied by audible clicks, and serrations were recorded on the stress-strain curves which were thought to be due to the discontinuous propagation of twins. Four variants of the (1 11) ( 1 l2> twin system were observed to be augmented by (OOl)[llO] slip at high temperatures, and this observation is consistent with the slip-twin conjugate relationship in the structure (Table 3). Twinning plays an ~ m ~ o r t a nrole t in the plastic deformation of A1,N b (Shechtman and Jacobson, 1975). Conipressive ductility of AI,V was found to increase with replace~entof vanadium by titanium, e.g. Al,(.95V-.O5Ti) showed 7 % compressive fracture strain at room tenipemture (Umakoshi et al., 1988). The i ~ p ~ o v e in ~ ~~n to ~ ~ ducti1ity ~ ~ of ~ the s s ~
~
T ~ ~ i nand ~ i ~~e gc E ~ a ~ iBehavior cu1
ternary alloy was attributed to a substantial increase in the activity of ( 1I I ) ( I I 2) true twinning which was not operative in the binary Al,V compound.
415
Crystallographic elements of twins observed in Ni,Nb single crystals (Hagihara et al., 2000) in tcims o f the Miller-~ravais indices based on the DO, structure
YI 3.1.4 DO, (oP8) C o ~ ~ o u ~ ~ s Tensile strains in excess of 11TOwere reported in a NiNi,Nb composite at room te~peratLire~ which were attributed to extensive twinning on { 112) planes under tensioii along the [loo] growth direction and (011) planes under compression of the ertzberg, 1971). Afte of the directionally solidified r(Ni)/y'(Ni,Al)-G(Ni,Nb) wal et al. (1978) reported that no (011) observed, whereas the hysteresis loop and TEM characteristics could be fully interpreted by means of twinning and untwinning from two specific variants of the four (21 I > twinning planes. Grossiord et al. (1972) determined the (21 1) twinning elements in Ni,Nb to be K , = (21 1) and q2 = ( I1 1) in terms of the Miller-~ravais indices based on the g = 0.384. A systematic study of plastic deformation of Ni,Nb single crystals was performed by Hagihara et al. (1999), and the crystallographic elements of three twin systems were obtained as given in Table 4. The temperature~dependentCRSS plot (Hagihara et al., 2000) showed that while (012) (021) twinning occurred at low temperatures (0 to 200 "C), (01 1) ( o i l ) twinning and (21 1)'(m7 13)' twinn~ng(quotes indicate irrahigh temperatures (200" to for the former mode was about 70 MPa, whereas that for the (01 1) (011) twinning was
3.1.5 C15 (cF24) C o ~ p o u ~ ~ ~ ~
The Laves phases (sometimes designated as FriaufLaves phases), with an AB, composition in the binary case, form a very large group of intermetallics which crystallize into the hexagonal C14 (hP12) structure, the cubic C 15 (cF24) structure, or the dihexagonal C36 (hp24) structure (Laves, 1967; Sauthoff, 1996). These t h e e structures belong to the class of topologically closepacked (TCP) structures (Gladyshevskiiand Bodak, Ch. 17 in Vol. 1). Any one of these structures niay be transformed into any other by shear, and, in this sense, twinning of the cubic C15 phase is just an example of polytypic transformation (IComura and Kitano, 1977). In the C15 prototype MgCu, at 600 "C, deformation twins were observed by Moran (1965). The deformation microstructures of NbCr, observed ming TEM
(211) (011) (012)
'(40nB)' (oil) (010)
'[m7 131' [Oil] [021]
v2
[111] [OI 17 [OOl]
g
Kind
0.40 Type I 0.13 Compound 1.07 Compound
'(hkl)' or '[uvw]' means irrational indices.
were dominated by twins up to 1400"6,whereas at higher temperatures the deformation appeared to proceed by a mixture of twinning and slip et aE., 1997). In all cases the twins appeared composition plane within each grain and this could be attributed to an autocatalytic nucleation effect. Livingston and Hall (1990) showed in plastically deformed (Hf,Nb,Ti)V, alloys that { 111) (1 12) twinning was the major deformation inode at room temperature, and they linked the twinning mechanism to a synchroshear process (Kronberg, 1957). In HLf-22Nb-64V alloy, Chu and Pope that at elevated temperatures (25-300 " fairly ductile due to ( 11 1) ( 112) type defori~ation twinning without dislocation slip. Twinning at low temperatures (below 25 "C) in ternary alloys of composition Hf-25Nb-62V and Hf-26~b-64Vwas investigated by conventional and high-re 1998). A large concentration homogenized alloy confirme been reduced in the ternary deformation twin clusters after compressive deformation was similar to that of stacking faults in the undeforrned alloy The twin plane was deteri~inedto be the net of vanadium atoms which comprises the highest density atomic plane in the Laves phase. The reason for the intrinsic brittleness of Cl5 Laves phase at room temperature is believed to be that slipI twinning, and stress-induced polytypic transformation are all accomplished by synchroshear rather than by ordinary shear processes. In each case, tlie rate-lin~iting step could be the motion of synchro-Shock tions wh~chis d i ~ c u l at t low temperature. (I 994) described the crystallography and geometry of the defects responsible for twinning in the Cl5 structure and proposed a twin nucleation model based on the partial source m e c h a n i s ~ (Pirouz, 1987). He also discussed niechanisnis by which synchro-Shockley dislocations may become mobile, such as the possible role of vacancies in the cooperative atomic shuHing associated with the motion of a kink.
res
Following the original remarks by Laves (1952), a s were made to produce twins in the en /?-CuZn single crystals were aded at several temperatures after various thermal treatments, pseudo-twinning of the (11?)(111) system (Table 1) was observed to occur when some disorder arose (~ouchardet al., 1970). It was concluded that the absence of ‘twinning’ in the ordered stale was due to a ‘detwinning’ ineclianisrn rather than i~capabilityof ‘twinning’. i-50Ti-3Fe alloys, deformation twins of two pseudo-twin types with the {112} and 14) twin planes were identifie~in the TEM study by 00 et aE. (1985). T ~ e ~ cycling a l under a constant load produced a high density of these twins. The first
structure. An apparent (1142 twin ‘double twinning’ rcus, 1967), but this was not believed to be the case since the observed composition plane was the twin plane 1985). ~ o b ~ r liJty nl. (1990) further t ~ ~ e r ~ o - ~ e c h ~snt ri ~ c a~ l~ t h e n oi nf gthe alloy and f o u that ~ ~ defor~~ation twinning on { 114) planes, together with concurrent dislocation slip o f the (0 10) type, enabled the polyc~ys~~liine ~ a t e r i to a ~yield greater than 50 % r o o m ~ ~ e ~ ~ e r a~ucti1ity. ture ~ndividual twins did not grow thicker than 50-150nm, tzrid the density of twins i ~ i ~ r e a swith ~ d the extent of cold working.
