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Physical Methods for Materials Characterisation Second Edition
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Series in Materials Science and Engineering
Physical Methods for Materials Characterisation Second Edition
P E J Flewitt Nuclear Electric plc and
R K Wild (formerly Nuclear Electric plc) Interface Analysis Centre, University of Bristol
Institute of Physics Publishing Bristol and Philadelphia
Copyright © 2003 IOP Publishing Ltd.
# IOP Publishing Ltd 2003 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher. Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency under the terms of its agreement with Universities UK (UUK). British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ISBN 0 7503 0808 7 Library of Congress Cataloging-in-Publication Data are available
Series Editors: B Cantor and M J Goringe Commissioning Editor: Tom Spicer Production Editor: Simon Laurenson Production Control: Sarah Plenty Cover Design: Victoria Le Billon Marketing: Nicola Newey and Verity Cooke Published by Institute of Physics Publishing, wholly owned by The Institute of Physics, London Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK US Office: Institute of Physics Publishing, The Public Ledger Building, Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106, USA Typeset by Academic+Technical, Bristol Printed in the UK by MPG Books Ltd, Bodmin, Cornwall
Copyright © 2003 IOP Publishing Ltd.
To our wives Ann & Gillian
Copyright © 2003 IOP Publishing Ltd.
‘‘Whence it is that nature does nothing in vain; and whence arises all that order and beauty which we see in the world’’ Isaac Newton 1642–1727
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Contents
Preface to second edition
x
Preface
xi
1 Introduction 1.1 Introduction 1.2 Atom bonding 1.3 Ceramics 1.4 Semiconductors 1.5 Glasses 1.6 Metals and alloys 1.7 Polymers 1.8 Composite materials 1.9 Microstructure 1.10 References
1 1 1 6 8 9 11 11 13 14 18
2 Interaction of radiation with materials 2.1 Radiation sources 2.2 Penetration depths 2.3 Material damage 2.4 Resolution 2.5 Loss processes 2.6 Atom and ion processes 2.7 Effect of high electric fields 2.8 Acoustic phenomena 2.9 References
21 21 22 33 38 38 47 48 49 50
3 Vacuum systems 3.1 Introduction 3.2 Kinetic theory of gases 3.3 Production of vacuum 3.4 Vacuum pumps
53 53 53 55 60 vii
Copyright © 2003 IOP Publishing Ltd.
viii
Contents 3.5 3.6 3.7 3.8
Pressure measurement Leak detection Specimen handling References
68 73 74 74
4
Diffraction 4.1 Electromagnetic radiation 4.2 Photons 4.3 X-ray diffraction 4.4 Electron diffraction 4.5 References
76 76 78 89 129 171
5
Photo/electromagnetic sources 5.1 Introduction 5.2 Resolution 5.3 Lens defects 5.4 Light microscopy 5.5 Laser microscopy 5.6 Acoustic microscopy 5.7 Infrared microscopy 5.8 X-ray microscopy 5.9 X-ray topography 5.10 X-ray photoelectron spectroscopy 5.11 Autoradiography 5.12 Mo¨ssbauer spectroscopy 5.13 Nuclear magnetic resonance 5.14 Total reflection X-ray fluorescence spectroscopy 5.15 References
176 176 177 179 182 199 213 223 226 233 236 254 256 263 266 268
6
Electron sources 6.1 Introduction 6.2 Scanning electron microscopy 6.3 Electron probe microanalysis 6.4 Transmission electron microscopy 6.5 Electron energy-loss spectrometry 6.6 Auger electron spectroscopy 6.7 References
274 274 274 297 324 393 411 440
7
Atom/ion sources 7.1 Introduction 7.2 Ion scattering spectroscopy 7.3 Rutherford backscattering 7.4 Proton backscattering 7.5 Secondary ion mass spectroscopy
451 451 452 457 463 463
Copyright © 2003 IOP Publishing Ltd.
Contents 7.6 7.7 7.8 7.9 7.10 7.11
Sputtered neutral mass spectroscopy Field ion microscopy Scanning probe microscopy Particle induced X-ray emission Glow discharge spectroscopy References
ix 489 493 501 513 517 519
8 Application of computers 8.1 Introduction 8.2 Instrument control 8.3 Computer aided instruction 8.4 Data acquisition 8.5 Data processing and analysis 8.6 Image quantification 8.7 Data bases 8.8 Data transfer 8.9 Expert systems 8.10 Computer simulation 8.11 Future developments 8.12 References
523 523 524 525 527 530 542 556 558 558 562 568 570
Appendix 1
574
List of symbols used in book
Appendix 2.1
Commonly used conversion factors
576
Appendix 2.2
Wavelength of selected radiation sources
577
Appendix 3
Physical constants
578
Appendix 4
Acronyms for techniques
574
Appendix 5
Electron structure of elements
583
Index
Copyright © 2003 IOP Publishing Ltd.
587
Preface to second edition
Over the period since this book was first published in 1994 there have been, as anticipated, advances in the field of the physical methods used to characterise materials. These developments have been made to reflect the requirements and needs to understand the interrelationship between the microstructure and the physical, mechanical and chemical properties of materials. In particular the emphasis from the electronic industry on nanoscale materials has resulted in significant developments in the scanning probe techniques originally proposed by Binnig and Roher, and by Gerber and Weibel in 1982. As a consequence, for this second edition of the book the authors have attempted to reflect incremental developments as well as the more significant techniques that have emerged over the past years. However, as the readers will appreciate, the principles and physics upon which many of the techniques describe are based remain unaltered and as a consequence the basic format of the book remains unaltered. A chapter that again has been subject to consideration in this context is chapter 8, where the emergence of computer technologies have a significant impact across all sections of the techniques addressed in this book.
Acknowledgments to second edition In the preparation of this second edition the authors would like to acknowledge the interaction with colleagues at Bristol University both in the Interface Analysis Centre and the Department of Physics. P E J Flewitt would like thank BNFL Magnox Generation for the secondment to Bristol University. Also to considerable positive interactions with a range of colleagues including Professors L M Brown FRS, J F Knott FRS, R Faulkner, D Bacon and G W Greenwood FRS.
Copyright © 2003 IOP Publishing Ltd.
Preface
This book was initiated as a consequence of discussions that led to the conclusion that over the past decade significant advances have been made on the range of techniques now available for interrogating the microstructure of materials. In some cases these developments have been a consequence of the flexibility offered by the ability to interface small but powerful computers to instruments to effect both instrument control and acquisition of data. This has been coupled with the ability to process the acquired data rapidly in such a way that even small signals contained within a large background noise can be used and interpreted. The developments have been promoted by the need to evaluate the microstructure of material to fulfil various technological needs such that it is necessary to ensure reproduction of the properties and to interpret features that lead to departures as a consequence of defects, such as those in the crystal structure or the fine scale chemistry. The interrelationship between the physical and mechanical properties of materials and their microstructure is being progressively developed. It is certainly evident that the properties for which materials are selected for a particular application depend upon the microstructure which, in itself, can be considered to extend to the atomic level. Microstructure is a generic term which has been used to describe the constitution of a material that can be visualised from a range of techniques extending from simple optical microscopy to those capable of atom resolution and indeed even indirect techniques such as X-ray diffraction. The interaction of electromagnetic radiation with crystalline solids is now understood in considerable detail, so it can be exploited to provide the necessary information. The concepts related to the use of light and electron imaging together with electron and X-ray diffraction are common to a range of microstructural evaluation techniques. The factors controlling both image formation and wave diffraction are described. The penetration depth of high-energy electrons, the dispersion of electrons through foils and the mean free path of slow electrons has been established for a variety of systems. This has paved the way for accurate quantitative determination of microstructural features within materials.
Copyright © 2003 IOP Publishing Ltd.
The book is directed primarily to senior undergraduate students and postgraduate workers to facilitate an appreciation of the underlying theory, the selection and application of the range of techniques available to examine a microstructural feature. It is clear that on many occasions more than one technique can be selected to provide the appropriate microstructural information; indeed it is often desirable to select a combination of complementary techniques to provide this detail. Many of the techniques described have now reached a stage of development where they are appropriate, not only to the dedicated research worker, but are of equal importance to applied research and those undertaking development used to promote and support a range of industrial and commercial activities. The content of the book has been structured to allow the reader to acquire both a background to the microstructure of materials (chapter 1) and an appreciation of the principles (chapter 2) which underline many of the techniques described in the subsequent chapters. In view of the importance that it has in many of the techniques presented, in chapter 3 we have described the control of instrument environment. Chapters 4 to 7 set out a range of techniques divided on the basis of those using diffraction (chapter 4), photon and electromagnetic sources (chapter 5) electron sources (chapter 6) and atom/ion sources (chapter 7). Finally, in view of the emphasis placed upon computers, chapter 8 is devoted, albeit briefly, to the application of computers. Throughout the book we have attempted to provide clear and simple diagrams to assist the understanding of the techniques and support this with selected examples to illustrate their use and application. In this way we hope we provide the reader with an appreciation of those techniques and procedures currently available which enable the microstructure of materials to be characterised. We would like to acknowledge the help of our colleagues with Technology Division of Nuclear Electric and Dr D A Dominey for encouraging the production of this book. P E J Flewitt would like to acknowledge the interaction afforded by the Department of Physics, University of Surrey and to express personal gratitude to Professor A G Crocker. In addition, P E J Flewitt is grateful for invaluable collaboration with Dr P Doig, Mr D Lonsdale and Mr R A Stevens over a number of years. R K Wild would like to express his thanks to all at the Interface Analysis Centre at the University of Bristol for their help and encouragement and in particular Professor J Steeds, Professor G C Allen, Dr J Day, Mr I T Brown, and Dr K Hallam. R K Wild would also like to acknowledge the help and collaboration over many years of Dr P A Tempest. Finally we would like to thank Mrs Rita Pollock for editorial assistance. P E J Flewitt and R K Wild
Copyright © 2003 IOP Publishing Ltd.
Chapter 1 Introduction 1.1
Introduction
This book provides a guide to those techniques and procedures which enable the microstructure of materials to be completely classified and characterised. As a consequence, it is appropriate to those studying and working in the interrelated fields of metallurgy, materials science, ceramics, polymer science and solid state physics. Material is the generic term used to describe physical matter in the solid state which occurs naturally or is manufactured to achieve particular physical properties and characteristics. Materials have been classified in various ways, but perhaps the simplest and most complete classification divides into two categories (table 1.1) (Bever (1986)), one based upon the nature of the material and the other upon the application. Such a classification is flexible, accommodating existing materials and perceived future materials. It is not appropriate to address each of the materials set out under the heading of nature in table 1.1 in detail, but rather to consider briefly how their atomic and molecular structure influences the mechanical and physical properties associated with some of the more important of these. It is to this nanoscale level that microstructure has to be resolved ultimately, although there are essentially many lower-resolution techniques covering the meso and microscale that assist this understanding.
1.2
Atom bonding
There is an attractive force between atoms and a repulsive force which prevents them from approaching beyond a minimum distance. The stable position for the atoms is best addressed by considering how the potential energy of a pair of atoms varies with their separation. The repulsive force gives rise to a positive potential energy which results in work being done on the system to bring the atoms closer together; this energy varies as an inverse power of the atomic separation r as A=rn . The attractive force gives a negative potential energy of the form B=rm which tends to zero when the
Copyright © 2003 IOP Publishing Ltd.
2
Introduction
Table 1.1. Classification of materials based on nature and applications (Bever (1986)). Nature
Applications
Ceramics Glasses Metals and alloys Other inorganic materials (including semiconductors) Polymers Elastomers Fibres Composite materials Wood Paper and paperboard Other biological materials
Industrial materials Electrical materials Electronic materials Superconducting materials Magnetic materials Nuclear materials Materials for other energy applications Optical materials Biomedical materials Dental materials Building materials
atoms are widely separated and increases negatively as they are brought together. The combined curve in potential energy, A=rn B=rm , as a function of the interatomic spacing is shown in figure 1.1 and this passes through a minimum. The atomic separation r0 at which this minimum potential energy occurs is the stable spacing for the pair of atoms; the negative and positive forces balance. This minimum in the potential energy arises
Figure 1.1. The potential energy of two atoms as a function of their separation r. The minimum in the potential energy at a separation r0 corresponds to the equilibrium separation.
Copyright © 2003 IOP Publishing Ltd.
Atom bonding
3
Table 1.2. A summary of physical and mechanical properties associated with interatomic bonds. Property
Ionic
Covalent
Nondirectional; Directional; Structures of high structures of low coordination coordination and low density
Metallic
Van der Waals
Nondirectional structures of high coordination and high density
Analogous to metallic bond
Mechanical Strong, hard crystals
Strong, hard crystals
Variable crystals
Weak, soft crystals
Thermal
High melting point, low expansion coefficient
High melting point, low expansion coefficient
Range of melting points, extended liquidus range
Low melting point, large expansion coefficient
Electrical
Weak insulator, Insulator in solid conduction by ion and liquid state transport when liquid
Conduction by Insulator electron transport
Optical
Absorption and other properties mainly of the individual ions
Opaque, with similar properties in liquid state
High refractive index, absorption different in solid or gas
Properties of individual molecules
because the power n in the repulsive term is greater than m in the attractive term. If m is less than n an unstable situation would develop and all the atoms collapse together. Since the mechanical and physical properties of materials are a direct consequence of their interatomic force (Cottrell (1967), Mott and Jones (1958) and Mott (1976)) (table 1.2), it is appropriate to consider the different bonding configurations that are associated with various materials and the potential crystalline and molecular structures that can form. However, it has to be remembered that the bond descriptions given here are simple and idealised. Moreover, many materials used for practical applications are in the form of either polycrystalline arrays or aggregates, rather than simple single crystals. It is the specific type of interatomic bond that leads, in solid crystals, to the development of atoms or molecules into particular periodic arrangements in three dimensions and thus specific materials. Crystals differ from liquids and gases because the atomic arrangements in the latter do not possess this periodicity. However, not all solids are crystalline; some are amorphous, such as glasses, a state that does not have any periodic arrangement of atoms. The regularity of the array can be described in terms of symmetry elements (Kelly and Groves (1970) and Barrett and
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4
Introduction
Figure 1.2. A simple point lattice defining a unit cell (Cullity (1979) (reproduced with permission of John Wiley and Sons).
Massalski (1986)) and these elements determine the directionality of the physical properties of crystals. For example, the symmetry elements reveal directions where electrical resistance in a crystal will be similar. Figure 1.2 shows a simple crystal lattice where all the cells are identical. The size and shape of the outlined unit cell can be described by three vectors, a, b and c, which define the crystallographic axes (figure 1.3). The lengths a, b and c and the angles between them , and , are the constants which describe the crystal uniquely. Figure 1.4 shows the 14 possible lattice arrangements, Bravais lattice, for crystalline materials. Figure 1.5 shows the five types of interatomic bond that can exist for all materials, either individually or in combinations. These are: (a) ionic, (b) covalent, (c) metallic, (d) molecular and (e) hydrogen. In the case of the ionic bond, the atoms either gain or lose an electron so that their outer electron shell is complete. As a consequence, the atoms are electrically charged,
Figure 1.3. The unit cell can be described by three vectors a, b and c; the lattice constants are a, b and c and , and (Cullity (1979) (reproduced with permission of John Wiley and Sons).
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Atom bonding
5
Figure 1.4. The fourteen crystal systems for all crystalline solids. Generally pure metals adopt either the body centred cubic (bcc), face centred cubic (fcc), or hexagonal close packed (hcp) packing arrangements.
either positively or negatively, and thereby attract atoms of opposite charge. For the covalent bond, pairs of atoms share outer electrons to fill the outer electron shells; this differs from the metallic bond where all atoms share the valence electrons. The molecular bond (van der Waals) arises from the displacement of charge within electrically neutral atoms or molecules
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6
Introduction
Figure 1.5. Schematic diagram showing the five types of atomic bond in materials (a) ionic, (b) covalent, (c) metallic, (d) molecular and (e) hydrogen, together with examples of each.
producing a weak attractive force between them. The hydrogen bond is weak and mediated by the hydrogen atom. It arises because hydrogen is a small atom and the charge is easily displaced.
1.3
Ceramics
The term ceramic describes those products that are made from inorganic crystalline materials and have non-metallic properties. Natural stone is a ceramic that was one of the first solid materials used by man. Indeed, stone has the characteristic properties associated with a ceramic of high hardness and strength, brittleness, low thermal and electrical conductivity together with a resistance to chemical attack. The constitution of a ceramic is usually a combination of one or more metals with a non-metallic element, usually oxygen. As a result, the atoms in a ceramic crystal are linked by a combination of ionic and covalent bonds. The combination of oxygen atoms with the metal atoms provides a strong ionic bond because oxygen, with two electron vacancies in the outer electron shell, effectively borrows two electrons from the neighbouring metal atoms. The associated ionisation of both atom species, one negatively and one positively, provides
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Ceramics
7
Figure 1.6. A silica unit, which forms the basic building block of many ceramics, consists of a silicon atom surrounded by four oxygen atoms.
strong electrostatic attraction. It is this combination of atomic bonds that establishes the stability and strength associated with a ceramic. Simple examples are ionically bonded magnesia, MgO and covalently bonded silicon carbide, SiC. These have the sodium chloride and diamond crystal structures respectively. The physical and mechanical properties of ceramics are controlled by the crystal structure and the chemical composition (Davidge (1980) and Kingery et al (1976)). This is demonstrated by considering the important but varied structures generated by silica (SiO2 ). The silicon atom, like carbon, has four valence electrons and forms a tetrahedral grouping with the oxygen atoms positioned so that four oxygen atoms surround each silicon atom (figure 1.6), and it is these groups of atoms that can link together in various ways. If attached end to end by one of the oxygen atoms a chain is formed giving fibrous asbestos (figure 1.7), whereas if built-up into sheets they produce layer minerals such as talc or mica. However, this tetrahedral grouping can link to produce a three-dimensional network, an arrangement that results in the quartz crystal. The versatility of these silica tetrahedrons in forming bonds with one another and, indeed, with other groups of atoms, explains how silica serves as the bonding material for clay particles in bricks and earthenware and bonds a glaze to porcelains.
Figure 1.7. Each atom of silicon has four valence electrons passed to the surrounding oxygen atoms, leaving the outer shell one electron short. The linking into a chain is one basic grouping leading to, for example, the asbestos fibre structure.
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8
Introduction
If ceramic crystals were of perfectly organised structures and uniform microstructure, these materials would have mechanical properties that exceed those achieved. Indeed, failure of a ceramic is generally a consequence of a microstructural defect, or combination of defects, such as inclusions, pores, voids and distributions of irregular size grains. Mechanical failure occurs from pre-existing flaws: high mechanical stresses which exceed the local tensile strength effect crack propagation from flaws followed by rupture. Apart from their known high-temperature applications, some polycrystalline electronic ceramics are used extensively by communications, electronic and appliance industries. Among the best known of the ceramics for these applications are the ZnO varistors, boundary layer capacitors, ferrites and positive temperature coefficient devices. These owe their unusual electrical properties to the presence and character of their grain boundaries since the single crystals of these materials do not exhibit the same phenomena as the polycrystals. A single defect in a ceramic capacitor can cause electrical breakdown and short circuiting and similarly for piezoceramics, where during the ensuing polarisation the electrical breakdown can be followed by mechanical failure. As in other materials, crystal lattice imperfections, in particular lattice vacancies and dislocations, influence thermal conductivity, electrical and magnetic properties.
1.4
Semiconductors
Many of the traditional semiconductor materials have crystal structures that are related to the simple diamond cubic lattice where each atom is tetrahedrally coordinated, but the local atomic environment is not identical for all atoms. Table 1.3 gives the values of basic physical parameters of some commonly encountered semiconductor materials. Most semiconductor compounds and alloys are designed to keep the average electron to atom ratio to a value of four. The simplest illustration is given by the range of AB-type semiconductor materials formed between Group III and Group V elements in the Periodic Table of Elements. These so-called III to V semiconductors include GaAs and have a sphalerite superlattice structure, whereas the Types II and VI and IV and VI compounds usually have crystal structures of the sphalerite and rock salt respectively. Here the lattice constants of these materials lie in the range 0.50 to 0.65 nm and are generally larger than for metallic elements. This makes it generally easier to obtain details of the crystalline defects. Moreover the binary semiconductor compounds have band gaps in the range 0 to 3 eV. Although covering the band gap range for applications to microelectronic devices it is not possible to prepare such devices from this limited range of materials. This is due to (i) difficulties in preparing suitable defect-free pure materials and (ii) the need to have precisely controlled band gaps to optimise the performance of
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Glasses
9
Table 1.3. Crystal structure and basic electrical properties of some important semiconductor elements and compounds (after Grovenor (1989)). Crystal structure
Lattice spacing (nm)
Band-gap width (at 300 K) (eV)
D D
0.5431 0.5646
1.12 0.66
III–V compounds GaAs GaP GaSb InAS InP InSb AlAs AlSb
S S S S S S S S
0.5653 0.5451 0.6096 0.6058 0.5869 0.6479 0.5661 0.6136
1.42 2.26 0.72 0.36 1.35 0.17 2.16 1.58
II–VI compounds CdS CdSe CdTe ZnS ZnSe ZnTe HgTe
S/W S S S/W S S S
0.5832/a ¼ 0:416, c ¼ 0:6756 0.605 0.6482 0.542/a ¼ 0:382, c ¼ 0:626 0.5669 0.6089 0.644
2.42 1.7 1.56 3.68 2.7 2.2 0
Chalcopyrite CuInSe2
S
a ¼ 0:5782, c ¼ 1:1564
1.04
IV–VI compounds PbS PbSe PbTe SnTe
R R R R
0.594 0.612 0.646 0.632
0.41 0.27 0.31 0.18
Element Si Ge
D is diamond cubic, S is sphalerite, W is wurtzite and R is the rocksalt lattice.
particular devices. Hence the need to create materials by a combination of binary semiconductor compounds to give ternary and even quaternary semiconductors (Pollock et al (1982)).
1.5
Glasses
Glass is a class of material that does not crystallise when cooled from the molten state and, therefore, does not have long-range periodicity within the atomic structure (Hlavac (1983)). A pure oxide glass consists of a random three-dimensional network of atoms where each oxygen atom
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10
Introduction
Figure 1.8. Pure oxide glass consisting of a random three-dimensional network in which each oxygen atom is bonded to two metal atoms.
(figure 1.8) is bonded to two atoms of a metal, such as boron, and each metal atom is bonded with three oxygen atoms. However, there are many types of glass, and in the case of silica glass each metal atom is bonded with four oxygen atoms producing a more complex atomic configuration. The addition of fluxing atoms such as sodium reduces the number of bond cross links (figure 1.9). The major constituents of glasses are contained in two widely
Figure 1.9. Flux containing glass consists of a random three-dimensional network where the flux atoms such as sodium have reduced the number of cross-links.
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Polymers
11
separated regions of the Periodic Table, Group VI and Groups I and II. The chief glass-forming elements in Group VI are oxygen, silicon, selenium and tellurium. However, it is the neighbouring elements that enter into the chain-forming structures that result in the different types of glass. Elements from within Groups I and II are used primarily as fluxes and indeed, they control the viscosity and viscoelastic properties of glasses.
1.6
Metals and alloys
Metals and alloys are opaque, lustrous and relatively heavy, easily fabricated and shaped, have good mechanical strength and high thermal and electrical conductivity. All these properties are a consequence of the metallic bond in which all the atoms share their electrons in the outer electron shell forming an electron cloud and the bonding is by Coulomb attraction. Changes in the strength of this metallic bond cause differences in optical, electrical, mechanical and thermal properties of various metals and alloys. The simple, regular crystalline structures of metals and alloys result from the metallic bond which retains atoms in close packed arrangements, so that pure metals, in general, have one of the face centred cubic (fcc), body centred cubic (bcc) or hexagonal close packed (hcp) structures of the 14 crystal systems (figure 1.4). With these crystal structures, metals and alloys have relatively high ductility since they are resistant to tensile stresses and less resistant to shearing forces. However, the overall mechanical properties of metals and alloys are controlled by the crystal lattice defects, such as dislocations and vacancies (Nabarro (1967), Bollman (1970) and Honeycombe (1968)). Mechanical and chemical properties can be modified by the addition of alloying elements in varying proportion which are used to advantage in a range of commercial alloys. In many, alloy systems compositions and heat treatments are selected that produce complex distributions of phases to give the required properties (Barrett and Massalski (1986)).
1.7
Polymers
Polymers are by definition materials composed of long-chain molecules, typically 10 to 20 nm, that have developed as a consequence of the linking of many smaller molecules, monomers (Odian (1970)). Polymers which can be either natural or synthetic and have a wide range of characteristic physical properties such as strength, flexibility and the ability to soften when heated. Indeed, it is the particular combination of tensile strength and flexibility that make these materials attractive. If the molecular chains are packed side by side (figure 1.10) the molecules form an array with a crystalline structure. However, naturally occurring polymeric materials typically have a complex
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12
Introduction
Figure 1.10. Schematic diagrams of the molecular structures of polymeric materials. (a) A polymer with few branched chains; chains are regularly packed with extensive crystalline regions. (b) A polymer with many branched chains; chains are regularly packed and largely amorphous with few crystalline regions. (c) A polymer with extensive cross-linking.
microstructure comprising a mixture of crystalline and amorphous material. Generally, if the crystalline structure predominates, the material is relatively rigid with a higher tensile strength and is more resistant to heat than a material which contains a greater proportion of amorphous material. In the synthetic polymers, the proportion of crystalline to amorphous material is controlled and depends upon the chemical composition, molecular arrangement and the processing conditions used to produce the material (Ward (1971) and Kinlock and Young (1983)). In the case of polymeric materials, the interatomic bonds between molecular chains are the weak van der Waals forces, but in the crystalline structures, the chains are closer together over comparatively large distances so that the contribution of intermolecular forces has the effect of producing a more rigid material. The production of a crystalline structure is one of two methods used to develop stronger, more rigid, polymers such as polyethylene and nylon; the other is the formation of a strong covalent bond between the molecular chains by cross linking. A typical example of the latter is the established process of vulcanising raw rubber by heating with the controlled addition of sulphur atoms. Under these conditions, a proportion of these sulphur atoms cross-link between adjacent rubber molecules to increase both stiffness and strength. As the heating time is increased, more crosslinks are developed, and the rubber further stiffens, leading ultimately to the hard material ebonite. These materials are the thermosetting plastics which retain comparatively high tensile strength until excessive heating leads to breakdown of the cross-links and chemical deposition. By comparison in thermoplastics, only weak van der Waals forces bond the molecular chains together and these materials are softened by heating and, if necessary, can be remoulded. The heat treatment can be repeated provided the temperature is kept below that affecting chemical decomposition since at that stage the covalent bonds bind the atoms together in a long chain break-down.
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Composite materials
1.8
13
Composite materials
A composite material was originally considered to be a combination of two materials but now this class of material is regarded as any combination which has particular physical and mechanical properties (Kelly (1973) and Hale (1976)). The concept of composite materials has led to the design and manufacture of a new range of structural materials that are generally lighter, stiffer and stronger than anything previously manufactured. Figure 1.11 shows a simple schematic representation of the various ways of combining constituent materials to make a composite. Like synthetic polymeric materials, composite materials are often designed to replicate naturally occurring materials. Wood, for example, is a composite consisting of cellulose and lignin. The cellulose fibres have a high tensile strength and flexibility whereas the lignin provides the matrix for binding these fibres and adds the property of stiffness. Bone is another composite material, comprising the strong, but soft, protein collagen and the hard, brittle mineral apatite. The developed synthetic composite materials attempt to achieve similar total properties to naturally occurring materials by combining individual properties such as strong fibres of a material, for example carbon, in a soft matrix, such as an epoxy resin. Thus, the microstructure of significance in these materials spans the simple, relatively macrofeatures associated with the
Figure 1.11. Schematic representation of the various types of composite materials.
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14
Introduction
overall distribution of the mixture down to the microstructure of the individual components and their actions in concert. As we have discussed in this chapter, the basic chemical reason metals and alloys and polymeric materials are so much more resistant to cracking than ceramics is that interatomic forces in metals and alloys and intermolecular forces in polymers do not depend critically upon a particular directional alignment to achieve tensile strength. Moreover, the atomic bonds of metals and alloys and polymers are essentially unsaturated and are capable, therefore, of forming new bonds. Ceramics have highly oriented interatomic forces and saturated atomic bonds. The large amounts of plastic strain, more usually accommodated in metals and alloys and polymers as a result of plastic flow, provide a better resistance to crack extension than in a ceramic or glass. To overcome such a limitation of a ceramic or glass, but to make use of the potential strength of this class of material, modern composite materials divide the ceramic or glass into small pieces and bond them in a matrix. Thus, any inherent or developing cracks do not find a continuous, easy path through the total material. The ceramic or glass is often introduced into the composite in the form of fibres. However, the properties of the associated matrix are also extremely important. Under such circumstances, the matrix would be required to have specific properties so that it must (i) not cause mechanical or chemical change to the fibres that would introduce cracks, (ii) have sufficient plasticity to allow the transmission of stress to the fibres and should be adhesive with the fibres and (iii) have appropriate elastic and fracture properties. Fortunately there are other stiff materials with fibres that are covalently bonded and indeed, examples of these, boron and carbon, also have high melting points. These two physical properties are associated with the covalent bond which requires a high energy to break it. Therefore, materials that replace glass fibre because of their greater stiffness also, in many cases, overcome temperature limitations. Stiff fibres of graphite, boron and silicon carbide are used for a wide range of commercial composite materials.
1.9
Microstructure
It is obvious from the brief descriptions of the various materials given in the preceding sections of this chapter that to understand the physical properties and the response of materials to static, dynamic and cyclic stresses, various environments and temperatures, it is essential to be able to describe the ‘total microstructure’. For this, it may be necessary to combine a knowledge of the distribution, proportion and types of phases present, the chemical composition and state, and crystal and defect structure. On many occasions the term microstructure is still confined to describing objects that are visible by optical light microscopy (Saltykov (1974) and
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Microstructure
15
Table 1.4. A classification of microstructural elements in metal alloys after Hornbogen (1984) based on Euclidean dimensions and specific energies. Geometrical
Type of elements
Density, densities
Specific energy (U)
0 1 2 3
Vacancy Dislocation Grain Boundary Dispersed particle, pore or void
m3 m2 m1 m0
J J m1 J m2 J m3
Underwood (1970)). In reality the dimensions of microstructural elements that are significant in the investigation of materials commence at the level of the atomic spacing and, therefore, size alone is an insufficient definition of microstructure. Microstructure can be considered simply as the identical arrangement in three-dimensional space of atoms and all types of nonequilibrium defects and, therefore, both single phase and multiphase materials have a microstructure. Hornbogen (1984) considered the basic elements of microstructure for metal alloys and put these into a systematic order based upon geometric dimensions (Table 1.4). This quantitative characterisation of microstructure starts with information on structure characterised by the Euclidean dimension (Stanley and Ostrowsky (1986)) assigned zero to three for discontinuities in the phase structure followed by information on the density, . The dimension of these densities varies with geometric dimension of the defects so that for: P N=V ¼ ½m3 0-dimensional: 0 ¼ v ¼ P 1-dimensional: 1 ¼ d ¼ L=V ¼ ½m2 ð1:1Þ P 2-dimensional: 2 ¼ b ¼ A=V ¼ ½m1 P 3-dimensional: 3 ¼ p ¼ Vp =V ¼ ½m0 where N, L, A and V are number, length, area and volume and the subscripts refer to the dimension of the defect type: v ¼ vacancy, d ¼ dislocation, b ¼ boundary, p ¼ particle or void. The relationship between density i and average spacing Si of defects is given by Sv 3 v ¼ ½m Sd 2 d ¼ ½m Sb 1 b ¼ ½m 1=3
S f 1=3 f
ð1:2Þ
¼ ½m
where refers to the volume fraction of the phase which for a discrete dispersion of second phase particles 0 < f < 1. The units for the density of these elements depend upon the dimension 0 d 3. The product of
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16
Introduction
density and specific energy gives a bulk microstructural energy with the unit of an energy density (J m3 ) which describes reactions such as recovery, recrystallisation and particle coarsening (Hornbogen (1989)). Thus elements may transform during certain solid state reactions, an example being when vacancies in a crystal lattice with d ¼ 0, condense to dislocation loops with d ¼ 1. Thus transformations of this type imply a change in dimension. In addition to spacing, both geometrical and statistical functions are required to describe microstructure; these include the distribution of crystal orientation, the local distribution, the shape of one-, two- and three-dimensional elements and the orientation of these elements in space (Hornbogen (1984). This concept of microstructure may be sufficient to describe metal alloys and ceramic materials, but in the case of polymeric materials as discussed here, the appropriate structural level is the molecule. Certainly the configurations of the molecules and chains are necessary supplements to the microstructure (Ward (1971)). These concepts have to be further added to for other materials such as concrete where pores, fissures and structural gradients play an important role (Huang (1982)). Furthermore, there is the need to address the simple and complex periodic sequences of layers produced, for example, by sputtering techniques (Gibson and Davidson (1985)). The thickness of each layer can be controlled at minimum scatter and a very high degree of microstructural order, and the resulting diffraction effects can be obtained from such artificially produced microstructures. As a consequence there is no strict and unified definition of microstructure. Fractal analysis offers a way forward to quantify microstructures that are not in thermodynamic equilibria and cannot be easily classified or described by parameters such as particle size and spacing (Mandlebrot (1983)). This is briefly discussed in chapter 8 but the reader is directed to the review by Hornbogen (1989) who discusses this approach and draws upon experience derived from work undertaken in the area of the chemistry and physics of surfaces. The basic approaches to the investigation of the microstructure of materials were laid over a hundred years ago by Henry Clifford Sorby with his development of a preparation method and etching treatment to allow metal, mainly steel, specimens to be viewed under a reflected light microscope (Quarrell (1963)). Indeed this technique, progressively refined, remains a powerful tool for establishing essential microstructural features such as grain size and shape and distributions of phases, to the limit of resolution of the optical microscope which is approximately 300nm. The development in the early 1950s of a theoretical understanding of the principles controlling the strength of materials resulted in a need to apply techniques with a resolution approaching that of the interatomic spacing. This led to the development and use of electron based techniques where the shorter wavelengths of the electrons enable the resolution of atom dimensions to be achieved
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Microstructure
17
with current generation electron microscopes. The electron microscope, developed in 1931, was initially used to study biological systems (Ruska (1962)), but techniques for specimen replication and the preparation of thin metal foils in the mid-1950s enabled microstructural investigations to be undertaken on metals and alloys (Ruska (1962), Hirsch (1954) and Thomas (1962)) and later ceramic and polymeric materials (Thomas (1984)). Since then the resolution has been improved and the accelerating voltages increased (Isaacson et al (1979) and Jouffrey (1976)). An area of advance has been to extend the atomic, structural and crystallographic information obtained by X-ray diffraction techniques to the small-scale features contained within thin foil specimens using methods based on electron diffraction. In the early 1960s the introduction of the electron probe microanalyser enabled relatively high spatial resolution chemical analyses, using characteristic X-ray emissions, to be obtained from features down to approximately 1 mm diameter. However, since that time it has become evident that chemical changes over distances approaching atomic dimensions have a profound effect on mechanical and chemical properties of materials (Hondros and Seah (1977), McMahon (1980) and Flewitt and Wild (2001)). For example, the segregation of trace impurities to grain boundaries in polycrystalline metals to give single atom layer coverage can drastically modify the properties of metal alloys and fine scale distributions of impurity elements control the properties of many semiconductor devices (Doig and Flewitt (1987) and Grovenor (1989)). To study such fine scale distribution of elements, a number of techniques have been developed with good depth resolution for surface analysis such as X-ray photoelectron spectroscopy, Auger electron spectroscopy and secondary ion mass spectrometry. These together with the high spatial resolution techniques of scanning and transmission electron microscopy used in conjunction with energy dispersive X-ray and electron energy loss spectroscopy have further improved knowledge by examining both the chemical composition and state (Newbery and Williams (2000)). Over the past decade scanning tunnelling microscopy has stimulated an entire family of instruments referred to generically as scanning probe microscopes (Binnig et al (1982), Saiid (1991) and Wiesendanger (1994)). Since these instruments are capable of measuring a range of microstructural parameters on the nanoscale they have extended the understanding of materials. The innovation in the approach is that these new microscopes are not limited by wavelength since their resolution is controlled by the size of the interacting probe. As a consequence they come under the general class of super-resolution or near field scanning probe microscopes (Wickramasinghe (2000)). In this book, we review the techniques which permit the complete characterisation of the microstructures of materials. However, before proceeding to that stage we consider, in chapter 2, the interaction of various particles and radiations, including photons, electrons, atoms and ions with materials. It is
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18
Introduction
these interactions that provide many of the signals that are used subsequently to evaluate the microstructure of materials. Certainly, many techniques are reaching, or indeed have reached, a stage where it is possible to establish the information necessary to correlate existing theoretical models which describe high and low temperature deformation and fracture, corrosion, oxidation, environmentally assisted fracture, electrical and other physical properties with the microstructure of the material. After considering the basic theory behind the techniques that may be used to investigate the microstructure of materials, we address the specific techniques, the underlying theory, their benefits and their application in the succeeding chapters. Many of the techniques described have reached a stage where they are widely available as tools for use by research scientists although not necessarily suitable for routine applications without either a clear understanding and ability to interpret the data or modifications to the hardware. In this book, certain basic techniques are assumed and as a result less attention given, for example, to optical microscopy although this remains a simple, but powerful technique for investigating the microstructure of materials. Indeed, the advent of computer-based image analysis and pattern recognition techniques (Bruggins (1983), Saxton (1978) and Horne and Markham (1973)), have advanced the quantitative evaluation of certain microstructural parameters using optical methods. It is here that the material has to be investigated and understood over a multi-dimensional range of scale that spans the atomic dimension, nanoscale, through the meso range to the microscale. As a consequence it is important to appreciate that to establish this understanding it is unlikely that one particular technique will provide all the necessary information. Indeed, it is generally only by the use of several techniques in the correct combination that this will be achieved. By presenting in this book the range of techniques now available, together with a description of their use and how the information is processed, the reader is provided with the basis to select the correct combination of techniques. To assist with this selection, we have provided applications of techniques to demonstrate how essential information can be extracted and interpreted.
1.10
References
Barrett C S and Massalski T B 1986 Structure of Metals (New York: McGraw-Hill) (third edition) Bever M B (ed) 1986 Encyclopedia of Materials, Science and Engineering vol 1 ed R W Cahn (Oxford: Pergamon) Binnig G, Roher H, Gerber Ch and Weibel E 1982 Phys. Rev. Lett. 49 57 Bollman W 1970 Crystal Defects and Crystalline Interfaces (Berlin: Springer) Bruggins D 1983 Opt. Electron Microsc. 3 9 Cottrell A H 1967 An Introduction to Metallurgy (London: Edward Arnold) Cullity B D 1979 Elements of X-ray Diffraction (New York: Addison-Wesley)
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References
19
Davidge R W 1980 Mechanical Behaviour of Ceramics (Cambridge: Cambridge University Press) Doig P and Flewitt P E J 1987 Met. Trans. 18A 399 Flewitt P E J and Wild R K 2001 Grain Boundaries: Their Microstructure and Chemistry (Chichester: Wiley) Gibson J M and Davidson R L 1985 Layered Structures, Epitaxy and Interfaces, Mat. Res. Soc. Symposium 37 Grovenor C R M 1989 Microelectronic Materials (Bristol: Adam Hilger) Hale D K 1976 J. Mat. Sci. 11 2105 Hirsch P B 1954 Proceeding of the Third International Conference on Electron Microscopy (London) p 231 Hlavac J 1983 Technology of Glass and Ceramics (Amsterdam: Elsevier) Hondros E D and Seah M P 1977 Met. Rev. 22 262 Honeycombe R W K 1968 The Plastic Deformation of Metals (London: Edward Arnold) Hornbogen E 1984 Acta Metall. 32 615 Hornbogen E 1989 Int. Met. Rev. 34 277 Horne R W and Markham R 1973 Application of optical microscopy in Practical Methods in Electron Microscopy ed A A M Glauert (Amsterdam: North-Holland) p 327 Huang G 1982 Concrete and Reinforced Concrete (China) 5/6 Isaacson M, Ohtsuki M and Utlaut M 1979 Electron microscopy of individual atoms in Introduction to Analytical Electron Microscopy ed J J Hren, J I Goldstein and D C Joy (New York: Plenum Press) Jouffrey B 1976 Electron Microscopy in Materials Science part III ed E Ruedl and U Valdre´ (Brussels: Commission of European Communities) p 981 Kelly A 1973 Strong Solids (Oxford: Clarendon Press) Kelly A and Groves G W 1970 Crystallography and Crystal Defects (London: Longmans) Kingery W D, Bowen H K and Uhlmann D R 1976 Introduction to Ceramics (New York: Wiley) Kinlock A J and Young R J 1983 Fracture Behaviour of Polymers (London: Elsevier) McMahon C J 1980 Mat. Sci. Eng. 42 215 Mandlebrot B 1983 The Fractal Geometry of Nature (San Francisco: W H Freeman) Mott N F 1976 The Solid State, Scientific American p 80 Mott N F and Jones H 1958 The Theory of the Properties of Metals and Alloys (New York: Dover) Nabarro F R N 1967 Theory of Crystal Dislocations (Oxford: Clarendon Press) Newbery D G and Williams D B 2000 Acta Mater. 48 323 Odian G 1970 Principles of Polymerisation (New York: McGraw-Hill) Pollock G A, Deline V A and Furman B K 1982 Grain Boundaries in Semiconductors ed H J Leamy, G E Pike and C H Seager (New York: North-Holland) Quarrell A G 1963 15th Hatfield Memorial Lecture, ‘Metallography’, ISI Special Report No 80 (London: Eyre and Spottiswoode) p 1 Ruska E 1962 Fifth Int. Congress for Electron Microscopy; Philadelphia ed S S Bleese (London: Academic Press) Saiid D 1991 Scanning Force Microscopy with Applications to Electric, Magnetic and Atomic Forces (New York: Oxford University Press) Saltykov S A 1974 Stereometrische Metalloghie (Leipzig: VEB Dt Verlag fu¨r Grundstoff Industrie)
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20
Introduction
Saxton W O 1978 Computer techniques for image processing in Electron Microscopy (New York: Academic Press) Stanley H E and Ostrowsky N 1986 On Growth and Form (Boston: Martinus Nijhoff) Thomas E L 1984 Structure of crystalline polymers in Transmission Electron Microscopy of Polymers ed I H Hall (London: Chapman and Hall) ch 3 Thomas G 1962 Transmission Electron Microscopy of Metals (New York: Wiley) Underwood E E 1970 Quantitative Stereology (Reading: Addison-Wesley) Ward I M 1971 Mechanical Properties of Solid Polymers (London: Wiley-Interscience) Weisendanger R 1994 Scanning Probe Microscopy and Spectroscopy: Methods and Applications (Cambridge: Cambridge University Press) Wickramasinghe H K 2000 Acta Mater. 48 347
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Chapter 2 Interaction of radiation with materials 2.1
Radiation sources
To characterise a microstructure it is necessary to perturb the material by interacting in some way with it. Indeed in order to see a surface it is necessary to bombard that surface with photons of wavelengths within the visible range and this in itself may alter the material. A typical example of damage caused by photons is the response of a photographic film. To achieve higher resolution and thereby magnification it is possible to use, for example, a scanning electron microscope where the photon source is replaced with electrons with an energy in the region of 10 to 30 keV. These are more damaging than photons since they penetrate a considerable distance on the atomic scale into the material. Many modern analytical instruments require high spatial resolution, while at the same time needing high sensitivity for the detection of elements within the material. Often this involves bombarding the surface with ionised atoms of high energy which, although extremely damaging, provides microstructural information that outweighs this disadvantage. With any characterisation of a material the objective must be to obtain the maximum information whilst incurring the least amount of damage to the specimen. Thus, in general, initial examinations of a surface should be carried out using a low intensity beam of low energy photons. To obtain more information the source energy may have to be increased, for example with the use of X-rays initially and progressively through electrons to finally ions. There are, of course, situations where this simplistic approach may not hold; in the technique of ion scattering spectroscopy (ISS), the ions reflect from the surface and do not perturb it as much as a high energy photon or electron, so care must be taken when deciding how to examine a material. It is the purpose of this chapter to summarise the processes that occur when photons, electrons, ions and particles interact with materials. The various sources available will be considered, their properties described, and their potential uses outlined.
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2.2
Interaction of radiation with materials
Penetration depths
The penetration depth or mean free path of the incident beam determines the depth and volume of material that will be sampled. In many cases one is probing with one type of radiation but detecting a second type. This occurs in X-ray photoelectron spectroscopy (XPS) where the incident probe is a beam of X-ray photons but emitted electrons are detected, whereas this is reversed for the technique of energy dispersive X-ray (EDX) analysis. Generally the particle or radiation which has the shortest mean free path in the material will determine the volume analysed. Whatever beam is selected we must be aware of its interaction with the material, what photons, electrons or other particles are ejected and how they, in turn, interact with the material. Only in this way can we use the emitted signals to gain an understanding of the material being examined. 2.2.1
Photons
Photons are discrete quanta of electromagnetic radiation. The photon is identified by the wavelength, , energy, E, and frequency, , all of which are related by the equation h ¼ E ¼ hc=
ð2:1Þ
where h is the Planck constant and c the velocity of light. The electromagnetic spectrum spans a vast range with wavelengths varying from 106 m down to 1014 m. The frequency, energy and wavelengths of the different types of electromagnetic radiation are illustrated in figure 2.1. If we are to use electromagnetic radiation for microstructural characterisation of materials a photon wavelength is needed that is of comparable size to the features being studied. This means that photon wavelengths greater than 104 m would result in an inadequate spatial resolution and we do not require radiation less than about 1010 m. The penetration of photons shows considerable and dramatic variations between different types of material and photon energy or wavelength. It is not possible or instructive to go into any detail regarding penetration depths over the whole of the electromagnetic spectrum, but only some specific wavelengths that are important for interrogating the microstructure of materials. The long wavelength infrared radiation is used to characterise materials by determining how specific wavelengths are absorbed, visible light is used in a variety of instruments mainly to obtain a visual image of the surface while at the shorter wavelength ultraviolet radiation is often used to obtain information concerning the electron distribution in the surface atoms. Some materials are opaque while others are transparent to this range of wavelengths. However, even the most opaque or highly reflecting of these materials will allow the radiation to penetrate at least a fraction
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Penetration depths
23
Figure 2.1. The electromagnetic spectrum illustrating the relationship between energy, frequency, wavelength and wave number.
of a wavelength below the surface. In the case of visible light, where the wavelength is approximately 500 nm this penetrates an average of between 50 to 300 nm into the bulk so that any analysis performed or image obtained will average over several hundred atom layers. After visible light, X-rays are probably the most utilised photon source for investigating the microstructure of materials. The whole subject of X-rays and their interaction with matter has been thoroughly treated by Cullity (1979). X-rays are produced by bombarding a metal target with high energy electrons to produce a band of ‘white’ radiation. The intensity of the X-rays within this band varies with the wavelength determined by the energy of electrons incident on the target material (figure 2.2(a)). Superimposed on the ‘white’ X-radiation are a series of discrete maxima whose wavelength and intensity is determined by the electron binding energies of the atom making up the metal target being bombarded. These characteristic X-ray photons, shown for a copper target in figure 2.2(b), result from electrons falling into holes created in core electron levels by the incident electron beam with the emission of a photon whose energy is
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Interaction of radiation with materials
Figure 2.2. The X-ray spectrum produced by bombarding metals with electrons: (a) the relationship between the X-ray intensity and wavelength for electron beam energies from 20 keV to 50 keV and (b) the spectrum from copper showing the characteristic K and K peaks.
given by replacing E in equation (2.1) by E1 E2 , the energy difference between the electron shells. The penetration of X-rays into a material shows less variation from one material to another than visible light and is easier to predict. The penetration distance varies both with wavelength and material and is typically several micrometres. The absorption coefficient, , which increases with atomic number determines the depth of penetration. The intensity of transmitted radiation, I, through a layer of material of thickness, t, is given by Peiser et al (1960): I ¼ I0 expðtÞ
ð2:2Þ
where I0 is the intensity of the incident X-ray beam. Gamma rays have very high energies in the region of 50 keV to 50 MeV and wavelengths that are considerably less than X-rays, and would typically be in the region of 102 nm (Seigbahn (1965)). When a beam of gamma rays passes through a material photons are removed from the beam in individual events, thus the number of gamma ray photons removed is proportional to the thickness traversed. Therefore the intensity of the gamma ray decays as I ¼ I0 expðxÞ
ð2:3Þ
where is the absorption coefficient and x is the distance traversed by the beam. Gamma rays can penetrate considerable distances through materials but the penetration distance tends to vary inversely with the atomic number. However, gamma rays will pass through the bulk of almost all practical specimens.
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Penetration depths 2.2.2
25
Electrons
The penetration depth of electrons varies dramatically with both the energy of the electron and the atomic number of the material that is being examined. Figure 2.3(a) reproduces the mean free path of electrons in stainless steel as a function of incident beam energy (Castaing (1960)). The mean free path length increases from a fraction of a micrometre, at energies in the region of 10 keV up to 2 mm at 30 keV. In figure 2.3(b) the mean free path of electrons is plotted as a function of atomic number for three incident electron energies—10, 20 and 30 keV. Here, even more dramatic changes can be seen: the mean free path of electrons in elements of low atomic number is very large and can be as great as 10 mm for elements with atomic number below 20, while elements with high atomic numbers greater than 40 have short electron mean free paths generally less than 2 mm. This clearly has important consequences for any microstructural characterisation since materials will invariably be composed of elements with different atomic numbers; there may be precipitates such as carbides with low atomic mass in a matrix with a high mean atomic number and this will modify the images for each constituent. A situation often encountered when examining a metal alloy in the scanning electron microscope is that the surface images differently as the interrogating beam
Figure 2.3. The mean free path length of electrons (a) in stainless steel as a function of electron energy and (b) as a function of atomic number of the material being probed for 10, 20 and 30 keV electrons (after Castaing (1960)).
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26
Interaction of radiation with materials
Figure 2.4. Secondary electron images from a specimen of colloidal silver and colloidal carbon on an aluminium stub recorded using an incident electron beam of (a) 20 keV and (b) 900 eV (reproduced by permission of ETP Ltd (1990)).
energy is changed and, indeed, different analyses can be obtained using the emitted characteristic X-rays. This is because the metal alloy specimen almost certainly has a thin oxide surface layer which can on occasions be further covered with a layer of carbon as a result of contamination. An example of this effect is shown in figure 2.4 where two images are obtained with incident beam energies of 900 eV and 20 keV (ETP (1990)) from colloidal silver and carbon on an aluminium substrate. The high energy electron beam produces an image in which the silver appears very bright and the carbon is poorly imaged. The low energy beam, on the other hand, produces a clear image from the carbon but a mottled image from the silver. The differences in the two images can be explained in terms of both the penetration of the electrons into the bulk and the backscattering of electrons by atoms of different atomic number. The low energy image is different from that obtained using the higher energy incident beam because the thin layer of carbon is penetrated only by the higher energy electrons. We have so far only, in general, considered the penetration of relatively high energy electrons, above 10 keV. However, many techniques detect electrons with energies much lower than this in the region 0 to 2 keV, where the effect of the material on the mean free path of the electrons is much reduced (figure 2.5) (Seah and Dench (1979)). Clearly the mean free path is very short over the whole of this energy region, varying from approximately 0.4 to 300 nm, which is a hundred to a thousand times less than for high energy electrons. Moreover the mean free path of electrons for elements with low atomic number is essentially the same as for elements with high atomic number and the mean free path increases, to a first approximation, as the square root of the electron energy over the range 0.1 to 2 keV. These changes in electron mean free path can be used in many ways to obtain additional microstructural information concerning a surface, but it also indicates the great care that must be exercised when using electrons to probe a material.
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Penetration depths
27
Figure 2.5. Electron mean free path lengths in materials for electrons in the energy range 0 to 2000 eV (Seah and Dench (1979)) (reproduced with permission of John Wiley and Sons).
Since an incident high energy electron beam is scattered as it penetrates a material (figure 2.6), the resolution will be influenced by the spread of electrons around the incident beam. Figure 2.7 is a plot of the intensity of the secondary electrons as a function of distance from the centre of 5 and
Figure 2.6. Schematic diagram illustrating the volume of material that is probed by an incident electron beam together with the volumes from which X-rays and backscattered, Auger and secondary electrons emanate.
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Interaction of radiation with materials
Figure 2.7. The scattered electron distribution following bombardment of gold and aluminium by electron beams of 5 and 50 nm diameter (Seah (1986)) (reproduced with permission of John Wiley and Sons).
50 nm electron beams incident on aluminium and gold. The majority of the electrons come from the area of the incident beam, but a fraction emanate from an area around the incident beam (Seah (1986)). This is the result of electron processes taking place within the material; the scattered secondary electrons are detected up to 2 mm distant from the centre of the electron beam in the aluminium specimen but only 0.2 mm from the centre for the gold. However, the intensity of these scattered electrons is lower in aluminium than gold. In general the scattered electrons will not significantly degrade the image except where the intensity of the scattered electrons makes a significant contribution to the total, as for gold with a 50 nm incident electron beam. However, the scattering of secondary electrons places an ultimate spatial resolution on images that can be obtained in the scanning electron microscope and it is for this reason that the images obtained have generally lower spatial resolution than images obtained using transmission electron microscopy. At the same time a large number of electrons are produced with relatively low energy as the result of atoms being ionised by the removal of electrons from the valence band. In addition, a smaller fraction of atoms are ionised by the ejection of core level electrons and these atoms can rearrange and eject either photons (X-rays) or Auger electrons (see chapter 6). Finally a number of incident electrons may be scattered back towards the specimen surface without losing a significant amount of energy. The Auger electrons are generally confined to energies in the range 0 to 2 keV and escape from the surface only if they emanate from within the top few
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Penetration depths
29
atom layers and laterally not beyond the incident beam diameter. Secondary electrons also have relatively low energies, and although produced by many of the electrons travelling within the subsurface volume those that escape are restricted to the surface volume and to a relatively small distance laterally outside the diameter of the incident beam. It is these electrons that are used to form an image in the scanning electron microscope and as a result the image has a resolution essentially defined by the incident electron beam diameter. The backscattered electrons have high energies, large mean free paths and can originate from a greater depth in the material. They are scattered with components normal to the direction of the incident beam and, therefore, define a volume of diameter that is much larger than that of the incident beam. Finally, the X-rays produced can penetrate much greater distances than electrons and potentially all the X-rays produced which travel towards the surface can escape. Thus X-rays originate from any point that the scattered electrons reach and this defines a volume of excitation. 2.2.3
Neutrons
Although a neutron is approximately one thousand times the mass of an electron and as a consequence is more particle-like, it still possesses sufficient wave character to be diffracted by materials. However, since it does not have an electric charge it is not affected by the electron cloud surrounding the nucleus and on passing through a material effectively interacts only with the atom nucleus. As a consequence neutron penetration distances are much greater than for electrons and even X-rays. The precise penetration depth depends on the atomic species being examined but for most materials neutrons will penetrate distances of several millimetres (Hutchings and Windsor (1986)). Neutrons can be used to study the microstructure within the bulk of a material. 2.2.4
Protons
The interaction of a proton beam with a material has many similarities to the electron but there are some important differences. The proton being charged is influenced by the electrostatic forces within the material but because the mass is 1836 times that of the electron a proton of a few MeV energy has a much greater momentum than electrons of say 50 keV. The proton loses a small fraction of momentum in each atom collision and will not be deviated significantly from the incident beam direction. Therefore protons will travel much farther into a material than electrons of the equivalent energy with little scattering. The stopping power, S, is the term which defines the depth to which protons penetrate a material. The stopping power decreases with increasing proton energy and with increasing atomic number. A 2.5 MeV proton has a range of 55 mm (S ¼ 123 keV mg1 cm2 ) in carbon and a
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Interaction of radiation with materials
Figure 2.8. The stopping power for protons entering aluminium, nickel and silver as a function of incident energy (Ziegler et al (1985)) (reproduced with permission of Pergamon Press).
range of 28 mm (S ¼ 56 keV mg1 cm2 ) in silver. Figure 2.8 shows the stopping power as a function of proton incident energy for aluminium, nickel and silver (Ziegler et al (1985)). Protons are frequently used to excite X-rays in a technique known as particle induced X-ray emission (PIXE) (Johansson and Campbell (1988)) (see chapter 7). 2.2.5
Ions/atoms
It is natural to move on from protons to consider ions. Invariably if ions penetrate a material so much damage occurs that it is more accurate to address the stopping distance rather than a penetration distance. It is perhaps instructive to describe what happens when either an atom or an ion impinges on a surface. At very low energies of a few eV an atom is simply reflected from the surface. When a primary ion of mass M1 and energy E1 impinges on a surface of atoms mass M2 it will be reflected with a kinetic energy E2 determined by the relative masses of the incident and surface atoms and the angle between the incident and reflected atom. Kinetic energy is transferred to the surface atom M2 but the impinging ion does not penetrate into the surface (see chapter 7). At higher energies the atom burrows into the material, causing atoms, atom clusters, ions and ion clusters to be ejected from the surface while, at the same time, atoms are knocked farther into the material (figure 2.9). Here the incident ion of relatively high energy knocks surface atoms farther into the material. These in turn collide with other atoms, establishing a cascade process where atoms collide with one another, and atoms move in both forward and backward directions. Some atoms, and atom clusters, will be ejected both in the
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Penetration depths
31
Figure 2.9. Schematic diagram illustrating the sputtering of ions from a surface during ion bombardment.
ionised and neutral state together with some electrons. The original ion will either come to rest within the body of the material or may be ejected as part of the scattering process. The distance penetrated is determined by the kinetic energy of the incident ion, the atomic number of the ion and the atomic number of the material. Figure 2.10 shows the penetration distance for krypton ions of energies from 5 to 50 keV impinging on germanium (Littmark and Hofer (1980)). Considerable effort has been devoted to the
Figure 2.10. The penetration distance of krypton ions with energies from 5 to 50 keV in germanium (Littmark and Hofer (1980)) (reproduced with permission of North-Holland Publishing Company).
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Interaction of radiation with materials
Figure 2.11. Schematic diagram illustrating the penetration of ions into a solid. R ¼ range and x ¼ penetration depth.
study of implantation of specific atom species into semiconductor materials because of the importance in silicon chip technology. In this example the krypton ions with energies of 5 keV do not penetrate deeper than 13 nm whereas those with 50 keV energy can be implanted to depths greater than 50 nm. Penetration distance and damage cannot be separated for ions. When an ion enters a polycrystalline material it will follow a path which is not necessarily normal to the surface and travel a distance before coming to rest at a point (figure 2.11). The distance travelled by the ion is greater than the range R or the penetration depth x, but cannot readily be measured. It is therefore customary to define the penetration depth, x. The range along the direction of the incident beam is defined as the projected range Rp . Naturally this will vary with the ion and the material but for ions in the energy range 0:002 E 0:1 keV (Schiøt (1972)) is given by 2=3 2=3 2=3 Z1 þ Z2 E ð2:4Þ Rp ¼ C1 ðÞM2 Z1 Z2 where M2 is the atomic mass of the material, E the energy in keV, Z the atomic number and C1 ðÞ is obtained from experimental values shown in figure 2.12. However for ions with energies 0:5 E 10 keV 2=3 2=3 2=3 ðZ1 þ Z2 Þ1=2 E : ð2:5Þ Rp ¼ C1 ðÞM2 Z1 Z2 If the ion enters a single crystal in a direction close to a low index crystallographic axis then the ion will be channelled into that direction so that there will be less deviation from the incident direction and the penetration distance will be considerably enhanced compared with the polycrystalline case.
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Material damage
33
Figure 2.12. Experimental values for C1 ðÞ as a function of for (a) M1 > M2 and (b) M1 < M2 where M1 and M2 are the respective masses of the ions and the parent material (Schiøtt (1972)) (reproduced with permission of Gordon and Breach Science Publishers Ltd).
2.3 2.3.1
Material damage Photons
Generally a photon source is regarded as the least damaging of the analytical probes, but the degree of damage is never zero and can in some instances be quite severe. The photon wave packet will have a momentum determined by either the energy or wavelength. This momentum is clearly small for light quanta and other radiation sources of longer wavelengths such as infrared radiation, microwaves etc. However, one only has to look at the results of leaving the Christmas pudding in a microwave oven too long to realise that the damage is not negligible. In general the damage caused by photons is the result of heating and the degree and extent is determined by the penetration of the photon source into the material, the energy of the radiation and the photon flux (Smith (1971)). X-ray beams can cause the surfaces of certain oxides to be reduced and laser beams can burn holes through metal by heating to temperatures that result in the instantaneous melting and evaporation in the immediate vicinity of the beam. Indeed this is the basis of one technique (laser induced mass analyser (LIMA)) where a small volume of the material surface is vaporised by a pulsed laser beam and the evaporated material is then mass analysed. Figure 2.13 shows the effect of a laser beam used in a laser induced mass analyser on a metal surface. However, most photon sources selected cause very little damage and the surface being
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Interaction of radiation with materials
Figure 2.13. Laser damage on a metal specimen in a laser induced mass analyser (courtesy of M D Crapper).
studied does not alter over very long periods of exposure. As a general rule, if the results for a microstructural investigation can be obtained using a photon source, then this should be used. 2.3.2
Electrons
While electrons are readily described as having a dual wave particle character, their mass allows a considerable momentum, particularly when accelerated to several hundred keV in the transmission electron microscope, to be transferred. Again the resultant damage is related to the amount of energy or heat transferred to the material and to the thermal conductivity of the material. At low incident beam energies atom bonds do not break in the target material, so in general metals and alloys can be examined without any significant degree of damage taking place. However, in the case of oxides and polymeric materials the damage can be considerable. Indeed it is not usually possible to obtain a secondary electron image in the electron microscope from most polymeric materials before they degrade. One approach to obtaining images of these materials can be obtained is to coat the surface with a conducting material such as gold, but this renders any chemical determination almost impossible. Oxides are also damaged by the electron beam although if the oxide layer is thin and in contact with a metal substrate the damage is rarely so great that an image cannot be obtained. Figure 2.14 is an Auger electron spectrum obtained from the surface of a stainless steel which initially contained a thin silicon oxide, SiO2 , layer (Wild (1985)). The top spectrum (a) was recorded using an electron beam of 10 keV and approximately 100 nA current focused into a spot size of 100 nm but rastered over an area of 200 mm 200 mm. The spectrum is typical of that expected from SiO2 with two peaks at 62 and 77 eV. The rastering of the beam was then turned off
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Figure 2.14. The effect of a 10 keV electron beam focused on an SiO2 layer on stainless steel showing reduction of the oxide to silicon (a) rastered beam (b) static beam (Wild (1985)) (reproduced with permission of Pergamon Press).
so that it was stationary when the second spectrum (b) was obtained. Here the spectrum is essentially that from silicon with a peak at 92 eV indicating that most of the oxide has been reduced by the influence of the electron beam. This result indicates oxide reduction caused by electron beam heating and reducing the oxide; the beam does not cause atom bond breaking. A further dramatic demonstration of the heating effect of electrons is shown in figure 2.15 where a metal surface is examined under similar conditions to the previous example. The metal surface has oxide particles loosely adhering and the thermal conductivity between the particles and the metal is poor. In figure 2.15(a) the particle in the centre is rectangular in shape but after this image was recorded the electron beam was focused on the particle
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Interaction of radiation with materials
Figure 2.15. The heating effect of a 10 keV, 5 109 A˚ electron beam on an oxide particle when there is poor conductivity between the particle and the substrate.
to obtain a chemical analysis. Following analysis, the secondary electron image in (b) was recorded and this indicates that the oxide particle, which was a chromium iron oxide, had melted and had been heated to a temperature in excess of 2800 K. We have been considering the damaging effect of electrons in conventional instruments where the incident beam energy does not normally exceed 100 to 200 keV. However, there exist electron beam instruments which use considerably more energetic electrons and these can cause atoms to be displaced from normal lattice positions by the transfer of momentum (Madden et al (1979)). Such damage occurs in the million electron volt transmission electron microscope. Indeed such is the effect at this energy that the microscope is often used to simulate the damage that is caused by fast neutrons in nuclear reactors. Figure 2.16 shows damage that has occurred in a thin foil specimen of stainless steel where voids and dislocation loops have formed by electron interactions. 2.3.3
Ions and atoms
When ions or atoms penetrate a material they either interact in essentially a totally non-damaging manner as in ion scattering spectroscopy (ISS) (Niehus and Baner (1975)) where they interact elastically with the surface or they cause severe damage. Ion damage is effected by displacing atoms from their normal lattice positions and a minimum energy is required by the ion to exceed the binding energy of the atom. In addition a certain amount of energy is required to displace the atom and this varies with the direction of the incident ion relative to the crystallographic directions of the material. However, the threshold displacement energy is some ten times the energy required to break the atom bonds. If the ion has sufficient energy to displace an atom then the total damage caused will be related to the ion energy and
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Figure 2.16. Damage produced in stainless steel foils by 1 MeV electron beams (courtesy J Buswell).
the flux. At a low flux the damage regions are isolated one from the other since the ion produces a region of amorphous material surrounded by regions containing large numbers of defects. As the flux increases so these regions overlap and an amorphous layer is found. The processes involved in ion cascade events are described by Benninghoven et al (1987) and Sigmund (1981). An example of the damage caused by ions penetrating a material is shown in figure 2.17. Here a transmission electron micrograph is reproduced
Figure 2.17. Damage caused in Type 316 stainless steel following bombardment with 4 MeV iron ions at 813 K. Each incident ion displaces five stainless steel ions on average (Ward and Fisher (1992)) (courtesy A Ward).
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Interaction of radiation with materials
showing the damage in Type 316 stainless steel following bombardment with 4 MeV iron ions at 813 K. Here each iron ion causes five displacements in the stainless steel. Ion penetration depth varies with ion energy and with ion species. Ions will be stopped over a range of distances and the penetration distance is normally defined as the maximum in the implantation profile, i.e. the stopping distance for the largest number of ions.
2.4
Resolution
In the earlier sections of this chapter we discussed the penetration of various types of radiation into materials. This determines the depth resolution and will have a distinct bearing on the spatial resolution that is obtainable for investigating microstructural features. The resolution normal to the direction of the incident beam, frequently referred to as spatial resolution, is influenced by the diameter of the incident beam, the wavelength of the incident radiation and the mean free path of the incident beam in the material. An image of an object can be obtained in two basic ways. One method is to illuminate the object over its entire surface by using a suitable source of radiation (photons, electrons or ions) and then use a lens arrangement to form an image by focusing the radiation that is either reflected or emitted from the object. This is achieved such that a point on the object is focused to an equivalent point on an image plane. In such systems the spatial resolution is determined by the lens system and the wavelength of the emitted or reflected radiation. In general optical microscopes, certain X-ray microscopes and some ion microscopes operate in this way. The second method is to direct a very narrow beam of radiation on to the object and to detect either the absorbed or reflected radiation. The incident beam is rastered over the object surface and changes that occur in absorption and reflection allow an image of the surface to be built up. In these cases the spatial resolution is determined by the diameter of the incident beam, the wavelength of the incident radiation, and the scattering of the incident radiation within the object surface. Most electron and ion optical instruments form their image in this way although the advent of lasers has meant that some light microscopes also use this method. Details of the resolution achieved for the specific techniques is discussed in the following chapters where each technique is discussed.
2.5
Loss processes
The previous part of this chapter has been concerned primarily with processes which describe how photons, electrons, neutrons, atoms and ions interact with, and can be used to give images of, the surface and bulk
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materials. We now move on to describe the interactions of these particles with the material and how processes transfer energy to the material under investigation. This energy transfer is used to determine information concerning the type of atom, its environment or chemical state. Any process that involves the incident beam surrendering some energy is described as a loss process. We will attempt to identify the loss processes that are currently utilised to characterise the microstructure of a material. Most, although not all, of the techniques mentioned briefly here will be described in more detail in later chapters. 2.5.1
Photons
Very long wavelengths (>1 mm) (including radio and micro-waves) A molecule with either a magnetic nucleus or an unpaired electron will have nuclear and electron energy levels that can be influenced by a magnetic field. The magnetic field, B, causes the electron to take up new quantized values of ð12Þðh=2pÞ, where h is the Plank constant, and with each of these is associated an energy level, one above and the other below the original energy level. The separation of these energy levels is B, where is the magnetic dipole moment, and this is linearly dependent on the magnitude of the applied magnetic field, B. By combining a magnetic field with an appropriate electromagnetic radiation, transitions between the two energy levels can be induced. With magnetic fields that can be applied routinely to materials it is necessary to use radio-frequency waves to excite the nuclear magnetic resonance (NMR) (Akitt (1983) and Cudby and Williamson (1990)) and micro-waves to excite the electron spin resonance (ESR) (Symons (1978)) and electron paramagnetic resonance (EPR) (Thomson (1990)). The magnetic moments of certain nuclei also interact with the unpaired electron to produce additional fine structure on the major resonance. This technique has been used extensively to study kinetic processes in organic material reactions and to follow catalytic reactions. NMR has been used to determine the structure of organic materials, and degradation in microstructure of resins, rubbers and other hydrocarbons under certain conditions. Long wavelengths As considered in chapter 1, materials are composed of atoms bonded together where the distance between the ions is determined by a balance between the attractive long range interactions of the ions with charge þq and the repulsive short range interactions between the ion cores. If given sufficient energy the atoms are able to vibrate and this process can be visualised by imagining the atoms as hard spheres connected by springs. The simplest case is to consider two atoms connected together and, by applying Hookes’s law for elastic expansion under a force, the frequency
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Interaction of radiation with materials
of vibration of the two atoms, , is given by 1 Fc 1=2 ¼ 2c M0
ð2:6Þ
where c is the velocity of light, Fc is the force constant of the atom bond and M0 is the reduced mass of the system given by M0 ¼
M1 M 2 M1 þ M 2
ð2:7Þ
where M1 , M2 are the masses of the two atoms. When a material is illuminated with light then the wavelengths which correspond to the vibrational frequencies are absorbed. This simplistic approach produces surprisingly good agreement between theory and experiment with the vibration frequencies for, say, a hydrogen atom bound to carbon being fairly well predicted. As the complexity of the molecule increases so the number of vibration frequencies increases. A nonlinear molecule containing n atoms has 3n degrees of freedom and 3n-6 vibrational modes each with a characteristic band frequency. As the molecule becomes more complicated with atoms bound to more than one atom and when there are nonlinear chains of atoms, vibrations can take place in directions with components normal to the bond direction. The vibrations in the direction of the bond are referred to as stretching vibrations while those normal to the bond direction are known as bending or deformation vibrations. Figure 2.18 illustrates some of the different ways a molecule can vibrate (Cross (1960)). These vibrations may be determined by observing the absorption of infrared radiation either
Figure 2.18. Some of the possible molecular vibrations for two identical atoms bonded to a third dissimilar atom.
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in the transmission or reflection mode. This, in turn, permits substances to be identified and molecular structure to be determined and allows reaction kinetics to be studied. Infrared spectroscopic techniques (Herzberg (1945) and Wilson et al (1955)) use radiation with wavelengths from approximately 1 mm (wave number 104 cm1 ) to 1 mm (wave number 10 cm1 ) to study these vibrational absorption bands. The wave number has been quoted here because it is conventional, in infrared spectroscopy, to refer to the wave number rather than the wavelength; the wavelength, , and wave number, , are related by ¼ 1=. There are now many cases where lasers are being used to provide the source of infrared radiation with the advantage that high intensities are confined to relatively small areas with the associated improved spatial resolution. Intermediate wavelengths (including visible and ultraviolet light) As wavelength is decreased so the energy available to excite an atom increases until a stage is reached where it becomes possible to raise electrons from their ground state to higher electron orbitals (Rao (1961)). The binding energies of electrons in atoms are specific to a particular element and by determining the difference in energy between two electron levels, by measuring absorption lines, it is possible to identify the type of atom. Consider the hydrogen atom illustrated in figure 2.19 which contains a series of energy levels where electrons may be present or absent. The energy levels are filled from the lowest level in pairs, one with spin up and one with spin down, until all the lowest levels are filled. Energy may then be given to the electrons in the outermost orbits which may be excited to higher levels. The effect of
Figure 2.19. Energy levels and possible transitions in the hydrogen atom.
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Interaction of radiation with materials
Figure 2.20. The hydrogen spectrum showing characteristic absorption bands.
this on a beam of white light is to absorb light of frequency, , since: h ¼ E1 E2
ð2:8Þ
where E1 and E2 are the initial and final electron levels. Thus a beam of white light when passed through a gas or material will have a series of missing wavelengths corresponding to the difference in electron binding energies of the atoms. By measuring the wavelengths of the absorption band the atom type can be identified. Absorption bands have been catalogued according to the lowest energy level which takes place in the absorption. Those in which the quantum number of the lowest level is 1 are referred to as the Lyman series, for n ¼ 2 the Balmer, n ¼ 3 the Paschen and n ¼ 4 the Brackett. The atom that has been excited by an electron being transferred to a higher orbital will subsequently decay to the original ground state by the emission of light. The decay may be by a direct transition to the original electron energy level or it may be by a series of transitions. Thus a spectrum is observed which contains a number of discrete lines. Figure 2.20 shows an absorption spectrum for hydrogen and shows the Balmer series of absorption bands which gradually close together as the quantum number n increases. In practice visible and ultraviolet radiation is used to study the electron energy levels of the outer shell electrons because the energy supplied by the incident radiation is insufficient to excite core level electrons from most elements to the next highest state. When light is incident on a material certain resonance frequencies are absorbed in raising the atom to an excited state. When the atom decays that same frequency may be re-emitted in a random direction and not necessarily in the direction of the incident beam (Baranska et al (1987), Clark and Hester (1983–5) and Andrews and McCoustra (1990)). This is known as Rayleigh scattering. However, the material illuminated will contain electron energy levels at both higher and lower energies than the energy level of the electron that was initially excited. These energy levels may be unfilled because they too may have been excited to higher levels. The atom may, therefore, decay by the excited electron falling into one of these other energy shells effecting emission of radiation at both higher and lower frequencies than the Rayleigh line. These lines are known as Stokes (at lower energies than Rayleigh) and anti-Stokes (at higher energies than
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Figure 2.21. Processes involved in Rayleigh and Raman radiation and the production of Stokes and anti-Stokes lines.
the Rayleigh line) while the effect is known as the Raman effect (figure 2.21). The effect is most easily observed if a material is illuminated with an intense beam of radiation. Lasers are therefore used to illuminate materials in the technique of laser Raman spectroscopy, which provides information concerning the electron energy levels in atoms which constitute the material with relatively good spatial resolution (Baranska et al (1987)). Short wavelengths (1012 to 109 m) (including ultraviolet excitation) In the previous section we considered the absorption of infrared and light radiation which has an intermediate wavelength and hence low energy and does not have sufficient energy to excite core-level electrons to higher orbits. However, as the wavelength of the incident radiation is decreased so the number of energy levels available for excitation increases and electrons positioned closer to the nucleus of the atom may be excited. The energy of light and ultraviolet radiation is sufficient to excite energy levels in materials of low atomic number but for higher atomic number elements it is capable of exciting only outer shell and valence electrons. However, if the material is bombarded with X-rays then many of the core shell electrons can be excited and will, in most cases, be given sufficient energy to be ejected from the atom (see the photoelectric effect below). The atom then rearranges, with the electrons falling into the hole created by the initial excitation, and energy is released as a photon or by the emission of an Auger electron (see below). The energy of this photon is determined by the difference in the
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Interaction of radiation with materials
electron energy levels E1 , E2 by the expression h ¼ E1 E2 . This is the basis of X-ray fluorescence (XRF) spectroscopy where the material is bombarded with a beam of X-rays and the emitted X-ray energy is measured using a either a wavelength dispersive or energy dispersive analyser. In the previous section we have described how photons may excite electrons to higher energy levels. However, as the energy of the photon increases it may supply sufficient energy to the electron such that it overcomes the work function of the material and eject the electron into the vacuum. This is known as the photoelectric effect. The energy of the ejected photon is given by E ¼ h EB
ð2:9Þ
where EB is the electron binding energy of the ejected photoelectron and is the work function of the material. If the energy of the incident photon is known, the energy of the photoelectron is measured then the work function allows the binding energy of the electron in the atom to be determined. Therefore an atom can be identified and this is the basis of ultraviolet photoelectron spectroscopy (UPS) (Williams (1977)) and X-ray photoelectron spectroscopy (XPS) (Briggs and Seah (1990) and Rivie`re (1990)) described in chapter 5. Following ionisation of the atom by the incident photon, the atom will decay to the ground state either by the emission of a photon or by ejecting an electron. In the first case an electron in a higher orbital will fall into the hole created by the initial ionisation event with the emission of a photon of a wavelength determined by the difference in energy of the two electron energy levels, while in the second case an Auger electron is ejected. Emissions of longer wavelengths resulting from a sequence of decays is also possible as the atom rearranges. The process in which an Xray ionises the atom and an X-ray photon is emitted is known as X-ray fluorescence (XRF). In 1925 Pierre Auger (1925) was studying cosmic ray tracks in a Wilson cloud chamber and realised that certain tracks could be explained only if the ionised atom was decaying by emitting another electron. This process has since become known as the Auger effect and the emitted electron as the Auger electron. Here the atom is ionised and rearranges with an electron from an outer electron shell falling into the hole created by the initial ionisation, but, instead of the energy being emitted as a photon, it is transferred to a third outer shell electron that is then ejected. The energy of the ejected Auger electron is determined by the binding energies of the electrons which take part in the process and is given approximately by the equation EAuger ¼ E1 E2 E3
ð2:10Þ
where E1 , E2 , E3 are the energies of the electron shells taking part and is the work function.
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Very short wavelengths (<1012 m gamma rays) In 1958 R L Mo¨ssbauer (1958, 1964) discovered nuclear gamma ray resonance in a solid and this technique has become a popular method for studying both composition and crystal structure. The basic principle of the method involves processes that occur when an atom emits a gamma ray (Long (1984), Frauenfelder (1962) and Wertheim (1964)). When atoms decay by the emission of either a photon or an electron, momentum is transferred to the emitted particle and to conserve momentum in the system the atom must recoil in the opposite direction. This is manifested by induced lattice vibrations or heating within the material. However, the quantum theory states that the energy states within an atom are not continuous but increase in discrete steps. If an atom is, say, in a ground state it can increase to the next level only if it receives an amount of energy equal to or greater than the difference between the ground state and the next energy level. The momentum of the photon emitted from the atom may be less than the quantum of energy required to excite the lowest energy level to the next highest. As a consequence there is a finite probability that the gamma ray will not lose energy and the event will be recoil-free. Similarly a gamma ray has a finite probability that it will be absorbed in a recoil free event by an atom. If energy is not lost by emission or absorption then the associated lines may overlap to allow nuclear gamma ray resonance. In the event that the emission and absorption lines do not overlap it is possible to bring them into coincidence by moving the emitter or absorber relative to one another and utilising the Doppler shift to vary the frequency of the gamma ray. This technique, described in more detail in chapter 5, is used to identify the environment of atoms in materials in which the Mo¨ssbauer effect occurs. While iron is the most commonly studied metal there are many others which have been utilised.
2.5.2
Electrons
In many respects the loss processes involving electrons have many similarities with higher energy photon loss processes. When an electron impinges on an atom in a material it may interact with that atom to either excite an electron in the atom to a higher orbital or give an electron in the atom sufficient energy to escape. In the former case the incident electron will lose a discrete amount of energy equal to the difference in binding energy of the two electron energy shells involved. By measuring the amount of energy the incident electron has lost, the difference in electron binding energies may be determined. This is utilised to identify the atoms causing the energy loss in a technique known as electron energy loss spectroscopy (EELS) (Ibach and Mills (1982), Joy (1979)). If the electron is ejected, however, the incident
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Interaction of radiation with materials
electron will lose energy that is equal to or greater than the binding energy of the electron in the atom. Thus the energy loss spectrum of the incident electron appears as a series of edges with tails to higher electron energies. It is frequently used in conjunction with the transmission electron microscope to determine the presence and concentration of elements of low atomic number. Ionisation with photon emission We have described the effect of excitation or ionisation on the incident electron, but following the initial excitation, processes take place within an atom which are identical to those described in the section dealing with photons. Clearly in the excited or the ionised condition the atom contains an inner electron shell with a hole and the atom can relax by an electron from an outer orbital falling into this hole. When this occurs an amount of energy is released, equal to E1 E2 , as a photon. By determining the energy of the photon the type of atom may be identified. The photon energy may be measured using a Li drifted silicon crystal in a technique known as energy dispersive X-ray (EDX) spectroscopy (chapter 6) or by using single crystals to determine the wavelength and hence wavelength dispersive X-ray (WDX) spectroscopy (Gilfrich (1974). Ionisation with Auger electron emission There is another way in which the ionised atom can decay, that is with the emission of an Auger electron in exactly the same manner as described for the photon ionised atom. In this process the atom relaxes by an electron from a higher orbital falling into the hole created by the initial ionisation
Figure 2.22. The probability that an atom will decay with the emission of a photon or an Auger electron for K and L shell electrons.
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process in the same manner as electron fluorescence. However, instead of the energy being released as a photon, it is transferred to an electron in an outer orbital which may have sufficient energy to escape from the atom. This electron is known as the Auger electron and has an energy given by equation (2.10). The probability, W, that the atom will decay with the emission of a photon or an electron is given by (Burhop (1952)) W ¼ ð1 aZ 4 Þ1
ð2:11Þ
where a is a constant and Z is the atomic number. This function is plotted in figure 2.22 for both K and L shell electrons. For elements of low atomic number the predominant form of decay is by Auger emission but as the atomic number of the element increases so the likelihood of Auger emission decreases and photon emission increases.
2.6
Atom and ion processes
Finally we turn to the interaction of atoms and ions with materials. Compared with the photon and electron beams, an atom or ion is massive and the wave nature may effectively be ignored and the atom or ion can be treated by Newtonian mechanics. 2.6.1
Scattering
Ions with very low energy can be elastically scattered from a material surface as shown schematically in figure 2.23. If the incident ion has a mass M1 and an energy E1 and is scattered through an angle such that, after deflection by atoms of mass M2 , it will lose energy. The energy of the deflected ion, E2 , is, for the case when M2 > M1 , given by E2 ¼
½M1 cos þ ðM22 M12 sin2 Þ1=2 2 E1 : M2 þ M 1
ð2:12Þ
When ions of higher energy impinge on a surface, considerable damage occurs by inelastic scattering. The ion will embed into the surface, knocking atoms of the material in random directions. Some of the initial momentum will be transferred to ions, or ion clusters, in a backwards direction. A proportion of these are ejected from the surface together with electrons. The electron current can be detected in a similar manner to the scanning electron microscope and an image built up or the ions can be mass analysed and the composition and chemical form of the material determined. Atoms will be ionised and will decay with the emission of photons and Auger electrons which may be detected and analysed in exactly the same manner as for photon and electron ionisation described above.
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Interaction of radiation with materials
Figure 2.23. Elastic scattering of ions of mass M1 by a surface composed of atoms of mass M2 .
2.7
Effect of high electric fields
There are a few techniques that utilise the effects of high electric fields to obtain microstructural information concerning materials. In order for electrons to leave an atom they have to surmount a potential barrier, V. If an electrostatic potential is applied to the specimen both the shape and height of the barrier are modified as shown in figure 2.24. The field at certain points can be made very large by appropriate specimen design such that electrons can be induced to leave the surface in a technique known as field emission microscopy (FEM) (Muller (1956)) and in related techniques atoms near the surface may be ionised and accelerated to form an image in field ion microscopy (FIM) (Kane (1979), Muller and Tsong (1969) and Panitz (1982)) while individual atoms may be induced to desorb from the surface and are subsequently identified using a mass spectrometer in atom probe microscope (Muller et al (1968)). When two conducting materials are separated by an insulator the insulator acts as a barrier to the flow of electrons. This is because the electron shells in the insulator are completely full or empty and the requirement for conduction that one or more electron shells be only partially full is not satisfied. If an electron from a full shell can surmount the potential barrier then the material acts as a conductor. There is a finite probability that an electron that does not have sufficient energy to surmount the potential barrier may ‘tunnel’ through it. A similar phenomenum occurs with electron tunnelling through a thin insulating layer. If the distance between two conductors is
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Figure 2.24. Potential energy curves for an atom (a) and an atom in the presence of a field (b).
sufficiently small, typically 1 nm, then there is a significant probability that the electron will pass through the barrier. This phenomenon, known as electron tunnelling, is utilised in the scanning tunnelling microscope (STM) (Bessenbacher et al (1989)) and can be used to identify surface features to a sub-atomic spatial resolution.
2.8
Acoustic phenomena
Before leaving this chapter acoustic waves should be mentioned. These waves travel through a solid medium by exciting vibrations in the material. Imperfections in the lattice, such as strain fields, particles, voids and cracks, will interact with the acoustic wave and, by detecting the scattered wave, information relating to the imperfection can be obtained. Acoustic waves range from the relatively long sound waves to the much shorter ultrasonic waves. The long wavelength waves will penetrate many centimetres into a solid and can detect, non-destructively, defects buried in the bulk. However, the long wavelength results in poor spatial resolution. On the other hand, the short wavelength ultrasonic energy can have much better spatial resolution but is absorbed more rapidly. Acoustic phenomena are often combined with other techniques to obtain additional information concerning a solid (Smith (1986) and Briggs (1985)). An example is the use of a laser to scan a surface while the reflected light is detected and simultaneously the acoustic wave transmitted through the solid defects below the surface may be detected
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Interaction of radiation with materials
Figure 2.25. A secondary electron image (SEI) and its corresponding electron acoustic image (SEAM) (reproduced by permission of Cambridge Technology Ltd).
in a technique known as scanning laser acoustic microscopy (SLAM). Similarly when an electron beam is rastered over a material surface, as in the scanning electron microscope, acoustic waves are generated and travel through the material. By detecting the acoustic waves, flaws in the solid may be identified. This technique is known as scanning acoustic electron microscopy (SEAM) and is used to identify regions in the material for study by other techniques. Figure 2.25 shows a secondary electron image together with the electron acoustic image from the same area where subsurface defects have been resolved.
2.9
References
Akitt J W 1983 NMR and Chemistry 2nd edition (London: Chapman and Hall) Andrews D L and McCoustra M R S 1990 in Perspectives in Modern Chemical Spectroscopy (Berlin: Springer) ch 8 Auger P 1925 J. Phys. Radium 6 205 Baranska H, Labudzinska and Terpinsk J 1987 Laser Raman Spectroscopy; Analytical Applications (Chichester: Harwood) Benninghoven A, Rudenauer F G and Werner H H 1987 Secondary Ion Mass Spectrometry (New York: Wiley) Bessenbacher F, Laegsgaard E and Stensgaard I 1989 Microscopy and Analysis July 17 Briggs D and Seah M P 1990 Practical Surface Analysis 2nd edition vol 1 (Chichester: Wiley) Briggs G A D 1985 An Introduction to Scanning Acoustic Microscopy (Oxford: Oxford University Press) Burhop E S 1952 The Auger Effect (Cambridge: Cambridge University Press) Castaing R 1960 Adv. Electron. Electron Phys. 13 317 Cazaux J 1982 J. Appl. Surf. Sci. 10 124
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References
51
Clark R J H and Hester R E ed 1983–5 Advances in Infra-Red and Raman Spectroscopy (Chichester: Wiley) Cross A D 1960 Practical Infra-Red Spectroscopy (London: Butterworths) Cudby M E A and Williamson D J 1990 Multinuclear High Resolution NMR in Solids, in Perspectives in Modern Chemical Spectroscopy ed D L Andrews (Berlin: Springer) ch 7 Cullity B D 1979 Elements of X-ray Diffraction (Reading, MA: Addison-Wesley) ETP Semra Pty. Ltd. 1990 Technical Bulletin March 3 Frauenfelder H 1962 The Mo¨ssbauer Effect (New York: W A Benjamin) Gilfrich K V 1974 in Characterisation of Solid Surfaces ed P F Kane and G B Larrabee (New York: Plenum Press) ch 12 Hertzberg G 1945 Infra-Red and Raman Spectra of Polyatomic Molecules (New York: Van Nostrand) Hutchings M T and Windsor C G 1986 in Neutron Scattering ed K Skold and D L Price (London: Academic Press) ch 25 Ibach H and Mills D L 1982 Electron Energy Loss Spectroscopy and Surface Vibrations (New York: Academic) Johansson S A E and Campbell J L 1988 PIXE: A Novel Technique for Elemental Analysis (Chichester: Wiley) Joy D C 1979 in Introduction to Analytical Electron Microscopy ed J J Hren, J I Goldstein and D C Joy (New York: Plenum Press) Kane P F 1979 in Introduction to Analytical Electron Microscopy ed J J Hren, J I Goldstein and D C Joy (New York: Plenum Press) ch 6 Littmark U and Hofer W O 1980 Nucl. Instrum. Meth. 170 177 Long G J ed 1984 Mo¨ssbauer Spectroscopy Applied to Inorganic Chemistry vol 1 (New York: Plenum Press) Madden P K, Buswell J T and Fisher S B 1979 CEGB Report RD/B/N4568 Mo¨ssbauer R L 1958 Z. Phys. 151 124 Mo¨ssbauer R L 1964 Recoiless nuclear resonance absorption of gamma radiation in Nobel Lectures 1961 Laureates, Biographies and Presentation Speeches (Amsterdam: Elsevier) p 583 Muller E W 1956 Field emission microscopy in Physical Methods in Chemical Analysis vol III ed W G Bel (New York: Academic Press) p 135 Muller E W, Panitz J A and McLane S B 1968 Rev. Sci. Instrum. 39 83 Muller E W and Tsong T T 1969 Field Ion Microscopy (New York: Elsevier) Niehus H and Baner E 1975 Surf. Sci. 47 222 Panitz J A 1982 J. Phys. E: Sci. Instrum. 15 1281 Peiser H S, Rooksby H P and Wilson A J C 1960 X-ray Diffraction by Polycrystalline Materials (London: Chapman and Hall) Rao C N R 1961 Ultra-Violet and Visible Spectroscopy (London: Butterworths) Rivie`re J C 1990 Surface Analytical Techniques (Oxford: Clarendon) Schiøt H E 1972 Radiat. Eff. 14 39 Seah M P and Dench W A 1979 Surf. Interface Anal. 1 2 Seah M P 1986 Surf. Interface Anal. 9 85 Siegbahn K ed 1965 Alpha-, Beta- and Gamma-Ray Spectroscopy (Amsterdam: NorthHolland) Sigmund P 1981 in Topics in Applied Physics 47 Sputtering by Particle Bombardment I ed R Behrisch (Berlin: Springer) Smith D P 1971 Surf. Sci. 25 335
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Interaction of radiation with materials
Smith G C 1986 Mater. Sci. Technol. 2 881 Symons M 1978 Electron Spin Resonance Spectroscopy (New York: Van Nostrand Reinhold) Thomson A J 1990 Electron paramagnetic resonance and electron nuclear double resonance spectroscopy in Perspectives in Modern Chemical Spectroscopy ed D L Andrews (Berlin: Springer) ch 12 Wertheim G K 1964 The Mo¨ssbauer Effect: Principles and Applications (New York: Academic Press) Ward A and Fisher S B 1992 Proceedings of the 15th International Symposium on Effects of Radiation on Materials (Nashville) eds R E Stoller, A S Kumar and D S Gellos (Philadelphia: ASTM) Wild R K 1985 Spectrochimica Acta 40B 827 Williams P M 1977 in Handbook of X-Ray and Ultraviolet Photoelectron Spectroscopy ed D Briggs (London: Heyden) ch 9 Wilson E B, Decius J C and Cross P C 1955 Molecular Vibrations—The Theory of InfraRed and Raman Spectra (London: McGraw-Hill) Ziegler J F, Biersack J P and Littmark U 1985 The Stopping Range of Ions in Solids vol 1 (New York: Pergamon Press)
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Chapter 3 Vacuum systems 3.1
Introduction
Within the wide variety of techniques for characterising the microstructure of materials, some operate using a relatively simple environment such as the normal atmosphere whereas others require sophisticated containment systems usually to produce extremely good vacuums. For example, simple electron microscopes operate with a vacuum that is less than 102 Pa and, indeed, with the addition of sophisticated analytical attachments such as windowless spectrometers there is now a trend to achieve pressures of 105 Pa or better. Any technique that is required to analyse a surface either chemically or crystallographically is compelled to operate with vacuums in the region 107 to 109 Pa. Figure 3.1 indicates some of the techniques that are currently available for microstructural evaluation and their vacuum requirements. Since so many methods of characterising material microstructure require the production of high and ultra-high vacuums (UHV) we will describe the various methods for producing, containing and measuring vacuums (O’Hanlon (1989), Leybold (1987)).
3.2
Kinetic theory of gases
We do not propose to describe the kinetic theory of gases in detail, but since a number of conclusions of the theory are essential for determining the requirements for various instruments we will set out the basic elements of the theory. For a more thorough description the reader is referred to Dushman (1962), Weber (1968) and Diels and Jaeckel (1966). In essence the kinetic theory of gases is the result of theoretical considerations concerning the movement of discrete particles between which no forces are acting. The number of particles, atoms or molecules, per unit volume or density, , their speed, c, and their molecular mass, M, determine the pressure, p, within a system where the pressure is related to the number of molar particles, n, in unit volume, V, and the temperature, T, by the
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Vacuum systems
Figure 3.1. Pressure regions based upon existing terminology and their relationship to some common microstructural evaluation techniques.
ideal gas equation PV ¼
nkT NA
ð3:1Þ
where k is the Boltzman constant and NA is the Avogadro number (k ¼ R=NA ; where R is the molar gas constant). Two measures of the speed of the particles are used: the mean particle velocity, v, and the mean square velocity, v2 , which are given by rffiffiffiffiffiffiffiffiffi 8kT ð3:2Þ v ¼ M and v2 ¼
3kT : M
ð3:3Þ
The pressure in the system is given by v2 ¼ 13 nM v2 : P ¼ 13
ð3:4Þ
The particles travel in straight lines until they collide with the walls of the vessel or other particles. The collision rate, n_ , is defined as the number of collisions per second and the mean free path, l, is the distance a particle travels, on average, between two collisions. These are given by equations n_ ¼ v=l ð3:5Þ l ¼
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2
1=2
1 nð2rÞ2
ð3:6Þ
Production of vacuum
55
where r is the particle radius. Thus the mean free path length is inversely proportional to the number density and to the pressure. The impingement rate is of considerable interest when evacuating a system since it determines the contamination rate of a surface of the containing vacuum chamber or that of the specimen being examined. The impingement rate, N_ , of particles on to a surface is given by n v ð3:7Þ N_ ¼ : 4 The length of time that is required to contaminate a specimen is often referred to as the time to form a monolayer of containing environment particles on a clean surface. If all the particles that strike a surface stick to that surface, i.e. the sticking probability is unity, and if the number of free spaces per unit of surface area, A, then the time to form a monolayer ðÞ is ¼
A 4A ¼ n v N_
ð3:8Þ
Substituting in the above gives the monolayer time in terms of pressure, molecular mass and temperature. If the pressure, , is measured in Pascals the time, in seconds, to completely cover the surface with a single layer of oxygen at room temperature is ¼
5 104
ð3:9Þ
Thus if a specimen is examined in a vacuum of 5 104 Pa, a surface will be completely covered by the containing environment particles in one second. In practice to obtain a chemical analysis of a surface it is necessary to keep the specimen under investigation relatively free from contamination for a period of say one hour. To achieve this it is necessary to produce a vacuum that is in the region of 108 to 109 Pa. Typical growth rates for various gases as a function of gas pressure assuming a sticking coefficient of unity are reproduced in figure 3.2. In practice sticking coefficients are often less than unity, particularly for inert gases and for active gases on oxide surfaces. In addition many analytical techniques sample from many thousands of atom layers, and in such cases the build up of one or two atomic layers of contaminant would not degrade the results significantly. Thus UHV conditions, whilst required for certain surface analytical techniques, are not used in all cases because a balance is required between the practicality of achieving the vacuum and the ability to produce the required accuracy of the analysis.
3.3
Production of vacuum
There are two stages in the production of a vacuum. First, a vessel must be constructed from materials that do not outgas significantly compared with
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Vacuum systems
Figure 3.2. Rate of contamination of a surface, assuming a sticking coefficient of unity, as a function of pressure for some common gasses.
the speed of the vacuum pumps. Second, design is such that it does not permit gas to enter from the outside atmosphere, either by diffusion through the walls or by leaking passed seals. The chamber must then be evacuated to the desired pressure by pumps that do not introduce any deleterious gases into the chamber whilst removing the original atmosphere. We will first describe the construction of vacuum chambers and then typical pumping systems available. 3.3.1
Construction of vessels
Materials used in the construction of vacuum systems must be readily available, capable of being machined and have low rates of outgassing under the conditions of use. The outgassing rates for a number of common metals as a function of temperature are given in figure 3.3. Materials may have to operate at elevated temperatures and these must clearly have a very low saturation vapour pressure at the temperature of operation. Cadmium and magnesium have relatively high vapour pressures and should not be introduced into systems that operate above room temperature. Indium, copper and gold are all ductile materials and are often used as seals between components, although indium should only be used at room temperature or below. Gold is clearly preferable to indium from the outgassing properties but indium is cheaper and normally acceptable. Iron and steels all have low vapour pressures at temperatures between room temperature and 600 K and are suitable for construction of vessels. Many applications, particularly electron optical and others, where the beam used to interrogate the material is influenced by a magnetic field, require that the containment vessel be manufactured from non-magnetic material. In such cases an
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Production of vacuum
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Figure 3.3. Outgassing rates of some common elements as a function of temperature.
austenitic stainless steel (usually AISI Type 304) is adequate although for specialised applications other materials, for example Invar, which has a low coefficient of expansion and has magnetic properties, is used where the effect of external magnetic fields must be reduced. Filaments for ionisation gauges are normally made from tungsten, which may be thoriated to increase the electron emission yield while reducing the operating temperature. Windows are manufactured from quartz or silica and when it is necessary to mount these in stainless steel a graded seal is added between the main part of the window and the metal. A graded seal is constructed of materials that have thermal expansion coefficients ranging from that of the window to that of the steel to prevent the build-up of thermal stresses when the system is heated. Electrical connections are frequently manufactured from tungsten and set in a ceramic graded seal that is bonded to the steel flange. Outgassing of components is reduced by giving the steel a fine ideally polished surface finish. This effectively reduces the surface area and hence the area available for adsorption of gases. A low pressure oxidation to produce a thin chromium-rich surface oxide on stainless steel can also help to reduce the outgassing rates. Transfer of heat is best carried out using components constructed from copper and insulated using a combination of ceramics and stainless steel. The production of ultra-high vacuum requires the entire vacuum system to be baked to a temperature between 400 and 500 K to drive off adhered gases from the component surfaces and chamber walls and hence reduce the outgassing rate when the system is operated at room temperature. Vacuums better than 106 Pa can rarely be achieved without baking and, therefore, considerable thought has to be given to the choice of materials used in their construction.
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58 3.3.2
Vacuum systems Medium to high vacuum (102 to 105 Pa)
These are vessels which normally contain equipment designed primarily for bulk specimen examination and analysis. This would involve the analysis of layers greater than a few hundred nanometres thick where a few atom layers of contamination is not a serious problem. Transmission electron microscopes, scanning electron microscopes, ion source and some plasma research instruments are in this category. The bulk of these instruments are constructed from a range of steels including stainless and often contain large electromagnetic lenses for focusing the incident electron beams which travel down a narrow column. These components are, in general, not capable of being heated and as a result outgassing is relatively high. Sections of the instrument are connected by ‘O’ rings made from a synthetic rubber compound such as Viton. The ‘O’ rings may require sealing with a vacuum grease which, in turn, may outgas hydrocarbons into the system.
3.3.3
Ultra-high vacuum (106 to 109 Pa)
Ultra-high vacuum is obtainable using current technology and is required for all the surface analytical techniques such as low energy electron diffraction (LEED), X-ray photoelectron spectroscopy (XPS), Auger electron spectroscopy (AES), secondary ion mass spectroscopy (SIMS), secondary neutral mass spectroscopy (SNMS), field ion microscopy (FIM) and the atom probe. The objective is to create an environment with as low a pressure as possible and with the residual partial pressures being composed primarily from inert gases. Such vessels are manufactured from a Type 304 stainless steel and the whole vessel would be capable of being baked at temperatures about 500 K to drive off any adsorbed water vapour and reduce outgassing. Thus ‘O’ rings that require grease cannot be used and Viton ‘O’ rings are avoided wherever possible. Sections of the system that require connecting together are joined in one of two ways shown in figure 3.4. The cheapest and easiest is to use the knife-edge copper gasket system (figure 3.4(a)). In this method a knife-edge shaped in the form of a tilted ‘V’ is machined on to each of the faces to be joined in such a way that the top of the knifeedge is approximately 1 mm below the level of the flange edges. An annealed copper gasket is then positioned between the two knife-edges which are tightened using a series of bolts. The knife-edge cuts into the copper gasket making a good vacuum seal. The alternative method is to machine flat surfaces on to the flange and to position an annealed gold, or in some cases an aluminium or indium, ‘O’ ring between the flanges. The two flanges are then tightened down, compressing the ‘O’ ring and making a good vacuum seal. The gold ‘O’ ring approach is generally used where the flange diameter is large, normally 400 mm or greater, or in situations where the seal is intended to remain undisturbed. The copper gasket type
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Figure 3.4. Methods for connecting rigid components to construct UHV vessels: (a) copper gasket, (b) gold ‘O’ ring.
of seal has the advantage that it is cheap and easy to replace, particularly where the flange is vertical or at an angle to the horizontal. Components, such as specimen stages and x–y–z position manipulators, require to be moved within the vacuum chamber and the motion must be transmitted through the vacuum walls. This is effected by a series of edge-welded stainless steel bellows (figure 3.5). This method of construction of ultra-high vacuum systems leads to a characteristic design of instruments.
Figure 3.5. The use of edge-welded stainless steel bellows to translate motion to a UHV system.
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Vacuum systems
Figure 3.6. A typical UHV system constructed in stainless steel and fitted with all-metal seals.
One such system (figure 3.6) is a multipurpose instrument designed to use the techniques of Auger electron spectroscopy, X-ray photoelectron spectrscopy and secondary ion mass spectroscopy to study material surfaces. The characteristic feature of the construction is the few interconnecting chambers with many removable ports. Instruments tend to be made with the maximum number of optional ports included, since the cost of incorporation at the manufacturing stage is low but at a later date would prove difficult and expensive and this offers maximum flexibility for future applications. In the example shown the right-hand chamber houses all the analytical techniques while the chamber to the left contains the preparation equipment. This particular instrument is fitted with two fracture stages, one for impact fracture at liquid nitrogen temperatures and one for tensile fracture. Specimens are moved from the atmosphere to the preparation chamber via an introduction chamber using a transfer probe. After fracture, followed possibly by ion cleaning, the specimen can be moved on to an x–y–z manipulator in the analytical chamber situated to the right-hand side of the system.
3.4
Vacuum pumps
3.4.1
Pumping media
While many vacuum pumps used in modern systems can be regarded as clean, employing no liquids or greases, a large number rely on oils to
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Figure 3.7. Saturation vapour pressure of some frequently used pump oils and mercury.
produce the vacuum. The saturation vapour pressure of the liquid will determine the ultimate pressure that can be attained. Figure 3.7 gives the saturation vapour pressure of a number of oils as a function of temperature. Mercury, once a common diffusion pump liquid, has a vapour pressure greater than all the oils listed and if this is to be used as a pump liquid to attain low pressures a liquid nitrogen cold trap must be used. However, for reasons of safety and health this liquid is rarely used now. There is a large range of vapour pressures between the different oils with almost seven orders of magnitude between the highest and the lowest at room temperature. The choice of pump oil will be determined by the vacuum required and the conditions under which it has to operate. Diffusion pumps tend to use mineral oils, silicone oils and oils based on polyphenyl ethers. Silicone oils are more resistant to air than mineral oils and can withstand higher temperatures. Certain polyphenyl ether based oils and silicone oils can have extremely low vapour pressures and are recommended where robust oils are required to achieve low ultimate pressures. 3.4.2
Low to medium vacuum pumps
These are pumps used to reduce the system from atmospheric pressure to a rough vacuum or 101 Pa, a condition that would permit high vacuum pumps to take over. They include rotary pumps, sorption pumps and turbomolecular pumps, although the latter can operate over a much wider vacuum range.
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Vacuum systems
Rotary pumps There exists a large number of types and many different designs of rotary pump (Bode (1960), Flecken (1966), and Ba¨chler and Knobloch (1971)). Some are more efficient than others but they all work on the same basic principle of compressing gas in one region of the pump, and then moving it to a second region from which it is then expelled. Gas from the chamber being evacuated then moves into the first region of the pump and the process of compression and evacuation begins again. Figure 3.8 shows the pumping stages of a trochoid rotary pump which consists of an elliptical piston driven in eccentric rotation by toothed wheels fixed to the drive shaft and piston. Consider the pump in position (1) with a small volume of gas on the input side of the pump and a large volume on the output side. As the piston rotates, the gas on the output side is compressed and at the same time evacuated, while gas enters the input side from the chamber (stages 2 to 4). The piston is shaped such that a part of it is always in contact with the pump wall at position P, ensuring that no gas can travel from the output side to the input. There are many variations on this pump. One common version is the rotary vane pump which has a circular cylinder with vanes on either side that are arranged to be always in contact with the pump walls. Other pumps have two stages with two rotating vanes and some have two pistons rotating in one chamber. The rotary pump will pump out chambers at atmospheric pressure and reduce the pressure to 1–102 Pa with an efficiency which varies with the gas
Figure 3.8. The stages (1 to 4) in one cycle of a rotary pump (reproduced with permission of Leybold AG).
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Vacuum pumps
63
being pumped. They are, in general, very efficient at handling large quantities of gas, tolerate corrosive gases and are the workhorses of vacuum technology. They pump air and inert gases such as argon and nitrogen very well but are less well equipped to pump the compressible gases such as CO2 . Adsorption pumps These pumps operate by the physical adsorption of gases on to the surface of molecular sieves. Zeolite, an alkali alumino-silicate, has a very large surface area for a given mass, approximately 103 m2 for each gramme of material. It has a pore diameter of 1.3 nm which is comparable with the diameters of most atmospheric gases such that a gramme of this material is capable, at liquid nitrogen temperature, of adsorbing 133 mbar per litre of nitrogen gas. However, the adsorption of gas on the zeolite surface varies with temperature and is, in general, three to four orders of magnitude less at room temperature than at liquid nitrogen temperature (77 K). A schematic diagram of this type of pump is shown in figure 3.9. The pump is first isolated from the chamber to be evacuated and cooled by immersing in liquid nitrogen, and when equilibrium is reached a valve to the chamber is opened and the gases allowed to adsorb on the zeolite surface. The ultimate pressure that can be reached is dependent on the amount of gas to be pumped and the volume of zeolite in the adsorption pump; as the surface sites become filled the pumping speed will decrease. However, if sufficient zeolite is used the ultimate pressure attainable should be in the region of 102 Pa. The advantage of this type of pump is that it is very clean since there are no oils present to backstream and contaminate. It is, therefore, primarily
Figure 3.9. A schematic of a typical sorption pump. 1, inlet port; 2, degassing port (safety outlet); 3, support; 4, pump body; 5, thermal conducting vanes; 6, adsorption material (e.g. zeolite) (reproduced with permission of Leybold AG).
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Vacuum systems
used as the first stage of pumping UHV systems that must be kept free from contamination. Moreover, it has the secondary advantage that no moving parts are involved and maintenance is minimal. The drawbacks are that pumping is not continuous so that after the chamber has been evacuated the pump must be isolated from the chamber and allowed to warm up to room temperature to release the adsorbed gas through a release valve before it can be cooled and used again. If large quantities of water vapour are to be pumped it is advisable to heat the pump to 500 K before reusing. In addition while it pumps most large compressible gases such as oxygen, nitrogen, water vapour and CO2 well it is poor at pumping inert gases such as helium or neon. Turbomolecular pumps Turbomolecular pumps (Frank (1972), Fle´cher (1977) and Henning and Knorr (1980)) (figure 3.10) work on the principle that a gas molecule striking a moving surface will be given a component of momentum in the direction of the moving surface, the principle used by fans to circulate air. However, it is only comparatively recently that this principle has been used to attain
Figure 3.10. A diagram showing a cross-section through a turbomolecular pump. 1, stator blades; 2, rotor body; 3, intake flange; 4, blades of the suction stage; 5, blades of the compression stage; 6, drive shaft; 7 and 8, ball bearings; 9, high frequency rotor (reproduced with permission of Leybold AG).