3.2.2 DO3 (cFI6) ~
~
~
~
As was discussed in the Introduction, the profuse
1,/&
and 4 5= 8 as listed in
Table 1.
atomic s h u ~ i n g(q > 2) acco~panied the twinnin process. Therefore, the (114) twinning does result in
ati ion twin bands were ~ e ~ o r t eind Fe3 y a n ~ ~ b of e ri~vesti~ators (e.g. Cahn a Coll, 1961; Guedo et al., 1978). Using the ~ o r i ~ u l a t i o n evis and Crocker ~ 1 9 ~ ~ , 1 9 ~ 9 ) ~ (199 1) derived the c r y s t ~ ~ l l o ~ r ~ pelements hic of
Variation of the twinning shear ( g ) with the axial ratio in hcp metals and DO,, c o ~ p o u n d s
~
T w i n n i ~and ~ ~ e c ~ a n i Belzavior ca~ deformation twins in Fe,Al to be I(i = ( 2 i i ) , q l = [ i l l ] , K, = (211), r2= [TTI].The density of twin bands in specimens compressed at liquid-nitrogen temperature was higher than that in the deformed specimens at room temperature. res
3.3.1 DO19 (hP8) C O ~ ~ O ~ ~ ~ ‘ ~ in hcp metals was reviewed by Yoo (1981) who showed a plot of twinning shear vs. the axial ratio. This g vs. ;1 plot was extended to include A, compounds of the DOl9 structure as shown in Figure 1 1. The largest and the smallest axial ratios correspond to A = 1.70 for Pt,U and /I= 1.43 for A1,Ce. There are many compounds which have axial ratios in the range to those five (Mn,Ge, In) shown in Figure Fe,Mn, Ni3Sn, Ti, tion twinning has been observed in only one of them, viz., Ti,Al, The {ioiz} (ioii) twin system (Table 2), which is most comnion in hcp metals and alloys, gives a socalled ‘tension twin’ (in reference to an uxiiaxial applied stress along the c axis) because ;1< 1/3 for all known DO,, compounds. That atomic shuffling is necessary in the disordered hcp alloys ( q> 2) is demonstrated with the aid of Figure 12. Th divided conceptually into shear of atomic motif shuffling. Figure 12(a) shows the homogeneous shear the unit cell for the (10i2)[TOll] 19 structure. In the fully disordered n four layers (q = 4) must shuffle by small additional displacements, as indicated by short arrows in Figure 12(b). In the case of the fully ordered state, on the other hand, all the a t o m in eight layers ( q = 8 ) must shuffle, but the i ~ p o r t a n t difference between the two cases is the fact that in the ordered DOl9 structure the atomic motif pairs situated at tlie four face-centered positions of the unit cell must shuffle by much larger displacements as shown by long arrows in Figure 12(c). Christian and Laughlin (1988) suggested the term ‘interchange shuffling’ or ‘order shuffling’ for this process. Inspecting the shLifI-ling displacements of those atoms labeled A in Figure 12(b), one notices coordinated combinations of a ~ t e r n a t i n ~x- and ymechanisms (Jaswon and ove, 1960) which together appear like a ‘ring mechanisni3 in the clockwise direction, This is consistent with the synchroshear of
417
atoms in the core of an edge zonal twin dis~ocationin the A3 structure ( senbaum, 1964). In an A compound of the D structure, such a coordinat motion of atoms is disrupted because of the required interchange of A and atoms over relatively large distances as shown in Figure 12(c). This is the likely twinning 1s intrinsically In the tensile deformation study of Ti,Al by Lipsitl et al. (1980), no twins were observed over the temperature range of 25-900 “C; however, some extended Pdults, or micro-twins, were observed at 900 “C. The occurrence of twin-like def~rmation bands in Ti-24Al alloys q d from observa temperatures was ted from by Morris and Morris (1991). but no confirmation of the twinned orientation by select~d-areadiffraction (SAD) patterns was given. Qhtsuka (2991) reported that twin-like deformatioii bands were observed during creep tests of Ti,Al polycrystals, and the occLirrence of
i ~ l? ~ Atomic ~ econfigurations associated with the process of (1012)[70!1] twinning in the DO^, structure: (a) homogeneous shear t r a n s f o r ~ ~ t i o n(b) , atomic shuffling, and (c) i ~ t e r c ~ a n gshuBing e
418
Meclzcanicul Properties
these bands became pronounced with a deviation from stoichionietry to an Al-rich composition. eformation twinning was reported in a liyperstoichiometric Ti-34A1 polycrystalline alloy in the temperature range of 800-1 100 "C (Lee et al., 1995). The doininant twin system was identified to have K1= (IOU),tlr = [ioiZ], li=j = ,(mi3), y ~ = ? [3032],and g = 0.122; and { 1122) and { 1012) twins were also observed with a relatively low density. The { 10T1) twins showed fine stru~tureswhich were characterized as having { 1012) habit planes, suggesting that the fine plates were secondary twins. Most deforlnatlon twins were niacroscopically lens-shaped and their thickness appeared to increase with increasing temperature. Also, the volume fraction of deformation twins was observed to increase with temperature in the range from 800 "C to 1000 "Cand with increasing strain at 1000 "C. 3.3.2 DR,y (
~~
~~
1~
~~
o~
~
n
A compressive deformation study of Ti,Si, single crystals at very high te~~peratures (1300-1 500 "C) was conducted by Umakoshi and Nakashima (I 994). Numerous twins were observed in deformed samples, and these were characterized to be the {10i2){10ii) type twin in terms of ravais indices based on the D8, structure. Th tion dependence of the SS suggested that the plastic deforination of Ti,Si, might be controlled by this twin system.
Deformation twins were observed in Cu,Sb which is the prototype of the C38 (tP6) structure (Paxton and Entwisle, 1985). Twins in five separate crystals were analyzed by two-surface inethods iii order to estimate the composition plane and the angle of shear. The twinning elenients were deter ned to be KI = (T12), rll =[ni 11, K = (I 1 3 , qt= [i111 =[liO], aiidg=0-152. Deformation twinniiig has also been reported in other non-cubic superlattice structures. Nesbit and investigated slip and defornzation 1, (1110) structure of a fixlly ordered i,Mo alloy and found that wide SZSFs and deformation twins were pronounced features of deformation. Tawancy (1 98 1) reported that the ordered Pt,Mo prototype phase in certain Ni-MO-Cr alloys (commerastelloy) deformed predominantly by twinning. In aged samples of Ni-25Mo-8Cr alloy, Kuinstr and Vasudev 4) observed that the ,er) precipitates of the deformation mode of
o structure changed from crystallogra~hicslip to microtwinning of the true-twin type at large strains. I
The homogeneous twin nucleation suggested by rowan (1954) is based on a model that a l e n ~ i c u ~ ~ r uiided by twin dislocation loops of lying on the K , habit plane. The of a twin and the stress field of a calculated using a dislocation rth, 1991). According to nucleation of a deformation twin by homogeneous lattice shear can take place with the aid of a local stress concentratio~iin the absence of any thermal activation. In. the analysis of a competitive relationship between twinning and crack initiation in hcp metals, Yoo (19'79a,b) treated the twin lamella as if it were a slit crack, being ~ c t i v a t ~by d a ~ ~ , ~ mode-ZI shear slate. Extending this concept further, Lebensohii and Toiiii (I 993) investigated the stress state associate^ with the activati elastically anisotropy materials. inclusion theory (Eshelby, 1961 bifurcation theory (Johnson and and Yoo (1990) analyzed the effects of applied stress on the elastic strain energy of an ellipsoidal twin and the stress state around the twin tip in tetra~onal crystals, and this work was later extended to hexagonal crystals (Yoo and Lee, 1991). Using a modified Monte Carlo technique, Lee and Yoo (1994) made an attempt to atomistically simulate heterogeneous twin nucleation in a bcc crystal under stress. The i n ~ ~ ~ ofactors r ~ ~ nthat t control the twin formation at heterogeneous nucleation sites depend on the niicrostructure and the internal stress state of a given material. The following statement made by Frank arid Stroh (1952) still applies today for iiiter~e~ailic compounds: 'Bounded slip-bands, ~ s ~ r i k - b a ~plates ds, of deforiiiation, twin or inarteiisitic transformation product, and thin cavities, cracks or notches under tangentid stress, all produce stress fields of the same kind: in various circuinstances any one of these may serve as the source of any other.' In addition to these bouiided lattice inhoinogeneities, we also include surfaces, grain boundaries, and heteroyhase interfaces as possible sites for twin initiation, Once a twin i s nucleated, the increase in twinned volume takes place by its lengthening in the yl direction, widening in the S direction, and tliiclseii~ng in the direction normal to the K , plane. The former
419
~ w z n ~ iund n ~~ e ~ h a i ~Behavior i~al two results from propagation of twin dislocations at the incohereiit twin boundary, and the latter from acquiring additional twin dislocations, either by the incorporation of slip dislocations into the twin or by the nucleation of partial dislocation loop(s) with the aid of an internal stress concentration.
Stress-indLiced ‘microtw~nning’in the y-phase of a twophase TiAl alloy was observed during an in situ field ion microscopy (FIM) study by Larson and Miller (1998). The thickness of a typical twinned region was estimated to be between 0.5 and 3.5 nm, so these may be called nanotwitis. These twins differed from preexisting y / y lamellae in that they were created in response to the internal stress associated with the lattice expansion due to field-induced strains in the sample. This twinning process is similar to the in situ TEM observation of twin nucl~ationat a r e - e ~ t r a ~ t corner of the surface of a nearly perfect zinc whisker (Price, 1960). Two types of twin formation at a crack tip are sclie~iiaticallyillustrated in Figure 13, as observed by han-Couson (1993) and Appel et al. (1995). Tlie former type of anti-twinn a mode-1 crack (Figure 13(a)) was discussed in on 3.1 (b). When the mode-IT or mode-111 corn eiit of an external loading is mixed with a (1 11) [ 1TO] mode-1 crack as depicted in Figure 13(b) or 13(c), coplanar deformation twinning or ordinary slip at the crack front can occur so as to shield the crack-tip shear stress field (Yoo et al., 1995). crack-tip twinning was directly the leading process of translagation in Ti-rich TiAl alloys by Appel et al. (1995). Grain boundaries provide the most potent sites for twin nucleation in polycryst Iloys, e.g. in TiAl (Sriram et al., 1994; Jiii and 299%; Seo et al., 1997; Morris and Leboeuf, , FePt (Gao and Whang, 1994), Ti,Al (Lee et 1995), and NbCr, zantzis et al., 1997). At a = 9, 1221) type tilt ndary in the Ll, structure, in formation in one grain by a pile-up of slip dislocations in the adjacent rain is crystallograpliically possible (Yoo and King, 1988). In the case of C15 Laves phases, such as NbCr, and (Hf,Nb)V, alloys (Luzzi et al., 1998). parallel twin bands of tliickness ranging from lattice dimensions to app~oximately8 nm were observed to form collectively in an a~tocatalyticmanner ( azantzis et al., 1997). The occurrence of a group of parallel twins, rather than a single twin, is a simple nia~ifestationof free
energy i~inimizationfor the system ( 1994). In two-phase alloys, it i s now well establish~dthat deformation twins are readily nucleated at a variety of homo- and hetero-phase interfaces. Twin initiation in the y-phase at yl/y2 and a2/y lainella phase TiAl-Ti3AI alloys IS widely conventional TEM, REM, and in situ straining investigations. For example, the Figure 14 shows (a) a typical example of the formation of a SISF at an a,/y interface and two ~istinctly different types of twin nucleation at (b) a true-twin
initiation of a true twin in a y 2 lamella at the head of a pileup of ordinary dislocations in a y, lamella was analyzed to be energetically feasible (Yoo c Hsiung and Nieh (1997) reported direct TE for twin nucleation as a result of i n t e r ~ ~ cd~i ~ a locatio~ pileup against ledges along the a2/y lamellar boundaries
m I
[m]
mode I
r
mode I
mode I
mode II
mode 111
~ i 13 ~Crack-tip ~ twiiining r ~ and slip in the L1, structure: (a) two symmetric tension twins, (~b)coplanar primary twinning (edge type), and (c) coplanar ordinary slip (screw type)
Fi Slacking fault initiation and twin nucleation in 1'TiAI deformed about 3% at room t e ~ ~ e r a t u r(a) e : formation of a stacking fault at a misfit d i ~ ~ o c a tof i oan ~ a,ly interface in Ti-47Al-lCr with additions of Nb, Mn, Si, and B, (b) generation of deformation twins (I and 2) and an embryonic twin (3) at an interface of the ~rue"twin boundary contain in^ misfit dislocations (arrowed), and (c) nucleation of a deformation twin at a small-angle grain boundary in the samc alloy as in (a) (from Appel and Wagner, 1998, reproduced with permission of Taylor & Francis)
42 I
2
2
Twin formation by a pileup of niterfacial dislocations on an boundary in Ti-47Al- 2Cr-2Nb: (a) a bright-field TEM image showing several (11I)[ 1121 d~formatioiitwins formed in lamellae, and (b) a s c ~ e ~ a t i c representation of twin formation showing mterfacral ( stair-rod (bJ, and twinning (b,) partial dislocations (from Wsiung and Nieh, 1997, reproduced with permission of Taylor & Fraiicis)
in a two-phase TiAl alloy as shown in Figure 15. When T i - 4 7 A l - ~ ~ r - 2alloys ~ b were stressed at hard orientations (i.e. either parallel or normal to the a,/y i~terface),a defori~at~on twin in a y lamella was observed to pile up against an aZ/y boundary. The response of the adjacent cxZ lamella was the generation urgers vector on a of dislocation§ with the e + pyrainidal plane in a ~ i - 4 7 ~ 1 - 2 ~ r alloy - 2 ~ bat room temperature (Codfkey et ul., 1 observed to occur in a binary Ti
but not at room temperature ( iezorek et al., 1997). It is conceivable, under an appropriate applied stress of the opposite sense, that this process could be reversed to facilitate a twin ~ucleationmechanis~in TiAl as a result of slip transfer from Ti,Al.
Many types of dislocation sources for twinning partial dislocations in cubic and ~ e ~ a g o ncrystals al have been
proposed, as given in several reviews (Christian and Crocker, 1980; Yoo, 1981; Narita and Takamura, 1992; C h r ~ s t and ~ ~ ~~ na h a ; a n ,1999, and some of these may be applicable to deforniation twinning in cubic and non-cubic superlattice structures. Dislocation models for twinning may be divided into two main types: (a) pile-up mechanisms (Cohen and Weertman, 1963; Fujita and Mori, 1975) and (b) pole mechanisms (Cottrell and Rilby, 1951; Venables, 1961). The pileup inechanisms are based on a ‘glide’ source, and the pole mechani~msoperate from a ‘prismatic’ source (Venables, 1961). In addition, Maliajan and Chin (1973) proposed a model for the formation of twin embryos stacking faults in close-packed crystal Many dislocation models for twinning in the L1, structure were proposed, and these have been discussed in recent review papers (Yoo, 199817; Yoo and Fu, 1998a). First of all, using a (111) APB energy of 200 mJ/m2 ~ ~ a r c i n k o 1963) ~ v ~and ~ ~ an , SISF energy of less than 10mJ/m2 ( A ~ r i a ~ o v set~ ial., i 1971) for reeiiberg (1970) investigated many plitting configurations of both glissile and sessile types aiid identified one of them (tlie socalled C-configuration) to be a twin source. The model based on this twin source was found to be a distinctly glissile type in that imperfect twins niay result, i.e. not all STSFs necessarily lie in adjacent planes. On the other hand, tlie TEM study of an ordered CuAu-I alloy by A~rianovskii et al. (1971) proved that deformation twins origimte within the domains due to the action of a spiral source (i.e. a prismatic source) and not at their interfaces. A nuniber of possible mechanisms for the formation of twin sources in y-TiAl have been suggested on the basis of dislocation dissociations or transformations in their core structure: (a) expansion of an SISF loop resulting from a [101] superdislocation (Fu and Yoo, ite dissociation’ of a [112]/2 et al., 1986; Girshik and Vitek, e niechanism anchored by a 110 >. /2 ordinary dislocation (Farenc et al., 1993; Voo, 1997). Using an i~ situ straining TEM technique, Couret et al. (1994) found direct evidence for a single pole at advancing twin tips in Ti-54A1. In a post analysis, Zghal (1997) observed a ‘pole d by a Shockley partial when it met with a forest dislocation of the ordiiiary type. To explain the experimental results of Figure 10 that the apparent SS for twinning in Ti-56A1 is in the range of 200 MPa at 1000 K and about 100 MPa at 1200 K (Inui et al., 1997), Yoo (1997) proposed a dislocation pole
mechanism 011 the basis of dissociation of a jog on an ordinary [ 1 l0]/2 dislocation. The prisniatic source in this case is schei~aticallyillustrated in Figure 16. An important finding of this work is that a repulsive interaction between Frank and Shocltley partials exists in the near-edge orientation due to elastic anisotropy, and this promotes the spontaneous expansion of the Shocltley partial loop. Based on their ~ o s ~ ~ 7 ~weak-beam z ~ ) ~ t ~ TEM ~ i rr-doped Ti-54A1, Hug and Veyssikre (1989) suggested a twin nucleation mechanism involving a [112]/2 screw ~uperdis~o~ation, but no direct evidence for pole dislocations was given. In the TEM investigation of the Ti-57Al-SCr alloy after compression along the near [001]-[011] orientation, Morris et [ 1 12]/2 superdisloal. (1994) observed p~edo~niiiantl~ cations and a microtwin created by the movement of [T12]partials on a (1 1I ) plane. Singh and Howe (199 I ) observed that nucleation of nanotwins occurred by superposition (overlapping) of extended SESFs on alternate (111) planes in Ta-doped Ti-48A1 alloy. Direct observation of twin formation by electron niicroscopy techniques is inherently difficult because of the dynamics of’ twin nucleation and propagation. While unambiguous characterization of the pole e ~roposinga pole dislocation(s) is a p r e r e ~ ~ i s i tfor mechanism (Farenc et al., 1993; Couret et al., 1994; Zghal, 1997), identification of an array of stair-rod dislocations is often used to support a pile-up mechanism by interfacial dislocations (Hsiung and Nieh, 1997).