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Vacuum pumps
65
relatively high vacuums since the rotors must move at high speeds and tolerances between the rotors and the walls must be small to prevent gas backstreaming. Gas enters from the chamber being pumped through the large port (3) to a series of large rotor/stator blades designed to capture the gas (4) which is then compressed in stages by the smaller rotor/stator blades (5) before being exhausted. Turbomolecular pumps rotate the blades typically at 500 Hz and are capable of pumping from relatively high pressures down to ultra-high vacuum. Whilst they are capable of pumping from atmospheric pressure this puts considerable strain on the pump and it is advisable to use some other form of pumping to achieve pressures of approximately 102 Pa before bringing in the turbomolecular pump. These pumps are very reliable but may cause some vibration in the system which can be reduced to a minimum by using magneto-bearings. There is also a danger that oil, used to lubricate the bearings, may creep past and enter the vacuum system. To reduce this risk it is advisable to install a valve close to the top of the turbomolecular pump and to close it at all times when the pump is not in use. Diffusion pumps Diffusion pumps are used to remove large volumes of gases at high speeds over the pressure range 101 to 109 Pa (Noller (1966)). They are simple and robust and resilient to pumping corrosive gases. Figure 3.11(a) shows schematically the design and operation of a typical diffusion pump. The pump fluid, usually oil, is heated at the base of the pump and the vapour rises up the chimneys and emerges at supersonic speeds from the nozzles. These jets travel towards the sides, which are water cooled, where they condense and flow back to the reservoir. Gases in the region of the top of the diffusion pump get entrapped by the oil stream and are taken down to the outlet. In this region the oil is reheated to about 400 K to drive off the entrapped gases, which are removed by a rotary backing pump maintained at 101 Pa. Oil does not only travel in the direction of the pump walls, but some of the oil will make its way into the chamber being evacuated where it can become a source of contamination. This is a very serious problem for UHV systems and it is necessary to incorporate a series of devices to reduce this risk. Figure 3.11(b) shows the standard arrangement to prevent oil backstreaming into the vacuum chamber. It consists of a baffle arrangement, an anti-creep barrier and a liquid nitrogen cold trap placed above the oil diffusion pump. In normal operation this system works well and little oil contamination reaches the main system. However, it relies on the liquid nitrogen cold trap operating at all times that the pump is running and the danger of contamination is always present. If it is important that a chamber is to be kept free from contamination such oil diffusion and rotary pumps should not be used.
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Vacuum systems
Figure 3.11. The operation of oil diffusion pumps. (a) Diagram showing oil streaming to effect pumping: 1, heater; 2, boiler; 3, pump body; 4, cooling coil; 5, high vacuum flange connection; 6, gas particles; 7, vapour jet; 8, backing vacuum connection port; A–D, nozzles. (b) Addition of a cold trap arrangement to reduce backstreaming: 1, diffusion pump; 2, shell or chevron baffle; 3, anti-creep barrier; 4, sealing gasket; 5, bearing ring; 6, cold trap (chilled with liquid nitrogen); 7, vessel (reproduced with permission of Leybold AG).
3.4.3
High to ultra-high vacuum pumps
Sputter-ion pumps These pumps operate by ionising the gas to be evacuated and then utilising electrostatic and magnetic fields to remove the ions (Wutz (1969)). One such pump, known as a diode ion pump (figure 3.12), consists of a cathode constructed from titanium with the anode and chamber walls made of stainless steel. The pump is surrounded by large magnets to produce a magnetic field, B, in the direction indicated (figure 3.12(a)). These pumps operate by producing a cold cathode discharge which ionises gas atoms in the body of the pump. These are accelerated to the cathode where they sputter titanium ions from the cathode walls (figure 3.12(b)). The ionised gas atoms become buried in the cathode, titanium atoms trap other gas atoms as they impinge on the cathode and anode walls and also pump active gas atoms by reacting with them. The pumping speed of these pumps varies with the type of gas being pumped. There is more than one mechanism by which active gases can be pumped but inert gases can be pumped only by ionisation followed by burial in the
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Vacuum pumps
67
Figure 3.12. Schematic diagrams showing the principle and operation of a diode ion pump. B is the direction of the magnetic field (reproduced with permission of Leybold AG).
cathode wall. In general most gases pump at rates similar to that for air or nitrogen, but argon and helium are pumped at rates approximately three times slower. In addition, the inert gases that are trapped in the cathode will eventually be released by further ion implants and the effectiveness for pumping these gases will decrease. Triode ion pumps have a different geometrical arrangement which makes them more efficient for pumping inert gases. Sputter ion pumps are very clean and there is no risk of contamination of the vacuum chamber. They perform best at low pressures, <104 Pa, but can be started at 102 Pa and if operated at pressures better than 108 Pa for most of the time will last up to ten years before it is necessary to replace the cathodes. They should not be used where there is a requirement to pump large volumes of gas, particularly if the gas is inert. Cryopumps Cryopumps operate by condensing the gas to be pumped on to a cold surface (Klipping (1974) and Schafer (1978)). Indeed, any ‘cold finger’ cooled to liquid nitrogen temperature (77 K) is a form of cryopump. Cryopumping takes place in three ways. A gas which has a boiling point higher than the cold surface will condense on that surface. A gas with a boiling point lower than that of the cold surface will be trapped by a high boiling point gas as it condenses (cryotrapping). Gases with a very low boiling point may bond to a gas with a high boiling point and thus be pumped (cryosorption) and hydrogen can be pumped in this way using ammonia. Whilst liquid
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Vacuum systems
nitrogen can be used as a coolant for cryopumps, high and ultra-high vacuums can be achieved only if liquid helium is used. The loss of liquid helium is reduced by surrounding the helium reservoirs with the less expensive liquid nitrogen. In a typical cryopump liquid helium is pumped through a heat exchanger to provide the cold surface. The rate at which the helium is pumped will determine the temperature of the heat exchanger surface. The helium which evaporates during this process is used to cool a surface around the heat exchanger and thus reduce heat flow into the heat exchanger. These pumps clearly require large volumes of liquid gases and are expensive to operate but provide the cleanest vacuum available with no unwanted gas atoms involved. Titanium sublimation pumps This pump is simply a titanium filament enclosed in a stainless steel chamber which is heated by passing a large current through it to evaporate titanium on to the chamber walls. The evaporated titanium pumps active gases by combining chemically with them. In most cases the walls of the pump are maintained at room temperature but in some cases are cooled by liquid nitrogen to improve the efficiency. Generally these pumps are used in conjunction with ion pumps to improve the speed or to attain lower base pressures. The filaments need to be changed on a regular basis and to increase the time between changes multiple titanium filaments are mounted in one chamber.
3.5
Pressure measurement
It is important to be able to measure the pressure in a vacuum chamber and on occasion to be able to identify and measure the partial pressures of the constituent gases. We will describe vacuum gauges that are commonly installed in analytical instruments and not the more fundamentally based instruments against which many of these gauges are calibrated. 3.5.1
Pirani or thermal conductivity gauges
As the gas pressure in a system falls so the number of atoms per unit volume decreases and the mean free path increases. This causes the thermal conductivity of the gas to vary with the pressure and it is this property that is used to determine the pressure in the range 1–101 Pa using gauges known as Pirani gauges. The Pirani gauge has a metal filament through which a small current is passed, causing it to heat up. The filament can lose heat by conduction, convection and radiation but at pressures between 102 and 101 Pa heat is lost primarily by conduction. By making the filament one arm of a Wheatstone bridge circuit the change in resistance can be determined and this, in turn, is calibrated to measure the pressure. At pressures above 100 Pa the major heat loss is
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Pressure measurement
69
Figure 3.13. A schematic diagram showing the cross-section of a Penning pressure measurement gauge (reproduced with permission of Leybold AG).
through convection and below 101 Pa it is lost by radiation and since both are independent of pressure this limits the range of operation for the gauge. 3.5.2
Ionisation gauges
The number of atoms in the vacuum chamber varies with the pressure. By ionising a fraction of these atoms, a current can be made to flow to a detecting electrode. The magnitude of the current will then be proportional to the pressure (Meinke and Reich (1967) and Beek and Reich (1974)). In the Penning or cold-cathode ionisation gauge, ionisation of atoms is produced by a cold discharge similar to the process adopted for sputter-ion pumps. In a Penning gauge (figure 3.13), the cold discharge is produced by applying a potential of approximately 2 kV between two electrodes. To make the mean free path of the electrons as long as possible, a magnet is added to the gauge in a position so that the magnetic lines of force are normal to the lines of electrical potential. This causes the electrons to travel in a spiral path and increases the probability of ionising an atom. The current produced is then calibrated to measure the pressure to an accuracy limited to about 50%. These gauges do not operate at pressures above 1 Pa because the gas forms a glow discharge but they can operate down to ultra-high vacuum and are cheap, simple to operate, and reliable. In the hot-cathode ionisation gauge shown schematically in figure 3.14, electrons are produced by a heated filament. These electrons are accelerated by a grid at a positive potential of a few hundred volts (figure 3.14(a)) and thereby ionize gas atoms in the region between the grid and the ion collector. The collector is negatively biased with respect to the grid and so reflects electrons and collects ions; the ion current is proportional to the pressure. These gauges operate below approximately 1 Pa down to ultra-high
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Vacuum systems
Figure 3.14. Principle of a hot cathode ionisation gauge together with some practical arrangements for pressure measurement.
vacuum, where they are limited by the photon (X-ray) emission caused by electrons impinging on the grid. Some of the photons that strike the collector in turn produce photoelectrons which travel to the grid, which is identical to a small positive charge hitting the collector, and this limits the pressure measurement range for these gauges. Several versions of the hot cathode ionisation gauge exist. In addition to the type shown in figure 3.14(b) there is the Bayard–Alpert ionisation gauge which attempts to reduce the X-ray effect by separating the cathode from the anode grid and making the collector as small as possible. Several alternative arrangements for the hot cathode ionisation gauge are shown in the figure ((c)–(f )). The probability that an atom will be ionized varies with the type of gas such that two different gases, present at the same partial pressure, will be measured as different pressures by the gauge. Most gauges are calibrated with respect to nitrogen and the difference between this and air is small, but helium will give a reading six times greater while xenon will be a factor of three lower. Therefore care must be exercised in placing too much reliance on an ionisation gauge reading without also determining the partial pressures of the different gases in the chamber. 3.5.3
Partial pressure measurement
This ideal method of pressure measurement has the objective of determining the pressure of each of the constituent gases making up the total gas pressure in the vacuum chamber. To do this requires the use of mass analysers and two commonly encountered types will be briefly described. Magnetic sector mass spectrometers A magnetic sector mass spectrometer (Polaschegg (1976)) is one of the less frequently used for partial pressure determination in analytical instruments
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Figure 3.15. Schematic diagram of a magnetic sector mass spectrometer for partial pressure measurement. 1, flange of the ion source unit; 2, cathodes; 3, anode (heated); 4, shield tube; 5, diaphragm (also used as ion collector for measuring total pressure); 6, intermediate diaphragm; 7, magnetic field; 8, cylindrical condensor; 9, diaphragm; 10, ion collector; 11, flange of the deflector unit (reproduced with permission of Leybold AG).
because it is bulky and can produce stray magnetic fields which may influence the analysis system (figure 3.15). It operates by a hot filament producing electrons which are accelerated across the entrance slit of 180 sector magnetic detector. A fraction of the atoms are ionised and accelerated to the entrance slit. Only those atoms with the correct velocity, mass and charge will travel around the spectrometer and pass through the exit slit and be collected by the detector. By varying the accelerating potential on the entrance slit a spectrum can be produced giving peaks at different mass numbers that allow the gas to be identified. Knowledge of the relative ionisation efficiencies of the different gases together with the characteristics of the mass spectrometer enable the partial pressures of the gases within the chamber to be determined. The quadrupole mass spectrometer The quadrupole mass spectrometer (Knoopmann (1980)), shown in figure 3.16, is now the most common source of partial pressure measurement in analytical systems. It is small, often less than 10 cm long and 5 cm in diameter, can be mounted on small flanges and provides a total pressure measurement in addition to partial pressures. Again the ions are produced in the source by electrons from the hot filament and are the accelerated to the entrance of the quadrupole. This consists of four electrodes positioned as shown in figure 3.16(b), to which a constant high frequency voltage, 2.5 MHz, and a d.c. voltage are applied. The ions travel along the axis of the rods oscillating in the high frequency field. Only those ions with the correct charge to mass ratio for the specific conditions will reach the detector
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Figure 3.16. (a) A typical example of a quadrupole mass spectrometer together with (b) a schematic diagram showing the operating principle (reproduced with permission of Leybold AG).
and be collected. The others oscillate increasingly towards the electrodes and eventually hit the sides. Both the high-frequency and the d.c. voltages are increased ensuring that the ratio between them is kept constant and in this way a mass spectrum (figure 3.17) is obtained. Quadrupole mass spectrometers are cheap, small and easy to fit to existing systems and enhance control over the vacuum, particularly when attempting to find a leak.
Figure 3.17. Two mass spectra obtained from the same environment using a quadrupole mass spectrometer (a) with constant peak width and (b) with constant sensitivity (reproduced with permission of Leybold AG).
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Leak detection
3.6
73
Leak detection
A major problem with all vacuum systems is the location of leaks, which if very large are easy to find but if small may be difficult to confirm and locate. When a leak in the system is suspected it must first be confirmed. The best way to do this is to switch off the pumping system and watch the pressure rise on the ionisation gauge or better still the mass spectrometer (figure 3.18(a)). In any vacuum system there will be constant outgassing from the chamber walls and other components. If there is no leak then the pressure rise will be initially linear but will soon achieve a limiting value (figure 3.18(b)). If there is a leak there will be a constantly rising component which will continue albeit at a slower rate (figure 3.18(c)). If a mass spectrometer is fitted to the system with no leak present then the outgassing components water vapour (18 amu) CO (28 amu), H2 (2 amu) will all increase but if there is a leak then oxygen (16 amu) and nitrogen (28 amu) will both increase with an O2 :N2 ratio of 1 :4. Here it is important not to confuse CO with nitrogen as both have the same atomic mass unit. Having confirmed that a leak exists the next stage is to locate its position. Clearly seals between components must be suspect, particularly if they have recently been changed. If the system has an ionisation gauge fitted then the change in sensitivity of the gauge to different gases can be utilised. Helium is six times more sensitive than air and by applying a small jet of this gas to all possible areas where there may be a leak should produce a rise in pressure on the gauge when the leak is found. It is important to start at the top of the system because the spent helium will rise from the area just tested. If the system has a mass spectrometer fitted, adopt the same procedure but adjust the mass spectrometer to sit on the helium peak position (4 amu) and watch for a rise in the partial pressure. As an alternative
Figure 3.18. Pressure changes observed on turning the pumps off in the presence of (a) a leak, (b) outgassing and (c) a leak with outgassing.
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to a source of helium, apply a small quantity of acetone to the suspect areas—but this should only be used in a well ventilated area.
3.7
Specimen handling
All materials outgas in a vacuum by the amount determined by the history and form of the specimen. Tomkins (1998) has reviewed ultra-high vacuum techniques and the vacuum compatibility of materials, while Lindfors (1998) deals with aspects of the handling, cleaning and processing of specimens. Thus it is necessary to avoid touching the specimen, since hands contain many oils with high vapour pressures and will degrade the vacuum for some considerable time. Always wear cotton gloves and use tweezers to handle the specimen. If the specimen has been in a solution, if possible, wash in distilled water then displace the water with a wash in iso-propanol. If it can be warmed in an oven without risk of damage, this will drive off adsorbed vapour and reduce outgassing. If specimens are to be stored this should be in a dry environment, ideally dry nitrogen, but failing this in a desiccator with silica gel. In some cases it is desirable to retain them in a vacuum chamber prior to transferring to the instrument for examination. Adopting these practices will ensure fast pump downtimes to achieve the desired vacuum and it will also reduce the amount of servicing necessary on the pumps. The subject of specimen handling, preparation and treatment is comprehensively covered by Czanderna et al (1998).
3.8
References
Bachler W and Knobloch D 1971 J. Vac. Sci. Technol. 9 402 Beek U and Reich G 1974 Vacuum 24 27 Beek U and Reich G 1975 Vacuum 25 223 Bode H 1960 6th Nat. Symp. on Vacuum Technology Transitions (London: Pergamon Press) p 268 Czanderna A W, Powell C J and Madey T E ed 1998 Specimen Handling, Preparation and Treatments in Surface Characterisation (New York: Kluwer Academic/Plenum Publishers) Diels K and Jaeckel R 1966 Leybold Vacuum Handbook (London: Pergamon Press) Dushman S 1962 Scientific Foundation of Vacuum Technique 2nd edition ed I M Laferty (New York: Wiley) Flecher P 1977 Proc. 7th Intern. Vac. Congress (Vienna) 1 25 Flecken F A 1966 Uber die Anwendung von Verdvangerpumpen in der Kabelindustrie Draht-Fachzeitschrift 17 3 Frank R 1972 Suppl. de la Revue le Vide 157 257 Henning H H and Knorr C 1980 Proc. 8th Intern. Vac. Congress (Cannes) Suppl. ‘Le Vide’ 2 283
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Klipping G 1974 Japan J. Appl. Phys. Suppl. 2 81 Knoopmann G 1980 Proc. 8th Int. Vac. Congress (Cannes) Suppl. ‘Le Vide’ 2 215 Meinke C and Reich G 1967 J. Vac. Sci. Tech. 4 356 Leybold AG 1987 Vacuum Technology; its Foundations, Formulae and Tables (Ko¨ln: Leybold) Lindfors P A 1998 Specimen Handling, Preparation and Treatments in Surface Characterisation ed A W Czanderna, C J Powell and T E Madey (New York: Kluwer Academic/Plenum Publishers) p 45 Noller H G 1966 Theory of vacuum diffusion pumps in Handbook of Vacuum Physics vol 1 ed A H Beck (London: Pergamon Press) O’Hanlon J F 1989 A User’s Guide to Vacuum Technology 2nd Edition (Chichester: Wiley) Polaschegg H D 1976 Appl. Phys. 9 223 Schafer G 1978 Vacuum 28 399 Tomkins H G 1998 Specimen Handling, Preparation and Treatments in Surface Characterisation ed A W Czanderna, C J Powell and T E Madey (New York: Kluwer Academic/Plenum Publishers) p 1 Weber F 1968 Dictionary of High Vacuum Science and Technology (Amsterdam: Elsevier) Wutz M 1969 Vacuum 19 1
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Chapter 4 Diffraction 4.1
Electromagnetic radiation
The wave nature of electromagnetic radiation provides a basis to describe a medium in which transverse waves propagate and from which the phenomena of interference, diffraction and polarisation can be derived from Maxwell’s electromagnetic theory of light in 1880 (Ditchburn (1952) and Jenkins and White (1951)). The basic equations of physical optics are derived from the differential form of the Maxwell equations and will be used here (Carlson (1977), Kline and Kay (1965), Lipson and Lipson (1969), Stratton (1941) and Tatarski (1961)). 4.1.1
The wave equation
A wave may be represented as a perturbation " which is described as " ¼ a sinð! þ Cx þ Þ þ a sin
ð4:1Þ
where ! is the frequency, is the phase which is a function of distance x and time , is the phase angle, and a and C are constants. More generally ¼ ! Cðx þ y þ zÞ þ
ð4:2Þ
where , , are constants such that 2 þ 2 þ 2 ¼ 1. Differentiation of equation (4.1) gives 2 "= 2 ¼ !2 "
ð4:3Þ
2 "=x2 ¼ C 2 2 ":
ð4:4Þ
Combining these plus differentials with respect to y and z gives 2 " 2 " 2 " C 2 2 " 1 2 " þ þ ¼ ¼ x2 y2 z2 !2 2 b2 2 which is the general equation of propagation in three dimensions.
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Figure 4.1. Vector representation of the addition of a series of waves.
Consider the situation where we have a series of waves "1 , "2 , "3 , . . . which if combined produce a resultant wave " ¼ "1 þ "2 þ "3 þ . This is known as the ‘principle of superposition’ which states that the disturbance due to a number of waves is equal to the algebraic sum of the disturbances produced by individual waves. If the waves "1 , "2 , "3 , . . . are represented by vectors then the resultant wave is simply the sum of these vectors (figure 4.1). 4.1.2
Huygens’ principle
Huygens postulated that each point on an advancing wavefront is a source of wave motion and that the resultant wavefront at some later time is a consequence of the superposition of the point sources. This principle allows topics such as reflection and refraction to be treated by simply considering the point sources on a surface and deriving the resultant wave in the new medium or direction. This approach is illustrated for reflection and refraction in figure 4.2, where the velocity of light in medium 1 is v1 and in medium 2 is v2 . A plane wave incident on the surface XOZ reaches O at time ¼ 0 when it becomes the source of the secondary wave. The side B of the plane wave would reach R at a later time given by ¼
distance OB R OR sin 1 ¼ ¼ v1 velocity v1
ð4:6Þ
The spherical wave leaving O reaches OP at a time ¼
OP OR sin 01 ¼ v1 v1
ð4:7Þ
or sin 01 ¼ OP=OR ¼ sin 1
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ð4:8Þ
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Diffraction
Figure 4.2. Reflection and refraction of light through a surface.
where 1 and 2 are defined in figure 4.2. In other words the angle of incidence equals the angle of reflection.
4.2
Photons
It is worth briefly describing some of the properties of light before going on to describe diffraction and interference. 4.2.1
Reflection and refraction
When light is incident upon a plane surface it may be absorbed, reflected or transmitted. Most surfaces of materials and media such as glass, water etc. reflect and transmit a proportion with the remainder being absorbed. The amount of light reflected is determined by the type of surface, the angle of incidence and the wavelength of the light. Consider again figure 4.2 in which light is incident on a plane surface at an angle 1 to the surface normal. As we have shown above light, will be reflected at an angle 01 where 1 ¼ 01 . Generally a fraction of the incident light will also be refracted through the surface at an angle 2 . Light travels at different velocities in different media. If we consider the case of light from points O and R in the figure the light incident on the surface will reach R at a time OR sin 1 =C1 later than O. The refracted light in the second medium will then travel a distance c2 in this time, where c1 and c2 are the velocities of light in the mediums 1 and 2 respectively. Since c2 ¼ OR sin 2 we can rearrange to give the ratio of the refractive indices in the two media sin 1 c1 ¼ : sin 2 c2
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ð4:9Þ
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Photons
Figure 4.3. The change in refractive index of fused quartz with wavelength at 291 K.
Since the velocity of light in a particular medium is also a function of the wavelength the refractive index will vary with wavelength. Figure 4.3 shows the change in refractive index as a function of wavelength in the visible region of the spectrum for fused quartz at a temperature of 291 K. When light passes from a medium of low refractive index to one of high refractive index it is bent towards the surface normal and conversely away from the surface normal on passing from a medium of high refractive index, n1 , to that of a low refractive index, n2 . In the latter case as the angle of incidence increases the refracted beam is bent towards the plane of the surface. Eventually a point is reached when n1 sin 1 ¼ n2 sinð=2Þ
ð4:10Þ
or sin 1 ¼
n2 : n1
ð4:11Þ
No light is then refracted and all the light is reflected (figure 4.4), which is known as total internal reflection and is the basis for many applications in
Figure 4.4. Total internal reflection given by 3–30 .
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Figure 4.5. Constructive and destructive interference of two waves. (a) and (b) are in phase and (c) and (d) are out of phase.
modern technology. Light pipes, fibre optics all rely on total internal reflection to transmit light and hence information over large distances. 4.2.2
Interference
Light can be considered either as continuous waves or discrete quanta of electromagnetic energy, photons. The quanta are in fact discrete bundles of waves and the wavelength determines the energy that our eye recognises as colour. Light of a single colour contains quanta with identical wavelengths, while white light is made up from quanta with a range of wavelengths from 200 to 800 nm. When quanta reach a point they interfere either constructively to form brighter regions or destructively to form darker regions. The result of this interference is determined by the difference in the phase of the different waves. Extreme cases are illustrated in figure 4.5, where two waves of the same wavelength (a) and (b) are exactly in phase, i.e. their phase difference is zero or a multiple of 2, and the resultant wave has the intensity of (a) plus (b) while waves (c) and (d) are out of phase by or multiples of and the resultant wave intensity is the intensity of (c) minus (d) which for two waves of equal amplitude results in complete destructive interference. This interference effect is illustrated by considering (figure 4.6) a beam of monochromatic light of wavelength incident on the slit positioned at S0 which causes waves to emanate from S0 , radially but in phase. If these waves then impinge on the second surface which has slits at S1 and S2 , spaced equally from the axis, then two new radial in phase waves will emanate from these slits. The image formed on a final screen is the result of interference of these waves with each other at points along the screen. Consider the point C, a distance y from the axis, and with the screen
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Figure 4.6. Interference from two slits, S1 and S2 .
placed a distance D from the slits S1 and S2 which are themselves separated by a distance d. The condition for a maximum at C is that the path difference between the rays r1 and r2 be an integral number of wavelengths, that is S2 C S1 C ¼ n . For this to be achieved, to a first approximation, n ¼ d sin
ð4:12Þ
where d D and the integer n ¼ 0; 1; 2; 3; . . . and where is the angle between the slits and the axis normal and the point C. The effect is illustrated by using the well known example of Newton’s rings observed when light passes through a lens resting on a flat reflective plate as shown in figure 4.7. The rings are in fact maxima in the interference between the reflected waves. Consider a ray of light incident on the centre of the plate and one incident a distance r from the centre. If R is the radius of the curved surface then the ray at a distance r from the centre will travel a distance 2d greater than the central ray in reaching its starting point. For
(a)
(b)
Figure 4.7. (a) Schematic representation and (b) an example of Newton’s rings.
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Figure 4.8. Use of interference to identify and measure the height of slip bands in copper– aluminium alloy (a) using white light and (b) monochromatic light.
the intensity to be a maximum 2d ¼ ðn þ 12Þ
ð4:13Þ
where n and are defined above. The 12 arises from the phase change of the light suffers when reflected. Thus the path difference is given by d ¼ R ðR2 r2 Þ1=2 ¼ R Rð1 ðr=RÞ2 Þ1=2 :
ð4:14Þ
If r=R 1 then d ¼ R Rð1 12 ðr=RÞ2 þ Þ ’ r2 =2R
ð4:15Þ
r ¼ ððn þ 12Þ RÞ1=2 :
ð4:16Þ
or An example of the use that can be made of this effect is in the interference fringes that are used in the light microscope, when used as an interferometer, to detect and measure small changes in height. This is particularly useful when determining the height of deformation bands or slip traces. An example is shown in figure 4.8, taken from deformation bands in single crystal copper–aluminium alloy (Mitchell et al (1968)). 4.2.3
Polarised light
The light that has been considered so far can be described by its wavelength, phase and amplitude and the wave by scalar quantities with planes equivalent. There is, however, another property of light which requires that the wave be specified by a vector and both direction as well as magnitude must be identified because the light behaves differently in different planes. Such light is known as polarised light and there are a number of forms of polarised light (figure 4.9). The vector describing the polarised light varies in amplitude
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Figure 4.9. Polarised light: (a) Plane polarised, two beams in phase and polarised normal to one another. (b) Circularly polarised, two beams of equal amplitude polarised normal to one another separated in phase by p=2.
and direction as the phase changes. When the direction remains fixed and only the magnitude changes the light is referred to as plane polarised (figure 4.9(a)). When the amplitude remains constant but the vector direction changes in a uniform way so that it describes a circle, then the light is said to be circularly polarised (figure 4.9(b)). When the magnitude and the vector direction change such that the vector describes an ellipse the light is said to be elliptically polarised. If two plane polarised waves have their vectors inclined at an angle to one another this is equivalent to a third plane polarised ray with a vector that is the vector sum of the two vectors describing the original waves. Circularly polarised light can be produced by combining two plane polarised waves of equal magnitude but out of phase by /4 or
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Figure 4.10. The various methods of producing polarised light using calcite crystals (a) Rochon prism, (b) Wollaston prism (dots indicate optic axis normal to lines), (c) Nicol prism.
3 /4. Here the plane of polarisation for the wave rotates with position along the ray. Elliptically polarised light can be produced by combining rays of equal magnitude but out of phase by /8 or 3 /8. A beam of unpolarised light may be regarded as the resultant of two beams, polarised in two different planes with no phase relationship. The simplest method of polarising ordinary light is to reflect it from the surface of a transparent medium such as glass or water. Light that has been reflected by a sheet of glass will be polarised in a direction normal to the surface of the glass. Here polarisation can be confirmed by reflecting this beam by a second sheet of glass: it will be strongly reflected in one direction but weakly reflected at an angle /2 relative to the strong direction. It is the normal convention that the plane in which the beam is most strongly reflected is known as the plane of polarisation. Light is polarised also when it is transmitted through a transparent medium unless it is incident normally on that surface. In this case the plane of polarisation of the transmitted light is normal to the plane of polarisation of the reflected light. Production of polarised light by reflection or refraction is, however, very inefficient. Certain transparent crystals such as calcium carbonate (calcite or Iceland Spar) are optically anisotropic and when a beam of light passes through such a crystal it is split into two parts which are refracted in different directions. The two refracted beams are each plane polarised with the plane of polarisation normal to each other, thus removing one of the beams produces a single plane polarised beam. In practice this is done by combining two prisms such that the second prism blocks one ray while allowing the other to pass the beam through (figure 4.10(a) and (b)). An alternative method is to use two prisms, cemented together, but arranged such that one of the polarised beams will be totally reflected from the second prism surface while the other is allowed to pass as in the Nicol prism (figure 4.10(c)).
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Figure 4.11. The use of polarised light to detect strain fields in a flat diamond plate.
Polarised light has many uses in the study of materials, particularly for cases when crystallographic materials are examined using light microscopes. Polarised light can be used to identify grains with different orientations or to detect deformation twins, because the reflection of the polarised light is dependent on grain orientation. An example of the use of polarised light to study the plastic deformation in an anisotropic material is shown in figure 5.10. Here polarised light has been used to study the strains that are put into cadmium as a result of deformation. Polarised light may also be used to show up strain patterns in transparent media. A beam of plane polarised light will have the direction of the plane of polarisation rotated by a strain field. By viewing the material through a second polariser placed normal to the plane of polarisation of the incident beam, areas where the plane of polarisation have been rotated will appear bright. Thus regions of strain appear as light areas on a dark background. Strain fields in a single crystal of diamond have been revealed by this process and a typical example is given in figure 4.11 (Wild et al (1967)). 4.2.4
Diffraction
Light is diffracted on passing through a narrow slit so that when monochromatic light passes through a single slit of width AB ¼ d, two diffraction cases can be envisaged (figure 4.12). In the first, light from a point source near to the screen produces a point at a screen and in the second a parallel beam from a source infinitely distant from the screen produces a parallel beam on the far side of the screen. The first case is known as Fresnel diffraction (figure 4.12(a)) and the second as Fraunhofer diffraction (figure 4.12(b)). Fraunhofer diffraction can be produced by using a lens combination to produce a parallel beam of light from a point source and to focus the beam on to a screen after passing through the slits. Diffraction can be described if we consider the slit to be split into two halves with a continuum of waves passing through from the top to the centre. Consider the case of Fresnel
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Diffraction
Figure 4.12. Conditions leading to (a) Fresnel and (b) Fraunhofer diffraction.
diffraction with a wave (1) starting from the edge of the slit at D and a wave (2) from the centre of the slit. If d, the width of the slit, is very much less than D, the distance from the slit to the screen, then the path difference between rays (1) and (2) is d=2 sin . The condition for a minimum is that the path difference be /2. If is chosen so that d=2 sin ¼ /2 then every ray from the top half of the slit will be cancelled by a ray from the bottom half. Thus the resultant intensity will be zero and we have the position of the first minimum. Extending the argument to the general case, the condition for the nth minimum is d sin ¼ n where n is an integer. If we now turn to the case where there are a series of equally spaced slits separated by a distance d and the parallel beam is focused on to a screen at a distance D from the focusing lens as illustrated in figure 4.13. The series of parallel slits constitutes a diffraction grating and the principal maxima is given by d sin ¼ n . The principal maxima do not change position with the number of slits, N, in the grating but rather the sharpness of the maxima increases with number. It can be shown that the position of zero intensity occurs, on either side of the central principal maximum, when ¼
d: N
ð4:17Þ
Thus as N increases so decreases and the peaks become narrow. For visible light is about 300 nm and thus to obtain a diffraction pattern where the first minimum is at an angle of 18 to the direction of the incident
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Figure 4.13. Diffraction using multiple slits separated by a distance d and total number N.
beam would require d to be of the order of 0.1 mm. It is certainly possible to produce mechanically diffraction gratings that can have a thousand slits and hence of a few micrometres. 4.2.5
Optical diffraction in transmission electron microscopy
Fourier realised that any waveform can be reconstructed from a series of sine waves. He and others have utilised the method to describe complicated waveforms in terms of the simple sine wave and the technique has become known as Fourier transform. A diffraction pattern, which is also a sinusoidal variation of intensity with distance, can be used to determine the form of the diffracting object. This is because a diffraction pattern is a Fourier transform of the diffracting object and this can be most easily visualised by considering the Fraunhofer diffraction pattern from a single slit. The ‘reciprocal space’ of the Fraunhofer diffraction pattern can be used to reproduce the spatial data. A simple example is given in figure 4.14, which is a Fraunhofer diffraction pattern from a rectangular aperture (Mulvey (1991)). The symmetry indicates
Figure 4.14. Fraunhofer diffraction pattern from a rectangular aperture. The difference between the vertical and horizontal components allows the size of the rectangle to be determined (Mulvey (1991)) (reproduced by permission of Rolston Gordon Communications).
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Diffraction
Figure 4.15. High resolution (0.4 nm) TEM focal series of a carbon support foil and associated optical diffraction pattern at various focal settings. Top left: over focus. Top right: Gauss focus. Bottom left: Scherzer focus. Bottom right: Under focus. (Courtesy of the Director of the Institute for Solid State Physics and Electron Microscopy, Halle (Saale), Germany.)
that the diffracting object has two-fold symmetry but the difference between the horizontal and vertical components reveals that the diffracting object is rectangular with the dimensions that can be determined from the intensity variation with distance. This method is used to quantitatively determine the size, spacing and symmetry of objects imaged in the transmission electron microscope (TEM) and, in particular, to give a quantitative measure of the ultimate spatial resolution. A transmission electron micrograph is first obtained and a laser optical system used to form a Fraunhofer diffraction pattern from the micrograph. If the image in the micrograph is formed from particles uniformly spaced, then a ring pattern will be obtained similar to that observed in Fresnel diffraction patterns. The fringe separation is then a direct measure of the best resolution that can be achieved. Figure 4.15 shows four micrographs, together with their associated diffraction pattern, from a carbon support foil at various focal settings. These indicate high spatial resolution of 0.4 nm (Mulvey (1991)). If the TEM has sufficient
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X-ray diffraction
89
resolution to resolve individual atom positions the optical diffraction method may be utilised to detect changes in the structure of the material. For example, in a study of electron beam damage in rutile (TiO2 ) (Buckett et al (1989)), optical diffraction patterns obtained at different points indicate that -TiO2 has been formed near to the surface as the result of electron bombardment but that -Ti2 O3 is present below a depth of 100 nm. Optical diffraction methods of determining size and spatial resolution in the TEM are described by Thon (1966, 1971) and Chapman (1986) and are to be preferred because they remove the subjective bias that is difficult to avoid with many other methods.
4.3 4.3.1
X-ray diffraction Simple theory
X-ray diffraction has been treated extensively in many texts, including those by Cullity (1979), Peiser et al (1960), Klug and Alexander (1954), Barrett and Massalski (1967), Kalbe (1968), Warren (1969) and Hammond (1997). Xrays are photons with a wavelength of the order of a fraction of a nanometre compared with the hundreds of nanometres of light waves. It is impractical to consider making a grating to diffract X-rays because the size and spacing would be too small. A separation of the order of 0.1 to 0.5 nm would be required. This condition, however, is inbuilt into crystalline materials where rows of atoms have a spacing of 0.3 nm. Thus an X-ray beam incident on a material penetrates many micrometres into the bulk and the direction of the diffracted beam intensity is determined by the periodicity of the atom planes in the crystalline solid; we will later meet cases where in electron diffraction it is possible for the periodicity of atoms in the topmost surface layer to determine the diffracted beam intensity. In chapter 2 we described the source of white X-rays and characteristic Xrays. Consider the case where a beam of characteristic X-rays of wavelength is incident on a single crystal surface at an angle (figure 4.16) which
Figure 4.16. X-ray diffraction from atoms in a crystalline material.
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produces a diffracted beam at an angle . The ray from the second row of atoms travels a distance (DA þ AC) greater than the ray from the top row. The two rows of atoms are separated by a distance d. For this to produce a diffraction maxima the path difference must be an integral number of wavelengths. But DA and AC both equal d sin and thus the condition for diffraction maxima is 2d sin ¼ n :
ð4:18Þ
This is the now famous Bragg equation for diffraction. By measuring , and knowing , d may be determined and the crystal spacing identified. Specific atom species will have an influence on the phase of the diffracted beam and dissimilar atoms in specific positions can cause certain diffraction peaks to be absent. A large library of expected diffraction patterns has been accumulated which allows most compounds to be identified from the observed diffraction positions and intensities. The application of this approach is now developed more fully. 4.3.2
The reciprocal lattice
Before proceeding further with X-ray diffraction it is appropriate to consider the reciprocal lattice (Peiser et al (1960)) that is constructed to aid the interpretation of diffraction from crystal lattices. In real space crystal planes are defined by their intercepts on coordinate axes, usually with axis units being defined as integral multiples of the unit cell dimensions (figure 1.2). For example the plane that intercepts the x, y and z axes at 3a0 , 2b0 and 4c0 , where a0 , b0 and c0 are unit cell dimensions in the x, y and z directions, would be referred to as the 3, 2, 4 plane. Planes with intercepts h, k, l have families of planes nh, nk, nl that are parallel to h, k, l and contribute to a diffracted beam. These planes are separated by a distance dh;k;l =n. The planes in real space can be represented by a point in reciprocal space. The reciprocal lattice is constructed for a defined crystal lattice by drawing a line from the origin, normal to the lattice plane h, k, l. This will be of length dh;k;l and is equal to the reciprocal of the interplanar spacing dh;k;l . The construction of part of a reciprocal lattice for a face centred cubic lattice is shown in figure 4.17. The reciprocal lattice points correspond both to planes with Miller indices h, k, l and those with indices nh, nk, nl where n ¼ 1; 2; 3; 4 . . . which also contribute to diffraction. Thus, the reciprocal lattice defines a range of potential lattice sites that may lead to diffraction. A particular lattice type may be characterised by ‘absent’ diffraction positions and the corresponding points in the reciprocal lattice will be missing, for example a face centred cubic Bravais lattice is equivalent to a body centred cubic reciprocal lattice and vice versa. The diffraction of an X-ray beam can be predicted from the reciprocal lattice using the Ewald construction illustrated in figure 4.18. The incident
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Figure 4.17. The reciprocal lattice construction.
X-ray beam is considered to pass through the origin in both real space and reciprocal space. A sphere is then drawn with a radius of 1/ , where is the wavelength of the X-ray photon, with its centre on the incident beam direction and position such that the surface of the sphere passes through the origin. This sphere is known as the Ewald sphere. Diffraction of the X-ray beam will occur if the Ewald sphere passes through a reciprocal lattice point. The direction of the diffracted beam is then given by k1 the vector from the centre of the Ewald sphere, to rh;k;l , the point where the sphere passes through a reciprocal lattice point. Thus, the diffracting planes have a reciprocal point at rh;k;l which satisfies the equation g ¼ k1 k0
ð4:19Þ
Figure 4.18. Use of the reciprocal lattice to predict diffraction: Ewald construction.
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where g is the reciprocal lattice vector corresponding to the diffracting planes, k0 is the incident wave vector and k1 is the diffracted wave vector. Diffraction can be guaranteed by either rotating the crystal and hence the reciprocal lattice points or replacing the single crystal with a powder giving an infinite variety of orientation of planes. Clearly no reciprocal lattice points outside a sphere of radius 2/ can pass through the Ewald sphere and therefore cannot diffract the X-ray beam so that this is the limiting sphere. 4.3.3
Intensity of diffracted X-ray beams
The problem of calculating the intensity of a particular diffraction peak is related simply to adding sine waves of different amplitude and phase but of the same wavelength. X-ray diffraction has proved to be invaluable in the evaluation of the microstructure of materials because it is possible to predict the diffracted beam positions with considerable accuracy together with their relative intensities. Therefore it is possible to compare with the measured values to establish the lattice parameters and, therefore, the types of crystal planes present. Thus the libraries of diffraction patterns utilise both position and intensity to determine the crystal structure under investigation (Cullity (1979), Peiser et al (1960), Kalbe (1968) and Warren (1969)). It should be pointed out that in this section we will concern ourselves with the intensity of diffracted beams resulting from atoms at various positions within the crystal lattice. The direction of a diffracted beam is not affected by the type of atom at a particular site, and two unit cells of the same size but with differing arrangements of atoms will diffract X-rays in precisely the same directions. However, the intensities of those diffracted beams may vary and, indeed, the intensities of certain beams may be zero. The approach adopted to determine the intensity of a diffracted beam involves the following three steps: (a) scattering of X-rays from a single electron, (b) scattering of X-rays from a single atom using the scattering from a single electron, and (c) diffraction of X-rays from a unit cell using the scattering from a single atom. Scattering by an electron Since an X-ray photon is an electromagnetic wave it will be strongly scattered by an electron, either coherently or incoherently. For coherent scattering the wavelength of the incident X-ray beam is unaltered by the interaction and there is a phase difference between the incident and scattered beams, /2. This difference is the same for all electron interactions and led J J Thomson to determine that an electron would scatter an X-ray beam of intensity I0 so that the intensity emitted at a distance r from an electron of charge e and mass M is given by I ¼ I0
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e4 sin2 2 r M 2 c4 2
ð4:20Þ
X-ray diffraction
93
Figure 4.19. Scattering of X-rays by an atom, electrons at positions A and B are considered.
where c is the velocity of light and 2 is the scattering direction. The incoherent, Compton, scattering arises because on impact with an electron the X-ray beam loses energy, h , so that the wavelength of the scattered beam is greater than that of the incident beam (see equation (2.1)). Since there is no fixed phase relationship between the incident and scattered X-rays the contribution is to the ‘background’. Scattering by an atom An atom consists of a relatively massive positively charged nucleus surrounded by a number of negatively charged electrons. The incident Xray beam will be scattered by both the nucleus and the electrons. However, an examination of equation (4.20) shows that the large mass of the nucleus, which is several thousand times that of the electron, results in negligible scattering of the incident beam by the nucleus. The total scattering from the atom is therefore essentially the result of the scattering from all the individual electrons (figure 4.19). As shown in figure 4.19 since the atom has a finite size waves scattered by electrons located at positions A and B have different path lengths. For those X-rays, however, scattered in the forward direction on reaching plane XX 0 they will be in phase because each wave has travelled the same total distance before and after scattering. As the angle of diffraction increases so the path difference, CB AD, for the X-rays scattered from electrons A and B increases with a consequent fall in the amplitude of the resultant wave at YY 0 . The total scattering by an atom is known as the electron density distribution. A shorter incident X-ray wavelength will produce a greater decrease in amplitude. However, it is the quantity f , known as the atomic scattering factor, that describes the efficiency of scattering in a
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Figure 4.20. The variation of the atomic scattering factors, f , for copper as a function of sin = .
particular direction where f ¼
amplitude of the wave scattered by an atom : amplitude of the wave scattered by one electron
Since f is equal to the number of electrons in the atom for ¼ 0, then f equals the atomic number, Z, but the value decreases as increases and decreases. A plot of f as a function of sin = for copper in figure 4.20 is an example of how f decreases from atomic number 29 as the value of sin = increases. Diffraction from a unit cell We now move on to consider the effect of the position of the atoms in the unit cell on the amplitude of the scattered wave. Since the unit cell is the smallest repeat constituting the crystal this is the last step in determining the intensity of the diffracted beam. The situation is similar to scattering by electrons at different positions in the atom except that here we have phase differences as a result of scattering by atoms at different positions in the unit cell. If we consider first two atoms A and B with atom A positioned at the origin and atom B at a point u; v; w (figure 4.21), then the phase difference between the wave scattered by atom B and that scattered by atom A for an h; k; l reflection is ¼ 2ðhu þ kv þ lwÞ:
ð4:21Þ
If the atoms are of the same kind, the amplitudes of the wave scattered by each atom will be the same; but in the case of unit cells containing more
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Figure 4.21. Diffraction of X-rays by atoms at positions A and B.
than one type of atom, waves of different amplitude as well as phase must be combined to arrive at the resultant intensity. The amplitude of the scattered wave may be described as a complex exponential function A ei . The intensity of this wave is simply the square of the amplitude, i.e. jA ei j2 , and the amplitude is the value of f for the scattering of the atom under consideration. Thus, using the expression for the phase we have A ei ¼ f e2iðhu þ kv þ lwÞ :
ð4:22Þ
The resultant wave from the unit cell is simply the sum of the waves from all the atoms and is referred to as the Structure Factor, F. It is the sum of the waves of amplitude A1 , A2 , A3 , . . . and phase angle 1 , 2 , 3 , . . . in the unit cell. If the amplitude of each wave is represented by the length of a vector and the phase by the direction of a vector, then the diffracted beam is the vector sum of the waves (figure 4.22). Thus the wave from the jth atom is resolved into horizontal and vertical components of lengths fj cos j and fj sin j respectively. These produce a triangle of sides with a
Figure 4.22. Vector addition of X-rays diffracted from atoms.
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hypotenuse of F where jFj2 equals the intensity. Thus X 2 X 2 jFj ¼ fj cos 2ðhuj þ kvj þ lwj Þ þ fj sin 2ðhuj þ kvj þ lwj Þ j
j
ð4:23Þ or jFhkl j ¼
n X
fn e2iðhun þ kvn þ lwn Þ
ð4:24Þ
1
since the power series is given by eix ¼ cos X þ i sin X. Equation (4.23) can be simplified by considering when a crystal has a centre of symmetry which is possible if atoms in the unit cell are divided into sets that are related by the symmetry of the space group. For centrosymmetric crystals the second term in equation (4.23) is zero since sin 2 ¼ 0 and for planes where the intensity is zero no diffraction occurs. For commonly occurring crystal lattice planes in simple symmetry crystals, the conditions for the presence or absence of a diffracted X-ray beam may be established (Cullity (1979)) such that for a simple cubic crystal all planes diffract. For a body centred cubic crystal diffraction occurs if h þ k þ l is an even integer but not if odd and for a face centred cubic crystal h, k and l are unmixed for diffraction and mixed for no diffraction. Other extinction rules apply to crystal lattices that do not fall into this category. An example is the application to the caesium chloride crystal which has the B2 ordered structure based upon the body centred cubic structure, with a caesium ion at 000 and a chlorine ion at 12, 12, 12. Here the f factors for the two ions are not the same, so that the lattice can no longer be regarded as simply body centred cubic and the structure factor is given by F 2 ¼ ½ fCs þ fCl cos ðh þ k þ lÞ2 þ ½ fCl sin ðh þ k þ lÞ2 2
ð4:25Þ 2
which reduces to ( fCs þ fCl ) when (h þ k þ l) is even and ( fCs fCl ) when (h þ k þ l) is odd. Since fCs is not equal to fCl the latter diffraction intensity is not zero as it is for the simple body centred cubic structure. The structure factor can be determined for a unit cell provided the positions and atomic scattering factors for each atom are known. For example, a face centred cubic material has atoms at 000, 12, 12, 0; 12, 0, 12; and 0, 12, 12 positions in the unit cell. If all the atoms are of the same type then the structure factor will be given by: F ¼ f e2ið0Þ þ f e2iðh=2 þ k=2Þ þ f e2iðh=2 þ l=2Þ þ f e2iðk=2 þ l=2Þ iðh þ kÞ
F ¼ f ½1 þ e
þe
iðh þ lÞ
þe
iðk þ lÞ
ð4:26Þ ð4:27Þ
If all the indices h; k; l are odd or even then the exponentials will each equal one and F ¼ 4f , here enI ¼ ð1Þn . However, if h; k; l are mixed odd and even then the sum of the exponentials will be equal to 1 and F ¼ 0. Thus
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X-ray diffraction Table 4.1. Diffraction peaks present and absent in some common Bravais lattices. Bravais lattice
Diffraction present
Diffraction absent
Simple Base-centred Body-centred Face-centred
All h and k not mixed ðh þ k þ lÞ even h, k and l not mixed
None h and k mixed ðh þ k þ lÞ odd h, k and l mixed
diffraction peaks of the type (111), (200) and (220) will be present but of the type (100), (110) and (112) will be absent. Table 4.1 summarises the diffraction peaks that will be observed for some of the common Bravais lattices. The structure factor establishes the conditions simply for the presence or absence of a diffracted peak, but it does not provide information on the relative intensity of these peaks. There is a need to determine the proportionality constant in the condition I / jFj2 :
ð4:28Þ
This will depend upon the particular application or method used and these various options are described in subsequent sections 4.3.5 and 4.3.6 in particular. For single crystals, white X-rays are used with a range of wavelengths and this calculation is complex and rarely invoked. However, for those methods that adopt monochromatic X-ray sources such as the powder method, section 4.3.6, five factors, in addition to the structure factor, have to be taken into account to derive the relative intensities: (i) Lorenz, (ii) polarisation, (iii) multiplicity, (iv) absorption and (v) temperature. It is usual to consider the contribution for the Lorenz and polarisation factors together. An X-ray source produces an unpolarised beam but the vibrating atoms in the crystal do not scatter these waves in all directions with equal efficiency. This results in a partially polarised diffracted beam with a decrease in intensity given by I ¼ 12 ð1 þ cos2 2Þ:
ð4:29Þ
Thus the greatest reduction in diffracted intensity is a 2 ¼ /2 and the least reduction at 2 ¼ 0 or . In addition there are further geometrical contributions, one related to the relative time a given set of crystal planes will be sampled and the second to the proportion of the diffracted cone of the X-rays sampled. These can be combined to give a geometrical factor equal to (4 sin2 cos )1 . Hence the Lorenz polarisation factor is given by Lp ¼
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1 þ cos2 2 : sin2 cos
ð4:30Þ
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Figure 4.23. The effect of increasing temperature on f .
The overall effect of this factor is to reduce the intensity of the diffracted X-ray beam at the intermediate 2 values compared with the low and high values. By comparison the multiplicity factor, p, accommodates the number of crystal planes which contribute to a given diffraction peak. These can be generalised for groups of planes in a given crystal system (see Table 4.1). As discussed in section 2.2.1 the intensity of an X-ray beam after passing through material of a given thickness depends upon the linear absorption coefficient (see equation (2.2)). As a consequence there is a need to accommodate the absorption of the particular specimen, A(), for the particular the method of diffraction selected; for a flat specimen of the type used in a diffractometer system the relative intensity can be taken as unity since it is independent of 2. Values of absorption factors for different specimen geometries are given in International Tables. The final contribution temperature, T, is addressed, in part, via the atomic scattering factor f whereby thermal vibrations lead to an increase in the size of the atoms. Hence in figure 4.20, f will decrease more rapidly for the idealised stationary electron model of the atom. It can be shown theoretically and experimentally that f is given by f ¼ f0 eM
ð4:31Þ
where f0 is the value for an atom at rest and M is given by M ¼ Bðsin = Þ2 where B ¼ 82 2 . Here is the mean square amplitude of atomic vibration. Figure 4.23 shows the effect of increasing temperature on f . As a consequence the relative intensity of a diffracted peak for polycrystalline material subject to monochromatic X-rays is given by IRel ¼ jFj2 Lp pAðÞT:
ð4:32Þ
To give absolute intensities of X-ray diffracted peaks it is necessary to include the specific instrumental conditions adopted so that I ¼ I0 ½X½Y
ð4:33Þ
where X is the instrumental term and Y is described by equation (4.32).
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X-ray diffraction 4.3.4
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X-ray production
X-rays can most easily be produced by bombarding a material surface with relatively high energy electrons. When a high energy electron impinges on the material X-rays are produced in two ways. All charged particles emit electromagnetic radiation when they are accelerated. As the incident electron is decelerated it generates a continuous spectrum or bremsstrahlung. The intensity of the X-rays at a specific energy is a function of the electron energies and is of the form IðEÞ ¼ CZðE0 EÞ=E
ð4:34Þ
where E0 is the incident electron energy, E is the energy of the electron following deceleration and Z is the atomic number of the target and C is a constant. The incident electron also causes the surface atoms to be ionised by the removal of an inner shell electron. As the atom rearranges with electrons from outer orbitals falling into the hole created (e.g. an L shell electron falling into a hole in a K shell) energy is released in the form of a photon, EX-ray ¼ EK EL :
ð4:35Þ
The probability that these characteristic X-rays will be emitted is called the Xray fluorescence yield and increases with atomic number and is larger for K line emissions than for L line emissions. In practice it is normal to use metals to produce X-rays for use in X-ray diffraction instruments. This is because an intense beam of X-rays is desired and the good thermal conductivity of the metal allows the heat produced during bombardment with an intense high energy electron beam to be readily removed thus avoiding damage to the source. When a metal is bombarded with electrons the X-ray spectrum produced is similar to that shown in figure 4.24. There is a continuous band of X-rays emitted from an edge which corresponds to the energy of the incident electron to much longer wavelengths. Superimposed on this background are characteristic peaks resulting from specific transitions within the metal atoms. Normally the characteristic peaks, which may be enhanced by monochromators are used to produce diffraction patterns but in some instances the ‘white’ background radiation may be employed. Since electromagnetic radiation is emitted when a charged particle is accelerated, X-rays can be produced by deliberately accelerating electrons. Very high energy electrons are made to follow circular orbits by confining the electron beam using magnets. Such a device is known as a synchrotron. Here the energy or wavelength of the emitted X-ray is determined by the electron energy and the radius of curvature. The synchrotron produces a narrow cone of X-rays tangential to the electron path. While such an Xray source is highly specialised and very expensive it does have many advantages over conventional sources.
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Figure 4.24. The characteristic X-ray spectrum from a metal illustrating K and L peaks superimposed on the continuous bremsstrahlung background.
4.3.5
Single crystal diffraction
In figure 4.25 we show a schematic diagram of the experimental arrangement for Laue back diffraction together with an example of a typical back diffraction pattern. A beam of white X-radiation is incident on a single crystal specimen. The incident X-ray beam passes through a hole in a photographic plate and the diffracted beams are detected as spots on the film. This method of recording diffraction patterns is less common today and present-day techniques will be described later. The white X-radiation provides the range of wavelengths necessary to ensure that the Bragg Law is satisfied for all planes. With the experimental arrangement shown in figure 4.25 the film can be positioned to record the back diffraction patterns as hyperbola or a transmission pattern can be recorded as ellipses as shown in figure 4.26. Therefore a Laue pattern provides details of the crystal
Figure 4.25. Location of Laue spots on hyperbolas in the back diffraction of X-rays together with an example of a Laue back diffraction pattern.
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Figure 4.26. Location of Laue spots on ellipses in the transmission method of X-ray diffraction together with a typical pattern for a {110} orientation niobium single crystal.
symmetry and the orientation of the single crystals. Moreover, if the grain size of a polycrystal exceeds the incident collimated beam diameter <0.5 mm, then for a conventional experimental system individual grains may be oriented (Cullity (1979)). However, the diffracted spots contain additional information concerning grain size and crystal perfection. This technique can be particularly useful for the examination of microstructure since from the orientation of a given grain it is possible to establish using (a) single and (b) two surface trace analysis procedures the habit plane for a range of precipitates and second phase transformation products e.g. martensite plates, together with their orientation relationship with the parent matrix (Crocker and Flewitt (1984)). A serial sectioning, single surface technique determines the angle that a feature, such as an interphase boundary, makes with a surface by measuring the shift in position as the surface is polished to remove known depths of material (figure 4.27(a)). Depth measurements may be achieved by determining the change in dimension of hardness or similar reference indentations. For this it is necessary that the hardness impressions have planar sides and the indentation images can be superimposed to achieve register. The precision of depth measurement is approximately 5% which gives a possible error in establishing the feature angular relationship of <58 (Bevis and Swindells (1967)). In the case of two surface trace analysis (figure 4.27(b)), if the features have a relatively high aspect ratio the sample may be ground and polished to produce an apex (included) angle of approximately 1608 rather than the 908 which is more usually used (Cullity (1979)). The angular relationship between the two measurement surfaces can be determined by using a tilting stage on an optical microscope. If one surface is oriented by X-ray diffraction, both surfaces can be used to establish trace angles and, indeed, these procedures may be applied to a range of samples and microstructural features. The results of such two surface trace analyses to establish the habit plane for 1 plates formed in binary Cu–40%Zn and ternary Cu–9%Au–40%Zn alloys are shown in figure 4.27(c) (Doig and Flewitt (1983)). Although limited spatial resolution restricts the application of X-ray diffraction,
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(a)
(b)
(c)
Figure 4.27. Trace-trace analysis. (a) Single surface; microstructure and the stereographic projection on matrix plane (hkl). (b) Two surface; traces where the included angle between the surfaces is ( ) together with the corresponding stereographic projection. (c) Measured and predicted 1 plate habit planes for binary Cu–40%Zn and ternary CuAu9 Zn40 aged metastable 0 phase (Doig and Flewitt (1983)) (reproduced with permission of the Institute of Materials).
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(a)
103
(b)
Figure 4.28. Slip in copper (fcc) single crystals. (a) Slip traces in the surface of a deformed copper single crystal. (b) Lattice rotation during deformation of copper single crystal with an initial orientation given by the pole marked 1.
these procedures for microstructure evaluation can be applied equally to other higher resolution methods such as Kossel X-ray diffraction and electron diffraction. However, using the X-ray Laue back diffraction technique it is possible to analyse, for example, slip traces developed on prepolished surfaces of deformed single crystals (figure 4.28(a)), and establish the slip processes which effect the deformation. Moreover, changes in orientation which occur can be followed stereographically as shown in figure 4.28(b) (Cullity (1979) and Honeycombe (1968)). Here the initial tensile axis for the fcc crystal is given by the pole 1, but with the progressive deformation the related extensions cause the position of the axis to move through 2 to 4 along the [ 101] slip direction. Since the slip plane is (111) the lattice orientation causes both the slip plane and direction, in that plane, to rotate towards the stress axis. The size of grains and subgrains in polycrystalline metals and alloys may be established from Laue back diffraction patterns. In conventional Laue back diffraction patterns the rings become discontinuous when the size of either the grains or subgrains exceed a certain dimension, the value of which depends upon the diameter of the incident X-ray beam (Hirsch (1955) and Lonsdale and Flewitt (1984)). This technique, therefore, provides a means of establishing the dimensions of microstructural features within a single phase region of a material simply from a measure of the number of diffraction spots contained within a specific diffraction ring. The method has the inherent advantage that statistical accuracy is high since many grains or subgrains are sampled within the analysed volume. Stephens and Barnes (1937) established an empirical relationship between the number of diffraction spots in a given ring observed on a photographic film and the known grain size for a series of aluminium samples. The method depends
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on Bragg diffraction of X-rays from a given set of {hkl} planes within individual subgrains contributing to the final ‘spotty’ diffraction pattern. As a consequence the greater the number of subgrains sampled by the incident X-ray beam the larger the number of diffraction spots produced. There is an upper and lower limit to the size of subgrains measured since if the number is too large (small grains) the ring becomes continuous and if too small (large grains) the number of diffraction spots is insufficient for statistical confidence to be placed on the measured value (Lonsdale and Flewitt (1984)). Assuming cuboidal shaped subgrains, the subgrain size, d , is given by (Andrews and Johnson (1959)): dhkl ¼ ½V pB cos =2DN1=3
ð4:36Þ
where B is the effective diameter of the incident X-ray beam, is the diffraction angle, p is the multiplicity factor, D is the film to specimen distance, N is the number of diffraction spots given for {hkl} diffraction planes and V is the volume irradiated such that V ¼ =4B2 di , where di is the depth of penetration of the X-ray beam (a function of the absorption coefficient, , for the material). Unfortunately this simple procedure fails to account for contributions from either sectioned subgrains at the surface or the larger grains they are contained within. Several procedures have been proposed to overcome this restriction. One is the double exposure method (Andrews and Johnson (1959)) which relies on the exponential relationship between diffracted X-ray intensity and depth within the sampled volume. A film exposed for a short period, 1 , contains information derived from the near surface volume defined by the depth d1 in figure 4.29, and a second exposure for a substantially longer period, 2 , produces diffraction spots representative of the volume given by the depth d2 . Clearly the difference between the two defines the volume irradiated (d2 d1 ) and eliminates surface and grain size contributions and equation (4.36) becomes: ¼ ½B3 p cos lnð2 =1 Þ=8DN ð1 sec 21=3 : dhkl
ð4:37Þ
This predicts the variation of number of diffraction spots contained within a ring fh k lg for a subgrain size specimen. A measure of the subgrain size is important, for example in creep deformation studies, since it is inversely proportional to the applied stress (Lonsdale and Flewitt (1984)). The technique has been rigorously examined by Hirsch and Keller (1951, 1952) who devised procedures for extending the lower size limit evaluated to below the 0.5 mm obtainable with conventional back diffraction cameras by using microbeam techniques where the incident X-ray beam is collimated by a capillary tube. Laue diffraction spots from a perfect crystal are sharp and their size is determined by the diameter and divergence of the X-ray beam and the film to specimen distance. From bent crystal planes or misorientations associated with a dislocation substructure the spots become elongated in a radial
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Figure 4.29. Subgrain size determination showing interaction of an incident X-ray beam of diameter, b, with specimen; d1 and d2 represent depth of sampling for two exposure times 1 and 2 , where 2 1 (Lonsdale and Flewitt (1984)) (reproduced by permission of Pergamon Press).
direction (asterism) (Cullity (1979) and Masing et al (1959)). The direction and amount of elongation is a function of the orientation of the bending axis and/or the range of orientation of the lattice planes sampled by the incident beam of X-rays. Typically Laue diffraction can be used to follow the kinetics of recrystallisation by observing the progressive formation of sharp diffraction spots derived from newly formed, strain free grains. 4.3.6
Powder methods
The method devised by Debye and Scherrer is the most widely applied powder X-ray technique (Cullity (1979)). Here an incident beam of monochromatic X-radiation interacts with a specimen which is in the form of either a small non-diffracting filament containing bonded powder or a polycrystalline fibre of very small grain size. These specimens must contain sufficient particles with the correct orientation to allow diffraction from all possible diffracting planes when rotated in the X-ray beam (figure 4.30(a)). The angle between the incident and diffracted X-ray beam is 2 and consequently each set of crystal planes produce X-rays of semi-angle 2. A film placed around the specimen intersects the different conics and produces curves concentric with the entrance and exit apertures. Figure 4.30(a) shows the arrangement of the powder sample, film and X-ray beam while figure 4.30(b) shows the equipment with the light-tight cover removed. The position of intensity peaks in the diffracted beam is characteristic of the material being examined and unknown phases may be identified by comparison with
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Figure 4.30. Powder diffraction. (a) Schematic diagram of the Debye–Scherrer method. (b) A Debye–Scherrer camera.
standards (JCPDS Powder Diffraction File). From the Bragg Law the peak positions provide both the crystal structure and the lattice parameter for each phase contained in the powder sample. The diffracted beam intensity provides a measure of the distribution and position of atoms within the crystal. Precise lattice parameter determination is important in many areas of microstructural evaluation such as the study of equilibrium phase diagram boundaries, thermal expansion coefficients, density determinations, variation of properties with composition, precipitation processes and solid state phase transformations (Cullity (1979), Warren (1969), Kalbe (1968), Andrews and Johnson (1959), Barrett and Massalki (1966), Donachie and Krieg (1972), Goldschmidt (1967) and Pearson (1967, 1972)). To overcome limitations associated with photographic recording, the diffracted X-ray beam may be detected using a counter tube, usually a proportional or scintillation counter, linked with associated electronic circuitry (Cullity (1979)). This is incorporated into an X-ray diffractometer
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Figure 4.31. Powder diffraction. (a) Geometry of a conventional diffractometer. (b) A modern diffractometer (courtesy Siemens Ltd).
(figure 4.31(b)), where a divergent beam of either filtered or monochromatic X-radiation is incident on a powder specimen which is rotated at half the angular speed of the receiving slit to maintain constant angular relationship between the incident and diffracted beams. A receiving slit mounted in front of the counter tube is attached to a carrier tube arm behind which is located a scatter slit to ensure that only radiation is received from the area of the specimen exposed to the incident X-ray beam. A typical modern X-ray diffractometer is shown in figure 4.31(b) where the specimen is placed in the centre. This is contained in an enclosure which is safety interlocked to prevent X-rays being generated while the specimen is being handled. The X-ray source is visible to the left of the specimen while the detector is to the right hand side. The intensity of the diffracted beam is automatically recorded either on a chart or as digitised data which can be processed by a small computer to enable direct output of 2 and d values. Indeed with the current generation instruments, further direct interaction with the computer is achieved so that standards of known substances stored on the JPDS powder diffraction file can be directly accessed and the specimen identified without the need for operator interaction. Figure 4.32 shows diffraction traces obtained for specimens containing mixtures of carbides and Laves phases extracted from Type 316 austenitic stainless steel. This is a typical application of this method for the quantitative determination of the weight fraction of phases (Lai and Galbraith (1980)). To enhance the speed of data acquisition using a diffractometer, the counter can be replaced either with a linear position-sensitive proportional counter (Go¨bel (1978)) or an energy dispersive spectrometer (Bivas et al (1978)). The former counter accepts X-ray counts over a fixed angular range, typically 108 but this can be as high as 1608 for a large exposure counter, at a high rate so the detector can then be precessed rapidly over the required 2 range.
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Figure 4.32. X-ray diffractometer traces obtained from precipitates extracted from three Type 316 stainless steels variously aged, showing the proportion of -phase (D8b complex tetragonal), -phase (hcp) and M23 C6 type carbide (fcc) established using an internal standard ZnO calibration (Lai and Galbraith (1980)) (reproduced by permission of the Institute of Materials).
There continue to be developments associated mainly with the optics of X-ray diffractometer systems to improve the collimation and focusing of the X-rays. The slit system in the goniometer shown in figure 4.31 has a limitation since it rejects most of the output of the X-rays from the source and hence reduces the flux of X-radiation to the specimen. Several approaches have been adopted to overcome this. One uses hollow glass capillaries of 3 to 5 mm inner diameter so that the X-rays that undergo total internal reflection at the capillary surface can be directed more closely. Another makes use of X-ray mirrors that consist of a stack of nanometre-thick layers of nickel and carbon or tungsten and silicon, Go¨bel mirrors, to form a parabolic mirror for collimating and an elliptical mirror for focusing these beams (Mai (1999) and Dietsch et al (1998)). The current generation of X-ray diffractometers are designed to be used in different operating modes. For example the preferred orientation (texture) which arises from deformation processes, recrystallisation and the orientation of surface films such as oxide layers or vaporised electrolytic deposition
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Table 4.2. Proportion of -phase, -phase and M23 C6 type carbide in X-ray diffractometer traces in figure 4.32.
Specimen
Total amount of precipitate (wt%)
(wt%)
M23 C6 (wt%)
(wt%)
1 2 3
4.55 3.3 1.1
0.91 0.25 0.01
0.86 0.53 1.1
2.78 2.52 0.01
products can be investigated. Transmission and back diffraction methods may be used by means of a method originally developed by Schultz (Schultz (1949)). The principle of this is shown in figure 4.33 where the angles of rotation and are defined. The vertical height of the beam is restricted because the -rotation destroys the focusing condition except along the AA0 direction. One advantage of the technique is that no absorption correction is required for the various - and - measurements. The development of a deformation texture is shown in figure 4.34 for a low interstitial content, ferritic stainless steel which has been cold rolled to given thickness reductions, 35, 75 and 95% (Lewis and Pickering (1982)). After 35% reduction the texture is mainly {111}h112i with {100}h011i with no evidence of rotational freedom about the strip normal and rolling direction. Increasing the cold rolling reduction to 75% causes the {111}h11 2i texture to be replaced by {1 11}h1 10i and the {112}h110i components together with an increase in the {111}h01 1i component. At the highest reduction the major component becomes the {100}h011i with a minor component from {112}h1 10i.
Figure 4.33. Schematic arrangement of the diffractometer technique for determining the rolling texture of a sheet specimen together with the method of plotting the intensity results on a pole figure.
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Figure 4.34. Development of deformation textures in low interstitial 17% Cr stainless steel, (a) 35%, (b) 75% and (c) 95% reduction (Lewis and Pickering (1982)) (reproduced by permission of the Institute of Materials).
4.3.7
Layer thickness measurements using X-ray diffraction
X-ray diffracion is used to determine the relative thickness of layers present on a bulk substrate. This can be particularly useful when the thickness is changing with time and it is necessary to monitor the relative thickness non-destructively. If we have two layers of thickness tS and tR on a stainless steel substrate A (figure 4.35), the relative intensities of peaks from the two layers is given by (Tempest and Wild (1982)): 2 S tS ½1 expð2 S tS = sin S Þ ð4:38Þ IS =IR ¼ AS =AR exp sin R ½1 expð2 R tR = sin R Þ where AS ¼
jFS j2 sin S 1 þ cos2 2S p S 2 S sin2 S cos S VS2
ð4:39Þ
with a similar expression for the rhombohedral equivalent term, AR , and where FS and FR are the structure factors, VS and VR are the volumes of the unit cell, pS and pR the multiplicity factors, S and R the linear absorption coefficients and S and R are the Bragg angles for the spinel and rhombohedral phases respectively.
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Figure 4.35. Schematic of method for using X-ray diffraction to determine thicknesses wS and wR of layers S and R. Peaks are chosen such that the Bragg angle for the diffraction from two layers are similar (Tempest and Wild (1982)) (reproduced by permission of Plenum Press).
In practice it is often possible to select two peaks such that S R in which case equation (4.38) simplifies to expð2 S tS = sin Þ 1 : ð4:40Þ IS =IR ¼ AS =AR 1 expð2 R tR = sin Þ This method has been used to study the growth of oxide layers on austenitic stainless steel. At high temperature and pressure, stainless steel oxidises in CO2 gas by first forming a spinel oxide layer but gradually a more protective rhombohedral oxide, rich in chromium, forms between the spinel layer and the parent steel. Figure 4.36 shows three diffraction peaks from an oxidised surface, two from the rhombohedral oxide phase and one from the spinel oxide phase. The intensity of these peaks varies with time exposed to the gas at 1123 K such that after 100 h exposure the spinel peak is the largest but by 200 h the peaks are of approximately equal intensity and after 500 h the rhombohedral peaks are dominant. Thus the relative thicknesses of the two layers can be determined (figure 4.37). The combined oxide thickness is made up from the spinel layer which grows at a parabolic rate and the underlying rhombohedral oxide which grows linearly with time over the period of the experiment. This method can be applied to any layer system where the two layers give separate diffraction peaks provided the total thickness is within the penetration depth of the X-rays.
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Figure 4.36. X-ray diffraction peaks from spinel and rhombohedral oxide layers on austenitic stainless steel as a function of time exposed to CO2 –2%CO at 1123 K (Tempest and Wild (1982)) (reproduced by permission of Plenum Press).
4.3.8
Macrostress and microstress measurement by diffraction
The changes in interplanar spacing in a crystal when subject to an elastic strain can be used as an internal strain gauge through a knowledge of the Bragg equation, equation (4.18). Here the change in the interplanar spacing, d, is given by differentiating the Bragg equation: " ¼ d=d ¼ cot :
ð4:41Þ
This effect on the position of the recorded diffraction peak is shown schematically in figure 4.38. It is necessary to have a measure of the stressfree interplanar spacing and then the strain can be converted to stress using elasticity theory (Hauk (1997) and Winholz and Kranitz (1996)). The fundamental relationship for evaluating a general strain state using diffraction is " ¼ "11 cos2 sin2 þ "12 sin2 sin2
þ "22 sin2 sin2 þ "13 cos sin2
þ "33 cos2 þ "23 sin sin 2
ð4:42Þ
where " is the strain in the direction defined in figure 4.39. The strain components on the right of equation (4.42) are related to the coordinate
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Figure 4.37. Thicknesses of the oxide layers formed on austenitic stainless steel as a function of time exposed to CO2 –2%CO at 1123 K determined by X-ray diffraction (Tempest and Wild (1982)) (reproduced by permission of Plenum Press).
system shown in figure 4.39. Hence the stress is given by ij ¼ Ehkl =ð1 þ hkl Þð"ij þ ½ hkl =ð1 2 hkl Þ"kk ij Þ
ð4:43Þ
where E is the elastic modulus for the particular crystal planes being considered, is the Poisson ratio and ij is the Kro¨necker delta function (Noyan and Cohen (1987)). In many cases the principal stress directions can be deduced by symmetry considerations so that three strain values are
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Figure 4.38. The effect changes in interplanar spacing, d, on the position of the recorded diffraction peak.
sufficient to establish three principal stresses: ij ¼ fEhkl ½ð1 hkl Þð1 2 hkl Þgfð1 hkl Þ"11 þ hkl ð"22 "33 Þg
etc: ð4:44Þ
In addition it is possible to determine the near surface biaxial stress by considering the simplification that 11 ¼ 22 and 33 ¼ 0. X-ray diffraction The wavelength of X-rays is between 0.1 and 0.2 nm and as such the penetration into materials is limited to about 10 mm so that the material sampled is confined to the surface layers where the stress state can be considered to be biaxial. Hence the interrelationship between the measured change in the diffraction peak position and the stress is given by 2 ¼ ½2 ð1 þ hkl Þ tan =Ehkl ½sin2
ð4:45Þ
where in radians and is the angle of the specimen with respect to the incident X-ray beam. Therefore a plot of 2 versus sin2 results in a straight
Figure 4.39. The strain ellipsoid where the principal strains are "1 , "2 and "3 .
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Figure 4.40. The strain components on the right of equation 4.42 related to the coordinate system .
line with a slope equal to the first term in equation (4.45) (figure 4.40). Here the term (1 þ hkl )/Ehkl is specific to the particular material and diffraction planes examined and is determined by prior calibration. The basic relationships given by equation (4.45) reveals requirements for the X-ray diffraction conditions (Doig et al (1985)). The sensitivity for stress measurement increases both as and tend to /2. A practical limit to is /3 and this is controlled by the spread of the X-ray beam and focusing for most diffraction systems. Moreover since the value of tan increases rapidly as tends to /2 it is preferable to select an appropriate diffraction peak, free from overlap, at a large diffraction angle. In general to achieve an accuracy of 10 MPa in evaluated stress the position of the diffraction peak has to be measured to better than 0.018. For stress measurement both laboratory and dedicated transportable computer controlled X-ray systems can be used. Figure 4.41 shows an example of a transportable ganimeter fitted with a proportional counter. Also this ganimeter can be fitted with a linear position sensitive detector in the side inclination orientation. The results of the measured residual stresses across a repair weld made in a low alloy ferritic CrMoV steel plate with C– Mn steel weld metal is shown in figure 4.42 (McDonald et al (2002)) using Cr K X-radiation that gives a diffraction peak at a position of 2 ¼ 1568. Here the results, figure 4.42(a), are compared with a stress profile calculated by finite element analysis, figure 4.42(b). Stresses in thin films can be measured using a glancing incident arrangement where the depth of X-ray penetration is reduced by using incident beam angles of 18. This technique has been applied to the measurement of stresses in diamond like films (Mohrbrachen et al (1996)). An extension of this technique to incident angles of <0.58 leads to the X-ray beam forming an evanescent wave which penetrates 3 nm: grazing incidence diffraction (Marra et al (1979)). Here the detector is positioned at 2 to the incident
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Figure 4.41. An example of a transportable X-ray stress measurement system fitted with a proportional counter measuring stresses on a turbine alternator end ring.
beam, just above the specimen surface such that the diffraction plane normal is almost within the surface. In this way a direct measure of the in-plane strain is obtained. In general the shape of the diffracted X-ray peak is a convolution of line profiles arising from several sources of imperfection, but in particular crystallite size and microstrain (Suryanarayana and Grant-Norton (1998)). Certainly X-ray diffraction peak profile analysis has been widely used to evaluate the contribution of these different microstructural parameters (Sommers and Mittemeijer (1995) and Bilger et al (1996)). To study these contributions it is necessary to have a measure of the integral breadth and shape parameter of the peaks. In addition, there is a contribution from instrumental broadening that has to be separated from the peak broadening. Crystallite size: X-ray diffraction peak broadening arising from crystallite size is inversely proportional to the domain thickness, t, perpendicular to the particular diffraction plane. Hence the integral breadth of the peak due to the thickness is given by S / 1=t :
ð4:46Þ
Microstrain: This refers to the condition where the internal strains in a polycrystal vary from grain to grain. Here the elastic strain is given by " ¼ cot d
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Figure 4.42. The results of the measured residual stresses across a repair weld made in a low alloy ferritic CrMoV steel plate with C–Mn steel weld material (McDonald et al (2002)) using Cr K X-radiation that gives a diffraction peak at a position of 2 ¼ 1568 (a) compared with strain gauge measurements and (b) a finite element calculation of the stresses.
hence the peak broadening is given by D ¼ 2"= cot ¼ 2" tan
ð4:48Þ
and in terms of sin = ¼ "d where d is the reciprocal lattice distance. The total broadening for a given diffraction peak less the instrumental contribution is given by ¼ S þ D
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ð4:49Þ
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Figure 4.43. A plot of integral breadth versus d ð1=dÞ has a gradient proportional to the microstrain and an intercept proportional to the crystallite size.
and / 1=t þ "d :
ð4:50Þ
As a consequence a plot of integral breadth versus d ð1=dÞ has a gradient proportional to the microstrain and an intercept proportional to the crystallite size (figure 4.43). Synchrotron X-ray diffraction The use of diffraction techniques based upon hard X-ray emissions from synchrotron sources has evolved more recently with the advent of the third generation of sources such as the European Synchrotron Research Facility in Grenoble, France (Lebrun et al (1995), Daymond and Withers (1996), Webster et al (1996a,b) and Withers and Webster (2001)). Such sources produce X-ray beams of high energy (50–150 keV) and intensity. The latter is increased by up to about three orders of magnitude compared with the more conventional laboratory X-ray sources. This leads to a combination of improved resolution with this high intensity. As a consequence the technique has been applied to the measurement of strain within bodies based upon the approaches described earlier in this section. Certainly the potential to obtain data at fast acquisition rates and in materials with a significant strain gradient that can be readily resolved has resulted in increased use of this approach to measure strain. To date three main methods summarised in figure 4.44 have been used (Withers and Bhadeshia (2001)). These are (i) traditional 2 scanning
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Figure 4.44. Three main methods using hard X-rays. (a) 2 scanning; (b) low angle transmission; (c) energy dispersive.
(Withers and Webster (2001)), (ii) high energy low angle two-dimensional transmission diffraction (Poulsen et al (1997)) and (iii) whole beam high energy dispersive methods (Reimens et al (1998)). In each case small volumes of material 20 mm 1 mm can be sampled. Neutron scattering and diffraction Neutrons, with no charge, do not interact with the electrons surrounding the nucleus and are perturbed only by the atomic nucleus in a ball-type collision (Slattery and Windsor (1983) and Allen et al (1985)). As a result the neutrons penetrate many millimetres into most solids, which is an advantage in that little or no specimen preparation is required, but is a disadvantage when small specimens need to be examined. A major problem with the technique is obtaining a source of neutrons. An experimental nuclear reactor is required and these are few and far between. In the UK to overcome this limitation neutrons are produced at the ISIS facility by the spallation process (Withers and Webster (2001)). In this facility a heavy metal target is bombarded with pulses of high energy protons from a synchrotron accelerator. This ejects neutrons from the nuclei of the target atoms and produces an intense neutron pulse with a relatively small level of heat production in the target material. The neutrons produced have high energies and are slowed to speeds that then result in wavelengths suitable for diffraction experiments and other investigations. This is achieved by placing hydrogenous moderators around the target. As a consequence the source of neutrons is appropriate for investigating a range of material parameters.
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Figure 4.45. A neutron diffraction pattern from a bent mild steel bar (Allen et al (1985)) (reproduced by permission of Taylor and Francis).
Neutron beams can be monochromated by diffraction from a germanium single crystal and collimated using cadmium slits before impinging on the specimen. The diffracted beam is detected using counters of a type similar to the proportional gas counters used in X-ray diffraction but with BF3 as the gas. Several counters are required and these are placed around the diffracting zone. Neutron diffraction takes the same basic form as Xray, electron and photon diffraction. A monochromatic beam of neutrons incident on a material will be diffracted by the atoms according to the Bragg equation. A typical diffraction pattern obtained from a bent mild steel bar is shown in figure 4.45 and illustrates the good energy resolution that can be achieved. The neutron scattering amplitude, which is defined as the intensity of the diffracted beam at a distance of 1 cm from the nucleus as a fraction of the incident beam intensity, appears to vary in a random manner throughout the Periodic Table. This is unlike electrons and X-rays where the amplitude increases systematically with atomic number. This response by neutrons has certain advantages for the technique. For example, in certain ordered alloy systems such as Cr–Ni alloys the superlattice reflection intensities are a function of the difference in scattering amplitudes of the Cr and Ni atoms. This leads to significant superlattice neutron diffraction peaks, whereas using X-ray diffraction such peaks
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Figure 4.46. Neutron diffraction patterns of Yba2 Cu3 O7 recorded at room temperature for (a) fresh specimen, (b) after a gap of 100 h and (c) 175 h. Dashed line indicates room background (Dasannacharya and Sequeira (1988)).
would be negligible. Furthermore it allows the location of light elements in the presence of heavier atoms or distinquishing between adjacent elements in the Periodic Table. Neutron diffraction allows lattice parameter measurement, the identification of phases, the detection of preferred orientation and the determination of residual stress. Particularly neutron diffraction is important for investigating cation ordering in alloys, mixed oxides and minerals, microstructural changes involving low atomic mass elements during phase transformations in a variety of hydrogeneous materials and ceramics. Hydrogen has a large scattering cross-section to neutrons and a feature used to investigate moisture absorption in high Tc superconducting ceramics. Figure 4.46 shows neutron diffraction patterns obtained from YBa2 Cu3 O7 which has a 1 :1 :3 stacked perovskite crystal structure (Dasannacharya and Sequeira (1988)). It has been noted that the superconducting properties change with environmental changes and this is related to changes in the ordered structure as shown in figure 4.46. A benefit of neutron diffraction is that it can be used to probe, nondestructively, the state of strain within a polycrystalline material which for typical engineering components can be to a depth of many centimetres. By limiting the irradiation volume and the field of view of the detector, it is possible to sample a small volume, 1 mm3 , within the body of a specimen. In general, one of two techniques are used for these measurements: conventional
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/2 scanning as described for X-ray diffraction or a time-of-flight approach (Withers and Bhadeshia (2001), Winholz and Kravitz (1996), Yagchi et al (2000) and Todd et al (1997)). The former is well suited to neutron beams produced by reactor sources whereas the latter is appropriate to the pulsed beam generated from a spallation source. In the time-of-flight method the Bragg angle is held constant, usually at 2 ¼ /2, and the incident wavelength is varied. In this case each pulse of neutrons leaving the moderated spallation target has a range of neutron energies. The most energetic neutrons arrive at the target in advance of the least energetic so that the energy and, hence, the wavelength of each detected neutron can be obtained from the time that has elapsed since the neutron pulse was produced. In this case the strain " is given by " ¼ t=t
ð4:51Þ
where t is the time of flight. As strain resolution depends upon the accuracy of the measurement of t, high resolution instruments invoke large flight paths, 100 m. An approach adopted to analyse these diffraction spectra is to use the Rieveld refinement (Webster (2000) and Young (1993)) to derive a single value of the lattice spacing by simultaneously fitting a curve to the intensity profile obtained from all the diffraction peaks obtained within the time of flight measurements (Daymond et al (1997)). This value is weighted towards the most intense peaks. The approach has been experimentally and theoretically demonstrated to provide a good representation of the bulk elastic response as compared to the relative insensitivity to tensile and compressive shifts of the various diffraction peaks. A complication when interpreting neutron diffraction data is the contribution of apparent strain arising as a result of diffraction from internal and external surfaces because the diffracting volume is only partially filled. These contributions are accommodated by including the diffraction geometry and attenuation. An alternative is to use the so-called z scan geometry where the surface is approached by bringing the specimen into the gauge volume vertically to eliminate lateral displacement of the centre of gravity of the scattering volume, thereby eliminating geometrical peak shift (Spooner and Wang (1997)). Additional information can be obtained from small angle neutron scattering (SANS) of long wavelength neutrons (Hutchings and Windsor (1986) and Windsor et al (1984)). Long wavelength neutrons are not diffracted by periodic arrays of atoms but are diffracted by fluctuations in the scattering density of the matrix as a result of the presence of particles, precipitates, voids etc. Defects in the range a few nanometres to 50 nm are detected in specimens up to 20 mm thick. Neutron diffraction is expressed in terms of a macroscopic scattering cross-section: the effective area A which scatters neutrons into a solid angle T. If, for example, particles have a mean diameter D then for a low volume fraction V the macroscopic
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Figure 4.47. Plot of dA=d versus Q2 for a collection of spherical defects (reproduced by permission of the Institute of Materials).
cross-section is given by dA VD3 ðp m Þ2 expðQ2 D2 =20Þ ¼ 6 d
ð4:52Þ
where is the neutron scattering solid angle, Q is a scattering vector and p , m , are scattering length densities of the particle and the matrix. If ln (dA=d) is plotted against Q2 , a straight line is be obtained with a slope of D2 /20 from which the particle size can be obtained (figure 4.47). The technique has been applied to the study of gamma prime precipitation in nickel based superalloys. It is possible to determine the size of these particles by TEM but it is more difficult to establish their volume fraction by this technique. By comparison, SANS measures both the mean particle size and the volume fraction in material and has been compared with TEM values (Windsor et al (1984)) (figure 4.48). The SANS and TEM results agree for all gamma prime particles detected and there is agreement between the two techniques for the volume fraction for ageing times up to 1000 h at 700 8C, but above this time SANS gives a decreasing volume fraction whereas TEM indicates the volume fraction to be essentially constant. Here the poor resolution of SANS is responsible for the divergence. However, it should be remembered that SANS is a relatively straightforward technique and results can be obtained quickly, whereas there is considerable laborious and time consuming work required in producing thin specimens for TEM. An extension of neutron diffraction is neutron interferometry. Figure 4.49 shows a typical three crystal interferometer constructed from a perfect silicon single crystal to give three identical thickness parallel slabs (Dasannacharya and Sequeira (1988)). This provides an emerging neutron beam with a sinusoidal interference as a function of angular position of the phase shifts. Figure 4.50 shows typical measured patterns such that the periodic of modulation is directly related to the average scattering length of the nuclei
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Figure 4.48. Mean particle size and volume fraction of gamma-prime precipitates in alloy PE16 determined by SANS and TEM (reproduced by permission of the Institute of Materials).
distributed in the phase shifter. Here estimates of small quantities of hydrogen in vanadium have been undertaken (Ranch and Seidli (1987)). Proton scattering Proton scattering is dealt with in more detail in chapter 7 on atom/ion sources and will only be briefly mentioned here. The proton has the same mass as the neutron but has a charge equal in magnitude but of opposite sign to the electron. It will therefore interact with the electron cloud but, although the forces exerted by the electrons will be of similar magnitude to interactions between electrons, the effect on the proton motion will be less marked because of the vastly greater momentum of the proton. Protons therefore penetrate much farther into materials than electrons but the diffraction of protons has
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Figure 4.49. A schematic picture of a typical three crystal neutron interferometer (reproduced by permission of North-Holland Publishing Company).
similarities to both electron and neutron diffraction. Considerable channelling of protons takes place down suitable crystallographic directions and in this case the number of scattered particles is reduced. Figure 4.51 illustrates the effect of orientation on scattering with a silicon model oriented in (a) a random direction, (b) with planes aligned and (c) with an axis aligned. Proton and ion scattering can be recorded either by using a setup with a specimen placed in front of a photographic plate or by detecting the scattered ions in specific directions. Figure 4.52 shows schematically the arrangement for production of channel patterns while figure 4.53 shows schematically the spectra (Rutherford backscattering (RBS)) that would be obtained for a layer of amorphous silicon on a single crystal of silicon containing a buried impurity.
Figure 4.50. Neutron interference patterns resulting from small quantities of hydrogen (0.004 to 0.035) in vanadium (reproduced by permission of North-Holland Publishing Company).
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Figure 4.51. Model of silicon aligned (a) randomly, (b) with a plane parallel to and (c) with an axis parallel to the ion beam (Courtesy AEA Technology). # UKAEA 1992.
It is worth noting here that ion scattering can take a similar form to proton scattering, but as the mass of the ion increases so the damaging potential becomes greater and diffraction or channelling is less likely. As yet this technique is little used.
Figure 4.52. Schematic diagram for obtaining a proton channelling pattern.
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Figure 4.53. Random alignment and channelling spectra for a structure containing an amorphous surface layer and a substitutional impurity (courtesy AEA Technology). # UKAEA 1992.
Kossel diffraction In scanning electron optical instruments the electron beam has sufficient energy, >15 keV, to generate characteristic X-rays from a specimen, but as discussed in chapter 2 the electron interaction volume is small giving a point source typically 2 mm diameter of generated X-rays when the beam is stationary. When Bragg diffraction is satisfied, a divergent beam produces an X-ray diffraction pattern called a Kossel pattern (Kossel (1936), Morris (1968), Swindells (1979) and Rowlands et al (1968)) (figure 4.54) which
Figure 4.54. Geometry of diffraction and absorption Kossel line conics derived from a single crystal (after Swindells (1979)).
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Figure 4.55. Kossel diffraction pattern from a martensite plate in a 32% Ni steel (b) together with the stereographic projection showing the martensite habit planes, (a), and a corresponding optical micrograph (c) (Rowlands et al (1968)) (reproduced by permission of the Institute of Materials).
provides a measure of interplanar spacing and lattice orientation. The pattern can be recorded on a photographic emulsion as a back diffraction pattern, with the lines showing dark against a lighter background, or by transmission through thin samples as absorption or deficiency patterns. The advantage of generating these patterns with a scanning electron beam instrument is that the beam can be located accurately within specific microstructural regions. As a result individual phases in a multiphase material can be examined by X-ray diffraction on a scale comparable with the resolution in an optical microscope. The pattern is related directly to the specimen since it is not processed by the instrument and is independent of the incident electron beam direction. Kossel patterns provide orientation data which can be combined with twosurface trace analysis (section 4.3.5) to define crystallographic features observed by the optical and scanning electron microscopy of a few micrometres in size. Many applications exist which demonstrate the ability to provide a complete crystallographic description of the microstructure. Figure 4.55 shows a diffraction pattern obtained from a martensite plate in a 32% Ni steel that enables the habit plane to be established in the associated stereographic plot (Rowlands et al (1968)). Kossel X-ray diffraction from bulk crystalline materials is now becoming a less specialised technique since patterns which are easily interpreted can be obtained from specimens with grain sizes <5 mm. Swindells (1979) has
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pointed out that the availability of this technique should lead to a reappraisal of the use of more conventional X-ray diffraction. For example, there is little point in reducing a polycrystalline substance to powder to establish lattice constants by the Debye–Scherrer method if information can be obtained to the required precision using Kossel microdiffraction. Moreover, with polycrystalline multiphase specimens each phase can be studied separately instead of as a mixture.
4.4 4.4.1
Electron diffraction Wave nature
For many years following its discovery the electron was considered to be a particle carrying a negative charge. It was Davisson and Germer (1927) who conclusively demonstrated that electrons also have a wave character by producing a back electron diffraction pattern from mica. The dual particle/wave nature of the electron is firmly established and for many purposes such as diffraction, the behaviour parallels that of the photon. Indeed two-slit diffraction has been demonstrated by Tonomura et al (1989) by firing individual electrons at each slit. In the sequence shown in figure 4.56 each spot on the television screen represents the arrival of one electron. After a few hundred electrons passed through the slits (figure 4.56(a–c)), the pattern remains apparently random but when a few thousand electrons had arrived the characteristic fringe diffraction pattern is developed (figure 4.56(d,e)), demonstrating the wave characteristic. The wavelength of the electron is determined by its energy. If the electron beam is characterised by a propagation vector K0 then the wavelength is given by the expression ¼
2 : K0
ð4:53Þ
The interrelationship between the wavelength and the accelerating voltage of the electron beam is also discussed in chapter 6. However, the relativistic corrected relationship is given by ¼
1:226 ½Eð1 þ 0:96 106 EÞ1=2
ð4:54Þ
where is in nm and E is the electron energy in volts. The variation of the wavelength with relativistic accelerating voltage is shown in table 5.2. We now move on to consider the diffraction of electrons by crystalline materials. While the basic principles involved are similar to those described earlier in this chapter there are a variety of situations where specific differences are encountered. The wave nature of the electrons means that they can be used
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Figure 4.56. Demonstration of double-slit diffraction for electrons (Tonomura et al (1989)). Each spot represents the arrival of a single electron. When a few hundred electrons have reached the screen, (a), (b) and (c), the pattern appears to be random but interference effects can be observed after the arrival of a few thousand electrons, (d) and (e) (reproduced by permission of the American Association of Physics Teachers).
to study materials by observing electrons that are scattered back from a surface or by allowing them to be transmitted through thin foils of material. In back diffraction the observed effects are strongly dependent on the energy of the incident electron beam. In this section we will separately consider diffraction in transmission, high energy back diffraction, low energy back diffraction and the corresponding high energy processes. 4.4.2
Transmission of electrons
The number of diffraction methods that have become available for studying materials to a high spatial resolution has increased significantly over the
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past 10 to 20 years with the development of electron microscopies that have improved vacuum systems to reduce specimen contamination and the ability to produce convergent electron beams and indeed various beam operating modes including scanning and rocking. This capability provides the opportunity to evaluate fine-scale phases and lattice defects more uniquely than by other techniques that sample larger volumes of material. In the transmission electron microscope the incident electron beam passes through a thin foil of material and depending on the lens conditions selected an image of the foil or a diffraction pattern is observed (Hirsch et al (1965), Amelinckx et al (1978), Loretto (1984), Jones (1988), Edington (1976), Warren (1979) and Beeston et al (1983)). Normally a transmission electron microscope produces a diffraction pattern by a method known as selected area diffraction (figure 6.36). For this condition the beam of incident electrons is parallel at the specimen surface and part of this beam passes without diffraction, but a small fraction of the electrons is diffracted out of the beam in directions determined by the Bragg diffraction condition. These beams are focused by the objective lens to form a diffraction pattern on the back focal plane and an image at the fluorescent screen. The image results from a beam defined by the diameter of the selecting aperture. By altering the conditions of the intermediate lenses it is possible to focus the diffraction pattern on to either the fluorescent screen or photographic plate. As the electron beam travels through the thin foil so a fraction of the electrons will be diffracted out of the primary incident beam. Thus the primary beam will lose intensity on passing through successive atom layers of the specimen while the diffracted beams will become increasingly intense. Similarly the diffracted beams will further diffract and lose part of their intensity and indeed a fraction will be diffracted back into the main beam. Electron diffraction in transmission is described essentially by the kinematical and dynamical theories. In the kinematical theory it is assumed that the incident beam does not lose intensity in passing through the foil and that there is no subsequent interaction between diffracted beams. However, the dynamical theory accounts for these effects and is therefore a more complete description, albeit more complicated. Kinematical theory of electron diffraction This theory assumes that the intensity of the main beam remains constant as it travels through the foil and ignores the scattering of diffracted beams back into the main beam. Therefore it is essentially the same theory as used to describe X-ray diffraction (Cullity (1979)). Initially an incident plane electron wave of the form eikz is assumed to be scattered by point sources in a regular lattice which identifies the positions of intensity maxima and minima. This is then modified by considering the positions of the atoms with respect to the array and by including a term to account for the scattering of electrons by
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Figure 4.57. Bragg conditions for electron diffraction where g is the reciprocal lattice spacing and LO ¼ 1= .
individual atoms. As for the treatment of X-ray diffraction an atomic scattering factor f is derived (Mott and Massey (1976)) which is given by Me2 2 ðZ f Þ ð4:55Þ f ¼ 2 8h "0 sin2 where Z is the atomic number, f the X-ray atomic scattering factor and "0 is the permittivity of vacuum. The amplitude of the scattered wave is described by ¼
eik:r X X fi expf2i½ðmi þ ii Þgi þ g r m i ¼ eik:r =rFL
where F ¼ structure factor ¼ L ¼ Lattice factor ¼
X
X
ð4:56Þ ð4:57Þ
fi expf2iði1 g1 þ i2 g2 þ i3 g3 Þg
ð4:58Þ
expf2iðm1 g1 þ m2 g2 þ m3 g3 Þg:
ð4:59Þ
i
m
F depends on the distribution of atoms in the unit cell while L depends on the type, shape and size of the crystal. The intensity is therefore ¼ 1=r2 jFj2 jL0 j2 :
ð4:60Þ
The maximum in L occurs when gi is a scalar with integer value when g ¼ ðS S0 Þ= ; S, S0 are unit vectors in the direction of the incident and diffracted electron beams (figure 4.57(a)). Since g is the reciprocal of the lattice spacing d and LO is constructed to be 1/ (figure 4.57(b)). sin ¼ OG=2OL ¼ g=2ð1= Þ ¼ ð1=dÞ=ð1= Þ
ð4:61Þ
d sin ¼ :
ð4:62Þ
or
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The theory here assumes that there is an average of one electron per unit volume in the beam. If v is the electron velocity then from equation (4.61) the number of electrons in the diffracted beam which cross an area dS, perpendicular to the beam, and at a distance r from the crystal surface is v dS ¼ v=r2 F 2 L2 dS
ð4:63Þ
Since dS=r2 is the solid angle subtended at the crystal by dS, the number of electrons scattered into unit solid angle per unit time is vF 2 L2 . Thus the scattering cross-section of the crystal, , is given by the number of electrons diffracted per unit solid angle/unit time divided by the number of electrons in incident beam crossing unit area/unit time F 2 L2 . It has been assumed to this point that the incident beam is parallel, has a single incident energy and is not distorted. Also crystals will not be perfectly formed, there will be some elastic deformation, dislocations and crystal misorientations. These will result in the cross-section having a value which depends on the mean value of L2 . It can be shown that (Rymer (1970)) the observed scattering cross section will have a value, given by ¼ ½V=v1 NF 2
ð4:64Þ
where V is the volume of the unit cell, v1 is the volume of the diffracting shell, N is the total number of unit cells in the crystal and F is the structure factor. The term V=v1 depends on the experimental conditions and in an experiment would be constant. Thus the intensity of the diffracted beam is determined by F 2. Consider a face centred cubic crystal with atoms at positions i1 , i2 , i3 ¼ 0, 0, 0; 0, 12, 12; 12, 0, 12; 12, 12, 0 (see chapter 1). From equation (4.59) substituting F 2 ¼ f ½1 þ expfiðg1 þ g2 Þg þ expfiðg2 þ g3 Þg þ expfiðg3 þ g1 Þg ð4:65Þ since the g are integers and the exponential terms are 1, there are two possible situations: (i) the values for g are either all even or all odd and the terms are all þ1 so that F 2 ¼ 4f ; (ii) the values for g are mixed, two 1 and one þ1, when F 2 ¼ 0. Therefore the diffracted beams are associated with these specific locations on the reciprocal lattice and are identified by g1 , g2 , g3 known as Laue indices, and are identical with the Miller indices specifying the direction of the atom planes leading to the diffraction. To determine the intensity of the diffracted beam it is appropriate to consider the general case where there are many crystallites with all possible orientations and the diffraction pattern will be a continuous ring. If the incident and diffracted beams have a small divergence then g will vary over a small range and the volume occupied by the diffracted beam, V1 , will be V1 ¼ 4g2 g
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ð4:66Þ
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Figure 4.58. Projection of the electron diffraction pattern onto a photographic plate.
The pattern observed, if recorded on a photographic plate will be magnified in proportion O0 G0 =OG ¼ L (figure 4.58), and the radius, R, and width, , of the diffracted ring are related by V1 ¼ 4R2 R=ð LÞ3
ð4:67Þ
which if I0 is the intensity of the incident beam then the number of electrons, Ne , diffracted into unit solid angle per unit time is Ne ¼
I0 VNF 2 ð LÞ3 : 4R2 R
ð4:68Þ
The area of the ring is 2R R=L2 therefore the number of electrons diffracted into the ring is I0 VNF 2 3 L=2R. If I0 is the incident electron beam current, I the diffracted electron beam current and A the area of the specimen sampled then I=I0 ¼ F 2 2 A=2R2 :
ð4:69Þ
In principle all the quantities except F can be measured; F is determined by calculation or experiment. The dynamical theory of electron diffraction In the more complete dynamical theory of electron diffraction, account is taken of incident electron beam intensity losses by diffraction as it passes through successive crystal layers, but at the same time gains intensity by
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diffraction of the initially diffracted beams back into the direction of the incident beam. After the incident electron beam has passed through a certain distance of the crystal, an equilibrium or dynamical situation occurs in which the ratio of the intensity of the incident beam to the intensity of the diffracted beam is a constant for all thicknesses greater than this minimum value. In electron diffraction this distance is approximately 10 nm compared with about 0.1 mm in X-ray diffraction, and is the reason why the kinematical theory can accurately predict X-ray intensities while the dynamical theory is required to describe electron diffraction. The theory considers the diffraction of electrons through either a wedgeshaped crystal, which is the case for most specimens thinned for examination in the transmission electron microscope, or a parallel sided crystal by obtaining a solution to the Schro¨dinger equation representing the primary and diffracted wave. A significant difference between the predictions of the kinematical and dynamical diffraction theories concerns the diffracted beam intensity when the Ewald sphere passes close to a reciprocal lattice point. In the kinematical theory, a diffracted intensity is predicted only if the Ewald sphere actually passes through the reciprocal lattice point. However, the dynamical theory predicts a significant intensity for the diffracted beam if the Ewald sphere is close to the reciprocal lattice point. Indeed, it is sufficient that the reciprocal lattice point be within 103 of the radius of the Ewald sphere to give a diffracted intensity. It is possible to compare the predictions of diffracted intensity by the dynamical and kinematical theories. Essentially the two theories give similar results if the crystal thickness does not exceed one extinction distance, that is the distance between two diffraction maxima. However as crystal thickness increases so the accuracy of the kinematical theory decreases and it becomes increasingly necessary to employ the dynamical theory (Cowley (1986)). 4.4.3
Electron diffraction with static beams
As described more fully in chapter 6, the evacuated column of an electron microscope contains an electron source or gun together with an assembly of lenses (Agar (1974), Cosslet (1970) and Grundy and Jones (1976)). On leaving the gun the electrons are formed by the lens into a crossover and this demagnified source image is projected on to the specimen by condenser lenses. The first condenser forms a demagnified image of the source about 1 mm diameter (figure 6.34), that is subsequently projected on to the specimen by a second condenser lens with a magnification of about two. The final illumination electron beam which is incident on the specimen may be as small as 2 mm in diameter which is sufficient to fill the screen at highest magnifications. The current density at the specimen depends upon the electron source characteristics and the divergence angle (Hirsch et al (1965) and Gronsky (1980)); however, typically the condenser aperture and
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the operating divergence angle would be 400 mm in diameter and 103 rad respectively for a 100 keV instrument. This second lens gives both fine control over the area illuminated, thereby reducing contamination from neighbouring areas and a beam of low divergence for an equivalent amount of defocusing. A smaller value of reduces the effective electron source size, and increases the coherence length of the beam, thereby providing improved contrast and resolution in images and diffraction patterns. On passing through a thin foil specimen the electrons enter an objective lens whose design and aberrations critically affect the performance of the microscope. Figure 6.34(b) shows coherent Bragg diffracted electron beams leaving the specimen to form an intermediate low magnification image I1 . The intermediate lens produces a second intermediate image I2 which is magnified at the viewing screen by the final projector lens. For a parallel incident electron beam the diffracted beams leaving the specimen are focused on the back focal plane of the objective lens (figure 6.36). This diffraction pattern is observed if the back focal plane is projected on to the viewing screen by reducing the excitation of the first projector lens (figure 6.36). Interchangeable objective apertures varying in size from 50 mm to 200 mm are located close to the back focal plane of the objective lens enhance contrast. Figure 4.59(a) shows a typical single crystal transmission electron diffraction pattern obtained from an M23 C6 type carbide precipitate. For 100 keV electrons the radius of the Ewald sphere (figure 4.57), is 2.5 nm and the Bragg angles are small, 102 radians, so that the diffraction sphere approximates to a plane. When the electron beam is parallel to a prominent zone axis in the diffracting crystal, several reciprocal lattice points intersect the diffracting sphere giving a projection of the prominent zone in the reciprocal lattice. Increasing the accelerating voltage of the electrons from 100 keV to 1000 keV allows diffraction patterns to be obtained from thicker regions of a foil specimen, and since the radius of the diffracting sphere is increased Laue zones are more extensive. Typical zones for a bcc crystal are shown in figure 4.59(b). To interpret an unknown pattern the diffraction spots or rings (if polycrystalline) it is necessary to assign Miller indices corresponding to the diffracting lattice planes. Figure 4.60 shows the diffraction pattern from a thin foil of a nickel based PE16 alloy, a face centred cubic (fcc) matrix, which shows the pattern of superlattice spots from the 0 phase. The terminology used to describe these patterns includes incident beam divergence, angular resolution and the spatial resolution. The divergence is the half apex angle of the cone of the incident electron beam, . Divergence can be either measured from an electron diffraction pattern or calculated from a knowledge of the particular electron microscope geometry. The angular resolution of the diffraction pattern is simply the angular width of the smallest intensity fluctuation in the pattern that can be attributed to the specimen.
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Figure 4.59. Electron diffraction (a) extracted carbide ðxÞ from 2.25%Cr–1%Mo steel is a composite of two carbides; corresponding electron diffraction pattern showing [2 33] fcc zone pattern where splitting of diffraction spots corresponds to lattice spacing for M23 C6 and M6 C carbides (courtesy D Lonsdale). (b) Commonly occurring diffraction patterns for bcc crystals.
Figure 4.60. Diffraction pattern obtained from thin foil of fcc matrix (PE16 alloy) showing superlattice spots from the 0 phase (courtesy C Baker).
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Selected area The advantage of selected area electron diffraction in the transmission electron microscope is that a small area of foil specimen about 1 mm diameter can be identified and from this structural information recorded rapidly. By comparison the minimum area selected using X-ray diffraction is approximately two orders of magnitude greater and requires commensurately longer exposure times. The basic information obtained from either a single or a sequence of electron diffraction patterns is the orientation of the planes of atoms with respect to the electron beam direction and the image and, therefore, in the case of a multiphase system the individual crystal structures and orientation relationship of one phase to another. To achieve this, a selecting aperture of appropriate size is used to identify the feature of interest and then the aperture and image are set to ensure they have a coincident focal plane. A single crystal in the electron beam will produce essentially a regular and symmetrical arrangement of diffraction spots, each with a value of h; k; l. Spots equidistant from the centre and diametrically opposite are associated with the same crystal planes of indices h; k; l and h; k; l respectively. Their simultaneous appearance is a consequence of the small wavelength of the electrons, the small divergence angle and other instrumental parameters. To establish the solution of these patterns requires that the distances and angles can be related. This is achieved by determining the camera constant for the particular instrument where ðDdÞ ¼ CL
ð4:70Þ
where L is the effective camera length, is the wavelength, D is the ring diameter of a standard electron diffraction pattern and d is the interplanar spacing; CL is the camera constant. Various methods are used to establish this constant and these have been described by Andrews et al (1971). Figure 4.61 shows the diffraction pattern obtained from an area of foil containing 0 plates (hcp) in a niobium 40% Zr alloy (the TEM image of this is illustrated in figure 6.46). This pattern contains diffraction spots showing the foil normal corresponds to the {111} plane for the bcc phase matrix. However, the additional diffraction spots match with two variants of the [00.1] zone for the hcp 0 plates and, indeed, there is streaking in the h100i directions. From this and similar electron diffraction patterns it is possible to show that the orientation relationships between the 0 plates and the matrix satisfies the Burgers relationship where (110) ||(00.1) and the [111] ||[11.0] (Burgers (1934)). High resolution To form a high resolution diffraction pattern the specimen is mounted on a special stage positioned below the final projector lens of the transmission electron microscope (figure 4.62(a)), at a distance of 300 mm from the
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Figure 4.61. Selected area electron diffraction pattern taken from an area of phase niobium 40% zirconium alloy containing 0 plates. Foil normally corresponds to the [111] and shows two variants of the Burgers orientation relationship for the 0hcp and bcc product and parent phases.
photographic recording plate. Under these conditions all the lenses are used to focus the electron beam to a small spot, thereby reducing both the aperture angle and interference from chromatic aberration and lens instabilities. Such a procedure is suited for determining both lattice parameter and crystal structure and hence identification of phases. A typical application is the determination of the various types of carbide precipitates in steels. Figure 4.62(b) shows the ring pattern produced from fine grained gold and a G-silicide ( fcc, a ¼ 1 nm) in an iron alloy containing silicon and tantalum (Brown and Whiteman (1969)). Micro area There are obvious advantages to obtaining diffraction patterns from areas less than 500 nm in diameter in multiphase phase alloys (Warren (1979)). The region of interest may be a small second phase precipitate, a particular grain in a small grain size material, a sub-grain developed in a mechanically deformed material or a region of the strain field of a second phase precipitate. Prior to the introduction of the STEM the lens configuration used for diffraction was limited to areas greater than 500 nm by the sperical aberration of the objective lens. Nano-area electron diffraction in a scanning transmission electron microscope is extensively applied to a range of
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(a)
Figure 4.62. High resolution electron diffraction. (a) The standard mode of operation. (b) Typical pattern obtained from fine grain size gold and G-silicide in an iron base alloy containing silicon and tantalum (Brown and Whiteman (1969)).
specimens, in particular semiconductors (Cowley (1986)). A nanometre-size electron beam is formed by the two condenser lenses and the pre-field of the objective lens of the electron microscope. The resultant electron diffraction patterns from areas down to about 2 nm diameter are then recorded on
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Figure 4.63. Bright field image of a wedge of the Ga0:63 Al0:37 As/GaAs superlattice, (a) showing the equal-thickness fringes and (b) nano-diffraction patterns from the Ga0:63 Al0:37 As and GaAs regions (Tanaka and Mikama (1988)).
high sensitivity film or continuously in a real time cathode ray tube system (Tanaka (1989) and Tanaka and Mikama (1988)). Figure 4.63 shows the application of this technique to a superlattice of Ga0:63 Al0:37 As/GaAs. The 2 nm diameter electron beam is traversed across the bright field image contrast of the interface of interest as shown in figure 4.63(a). The pattern obtained from the Ge0:63 Al0:37 As compared with that of the GaAs shows that the 200 reflection becomes weak and almost disappears in the GaAs due to the small structure factor for this diffraction condition in this material. Certainly it is now possible to undertake high resolution electron diffraction to a scale comparable with the resolution of the images that can be obtained. Kikuchi diffraction A special type of diffraction pattern is obtained from thin foils specimens of greater than a few hundred nanometres thick (figure 4.64). As the thickness of the crystal increases so the intensity of the diffraction spots decreases until eventually they are masked by the background. On this background are bright and dark lines oriented with directions related to the crystal symmetry.