In the past decade, a significant advance has been made in our understanding of point defects and diEusion in intermetallic compounds ( Point-defect properties and diffusion coefficients of titanium aluminides were reviewed recently by Yoo and Fu (1998a). In TiAl, no structural vacancies were predicted from first-principles totnl-energy calculations (Fu and Uoo, 19931, and the dominant point-defect types are therefore aistisite defects on both sublattices, as in the case of intermetallics having a close-packed structure such as Ni,A1 (Fu and Yoo, 1994). Thermal vacancy ~onceiitrationsin TiAl are predicted to be very low, even at high temperatures (e.g. co= 10A7-10-6 at 1500K). In explaining twin formation in TiS6A1 under low stresses and high tem~eratures(Figure lO), excess thernlal vacancies that can expand Frank partial segments are thought to play an important role in the early stage of the pole mechanism (Yoo, 1997).
423
.
-
.
ure 16 Schematic illustrations of a pair of Frank and Sliockley partials resulting from an ordinary [I 10]/2 dislocation of the edge type in the Ll, structure: (a) atomic configuration showing the primary (K,, yl) and conjugate (K2,yz) t ~ i n i ~elements, i i ~ ~ and (b) the in-plane and out-of-plane c o ~ p o n e ~(FX, t s Fy)of the elastic interaction force
Tn the absence of stress concentration, the sufficient condition for a chemical stress that comes solely from a vacancy sui~ersaturatioii is c/co>, 13. In an actual case, the climb stress can be overcome by a combination of the stress concentration and a more reasonable vacancy supersaturation (c/co < 13). In addition to the effect of vacancy condensation, clustering of supersaturated self-i~terstitial atoms could also assist the nucleation of deformation twins, The so-called radiation-~nduced ductility (RI reported in Ti-47Al alloys at 600°C ( ~ i s h i n u ~eta al., 1996) was attributed to the effective formation of twin embryos (prismatic sources) in the presence of interstitial-type Frank loops and the subsequent nLicleation and growth o f twins during plastic deformation (Yoo and Hishinunia, 1997). In austenitic stainless steels of the fcc structure, Frank loops of interstitial type are also formed during neutron or heavy-ion irradiation, and twinning is the predominant deformation mode in irradiated steels at room
temperature (references in Yoo and 1999). Two reasons, of energetic and kinetic origins, were offered to explain the st~bilityof large faulted Frank loops that act as het~rogeneoussites for twin.
the mobility of a composite Slisckley partial (Hug et al., 1986), which was originally called a I)-type Shockley by ~ e ~ r t m a and n ~ e e r t m a n (1964), nucleated on an interstitial-type loop is considered to be much lower than that of a hockley partial on a vacancy-type loop. Formation of Shockley partial dislocations by intersection of glide dislocations with Frank loops in fcc lattices was analyzed by Song twin nucleation model proposed by and the model by Yoo and Hishinim essentially the same end result: A t w i ~nucleus can
424
~ e ~ h aProperties ~ i ~ a ~
emerge from a Frank loop as a result of the slip-loop interactions. The main difference between the two models is that the former model gives an imperfect twin nucleus with the thickness limited to the number of slip dislocations that intersect the loop, and the latter provides a three-dimensional description of twin nucleation and growth beyond the twin thickness of six atomic layers. While the profuse activity of deforniation twinning in y-TiAl in two-phase TiAl alloys of fully l a ~ e l l ~ r microstructure is well establis~ed,it i s also known that d e f o i ~ a t i otwinning i~ becomes more difficult as the microstructure clianges from fine lamellar, to duplex, and then to fully singl~-phasey-TiAl over the compoto 54 at.% Al. This variance in be rationalized in terms of two factors: (a) the decrease in area1 density of heterogeneous nucleation sit interfaces and (b) the increase in SISF and s as the composition of y-TiAl varies fr chiometry (4 at.% Ti-rich) to hyperstoichioi~etry(4 at. % AI-rich). Investiga -y T~-(48-52)AIpolycrystalline alloys, Hall and 1989) reported that the ~icrostructureof the lloy after room-tei~~perature deformation consisted primarily of deformation twins and ordinary slip dislocations. In the same composition range, Si-iram et aE. (1994) noted that twin activity in all alloys increased with increasing temperatures, and at aiiy given tei~perature,the nuniber density of deformation twins was higher for the Ti-rich alloys. This has been ~ttribLitedto mi~rostructuraleffects, e.g. the fine grain size, rather than to intrinsic effects of A1 content. From the viewpoint of dislocation core s t ~ c t ~ r and e s their behavior under t of an applied stress (Cirshik tra et al., 1995), Vitek and his both SISF and CTB energies increase sharply with increasing A1 content, and thus, twinning stress is also increased. o far, this conjecture on the composition depency of twinning in y-TiAl has not received support from the available experimental data and theoretical results. For instance, the TEM *
ry weak composition energy, and the experimental showed an opposite ossible roles of extrinsic substitutional and interstitia~ imp~rities in twinning in intermeta)lic coniyounds are not fully understood. The absence of twinning in the a2 phase of two-phase TiAl alloys may
be attributed either to the d i ~ c u l t yas~ociatedwith the interchange shufffling neces (Christian and Lauglilin, 19 is an intrinsic eflect, as men to an extrinsic effect due to the presence of interstitial iinpurities. The extrinsic-effect the oxyge~-scavengingeffect ( due to tbe fact that interstitial elements have a higher solubility in Ti,Al than in TiAI. It was proposed by ~ ~ s u d e v aetn al. (1989b) that ~ ~ t e r ~ te~ ~t ~ea l~ ~ ~ t enhance the degree of directionality of the Ti-Ti bonds, and so their removal reduces this directionality and therefore the anisotropy of the Peierls stress in y-TiAl. Since the oxygen content in a2 phase can be as high as 20 OOOppm even when the average oxygen con the two-phase Ti-A1 alloy is only 40Oppm Partaix and ~ e n n a n d 1996), , this level of oxygen may be expected to hinder the twinning process in a,-Ti,Al.