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Figure 4.64. Kikuchi lines observed in transmission foils.
These lines were first discovered by Kikuchi in 1928 and his name has since been used to describe them. They arise from Bragg diffraction of elastically scattered electrons as the incident beam penetrates the foil (figure 4.65). The angular spread of these electrons is large and leads to elastic scattering by the crystal lattice oriented at the Bragg angle. Therefore, electrons inelastically scattered in the direction OA will be diffracted into direction OB and vice versa. If the numbers of electrons diffracted in these two directions are equal there is no gain or loss of electrons travelling parallel to the OA and OB directions. However, as the scattering angle increases so fewer electrons are scattered. Following electron scattering more electrons follow OA than OB but on Bragg diffraction there is an overall loss of electrons travelling parallel to OA and a gain in electrons following OB. Scattering is such that conic sections of bright and dark Kikuchi lines are developed within the overall diffraction pattern (figure 4.65). These lines provide an accurate determination of specimen orientation since, while diffraction spots only change intensity when a crystal is tilted, the Kikuchi line pairs (bright plus dark) traverse the diffraction pattern as though rigidly fixed to the specimen (figure 4.65). The angle is small in Kikuch line formation and we may approximate the Bragg condition to 2d ¼ , where d is the interplanar spacing. If the distance between the Kikuchi lines is D and the specimen to photographic plate distance is L then D=L ¼ 2:
ð4:71Þ
Dd ¼ L:
ð4:72Þ
Thus The Kikuchi lines move as the crystal is tilted and only those Kikuchi lines corresponding to planes which make a small angle to the beam direction are viewed. As the specimen orientation is changed the visible Kikuchi lines alter depending upon the crystallographic axis of rotation. Twodimensional Kikuchi maps can be produced either by calculation or experimentally (figure 4.66). The latter figure shows a schematic Kikuchi
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Figure 4.65. (a) The origin of Kikuchi lines. (b) Schematic diagram showing Kikuchi line positions near (200) orientation for a fcc crystal: beam exactly parallel to [200], crystal tilted by about [002] direction into exact position for 020 diffraction, crystal tilted so that 020, 002 and 022 spots are simultaneously in exact diffracting condition. (c) The variation of the dislocation cell misorientation (angle) with strain (Lonsdale and Flewitt (1978)).
map for a bcc crystal centred on a [001] electron beam direction. An important parameter to determine is the precise deviation from the Bragg angle of crystal planes which give rise to spot diffraction patterns. This deviation parameter, Sg , is defined in figure 4.67 as the distance from the Ewald sphere in a direction parallel to the beam direction of the reciprocal lattice point giving rise to a diffraction spot. The simplest way to establish, Sg , is to measure the displacement of a Kikuchi line from the corresponding diffraction spot. When the precise Bragg condition is satisfied, the bright Kikuchi line will pass exactly through the directly transmitted beam and the corresponding dark line through the associated diffraction spot. The
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Figure 4.66. Schematic Kikuchi map for a bcc crystal centred on [001].
value of Sg at a particular deviation from the Bragg condition is given by geometry to be Sg ¼ g2 =2
ð4:73Þ
where g is the diffraction vector (see figure 4.67). Thus Kikuchi diffraction provides an invaluable method of establishing the electron beam direction, a measure of the deviation parameter and an ability to orient specific microstructural features accurately. An accuracy of 0.18 for orientation determination may be achieved from Kikuchi line measurements (Ball (1981) and Bendersky et al (1982)). The method is well suited for determining the small misorientations between sub-grains developed, for example, during
Figure 4.67. (a) Schematic diagram illustrating the method for determining S at the symmetry position. (b) Schematic diffraction pattern which would be obtained at the symmetry position.
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creep deformation. Indeed it has been possible to follow the progressive change of misorientation with creep strain in a-iron (Lonsdale and Flewitt (1978)) (figure 4.65(c)). Convergent beam patterns This class of diffraction patterns was first demonstrated in 1939 by Kossel and Mollenstedt but their use and application has only recently become widespread following the ability to produce electron beams with a small diameter in the TEM and STEM. The effect has many similarities to Kikuchi diffraction. In convergent beam electron diffraction the operating conditions in the microscope are arranged such that the electron beam is focused on to the crystal specimen. Thus the specimen is traversed by a cone of electron beams. Convergent beam diffraction differs from Kikuchi diffraction only in that for the convergent beam the cone of electrons is produced externally while in Kikuchi diffraction the cone of electrons arises from the diffuse scattering within the crystal. The principle is illustrated in figure 4.68 where the cone of electrons is incident on the specimen surface at the plane BB0 , the objective lens then focuses the diffracted beams on to the back focal plane at CC 0 and DD0 . The ray diagrams for the production of convergent beam diffraction (CBD) is shown in figure 4.69 for both the TEM and STEM modes. Here, the
Figure 4.68. Ray diagrams illustrating the formation of convergent beam patterns (CBPs). The direct, zero order, and one diffracted spot are shown.
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Figure 4.69. Ray diagrams for convergent beam diffraction (CBD) using a condenser objective lens: (a) TEM mode, (b) STEM mode.
second condenser aperture determines the convergence angle and a large number with varying diameters is required. The objective lens focuses the electron beam on to the back focal plane after passing through the specimen. For a more detailed description of the technique the reader is referred to Steeds (1979) and Tanaka and Terauchi (1985). These patterns display the variation in intensity of transmitted or diffracted beams as a function of the angle between the incident electron beams and the crystal. These patterns have been given the generic name ‘Tanaka patterns’ and a typical bright field pattern is shown in figure 4.70 for a stainless steel specimen. This is essentially a map of the intensity of the direct beam variation with angle, over a range of angles in the general region of the [001] zone axis (Eades (1988). Specimens greater than 100 nm thick can be examined by this technique but the beam is broadened as it passes through the foil and this limits the spatial resolution obtained (Kyser and Geiss (1979) and Hutchins et al (1979)) (see figure 2.7). CBD patterns are very sensitive to strain fields from dislocations, precipitates or surface films and it is essential that such regions are avoided. Contamination of the specimen can also cause problems so that an area studied over long periods of time with the potential for contamination, which results in consequent degradation. To achieve the best from the technique, steps must be taken to reduce contamination, usually by obtaining the best possible vacuum in the microscope and here a microscope operating at UHV pressures is invaluable (see chapter 3). A
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Figure 4.70. Zone axis diffraction (Steeds (1979)). (a) Zone axis pattern for stainless steel [110] at 100 keV. (b) [001] convergent beam pattern of a phase precipitate in Type 316 austenitic stainless steel taken at 100 keV. (c) Image of M23 C6 precipitates where the convergent beam pattern is obtained from the central carbide, the pattern is a [111] axis at 100 keV. (d) Nickel [111] and 316 stainless steel zero order convergent beam patterns showing higher order Laue zone (HOLZ) lines at 100 keV. Using a standard, it is possible to deduce a ¼ 0:3516 nm for nickel and a ¼ 0:3589 nm for Type 316 austenitic stainless steel (courtesy J W Steeds).
cold finger, cooled to liquid nitrogen temperatures, and placed close to the specimen, will reduce contamination. Higher order Laue zones The Ewald sphere for electrons of energy of the order of 100 kV has a diameter that is much greater than the reciprocal lattice spacing (figure 4.71). As a result diffraction occurs at the origin and for some distance away from the origin until the Ewald sphere is sufficiently distant from the zero
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Figure 4.71. Ewald sphere construction in plan and section showing the formation of zero order and higher order Laue zones. d is the distance from the origin to the Ewald sphere.
reciprocal lattice plane for the effect to be negligible. At a greater distance from the origin the next layer of reciprocal lattice points will be encountered, giving rise to a ring of diffraction spots for the first order Laue zone (FOLZ). As the distance increases, further higher order Laue zones (HOLZ) are encountered but the intensity decreases with distance from the pattern centre. Figure 4.72 is a CBD pattern obtained from silicon carbide and is a good example of diffraction from the zero order, the central spot with its associated diffraction effects, the first order Laue zone, the next six spots and three higher order Laue zones. The zero order zones are shown in greater detail in figure 4.73. Applications Since convergent beam patterns provide information to establish small differences in both crystal structure and lattice parameter, they can be used to identify precipitates and, indeed, to measure small changes in lattice parameter between coherent precipitates and the parent matrix. Figure 4.70(c) shows [111] zone axis convergent beam diffraction patterns from M23 C6 and M6 C carbides. Steeds (1979) has pointed out that a powerful way to use these patterns is a ‘fingerprint’ of the relevant zone axes of commonly encountered materials and phases, and identification of over sixty different materials has been achieved. For this approach a reference accelerating voltage has to be adopted and, to accommodate changes resulting from specimen thickness variations, a series of patterns have been generated to cover a range of foil thicknesses. Additional information may be obtained from the HOLZ lines contained within the zero order disc of the convergent beam pattern (figure
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Figure 4.72. Convergent beam pattern from silicon carbide showing the zero order and higher order Laue zones (HOLZ) (courtesy N Tanaka) (reproduced by permission of JEOL).
Figure 4.73. Detail contained within the zero order direct beam CBD from silicon carbide (courtesy N Tanaka) (reproduced by permission of JEOL).
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4.70(d)). These lines in electron diffraction are the equivalent of Kossel lines in X-ray diffraction. HOLZ lines do not occur in all convergent beam diffraction patterns but are present usually in those produced by large unit cell metals and alloy phases, particularly nitrides, carbides and borides. The position of the HOLZ lines can be used to determine local crystal lattice constants with an accuracy of about 0.2%. The detailed symmetry information further aids the interpretation of the ‘fingerprint’ of different phases. A major application of CBD is the determination of lattice parameters and small changes in lattice parameters that can arise from local lattice strain. A small change in the lattice parameter will alter the position of the reciprocal lattice point, which will in turn move the HOLZ line. For a cubic material because the change in lattice parameter, a, produces a change in Bragg angle, , then = ¼ a=a:
ð4:74Þ
This method may be extended to determine strains in the lattice, particularly at planar interfaces and around large precipitates. If the strain is caused by a change in the chemical composition then measurement of the strain can be used to determine the concentration of the elements. The technique has been applied to determine the local concentration of aluminium in copper-aluminium alloys (Merton-Lyn (1977)) where it is possible to determine the concentration of aluminium to an accuracy of 1 at%. In addition, this technique provides an extremely accurate method for evaluating the thickness of foils. This is discussed in chapter 6. 4.4.4
Electron diffraction from rocking beams
Prior to the introduction of the STEM, instrument lens configuration diffraction was limited by spherical aberration of the objective lens to areas greater than 500 nm. It is possible to improve the spatial resolution of the areas of electron images selected for diffraction by operating a STEM instrument in a rocking diffraction mode (Spence and Carpenter (1986)). A number of different rocking incident electron beam techniques have been developed for various applications (Geiss (1976)). Ray diagrams corresponding to some of these techniques are given in figure 4.74(a)–(c). Figure 4.74(a) shows rocking selected area diffraction which is the reciprocal of conventional selected area diffraction. Here the beam is focused at the front of the focal plane of the objective lens, producing an approximately parallel electron beam of the specimen at the lens image plane. The selected area aperture is positioned at the lens object plane to be conjugate to the specimen. The scan coils produce a translation of the crossover at the front focal plane, resulting in a rocking beam at a point on the specimen. This produces a diffraction pattern which can be recorded on the electronic detector. A method of reducing the size of the area selected is shown in figure
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(c)
Figure 4.74. Ray diagrams for rocking beam microdiffraction. (a) Rocking selected area diffraction. This technique is reciprocal to conventional SAD and is often used in DSTEM instruments. (b) The rocking beam method. (c) The double-rock (or rock– unrock) method. The double-rock method can be visualised in either direction, provided reciprocity for detector and collection apertures is considered. Rocking angle is . (d) Transmission electron micrograph and corresponding diffraction patterns of evaporated gold particles on a carbon substrate (courtesy JEOL).
4.74(b). Here the instrument is operated in the image mode so that is the image is conjugate with the viewing detector. Certainly it is possible to produce diffraction patterns from areas as small as 3 nm using large diameter, relatively parallel incident electron beams which minimise radiation effects within the specimen and therefore in the resulting diffraction patterns (Geiss (1976), Chevalier and Craven (1977) and Fujimoto and Lehampfuhl (1974)).
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Figure 4.75. Central portion of an energy filtered Eades double-rocked, wide angle CBED pattern from thin silicon, with beam direction [111]. The field of view increases with rocking angle. This pattern was recorded serially, through an electron spectrometer that collected only elastically scattered electrons with E 4 eV (Spence and Carpenter (1986)) (reproduced by permission of Plenum Press).
A technique, the double rock, is shown in figure 4.74(c) which is useful for investigating the symmetry of perfect crystals (Eades (1980), Tanaka et al (1980) and (Spence and Carpenter (1986)). Figure 4.75 shows a typical energy filtered double rocked, wide angle convergent beam pattern from a thin silicon crystal: the analogue of the static beam Tanaka method. Double tilt coils positioned above and below the specimen detect scattered electrons that are on the optical axis of the microscope. Moreover this arrangement allows either single filtering or energy loss analysis of the pattern, which is not achievable in the static case. The interrelationship between transmitted diffraction patterns Before leaving this section on transmitted diffraction of electrons, the reader is reminded of the close relationship between the Bragg lines in convergent beam, Kikuchi and Kossel patterns. This is a consequence of the fact that they are at the same positions because the lines are all loci to the condition for satisfying the Bragg Law and as such are at the same fixed orientation with respect to the crystal. However, a convergent beam pattern gives the intensity of a single direction diffracted beam whereas Kossel patterns superimpose all maps. Kikuchi patterns are more difficult to calculate since they depend upon the development of a diffuse inelastically scattered background. 4.4.5
Electron backscatter diffraction
Back diffraction of electrons, usually undertaken in a scanning electron microscope does not in general produce diffraction spots because these
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electrons originate from a significant depth from within the specimen, a situation analogous to transmission of electrons through very thick specimens (Coates (1967) and Joy et al (1972)). Back diffraction patterns are obtained when the electrons emanate from the top few atom layers and this is only possible for low energy electrons below 1 keV, where the electron mean free path is of the order of 1 nm (see section below on Low Energy Electron Diffraction). Certainly the success of electron backscattered diffraction in the scanning electron microscope has provided the new powerful technique referred to as orientation imaging microscopy (OIM). Channelling patterns High energy electrons travel a considerable distance into a specimen where they are scattered in all directions, some in the backwards direction which may escape from the surface. The number of electrons escaping is governed by the material type and the orientation of the crystallographic axes relative to the direction of the incident electron beam. The packing density of atoms varies with angle of incidence of the electron beam for a given crystalline material. For a random direction there is a high probability that a given electron will approach an atom nucleus sufficiently closely to be backscattered. However, if the incident electron beam is parallel to symmetry axes of the crystal the projected packing density is low (figure 4.76) so that electrons
Figure 4.76. Origin of electron channelling contrast showing the effect of changing incident electron beam orientation with respect to the crystal structure.
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Figure 4.77. Variation of backscatter signal intensity with incident electron beam angle to crystal lattice.
penetrate over significant distances. This leads to a modulation in the backscattered electron intensity related to the crystal symmetry (figure 4.77); the intensity of the backscattered signal, Ib , varies with the angle of incidence of the beam, 1 . The contrast is given by the Bragg relationship and is determined by the relative size of 1 (Spencer et al (1972)). Therefore when 1 < backscattering is large, falls when 1 ¼ , and is low when 1 > . If the material being studied is free from major surface contamination, oxidation and mechanical damage it is possible to observe contrast effects resulting from the change in surface electron yield with grain boundary orientation (figure 4.78). Channelling contrast is generally much weaker than backscatter
Figure 4.78. Channelling contrast in the backscattered image of a recrystallised aluminium alloy (Humpreys (1988)) (reproduced by permission of the Institute of Materials).
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Figure 4.79. Electron paths for production of channel patterns.
electron contrast (see chapter 6) and is most easily observed when using pure element specimens. Crystallographic orientation, structure and lattice parameters, together with a measure of crystal perfection, can be established from electron channel patterns produced in a scanning electron microscope from bulk specimens (Venables and Harland (1973), Booker (1979) and Coates (1967)). These backscattered images have many similarities to Kikuchi and convergent beam patterns (Dingley (1981)). Since the incident electron beam travels a considerable distance into the specimen, a 30 keV beam will penetrate several micrometres into most materials, and in the process these electrons are scattered in both the forward and back directions. For a thick transmission specimen the forward scattered electrons produce the Kikuchi patterns or some of the convergent beam Tanaka patterns described in the previous section, but for thicker specimens these forward scattered electrons are eventually lost in the material. As an electron beam is scanned over the surface of a single crystal (figure 4.79), the angle of incidence changes by appreciable amounts so that at certain points X and Y the exact Bragg diffraction condition is satisfied, producing a line pattern. The anomalous scattering responsible for the patterns occurs with both the backscattered
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primary and secondary electrons. Hence, electron channel patterns can be produced using either emission, backscattered or specimen-current modes of scanning electron microscope operation. Unfortunately contrast, which depends upon the value of the angle of incidence of the beam, is low so that large beam currents 109 A, are required and the angle of incidence is large. To effect this the incident electron beam is collimated to a small divergence angle to give sharp patterns. The convergence angle, , should not exceed about 0.3, which is of the order of a few milli radians since is typically about 20 mrad. This method for obtaining patterns has the disadvantage that single crystal specimens are required to be at least 3 mm in diameter, otherwise it is not possible to achieve a sufficient change in the angle of incidence. The limitation is partly overcome by using a selected-area method (Schulson et al (1969)) where the electron beam, focused on to the specimen surface, is rocked about the point of incidence to traverse a complete raster in angular rather than lateral motion. Orientation imaging microscopy (OIM) The orientation and elements of symmetry of a crystal down to 10 mm diameter can be determine from the observed pattern either analytically or by matching the pattern to a channelling map. As with any orientation evaluation, it is necessary to rotate and tilt the specimen to move through this pattern (figure 4.80), so that the position on the overall orientation map can be considered. As the crystal symmetry increases it becomes possible to obtain only unique patterns for a unit stereographic triangle of the type shown in figure 4.81. The simplest way of establishing orientation is by comparison with such standard computed patterns where the unit triangle contains all the symmetry elements of the crystal. In routine evaluation of patterns the accuracy for orienting a crystal is between 18 and 0.28. From the spacing of diffraction lines the atomic spacings can be determined and
Figure 4.80. Schematic showing (a) back diffraction of high energy electrons and (b) method for obtaining backscatter patterns in an SEM (Dingley and Baba-Kishi (1990)) (reproduced by permission of Rolston Gordon Communications).
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Figure 4.81. Computed channelling map for a bcc crystal unit stereographic triangle showing the major diffraction lines and poles.
can be used to obtain a computer simulation of the pattern. A match between the computer simulation and the recorded pattern is usually obtained by iteration. An example of the approach is shown in figure 4.82, where the back diffraction channel pattern is a montage of two patterns from a
Figure 4.82. Backscattered diffraction pattern from a zircon (ZrSiO2 ) crystal together with computer simulated diffraction pattern.
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zircon (ZrSiO2 ) crystal, shown together with the matching computer simulation. In the past ten years considerable advances have been made towards automated interpretation of electron backscatter diffraction (EBSD) patterns which have enabled quantitative analysis of grain and subgrain structures. This has led to the use of the term orientation imaging microscopy (OIM) These advances have been made possible by the development of fast computers with large memories that are now available at affordable prices. The EBSD technique has been reviewed by Randle (1992), Adams (1997), Field (1997) and Randle and Engler (2000) with a comprehensive review by Humphreys (2001). Dingley and Randle (1992) pioneered the use of low-light cameras to replace film for pattern acquisition and computers for online interrogation. Currently two methods are used to obtain orientation measurements: (1) the specimen remains fixed and the electron beam is scanned—this is the faster method but may suffer from defocusing of the electron beam as the beam is moved off-axis—and (2) the stage is scanned while the electron beam remains fixed—this is more reliable but much slower. At present, the time required for a single data point to be analysed is 0.1 to 0.2 s for beam scanning and 1 s for stage scanning. The spatial resolution that is obtainable is determined partly by the system and partly by the specimen. An SEM fitted with a tungsten filament will yield inferior resolution compared with a field emission source while, due to the increase in back diffraction with atomic number, the resolution for a light element will be less than for a high atomic number element. A FEGSEM analysing a brass specimen can orient grains to a spatial resolution of 9 nm, although for routine analysis a resolution of 200 nm is readily achievable. A typical EBSD map of a recrystallised specimen of commercial Al–Mg alloy with weak texture is reproduced as figure 4.83. This figure illustrates many of the features available with EBSD, such as quantitative analysis of grains and subgrains, texture analysis and boundary misorientation. EBSD may determine lattice misorientations and information may be obtained about the dislocation content of the material (Adams (1997)). For a subgrain diameter D, and boundary energy , then the stored energy E is given by (Humphreys and Hatherley (1995)) E¼
K D
ð4:75Þ
where K is a geometric constant 3. The subgrain structure is determined from EBSD data and the subgrain sizes together with misorientation allows the local stored energy to be obtained. This stored energy may be displayed as a map (figure 4.84). The example shown is from Al– 0.13% Mg deformed to a strain of 1.3 in which the mean stored energy is 0.38 MJ m3 with the stored energy in region A 0:27 MJ m3 and in region B 0:45 MJ m3 .
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Figure 4.83. A typical EBSD map of a recrystallised specimen of commercial Al–Mg alloy with weak texture. (a) shows the orientation map where the grains are shown in Euler contrast and high angle grain boundaries are shown as black lines. (b) Main texture components ¼ cubef100gh001i, grey ¼ GISS f011gh100i and white ¼ brass f011gh211i. (c) Boundary map with high angle (>158) grain boundaries shown as black and low angle boundaries as grey. (d) The distribution of grain sizes as measured by linear intercept. (e) The distribution of boundary misorientation as measured by linear intercept.
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Figure 4.84. Secondary electron image (a) and stored energy map (b) from Al–0.13% Mg deformed to a strain of 1.3. Subgrain structure is determined from EBSD data showing the subgrain sizes together with misorientation which allows the local stored energy to be obtained.
To collect EBSD patterns the specimen needs to be inclined to the incident beam so that it is about 208 off parallel to the surface. In most instruments this is accommodated by tilting the specimen. However, the alternative solution is to incline the incident beams to the specimen by constructing an instrument with an inclined column. The Camscan X500 Crystal Probe adopts such a configuration. This has the advantage that a range of specimens that are required to be mounted horizontally can be investigated (Wheeler et al (2002)). One example is the application to earth
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Figure 4.85. The secondary electron image of plasma vapour deposited diamond film (a) and the electron backscatter pattern (b) from the same region. (Courtesy Steeds and Parsley).
science investigations, but it has been used for testing microstructural models for recrystallisation and grain growth of steels. EBSD has been used to determine the crystallographic structure of plasma vapour deposited films of diamond (Steeds and Parsley (2002)). Diamond films tend to be polycrystalline with the diamond crystallites forming as columnar grains normal to the original silica surface on which they are grown. Figure 4.85 shows the secondary electron image of the diamond surface (a) in which the grains can just be resolved while the electron backscatter pattern (b) shows the grain structure clearly.
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Figure 4.86. Average intensity profiles of {111} bands present in electron backscatter patterns obtained for (a) annealed and (b) 8.5% strained material.
A further example of the use of diffraction techniques has been to study the stress at a surface induced by the formation of thin oxide films (MacKenzie and Dingley (1986)). If a backscattered channel pattern is obtained and there are no stresses present at the surface, the diffracted lines are sharp. As an oxide layer grows, dislocations are produced which cause a bending and dilation of the crystal lattice of the substrate material. Stacking fault density and point defect concentration will also increase. These phenomena all cause a blurring and contrast reduction of features seen in the electron backscattered pattern. By quantifying this degradation a measure of the strain in the surface layers can be obtained (Wilkinson and Dingley (1991)). This has been extended to measurements in steels (Buchanon and Randle (1997)). Figure 4.86 shows the average intensity profiles of {110} bands present in electron backscattered patterns from (a) annealed and (b) 8.5% tensile strained aluminium alloy 6061. The first moment of power spectra has been used to generate a value to quantify the quality of the line profiles (figure 4.87). This can then be used to determine the strain in the surface as the material oxidises. Low energy electron diffraction It was fortunate for Davisson and Germar (1927) that they used low energy electrons where the electron penetration distance in mica was only a few atom layers since this ensured that the diffraction that their experiment demonstrated was from, essentially, a two-dimensional structure. As a result the atoms in k space formed rods, not points, and the Ewald sphere would satisfy a condition for diffraction irrespective of the electron wavelength. Had they used high energy electrons the intensity distribution would have been such that no pattern could have been observed. Back
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Figure 4.87. Effects of specimen deformation on Kikuchi band contrast using the power spectrum first moment (PSFM) values for [112] axes in aluminium alloy 6061 (Wilkinson and Dingley (1991)) (reproduced by permission of Pergamon Press).
diffraction of low energy electrons (LEED) is used today to determine the structure of surfaces and the interaction of atoms and molecules with that surface (Farnsworth (1929), Scheibner et al (1960), Pendry (1974), Jona et al (1982), Legally and Martin (1983) and Seah (1969)). The condition for diffraction is illustrated in figure 4.88 and is given by d sin ¼ n
ð4:76Þ
where d is the spacing of atoms in the surface and n is an integer. The technique that Davisson and Germer so dramatically demonstrated was not used to interpret material surface structures until almost forty years later. The vacuum used was poor, probably no better than 102 Pa, and a clean metal surface would have been completely covered by contamination in a fraction of a second. The technique had to wait until vacuum technology had progressed to the stage that the vacuum in the LEED chamber could be such as to keep the specimen under investigation relatively clean for long enough to obtain the required measurements.
Figure 4.88. Diffraction of low energy electrons from a material surface.
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Figure 4.89. Experimental arrangement for observing low energy electron diffraction (LEED).
The basic system required to obtain low energy electron diffraction (LEED) patterns is shown schematically in figure 4.89. The specimen is maintained at earth potential and a beam of electrons with energies from a few eV to a few hundred eV are incident normally on the surface. The elastically scattered electrons, together with the secondary electron spectrum, then passes through the first of four, occasionally three, electron transparent fine mesh stainless steel grids. The first grid is maintained at earth potential and shields the specimen from the electromagnetic fields produced by the other grids. The remaining grids are maintained at a negative potential a few volts less than the incident electron beam energy and serve to prevent those electrons that have lost energy interacting with the specimen, and the inelastically scattered electrons, from reaching the fluorescent screen. Elastically scattered electrons pass through a further screening grid maintained at earth potential before being accelerated to about 5 keV by a large positive potential on the fluorescent screen. This provides the elastically scattered electrons with sufficient energy to cause the screen to fluoresce. A typical LEED pattern obtained from a silicon (111) single crystal surface recorded at 100 eV incident electron energy is shown in figure 4.90. Here the positions of the diffraction spots provide information concerning the crystallographic arrangement of atoms in the surface layer but equally important is the intensity of the diffracted spot. This example shows the 7 7 unit mesh structure of silicon and would appear to indicate that the surface layers are defect free; however, studies of this same surface using scanning tunnelling microscopy (chapter 7) show that on the atomic scale it contains many defects. The arrangement of atoms is deduced by proposing a surface structure, calculating the expected diffracted intensity and, comparing with the observed intensity, considerably more information can be obtained than from the diffraction maxima alone. The intensity of the diffracted
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Figure 4.90. A LEED pattern from a silicon (111) single crystal surface showing symmetry due to the 7 7 unit mesh (courtesy M Prutton).
beams can be measured from the photographic records of the LEED patterns. However, a more accurate method is to record the elastically scattered current directly by replacing the fluorescent screen with a Faraday cup and scanning the cup over the field of view while recording the current. Unfortunately, if done manually, this is time consuming, leading to excessive specimen contamination. Recently, with the advent of fast data collection systems and computer control of the Faraday cup, the intensity in a complete pattern may be obtained in minutes rather than hours. In chapter 2 we have shown how in three dimensions the reciprocal lattice describes a series of points where each point represents a crystal plane and diffraction occurs where the Ewald sphere intersects a point. However, in two dimensions the lattice planes are represented by rods and since the Ewald sphere has a radius equal to the reciprocal of the electron wavelength, then above a certain minimum electron energy the Ewald sphere always passes through a reciprocal lattice rod (figure 4.91). As the electron energy increases so more rods are intersected and the angle for diffraction decreases so that more spots are included and shifted towards the origin as the incident electron energy is increased. The effect can be seen in figure 4.92, which shows four diffraction patterns obtained
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Figure 4.91. The Ewald sphere construction for low energy back diffraction of electrons.
from the surface of nickel oxide using incident electron beam energies of 150, 240, 445 and 555 eV respectively. The symmetry is the same for all patterns but the distance of spots from the centre decreases as the electron energy increases.
Figure 4.92. LEED from nickel oxide at different incident electron beam energies: (a) 150 eV, (b) 240 eV, (c) 445 eV and (d) 555 eV.
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Having addressed the positions of the diffraction spots it is necessary to consider their intensity since LEED involves diffraction of incident electrons with energies ranging from 50 eV up to several hundred eV with an elastic mean free path of between 1 and 3 nm. There is a contribution from a number of atom layers below the outer, surface, atom layer. This requires a three-dimensional modification to essentially two-dimensional diffraction. Certainly when calculating the intensities of diffracted beams this must be taken into account together with the proportion of the incident electrons that contribute to the diffracted beam intensity. As a result it is necessary to employ the dynamical theory of electron diffraction to predict intensities rather than the simpler kinematical theory. The dynamical theory of high energy electron diffraction is not easily applied because this theory considers diffraction of a forward moving plane wave and assumptions have to be made that are not readily applied to the case of backward diffraction. The approach adopted and described in detail by Jona et al (1982) is to first treat diffraction from a semi-infinite crystal. Diffraction from individual layers is then considered. These are stacked on top of one another and finally diffraction from individual atoms has to be accommodated. In practice it is important to be able to describe quickly the observed changes in surface crystal structure associated with events like atom adsorption and a nomenclature has grown up with the LEED technique (Jona et al (1982)). Initially the two-dimensional reciprocal net was artificially converted into a three-dimensional structure by introducing a vector c, with a direction such that a , and b , lie in the same plane as a and b. The magnitude of c is not important. This is equivalent to looking down on the reciprocal lattice rods which then appear as points. The arrangement of atoms on a surface is then described in terms of the original surface matrix (figure 4.93). In figure 4.93(a) adsorbed atoms sit directly on the base matrix and this produces no change in the positions of the diffracted beams although the intensities would vary. Such an arrangement would be referred to as a (1 1). In the second example (figure 4.93(b)), the adsorbed atoms lie along directions which are common with the base matrix but there is now only one adsorbed atom for every two of the matrix. This is referred to as a primitive (2 2) or P(2 2). Such an arrangement would produce extra reciprocal lattice points and extra diffraction spots as shown. In the third example (figure 4.93(c)), the adsorbed atoms occur at every alternate matrix position but here the adsorbed lattice is centred and referred to as a centred (2 2). This increases the number of reciprocal lattice points but not to the same extent as in the P(2 2) example. An alternative method of describing the adsorbed order, which also uses the magnitude of the base matrix, is a b ð4:77Þ Rhkl i i AS a b
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Figure 4.93. Nomenclature used in identification of surface structures from LEED patterns.
where R is the chemical symbol for the substrate and {hkl} the surface plane, ai ¼ g11 a þ g12 b, bi ¼ g21 a þ g22 b, are the surface-net vectors identified from the unit mesh vectors a and b with g11 , g12 , g21 and g22 being integers, is the angle through which the surface unit mesh was rotated relative to the substrate and AS is the chemical symbol for the adsorbed species. Certainly the most common use for LEED is the investigation of the interaction of gaseous environments with materials surfaces. To achieve this the single crystal specimen surface is usually cleaned by argon ion bombardment and the damage introduced in this process is annealed out by heating the specimen to a relatively high temperature. This in turn may cause impurity atoms to diffuse to the new surface and the cleaning process must then be repeated until a clean annealed surface is obtained. This surface is characterised and then reacting gas is introduced in monitored quantities. The change in the LEED pattern is monitored as a function of gas adsorption, which provides a basis for establishing the mechanism of adsorption and desorption. It is common practice to use Auger spectroscopy, by modifying the LEED arrangement (see chapter 6), to assist in the characterisation. Many early LEED experiments have been shown subsequently to be severely influenced by impurity atom segregation. In the example shown in figure 4.94 a tungsten single crystal has an ordered layer of deposited thorium and then oxygen is adsorbed on to this layer. Dramatic
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Figure 4.94. Changes in the LEED patterns with increasing exposure leading to adsorption of oxygen on to a thoriated tungsten single crystal (reproduced by permission of NorthHolland Publishing Company).
changes occur both in position and intensity of the diffraction pattern as the oxygen exposure increases from 1 to 10 Langmuir. (A Langmuir is a measure of dose and is equivalent to an exposure of 104 Pa for 1 second.) Reflection high energy electron diffraction Back diffracted high energy electrons can also be used to study materials, but the intensity of these electrons decreases in proportion to the change in momentum on scattering. For a high energy electron beam incident normally on a surface the back diffracted beam is weak and the background intense so that the diffracted beams are hard to detect. However, if the high energy
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Figure 4.95. (a) A reflection high energy electron diffraction pattern from a silicon (111) 7 7 surface (Estrup (1971)) (reproduced by permission of North-Holland Publishing Company). (b) Ewald sphere construction for glancing angle reflection high energy electron diffraction (RHEED).
electron beam is incident on the surface at a grazing angle of less than 108 the momentum transfer is considerably reduced. A 50 keV electron beam incident on a surface at an angle of three degrees is equivalent to back diffraction from a 150 eV beam incident normally. This technique is known as reflection high energy electron diffraction (RHEED) (Estrup and McCrae (1971)). A RHEED pattern recorded from the surface of a silicon (111) surface is reproduced as figure 4.95(a) together with the reciprocal lattice and Ewald sphere construction (figure 4.95(b)). The type of diffraction pattern to be expected can be inferred from the reciprocal lattice using the Ewald sphere construction shown in figure 4.95(b). The radius of the Ewald sphere is large due to the high energy of the incident electrons and thus the interaction with the reciprocal lattice rods will occur over a substantial distance. Electrons will be diffracted over an angular range of several degrees in specific directions and therefore we expect the diffraction to appear as streaks or as spots that appear streaked. This effect is most marked in the example of RHEED shown in figure 4.95(a) for a silicon (111) 7 7 surface. The diffraction pattern contains considerable streaking in a direction normal to the crystal surface, the
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greatest streaking corresponding to the Ewald sphere interacting almost parallel to the reciprocal lattice rods. As the diffraction angle increases so the intensity decreases, due to the increase in the change in electron momentum, and the streaking becomes less because the Ewald sphere intersects the reciprocal lattice rods at greater angles. As with the LEED diffraction, RHEED patterns are generally interpreted using a two-index scheme to accommodate the two-dimensional nature of the scattering surface of the material. However, again it is helpful to address the bulk contributions to the RHEED patterns. Indeed Aindow et al (1987) adopted a method proposed by Frank (1965) for imaging the direct and reciprocal lattices for RHEED patterns accommodating three-dimensional contributions.
4.5
References
Adams B L, 1997 Ultramicroscopy, 67, 11 Agar A W 1974 The basic principles of the electron microscope in Principles and Practice of the Electron Microscope ed A M Glauert (London: North-Holland) ch 1 Aindow M, Eaglesham D J and Pond R 1987 EMAG 87. Institute of Physics Conference Series 90 127 Allen A J, Hutchings M T, Windsor C G and Andreani C 1985 Adv. Phys. 34 445 Amelinckx S, Gevers R and Van Landuyt (ed) 1978 Diffraction and Imaging Techniques in Materials Science (Amsterdam: North-Holland) Andrews K W and Johnson W 1959 Br. J. Appl. Phys. 10 321 Andrews K W, Dyson D J and Keirson C S R 1971 Interpretation of Electron Diffraction Patterns (London: Adam Hilger) Ball C J 1981 Phil. Mag. 44 1307 Barrett C S and Massalski T B 1967 Structure of Metals 3rd edition (New York: McGrawHill) Beeston B E P, Horne R W and Morkham R 1983 Electron diffraction and optical diffraction techniques in Practical Methods in Electron Microscopy ed A M Glauert (London: North-Holland) Bendersky L, Mager M and Rosen A 1982 Metallography 15 293 Bevis M J and Swindells N 1967 Phys. Stat. Solidi. 20 197 Bivas B, Numma N and Stann-Olsen J 1978 J. Appl. Cryst 11 137 Booker G R 1979 Modern diffraction and imaging techniques in Material Science ed S Amelinckx, R Gevers, G Remaut and J Van Landuyt (London: North-Holland) Brown G G and Whiteman J A 1969 J. Aust. Inst. Metals 14 217 Buckett M I, Strane J, Luzzi D E, Zhang J P, Wessels B W and Marks L D 1989 Ultramicroscopy 29 217 Burgers W G 1934 Physica 1 561 Buchanon P J and Randle V 1997 Scripta Met. 57 1511 Carlson F P 1977 Introduction to Applied Optics for Engineers (New York: Academic Press) Chapman S K 1986 RMS Handbook 08 ‘Monitoring and Maintaining the Electron Microscope’ Royal Microscopical Society (Oxford: Oxford University Press) Chevalier J P and Craven A 1977 Phil. Mag. 36 67 Coates D G 1967 Phil. Mag. 16 1179
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Cosslet V E 1970 IEE Reviews 117 1489 Cowley J M 1986 J. Electron Microsc. 3 25 Crocker A G and Flewitt P E J 1984 The migration of interphase boundaries by shear mechanisms in Reviews of Deformation Behaviour of Materials ed P Feltham (Tel Aviv: Freund Publishing House) Cullity B D 1979 Elements of X-ray Diffraction (New York: Addison-Wesley) Dasannacharya B A and Sequeira A 1988 Crystal Properties and Preparation 16 173 Davisson C and Germer L H 1927 Phys. Rev. 30 705 Daymond M R, Einsenberger P and Chio A Y 1997 J. Appl. Phys. 50 627 Daymond M R and Withers P J 1996 Scripta Met. 35 1229 Dietsch R, Holz Th, Mai H, Meyer C-F, Scholz R and Wehner B 1998 Appl. Surf. Sci. 127129 451 Dingley D J 1981 Scanning Electron Microscopy IV 273 Dingley D J and Randle V 1992 J. Mater. Sci. 27 4545 Dingley D J and Baba-Kishi K 1990 Microscopy 17 Ditchburn R W 1952 Light (London: Blackie) Doig P and Flewitt P E J 1983 Metal Science 17 601 Doig P, Lonsdale D and Flewitt P E J 1985 J. Appl. Cryst 14 124 Donachie M J and Kriege O H J 1972 J. Mater. 7 269 Eades J A 1980 Ultramicroscopy 5 71 Eades J A 1988 Advanced Techniques in Microstructural Characterisation. Crystal Properties and Preparation ed G S Amsell, D J Frister, P Haasen, J Wertman and F H Wohlbie (Switzerland: Trans. Tech. Pubs) Edington J W 1976 Electron Diffraction in the Electron Microscope vol 2 Phillips Technical Library (London: Macmillan) Estrup P J and McCrae E G 1971 Surf. Sci. 25 1 Farnsworth H E 1929 Phys. Rev. 33 1068 Field D P, 1997 Ultramicroscopy 67 1 Frank F C 1965 Acta Cryst. 18 862 Fujimoto F and Lehampfuhl G 1974 Z. Naturforsch. 299 1929 Geiss R H 1976 SEM 76 ed O Johani (Chicago: IITRI) Gobel H 1978 Adv. X-ray Analysis 22 255 Goldschmidt H J 1967 Interstitial Alloys (London: Butterworth) Gronsky R 1980 Direct imaging of grain boundaries in Grain Boundary Structure and Kinetics (Ohio: ASM) Grundy P J and Jones G A 1976 Electron Microscopy in the Study of Materials (London: Edward Arnold) Hammond C 1997 The Basics of Crystallography and Diffraction (Oxford: Oxford University Press) Hauk V 1997 Structural and Residual Stress Analysis by Non Destructive Methods (Amsterdam: Elsevier) Hirsch P B 1955 X-ray Diffraction by Polycrystalline Materials ed H S Perser, H B Rooksby and A J C Wilson (London: Institute of Physics) Hirsch P B, Howie A, Nicholson R B, Pashley D W and Whelan M J 1965 Electron Microscopy of Thin Crystals (London: Butterworths) Hirsch P B and Keller 1951 Proc. Phys. Soc. (London) 64B 369 Hirsch P B and Keller 1952 Acta Cryst. 5 152 Honeycombe R W K 1968 The Plastic Deformation of Metals (London: Edward Arnold)
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References
173
Humphreys F J 1988 Scanning electron microscopy in Microstructural Characterisation ed E Metcalfe (London: Institute of Metals) ch 3 Humphreys F J 2001 J. Mater. Sci. 36 3833 Humphreys F J and Hatherley M 1995 Recrystallization and Related Annealing Phenomena (Oxford: Pergamon) Hutchings M T and Windsor C G 1986 in Neutron Scattering ed K Skold and D L Price (London: Academic Press) ch 25 Hutchins R, Loretto M H, Jones I P and Smallman R E 1979 Ultramicroscopy 3 401 JCPDS Powder Diffraction File, International Centre for Diffraction Data (Swarthmore, Pennsylvania, USA) Jenkins F A and White H E 1951 Fundamentals of Optics (New York: McGraw-Hill) Jona F, Strozier J A and Yang W S 1982 Rep. Prog. Phys. 45 527 Jones I P 1988 Transmission electron microscopy in Microstructural Characterisation ed E Metcalfe (London: Institute of Metals) Joy D C, Newbury D E and Davidson D L (1972) J. Appl. Phys. 16 193 Kalbe E F 1968 Handbook of X-rays (New York: McGraw-Hill) Kikuchi S 1928 Japan J. Phys. 5 83 Kline M and Kay I W 1965 Electromagnetic Theory and Geometrical Optics (New York: Wiley Interscience) Klug H P and Alexander L E 1954 X-ray Diffraction Procedures (New York: Wiley) Kossel W 1936 Ann. der Physik 25 512 Kossel W and Mollenstedt G 1939 Ann. der Physik 36 113 Kyser D F and Geiss R H 1979 Ultramicroscopy 3 397 Lai J K L and Galbraith I F J 1980 Mat. Sci. 15 1297 Lebrun J L, Gergaud P and Belassel V Ji 1995 J. de Physique 4 265 Legally M G and Martin J A 1983 Rev. Sci. Instrum. 54 1273 Lewis D B and Pickering F B 1982 Advances in Physical Metallurgy and Applications of Steels (London: Metals Society) p 84 Lipson S G and Lipson H 1969 Optical Physics (Cambridge: University Press) Lonsdale D and Flewitt P E J 1978 Mat. Sci. Eng. 32 167 Lonsdale D and Flewitt P E J 1984 Acta Met. 32 869 Loretto M H 1984 Electron Beam Analysis in Materials (London: Chapman and Hall) MacKenzie R A D and Dingley D J 1986 Proc. XIth Congress on Electron Microscopy Kyoto p 709 Mai H 1999 Materials World 7 616 Marra W C, Eisenberger P and Chio A Y 1979 J. Appl. Phys. 50 627 Masing G, Lucke D and Notting P 1959 Zeit. Metal. 47 65 McDonald E J, Hallam K R, Bell W and Flewitt P E J 2002 Mat. Sci. Eng. A325 454 Merton-Lyn D N 1977 MSc Thesis (Bristol: University of Bristol) Mitchell J W, Ahearn J, Hockey B J, Monaghan J P and Wild R K 1968 Trans. JIM 9 769 Mohrbrachen H, Vanacker Blanpain B, Vanhoutte P and Calis J P 1996 J. Mat. Res. 7 1776 Morris W G 1968 J. Appl. Phys. 39 1893 Mott N F and Massey H S W 1976 Theory of Atomic Collisions of Materials (London: Edward Arnold) Mulvey T 1991 Microscopy and Analysis March 7 Noyan I C and Cohen J B 1987 Residual Stress: Measurement by Diffraction and Interpretation (New York: Springer)
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Diffraction
Pearson W B 1967 Handbook of Lattice Spacings in Metals and Alloys vols I and II (Oxford: Pergamon) Pearson W B 1972 The Crystal Chemistry and Physics of Metals and Alloys (New York: Interscience) Peiser H S, Rooksby H P and Wilson A J C 1960 X-ray Diffraction by Polycrystalline Materials (London: Chapman and Hall) Pendry J B 1974 Low Energy Electron Diffraction (New York: Academic Press) Poulsen H F, Lorentgen T, Feidenhansl R and Lui Y L 1997 Met. Mat. Trans. 28A 237 Ranch H and Seidli H 1987 Nucl. Inst. Meth. A255 32 Randle V 1992 Microtexture Determination (London: Institute of Materials) Randle V and Engler O 2000 An Introduction to Texture Analysis (London: Gordon and Breach) Reimens W, Broda M, Danty G, Liss K-D, Pygala A, Schmakens T and Tschenscher T 1998 J. Nondest. Eval. 17 129 Rowlands P C, Fearon E O and Bevis M J 1968 The Mechanisms of Phase Transformations in Crystalline Solids (London: Metals Society) Memo 33 Rymer T B 1970 Electron Diffraction (London: Methuen) Scheibner E J, Germer L H and Hartman C D 1960 Rev. Sci. Instrum. 31 112 Schulson E M, Van Essen C G and Joy D C 1969 Scanning Electron Microscopy (Chicago: IITRI) p41 Schultz L G 1949 J. Appl. Phys. 20 1030 Seah M P 1969 Surf. Sci. 17 132, 160, 181 Slattery G F and Windsor C G 1983 Metal. Mater. Technol. 15 67 Sommers M A J and Mittemeijer E J 1995 Met. Mat. Trans. 26A 57 Spence J C H and Carpenter R W 1986 Principles of Analytical Electron Microscopy ed D C Joy, A D Roring and J I Goldstein (New York: Plenum Press) Spencer J P, Humphreys C J and Hirsch P B 1972 Phil. Mag. 26 193 Spooner S and Wang X L 1997 J. Appl. Cryst. 30, 449 Steeds J W 1979 in Introduction to Analytical Electron Microscopy ed J J Hren, J I Goldstein and D C Joy (New York: Plenum Press) ch 15 Stephens R A and Barnes R T 1937 J. Inst. Met. 60 285 Stratton J A 1941 Electromagnetic Theory (New York: McGraw-Hill) Suryanarayana C and Grant-Norton M 1998 X-ray diffraction: A Practical Approach (New York: Plenum Press) Swindells N 1979 Kossel X-ray Microdiffraction in Electron Microscopy and Microanalysis of Crystalline Materials ed J A Belk (London: Applied Science) Tempest P A and Wild R K 1982 Oxidation of Metals 17 345 Tanaka M and Terauchi M 1985 Convergent Beam Electron Diffraction (Tokyo: JEOL Ltd) Tanaka M, Weno K and Harada Y 1980 Japan J. Appl. Phys. 19 L201 Tanaka N 1989 JEOL News 27E 10 Tanaka N and Mikama K 1988 Ultramicroscopy 26 37 Tatarski V I 1961 Wave Propagation in a Turbulent Medium (New York: McGraw-Hill) Thon F 1966 Imaging Properties of the Electron Microscope near the Theoretical Limit of Resolution. Proc. Sixth International Conference for Electron Microscopy Kyoto, Japan p 23 Thon F 1971 Electron Microscopy in Material Science ed U Valdre´ (New York: Academic Press) p 570
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References
175
Tonomura A, Endo J, Matsuda T and Kawasaki T 1989 Am. J. Phys. 57 117 Todd R I, Bourk M A M, Borsa C E and Brook R J 1997 Acta Met. Mater. 45 1791 Torchane L, Bilger P, Duley J and Gantois M 1996 Met. Mat. Trans. 27A 1823 Venables J A and Harland C J 1973 Phil. Mag. 27 1193 Warren B E 1969 X-ray Diffraction (London: Addison-Wesley) Warren J B 1979 Microdiffraction in Introduction to Analytical Electron Microscopy ed J J Hren, J I Goldstein and D C Joy (New York: Plenum Press) Webster P J, Mills G, Wang X D, Kang W P and Holden T M 1996 J. Neutron Res. 3 223 Webster P J, Wang X D and Mills G 1996 Mat. Sci. Forum 228 227 Wheeler J, Prior D J, Seward G G E, Howe A A, Bi Y and Pader R S 2002 Steel World 7 89 Wild R K, Evans T E and Lang A R 1967 Phil. Mag. 15 267 Wilkinson A J and Dingley D J 1991 Acta Met. 39 3047 Windsor C G, Rainey V S, Rose P K and Callan V M 1984 J. Phys. F: Met. Phys. 14 1771 Winholz R A and Kranitz A D 1996 Mat. Sci. Eng. A205 257 Withers P J and Bhadeshia H K D H 2001 Mat. Sci. Tech. 17 355 Withers P J and Webster P J 2001 Strain 37 19 Young R A 1993 The Rietveld Method (Oxford: Oxford University Press)
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Chapter 5 Photo/electromagnetic sources 5.1
Introduction
The electromagnetic spectrum spans wavelengths of many orders of magnitude from long radio waves (<105 Hz; >1 km) down to those of atomic dimensions (figure 2.1). Several of these radiations may be, and are, used to provide microscope sources for imaging materials, although apart from light in the visible spectrum the wavelengths are not visible to the eye. The various types of radiation addressed in this chapter are shown in table 5.1 together with the associated wavelengths. Also included here are electrons which are addressed in a separate chapter (chapter 2) in view of the large and significant range of techniques that have emerged based upon this particular source. The wavelength of visible light of the order 50 nm places this technique in the mid range of those considered in this chapter. Electromagnetic radiation can be considered to have the properties of a stream of particles, photons, and of waves. The former is the basis of geometrical optics theory which is the approach adopted when discussing lens aberrations, for example, whereas the latter tends to physical optics which is used for discussing, for example, polarising microscopy. Geometrical optics is based upon the familiar fundamental laws (i) light travels in a straight line, (ii) parts of a light beam can be treated as separate entities or rays, (iii) the law of reflection and (iv) the law of refraction (Snell’s Law). These laws emerge as approximations from the electromagnetic wave theory which is the basis of physical optics. The basic equations of physical optics are derived from the differential form of the Maxwell equations. Solutions of the differential equation as described in chapter 4 provide wave fronts associated with a geometrical optical representation of wave propagation. Geometrical optical solutions fail to account for diffraction effects since these are usually restricted to a small region close to the forward direction of propagation. They can, however, be the dominant physical effect in optical systems which are diffraction limited. When variations in amplitude are small, geometrical rayoptical methods are valid so that, for example, the simple laws for thin lens
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Table 5.1. Spectral ranges for electromagnetic radiation used in microscopy. Radiation
Wavelength (nm)
Acoustic Infrared Visible light (blue–red) Ultraviolet X-rays Electrons
>1000 700 to 860 400 to 700 25 to 400 0.01 to 15 0.005
optics may be used. This analysis considers electromagnetic radiation as classical waves where the electric and magnetic fields associated with radiation oscillate as a function of time in the propagation direction. This classical description is used to explain a variety of phenomena such as diffraction, reflection, refraction and interference of electromagnetic waves (chapter 4). However, this does not explain other phenomena such as the photoelectric effect where electrons are emitted from a material surface when irradiated with electromagnetic radiation (chapter 2). The development of the quantum theory of radiation and matter reveals that, apart from the wave nature, electromagnetic radiation has characteristics of particles, photons and wave properties associated with particles such as electrons. The quantum theory of radiation establishes the relationships underlying the description of photons where: (a) Electromagnetic radiation of frequency, , comprises discrete quantum of energy h, where h is the universal Plank constant; this quantum is a photon. (b) The mass of the photon is zero and in free space has a universally constant velocity of 3 108 m s1 . (c) The momentum associated with the photon is equal to hK0 , where K0 is the magnitude of the wave vector ( h ¼ h=2). This provides the necessary interrelation between these two approaches, since the frequency of the wave motion can be calculated in terms of the energy of a photon. It is this interrelationship between the wave and particle characterisation of electromagnetic radiation that enables either approach to be considered. However, it should be emphasised that the classical wave theory should be applied, wherever possible, to explain phenomena.