Once nucleated, the possible roles of twins in rnechanical behavior may be generally divided into two opposite ways: (a) wlzile slip-twin andlar twin-twin interactions contribute to work hardening, they can also cause the nucleation of a ~ i c r o c r a c ~and , (b) extension of pre-existing cracks can be suppressed by slip and/or twinning at the crack tip. In bcc metals and alloys, the available experi~entaldata show a dichotomy in that deformation twinning can eKectively strengthen a material under some circumstances and weaken it under others ( eid, 1981). In intermetallic compounds of a low-syrnmetry crystal structure, on the other hand, twinning is believed to play beneficial roles in contrib~ting to both strengthening and toughening. The case of 11-TiAl, which has been investigated extensively in the recent decade, is an excellent example. cts
The roles of deforniation twinning in the strength of monolithic Ti, Ti,Al, TiAl, and TiAl, single crystals were discussed in the review papers (Yoo et ul., 1991; Yoo and ~ a m a g u ~ h2000), i, Figure 17 shows schematically the temperature dependence of compressive yield the c axis at a nominal strain rate of Ti,Al inon on is hi and Yoo, l990), TiAl (Kawabata et al., 1985, 1990), and TiA1, (Uamaguchi, 1986). An anomalous (positive) t~mperaturedependence of fly
Twinning and Me1:hanical Behavior
COMPRESSION ALONG THE C-AXIS
*-
.A
600
TEMPERATURE, T (K)
FSgure 17 Temperature dependence of the coinpressive yield strength of titanium and Ti-aluminide single crystals
occurs in all except TiAl,, and deformation twinning plays an important role in all except Ti,A1. In Ti, the deformation mode at temperatures below the peak strength (Tpx650 K) was almost entirely (> 90%) by { 1122}( 1123) twinning. On the other hand, at temperatures above Tp, the major mode was (c + a) slip and the minor mode (10-30%) was {lOil}(lOT2) twinning. Therefore, the rise and fall of the yield strength with increasing temperature may be related to an apparent transition from twinning to slip involving the displacement vector along the same (c+a) directions (Paton and Backofen, 1970). Whereas, in Ti3Al, no twinning was observed, and the anomalous yield behavior at a relatively high level was attributed to the temperature dependence of the mobility of edge superdislocations (Minonishi and Yoo, 1990). In Ti-54A1 single crystals, no specific role of twinning in the yield strength anomaly was elucidated after the early experiments of Kawabata et al. (1985, 1990). The recent experimental data of Ti-54Al and Ti56A1 single crystals (Figure 10) by Kishita et al. (1996) indicated that the apparent CRSS for .( 1 1I } (112) truetwinning had a strong temperature dependence so that a transition of the active deformation mode from { 11l}(lOi) superlattice slip to deformation twinning occurred at about 750°C. The latter result, which is
425
only a part of the extensive experimental data (Inm et al., 1997), demonstrates also how much more difficult twinning nucleation in y-TiAl becomes in the absence of heterogeneous nucleation sites. such as interfaces and extended defects. The TiAl, compound shows the weakest yield strength among the four,
The von Mises criterion is a necessary condition for ductility in homogeneously-deformed polycrystalline solids, and methods for determining whether a set of slip systems satisfies the criterion are well established and presented in many textbooks (Groves and Kelly, 1963; Hirth and Lothe, 1982). In alpha-brass (Cu30Zn) polycrystals, the numbers of active { l l 1) slip planes were counted by etching freshly cut surfaces in deformed samples (Fleischer. 1987). For all strains and grain sizes tested, fewer than five independent slip systems were active in about 40% or the grains. It was therefore suggested that the demand of the von Mises criterion for five slip systems is not obeyed because the assumption of uniform deformation is not correct. As for the role of twinning m plasticity, Kocks and
424
Mec han ical Properties
estlake (1967) pointed out that ductility of polycrystalline hcp materials may not require five tlidependent slip systems, and that the internal stresses rain boundaries when inelastic strains are not compatible may be relieved by localized deformation by twinning. These statements are coiisistent with the experii~entalresults of active deformation modes observed in the case of y-TiAl alloys of fully lamellar ishida et al., 1998). A eth hod was intr~d~iced to determine if a set of twin systems satisfy the von Mises criterion by taking into account the midirectionality of twinning shear ark, 1989). The results are, for example, ing observed in the B2 structure criterion, but tlie basal and bined with the twin system in h.c.p. ~ e t a do ~ snot. 6.00 (1998) examined which of the slip and twin s y s t e ~ sobserved in TiAl and Ti3A1 are needed to satisfy the von Mises criterion in the cases of single (y or a2) and dual (a2/y)phases. In the y phase, the “easy’ { 111) ( 1TO) 12 slip system combined 2) true-twinning system do not herefore, the ductility some of the ‘hard’ ms must have been activated. In be met by slip with er with ~ l o i T } ( i o i ~ )
cube-type texture could be s i ~ ~ u l a t equite d satis~actoSS of equal magnitude to the rily by ascribing a ordinary slip and t modes and a value 2.5 times higher to tlie superdislocation mode. Typically, cast material of y-TiAl is made up of Pimellar grains with a strong morphological texture, since the lamellae are preferentially aligned perpen~icularto the direction of solidi~cati~n, The anisotropy is large and can be calculated rather accurately with the tal plasticity codes by employ in^ the (~ebensohnet al., 1998).
Fracture behavior of an intermetallic compound depends strongly on tts microstruct~rewhich is, tn turn, dependent on its chemical coi~position.The fracture behavior of binary Ti-A1 alloys at room temperature can be discussed with the aid of Figure 18 (Mitano et al., 1991), which shows s ~ ~ e ~ a t i c afour lly typical microstructures: (a) fully lamellar structure at =:44Al leading to intergranular fracture, (b) fine lamellar structure at x 48A1 leading to interla~ellar
40
orie~itation relationship (Willia 197Q),i.e. (1 1l ) ~ , / / ( O O O l ) ~and [lTO]y//[l 120],, the von es criterion may be satis~edby the easy ordinary and t r ~ ~ e ~ t ~ i i isystems n i i i ~ (without the hard s u ~ ~ r l a t t i cslip e system) provided that all three variants (six with directions) of the orientation relationships are present. Texture analysis f o l ~ o ~ i nthe g compression experiment of TiAl by Cheong et al. (1996) indicated that ~ l e ~ o r t i i ~ ttwinning ion occurred at very low strains and 850 “C,where thermal activation makes
30
20
!.E 8
w
10
t
0
0
44 t.%A!
rmation twi~ning.The topography of the yield surfaces depends on the relative values of the CRSS of odes (Mecking et al., 1996). In r m~crostructure,the hot-rolled
Composition dependence of the fracture toughness of as-cast and isothermally-forged-and-annealed (IF-A) binary Ti-A1 alloys and schematic drawings of typical crack paths (from Mitao et al., 1991, reproduced with permission of Taylor & Francis)
Twinning and Mechanical Behawor and/or iiitergranular fracture, (c) duplex structure at x5OAl causing cleavage fracture in the y phase, and (d) y-phase polycrystals at x 50Al exhibiting transgranular fracture. In addition to these, Ti-54/11 single crystals may be classified as a fifth type of structtire (e), for which fracture toughness was obtained to be KO (provisional .KIc value) > 7 ~ P a in ~ Mn-d~ped m crystals (Phan-Courson, 1993) and K1,* 1 MPal/m in 1997). The latter cal stress intensity ) = 0.89 and 1.04 MPaJm for the (100) and (001) surlaces at 0 I< (Yoo et al., 1995), respectively. This indicates that y-TiAl is intrinsically brittlc without aay appreciable crack-tip plasticity. The seven-fold increase in fracture tough-doped single crystals may be attributed, in enhanced crack-tip twinning. The isothermally forged and annealed (IF-A) Ti50.2A1 alloy which consisted of single phase y grains the lowest fracture toughness (KQ = in Figure 18, but this is still much higher Ti-54Ai single crystals by a factor of about 10. This difference may be due to the role of grain boundaries as sites for slip and twin initiation as the crack propagates through a polycrystal. In two-phase m u l t i ~ o ~ ~ oTiAl ~ i ealloys, ~ t fracture toughness is measured to be reasonably good, e.g. Ktc = 16-23 MPa t/ni from a fully lamellar structure (Chan and Kim, 1995), KO= 10-32 variety of microstructures (Figure MPaJm from a lamellar structure (Chan and Kim, 1994, and KO > 50 MPaL/m from fine (0.1-0.4 pm) laniellar iiiicrostructures (Liu et al., 1996). Deve and Evaiis (1991) reported that the fracture toughness o f TiAl alloys containing equiaxed y grains was greatly influenced by defori~ationtwinning, which resulted in it twinzone, a source for the crack-shielding effect. r, the work by Mitxo et d. (1991) indicated that the occurrence of cleavage cracking in the y grains was also an important controlling factor. Deve et al. (1992) reported that twinning occurred within both a process zone and crack bridging liga~eiits, with. about equal contri b ~ t i o narising ~ from the process and bridgiiig zones. Obviously, in two-phase TiAl alloys, the presence of various lamellar interfaces influences the crack-tip plasticity, which is strongly orientation dependent (Chan, 1992; Mi tao et al., 1992; Naltano et al., 1995; Yoltosliirna and ~ a ~ a g u c h1996), i, and therefore affects translamellar and interfacial microcracking in the crack-tip region in a complex manner (ChPtn, 1993). One area not examined in detail i s whether synergistic toughening
427
effects can be obtained by comb~ningmechanisl~s, which might include dLictile-p~~s~ blunting, ductilephase bridging, ligament ~oughening,and twin toughening (Chan, 1992). A quantitative assessment for the specific role of twinning in the crack-tip plasticity is yet to be made.