5.2
Resolution
The ability to resolve detail within a visual image is a basic requirement for microstructural investigations. Essentially resolution defines the smallest separation of two points in the object which may be distinctly reproduced
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Figure 5.1. A simple optical system comprising a condenser and objective lens.
in the image. For a simple, general, optical system (figure 5.1), applying the Rayleigh criterion to the Abbe´ formulation (Kline and Kay (1965), Born and Wolf (1959), Welford (1962) and Francon (1963)) defines the resolution for light microscopy, since this is limited by diffraction of each point within the object which is spread into a small disc in the image, the Airy disc. Thus, resolving power, , is given by ¼ C= sin
ð5:1Þ
where is the wavelength of the illumination, is the refractive index of the medium between the specimen and the lens, is the semi-angle subtended by the object at the lens and C is a constant usually taken to be 0.61 depending upon the coherence of the illumination. The quantity sin defines the numerical aperture of the lens. For an optical microscope with white light illumination, ¼ 50 nm, fitted with an oil immersion lens to give sin ¼ 1.35, it is possible to achieve a resolution of about 200 nm. Resolving power, however, is not the only factor to consider when assessing the performance of an optical microscope. Together with depth of focus, it is important that the image should contain sufficient contrast to discriminate against background and this is related to changes in amplitude and absorption characteristics produced by the specimen under incident light as distinct from a change of phase. In the case of electrons, the de Broglie relationship (Jenkins and White (1951) and Hirsch et al (1969)) relates the wavelength of electrons, , to the momentum, Mv (M is mass and v is velocity) by h (the Planck constant) such that ¼ h=Mv. Electrons accelerated by a potential difference of E volts have a kinetic energy of 12 Mv2 such that Mv2 ¼ 2eE
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ð5:2Þ
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Table 5.2. Variation of electron wavelength with applied voltage. Applied voltage (V) (keV)
Wavelength ()
Relativistic accelerating voltage (V ) (keV)
20 50 100 250 500 1000
20.0004 50.4 109.8 311.2 744.6 1300
0.008588 0.005355 0.003702 0.002191 0.001421 0.000872
where e is the electron charge. Therefore the wavelength is given by ¼ h=ð2MeEÞ1=2 :
ð5:3Þ
The energy term eE is expressed in electron volts and represents that energy required to pass an electron through a potential difference of one volt (1 eV ¼ 1:602 1019 J). When the velocity of the electron approaches the speed of light, c, then v tends to c and a relativistic correction is required for the voltage such that V ¼ V½1 þ eV=2M0 c2 where M0 is the mass of an electron at rest. This correction becomes important for V > 105 volts; at 100 keV it is about 5% which increases to about 30% at 106 keV. Wavelengths for the range of accelerating voltages commonly used in electron microscopy are given in table 5.2 (Grundy and Jones (1976)). Many of the current commercial electron microscopes operate with voltages in the range 100 to 300 keV with corresponding electron wavelengths of between 0.004 and 0.002 nm respectively. From equation (5.1) this gives a resolving power of 0.0025 nm and 0.0017 nm respectively for an efficiently designed lens. However, it is the spherical aberration that is a factor which limits the performance of electromagnetic lens systems.
5.3
Lens defects
Lenses used in optical and indeed electromagnetic radiation systems do not give perfect images because of defects and aberrations (Hawkes (1972), Hall (1966), Martin and Johnson (1947) and Geiss (1979)). We will now consider some of these factors. 5.3.1
Spherical aberration
For paraxial illumination and Gaussian imaging, there is a conjugate point to point correspondence between the object and the image. In figure 5.2(a)
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Figure 5.2. Lens defects: (a) Paraxial ray XAY and non-paraxial ray XBY illustrating spherical aberration in the image plane. (b) Commonly encountered distortions in either an optical or electromagnetic lens. (c) Rays leaving a point X with either different velocities due to potentials V and V þ V (electrons), or different wavelengths and þ (light) will be brought to a focus at Y and Y 0 , respectively; chromatic aberration.
the image of the object point X lies in the image plane at Y for all paraxial rays XAY. However, if the rays are not paraxial then sin tends to and the rays are bent more at the periphery of the lens such that image point Y is displaced by a distance D to Y 0 . Point Y now has an apparent radius D=M where M is the image magnification and the image is subject to spherical aberration which is defined by the spherical aberration coefficient, Cs . Spherical aberration is the main factor which limits the performance of electromagnetic lenses used in microscopes and results in being kept small in equation (5.1), which defines the resolution. Indeed resolving power is related to spherical aberration, Cs , by (Born and Wolf (1959)) 1=4
/ 3=4 Cs :
ð5:4Þ
For an electron microscope operating at 150 keV, and this applies for all electromagnetic radiation, with ¼ 0.0037 nm and Cs ¼ 2333 106 the limit of resolution is 0.12 nm.
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Unfortunately a lens corrected for spherical aberration may still show coma, which is aberration that affects rays from point objects which lie off the axis of the lens. Coma arises from differences in the refraction of rays from a point object passing through the inner and outer zones of the lens. Under these conditions the point images as a comet shape; hence coma. This effect is reduced by use of a suitable lens aperture, and an optical system is aplanatic if it is free from both coma and spherical aberration. 5.3.2
Astigmatism
If a lens does not have perfect axial symmetry, then the image plane for objects lying in one direction differs from the image plane for objects lying in another direction. Consequently, vertical components of the image focus in a different plane compared with the horizontal components and no sharp image plane exists, only a plane of least confusion between two sharply focused images. In the case of electron optical instruments, stigmators are used to compensate for this particular lens imperfection, whereas in optical systems this is inherent, and relates to the manufacturing quality of the glass lens. 5.3.3
Distortion
Spherical aberration in a lens results in the image magnification varying in proportion to the (distance)3 ; a point image displaced from the optical axis produces a distorted image (figure 5.2(b)). Pincushion distortion occurs when the magnification of the image increases with distance of the image point from the centre. The opposite to this is barrel distortion. Spiral distortion arises from the angular rotation of an image point which depends upon the distance of that point from the optical axis and as a result sigmoidalshaped images are produced. 5.3.4
Chromatic aberration
As a consequence of refraction by either a glass lens or an electromagnetic lens, either light or electrons respectively emitted from the source X in figure 5.2(c) with different wavelengths or velocities, equation (5.3), focus at different points Y and Y 0 ; the greater the velocity or the longer the wavelength the greater the focal length. As a result, point X will be imaged as a disc of radius D=M and this is called chromatic aberration Cc ¼ A0 ð=Þ=D
ð5:5Þ
where Cc is the chromatic aberration coefficient, = is proportional to V=V and A0 is then the proportionality constant.
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5.4
Photo/electromagnetic sources
Light microscopy
The optical light microscope provides a powerful tool for examining, evaluating and quantifying the microstructure of materials. It has a resolution of about 250 nm with a similar depth of field. Moreover, the instruments have the advantages of being relatively cheap in the simplest form and easy to operate. Although originally developed to operate in the transmission or reflected modes, the latter for polished and etched material specimens, the optical microscope remains the most useful and easily applied technique for establishing the microstructure of a range of materials. However, as with any visual technique the value of the information derived depends critically upon the sampling procedure selected since the region viewed represents only a small fraction of the total volume of material. Since specimen selection is such an important stage in any microstructural evaluation it must be undertaken to ensure that all necessary and appropriate information will be observed. Indeed it is often desirable to select specimens from different regions of a body as well as examining three orthogonal sections to provide the appropriate representative sampling. 5.4.1
Specimen preparation
Specimens are usually prepared by a mechanical lapping sequence followed, in certain special circumstances, by final chemical or electrochemical polishing to remove the ‘flowed’ surface layer (Samuels (1968)). We do not wish to develop the detail of the various lapping and polishing procedures but refer the reader to references for the underlying theory and to the practical details for mechanical polishing (Samuels (1968), Symposium on Methods of Metallographic Specimen Preparation (1960) and Lancombe (1963)), electrolytic (Lancombe (1963), McG.Tegart (1959), Hoar and Mowat (1950) and Brouillet (1955)) and chemical (Lancombe (1966), Smithells (1967), Encyclopedia of Materials Science (1986) and Greaves and Wrighton (1966)) polishing. Diamond knife microtomes developed for biological specimens are of value in preparing undistorted surfaces for some materials such as wood, polymers and paper. Diamond abrasives suspended in an appropriate liquid medium are used extensively for the wet mechanical lapping and polishing of metals and alloys. Indeed these procedures can be employed, in many cases with only minor modification, for the polishing of a range of materials including ceramics, plastics, glasses and composites. The contrast observed under the microscope results from either an inherent difference in intensity or wavelength of the light absorption characteristics of the different phases present within the specimen or by preferential staining or attack of the surface by etching with a chemical reagent. A range of methods are used to effect the desired contrast including
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Figure 5.3. (a) Schematic diagram showing contrast arising from etching a specimen. Optical micrographs showing (b) Cu–40%Zn alloy etched with ferric chloride to reveal the Widmanstatten rod-like precipitates. (c) Type 316 austenitic stainless steel etched with picric acid to selectively reveal the grain boundary -phase (Stratton (1941)). (d) A single crystal of niobium {111} orientation deformed under uniaxial tension and etched with pitting reagent described by Vardiman and Achter (1968) showing etch pits across a kink boundary (Flewitt and Crocker (1976)).
chemical, electrolytic, thermal, heat tinting and ion bombardment. Chemically etching specimens preferentially removes material, depending upon the orientation, and/or the composition of the specific phases, to reveal microstructural features under the optical microscope. In figure 5.3(a), for example, grain boundaries are revealed by preferential dissolution and second phases by differential dissolution. Composition or crystal structure variations are revealed by the use of film forming etchants that produce a transparent oxide, sulphide or other chemically distinct surface film. This is discussed more fully later in the chapter (see Interference Film Microscopy). A typical example of contrast arising from chemical etching is a polycrystalline Cu–40% Zn alloy etched with alcoholic 5% ferric chloride to reveal the Widmanstatten rod-like precipitates in the 0 -phase matrix (figure 5.3(b)). Here the quantity of light reflected into the objective of the optical microscope is determined by the orientation of crystal planes
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Figure 5.4. The variation of current with voltage showing the range of voltage used for electrolytic polishing and etching specimens.
within each phase. Such a dependence on contrast has resulted in a large bibliography describing the choice of etchants to produce appropriate images. For example, it is possible to use selective etchants to identify a given phase; figure 5.3(c) shows a Type 316 austenitic stainless steel which has been etched with picric acid to reveal the -phase precipitates positioned at the grain boundaries (Chastell and Flewitt (1979)). A similar approach provides a simple but positive method of phase identification. Chemical etching can be taken a stage further to develop crystallographically-shaped etch pits with the faces within the pits parallel to low index crystal lattice planes. Figure 5.3(d) shows etch pits in a niobium single crystal which has been subject to a tensile strain at room temperature. The threefold symmetry of the pits shows a {111} orientation for the crystal and reveals that the region of the kink band has been subject to a local rotation of the crystal lattice. Therefore these etching features provide a means of examining and determining crystal orientation (Flewitt and Crocker (1976)). A specimen may be etched by using an electrolytic technique. Following electrolytic polishing (figure 5.4), reducing the voltage takes the specimen to within a range of etching conditions. This method can be extended by applying potentiostatic control to maintain a selected dissolution voltage on the specimen (Lancombe (1966)). If the potential versus current curve (figure 5.4) is established for each phase present in the specimen the conditions may be set to preferentially etch in a controlled manner each phase within a multi-phase material. Thermal methods may be employed either to induce transparent oxide films by heating in a controlled atmosphere to produce interference colour contrast or to effect differential evaporation from the surface of a polished specimen by heating in a vacuum. Indeed, as shown in figure 5.5, etch pits can be produced at the boundary between the Widmanstatten -phase and the parent 0 -phase in a Cu–44.1% Zn alloy. Finally, there are many materials, including metals and ceramics, that prove to be resistant to more conventional etching techniques. A method
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Figure 5.5. Cu–44.1%Zn alloy thermally etched in vacuum revealing (a) a distribution of etch pits along the interface of the rod precipitates and (b) a carbon replica showing the detail of the etch pit geometry.
that can be adopted for such materials is to bombard the surface with ions of a heavy inert gas, such as argon. Figure 5.6 shows schematically such a system, where argon gas is admitted to maintain a pressure of about 104 torr. A glow discharge is produced by applying a potential of about 5 keV between the cathodic specimen and an anode. The etching characteristics depend upon the gas pressure voltage and time for a given specimen-to-beam geometry and particular inert gas selected (Flewitt (1971)). 5.4.2
Imaging techniques
Although image contrast is improved by etching to develop different local coefficients of scattering and reflection, it does not always reveal and
Figure 5.6. Schematic diagram of an argon gas ion bombardment system for undertaking etching. The specimen holder can be rotated and the optical microscope allows the specimen to be viewed.
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Figure 5.7. Vertical illumination light microscope used for routine metallography.
provide all necessary detail. However, there are in addition to conventional optical microscopy a number of purely optical methods for enhancing contrast which can be applied, including dark field and oblique illumination, polarised light, phase and interference contrast. Vertical illumination Incident vertical illumination is used for the examination of opaque specimens (figure 5.7) where the reflected light from the vertical illumination is axial and under these conditions normal surfaces appear bright, whereas inclined surfaces such as grain boundaries appear dark. Optimum illumination is achieved by eliminating unwanted light reflected from the numerous surfaces of the lens inside the microscope. Background glare can be removed by the use of coated lenses and by inserting an iris diaphragm at the position of the virtual image plane of the object in the condenser system. Further improvements in contrast are obtained by careful use of critical illumination. This is achieved by adjusting the condenser lens system so that the image of the light source lies close to the plane of the specimen, ensuring the objective aperture is uniformly illuminated, thereby making maximum use of the value of the numerical aperture for the particular system.
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Figure 5.8. Direct, oblique and dark-field illumination together with corresponding image intensity distributions showing progressive enhancement of image feature.
Oblique and dark field illumination A vertical illuminator can be tilted to secure either oblique or dark field illumination (Brandon (1966)) (figure 5.8). Oblique illumination is obtained by displacing either the condenser lens system or the condenser aperture from the optical axis. This illuminates the specimen from condenser aperture off the optical axis and thereby from one side (figure 5.8) and reduces the numerical aperture of the objective since only part of this lens is used to form the image thereby degrading the attainable resolution. The effect is to increase overall contrast from a surface feature, whilst providing a relief effect to the image, which is particularly useful for highlighting surface features such as slip traces (figure 5.9(a)). In dark field illumination the light beam strikes the specimen obliquely so that no specularly reflected light enters the objective. The best images are obtained by using an annular cone of rays focused in the object plane instead of tilting the illumination. Here feature contrast can be considerably increased by viewing against a black background. This is illustrated in figure 5.8, where the intensity difference from a low contrast topographic feature is given for the three illumination systems. The use of dark field illumination is usually limited by low image brightness since there is no increase in the amount of information recorded in the image, only an improvement in relative contrast. Figure 5.9(b) shows slip traces intersecting second phase precipitates which have imparted a tilt to the surface. Polarising illumination A light wave oscillates perpendicular to the containing ray in all planes (Philips (1967)) (figure 4.9), and if the motion is sinusoidal it can be considered to be
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Figure 5.9. The use of oblique and dark field optical microscopy: (a) slip traces on the surface of deformed (oblique), and (b) slip traces intersecting second phase bainitic 1 plates in a Cu–40%Zn alloy (dark fields).
rotated through 2 about the ray to generate a three-dimensional image and the phase is independent of the plane selected. However, as discussed in chapter 4, section 4.2.3, when oscillation occurs in one plane the ray is defined as plane polarised. If two waves with the same phase oscillating in planes at right angles are combined this is equivalent to a third wave of the same phase but in a different plane. Thus, any plane polarised wave can be resolved into two components lying in arbitrary planes separated by /2. Similarly combining two waves, which are out of phase by /4 or 3/4, produces a circularly polarised wave represented by a helix along the ray direction. Under such a condition the plane of polarisation for the wave rotates into a different position with position along the ray. Elliptically polarised light can be obtained if the phase difference is /8 or 3/8. By introducing a polariser into the condenser system of an optical microscope (figure 5.10(a)), the specimen is illuminated with plane polarised light, when reflected from the surface this undergoes a phase change and becomes elliptically polarised; the wave vector has a component at right angles to the plane of polarisation of the incident light. With a second polariser positioned between the objective lens and the eyepiece and the polarisation plane at /2 to the first polariser, the wave vector component perpendicular to the plane of polarisation of the incident light can be translated into a transmitted intensity at the eyepiece. This measure of the phase change at the reflecting surface occurs if it has either an anisotropic reflection coefficient or multiple reflections are produced from an isotropic surface. Figure 5.10(b) shows a plastically deformed anisotropic metal, cadmium (hcp), where deformation twins are revealed by the polarising illumination. Even for isotropic metals similar effects can be obtained by forming an
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Figure 5.10. Polarising microscopy: (a) optical microscope fitted with crossed polars, and (b) deformed cadmium showing deformation twins.
anisotropic surface film, of thickness at least /4, whose orientation depends upon that of the substrate. Indeed, the thickness of oxide coatings on aluminium base alloys can be established using this procedure. In addition, polarised light can aid phase identification in alloy systems (Pousey et al (1959)) where use is made of the behaviour on rotating a phase between crossed nichols using reflected light. For example sixteen of the phases commonly found in commercial aluminium alloys can be identified simply by using this method. Moreover, it can greatly aid the examination of
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Figure 5.11. Opaque stop microscopy: (a) basic components of microscope, and (b) displacement of the image of the ring stop arising from a surface tilt.
non-metallic inclusions in steels, and indeed has been used to classify and establish their identity (Perryman (1952)). Opaque stop microscopy Figure 5.11(a) illustrates the principle of the opaque stop technique (Brandon (1966)) where a ring stop in the form of a metal disc with an annular opening is positioned between the light source and the condenser. This forms a hollow cylinder of light focused on to the specimen so that if the surface contains areas inclined at a small angle each will produce an image of the stop ring in the back focal plane (figure 5.11(b)). These will be displaced from each other by 2 ; however, that part normal to the incident illumination will encounter the stop, thereby limiting the image to the inclined surface. Phase and interference contrast microscopy Light reflected from a surface forms an image of the condenser aperture in the back focal plane of the objective lens. Hence a proportion of light passes outside the direct image of the condenser aperture. If the latter is an annulus, small differences in height on a specimen surface change the path length of light reaching the image plane aperture giving a diminished intensity by the corresponding phase shift. Figure 5.12(a) considers a reflecting, dephasing and etched surface, where the optical path difference is 2d with respect to the reference plane and d is the height of the perturbations. If
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Light microscopy
191
Eyepiece
Matched objective
Beam splitter
Light source
Reference surface
Figure 5.12. Phase and interference microscopy. (a) Phase contrast due to reflecting dephasing object (b) Phase contrast microscope (c) The Normarski reflection interference microscope; principal feature beam splitting prism. (d) Surface relief due to ferrite precipitation in a low alloy steel (Normarski) (courtesy D Swinden). (e) Optical system. (f ) {112} twins formed in deformation phase Mo–10%Ru alloy; the interferogram is taken using monochromatic thallium illumination and shows the simple tilt displacement (a, a, a) of the surface associated with twinning shear.
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the phase change on reflection at points P and Q is identical, then the phase difference is given by
¼ 4d=:
ð5:6Þ
For phase detail to be visible the phase changes have to be converted into differences in light intensity, amplitude differences, which is achieved either qualitatively by phase contrast or quantitatively by interference contrast. The optical system used for phase contrast in the reflection microscope (figure 5.12(b)), includes phase plates made from magnesium fluoride which advance and retard the phase of the main beam. This allows features to be shown in direct or reverse contrast if the phase shift at the surface of the specimen is small, since the reflected beam is out of phase by /2 with the main beam. Usually contrast is obtained from surface irregularities of between 20 to 50 nm high with a resolution limit of 5 nm; however, small differences in surface height are revealed rather than slope (McLean (1952)). A development from phase contrast microscopy is the interference contrast technique described by Nomarski and Weill (1955) and to achieve this a double quartz wedge is incorporated into the optical system (figure 5.12(c)). When illuminated with polarising light a double image of a specimen surface is obtained with a small lateral shift between the two images. Since the path length of the two beams of light is identical they can be made to interfere, using an analyser, wherever features of the two images are noncoincident. Figure 5.12(d) shows the relief developed on a prepolished surface as a consequence of ferrite precipitation; small differences in level are reproduced in high contrast. Phase contrast arises from interference produced between light reflected from each region of a specimen surface and that diffracted from the same region. Other interference techniques use light reflected from a second, reference, surface to interfere with light reflected from the specimen producing either a two-beam or multiple-beam interference pattern (Tolansky (1962)). Alternatively, the image of the second surface may be projected on to the plane of the specimen. Two-beam interferometry is probably the most widely used of these techniques, figure 5.12(e) whereby monochromatic light reflected from the reference surface is out of phase with that reflected from the specimen by an amount dependent on the difference in path length at the final image. Extinction occurs when the phase difference is , that is when the difference in path length, dp is dp ¼ ð2n þ 1Þ=2
ð5:7Þ
where n is an integer, is the refractive index and the wavelength of the monochromatic light. Figure 5.12(f) shows a typical two-beam interference micrograph which reveals the magnitude of the surface displacements associated with twinning in a deformed molybdenum–ruthenium alloy. For monochromatic thallium illumination the fringe spacing =2 ¼ 270 nm, so
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Light microscopy
193
Figure 5.13. Multiple beam interference between light rays reflected from two film interfaces of the two surfaces of the film: air to film and film to specimen.
that a step of height greater than /2 on the surface produces a displacement of more than one fringe spacing. Since all fringes appear identical only a fractional fringe displacement can be established easily. To identify a unique displacement the pattern has to be observed a second time using white light (tungsten) where fringes are dispersed into spectral colours allowing the number of integral fringe displacements to be established (see figure 4.8). The sensitivity to differences in height of the surface is the order /20 or 25 nm. Compared with two-beam interferometry, multibeam techniques increase sensitivity a hundred-fold allowing step heights of 0.5 nm to be measured. However, the latter techniques are less widely used due to many practical difficulties including the need to coat both the specimen and reference flat with a thin partially transmitting, but largely reflecting film such as silver and using long working distance objectives to accommodate a reference flat positioned above the specimen surface. Interference film microscopy Interference film microscopy, first used by Pepperhoff (1960), provides an optical microscope technique for distinguishing phases. When a transparent thin film is deposited on to a polished specimen surface (figure 5.13), multiple beam interference occurs between light reflected from the two interfaces of the film, specimen to film and film to air (Buhler and Hougardy (1980)). The colours produced depend upon the wavelength of the incident light selected and correspond with the constructive and destructive interference
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Figure 5.14. The variation of reflectance with wavelength for a multiple beam interference layer on a substrate. The wavelength m of 550 nm corresponds with a minimum reflectance and for maximum saturation of colour the reflectance intensity Rm should be zero at m (Quested and Bennett (1988)) (courtesy Rolston Gordon Communications).
of the light rays. The colours produced are a function of the film thickness d, the refractive index, f , and the optical phase change at interface between the film and the specimen, r
r ¼ 2f p =ðf2 p2 2p Þ
ð5:8Þ
where p is the absorption coefficient and p is the refractive coefficient. For a film with zero absorption and assuming normal incidence light, the wavelength m corresponding to the minimum intensity of reflected light Rm in zero order is m ¼ 4f d= r
ð5:9Þ
Thus for a particular type of film of given thickness the wavelength, m depends upon only the optical constants of the substrate. When illuminated with white light, specimens containing constituents of different absorption and refractive indices generate different colours corresponding with the appropriate value of m ; maximum sensitivity is achieved when m has a wavelength of 550 nm (figure 5.14). The amplitude condition is satisfied when the amplitude of the light reflected from the film to air interface equals that from the specimen to film interface. Thus for maximum colour contrast, Rm tends to zero when the wavelength equals m Rm ¼ ½ðA1 A2 Þ=ð1 A1 A2 Þ
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195
Figure 5.15. Calculated loci of Rm ¼ 0 at m of 550 nm for different thickness interference films with absorption coefficient and refractive index of the specimen (Quested and Bennett (1988)) (courtesy Rolston Gordon Communications).
where A1 and A2 are the ratio of reflected light to incident light amplitudes at the air to film and film to specimen interfaces respectively. From a knowledge of the optical constants of the film and substrate together with the film thickness, d, it is possible to predict values for m and Rm . In figure 5.15 we show a plot for different types of surface films of absorption coefficient, kp , and refraction coefficient, np , where the shaded areas correspond with values for typical phases to be identified in a microstructure with the loci of Rm ¼ 0 and m ¼ 550 nm for various thickness films (Buhler and Hougardy (1980) and Allmond and Houseman (1970)). Thus it is possible to identify the particular film to apply to a given polished specimen that will produce maximum interference contrast. Two methods are commonly used to deposit an interference film on to a specimen surface: (i) vacuum evaporation and (ii) reactive ion sputtering.
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Figure 5.16. Sputtering system (1–5 keV) to allow observation of the specimen during deposition of the surface interference film.
Indeed it is possible to incorporate a small reactive sputtering chamber into an optical microscope system (Bartz (1973)) (figure 5.16) to monitor the progress of sputtering and conditions to produce the optimum surface film. However, the apparent advantages of this system are offset by the need to use a long focal length objective lens with the associated reduction in spatial resolution. Generally, however, specimens may be observed using an optical microscope with a continuous light source, although the interference colours observed will be influenced by the particular light source selected. Figure 5.17 shows a specimen of a nickel-base superalloy coated with a zinc sulphide film (m ¼ 555 nm). The precipitate originally considered to be a single phase carbide in fact comprises three distinct areas: (i) a central white area of alumina, (ii) a dark area which is predominantly TiN or Ti(C,N) and (iii) an outer grey region which is a TiTa carbide. The application of interference film microscopy discrimination allows identification of these different composition centres. Incorporating selective interference filters further enhances this technique by allowing phases to be distinguished preferentially and produces a basis for any subsequent quantitative assessment (Quested and Bennett (1988) and Schmidt et al (1985)). 5.4.3
Specialist stages
In addition to the range of optical microscopy techniques we have described there is often a need to study the kinetics of several processes above and
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Figure 5.17. A precipitate particle in a nickel-base superalloy. The inner portion is alumina, the outer is a TiTa carbide, with the intermediate dark area TiN. The interference film is iron oxide, ¼ 510 nm (Quested and Bennett (1988)).
below ambient temperature in materials, such as recrystallisation and phase transformations. For these studies use can be made of one of several hot (Smallman and Ashbee (1966)) and cold stage microscopes (Hull (1956)). As a consequence of geometrical constraints imposed by the need either to heat or cool the specimen under a controlled atmosphere, long working distance objective lenses are usually used. These lenses incorporate reflecting components with a normal objective lens which introduces a limitation to the value of the numerical aperture achievable. Despite restrictions these techniques have specific advantages; for example, in the case of high temperature microscopy a precipitation process can be followed provided the newly formed precipitate can be viewed, if a relief is imparted to a prepolished surface. Figure 5.18 shows a sequence involving nucleation and growth of Widmanstatten rods which precipitate during isothermal ageing of a metastable 0 phase in a Cu– 40% Zn alloy during heat treatment at 573 K. From such sequences recorded on film or video tape it is possible to establish the incubation period and lengthening kinetics of these rods. Polarised light microscopy allows the characterisation of the crystalline texture of polymeric materials. For example, the common spherulitic mode of crystallisation is easily revealed (figure 5.19) and the structure can be characterised from the sign and magnitude of the bi-refringence. This enables the size and spatial distribution of the spherulites to be established. This approach has been used to explore the sub-structure of the spherulites and also their growth kinetics (Sawyer and Grabb (1987)). For the latter a
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Figure 5.18. Hot stage microscopy: growth of Widmanstatten rods during isothermal ageing of the metastable 0 phase in a Cu–40%Zn alloy using a hot stage microscope (cine film sequence). Aged at 573 K for (a) t seconds, (b) t þ 20 seconds and (c) t þ 60 seconds.
micro-hotstage was attached to a polarising microscope and the growth of the spherulites monitored. Moreover it is possible with this system to determine the melting point of these polymeric materials and, indeed, any change in bi-refringence with temperature.
Figure 5.19. The spheruletic texture of a polypropylene revealed by polarised light microscopy. A micro-hotstage is used to establish the kinetics of the growth of the spherulites.
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Laser microscopy
5.5
199
Laser microscopy
The laser (Light Amplification by Stimulated Emission of Radiation) delivers intense, coherent electromagnetic waves that are in the spectral range between ultraviolet and the infrared (figure 2.1). The beam has produced good temporal and spatial coherence and is highly monochromatic. As a consequence directional light is produced with a nearly constant phase wavefront (Maiman (1960), Yariv and Gordon (1963) and Charschan (1972)). Temporal coherence is a measure of the ability of the beam to produce interference arising from path length differences, whereas the spatial coherence provides the capability of focusing the energy output into a small size spot. Figure 5.20 is a schematic diagram of a typical gas laser where the major elements of the system are an active lasing medium, for example a gas but this could be a solid or liquid, connected to a power supply to excite the active atoms. Since the laser operates as an oscillator to produce coherent light, mirrors are placed normal to the axis of the active medium to form an optical resonance cavity. These features differentiate lasers from sources of light used in section 5.4 and lead to the spatial, intense light characteristic of lasers. Certainly reflection studies in the near and far infrared spectral range are achieved by the use of the laser since, in many instances, it is possible to remove the energy limitations of
Figure 5.20. (a) Schematic diagram of a gas laser. (b) Essential features of a Brewster window, , usually fused silica, where the parallel component, Ep , of the electric field is not reflected at the window surfaces and the perpendicular component, Es , has losses at the window. The output is plane polarised with a parallel field component.
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Table 5.3. Typical features of gas and solid state laser systems. Wavelength (nm)
Type Gas lasers HeNe Ar CO2
CO2 (TEA) HeCd Solid state lasers Cr3þ : Al2 O3 (ruby)
632.8
Beam divergence (mrad)
451.9 to 514.5 488.0 to 514.5 10:6 103
0.8 1 0.8 0.8 2 2 2
325.0
0.5
694.3
Nd3þ : glass
1:06 103
Nd3þ : YAG
1:064 103
10 10 10 10 3 8 3
Beam diameter (1/e2 pt, mm)
1.4 1.1 1.4 1.4 10 10 10 30 0.25 1.3 6 6 6 6 4 4 4
non-coherent sources. Table 5.3 summarises some output characteristics of various types of commercial lasers (Maiman (1960), Yariv and Gordon (1963), Charschan (1972) and Oldham (1967)). As a consequence of these characteristics laser sources are used in several different instruments to provide information on the microstructure of materials. 5.5.1
Ellipsometry
Ellipsometry is the study of changes in the polarisation states of light after reflection from a surface. From a measure of the ellipsometric parameters, it is possible to establish the optical constants of materials such as metals and semiconductors and the thickness of films on such substrates (Oldham (1967), Holmes and Feucht (1967), Hilton and Jones (1966) and Spitzer and Tannenbaum (1961)). Figure 5.21 shows a laser ellipsometry system where a laser provides the source of monochromatic light. The polariser and analyser are mounted on graduated circles capable of providing rotation angular measurements to a resolution of at least 0.18. An optical compensator, usually a quarter-wave plate, offers the ability to either adjust for the polarisation of the incident light or an ability to analyse polarisation of the reflected light. The detector is selected to accommodate the wavelength of
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Figure 5.21. Schematic diagram showing the main features of a typical ellipsometry system.
measurement. By adjusting the elliptical polarisation of the incident beam, the reflected beam is plane polarised at some azimuth and can be prevented from reaching the detector by rotating the analyser. This combination of the polariser and quarter-wave plate is used to adjust the polarisation of the incident beam to any degree of elipticity, a value that results in a plane polarised reflected beam. The polariser and analyser are adjusted to a minimum signal at the detector so that the azimuth of the polariser, P0 , and the analyser, (Oldham A0 , are then related to the ellipsometric parameters and (1967)) by ¼ 2P0 þ =2
ð5:11Þ
and ¼ A0 :
ð5:12Þ
The equations relating and to the thickness, t, reflection coefficient, , and the refractive index, 1 , of a surface film are (Archer (1968))
1p þ e2p 2it 1 þ 1s e2s 2it i tan e ¼ ð5:13Þ 1 þ 1p e2p 2it
1s þ e2s 2it where t ¼ 360tð12 sin2 1 Þ1=2 =
ð5:14Þ
and 1p , 1s are the Fresnel reflection coefficients for light reflected at an air to surface film boundary, 2p , 2s are the corresponding coefficients for light at the surface film to substrate boundary, 1 is the index of the film, 1 is the angle of incidence, is the wavelength of light and d is the film thickness. To measure the thickness of a film, the thickness has to be less than the wavelength of the light used. Typically this technique is used for a wide range of applications including measurement of surface films on semiconductors, together with oxidation and corrosion deposits on substrates. In the electronics industry the development requirements for thin films has been stimulated by the use of optical systems such as transparent
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dielectric coatings on optical filters. These filters, which are used to select a proportion of transmitted and reflected light, have been traditionally fabricated from one of a range of materials including silicon dioxide, silicon nitride, titanium oxide, tantalum pentoxide and polycrystalline diamond. To prepare these thin coatings, vapour deposition and plasma enhanced vapour deposition, where the film growth is produced using gas phase precursors activated in a glow discharge environment, are used. To quantify the film, ellisometric measurements are undertaken including variable angle ellipsometry (Rivory (1999) and Martinin and Poitras (2000)). The application of this technique has been shown to have the required sensitivity for monitoring material deposition and, indeed, has been used for real-time monitoring of the coating thickness (Kildemo (1998) and Kildemo et al (1997, 1998)). 5.5.2
Scanning laser microscopy
In conventional light microscopy, section 5.4, images are formed either by direct imaging of the object at a desired magnification or by imaging the object on to a remote surface and converting this image to an electronic signal. In laser scanning microscopy, the object or specimen surface is scanned point by point by a focused laser beam (figure 5.22). The image or other characteristic of the object is then generated electronically. To achieve this the laser beam has to be focused to a size consistent with the resolution required. High resolution laser imaging systems have been developed generally to overcome inherent disadvantages associated with conventional light microscopy and it is possible to effect greater resolution and depth of focus (Alford et al (1982)). Essentially two different scanning systems are adopted in practical transmission or reflection instruments: one scans a focused laser beam across a stationary specimen and the other scans the specimen mechanically across a stationary beam. In the first case the scanning can be very fast so that many whole pictures can be built-up per second, offering the ability to observe rapid changes within specimens. As shown by the micrographs of
Figure 5.22. Schematic diagram of a scanning transmission optical microscope.
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Figure 5.23. Ledeburite eutectic cast iron etched with 2% Nital examined using (a) a conventional optical microscope and (b) a scanning optical microscope using He–He laser wavelength ( ¼ 6238 nm).
a ledeburite eutectic cast iron (figure 5.23), mechanical scanning produces undistorted images of a high quality. By comparison with conventional optical microscopy, electronic contrast enhancement has been used to produce this scanning micrograph and thereby reveal the phases. This electronic contrast enhancement allows the observation of weak detail and provides a more flexible microscopic system. A laser scanning microscope has good depth of focus and can be used to examine the surface topography of a specimen (figure 5.24(a)) (Hilton and Jones (1966), Spitzer and Tannenbaum (1961), Archer (1968), Alford et al (1982) and Munro and Cuthbert (1971)). In figure 5.24(b) gold nodules have been evaporated on to a smooth silicon substrate (Munro and Cuthbert (1971)) and these spherical gold nodules scatter the laser beam isotropically, whereas the substrate scatters light at large angles thereby providing the discrimination necessary to detect and image the gold nodules (Hilton and Jones (1966), Spitzer and Tannenbaum (1961), Archer (1968), Alford et al (1982), Munro and Cuthbert (1971) and Vand et al (1966)). Confocal scanning optical microscopes have two advantages over conventional instruments: (i) improved lateral resolution and (ii) depth discrimination (Wilson (1990)). It is this latter property which allows optical sectioning to be undertaken because the images of the regions of a thick object lie close to the focal region. As a consequence a thorough focal series of optical sections can be recorded and reconstructed to provide three-dimensional images (Pewley (1995)). Figure 5.25 shows the arrangement for a confocal microscope. Figure 5.26 is a three-dimensional representation obtained from confocal images. To obtain real-time three-
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Figure 5.24. (a) A scanning laser system fitted with reflection and transmission detectors. (b) Corresponding optical and laser images showing detail of gold nodules on a silicon substrate.
dimensional images, various approaches have been adopted including the use of many closely packed confocal systems. Here these systems image in parallel with no cross-talk between the channels to construct the real-time image (Wilson et al (1998)). 5.5.3
Ultramicroscopy
A laser ultramicroscope is used to study /2 scattering in transparent specimens. The instrument shown in figure 5.27(a) has a laser source, such
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Figure 5.25. Schematic arrangement for a confocal microscope.
as a 1 mW He–Ne laser and a microscope which is fitted with a rotator to allow adjustment of polarisation to any angle. The source is focused on to the specimen and the scattered light is observed using a conventional optical microscope. The contrast is maximised by viewing the scattered light
Figure 5.26. A three-dimensional representation obtained from confocal images.
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Figure 5.27. (a) Schematic diagram of the main features of the laser ultramicroscope. (b) Defects observed in a synthetic ruby using a laser ultramicroscope.
(Vand et al (1966)). The laser ultramicroscope has a theoretical limit for detectability of 30 nm and this can be extended by use of a more powerful laser source; 1 MW will give approximately 10 nm. Figure 5.27(b) shows defects within a synthetic ruby crystal imaged using this system. 5.5.4
Elemental microanalysis
Laser microanalysis (LIMA) provides an extension to the range of classical emission spectral analysers and electron-beam analysis techniques described in chapter 6 (Moenke-Blankenburg (1984)). It offers mainly qualitative but sometimes semi-quantitative elemental analysis under certain conditions, and indeed the ability to produce quantitative local analysis for both conducting and non-conducting materials over volumes of material of 10 to 300 nm diameter: thus a specific microstructural feature can be examined. The method adopted combines the principles and properties of a solid laser, the optical laser microscope and optical emission spectroscopy. A laser microanalysis system (figure 5.28) comprises a bulk specimen placed on the movable stage of a microscope to allow the region for chemically analysis to be selected and located. The coherent radiation from a solid-state laser with an output energy of between 0.1 and 1 J is focused by the optical
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Figure 5.28. Main components of a laser microanalysis system.
system of the microscope on to the region selected for microanalysis. This is then used to evaporate between a nano- and micro-gramme of the specimen to produce a microplasma which is imaged either directly or with additional excitation in an auxiliary spark gap on to the entrance slit of a spectrograph with a prism or grating as the dispersing element. The position of the lines emitted is specific for the particular element and the intensity is proportional to the concentration. Laser micro-emission spectral analysis requires about 1 ng of material to be sampled with a laser focused beam of 10 mm, and about 100 mg with a larger spot of about 300 mm diameter using a laser energy of 1 J (Genkin and Koroljev (1961)). Since emission spectral analysis is element specific it enables up to about sixty chemical elements to be detected simultaneously depending upon the spectral range covered by the spectroscope. Moreover, this can be used to undertake qualitative and quantitative analysis on small microscopically discrete areas of bulk materials down to 10 mm diameter. This can be further extended to cover line, area and layer analysis of specimens (Ehrlicl et al (1979)). Both conducting and non-conducting materials can be analysed directly with no need for specific surface preparation, in contrast to electron beam methods that require coating with conducting materials (chapter 6). Moreover, the surface of the specimen is not restricted to be flat, indeed it should not be polished since a polished surface increases vaporisation losses by increased reflection of the laser radiation. Analysis can be undertaken in an inert gas atmosphere, although for low atomic number elements a vacuum is required. In the vapour phase, under suitable conditions, each element emits a distinct spectrum which is characteristic of the element, in the wavelength range 100 to 1000 nm. When several elements are vaporized and excited simultaneously the spectra overlap but deconvolution of the signals can be achieved. Halogens, inert gases and O, N and H cannot be analysed and C, P and S only when present in relatively high concentrations. If the spectra range is extended into the ultraviolet range (Laqua (1979)), the limit of detection for P, C and S is lower and analysis of gases is possible. Table 5.4 shows typical examples of analyses undertaken. However, there remains a need to develop the vacuum ultraviolet aspect of laser microanalysis (Laqua (1979), Tassewa and Petrakiev
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Table 5.4. Typical examples of laser microanalysis.
Material
Elements
Detection
Reproducibility
Low alloy steel (CrMoV)
Ca, Mg, Si, V
–
Steel inclusions
Si, Al, Fe, Mn, Cr, Mg
GaAs (semiconductor)
Reference
Comments
–
Tassewa and Petrakiev (1971)
Investigation of welded joints
101 –102 g
10%
Janosikova (1973)
Si
2.3 ng
45%
Ohis (1973)
Quantitative analysis
Copper
Sn, Fe, Ni, Zn, Mn
1011 – 1012 g
–
Moenke– Blankenburg (1978)
Photoelectric recording with optical multi-channel analyser
Borosilicate glass
Sn
–
10.7%
Maul and Quillfeldt (1977)
Polymer
In, Sr
1–20 ppm
–
Laqua (1979)
Quantitative analysis
Graphite
Al, Ba, Ca, Cr, Fe, Mg
0.1–23 ppm 1012 – 1010 g
–
Nickel et al (1979)
Quantitative analysis of impurities— reactor graphite
(1971), Janosikova (1973), Ohis (1973), Moenke–Blankenburg et al (1978), Maul and Quillfeldt (1977) and Nickel et al (1979)). 5.5.5
Magneto-optic scanning laser microscopy
The magneto-optic scanning laser microscope provides a capability for examining the magnetic structure of a material at the sub-micrometre scale. Figure 5.29 shows the schematic layout of such an instrument where light from the argon-ion laser is passed through an acousto-optic modulator, polariser and beam expander before being focused on to the specimen. A modulator switches the beam on and off at a frequency of 3 105 Hz to allow lock-in detection to be applied. The specimen is mounted on a piezoelectric translator for fine vertical movement. The focused spot is rastered across the specimen using the X–Y translation stage and the overall system maintains optimum resolution. The beam is reflected from the specimen and passes via a beam splitter to the detector which comprises
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Figure 5.29. Block diagram of the scanning laser microscope.
quarter and half wave plates, a confocal pinhole, a polarising beam splitter and a pair of quadrant photodiodes. The output is passed to a computerbased processing system (Wright et al (1995)). Magnetic features within the specimen are revealed when the linearly polarised light undergoes a small rotation from the polarisation direction upon transmission through the specimen (the Faraday effect) or upon reflection from the specimen (the Kerr effect) (Wilson and Sheppard (1984)). A reflected image obtained using this technique is given in figure 5.30. This is a demagnetised TbFeCo alloy where the white regions correspond to areas that are magnetised parallel to the surface, the up-direction, and the darker regions are magnetised antiparallel to this normal, the down direction. 5.5.6
Laser Raman microscopy
Raman spectroscopy is a powerful analytical technique with applications that involve gas, liquid or solid phase materials. The spectra produced may be used
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Figure 5.30. Polar Kerr image of the domain structure in demagnetised TbFeCo thin film. White regions correspond to areas that are magnetised parallel to the surface, up-direction, and the darker regions are magnetised anti-parallel to this normal, down direction.
to identify the characteristic energies of the chemical bonds or to distinguish between different phases within the same material, for example diamond and graphite. Moreover it is also possible to obtain information on strain and periodicity in composition modulated materials. Generally little or no sample preparation is necessary and the technique is non-destructive. The Raman effect is an interaction between monochromatic light, generally from a laser source, and the chemical bonds within a specimen which produces a result similar to infrared absorption (see section 2.5.1) (Baranska et al (1987), Colthup et al (1990)). When a laser beam impinges on a material most of the light is scattered at the same wavelength (Rayleigh scattering) but a small number of photons may excite molecular vibrations in the specimen. These photons will lose an amount of energy equal to that imparted to the specimen and, therefore, will be scattered with a slightly longer wavelength. This difference in wavelength is known as the ‘Stokes shift’. When the excited atoms in the specimen subsequently relax they release energy back to the incident beam which is scattered with a slightly shorter wavelength (anti-Stokes). Since the change in wavelength of the Stokes and anti-Stokes lines is extremely small (/100) and the intensity is considerably reduced compared with the incident laser beam, it is necessary to use extremely sophisticated spectrometers to detect these photons. The depth of material sampled depends upon the wavelength of the incident beam but generally is of the order of a fraction of the wavelength. Figure 5.31 shows schematically the arrangement used in a commercial laser Raman imaging microscope. Considerable effort has gone into making these instruments compact and instruments can be purchased that are capable of fitting on to a small bench top. The laser can be either argon
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Figure 5.31. A laser Raman microscope showing the path of the light beam from the low power laser source through the focusing optics and dichroic splitter (D) to the specimen (O) and back through the splitter and filters (F) to the cooled camera detector (CCD) (reproduced by permission of Renishaw Transducer Systems.)
( ¼ 514 nm), helium neon ( ¼ 633 nm) or a semiconductor ( ¼ 780 nm). Monochromatic light from the laser passes through focusing optics and a dichroic beamsplitter to the specimen in the optical microscope. The scattered light then passes through the beamsplitter and filters to a cooled camera detector. The detector can be an optical multichannel analyser, an intensified photodiode array or a charge coupled device. A personal computer is used to scan, collect and process the data. Such an instrument will have high sensitivity so that spectra can be recorded in seconds with an overall wavelength resolution of less than a wave number. The specimen is mounted on a microscope stage so that a conventional image can be obtained and in the particular instrument illustrated a Raman image can also be recorded with a spatial resolution of 1 mm. There is considerable interest in the growth of diamond films on various substrates because of their unique mechanical, electrical and thermal properties (Geiss and Angus (1992)). Many methods are currently being investigated to produce such films and it is important to know the quality of diamond that is produced. Carbon and graphite both give Raman spectra with relatively broad bands whereas diamond gives a sharp peak at 1332 wavenumbers1 and so the technique can be utilised to determine the quality of the grown film. Figure 5.32 shows a spectrum recorded from the surface of a stainless steel specimen on to which a 5 mm thick film of diamond has been chemical vapour deposited (May et al (1993)). The spectrum shows a sharp peak at 1332 wavenumbers1 superimposed on a broad background, indicating that a good quality diamond layer has been grown but that there is also some graphite and/or carbide present. With this thickness of diamond the laser-Raman
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Figure 5.32. A laser Raman spectrum recorded from the surface of a stainless steel specimen on to which has been deposited a 5 mm thick diamond film.
instrument would be sampling the diamond film and the interface between this film and the substrate and this is the major cause of the broad peak. It is also possible to establish the magnitude of the stress present in a wide range of materials based upon shifts in the Raman spectra. For example, in the case of silicon (figure 5.33) the unstressed peak is measured at 520.8 cm1 but this is shifted to a higher value by a compressive stress (Anastassakis et al (1987) and Lucazeau and Abello (1998)). 5.5.7
Photoluminescence microscopy
Photoluminescence relates closely to Raman microscopy and is usually considered in terms of the initial excitation of an electron from the valence
Figure 5.33. Raman spectra from a polished Si wafer and a typical Vickers indentation.
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band to the conduction band by the absorption of a photon of a particular wavelength. Many types of energy can be used to excite luminescence, but photoluminescence arises when an ultraviolet or visible light source is adopted. As a consequence the material absorbs radiation of a certain wavelength and this is re-emitted as photons of a different wavelength. But to ensure conservation of energy the emitted wavelength is longer than that of the exciting radiation. The wavelength difference between the excitation source and the emission radiation, known as the Stokes shift, is typically larger for inorganic than for organic materials. When the source is replaced by electrons then the luminescence is known as cathode luminescence (see section 6.2.4). In general luminescence centres in a material are atoms, ions or groups of ions located near to imperfections in the crystal. Hence the emission spectrum presents a composite of several partial bands so that the position of the peaks can be attributed to defect levels created within the band gap of the material by these imperfections in the lattice. Photoluminescence microscopy can be undertaken in a system similar to that described for laser Raman spectroscopy. Here the spectra are generated by selecting a laser of appropriate wavelength, typically 325, 457.9, 488 and 514.5 nm at a chosen operating temperature. In general the specimen has to be a pure material. The problem is that the spectral lines broaden as the impurity element concentration increases within the parts per million range. However, within these constraints this technique has a high level of sensitivity. Low temperature photoluminescence microscopy is particularly helpful for characterising chemical vapour deposited diamond either for quality control or to address variations within different grains of this polycrystalline material (Steeds et al (1999)). Figure 5.34 shows the photoluminescence spectra for vapour deposited diamond obtained at a temperature of 220 K when subject to prior electron irradiation (Steeds et al (2000)). This specimen is boron doped. These spectra, displaced for clarity, are taken at a spacing of 10 mm across the electron irradiated area. Three major peaks are present: (a) the Raman peak, (b) a strong peak characteristic of a new centre and (c) that arising from a neutral isolated vacancy.
5.6
Acoustic microscopy
Since ultrasound penetrates optically opaque materials acoustic waves can be used to provide sub-surface images which are difficult to achieve by other methods. This ability has led to the development of various types of acoustic microscopes. Moreover, since the reflection of acoustic waves is determined by the mechanical properties of the material, acoustic reflections also provide a potentially quantitative measure of these properties (Kino (1987) and Lemons and Quate (1979)). In a solid material, acoustic waves propagate as longitudinal, transverse and shear waves, whereas in a fluid only
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Figure 5.34. Spectra obtained at 220 K and 10 mm spacing along a line across a liquid nitrogen temperature electron-irradiated area of a 10 B-doped diamond specimen containing 8 1018 B cm3 (displaced for clarity). The three marked lines are (a) the Raman LO phonon line, (b) the newly discovered centre and (c) GR1 (neutral isolated vacancy). On examination using a 488 nm laser line after electron irradiation only GR1 luminescence was detected. A 325 nm ultraviolet laser spot was focused on the electron irradiated area at liquid helium temperatures and the sample was re-examined with 488 nm laser excitation to produce the results illustrated. In the ultraviolet laser irradiated area GR1 has been replaced by the new centre.
longitudinal waves persist. The velocity of each acoustic wave varies with material type, table 5.5 (Somekh (1988)), but generally the velocity of an acoustic wave is about four orders of magnitude less than that for light wave. Thus, very short wavelengths can be established at comparatively low frequencies (figure 2.1); at microwave frequencies, 1 GHz, wavelengths approach those for light, approximately 1 mm. Currently there are many methods of producing acoustic images but we will address those appropriate to the formation of images for evaluating the microstructure of materials (Briggs (1985)). 5.6.1
Scanning acoustic microscope
The problems associated with producing diffraction limited resolution can be overcome by mechanically scanning a specimen in a raster relative to an acoustic lens (Lemons and Quate (1979)). A schematic diagram of an acoustic lens is shown in figure 5.35 where an acoustic transducer produces a plane wave in a buffer rod fabricated from a material such as sapphire. The latter is selected since it allows acoustic waves to propagate with a velocity of at least fourfold greater than the coupling fluid, water (table 5.5).
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Figure 5.35. A schematic diagram of an acoustic lens showing the main components.
When the acoustic wave impinges on the lens surface, the concave indentation which is filled with the relatively slower transmitting coupling fluid acts as a converging lens, refracting the acoustic wave to a focus. Sometimes a matching layer is incorporated between the lens and the water and thereby further reduces reflections at the surface of the lens. For this a quarter wavelength material is selected which has an acoustic impedance intermediate between the buffer rod and the coupling fluid, essential to sustain a high signal-to-noise ratio at frequencies about 1 GHz. Figure 5.36 shows acoustic waves focused below the surface of the specimen; the velocity of acoustic wave propagation in the specimen greatly exceeds that in the fluid couplant. Snell’s Law is obeyed and the waves are refracted from the normal Table 5.5. Approximate values of acoustic wave velocities for a range of commonly used materials.
Material
Longitudinal wave velocity (ms1 )
Shear wave velocity (ms1 )
Water Air Aluminium Fused quartz Gold Lead Nickel Sapphire (along z axis) Silicon Silicon nitride Steel (mild)
1 500 (30 8C) 331 (20 8C) 6 330 5 960 3 240 2 200 5 600 11 100 8 700 11 000 5 900
– – 3109 3760 1200 700 3000 6040 5200 6250 3200
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Figure 5.36. Modes of sub-surface imaging: (a) ultrasonic waves in coupling fluid; (b) transmission through specimen surface with mode conversion (longitudinal and shear waves have different sound velocities); (c) focus with longitudinal waves; (d) focus with shear waves.
to produce a focus at a position above the focal plane; to obtain larger depths of penetration longer focal length lenses are adopted. Moreover, off-axis rays are brought to a focus above the paraxial range so that spherical aberration is reduced for a lens with a small numerical aperture. The focused acoustic waves are scanned with a synchronised rastered system and displayed electronically using a greyscale recorder. Either a pulse echo or pulse transmission mode can be used (figure 5.37), where a zinc oxide transducer generates an acoustic signal which is focused by the sapphire lens to a spot of 1 mm diameter at frequencies of 1 to 3 GHz. A specimen area of typically 0:25 mm 0:25 mm is scanned and the specimen is sampled to depths of up to 150 mm. This results in images with resolutions which allow useful magnifications of up to 103 to be achieved. Reducing to 10 MHz focused probes increases the area scanned to 15 cm 15 cm and the penetration depth to 5 cm, but the resolution is reduced significantly so that magnifications of only 2 are achieved. The scanning acoustic microscope is used to examine subsurface microstructures, surface layers and the stress state of a material (Vetters et al (1989), Ilett et al (1984) and Quinten and Arnold (1989)). Thus changing the focal position provides the mechanism for varying the image contrast and thereby selective imaging to compare microstructure. Figure 5.38 shows delamination in a lacquered sheet after corrosive attack due to different bonding conditions at the interface. More generally this technique is used in the integrated circuit industry for the non-destructive imaging of
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Figure 5.37. Scanning acoustic microscope, pulse echo mode.
electronic components (Moore (1993)), Kho (1998), Canumalla and Kessler (1997) and Adams (2000)). Certainly, delaminations on a lacquered sheet after corrosive attack can be detected due to the different bonding conditions on the interface (figure 5.38). Moreover, the scanning acoustic microscope has the capability to correlate images and changes in sound
Figure 5.38. Lacquered sheet after corrosive attack examined in a scanning acoustic microscope (200 MHz); white areas show delaminated regions.