Deformation twinning is an i r n ~ o r ~ dmode n t of plastic defornia tioii not only during strain-controlled, shortterm deformation at ambient temperatures, either by monotonic loading or by cyclic loading (Sastry and Lipsitt, 1977; Yilsuda et al., 1996; but also during long-term deformiltion at elevated temperatures and very slow strain rates, such as creep conditions (Loiseau and Lasalmonie, 1984; Oikawa, 1990). In a Ti-53.4A1 sample crept in compression at 950 K under 317 MPa up to 0.3 strain, observed many deformation twins in optical microstructures. The iiuinber of grains that contained twins increased with increasing creep strain. As the total strain increased, bending of twins was observed, which indicates a significant slip deforrnatioii iii the matrix. Sinall recrystalli~edgrains were found locally at an early stage of deformation, and the recrystallized area increased as the creep strain increased. In as-cast binary TiAl alloys in the co~positionrange of 44-51 at.%Ai, Mitao et al. (1991) observed tkat, as aluminum content increased, dynamic re~rystalli~ation became more difficult at a given temperature, result in^ in an increase in creep resistance, Most of the experimental data in the literature, pertaining to the present subject, are on i~u~ticomponent alloy systems, part~cularly those based on titanium aluniinides. It is therefore difficult to discern the general mechanistic role of twinning in creep flow and fracture behavior of i n t e ~ e t a l l i ccompounds. In Ti-rich TiAl, alloying (Tsujimoto and Hashi Hall, 1990) increase However, these transition-metal al~oyingelements do not affect the ductility of Al-rich single-phase y-TiAl. An efYect of Mii addition to e ~ h a n c the e ~ropeiisityfor twinning in two-phase TiAl has been reported by several investigators (Hananiura et al. 1988; Hug arid Veyssiere, 1989; Tsijimoto and ~ a s h i m o t o 1989). , The reasons for this t w ~ n ~ i nen~ancement g were proposed to be as follows: (a) the pinning effect of the trailing twin dislocations that is caused by Mn segregation to transformation-twiii boundaries (
1 9 8 ~ (b) ) ~ the lowering of the SI F energy (Hug and yssikre, 1989), and hence the CTB energy anamura et al., 1988), and (c) the weakening of 1-A1 covalency bonds n replacing A1 in the Atsites (Tsujimoto and imoto, 1989), which is by electronic charge density calculations el! al., 1990). Also, additions of Ga (Mad r (Vasudevan et al., 1989c) were reported to promote a solid solution softening and an increased ~ o b i ~ i of t ytwin dislocations. In the latter case, it was concluded that the Er gettering of interstitial elements from the TiAl lainellae was
2Nb alloys of the duplex microinicrostructures at 700 "C under low stress of 280 MPa was observed to be the extensive twiiining activity which was already present after only 1% strain ( ~ o r and ~ s Leboeuf, 1997). Figure 19(a) shows an example, taken at it low magnification in the TEM, of one of the large y grains that was completely traversed by several twins, This twinned microstructure was confirmed to be produced by emission and glide of twin dislocations on {I I 1) planes. The extensive twinning activity was also responsib~efor the activation of a large number of ordinary dislocations at intersections with some of the 171 y interfaces. Details from some of these intersections ) are shown in Figures 19(b) and 19(c). It is noticed that some of the ordinary dislocations remain on the { 111) planes of the twin interface, as was situg TEM studies of twin also e v i ~ e n c ed~ ~ ~ inr ~ propagation in y-TA.1 by Couret ef al. (1894). Some of the twins do not propag the entire grain, as is seen w i t h the area labe igure 19(c). It appears was iiot sufficieiit1y that the local stress ca high to provide the driving force for twinning across the entire grain, as suggested by Jin and contribution of deformation twinning to the total creep strain was about 10 and 50% in the low and high stress regmes, respectively. A two-phase alloy of Ti-47.5AI-2.5Cr composjtion was studied under two different heat-treatment conditions in order to obtain different microstructures orris, 1995). While deformation twinning was observed in 90Y0 of the equiaxed y-grains, it was only observed in 50% of the coarse lamellar grains. This observation led to the conclusion that the
internal stress distri~utionin the equiaxed microstructure was more favorable for the initiation of twins than in the lamellar grains. In another two-phase Ti-48 alloy with equiaxed, fine-grain microstructure, deformation twinning was observed to occur in less than 50% of grains, while ordinary were active within all the y grains ( Leboeuf, 1998). The twins were responsi a sniall fraction of strain, but they led to a subdivision of the ~icrostructure and ~ e t e r ~ i n e(directly d or indirectly) the hardening process observed during the pninary stage of creep deformation.
peratures (650, 700, and 750°C) under tensile stresses varying between 150 and 300 M 1998). In this study, deformation twins were observed already after a small strain (0.3%) in y-grains as well as in lamellar grains. The lamellar spacing was reduced by a factor of two at strain of 0.3%0,which was not much affected by higher creep strains or applied stresses. is in good agreement with the results obtained by et al. (1997) who studied the twinning behavior o laniellar grains in a duplex alloy. They showed that twinning parallel to the lamellar in was other saturated after 0.2 to 0.5% creep strain. hand, in the y-grains, the mean interface spacing was found to decrease with increasing strain and stress, whereas it decreased with decreasing temperature. These results suggest that twins contribute to the deformation process of the y-phase in Mn~bearing alloys during the whole creep life. Instability of twin structures during creep flow at a low strain rate is an important factor for deformation ~crostruct~ires developed at elevated temperatures. The investigation by TEM mid HREM of Ti-48A1-2Cr deforiiied in tension at 1073 K (Appel, 1999; Appel et al., 1999) revealed that the twin-matrk niterfaces often contain local networks o f dislocations which are similar to subboundaries. These networks acted as the soiirces for dislocation loops which often caused f r a ~ i ~ ~ t a t i o n of twin lamellae. This result suggests that the competition between the generation and reconstruction of twins depends obviously on the applied stress conditions, and, consequently, a broad variation of the creep microstructures becomes plausible. A fine-grained ~ ~ - 4 7 A l - 2 C r -alloy ~ ~ b of fully lamellar structure (the same alloy used [or KQ measurements by Liu et al. (1996)) was creep tested at 760 "C under stresses between 69-723 MPa (Wan al., 1995). It was found that this alloy exhibited higher
Twinning und ~ ~ ~ ~ aBehavior n i ~ a l
429
Deformed microstructure o f the duplex Ti-4SA1-2Mn-2Nb alloy: (a) example of extensive twinmng traversing equiaxed y grains after 1% creep strain at 700 "C under 280 MPa, (b) and (c) details from areas A and B in (a) (from Morris and Leboeuf, 1997, reproduced wtth permission from Elsevter Science)
creep resistance than other TiAl alloys with s i ~ ~ l a r needed, particularl~in the kinetics of twinnin compositions. In this case, the evolution of deformaorder to develop 'constitutive laws for twinning'. tion substructure revealed that the deformation at the Some highlights and unresolved issues are noteprimary creep stage was mainly accommodated by soft worthy. The i~echanist~c role of Shockley partial lamellar grains tlirough the movement of interfacial dislocations in the inotion of incoherent twin bounddislocations in the a,/y and y / y boundaries, and aries is well established in the case of the El, structure. defor~ation twins were found to form within 1' They are instrume~tal not only in the growth of lamellae only at the secondary creep stage (Hsiung deformation twins, but also in the stability of and Nieli, 1997). If the blocking of the sliding motion traiisEorniatio1.l-induced true-twin and pseudo-twin of interfacial dislocations i s a controlling mechanism ~oundaries. Whereas, the possible role of rank of twin nucleation, the creep rate at the secondary partials in twin nucleation and growth i s essentially stage should increase with the number of interfaces. unresolved. The experimental finding of the radiationThe question as to whether twinning must be induced ductility in Ti- 7Al alloy at elevated temperaconsidered as contributing to a work hardening ox" to tures is remarkable in that a nearly two-fold increase in a niicrostructural softening process is difficult to tensile ductility was recorded without any appreciable answer. Several investigators (Seo et al., 1997; Hsiung changes in the yield and flow strengths. Additional orris and Leboeuf, 1998) concluded experiinents of this kind to validate the ra~iationfrom their studies that twin interfaces binder dislocainduced ductility result (which was attributed to an 'on motion and, therefore, harden the mici-ostructure. enhanced twinning activity) are needed for TiAl and ut another possibility is that twinning reorients the yother intex"~eta11ics~ In Ti,Si3 single crystals at elevated phase into a more Cavorable orientation for deformatemperatures, compressive twinning was reported to be tion, i.e., the formation and migration of dislocations the major mode of plastic deforniation. This is very become easier in the twinned crystal than in the parent encouragin~as we respond to the demand by materials y-crystal, which would result in a microstructural technology for tougher and stronger materials which softening process (Skrotzki et nl, 1998). Further work have very high melting temperatures and often possess on microstructu~alc~aracterizationis needed to clarify limited operative slip systems. There have been the answer to this question, as well as investigati~nsof increased rgsearch activities on twinning in Laves the interaction of twins with other eleinentary prophases, particularly of the Cl5 type. The motivation cesses like dislocation slip (Skrotzki, ~ 0 0 0 ) and for this research effort stems from the fact that there dynamic recrystallization. are hundreds of binary Laves phases and thousands of ternary Laves phases, mizny of tlneinn sharing the same family of crystal structures and deformation inechanisms. This i s a case in which a little unders~andin~ would go a long way ( In 1991 a couple of workshops on 'Scientific Issues on I n t e ~ e t a l l i cC o ~ p o u ~ -d Status s and Forecast for ~ u n d a i n e n t Research' ~l and 'Coniputztional Issues in avior of Metals and Intermetallics' The author would like to thank C. L. Fu and J. IS.Lee y reports of which address unrefor collaborations over the years and S. solved issues on the role of twinning in mechanical Appel, T. R. Bieler, . W. Cahn, J. W. Christian, E. behavior (Uoo et al., 1993; askes et al., 1992). Since COO,and R. C. Pond for helpful comments on the then, s i g n i ~ c a nadvances ~ have been made in our manuscript. This work was sponsored by the Divisi understanding of these issues owing to the extensive Materials Sciences and Engineering, Office of use of advanced techniques for microstructural and Energy Sciences, US t of Energy, under analytical cliar~cterizatioiiand the interpretive and Contract ~ E - A C 0 5 ~ 0 0 predictive capability of computational materials science. For example, the question 'is there a CRSS for twinning'!' has been partially answered in the case of y-TiAl, and interfacial structures and energies of twin boundaries are reasonably well understood. But, Anneuting t w i m those twins formed by a thermomore effort in experimental and theoretical interdiscimechanical process of cold-work and anneal plinary research at multi-levels of length scale IS
Twinning and ~peclzanicalBehavior
43 1
Type II twin: when Ka and q t both have rational, ~ n t i - t w ~ n n i twiniiing n~: on the primary K1 plane but low-index elements in the opposite direction, --ql C o ~ ~ o utwin: n ~ when ~ all four crystallographic elements (K,, K2, yl, and ya) are rational C o ? ~ ~ l p e ~ etwin: n t f ~that r ~ results from anti-twinning (Kb -4,) C o m ~ ~ ~~ , ~~formed s ~~ o ~ under n : compression applied along the c-axis of hexagonal or tetragonal crystals Conjugate twzn: (K2, +) twin as contrasted to the ., and Naltaniura, M. primary (K,, q 1 )twin A., Syutkina, V. I., ~ e ~ t w ~~~ n ~arn shear g : ~ d e f~o ~ ~ a~t i oprocess n~ z ~ ~ Shashkov, 0. D., aiid Yaltovlcva, E. S. (1971). P/?ys. caused by an exteixally applied stress Stat. Sol. ( U ) 6, 323. Double ~ w ~ ~ na~second-order ng: twinning within the Albert, D. E,. and Gray, G. T. (1994). Phil. Mag. primary twins Albcrt, D. E., and Gray, G. T. (1995). Phil. &fog. ~ ~ r twifznhg: ~ i the~same ~ as ~ pseL~do-twinnin~ n P. A., and Wagner, R. (1993). A G r o ~ ttwins: ~ those formed by a solidification 1. process from a liquid or vapor phase ph, U., aiid Wagner, M ~ c r o t ~ ~when i ~ , s twin : thickness is larger than that A, 72, 342. defined as a microtwin Appel, Fa,Qehring, M., and Ennis, P. J. (1999). In G f f ~ ~ u ~ e c ~ ~ n i c twinnifzg: aZ the same as deformation T i ~ a A~l ui~ ~ i n~i ~~(eds ~ e sV.