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Figure 5.39. The change in the velocity of sound as a function of applied stress for values of
shown.
velocities which provide a measure of stress and stress state (Vetters et al (1989) and Pac et al (1984)). The acousto-elastic effect depends upon the direction of the principal stress relative to that for acoustic wave propagation and the direction of polarised acoustic waves relative to the principal stress (Quate et al (1979)). For qualitative and quantitative measurements, changes in acoustic velocities must be defined as a function of the propagation direction and this is achieved using cylindrical lenses and a goniometer mounted after the specimen stage. Since acoustic velocity depends upon other material parameters such as crystal texture, homogeneity and surface topography suitable specimen preparation methods have to be used. Figure 5.39 shows the change in sound velocities due to applied stress for polymeric materials (Shimada (1987)). For metals, the difference in sound velocities is smaller and cannot be measured as readily using a mechanical stage. 5.6.2
Photoacoustic microscope
The absorption of light pulses at the surface of a solid material results in the production of acoustic pulses within the body. In the photoacoustic microscope (figure 5.40), an incident light pulse from a laser is focused on to the specimen surface where it is partly absorbed and reflected, producing heat which locally expands the surface layer; expansion displaces material upwards and there is an associated downward acoustic pulse. The acoustic image which results has a resolution which is a function of the incident spot size, the duration of the laser pulse and the thermal conductivity of
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Figure 5.40. Schematic diagram of photoacoustic microscope systems for a bulk specimen.
the material (Bein et al (1988) and Ash (1980)). Figure 5.40 shows schematically the arrangement for a simple photoacoustic microscope system which depend upon the thickness of the specimen to be examined. 5.6.3
Electron acoustic microscope
An extension of the photoacoustic microscope is the electron acoustic microscope (figure 5.41). The difference between the two is that now a chopped electron beam in a scanning electron microscope (see chapter 4) is used to generate the acoustic signals in the specimen (Cargill (1980), Brandis and Rasencraige (1980), Cantrell and Qian (1989) and Korpel et al (1971)). The specimen, contained within the electron microscope vacuum system, is attached to a goniometric specimen stage by a non-volatile fluid such as silicone oil. The stage is interfaced with a piezoelectric transducer which receives pulses from the area of the specimen with equal sensitivity. Although the dimension of the incident electron beam is approximately 0.1 mm, the resolution of this microscope is improved compared with the photoacoustic microscope because it is limited by the thermal conductivity of the specimen. However, by controlling the total energy within the incident electron beam, it is possible to obtain resolutions below 1 mm. Figure 5.42 shows images of the composite aluminium alloy (2618) which contains a 12% volume fraction of SiC particles. The images are obtained at different frequencies and are shown together with the corresponding secondary electron image. The contrast obtained in the acoustic range is sensitive to modulation frequency in a
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Figure 5.41. Schematic diagram of an electron acoustic microscope; here an incident electron beam is about 0.1 mm diameter and this excites acoustic waves within the specimen.
Figure 5.42. Images obtained using an electron acoustic microscope showing SiC particles in an aluminium matrix composite: (a) is a secondary electron image, and (b), (c) and (d) are scanning electron acoustic images obtained at 227, 280 and 284 kHz respectively. Electron beam accelerating voltage 30 keV (Cantrell and Qian (1989)).
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Figure 5.43. Scanning electron acoustic images obtained from GaAs with an undoped 1000 nm thick buffer layer together with rectangular areas of epitaxial doped GaAs of 600 nm thickness. The images are obtained with increasing accelerating voltage of the electron beam (a) 15 keV, (b) 27.5 keV and (c) 40 keV. All images are obtained at a fixed frequency of 87 kHz (courtesy L K Balk and M Maywald).
very narrow frequency band. Stray variations with pronounced maxima in contrast are achieved which correspond with nodes in the particular specimen and transducer combustion vibrational frequency spectrum (Cantrell and Qian (1989)). Figure 5.43 shows electron acoustic micrographs obtained from gallium arsenide with a buffer surface layer 1000 nm thick. The use of increasing accelerating electron beam voltage from 15 to 40 keV provides progressive depth information to ultimately reveal detail of dislocations at the interface. Moreover detail is also provided with respect to the epitaxially GaAs doped areas of 600 nm thickness (rectangular regions).
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Figure 5.44. Schematic diagram of a scanning laser acoustic microscope.
5.6.4
Scanning laser acoustic microscope
The scanning laser acoustic microscope (figure 5.44) uses a focused laser beam to scan the ripple pattern produced on the reflective surface of a specimen, where it is insonified by a continuous acoustic wave (Korpel et al (1971)). The frequency of the acoustic signal is typically 100 to 500 Hz and the amplitude of the surface ripples is modulated by the elastic properties of the material. The reflecting surface scanned by the laser is either the polished specimen or, for non-metals, is the cover slip or metallised polymer film attached to the specimen by a water or oil layer. Figure 5.45 shows a transmission image of metal ribbons on an A12 O3 substrate.
Figure 5.45. Scanning laser acoustic microscope transmission images of mesh composed of 25 mm diameter wires spaced on 100 mm centres.
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Infrared microscopy
5.7
223
Infrared microscopy
Although various instruments for recording optical and corresponding infrared images have been available since the early 1940s, it was not until more recently that infrared microscopes have become more widely available (Messerschmidt (1987), Crates et al (1953) and Barer et al (1949)). Moreover, it is the advent in recent years of Fourier transform infrared spectroscopy which enables imaging and chemical analysis of small specimens with dimensions of approximately 10 mm. The infrared microscope operates with wavelengths typically of the order of 103 nm, and has many features in common with the light microscope (figure 5.46) (Messerschmidt and Harthcock (1988) and Clark (1990)). Indeed with many instruments the specimen may be examined with either infrared radiation or white light. The optical train is parafocal and collinear with that adopted for the infrared radiation and this is achieved by viewing through a series of pinholes and then aligning the infrared energy with these. Glass lenses cannot be used effectively when recording infrared images, simply because glass is not transparent to the intermediate wavelengths of infrared radiation. Therefore,
Figure 5.46. A schematic diagram of the main features of the Fourier transform infrared microscope.
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Figure 5.47. Infrared micrograph of the intermetallic phase bond between a gold ball and aluminium substrate.
for analytical purposes, alternative lens systems are adopted to allow the infrared spectra to be recorded. Thus a reflecting or Cassegrainian objective and condenser lens are included and, similarly, changes in the direction of the infrared beam are achieved by employing front reflecting mirrors (Messerschmidt (1987) and Clark (1990)). For chemical analysis, the area to be evaluated is centred under the optical microscope, either in the reflection or transmission mode. Since the optical geometry is common for white light and infrared detection, the diffraction is degraded for detection due to the greater wavelength of the infrared radiation. Therefore, for Fourier transform infrared microscopy, the spatial resolution is defined by the ability to measure the spectrum from an object, determined by the apertures, without the introduction of stray radiation. Stray radiation can result from either spurious narrow band radiation from a nearby absorber or spurious broad band radiation from a nearby hole. Moreover, both accuracy and signal-to-noise ratio may be influenced by the spatial resolution of the microscope. Fourier transform infrared microscopy is a powerful tool for the characterisation of a range of materials, including polymeric materials, composites and silicon-based semiconductor devices (Clark (1990), Pandey (1989), Young (1988), Harthcock and Atkin (1988) and Fuller and Rosenthal (1986)). It is particularly suitable for obtaining subsurface information from semiconductor devices. At wavelengths of between 850 and 1300 nm, silicon is essentially transparent to infrared radiation; thus a range of potential semiconductor device problems can be examined to the limit of resolution of approximately 1 mm. Figure 5.47 shows an infrared micrograph of an intermetallic phase which is used to bond a gold ball to an aluminium substrate. The integrity of the intermetallic phase which forms the bond controls the performance of this particular semiconductor device. A typical use of this technique is demonstrated by the following example. Figure 5.48(a) shows an imperfection of approximately 200 mm diameter contained within a polyethylene film. A two-dimensional map
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Figure 5.48. (a) Optical micrograph of an imperfection in a polyethylene film. (b) Functional group image of the imperfection in the polyethylene film shown in (a). The image is based on an absorption peak at 1738 cm1 and is represented by both axonometric and contour plots.
(figure 5.48(b)) can be obtained by reducing a two-dimensional array of infrared spectra based upon the carbonyl absorption (1738 cm1 ) peak. This shows a higher localised concentration of carbonyl within the imperfection than the surrounding polyethylene film. Such data may be represented in one of several ways and figure 5.48(c) shows both the functional group image axonometric plots and a corresponding contour plot. This form of data presentation provides a basis for correlating the image and the chemical distribution and thereby an ability to establish the origin of the defect within the film. An important application of infrared microscopy has been in the field of microelectronic materials. One important development has been the passivation of a silicon surface with a thermal oxide to provide both chemical and electronic stability (Krivanek et al (1978)). Here Fourier transform infrared spectroscopy has been used to investigate the species on silicon passivated by hydrogen or oxides. Here the different S–H and Si–O chemical bond configurations can be investigated by their specific vibration modes, such as stretching, during and after electrochemical treatments (Ng et al (1998)) and
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Figure 5.49. The variation of the infrared band intersites when nitrogen is incorporated into plasma-deposited a-C(N) : H films.
(Grandjean et al (1996)). Another area of application has been to characterise amorphous hydrogenated carbon films (Schwarz-Selinger et al (1999)) and (Zou et al (1990)). A feature observed in the infrared spectra from diamondlike a-C :H films is a broad band in the 2900 cm1 region of wave numbers arising from C–H stretching vibration of CHn groups containing carbon atoms in all the hybridisation states. Nitrogen, when incorporated into these a-C :H films, gives rise to significant changes to the infrared spectra (Kaufman et al (1989)). Figure 5.49 shows the variation of the infrared band intersites when nitrogen is incorporated into plasma-deposited aC(N) :H films. These spectra reveal that the C–H stretching band decreases and the N–H stretching band increases as more nitrogen is incorporated. This reveals that hydrogen preferentially bonds with the nitrogen in these films (Schwan et al (1994)).
5.8 5.8.1
X-ray microscopy X-ray imaging
For conventional imaging, X-rays are less attractive than their potential would indicate. From the Abbe´ diffraction limit the wavelength of rays, which is about 0.1 nm, indicates a resolution considerably better than can be achieved using light, but less than for electrons. Unfortunately, since Xrays carry no electric charge they cannot be focused by either electrostatic or magnetic lens and, in addition, refraction cannot be used because the refractive index for this electromagnetic radiation is approximately equal
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Figure 5.50. Emission and absorption X-ray spectra for molybdenum radiation with a zirconium filter.
to unity, 0.99998 (Cosslett and Nixon (1960)). The latter parameter leads to focal lengths some four orders of magnitude greater than the effective radius of curvature of the lens, thereby introducing impracticably long focal lengths. However, considerable attention has been given to devising techniques which would allow X-rays to be used to form images with the maximum potential resolution and with sufficient image contrast (Cosslett and Nixon (1960), Schmuhl and Rudolf (1983) and Morrison et al (1987)). Contrast arises simply because of differential absorption of the incident Xrays between different regions of specimens. Although image contrast is produced by diffraction contributions, the absorption of X-rays depends upon a combination of the atom species and atomic number so that when microstructural features are imaged they contain composition information. Where a beam of X-rays passes through a specimen of thickness t the intensity is reduced from the initial value of I0 to a value I where I ¼ I0 et
ð5:15Þ
where is the linear absorption coefficient that depends upon the atomic number of the material and on the X-ray wavelength. Usually is replaced by the term m , the mass absorption coefficient, which is equal to = where
is the density of the material. This parameter is independent of the physical state of the material and varies with the wavelength (figure 5.50). Also included is the continuous X-radiation spectrum whose minimum wavelength is determined by the applied voltage (see chapter 2). The mass absorption coefficient is characterised by a series of abrupt changes called absorption edges at those energies, wavelength decreases as energy increases, where electrons are no
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Figure 5.51. Absorption of X-radiation in a specimen containing a second phase in a parent matrix.
longer displaced from the target material. The existence of absorption edges enables monochromatic X-radiation to be produced from a spectrum of the type shown in figure 5.50. Since conventional methods of image formation cannot be used with Xrays the two main techniques for X-ray microscopy are contact microradiography and X-ray projection microscopy; both produce a simple absorption contrast image. If a specimen (figure 5.51) contains a second phase of thickness a and linear absorption coefficient 2 embedded in a matrix of thickness b and absorption coefficient 1 then from equation (5.15): I2 ¼ I0 expð 2 t2 Þ exp½ 1 ðt2 t1 Þ
ð5:16Þ
I2 =I1 ¼ expð 1 2 Þt1
ð5:17Þ
such that
which is independent of the matrix thickness. The response of a photographic emulsion to X-rays of constant incident intensity, I, produced for a time is related to the optical density, , by the absorption of light in the image so that
¼ log10 I0 =I
ð5:18Þ
where I0 and I are the incident and transmitted intensities respectively. The optical density is related to the intensity I of the transmitted X-rays by
¼ 0 logðIÞ þ C
ð5:19Þ
where 0 is the response of the emulsion to X-rays and C is a constant. The difference in the density, 1 2 , due to the presence of the second phase in figure 5.51 is
1 2 ¼ 0 logðI1 t1 Þ=ðI2 t2 Þ:
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ð5:20Þ
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Table 5.6. The difference in absorption coefficients for iron-base alloys using K X-radiation. Target material Absorbing element
Atomic No. ðZÞ
Cr ¼ 0:229 nm
Fe ¼ 0:193 nm
Co ¼ 0:179 nm
Ni ¼ 0:166 nm
Si Ti V Cr Mn Mo
14 22 23 24 25 42
457 1762 438 257 161 3582
303 1097 1967 2947 98 2477
254 880 1580 2330 3080 1980
2944 2030 1470 850 520 1110
If 2 > 1 then
1 2 ¼ log expð 2 1 Þt1
ð5:21Þ
¼ 0:43 0 t1 :
ð5:22Þ
thus
The difference is independent of specimen thickness, t2 , but depends on thickness of the second phase, t1 , the difference in the absorption coefficients, , and the response of the photographic emulsion. The parameter in equation (5.22) which controls contrast is the differential absorption which has typical values for iron-base alloys given in table 5.6. 5.8.2
Imaging techniques
Generally X-ray microscopy is used to reveal the microstructure of materials in the form of high resolution images. The techniques separate into those where a form of X-ray optical element is used as part of the imaging process and those where no such element is used, the latter technique being a derivative of radiography. Radiographic techniques Contact and point projection microradiography are the simplest methods of X-ray microscopy, differing simply in the relative distances between the source, specimen and recording medium. For contact microradiography the system (figure 5.52) comprises a thin specimen placed close to the recording system, in this case a photographic film, so that no magnification is achieved. The resolution achieved is less than that revealed by the Abbe´ diffraction limit due mainly to geometrical blurring and grain size restrictions imposed by the photographic emulsion of the film. Geometrical blurring is
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Figure 5.52. A schematic diagram of a contact microradiographic microscope system.
shown in figure 5.53 where the width of the penumbra, dp , is given by dp ¼ dx Db =Da
ð5:23Þ
where dx is the width of the X-ray source, Db the specimen to film distance and Da the source to specimen distance. For optimum resolution the specimen has to be as close to the film as possible to reduce Db and in addition a small X-ray source aperture is used. The advantages of this technique for materials investigations arises from the depth of field achieved: metals up to 0.1 mm thick can be examined for the presence of inclusions or micro-cracks. This capability is coupled with sensitive control over the contrast within the image which is effected by selecting the degree of contrast desired for different regions of the microstructure by varying the incident X-ray wavelength and use of abrupt changes in the absorption coefficient (figure 5.50). A wide range of materials microstructural features have been investigated including inclusions, crack-like defects and compositional segregations.
Figure 5.53. The source, specimen and film geometry for the X-ray projection microscope.
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Figure 5.54. Schematic arrangement for an X-ray projection microscope.
X-ray projection microscopy In the X-ray projection microscope a magnified image is produced by using a system shown schematically in figure 5.54. In the case of the projection microscope the magnification is effected by making Da small with respect to Db in figure 5.53 so that a primary, magnified image is formed; magnification is equal to Db =Da . Since the primary image is magnified the resolution limit is not restricted by subsequent optical viewing but rather by the geometrical penumbra. As shown in figure 5.54, an incident electron beam is focused to a small spot on a target material which is usually a thin metal foil which provides the X-ray source and the specimen is placed within a millimetre of this. It is possible to achieve primary magnifications of up to 103 with a resolution of between 0.1 and 1.0 mm. Compared with the contact method this technique has the advantage of a greater depth of field that enables stereo-pair imaging and larger specimens to be examined. X-ray focusing techniques Another category of transmission X-ray microscopy uses either a reflective or diffractive optical element to focus the X-ray beam. Manufacturing problems associated with high resolution reflective optics are considerable but developments have centred upon grazing incidence reflection (Franks
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Figure 5.55. The use of curved mirrors to focus X-rays, utilising the fact that total external diffraction occurs at low incidence angles of <300 .
and Stedman (1985)) and large angle reflection from synthetic, multilayer structures (Spiller (1984)). Since the refractive index is just less than unity, at a certain angle of incidence total external diffraction of X-rays occurs. Thus the diffraction coefficient of X-rays is high at low incidence angles <300 from a polished surface. This has resulted in the use of curved mirrors to focus the X-rays (figure 5.55), and this allows a reduction in astigmatism for an incident beam of wavelength of 0.1 nm. By using an angular aperture of 0.48 a resolution of 8.5 nm can be achieved. An alternative approach has been to incorporate Fresnel zone plates into the scanning system as shown in figure 5.56. Here the specimen is
Figure 5.56. A schematic diagram of a scanning transmission X-ray microscope.
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Table 5.7. A comparison of scanning transmission X-ray microscopy (STXM) with scanning transmission electron microscopy (STEM) (Morrison et al (1987)).
Energy of incident radiation Wavelength Resolution Contrast mechanism Usable specimen thickness Specimen environment
STEM
STXM
100 keV 3.7 pm <0.5 nm Scattering 20 nm 104 –109 mbar
400 eV 3.1 nm 100 nm Photoelectric absorption 5 mm Ambient (air/He)
scanned by the incident X-ray beam and because all the optical elements that absorb radiation are located between the source and the specimen, the Xradiation impact on the specimen is minimised (Cosslett and Nixon (1960) and Vladimirsky et al (1984)). These microscopes can be operated in either the conventional transmission (CTXM) or scanning transmission (STXM) modes and as a consequence the modes are comparable with those used for electron microscopes. Indeed for materials microstructural investigations STXM has the potential for providing information that is complementary to that obtained with the scanning transmission electron microscope (STEM) (chapter 4). Table 5.7, prepared by Morrison et al (1987), compares the main features of each instrument. Although the resolution of the STXM is inferior to the STEM it is possible to obtain elemental contrast even from low atomic number elements and the instrument does not require a vacuum environment. Such instruments offer significant potential benefits for investigating the microstructure of materials which have yet to be exploited.
5.9
X-ray topography
X-ray topography provides methods of imaging derived from a diffracted beam of X-rays which are used to reveal lattice imperfections within crystalline materials, despite the inherent disadvantage of low spatial resolution (Tanner (1975)). An X-ray topograph is obtained by recording the spatial variation in the intensity of the beam diffracted from a crystal. The angular width of the diffracting range about reciprocal lattice points is smaller for X-rays than electrons (chapter 4), being typically 105 rad compared with 102 rad and as a consequence X-ray diffraction images are very sensitive to small crystal lattice strains. However, the width of a dislocation image is greater in X-ray topographs than in a corresponding electron micrograph. Therefore, a topograph may be considered simply as a two-dimensional map of X-ray scattering and is the analogue of a transmission electron micrograph (chapter 4). The
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Figure 5.57. X-ray topography. (a) Experimental arrangement for the Lang method. Specimen and film can be translated together and the slits are normal to the plane of the diagram. (b) Projection topograph of crystal 1.25 mm thick showing dislocations in deformed aluminium; [111] diffraction condition Ag K X-radiation (Lang (1959)).
spatial resolution is limited to about 1 mm by one or a combination of factors including weak scattering, instrument geometry, recording film resolution, and photoelectron tracking in the film. Lang developed both the section (Lang (1958)) and the projection (Lang (1959)) X-ray topographic techniques. Since that time, there have been several attempts to increase the speed and resolution of this technique (Weissman et al (1984) and Tanner and Bowen (1980)) and this has led to the technique being applied to the microstructural evaluation of semiconductor materials. The method commonly used is based on that described by Lang, where a thin specimen, typically 1 mm thick, is irradiated with a collimated beam of monochromatic X-rays emitted from a point focus tube (figure 5.57(a)), and the diffracted beam provides the image. If the specimen is held stationary, a photograph of the sampled section is obtained; a section topograph (figure 5.57(b). Although no scanning of the specimen is possible, making it unsuitable for general area surveying, if the crystal lattice defects are uniformly distributed or have certain symmetries it can be an extremely powerful method. For example, figure 5.58 shows a section topograph of a silicon wafer heat-treated to getter oxygen. A region denuded of crystal lattice defects has been produced below the surface, a feature that is used to allow devices to be fabricated on it. Traversing the specimen and the film during exposure produces a projection topograph which provides a two-dimensional map of the crystal
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Figure 5.58. Section topograph showing zone denuded in dislocations following heat treatment of a silicon wafer.
lattice defect structure throughout the volume. As the images are typically a few micrometres wide, the limit at which individual dislocations can be resolved is about 104 cm2 . As a consequence, the technique is particularly suited for identifying extensive dislocation arrangements such as those produced by slip. Figure 5.59 shows a high-resolution Lang topograph of in-plane dislocations produced at the edges of heavily doped regions in silicon wafers together with slip dislocations. Topographs can be obtained also in the reflection mode, although the crystal lattice defect contrast is usually very poor. This contrast can be improved by use of a double crystal system where a selectable reference crystal is placed between the X-ray source and the incident slit (figure 5.57), so the strain sensitivity can be matched to the specimen being investigated, e.g. using Si with InP removes double images that would be generated by characteristic X-ray lines. Figure 5.60 shows near-surface defects in a bipolar silicon wafer in a reflection mode topograph (Tanner (1989)).
Figure 5.59. Lang projection topography showing dislocations generated at the edges of silicon diodes (Tanner (1989)).
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Figure 5.60. Double crystal Bragg (reflection) geometry topograph of device related defects in a bipolar silicon wafer (Tanner (1989)).
5.10
X-ray photoelectron spectroscopy
5.10.1
Principle
The technique of X-ray photoelectron spectroscopy (XPS) utilises photons to ionise surface atoms and the energy of the ejected photoelectron is detected and measured (Siegbahn et al (1967), Briggs and Seah (1990), Carlson (1975), Hercules and Hercules (1974), Watts and Wolstenholme (2003) and Rivie`re (1990)). Most techniques require the surface of the specimen to be bombarded with low energy X-rays from an aluminium or magnesium source using the K peak. Occasionally higher and lower energy photons are used such as produced from silicon targets and ultra violet light sources in ultraviolet photoelectron spectroscopy (UPS) (Briggs (1977)). Figure 5.61 illustrates the underlying process of XPS and UPS where the specimen surface is bombarded with photons of energy E ¼ h and an electron is ejected from either a valence
Figure 5.61. The process of photoelectron emission.
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electron shell or an inner core electron shell. The energy of the ejected electron, E, is given by E ¼ h E1 where is the frequency of the incident photon, E1 the electron binding energy and the work function of the specimen, and by measuring this energy and knowing the energy of the incident photoelectron the electron binding energy can be determined. It is this binding energy that permits the atom to be identified and provides information gained concerning its chemical state. The main application of this technique is in the study of chemical reactions which can occur at the top few atom layers of materials. 5.10.2
Instrumentation
X-ray photoelectron spectroscopy (XPS) requires an ultra-high vacuum <106 Pa to prevent contamination of the surface of the specimen. Therefore the instrument normally consists of a preparation chamber to carry out initial cleaning and specific experiments, and an analytical chamber with a photon source, an electron analyser and a detector together with the equipment to clean and maintain the specimen surface (Rivie`re (1990)) (figure 5.62). The specimen is introduced to the main chamber via introduction and preparation chambers. The specimen is then moved into the analytical chamber where it is bombarded by the photon source and the ejected photoelectrons are focused on to the entrance slit of an electrostatic analyser by an electromagnetic lens system. The electrons then pass through the analyser. The electrons may be retarded to a fixed energy prior to entering the analyser when the potentials on the analyser hemispheres remain constant (fixed
Figure 5.62. A schematic diagram of an X-ray photoelectron spectrometer.
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analyser transmission (FAT)) or the electrons are not retarded and the analyser potentials are varied (fixed retard ratio (FRR)). These electrons are detected using an electron multiplier, usually a channel electron multiplier (channeltron), which is essentially a tube with the internal surfaces coated with a material which produces a large number of electrons when an electron is incident upon it. As electrons are accelerated down the tube, impinging on the walls, they produce more electrons in such a manner that the initial single electron interaction gives a large resultant signal. The spectrometer may contain several of these channeltrons across the exit to increase the acquisition speed of the analyser. It is necessary to have more than one photon source on an XPS instrument since at least two photon energies are required to distinguish between Auger and XPS spectral peaks (see below); it is an advantage to have a very accurately defined source as well as the more intense standard sources. X-ray sources The design of a dual X-ray source is shown schematically in figure 5.63 (Yates et al (1973)). The water-cooled anode is manufactured from copper with the top face machined to a tip, with each side coated with a different X-ray producing material. Two filaments are positioned to the side of and slightly below these faces and each is selected to produce X-rays from the respective anode faces. Electrons from the filament are accelerated to 15 keV to give a maximum power of 1 kW and bombard the anode surface producing an X-ray spectrum characteristic of the material coating the anode (figure 2.2). The X-ray spectrum from these sources will consist of the characteristic peak superimposed on a background of Bremsstrahlung radiation that extends to the incident energy of 15 keV together with subsidiary characteristic peaks which can also excite photoelectrons and produce peaks on the
Figure 5.63. Schematic diagram of a dual anode X-ray source (Yates et al (1973)) (reproduced with permission of the Institute of Physics).
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Table 5.8. Energies and widths of some characteristic soft X-ray lines. Line
Energy (eV)
Width (eV)
Y M Zr M Nb M Mo M Ti L Cr L Ni L Cu L Mg K Al K Si K Y L Zr L Ti K Cr K Cu K
132.3 151.4 171.4 192.3 395.3 572.8 851.5 929.7 1253.6 1486.6 1739.5 1922.6 2042.2 4510.0 5417.0 8048.0
0.47 0.77 1.21 1.53 3.00 3.00 2.50 3.80 0.70 0.85 1.00 1.50 1.70 2.00 2.10 2.60
XPS spectrum. Most commercially available XPS instruments are fitted with a dual anode coated with a layer of aluminium and magnesium approximately 10 mm thick giving a choice of the K peaks from these elements at 1486.6 and 1253.6 eV respectively. However, it is possible to use a wide range of elements to produce X-ray photons. These are listed in table 5.8 together with the energy of the characteristic radiation and the width, at half the full height, of the beam. The large Bremsstrahlung background radiation produces photoelectrons and increases the background on the XPS spectrum while the subsidiary characteristic X-ray peaks produce unwanted peaks on the spectrum. These subsidiary peaks are removed and the background reduced by using a monochromator (Kelly and Tyler (1972)) such as a quartz single crystal with the conditions arranged such that only the main characteristic X-ray peak satisfies the Bragg condition for diffraction. Normally aluminium monochromatic X-rays sources are commercially available on XPS instruments (figure 5.64). It is arranged that the anode, the quartz crystals and the specimen satisfy the condition that they all lie on the Rowland sphere so that these X-rays that satisfy the Bragg diffraction condition are focused on to the specimen. To produce X-ray beams with a narrow energy spread it is necessary to focus the bombarding electron beam into a small area. For a Rowland sphere of 0.5 m the dispersion is 1.6 mm/eV and to obtain a beam with a line width of 0.5 eV requires the electron beam be focused into less than 0.8 mm. If larger Rowland spheres
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Figure 5.64. A schematic diagram showing the design requirements for an X-ray monochromator source on a photoelectron spectrometer.
are used, the line width decreases as the radius increases for electron beams of constant width. To increase the X-ray flux it is necessary to increase the incident electron beam current on to the anode and usually the maximum power that can be dissipated is approximately 1 kW. To increase this power, rotating anodes are used such as that built by Scienta (Gelius et al (1990)) where the anode is a rotating disc of copper coated with aluminium. Here considerable problems have to be overcome, particularly with regard to providing water cooling to the rotating anode while maintaining the required vacuum. When a charged particle is accelerated it emits radiation and this principle is used in the synchrotron where electrons are accelerated to high energies and constrained to follow a circular path. The emitted radiation is tapped at specific points around the circumference (Farge and Juke (1979)). The intensity maximum of the emitted electromagnetic radiation is proportional to the radius of curvature and inversely proportional to the cube of the electron energy. At energies close to relativistic velocities the radiation is restricted to a narrow cone which is tangential to the electron orbit. To select the desired energy this cone of radiation is then passed into a monochromator. In theory a continuously variable range of X-ray energies from a few tens of eV to several keV should be achievable but this is not as yet possible because of the difficulties of design and construction within the constraints of an ultra-high vacuum system (see chapter 3). However, the monochromators are essentially continuously tuneable up to about 500 eV with specific energies available above this value. This type of source has the additional advantage that the intensity of the X-ray flux is typically
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Figure 5.65. Transmission of electrons through a concentric hemispherical analyser.
two orders of magnitude greater than from a conventional aluminium K Xray source. Unfortunately synchrotrons are massive structures, with a radius of curvature many tens of metres, and consequently are extremely expensive to construct. As a result few exist worldwide and it is necessary to take the experiment to the synchrotron, which is a less practical approach. Detector The photoelectrons ejected from the specimen surface are focused on to the entrance slit of a concentric hemispherical analyser (figure 5.65). A negative potential is applied to the outer cylinder and a positive potential to the inner cylinder such that in ideal circumstances the central line between the two cylinders is the line of zero potential. Electrons enter the analyser over a range of angles, , governed by the width of the entrance slit, the distance of this slit from the specimen and the focusing arrangement employed to extract photoelectrons. The energy resolution, E, of this analyser is given by d 2 E ð5:24Þ þ E ¼ 4 2R0 where E is the energy of the incident X-rays, R0 is the radius and d is the width of the slit. To increase sensitivity must be as large as possible but this degrades the energy resolution, E. A compromise is normally reached and it is arranged that 2 d=2R0 , and then equation (5.24) becomes d E ¼ 0:63 E: ð5:25Þ R0 In this case the energy resolution increases linearly with decreasing slit width, d. Hemispherical analysers of this type operate in two modes, one known as fixed retard ratio (FRR) the other as fixed analyser transmission (FAT). In the constant retard ratio mode the electrons are all retarded by a constant
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Figure 5.66. Spectrum collected using multiple channel plates (courtesy Thermo VG Scientific).
fraction prior to entering the analyser and as a result the energy resolution will be dependent on the electron energy. However, in the constant analyser transmission mode the electrons are retarded such that they enter the analyser at the same energy and as a result the resolution is constant over the entire spectrum. The speed of collection can be increased by adding additional detectors at the exit slit, thus allowing parallel signal collection. It is clearly not possible to position two detectors at the same location and as a result each detector collects electrons of a different energy. Use of multiple detectors can allow a complete spectrum to be collected and over 100 detectors have been used in this way. Figure 5.66 shows a spectrum collected for the narrow energy range of 90 to 110 eV using multiple detectors. Spatial resolution A major disadvantage of XPS is that it lacks a high spatial resolution. This was particularly true for the early spectrometers which illuminated areas of the specimen over several millimetres, and it was not possible to obtain any spatial discrimination. There has been considerable improvement in the spatial resolution although these instruments still have some way to go before they can be generally applied to the microstructural characterisation
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Figure 5.67. An X-ray photoelectron spectrum linescan using a small spot X-ray source (Coxon et al (1990)).
of materials. Two approaches have been used to obtain improved spatial information. In one case a small spot is rastered over the specimen, by moving the specimen, and the other uses a photoelectron spectrometer in a manner analogous to a light microscope. In each of these instruments the incident X-ray beam is collimated to a diameter on the specimen of between 20 and 200 mm. This approach is possible because although collimating the beam considerably reduces the photon flux the detection systems have been significantly improved and good spectra can be obtained. Figure 5.67 shows a linescan obtained from a stainless steel specimen using a small spot X-ray source. The second approach to this problem is to use the electrostatic energy analyser as a lens (Coxon et al (1990) and Adem et al (1990)) and to focus the electrons which leave a point on the specimen surface to an equivalent point on the exit focal plane. By selecting photoelectrons of a given energy, using the energy analyser, an image of the specimen is obtained from that photon energy and this can provide an elemental and a chemical state map of the surface. This instrument, shown schematically in figure 5.68, is capable of a routine spatial resolution of 3 mm. Figure 5.69 shows two images obtained from a a semiconductor device. In each case the silicon 2p peak has been imaged but in figure 5.69(a) the peak from elemental silicon is imaged while in figure 5.69(b) the peak from silicon in the oxidised state is reproduced. 5.10.3
Chemical analysis
Since electrons are detected over the energy range 0 to 1000 eV which have mean free path lengths of the order of 1 nm those escaping from the specimen surface originate from the top few atom layers. An XPS spectrum of counts
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Figure 5.68. A schematic diagram of the imaging X-ray photoelectron spectrometer (courtesy Thermo VG Scientific).
versus binding energy recorded from a steel surface using both Al K and Mg K radiation is shown in figure 5.70. The computer software in the data acquisition system is usually set to provide either kinetic energy or binding energy; the latter parameter makes elemental identification easier.
Figure 5.69. Images recorded using the imaging X-ray photoelectron spectrometer from a semiconductor device in which the silicon 2p peak has been imaged (a) for elemental silicon and (b) for silicon in the oxidised state (courtesy Thermo VG Scientific).
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Figure 5.70. X-ray photoelectron spectra recorded from steel using (a) Al K and (b) Mg K radiation. Note that the photoelectron peaks shift 233 eV (the difference in energy between the Al and Mg characteristic peaks) while the Auger peaks remain at constant kinetic energy.
The convention in XPS is to use the chemical notation describing the electron binding energy level to label the peaks. The quantum numbers, X-ray shell designation and spectroscopic level are given in table 5.9 for n ¼ 1 to 3. Thus iron, the major element of the steel, produces 2p photoelectron peaks while surface contaminants such as oxygen and carbon are identified by the 1s peaks. In addition there are peaks present resulting from Auger transitions following ionisation (see chapter 6). Since these peaks are superimposed on a steadily rising background, the presence of a major peak causes the background to rise over the width of the peak. Also some of the electrons Table 5.9. X-ray and spectroscopic notations. Quantum numbers n
l
j
X-ray suffix
X-ray level
Spectroscopic level
1 2 2 2 3 3 3 3 3
0 0 1 1 0 1 1 2 2
1/2 1/2 1/2 3/2 1/2 1/2 3/2 3/2 3/2
1 1 2 3 1 2 3 4 5
K L1 L2 L3 M1 M2 M3 M4 M5
1s1=2 2s1=2 2p1=2 2p3=2 3s1=2 3p1=2 3p3=2 3d3=2 3d5/2
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lose energy on passing through the matrix, particularly those ejected from depths several mean free path lengths below the surface. As a result the background intensity increases to the low kinetic energy side of a peak, causing the background to rise. Interpretation of spectra requires Auger peaks be specified before the binding energy data are used to identify the photoelectron peaks. This is not a trivial task but the problem is reduced if the spectrometer is equipped with a dual X-ray source. The energy of a photoelectron peak depends upon both the photon energy and the binding energy of the electron in the atom and, therefore, the kinetic energy of a photoelectron will change with incident photon energy. However, the kinetic energy of an Auger electron is determined by the binding energies of those electron shells involved in the Auger process and these remain unchanged when the photon energy is changed. Thus by recording two spectra, each using a different photon source energy, the Auger peaks are identified since they remain at a fixed kinetic energy while the photoelectron peaks shift. Figure 5.70 shows two spectra recorded from steel using Al K and Mg K sources; the iron Auger peaks remain at 700, 650 and 600 eV kinetic energy in both spectra while the photoelectron peaks move 233 eV. A major strength of XPS is the ability to identify chemical state changes that occur at a surface when two or more atoms combine. When two atoms combine to form a compound, electron transfer occurs between the atoms, one becoming more negative the other more positive. This has the effect of changing the electron binding energies of the electrons by a small amount, usually between a fraction of a volt and a few eV. From changes in peak position, therefore, the chemical state of the atoms can be determined in the XPS spectra. Figure 5.71 shows narrow scan spectra from iron during oxidation (Allen et al (1982)) where the iron 2p3=2 peak from clean metal appears at 706.9 eV, but on absorbing oxygen at a temperature of 600 K a broad peak appears in the region of 710 eV. As the oxygen exposure is increased this broad peak narrows and shifts to 711.0 eV. The broad peak is in fact a doublet resulting from two photoelectron peaks which can be deconvoluted to peaks at 709.3 eV and 711.0 eV (figure 5.71(b)). Iron can form oxides of magnetite (Fe3 O4 ) and haematite (Fe2 O3 ) when exposed to oxygen. In this oxidation sequence the Fe3 O4 forms initially where the iron atoms exist in both the 2þ and 3þ states and as a result two peaks are detected resulting from the binding energy changes in each state. However, Fe2 O3 only contains iron atoms in the 3þ state and therefore one peak is observed at the higher binding energy. 5.10.4
Additional structure in XPS spectra
When the atom is ionised a change occurs in the nuclear screening which leads to a rearrangement of atomic states or relaxation. The energy associated with
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Figure 5.71. Narrow scan X-ray photoelectron spectra from the Fe 2p peak during exposure to oxygen at 600 K together with deconvolution of the major peak in spectrum F (Allen et al (1982)) (reproduced with permission of Taylor and Francis Ltd).
this relaxation may excite a valence electron to an empty higher level and this is referred to as a ‘shake up’ process. The energy may come from the outgoing photoelectron which would then suffer a loss in energy and appear as a peak at a lower kinetic energy. The occurrence of shake up peaks is determined by the chemical state of the atom and is more likely for metals in the oxidised rather than the neutral state. In addition to the changes in peak position, the photoelectron peak may have fine structure associated with it known as multiplet splitting. This occurs when valence or core electrons shells contain unpaired electrons. The spin and angular momenta can then combine to give different energy states which result in an additional structure known as multiplet splitting. Often the fine structure peaks are too close to be resolved using conventional spectrometers although a monochromator will improve the resolution. 5.10.5
The Auger parameter
Bombarding a surface with photons and ejecting electrons causes the surface to become positively charged. This will cause the photoelectron peaks to move to a lower kinetic energy, which could result in an erroneous chemical state identification. There are many practical ways to reduce or eliminate surface charging. Either an electron flood gun is used to fire a wide beam of low energy electrons on to the surface to neutralise the charge, or a monolayer of conducting material, such as gold, is deposited on to the surface to provide paths for charge leakage. These methods are not always satisfactory
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for many insulating materials. It is, however, possible to utilise the difference in the change in the energy of an Auger peak and equivalent photoelectron peak to determine the chemical state and this is independent of charging. The difference between the Auger and photoelectron chemical shifts result from the difference in final-state relaxation energies between the chemical states (Briggs and Seah (1990)). A parameter, the Auger parameter A can be defined such that (Wagner (1975) A ¼ EAuger Ephotoelectron :
ð5:26Þ
In practical terms this is the difference between the most intense Auger transition and the most intense photoelectron peak. A can have negative values and to overcome the problem. Wagner et al (1979a)) defined a ‘modified’ Auger parameter, , where ðkineticÞ
A ¼ A þ h ¼ EAuger 5.10.6
ðbinding energyÞ
þ Ephotoelectron :
ð5:27Þ
Depth profiling
Thin Layers Angle-resolved XPS (Fadley et al (1974) and Cumpson (1995, 1999)) can provide information on the depth distribution of different atomic species in the top few monolayers of a specimen. Electrons of a given energy have a known mean free path in a solid and when travelling normal to the surface can escape from greater depths than those electrons travelling at a glancing angle to the surface. By collecting spectra from a series of known angles to the surface normal the variation in intensity of a peak can be determined as a function of angle. From this information the distribution of elements with depth in the specimen can be obtained. The best theoretical depth resolution, Z, that achieved at a depth Z is given by Cumpson (1999) Z ¼ 2Z sinhfð2 Þ=2 cosh1 ½ðn 1ÞðI=1 Þ2 g
ð5:28Þ
where (I =I) is the fractional precision of the peak intensities and n is the number of emission angles. It is possible to use the multichannel plate detector, now commonplace in hemispherical analysers, to obtain simultaneously a series of spectra at different angles (figure 5.72). The photoelectrons ejected from the surface are focused on to the entrance of the analyser and the multichannel plates located in the x-direction record electrons over a range of energy from a given angle, while channels located in the y-direction detect electrons of a given energy again for a range of angles. Figure 5.73 shows the detection of layers of oxide and nitride on silicon. Here parallel detection of the silicon 2p peak has been acquired over a range of angles from 308 to 808 and binding energies from 95 to 110 eV (figure 5.73(a)). These data have been
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Figure 5.72. Schematic diagram showing how a hemispherical analyser with a multichannel detector can be used to simultaneously obtain spectra over a range of photoelectron escape angles.
used to determine the thickness and position of layers to a depth of 15 nm from the surface of four different specimens (figure 5.73(b)). Thick layers It is possible to obtain elemental information as a function of depth into the surface with XPS instruments by bombarding the specimen surface with argon ions to remove atom layers sequentially and obtaining the corresponding XPS spectra. From the rate of removal of atom layers a distribution of elements with depth into the specimen body can be obtained. This technique has the drawback that the area that needs to be profiled must be several millimetres square, which is much larger than with Auger spectroscopy (see chapter 6), and as a result profiling rates are slow. In addition, ion bombardment may alter the chemical state of the surface and the advantage that XPS may provide chemical state identification may be lost. Figure 5.74 shows an elemental profile with depth obtained from the oxide formed on a specimen of 20%Cr–25%Ni–Nb stabilised stainless steel following oxidation for 1 h at 1123 K (Tempest and Wild (1985)). The oxide is duplex, the outer layer is a spinel of the type MnCr2 O4 rich in chromium and manganese but with an inner layer of rhombohedral oxide Cr2 O3 rich only in chromium. 5.10.7
Quantification
The most important factor in determining the intensity of a particular elemental peak in an XPS spectrum is the ionisation cross-section for the particular electron shell together with the electron escape depth, the angle of
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Figure 5.73. XPS spectra from the silicon 2p peak acquired over a range of angles from 30 to 808 and binding energies from 95 to 110 eV (a), which has been used to determine the thickness and position of layers to a depth of 15 nm on four different samples (b) (courtesy Thermo VG Scientific).
emission and matrix effects. The simplest case to quantify is a homogeneous mixture, where the concentration of element A (XA ) in B (XB ) is given by 1 X I =I XA ¼ FAB A A1 XB IB =IB
ð5:29Þ
where IA and IA1 are the signals from element A in the specimen and a pure standard respectively, IB and IB1 are the corresponding signals from element X is the matrix factor (Seah (1980a)). Values for IA1 and IB1 can be B and FAB
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Figure 5.74. An X-ray photoelectron spectrum depth profile through an oxide formed on 20%Cr–25%Ni–Nb stabilised steel exposed for 1 h at 1123 K to CO2 (Tempest and Wild (1985)) (reproduced with permission of Plenum Press).
obtained from measurements using pure element standards in the instrument or from published data (Wagner et al (1979b and 1981) and Evans et al 1978)). To achieve a quantitative measure using equation (5.29) it is necessary to determine the area under the specific peak which is complicated by the fact it is superimposed on a rising background; it is necessary to remove the background before the peak area can be measured. Many software packages simply draw a straight line between the two sides of the peak but this can lead to errors, particularly at positions where several peaks overlap. A more accurate method developed by Shirley (1972) applies a nonlinear correction that assumes the background at a point is proportional to the total peak intensity above the background. Other more sophisticated approaches have been proposed (Tougard (1988)). Quantification becomes more complicated for the situation where one has a thin overlayer of element A on element B but Seah (1979, 1980b) considers the signal from the substrate to be attenuated by A in a treatment of this problem. 5.10.8
Applications
Generally XPS is much less damaging than either Auger spectroscopy or SIMS and SNMS, because it bombards the surface with photons, and this technique is therefore preferred for the study of materials that are easily
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degraded such as polymers. However, the poor spatial resolution limits the analysis to large flat uniform specimens. Polymers Briggs (1983) has described the application of the technique to study polymer surfaces. XPS has been used to study many polymer systems and a considerable volume of data exists concerning the position of the carbon 1 s peak in the different environments. For the carbon atom the difference in the core binding energy is closely related to the difference in thermochemical energies. Jolly (1972) has plotted the relative C 1s binding energies versus the thermodynamically estimated values for a series of gaseous compounds (figure 5.75). It is possible to use this measured C 1s binding energy to determine the bonding of carbon to other atoms; similar approaches have been adopted to study the bonding of other elements contained in polymers such as fluorine and sulphur. Corrosion XPS is used to study the reaction of corrosive environments with metal and alloy surfaces (McIntyre (1983)) where emphasis is on understanding the bonding of the atoms with the surface. For a clean surface of nickel exposed to oxygen (Allen et al (1979)) the spectra show the oxygen 1 s peak recorded
Figure 5.75. Plot of the carbon 1s binding energies versus thermodynamically estimated energies (Jolly (1972)) (reproduced with permission of North-Holland Publishing Company).
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Figure 5.76. The oxygen 1s peak on nickel substrate as a function of time exposed to oxygen. (1) Non-dissociative adsorption of oxygen. (2) Oxygen begins to dissociate and form chemical bonds with Ni atoms. This stage is complete when there exists a monolayer of oxygen atoms in chemical combination with Ni. Non-dissociative adsorption of oxygen continues. (3) Diffusion of oxygen and nickel atoms to form NiO; at room temperature this is slow but at 500K a small percentage of NiO forms in 30 min while at 550 K several monolayers form in this period (Allen et al (1979)) (reproduced with permission of Plenum Press).
from the nickel surface as a function of exposure time (figure 5.76), together with the proposed surface atomic arrangement. At very low exposures the oxygen 1 s peak position is close to 531.6 eV and can be assigned to undissociated oxygen. As the exposure continues a new peak from dissociated oxygen bound to the nickel appears at the lower binding energy of 529.9 eV. Gradually the nickel atoms exchange position with the dissociated oxygen, a slow process at room temperature since the rate of exchange is governed by the jump frequency. However, at higher temperatures this process is accelerated and the O 1 s peak shifts to a slightly higher binding energy representative
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of NiO. By determining the temperature at which this occurs it is possible to estimate the activation energy for self diffusion in nickel.
5.11
Autoradiography
Autoradiography is used to describe any technique that demonstrates the macroscopic or microscopic location of a radioactive source in a specimen (Priestley (1992)). The macroscopic location is usually achieved by applying a film, such as X-ray film, to the section of the specimen that contains the radioactive source and after a defined period the film is developed to reveal the distribution of radioactivity. Detection of microscopic locations requires a procedure with a higher spatial resolution and this can be achieved by using a nuclear emission detector rather than a film, although, depending upon the size and distribution of the feature, in many cases the latter are still used (Rogers (1979)). The autoradiographic technique is direct and has been applied with success to a range of metallic and ceramic systems. For example, or emissions from the segregated species, have been used to identify the concentration at grain boundaries or within second phase precipitates. For example, in a range of systems including polonium in a Pb–Bi alloy, tin in a-iron, silver in Cu and Sn, nickel in Al2 O3 , titanium in Sn, phosphorus in a-iron and boron in Type 316 stainless steel (Thomas and Chalmers (1955), Thomas and Winegard (1952), Tiller and Winegard (1955), Ainsle et al (1960), Coulomb et al (1959), Miller et al (1960), Jorgenson and Westbrook (1964), Weinberg (1963), Yukawa and Sinnot (1955) and Harris and Marwick (1980)). The optical autoradiographs in figure 5.77 show the distribution of boron in Type 316 austenitic stainless steel specimens which contain 3 and 90 ppm of boron in the bulk respectively and following heating to a temperature of 1323 K and air cooling (Wild (1980)). This reveals non-equilibrium segregation of boron to the grain boundaries. To detect these segregations using this technique, theoretical considerations show that the concentration of the radioactive tracer element at the grain boundary must be between 102 and 103 greater than the concentration in the parent grain (Joshi (1979) and Weinberg (1963)) and the wavelength emitted should be long. The visibility of segregation is a function also of the penetration depth of the emitted radiation. Hence the sensitivity for detection of a particular atom species at a grain boundary is related to both the concentration and the range of emitted radiation. Since the radioactive emissions are a function of the concentration it is possible to quantify the amount of segregation using either microdensitometer measurements from the film or digitised images for use with quantitative image analysis procedures (Seger et al (1992) and Flewitt and Wild (2001)). As a consequence this technique has the advantages of quantification of composition,
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Figure 5.77. Autoradiographs of boron in Type 316 steel specimens with (a) 3 ppm and (b) 90 ppm of bulk boron and following heating to a temperature of 1323 K and air cooling (Wild (1980)).
but, more importantly, provides the ability to examine the distribution of a particular atom species within the overall microstructure. An example of how autoradiography can be used to detect elements present in materials in very low concentrations is given by Jones et al (2002). Figure 5.78 shows boron autoradiographs recorded from specimens of polished steel plate with a bulk boron content of only 40 ppm. The material is a Si–killed C–Mn steel which was manufactured by hot rolling and normalised at a temperature in the range 1213 to 1233 K, stress relieved at 873 K for 9 h and slow cooled at 5 K/h. In this example the boron has preferentially segregated to particles within the bulk and not to the grain boundary regions as in the previous example. The observation that the boron has not segregated to the grain boundaries has important implications for the mechanical behaviour of this steel when in service.
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Figure 5.78. Boron autoradiographs recorded from specimens of polished C–Mn steel plate with a bulk boron content of only 40 ppm.
5.12
Mo¨ssbauer spectroscopy
This technique, discovered by Mo¨ssbauer in 1958 for which he received the Nobel prize for physics, involves the emission and adsorption of rays to determine the chemical state of atoms in a lattice (Mo¨ssbauer (1964), Frauenfelder (1963), Greenwood and Gibb (1981) and Tricker (1977)). It is primarily
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used to study iron-containing materials but not exclusively since the effect has been observed associated with over 40 other elements. The nucleus of a radioactive isotope is in an unstable state and decays with the emission of and particles, neutrons and -rays; Mo¨ssbauer spectroscopy makes use of the emitted -rays. If the -ray is incident on an absorber of the same element and isotope as the emitter but with the atom in the ground state, then the -ray is absorbed and the atom raised to an excited level. When the -ray is emitted the decaying atom should recoil and there should also be a recoil in the absorbing nucleus as it absorbs the -ray. However, the photon energy is less than the difference in energy levels in the atom by an amount E02 =2Mc, where E02 is the energy of the nuclear transition, M is the mass of the nucleus and c is the velocity of light. Thus the emission and absorption is recoiless. For the 57 Fe isotope of iron the recoil energy is greater than the photon energy spread of approximately 108 eV and as a result the photon incident on the absorber will not excite the nucleus. Mo¨ssbauer realised that for the effect to occur both the emitting and absorbing atoms must be bound in a lattice where the lowest vibrational excitation energy is greater than the nuclear recoil energy. In such a situation the atom is unable to recoil and the -ray may be emitted and absorbed without loss of energy. This requires the atom to be fixed in a solid crystal lattice at a temperature below a certain minimum, the Debye characteristic temperature. Even when the recoil effects have been overcome the -ray will not be absorbed if the absorbing atom does not have the same energy gap, between the ground and the excited state, as the emitting atom. This situation will occur when the absorbing atom is chemically bound to other elements, which produces small shifts in the energy levels. Hence to make use of the Mo¨ssbauer effect the Doppler effect is employed where the wavelength of radiation either increases or decreases when the source or detector are accelerated towards or away from the radiation. By oscillating the source in the direction of the observer the energy of the -ray will be changed. The speed of the oscillations determines the energy spread and in this way the -ray photon energies can be tuned to cover the desired range. Iron, in particular the 57 Fe isotope, is ideally suited for study by Mo¨ssbauer spectroscopy since it has a Debye temperature of 473 K and the spectra can be observed at and below room temperature. There also exists a 57 Co source which decays to 57 Fe, which in turn decays with the successive emissions of 123 keV -rays and 14.4 keV -rays. The latter is used in the Mo¨ssbauer study of iron. 5.12.1
Experimental arrangement
The experimental requirements for Mo¨ssbauer spectroscopy are shown in figure 5.79. The cobalt source normally alloyed with a non-magnetic
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Figure 5.79. Schematic diagram of a transmission Mo¨ssbauer spectrometer.
rhodium matrix is placed on the end of an oscillating plunger and the -rays are arranged to pass through the specimen which is in the form of either a thin foil or a powder. The -rays are counted by number in narrow energy channels. A complete oscillation of the plunger constitutes a spectrum with the point at which the plunger is stationary with respect to the specimen giving the natural transition energy. The plunger velocity, Doppler velocity, E , can be converted to an energy scale by use of the equation Ev ¼ E ð1 =cÞ
ð5:30Þ
where Ev is the energy at velocity v and c is the velocity of light. Typical Mo¨ssbauer spectra for some commonly encountered ironcontaining materials are shown in figure 5.80. Some of these spectra are more complicated than others, for example that from stainless steel (figure 5.80(a)) contains a single peak whereas that from Fe3 O4 contains at least ten. This is the result of splitting of various electron energy levels that occurs within the atom which can be interpreted by reference to the electron energy levels shown in figure 5.81. If interactions within the atom are only electrostatic then one peak is observed corresponding to the absorption of the -ray in raising the atom from the 12 to the 32 level. The peak may not be exactly at zero on the spectrum energy scale (i.e. the position at which the energy of the emitted -ray equals the energy of the absorbed ray) because the electron orbitals can penetrate to the nucleus and the interaction of the negative charge with the positive nuclear charge causes the nuclear energy levels to shift causing the -ray energy to shift. This is known as
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Figure 5.80. Mo¨ssbauer spectra of counts with velocity from some iron-containing materials.
the isomer shift and is shown as in figure 5.81. A nucleus with a spin greater than 12 will have an electric quadrupole moment which will interact with an electric field gradient. The field gradient can be caused by nonuniform distributions of electrons within the atom or by non-symmetric distribution of atoms bound to the 57 Fe atom. This causes the 32 level in
Figure 5.81. Changes in nuclear energy levels caused by quadrupole and magnetic splitting together with the resulting Mo¨ssbauer spectra.
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iron to split into two with the result that two absorption levels are available and the single peak splits into two components. A magnetic field can produce further splits of the nuclear levels where each of the levels produced by quadrupole splitting can be further split into two new levels and the level with the nuclear spin state of 12 is also split into two. The result of this is to produce six lines and the magnitude of the magnetic field determines the extent of the split and hence separation of the absorption lines. The magnetic field may either result from internal arrangements of electrons or be applied externally. In figure 5.80 the spectrum (a) from 304 stainless steel shows the single degenerate peak, spectrum (b) is an example of quadrupole splitting while spectra (c) and (d) are examples of magnetic hyperfine splits with significantly different magnitudes. The final spectrum (e) from Fe3 O4 is an example of iron being in two different sites in the lattice each subjected to magnetic hyperfine splitting. 5.12.2
Conversion-electron Mo¨ssbauer spectroscopy
The method for detecting Mo¨ssbauer absorption described above requires that the -rays pass through the specimen to the detector. This imposes a constraint on the type of specimen that can be examined. While in principle it is possible to study thick specimens by detecting the re-emitted -ray, when the excited atom decays the process is very inefficient and there are other ways of determining the absorption. When the atom which has absorbed the 14.4 keV -ray decays it does so by re-emitting a similar ray. Only about 10% of these -rays escape the atom, the remainder may either eject a K-shell electron which will be emitted with an energy of 7.3 keV, creating a vacancy in the K-shell which may be filled by an electron from the L-shell and the emission of an X-ray of 6.5 keV, or alternatively the decay process may result in the ejection of a 5.6 keV Auger electrons (see section on Auger spectroscopy for more detailed description). In fact for every ten 14.4 keV -rays produced, ninety 7.3 keV electrons, sixtythree 5.6 keV Auger electrons and twenty-seven 6.4 keV X-ray photons are produced. The electrons and photons can be detected in a system shown schematically in figure 5.82 where the specimen is placed inside a proportional gas counter filled with helium or argon. The -rays enter the chamber through a thin aluminium window and impinge on the specimen. The electrons and X-rays ionise the gas, resulting in a current that is proportional to the energy of the ionising electron or photon and is collected on the anode. This method of detecting Mo¨ssbauer absorption is ideally suited to the study of large specimens, although the mean free path of the electrons allows only the top 500 nm of material to be studied so that the technique is well suited for examining thin surface layers on bulk specimens.