-W. , Kim, D. M. Dirniduk, twinning and M. €3. Loretto). TMS, Warrendale, PA, p. 603. Appel, F., aiid Wagner, R. (1994). In Twirzning in Advanced Microtwins: those twins with thickness on. the order ~ U t e ~ i (eds a l ~ M. ~ El. Yoo, and M. W u t t ~ ~ TMS, ). of seven thousand interplanar lattice spacings Warrendale, PA, p. 3 17 ~ ~ ~ ~ o t twins ~ i ? zof~ thickness s: on the order of the Appcl, F., and Wagner, R. (1998). M m r . Sci.Eng. R, 22, 187 lattice spacing Armstrong, R. W. (1968). Scimce 16 ~ r ~ p e r - t ~ ~ i n nthe i n gsame : as tr~~e-twi~ning V S., and Sargent, C. M. (1971).Scr. ~ ~ e t U 1 1 . Ar~i~iachalaiii, P o Z ~ s y n t ~ e t i ~ ~ Zt l~y i ~ n( Pe S~T ) . ~ t r ~ ~ t uar ~ : 949. repeated twinning structure that emerges as a result ., and Needleman, A. (1992). of the strain energy relaxation attendant to the atomic ordering reaction 1968). Proc. Roy. Soc. A 3 P~l-vtwinnpe~~ structure: the same as PST structure 123. Primary twin: the particular ( K l ,yl) twin system that Bevis, M., and Crocker, A. G. (1969). Proc. Roy. Soc. A 313, 509. receives the largest driving force for twinning Bhowal, P a., Prewo, K. M., and McEvily, A. J. (1978). P ~ e u ~ o - t ~a ~special ~ i ~ scase : (twinned orientation) of M e t d . Tram. A 9, 747. stress-induced niartensitic transforination Bilby, B. A., and Crocker, A. G. (1965). Proc. Xoy. Soc. A ~ $ i ~ ~ i - t w i n n the i n g same : as pseudo-twinning 288, 240. ~ e c ~ r o c atwin: Z the same as complementary twin Bolling, G . F., and Richman, R. H. (1965). Acta MetufE. Xecrystdlizatiovz twins: essentially the same as 709, 723, and 745. annealing twins Booth, A. 5.. and Roberts, S. 6.(1997). Acta M a ~ e ~ . ~ e c o fwins: ~ ~ those ~ r formed ~ by double twinning Bouchard, M., Claisse, F., Tardif, H. P., and Dub&,A. (1970). Szipper-twinning: true-twinning occ-tlrriiig in fullyCm. Metall. Quarter. 9, 395. ordered alloys Braisaz, T., Ruterana, P., and Nouet, G. (1997). Plziil. Mag. A 76, 63. T e ~ ~ i otwin: n formed under uniaxially applied tension along the c-axis of hexagonal or tetragonal crystals T r a ~ ~ ~ o r ~twins: a t i ~those n formed during a solidstate ~ransforniation ~ r ~ e - t w i n n i ndefined ~: as that when the twinned Cahn, R. W., and Coll, J. A. (1961). Ac portion of a crystalline body has the identical crystal Calbrick, C. J., and Marcus, R. B. (1967 structure with that of the parent matrix, including the Chakraborty, S. B., and Stark, E. A. (19 , state of chemical order 63. Tvpe I twin: wheii X I and y2 both have rational, lowChan, M. S. (1992). J . oif'Metals, May, 30. index elements Ghan, M. S. (1993). Metall. Trans. A
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t
s Czech ~ e p ~ Czech ~ l i ~ ~ stiizate of Physics, c a ~ e ~~ ~y S c i ~ nofc ethe
ion
The stacking-fault-type interfaces we explore in this chapter play a very important role in dislocation configurations and thus in plastic behavior of materials. The existence of inetastable APBs and stacking faults is of major significance for the structure of dislocations in a given intermetallic compound. In general, a vital characteristic of dislocations is their dissociation into partials connected by ribbons of metastable planar faults. Such dissociations, when energetically favorable, frequently determine the slip planes and thus control the operative slip systems. A simple example is the well-defined slip systems in fcc materials with dissociation into Shockley partials, in contrast to an uncertain plethora of slip systems in bcc metals in which no metastab e stacking faults exist (Christian, 1983; Duesbery, 1989). Nevertheless, understanding of dislocation dissociation involving metastable planar faults i s only the first step in comprehension of the atomic aspects of dislocation behavior. The next is the core structure of either uiidissociated lattice dislocations or partials. Here y-surfaces, defined and utilized in this review, may be an important source of physical information. In the case where the cores are planar, i.e. spread in the slip plane, the Peierls model, combined with the knowledge of the y-surface may be used to
determine the details of the core structure (~hristian and Vitek, 1970; Vitek, 1992; Schoeck, 1994; Duesbery and Vitek, 1998; Mryasov et aE., 1998). most significant core phenomena occur when the dislocation cores are non-planar, and spread into more than one crystallographic plane. This is well known for screw dislocations in bcc metals (~hristian, 1983; Duesbery, 1989; Duesbery and Vitek, 1998), but it may be at least equally important in intermetallic compounds. Indeed, the non-planar core of superpartials in L12 Ni3Al is, presumably, responsible for the anomalous increase of the yield stress with temperature ('Vitek et al., 1996), and non-planar cores were also found in TiAl (Girshick and Vitek, 1995; Simmons et al., 19971, NiAl (Schroll e significant in MoSi ng these studies is b An all-inclusive definition of an internal interface in crystalline materials is that it is the region of contact of two crystallites which are in some respect different from each other. These regions are domains of distinct atomic structure and composition that are, in general, substantially different from those of the bulk of either of the adjoining crystallites. As a consequence, the physical and chemical properties of interfacial re differ significantly from those of the bulk, and this i s
~ n ~ ~ r rC n~ ~~ t~ ~p o~Vol. ~~ ni 3, d~sPrincipkes ~ and Practice. Edited by J. H. Westbrook and 0 2 0 0 2 John Wiley & Sons, Ltd.
438
~ e & h u ~ iProperties &a~
the reason why interfaces phy a prominent role in a broad variety of physical, chemical and mechanical properties of materials. The character of an interface is determined by tlie nature of the difference between adjoining crystallites. The stacking-fault-like interfaces are formed by joining two identically oriented crystallites that are relatively displaced with respect to each other by a vector which is not a lattice vector of their crystal structure. In ordered alloys these faults involve various types of topological and/or chemical disorder in the interfacial region. Special cases are antiphase domain boundaries (APB) for which the displacement vectors are identified with one of the vectors connecting the sublattices of different species. Aiitiphase boundaries (APBs) were discussed in detail by Sun in Volume 1, Part IV, Chapter 21 (1995) and all tlie basic concepts can be fouiid in that review. In the present chapter we include some new data on energies of APBs that appeared since the publication of Volume 1, and thus update Tables 1-6 un. We then discuss other stackingfault-like defects and concentrate 01%aspects that have not been considered previously. An ii~portantnotion, employed throughout this chapter, is the concept of y-surfaces which are theoretical constructs that have been used extensively in studies of stackin~~fault-like defects and dislocations. An exact definition of y-surfaces is presented at the beginning of Section 2. For each specific crystal structure it is its s y m ~ e t r ywhich determines the most general features of these surfaces, while distinctions found for different materials with the same structure are controlled by the specific character of atomic interactions. This concept is then utilized when discussing possible stacking"~~ult-like defects in various types of crystal structures encountered in intermetallic compounds. The specific structures discussed in this chapter were selected to cover most c o ~ ~ o nstudied ly intermetallic compounds. After surveying the various crystal structures, we consider briefly effects of temperature on the structure and properties of stacking-fault-like defects. These effects mainly relate to segregation and disordering, which in turn may lead to thickening of ion. Since energies o f the faults s u ~ m a r i z ein ~ this review have been de~ermined from the measured widths of dislocation dissociations, we also discuss problems associated with such meas u r ~ ~ e n t These s. include the effects related to the formation of the contrast in the electron microscope, as well as effects of the core structure o f the dislocations. Finallv. we summarize. for all the structures
coilsidered in this chapter, the crystallographic planes on which the staclcing-fadt-like defects can be formed, the displacements leading to such faults, and discuss briefly some implications for dislocation behavior.
Interfaces discussed here are metastable planar translational faults confined to certain crystallographic planes. They encompass antipbase boundaries (AP and various types of stacking faults (SF) and play a prominen t role in dislocation dissociation, Such stackin~~fau~t-like defects can be very conveniently analyzed using the notion of y-surfaces. This concept was first introduced when searching for possible stacking faults in bcc metals (Vitek, 1968, 1992; Duesbery 1989); but it becomes even more useful in the case of more complex crystal structures siiice the variety o f planar defects increases with the structural complexity. To introduce the idea of y-surfaces, we first define a generalized stacking fault: Imagine that the crystal is cut along a given crystallographic plane displaced with respect to the lower parallel to the plane of the cut, as . The fault created in this way is ~~ j ~and~ it is not in called the g e ~ e ~ u s~ ~~ za ec .~~~~~ general metastable. The energy of such fault, y ( be evaluated, at least in principle, when an appropriate description of atomic interactions is available. In such calculations relaxation perpendicu~ar to the fault must be allowed but no relaxations parallel to the ed. Repeating this procedure for within the repeat cell of the gi