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Applications
Iron–chromium–nickel steels can form with either an austenitic (face centred cubic) or ferritic (body centred cubic) structure each having characteristic mechanical properties. The austenite phase is stabilised by nickel, carbon and manganese and the loss of these elements from the bulk can cause the material to transform from austenite to ferrite. Mo¨ssbauer spectroscopy can be used to detect the change from austenite to ferrite in the alloy. Figure 5.83 shows Mo¨ssbauer spectra obtained from Types 304 and EN58E stainless steels (Fisher et al (1975)) where for the former there are no peaks from the ferritic phase while the EN58E steel shows about 15% ferrite content. When exposed to flowing sodium certain elements leach from these steels. As a consequence the type 304 stainless steel remains unchanged after 85 days’ exposure but the ferrite content of the EN58E steel increases progressively with time of exposure to 78% ferrite (b) after a similar period. The exposure of iron to ammonia provides another good example of the ability of Mo¨ssbauer spectroscopy to identify transformation products, in this case the various iron–nitrogen phases (Bainbridge et al (1973)). Three nitrogen rich phases exist in iron, 0 -Fe4 N, "-Fex N and -Fe2 N. In the 0 Fe4 N phase there are two iron sites: those at the corner positions with the nitrogen atoms on the body diagonal (FeI sites) and those occupying the fcc positions with the nitrogen atoms lying in a direction perpendicular to the cube face (FeII sites). The orientation of the electric field gradient relative to the magnetisation direction divides the FeII sites into two categories, FeIIA and FeIIB . The resulting Mo¨ssbauer spectrum consists of three magnetic sextets with intensity ratios FeI :FeIIA :FeIIB : : 1 : 2 : 1. In the " phase the
Figure 5.82. Schematic diagram showing principles and practice of conversion-electron Mo¨ssbauer spectroscopy.
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Figure 5.83. Mo¨ssbauer spectra from stainless steel while exposed to liquid sodium.
nitrogen atoms are ordered on interstitial sites between the {002} planes of the hexagonal close packed iron lattice -Fe2 N contains eight iron and four nitrogen atoms in the unit cell arranged such that the iron atoms are positioned in two face centred orthorhombic units at 0 0 0, 14 12 0, 34 12 0, 12 0 0, 0 13 12, 14 56 12, 34 56 12, 12 13 12. The nitrogen atoms are at 14 16 14, 34 16 34, 0 23 34, 12 23 14. Included in figure 5.84 are Mo¨ssbauer spectra recorded from iron foils at a temperature
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Figure 5.84. Mo¨ssbauer spectra from iron while exposed to ammonia at 760 K (Bainbridge et al (1973)) (reproduced with permission of Pergamon Press).
of 760 K as a function of time exposed to ammonia. At low exposures the Mo¨ssbauer spectrum is essentially -Fe but the weak additional lines indicate the presence of "-Fex N. As the exposure time increases so the phases 0 -Fe4 N and "-Fex N become more intense until after 5 h -iron is barely detectable. At this stage -Fe2 N starts to dominate and after 50 h the -Fe2 N is the only phase detected.
5.13 Nuclear magnetic resonance Nuclear magnetic resonance (NMR) is a method that considers molecular properties by interrogation atomic nuclei with magnetic fields and radio frequency irradiation. The phenomenon arises from the resonant interaction
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Figure 5.85. The principle of NMR imaging. (a) The magnetic field varies linearly across the sample by application of a field gradient Gx in the x-direction. (b) Sample shapes in the two-dimensional xy plane. (c) The spectrum acquired in the presence of a magnetic field gradient provides a projection of the sample.
of magnetic moments in a time-invariant magnetic field with the magnetic component of an electromagnetic wave (Abragan (1961) and Blumich (2000)). The frequency wL of the atomic nuclear response, the Larmor frequency, is related to the strength of the magnetic field, jB1 j, at the site of the nucleus by wL ¼ jB1 j ¼ B1
ð5:31Þ
where is the gyromagnetic ratio. Nuclear magnetic resonance is widely used in the biological and medical fields as a non-invasive analytical technique that produces images of arbitrarily oriented slices through optically opaque objects. Such imaging is a form of multi-dimensional spectroscopy where the frequency axes convert to space axes by the application of inhomogeneous magnetic fields in the form of space invariant or constant gradient fields (figure 5.85). In isotopic fluids the applied field is shielded from the nucleus by the magnetic fields arising from electrons moving around the nucleus so that B1 ¼ ð1 ÞB0
ð5:32Þ
where is the degree of magnetic shielding determined by the binding of electrons between atoms in a molecule. In a space-dependent magnetic field the Larmor frequency depends upon position so that a variation along the x co-ordinate in figure 5.85 is given by a Taylor series @BZ 1 @ 2 BZ þ xþ x2 þ : ð5:33Þ BZðXÞ ¼ B 2 @x2 x ¼ 0 x¼0 @x x ¼ 0
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Figure 5.86. 1 H-NMR images of a bisque-fired alumina ceramic impregnated by benzene. The L/D ratio is 1.13 and the mean particle size is 0.4 mm. The three slices correspond to positions at (a) 6.1, (b) 12.4 and (c) 14.8 mm from the reference plane. Various defects with diameters ranging from 0.7 to 0.4 mm can be detected by decreased signal intensities from lowered porosities (Ackerman et al (1987)).
The second- and higher-order terms in this expression are negligibly small. In imaging experiments the space variation of the external field has to be sufficiently large to override the spread in the line width and thus can be given approximately by combining equations (5.31), (5.32) and (5.33) 1 @ 2 BZ 2 xþ x þ ð5:34Þ wL ¼ ð1 Þw0 Gx x¼0 2 @x2 x ¼ 0 where w0 is the normal magnetic resonance frequency in angular units and Gx is the field gradient. In figure 5.85 the total signal intensity is proportional to the number of nuclei with a given resonance frequency and is obtained by integration of the specimen magnetisation along the y and z coordinates and projection of the signal onto the x axis. Thus an image can be constructed. For a linear dependence of the Larmor frequency the spatial resolution is 1/x is given by Gx 1 ð5:35Þ ¼ jxj 2 0 where 0 ¼ wL =2. Soft tissue and elastomers have narrow lines at frequencies in the range 3–10 Hz to give a spatial resolution in the range 100–10 mm. However, for rigid solids such as glassy polymers, imaging is less readily achieved. To increase the spatial resolution requires the gradient strength to be increased but there is a reduction in the signal-to-noise ratio and thereby sensitivity (Mehring (1983) and Slichter (1989)). The porosity of a ceramic can be evaluated by magnetic resonance imaging when a contrast medium such as a liquid or gas is incorporated into the body. Figure 5.86 shows images of fired Al2 O3 that have been vacuum impregnated with benzene doped with paramagnetic chromium salts. This reveals the presence of pores of sizes in the range 0.7–4 mm diameter (Ackerman et al (1999)). By comparison Figure 5.87 shows the stress distribution obtained in a strained polydimethyl siloxane strip containing a sharp feature (Blumich and Blumich (1993)). Here the local strain is mapped using transverse relaxation time T2 and calibration of T2 with strain. Since the stress–strain
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Figure 5.87. Stress image of a stretched polydimethyl siloxane band with a cut (right). A heterogeneous stress distribution is observed which results from the cut as well as from filler inhomogeneities. The grey scale indicates local stress in the range from 0 to 2.4 MPa.
relationship for the material is known from mechanical testing, T2 can be also calibrated with stress. Here the T2 time becomes shorter as the segmental motion in this elastomer network becomes more anisotropic as it is stretched locally up to about 20%. Here the average measured stress is 1.5 MPa.
5.14
Total reflection X-ray fluorescence spectroscopy
This technique is primarily used to detect low levels of contamination on silicon and gallium arsenide wafers for semiconductor applications. It operates on the principle that X-rays which impinge on a silicon surface at a glancing angle are totally reflected since the refractive index for X-rays on silicon is less than one (see section 4.2). The reflected X-rays cause contamination atoms and particles present on the silicon surface to emit fluorescence X-rays at energies characteristic of the contamination atoms. Total reflection of the incident X-rays on the specimen reduces the intensity of the scattered X-rays. This allows greater intensity of fluorescence X-rays to be excited from the surface of the wafer. This results in a spectrum with large signal-to-noise and signal-to-background ratios. The technique has been described in detail by Boston et al (1992), Berneike et al (1989) and Mori et al (1995). A schematic of the experimental arrangement for total reflection X-ray fluorescence spectroscopy (TXRF) is shown in Figure 5.88. An intense
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Figure 5.88. Schematic diagram showing the X-ray source of experimental arrangement for total reflection X-ray fluorescence spectroscopy.
Figure 5.89. TXRF spectra recorded from (a) a clean silicon wafer and (b) a wafer with high levels of iron and zinc contamination (courtesy of Cascade Scientific).
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source of X-rays is generated by bombarding a rotating metal anode, usually of tungsten or molybdenum, with an intense electron beam. The X-rays generated are then reflected from a monochromator to remove all but the primary characteristic X-rays. These are then directed onto the sample surface at an angle less than the critical angle for total reflection. The fluorescence X-rays from the specimen surface are detected using a solid state detector (SSD) and the intensity of the reflected X-ray beam is measured with a scintillation counter. Using this arrangement the depth of measurement for surface contamination is less than 5 nm and the area of the wafer sampled is approximately 10 mm 10 mm. TXRF is not suitable for detection of low atomic number elements but is sensitive to elements with atomic number greater than 16. It can detect contamination levels where the coverage is as low as 1 1010 atoms/cm2 . The sensitivity of TXRF can be further increased by vapour phase decomposition (VPD) of the wafer surface (Shabani et al (1996)). Here non-volatile products produced by dissolving the surface oxide of the silicon wafer with an acid, normally pure hydrofluoric acid, is collected, dried and then the residue is analysed by TXRF. VPD-TXRF can increase the detection limits to 5 108 atoms/cm2 . Figure 5.89 shows two spectra recorded using TXRF. Spectrum (a) was recorded from a very clean silicon wafer and shows low levels of contamination whereas spectrum (b) is from a dirty wafer with relatively high levels of iron and zinc contamination.
5.15
References
Abragan A 1961 The Principles of Nuclear Magnetism (Oxford: Clarendon Press) Ackerman J L, Garrido L, Ellingson W A and Weyard J D 1987 in Proc. Joint Conf. on Non-destructive Testing of High Performance Ceramics eds A Vary and J Snyder Adams T E 2000 Micros and Analysis July p 31 Adem E, Champaneria R and Coxon P 1990 Vacuum 41 1695 Ainsle N, Hoffman R F and Seybolt A V 1960 Acta Metall. 8 523 Alford W J, Vanderneut R D and Zaleckas V J 1982 Proc. IEEE 70 641 Allen G C, Tucker P M and Wild R K 1979 Oxidation of Metals 13 223 Allen G C, Tucker P M and Wild R K 1982 Phil. Mag. B 46 411 Allmond T R and Houseman D H 1970 Microscope 18 11 Anastassakis E et al 1987 J. Appl. Phys. 62 3346 Archer R J 1968 Ellipsometry (Chicago: Gaertner Scientific Corp) Ash E A 1980 Scanned Image Microscopy (London: Academic Press) Bainbridge J, Channing D A, Whitlow W H and Pendlebury R E 1973 J. Phys. Chem. Solids 34 1579 Baranska H, Labudzinska A and Terpinski J 1987 Laser Raman Spectroscopy, Analytical Applications (Chichester: Ellis Horwood) Barer R, Cole A R H and Thompson H W 1949 Nature (London) 163 198
Copyright © 2003 IOP Publishing Ltd.
References
269
Bartz G 1973 Prakt. Met. 10 511 Bein B K, Krueger S and Pelzl J 1988 Photoacoustic and Photothermal Phenomena Optical Sciences 58 (Berlin: Springer) p 308 Berneike W, Knoth J, Schwenke H and Weisbrod U 1989 Freseius Z. Anal. Chem. 333 524 Blumich B 2000 NMR Imaging of Materials (Oxford: Clarendon Press) Blumich P and Blumich B 1993 Acta Polymerica 44 125 Born M and Wolf E 1959 Principles of Optics (Oxford: Pergamon Press) Boston M A, Klockenkaemper R, Knoth J, Prange A and Schwenke H 1992 Anal. Chem. 64 1115A Brandis E and Rasencraige A 1980 Appl. Phys. Lett. 37 98 Brandon D G 1966 Modern Techniques in Metallography (London: Butterworths) Briggs A 1985 An Introduction to Scanning Acoustic Microscopy Microscopy Handbooks, 12, Royal Micros. Soc. (Oxford: Oxford University Press) Briggs D A 1983 in Practical Surface Analysis ed D Briggs and M P Seah (Chichester: Wiley) Briggs D A and M P Seah ed 1990 Practical Surface Analysis (Chichester: Wiley) Briggs D A ed 1977 Handbook of X-ray and Ultraviolet Photoelectron Spectroscopy (London: Heyden) Brouillet P 1955 Metaux Corr. Ind. 30 141 Buhler H E and Hougardy H P 1980 Atlas of Interference Layer Metallography (Deutsche Gesellschaft fu¨r Metallkunde) Cantrell J H and Qian M 1989 Mat. Sci. Eng. A122 47 Canumalla S and Kessler L W 1997 Proc. Int. Reliability Physics Symp., Denver, Colorado p 149 Cargill G S 1980 Nature (London) 286 691 Carlson F P 1977 Introduction to Applied Optics for Engineers (New York: Academic Press) Carlson T A 1975 Photoelectron and Auger Spectroscopy (New York: Plenum Press) Charschan S S ed 1972 Lasers in Industry (New York: Van Nostrand Reinhold) Chastell D J and Flewitt P E J 1979 Mat. Sci. Eng. 38 153 Clark D A 1990 Microscopy and Analysis March Colthup N B, Daly L H and Wiberley S E ed 1990 Introduction to Infrared and Raman Spectroscopy 3rd edn (San Diego: Academic Press) Cosslett V E and Nixon W C 1960 X-ray Microscopy (Cambridge: Cambridge University Press) Coulomb P, Leymore C and Lacombe P 1959 Acta Metall. 7 691 Coxon P, Krizek J, Humpherson M and Wardell I R M 1990 J. Electron Spectrosc. Related Phenomena 51-52 Crates V J, Offner A and Suglis E H 1953 J. Opt. Soc. Am. 43 984 Cumpson P J 1995 J. Electron Spectrosc. 73 25 Cumpson P J 1999 Appl. Surf. Sci. 144-145 16 Ehrlicl G, Danzer K and Liebul V 1979 Second Meeting Festkorperanalytite Karl-MarxStadt Evans S, Pritchard R G and Thomas J M 1978 J. Electron Spectrosc. 14 341 Fadley C S, Baird R J, Sickhaus W, Novakov T and Bergstrom S A L 1974 J. Electron Spectrosc. 4 93 Farge Y and Juke P J 1979 European Synchrotron Radiation Facility Supplement I, European Science Foundation Fisher S B, Swallow G A, Hooper A J and Sparry R P 1975 CEGB Report RD/B/N3201 Flewitt P E J 1971 Ion Bombardment Symposium (1971) (London: Edwards)
Copyright © 2003 IOP Publishing Ltd.
270
Photo/electromagnetic sources
Flewitt P E J and Crocker A G 1976 Phil. Mag. 34 77 Flewitt P E J and Wild R K 2001 Grain Boundaries (Chichester: Wiley) Francon M 1963 Modern Application of Physical Optics (New York: Interscience) Franks A and Stedman M 1985 J. Microscopy 138 237 Frauenfelder H 1963 The Mo¨ssbauer Effect (New York: Benjamin) Fuller M P and Rosenthal R J 1986 Symposium on Infra-red Microspectroscopy FACSS XIII Sept 1986 Geiss M W and Angus J C 1992 Scientific American October 64 Geiss R H 1979 Introductory Electron Optics, Introduction to Analytical Electron Microscopy ed J J Hren, J I Goldstein and D C Joy (New York: Plenum Press) Gelius U, Wannberg B, Baltzer P, Fellner-Feldegg H, Carlsson G, Johansson C-G, Larsson J, Munger P and Vegerfors G 1990 J. Elec. Spec. 52 747 Genkin A D and Koroljev N V 1961 Geologija ruduyah Mestorozdewj 5 64 Grandjean N, Massies J and Leorux M 1996 Appl. Phys. Lett. 69 2071 Greaves R H and Wrighton H 1966 Practical Microscopical Metallography (London: Chapman and Hall) Greenwood N N and Gibb T C 1981 Mo¨ssbauer Spectroscopy (London: Chapman and Hall Ltd) Grundy P J and Jones G A 1976 Electron Microscopy in the Study of Materials (London: Edward Arnold) Hall C E 1966 Introduction to Electron Microscopy (New York: McGraw-Hill) Harris D R and Marwick A D 1980 Phil. Trans. R. Soc. (London) 295 197 Harthcock M A and Atkin S C 1988 Appl. Spectrosc. 42 449 Hawkes P W 1972 Electron Optics and Electron Microscopy (London: Taylor and Francis) Hercules S H and Hercules D M 1974 in Characterisation of Solid Surfaces ed P F Kane and G R Larrabee (New York: Plenum Press) ch 13 Hilton A R and Jones C E 1966 J. Electrochem. Soc. 113 472 Hirsch P B, Howie A, Nicholson R B, Pasheley D W and Whelan M J 1969 Electron Microscopy of Thin Crystals (London: Butterworths) Hoar T P and Mowat J H S 1950 J. Electrodep. Tech. Soc. 26 7 Holmes D A and Feucht D L 1967 J. Opt. Soc. Am. 57 466 Hull D 1956 PhDThesis (Cardiff: University of Wales) Ilett C, Somekh M G and Briggs G A D 1984 Proc. Roy Soc. London A393 171 Janosikova V 1973 XVII Colloquium Spectroscopium Internationale Florence p 766 Jenkins F A and White H E 1951 Fundamentals of Optics (New York: McGraw-Hill) Jolly W A 1972 in Electron Spectroscopy ed D A Shirley (Amsterdam: North-Holland) Jones R B, Younes C M, Heard P J, Wild R K and Flewitt P E J 2002 Acta Mater. 50 4395 Jorgensen P J and Westbrook J H 1964 J. Am. Ceramics Soc. 47 332 Joshi A 1979 Interfacial Segregation ed W C Johnson and J M Blakely (Ohio: ASME) p 39 Kaufman J, Metin S and Saperstein D D 1989 Phys. Rev. B39 13053 Kelly M A and Tyler C E 1972 Hewlett-Packard J. 24 2 Kho W F 1998 Microscopy Analysis Sept 15 Kildemo M 1998 Appl. Opt. 37 113 Kildemo M, Bulkin P, Drevillon B and Hunderi O 1997 Appl. Opt. 36 6352 Kildemo M, Drevillon B and Hunderi O 1998 Thin Solid Films 313 484 Kino G S 1987 Acoustic Waves (London: Prentice Hall)
Copyright © 2003 IOP Publishing Ltd.
References
271
Kline M and Kay I W 1965 Electromagnetic Theory and Geometrical Optics (New York: Wiley Interscience) Korpel A, Kessler L W and Palermo P R 1971 Nature (London) 232 110 Krivanek O L, Tsai D C, Sheith T T and Kamgar A 1978 Physics of SiO2 and its Interfaces ed S T Pantelides (New York: Pergamon) p 356 Lancombe P 1966 Metallography 1963 Proc. Sorby Centenary Meeting Sheffield Spec. Rep. 80 (London: Iron and Steel Institute) p 50 Lang A R 1958 J. Appl. Phys. 29 359 Lang A R 1959 Acta Cryst. 12 597 Laqua K 1979 Analytical Laser Spectroscopy ed N Omeneto (London: Wiley) Lemons R A and Quate C F 1979 Physical Acoustics 15 1 Lucazeau G and Abello L 1998 J. Mat. Res. 12 2262 McG.Tegart W J 1959 Electrolytic and Chemical Polishing of Metals (London: Pergamon) McIntyre N S 1983 in Practical Surface Analysis ed D Briggs and M P Seah (Chichester: Wiley) McLean D 1952 J. Inst. Metals 81 133 Maiman T H 1960 Nature 187 493 Martin L C and Johnson B K 1947 Practical Microscopy (London: Blackie) Martinin L and Poitras D 2000 J. Vac. Sci. Tech. A18 2619 Maul W and Quillfeldt W 1977 Jenaer Rundschau 20 234 May P W, Everitt N M, Trevor C G, Ashford M N R and Rosser K N 1993 Applied Surf. Sci. 68 229 Mehring M 1983 High Resolution NMR in Solids 2nd edition (Berlin: Springer) Messerschmidt R G 1987 The Design Sample Handling and Application of Infra-red Microscopes ed P B Roush ASTM STP 949 (Philadelphia: ASTM) Messerschmidt R G and Harthcock M A 1988 Infra-red Micro-spectroscopy Theory and Application (New York: Marcel Dekker) Miller T, Bartha L and Prohaszka J 1960 Zeit. Metall. 51 639 Moenke-Blankenburg L 1984 Advances in Optical and Electron Microscopy vol 9 ed R Baret and V E Cosslett (London: Academic Press) p 243 Moenke-Blankenburg L, Quillfeldt W and Spitzer R 1978 VIII Conference on Atomic Spectroscopy Varna–Druzbha, Bulgaria p 244 Moore T M 1993 Microelectronic Failure Analysis 3rd edition ed W L Thomas (ASM International) Mori Y, Uemura K, Shimanoe K and Sakon T 1995 J. Electrochem Soc. 142 3104 Morrison G R, Hare A R and Burge R E 1987 Electron Microscopy and Analysis Institute of Physics Conference Series 90 (Bristol: Institute of Physics) p 333 Mo¨ssbauer R L 1964 Recoilless nuclear resonance absorption of gamma radiation in Nobel Lectures 1961 Laureates, Biographies and Presentation Speeches p 583 (Amsterdam: Elsevier) Munro D F and Cuthbert J D 1971 Proc. Electro-Optical Systems Design Conference 71/ WEST (1971) May (Anaheim CA: ESCO) Ng H M, Doppelapude D, Koscakis D, Singh R and Monstakas T 1998 J. Cryst Growth 189-190 349 Nickel H, Peaser F, Mazurkiewicz M and Dorge W 1979 Jenaer Rundschau 22 199 Nomarski G and Weill A R 1955 Rev. Met. 52 121 Ohis K 1973 Z. Anal. Chem. 264 97 Oldham W G 1967 J. Opt. Soc. Am. 57 617
Copyright © 2003 IOP Publishing Ltd.
272
Photo/electromagnetic sources
Pac Y-H, Sachce W and Fukuoka H 1984 Phys. Acoustics 17 62 Pandey G C 1989 Analyst 114 231 Pawley J B 1995 Handbook of Biological Confocal Microscopy (New York: Plenum) Pepperhoff W 1960 Naturwissenschaften 47 375 Perryman E C 1952 Polarized Light in Metallography ed G K Conn and R J Bradshaw (New York: Academic Press) Philips V A 1967 Optical Techniques for Metallographic Examination in Techniques in Metals Research vol 1 ed R F Bunshah (New York: Wiley) Pousey J, Royez A and Georges J P 1959 Rev. Met. 56 215 Priestley J V 1992 Microscopy and Analysis Nov p 15 Quate C F, Atalan A and Wickramascringhe H K 1979 Proc. IEEE 67 1092 Quested P N and Bennett E G 1988 Microscopy and Analysis May p 7 Quinten A and Arnold W 1989 Mat. Sci. Eng. A122 15 Rivie`re J C 1990 Surface Analytical Techniques (Oxford: Clarendon Press) Rivory J 1999 Thin Solid Films 313-314 333 Rogers A W 1979 Techniques in Autoradiography (Amsterdam Elsevier/North-Holland) p 429 Samuels L E 1968 Metallographic Polishing by Mechanical Methods (London: Pitmans) Sawyer L C and Grabb D T 1987 Polymer Microscopy (London: Chapman and Hall) Schmuhl G and Rudolph D 1983 X-ray Microscopy Proc. of Int. Symp Go¨ttingen 1983 Springer Series in Optical Sciences (Berlin: Springer) Schmidt K, Hoven H, Koizlek K, Link J and Nikel H 1985 Gefugeanalyse Metallischen und Automatische Buildanalyse (Munich–Vienna: Carl Hanser) Schwan J, Dworschak W, Jung K and Ehrardt H 1994 Diamond Relat Mater. 3 1034 Schwarz-Selinger T, Von Kendell A and Jacob W 1999 J. Appl. Phys. 86 3988 Seah M P 1979 J. Catal. 57 450 Seah M P 1980a Surf. Interface Anal. 2 222 Seah M P 1980b J. Vac. Sci. Technol. 17 16 Seger L, Pinard R and Boulengrey P 1992 Microscopy and Analysis Sept p 1925 Shabani M B, Yoshimi T and Abe H 1996 J. Electrochem Soc. 143 2025 Shimada H 1987 Ultrasonic Spectroscopy and its Application to Materials Science ed Y Ware (Japanese Ministry of Education Science and Culture) p 5 Shirley D A 1972 Phys. Rev. B5 4709 Siegbahn K, Nordling C N, Fahlman A, Nordberg R, Hamrin K, Hedman J, Johansson G, Bermark T, Karlsson S E, Lindgren I and Lindberg B 1967 ESCA: Atomic Molecular and Solid State Structure Studied by means of Electron Spectroscopy (Uppsala: Almqvist and Wiksells) Slichter C P 1989 Principles of Magnetic Resonance 3rd edition (Berlin: Springer) Smallman R E and Ashbee K H G 1966 Modern Metallography (London: Pergamon) p 19 Smithells C J 1967 Metals Reference Book 4th edition (London: Butterworth) Somekh M C 1988 Microscopy and Analysis July Spiller E 1984 X-ray Microscopy Proc. of Int. Symp. Go¨ttingen 1983 Springer Series in Optical Sciences (Berlin: Springer) p 226 Spitzer W G and Tannenbaum M J 1961 J. Appl. Phys. 32 744 Steeds J W, Gilmore A, Charles S, Heard P, Howarth B and Butler J E 1999 Acta Mater. 47 4025 Steeds J W, Charles S J, Davies J and Griffin I 2000 Diamond and Rel Mat. 9 397 Stratton J A 1941 Electromagnetic Theory (New York: McGraw-Hill)
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References
273
Tanner B K 1975 X-ray Diffraction Topography (Oxford: Pergamon Press) Tanner B K 1989 J. Electrochem. Soc. 136 3438 Tanner B K and Bowen D K 1980 Characterisation of Crystal Growth Defects by X-ray Methods (New York: Plenum Press) Tassewa S and Petrakiev A 1971 XVI Colloquium Spectroscopium Internationale Heidelberg 191 Tatavski V I 1961 Wave Propagation in a Turbulent Medium (New York: McGraw Hill) Tempest P A and Wild R K 1985 Oxidation of Metals 23 207 Thomas W R and Chalmers B 1955 Acta Metall. 3 17 Thomas W R and Winegard W C 1952 Can. J. Metals 15 26 Tiller W A and Winegard W C 1955 Acta Metall. 3 201 Tolansky S 1962 Surface Microtopography (New York: Interscience) Tougard S 1988 Surf. Interface Anal. 11 453 Tricker M J 1977 Iron-57 conversion—electron Mo¨ssbauer spectroscopy in Surface and Defect Properties of Solids vol 6: A Review of Recent Literature up to mid-1976 (London: The Chemical Society) Vand V K, Vedam and R Stein 1966 J. Appl. Phys. 37 2551 Vardiman A G and Achter M R 1968 Trans. Met. Soc. AIME 242 296 Vetters H, Matthaci E, Schulz A and Mayr P 1989 Mat. Sci. Eng. A122 9 Vladimirsky Y, Kallne E and Spiller E 1984 Proc. SPIE 448 25 Wagner C D 1975 Farad. Discuss. Chem. Soc. 60 291 Wagner C D, Gale L H and Raymond R H 1979 Anal. Chem. 51 466 Wagner C D, Davis L E, Zeller M V, Taylor J A, Raymond R H and Gale L H 1981 Surf. Interface Anal. 3 211 Wagner C D, Riggs W M, Davis L E, Moulder J F and Muilenberg G E 1979 Handbook of X-ray Photoelectron Spectroscopy (Minnesota: Perkin-Elmer Corp) Warren B E 1969 X-ray Diffraction (Reading MA: Addison Wesley) Watts J F and Wolstenholme J 2003 An Introduction to Surface Analysis by XPS and AES (Chichester: John Wiley & Sons) Weissman S, Balibar F and Petroff J F 1984 Applications of X-ray Topographic Methods Applied to Materials Science (New York: Plenum Press) Weinberg F 1963 Trans. AIME 227 223 Welford W T 1962 Geometrical Optics (Amsterdam: North-Holland) Wild R K 1980 Mat. Sci. Eng. 42 265 Wilson T 1990 Confocal Microscopy (London: Academic Press) Wilson T, Neil M A and Juskaites R 1998 J. Microsc. 191 116 Wilson T and Sheppard C 1984 Theory and Practice of Scanning Optical Microscopy (London: Academic Press) Wright C D, Heyes N A E, Clegg W W and Hill E W 1995 Microscopy and Analysis March p 21 Yariv A and Gordon J P 1963 Proc. IEEE 51 4 Yates K, Barrie A and Street F J 1973 J. Phys. E: Sci. Inst. 6 130 Young P H 1988 Spectroscopy 3 24 Yukawa S and Sinnot M J 1955 TAIMME 203 996 Zou J W, Reichelt K, Schmidt K and Dischler B 1990 J. Appl. Phys. 67 487
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Chapter 6 Electron sources 6.1
Introduction
As we have pointed out in the preceding chapters (4 and 5) we have separated electron sources from other types of electromagnetic radiation used to image materials because of their significance and contribution to the evaluation of the microstructure. Indeed, it is our belief that of all the techniques presented in this book, those described here have, over the past 50 years, provided the greatest contribution to the advancement of our understanding of microstructures and thereby the associated electrical, mechanical and overall physical properties of materials. As described in chapter 5, electrons like electromagnetic radiation can be considered either as waves or photons. However, the majority of techniques use monochromatic beams of electrons with a wavelength that is a function of the applied accelerating potential.
6.2 6.2.1
Scanning electron microscopy The instrument
A schematic diagram of an electron optical column for a two lens scanning electron microscope (SEM) is given in figure 6.1. The electron gun operates typically over a voltage range 0–30 keV sometimes extending up to 60 keV depending upon the type of instrument and application where the specimen is maintained at earth potential. The microscope is a probe forming system where each lens condenses and demagnifies the electron source to a focused spot at the specimen surface (Howie (1965), Hearle (1972), Catto and Smith (1973), Van Essen (1979) and Flewitt and Wild (1985)) all within an evacuated column (<103 Pa). Electron probes of sizes down to 6 nm are achieved with conventional thermionic emission sources although smaller probes 3 nm require higher intensity, coherent field emission sources. The specimen is scanned by the incident electron beam and electrons emitted from the surface are collected and amplified to form a video signal.
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Figure 6.1. (a) Schematic diagram of a scanning electron microscope. (b) Ray paths in the scanning electron microscope; standard arrangement for image formation. The scan deflection is shown in figure 6.2. (c) Schematic diagram of the control systems for a scanning electron microscope.
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Figure 6.2. The deflection coils for scanning or beam alignment produce a field along the þx axis; the electron, travelling in the z direction, is deflected in the y direction while remaining in the yz plane.
Since there is insufficient space to effect the electron beam scanning after the final lens, this beam is deflected through the required angle before entering the final lens; further deflection is provided to ensure that the electron beam passes through the centre of the lens. Figure 6.1(b) shows the corresponding ray diagram for a complete microscope, including the double deflection system which comprises two sets of coils which introduce a magnetic field perpendicular to the axis of the microscope (figure 6.2). Apertures that are included at various positions to limit divergence of the electron beam. To achieve the smallest diameter electron probes incident on the specimen the final condenser lens must have low aberrations; however, the resolution of the final image cannot be less than the diameter of the scanning electron beam. Small electron beams and, therefore, high resolutions are obtained if the lens aperture is adjusted to an optimum size, 150 mm diameter. A large depth of focus is achieved for these instruments because the electron beam is focused from the aperture on to the specimen surface over a distance of typically 15 mm, and if the beam divergence is low ð ¼ 3:3 103 rad) this gives a depth of focus of several millimetres. It is the combination of the high resolution with a large depth of focus that makes the SEM well suited to examine topography, for example fracture surfaces. A range of specimen stages are available, the simplest of these allow x, y and z linear motion combined with tilting and rotation about one or more axis. However, a variety of specialist stages have been developed for dedicated work. The specimen is normally insulated and connected to ground and indeed the specimen current, if suitably amplified, can provide a usable signal. The major advance in recent years for the SEM, as with all electron optical equipment, has been the introduction of computer automation
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both with respect to instrument control and image processing (Reimer and Niemetz (1985) and Watt (1990a,b)). On many instruments the column parameters of accelerating voltage alignment and other functions can be monitored, controlled and presented in a menu format. Moreover these operating conditions can be stored and recalled from computer memory so that instrument parameters predetermined as optimum for the examination of a particular specimen may be recalled. In addition, control of the digital electronics facilitates automatic control of focus, astigmatism correction, contrast, brightness and other parameters that influence the quality of the image. Although the use of image processing is discussed more fully in chapter 8, it is important to make brief reference to the role of the framestore in the SEM system (figure 6.1(c)). Secondary and backscattered electron images can be digitized and stored in the framestore memory, usually from live time scan rates to the slower rates used for higher quality images. As a consequence the image can be improved with respect to the signal-to-noise ratio for poor quality images, for example by recursive filtering, and the digitised image can be subsequently processed by normal procedures such as grey scale expansion and binary quantisation. The potential of computer image processing systems is described further in chapter 8. One of the many new developments in scanning electron microscopy addresses the observation of samples in the specimen chamber of the instrument at high pressures. The instruments used are currently referred to by the generic title of the environmental scanning electron microscope (ESEM). For this type of instrument the working pressure of the specimen chamber is greater than about 600 Pa, the pressure of saturated water at 273 K (Danilatos (1988)). These conditions are achieved by separating the specimen chamber from other parts of the instrument column (figure 6.3) by a system of apertures that restrict the flow of gases in the system by use of differential pumping. 6.2.2
Theory
Detailed treatments of the theory underlying scanning electron microscopy are available (Jenkins and White (1951), Thornton (1968), Oatley et al (1965), Oatley (1972) and Wells (1974)). We will simply address factors that influence key parameters of performance for the SEM (depth of field, image noise and resolution) before considering the specific imaging modes and the associated performance. Depth of field Depth of field represents that distance along the microscope axis over which the specimen can be displayed within blurring the image. For a beam of fixed divergence angle, (figure 6.4), blurring is measured by the diameter of the
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Figure 6.3. Schematic diagram of the environmental scanning electron microscope.
‘disc of confusion’, d, which is related to the axial shift, D, where ðD=2Þ tan ¼ d=2
ð6:1Þ
where D tends to d= when is small and equals the depth of field when the diameter of the disc of confusion does not exceed the resolution obtained
Figure 6.4. The electron beam converging to the image plane with semi-angular aperture , where d is the resolution required and D the depth of field for a scanning electron microscope.
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Table 6.1. Depth of field and resolution of the SEM (final aperture 5 103 rad) compared with that achieved with the optical light microscope (Flewitt and Wild (1985)). Depth of field Magnification
Resolution
SEM
Optical
20 100 200 1000 5000 10000
5 mm 1 mm 500 mm 100 nm 20 nm 10 nm
1 mm 200 mm 100 mm 20 mm 4 mm 2 mm
5 mm 2 mm 0.7 mm – – –
at a particular magnification. The depth of field achieved at various resolutions is given in table 6.1 for an SEM with a final aperture of semi-angle of 5 103 rad. Noise Noise within the final image is present in all forms of microscopy and relates to the collecting efficiency of the imaging system. This has been analysed by Bowen and Hall (1975) who consider the processes which produce the image and those which produce scattering in the specimen; both are random. Noise influences the resolution achieved in the image since two points can be resolved only if the difference between the image signals exceeds the statistical uncertainty. Certainly in the SEM, resolution is improved if the signal is collected for longer periods of time and the contrast is increased; a large signal reduces the fractional error in the signal. Bowen and Hall (1975) consider the role of statistical noise on resolution for a given illumination system and contrast level by addressing two areas each of diameter d, which is the resolution to be achieved. It is assumed that the signal I1 from the first area has a standard error 1 , and from the second area is I2 with error 2 ; the signal is normally distributed to a confidence of 3m where m is the standard deviation of the mean. Then I1 þ 31 I2 32
ð6:2Þ
where I1 < I2 (figure 6.5). The contrast, H, is the change in signal divided by the original signal I2 ¼ I1 ð1 þ HÞ so that equation (6.2) becomes I1 H ð1 þ 2 Þ
ð6:3Þ
When random noise is present a larger signal is required from regions of weak contrast; however, 1 ¼ 2 ¼ s such that H 6s =I:
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Figure 6.5. The criterion to distinguish two signals that differ in contrast H [I2 ¼ I1 ð1 þ HÞ] (Bowen and Hall (1975)).
This approximation is conservative but small, since I1 < I2 and thus 1 > 2 . The problem addressed by Bowen and Hall was to decide the value of the standard error s . The final image signal is a product of i, the electron current leaving the specimen, p0 the efficiency of the collecting system, and g, the gain of the amplification system, thus I ¼ ip0 g0
ð6:5Þ
ðs =IÞ2 ¼ ði =iÞ2 þ ðp =p0 Þ2 þ ðg =g0 Þ2
ð6:6Þ
The fractional error s =I is: where p is zero since the efficiency of collection depends on geometrical factors and the collector voltage. As a consequence the current leaving the specimen is i ¼ ðn n0 Þe=
ð6:7Þ
where is the sampling time, e is the electron charge, n is the number of electrons arriving in time , and n0 is the number of electrons emitted per incident electron. Applying the propagation-of-errors equation and neglecting variations in the sampling time, Bowen and Hall (1975) show that ði =iÞ2 ¼ ðn n0 =n n0 Þ:
ð6:8Þ
If the number of electrons arriving at the collector in unit time is normally distributed about the most probable value (n n0 )>10, the standard error is (n n0 )1=2 . Thus: ðs =IÞ2 ¼ ð1=n n0 Þ þ ðs =g0 Þ2
ð6:9Þ
and from equation (6.4) H 2 36fð1=n n0 Þ þ ðs =g0 Þ2 g:
ð6:10Þ
Resolution is related to the constant by evaluating n . This is achieved by multiplying the beam intensity BD 2 (BD is the beam diameter) by the
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beam area d 2 /4 and the time , and dividing by e. Replacing by =N 2 where is the time to scan a whole frame and N is the number of lines per frame, then n ¼ BD d 2 2 2 =4N 2 e:
ð6:11Þ
Substituting this expression in equation (6.10) and rearranging: d 2 > 144N 2 e=2 1 BD n0 ½H 2 36ðg =g0 Þ2 :
ð6:12Þ
In a typical SEM, N is normally fixed at 1000 lines, B is controlled by the electron source and f by the specimen and the mode of contrast selected. The resolution improves with an increased time for one frame scan, contrast in the specimen and final aperture size. Unfortunately noise in the amplification system will also degrade the attainable resolution. Electron sources In the SEM, as with other electron optical instruments, an incident electron beam is focused on to the specimen, but in this particular case it is also scanned over it (Joy (1974)). The resolution is set by the diameter of the incident beam and the mode of operation. The coherence of the source is not as important as the energy spread within the electron beam, which should be as low as possible to minimise the chromatic aberration. Moreover, because images are time resolved, the stability of the electron beam and therefore the emitting source should be as high as practical. Thus the ideal source should maximise the current within the electron beam over the total size range available (Joy (1974) and Mulvey (1967)). The brightness of an electron source is controlled by the current density emitted into a unit solid angle; for the SEM this total incident current determines instrument performance. The apparent brightness, s , of the incident electron beam is s ¼ ð4IB Þ=ð2 d02 1 Þ2
ð6:13Þ
where d0 is the Gaussian electron beam diameter, 21 , is the incident beam divergence angle and IB is the incident beam current. But s equals i such that IB ¼ ð2 =4Þði d 2 1 Þ2 :
ð6:14Þ
When the incident diameter d0 is large the influence of aberrations is small so that the incident current IB varies as d02 for a fixed value of ; for a given d0 the incident current can be increased by increasing either 1 or i . The theoretical brightness of a tungsten thermionic source is given by the Langmuir equation: i ¼ Jc eV0 =kT
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Table 6.2. Comparison of the performance for different electron sources.
Source
Brightness relative to tungster
Source size
Energy (eV)
Stability spread (%)
Tungsten hairpin Pointed, W filament LaB6 Cold field emission
1 2–10 30 500
50 mm 10 mm 1 mm 5 nm
3 3 1.5 0.2
<1 3 <1 3–5
Hot field emission
500
3
>5
5 nm
Lifetime (h)
Vacuum (Pa)
50 20 300 Depends on vacuum 100
<103 <104 106 1010 107
where Jc is the cathode current density, e is the electron charge, V0 is the accelerating potential, k is the Boltzmann constant and T is the cathode temperature. Jc is given by Jc ¼ CT 2 ee =kT
ð6:16Þ
where C is a constant and is the cathode work function. The most direct way to improve the source brightness is to reduce the work function . Lanthanum hexaboride, LaB6 , has a value for of 2.7 eV compared with 4.5 eV for conventional tungsten. Table 6.2 compares the relative brightness achievable for various modifications of tungsten filaments and the LaB6 . The LaB6 source provides a very substantial brightness increase over the normal thermionic sources and is stable for long periods. Field emitters offer a further increase of at least 1000-fold in brightness compared with tungsten, but at the penalty of requiring an ultra-high vacuum system (Table 6.2). As shown in figure 6.6 a high field in the region of the cathode enhances electron emission because of the reduced height of the potential barrier (Joy (1974)). At large fields the barrier is narrow and electrons can pass through even at room temperature. Contrary to expectation, although the field emission source provides the highest brightness, it is not suitable or appropriate for all applications. Resolution The resolution is a critical parameter which governs the performance of an SEM and indeed resolution is a balance between the effects of the aberration of the final lens and diffraction effects (Smith (1986)). For most instruments currently available a resolution of about 5 nm is attainable. However, for ultra-high resolution in the SEM the key is to provide the smallest diameter and brightest electron source and to combine this with an ability to detect the emitted secondary electrons with the highest efficiency. The diameter of the
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Figure 6.6. Potential energy for a cathode to vacuum interface in the presence of an accelerating electric field. The effect of the field is to lower the work function to a lower effective value 0 (Joy (1974)).
incident electron beam, d, is given by d 2 ¼ f4ip =0:62i2 þ ð1:22Þ2 g2 þ ðCs =2Þ2 6 þ ðCc Vi =Vi Þ2 2
ð6:17Þ
where ip is the beam current, i brightness, wavelength of the electrons, Cs and Cc the spherical and chromatic aberration coefficients of the objective lens, Vi /Vi is the variation in electron potential and is the aperture semi-angle. By reducing values of Cc and Cs and using a LaB6 cathode it is possible to obtain resolutions approaching 1 nm at an accelerating voltage of 40 keV; (figure 6.7). 6.2.3
Specimen preparation
Of the techniques available for examining the microstructure of materials, the SEM is one which demands least for the preparation of the specimen to be examined (Yoshimura et al (1983) and Nonoka (1982)). However, if the desired information is not obtained the quality of the specimen is inappropriate for the imaging mode selected or for the detail of image required. Surfaces of bulk specimens of metals, polymers, ceramics, glasses and composites can be prepared easily by cutting, etching or fracturing. To reduce electrical charging of non-conducting specimens which can be induced by the incident electron beam, the surface can be sputter coated with a conducting metal such as gold. However, the sputtered layer is visible at higher magnifications and this limits the ability to resolve finescale features. Another limitation can arise from the history of the specimen and this is particularly true for metals and alloys whereby fracture surfaces
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Figure 6.7. The relation between accelerating voltage and diameter of the electron beam (resolution) ðCs ¼ 3 mm, Cc ¼ 4.2 mm, LaB6 ¼ cathode, ip ¼ 1 pA) (reproduced by permission of JEOL UK Ltd).
can become degraded by oxidation. Although a range of chemical and ion bombardment techniques can be used to remove the surface product, the oxidation process consumes the metal substrate and therefore degrades fractographic detail (MacMillan and Flewitt (1975)). The environmental scanning electron microscope enables the examination of non-vacuum compatible samples such as wet, oily or outgassing materials in their natural state. This is without any special form of preparation or the use of special specimen stages, such as cryostages. Moreover it also allows examinations to be undertaken under a range of gaseous environments, relative humidities (0–100%) and temperatures (typically 100–1700 K). As a consequence it is possible to perform a wide range of dynamic experiments within the chamber of this instrument without any special preparation of the specimen (Roever and Cosper (1996), Tiab and Donaldson (1996) and Messier and Vitale (1993)). 6.2.4
Imaging modes
To achieve an SEM image, use is made of the different signals produced when the electron beam interacts with the bulk specimen (see chapter 2). The three main methods used to collect these emitted electron signals (Thornton (1968)) are summarised in figure 6.8, and table 6.3 lists the imaging modes together with a measure of the spatial resolution attainable. Figure 6.8(a) shows a typical photomultiplier system used to detect the secondary electrons. Here a phosphor is guarded by a grid held at either a positive or negative potential (typically 200 to þ400 V) either to attract or repel electrons. The secondary electron yield, i , is a function of the angle of
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Figure 6.8. Methods of detecting electrons in a scanning electron microscope: (a) secondary electrons, (b) backscattered electrons, solid state detector, (c) backscattered electrons, scintillation counter and (d) absorbed electron current.
incidence, , of the electron beam to the specimen surface (Hearle (1972)): i ðÞ / exp½Cð1 cos Þ
ð6:18Þ
where C is a constant. To optimise the yield and, therefore, the input to the image (figure 6.9), it is necessary to select a mean orientation for the specimen surface (Catto and Smith (1973)). As indicated in figure 6.9, variations in the local electron yield with orientation form the basis of topographical imaging. Unfortunately for specimens with very pronounced surface roughness and re-entrant relief, contrast is modified by surface collection contributions but any improved contrast is usually accompanied by degradation of image detail.
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Table 6.3. The three most commonly used scanning electron microscopy imaging modes together with resolution attainable (Flewitt and Wild (1985)).
Mode
Information
Backscattered electrons
Topographic, crystallographic, composition Topographic Voltage Magnetic and electric field Topographic, composition
Secondary
Absorbed specimen current
Typical resolution (nm)
High resolution (nm)
10
3
10 100 500 50
3 50 100 20
Figure 6.10(a) shows a secondary electron image of a fracture surface for a specimen removed from a 214%Cr–1%Mo steel ‘V’ notch geometry impact specimen tested at a temperature below the ductile–brittle transition (Lonsdale and Flewitt (1978b)). This reveals ‘quasi-cleavage’ fracture on three mutually perpendicular {100} orientation cleavage facets. Figure 6.10(b), on the other hand, shows a specimen of Type 316 austenitic stainless steel superheater tubing which has been removed from service in a fossil fired electrical power generating station after 2 108 s operation. The specimen was fractured under liquid nitrogen and has separated along the austenite grain boundaries. Covering the intergranular fracture surfaces are creep cavities of a degenerate crystallographic shape and associated with many of these are small carbide precipitates. These cavities, typically in the size range 0.2–1 mm in diameter, coalesce resulting in the ultimate creep failure of the component. Here the carbide precipitates are shown in light contrast compared with the darker austenite parent; the contrast arises from the difference in the secondary electron yield between these two phases: this is not to be confused with atomic number contrast.
Figure 6.9. Secondary electron emission at surface irregularities; contributions from specimen collection are indicated.
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Figure 6.10. Secondary electron images: (a) fracture of a 214%Cr–1%Mo steel at 77 K, showing quasi-cleavage with mutually perpendicular {100} facets (Lonsdale and Flewitt (1978b)); (b) Low alloy ferritic steel steam pipe after 2 108 s operation at 820 K, fractured at 77 K; showing distribution of creep cavities on intergranular fracture surfaces (Chastell and Flewitt (1979)); (c) a rapidly cooled polyethylene where the morphology in the centre is revealed as a consequence of damage by the incident beam (Vesely (1988)) (reproduced by permission of Pergamon Press).
Electron yield varies with the accelerating voltage and therefore it is desirable to control the selected accelerating voltage to produce an image which contains the required information. In this respect, most modern instruments provide the facility for varying the voltage over the complete range available to allow the image to be produced at different voltages. In particular, the voltages are usually finely divided below 5 keV so that beam sensitive or easily charged specimens can be examined (Vesely et al (1976) and Vesely (1988)). To reduce electrical charging induced by the electron beam, non-conducting materials such as polymers or ceramics are sputtered with a thin metal layer such as gold. Although this degrades the attainable resolution it is usually sufficient for many applications.
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Figure 6.11. Variation of backscattered electron yield with specimen atomic number.
However, unless the incident voltage is carefully selected, for polymeric materials electron beam damage can lead to changes in the surface morphology (figure 6.10(c)), as a result of a decrease in mass of the specimen (Vesely (1988)). In some cases, these changes can be used to advantage but at present interpretation of the resulting morphology is not fully understood, especially for semi-crystalline polymers. Generally solid state detectors used for backscattered electrons are either of the dipole, quadrupole or the annular type (Smith (1956)); when dipole detectors are used they are often inclined to the specimen (figure 6.8(b)). The advantage of a multipole detector system is that it allows the detected signals to be selectively combined, an advantage since backscattered electron yield is a function of both atomic number (composition) and topography. An alternative for higher resolution backscattered electron images is a scintillator combined with a photomultiplier (figure 6.8(c)). Figure 6.11 shows the variation of backscattered electron yield, with atomic number of the specimen (Napchan (2001)). When the output signal is passed through a discrimination system it is possible to determine the mean atomic number of an unknown material to a difference of 0.1 using such a calibration curve (figure 6.11); discrimination is better for lower atomic number elements where the slope is greater. Figure 6.12(a) is an example of the use of atomic number discrimination for a leaded, free machining brass. The lead-rich areas have a high mean atomic number compared with the matrix and by filtering the backscattered image these areas are revealed. By mixing this image with the secondary electron image the distribution of the lead rich phase is established. The second example (figure 6.12(b)), shows various oxide types within the corrosion product on the inner surface of a boiler tube. By filtering the backscattered electron signal two oxides, magnetite (Fe3 O4 ) and haematite (Fe2 O3 ), are identified and their distribution mapped.
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Figure 6.12. Backscattered electron images: (a) Free machining leaded brass showing leadrich areas and (b) corrosion product formed on the inner surface of a boiler tube showing distribution of magnetite and haematite (Flewitt and Wild (1985)).
The contrast obtained from backscatter electron signals depends upon the local orientation of the surface to the incident electron beam offering the ability to provide quantitative topographic images. The backscattered electron (BSE) yield from a specimen in a SEM is dependent on the incident electron beam energy and intensity, the mean atomic number density and the surface orientation (Remer and Krefting (1976)). For an electron beam incident upon and normal to the specimen surface, the BSE yield, i0 , is i0 ¼ Cie cos
ð6:19Þ
where is the angle with respect to the incident beam (figure 6.13), C is a constant dependent on the specimen material and beam energy and Ie is the incident beam current. For a specimen tilted at an angle , with respect to the incident electron beam (figure 6.13(b)), the maximum BSE signal is peaked in the forward direction with a maximum at an angle 8. In addition the yield i 0 increases with approximately as (Arnal et al (1969) and Lebiedzik et al (1979)): i0 ¼ CZ 1=2 ie =9ð1 þ cos Þ
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ð6:20Þ
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Figure 6.13. Backscattering of electrons: (a) polar intensity plot for backscattered electrons at normal incidence showing the cosine dependence; (b) as (a) for an incident angle , showing forward peaking; (c) the principles of imaging a given tilt angle range, , using a voltage discriminating amplifier with a selecting window adjusted to the voltage range, N.
where Z is the atomic number. The angular distribution about the peak value varies more rapidly than for the normal incident. If an annular electron detector is located centrally above the specimen (figure 6.13(b)), the measured electron voltage, N(0; ) will decrease with increasing (figure 6.13(c)), thereby providing topographic contrast (Doig et al (1987)). Selective imaging from a limited voltage window, N, allows regions of fixed tilt range, with respect to the incident electron beam to be resolved. Such images produce black–white contrast with no intermediate grey scales thereby facilitating the interpretation of surface tilt. When applied to the examination of a fracture toughness test specimen (figure 6.14(a)), the ‘stretch zone’ within the transition region can be selectively imaged. This zone lies between the pre-crack produced by fatigue and the onset of stable crack growth during the test and is characterised by shear deformation at 458 to the applied stress direction. This inclined fracture surface is readily interpreted from the backscattered image compared with a corresponding
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Figure 6.14. Backscattered electron images: (a) compared with secondary electron image and (b) a stretch zone formed on the fracture surface of a compact tension fracture toughness test specimen (Smith et al (1984)).
secondary electron image (figure 6.14(b)). A measure of the fracture toughness of a material may be obtained from the mean stretch zone width (Smith et al (1984)). Oriented multipole detectors provide the capability of obtaining images at different relative surface orientations and allow unambiguous evaluation of orientation at any point. Indeed it has been demonstrated that sequential integration of the local slope allows topography to be established (Lebiedzik et al (1979) and Smith et al (1984)). The BSE signal recorded by each pole of a quadrupole detector is a convolution of the solid angle subtended by the detector and the BSE intensity distribution. For a quadrupole detector located symmetrically about the incident electron beam (figure 6.15(a)), the intensities recorded by opposite quadrants and are shown schematically in figure 6.15(b) (Smith et al (1984)). The shape of these curves varies with the working distance, the dimensions of the detector and any out of plane specimen tilt. The influence of the calculated recorded BSE signal for detector 1 is shown in figure 6.15(c) as a function of surface tilt. For any tilt the signals into both detectors vary and the total intensity is not a constant: the signal intensity from each detector must be normalised to give an unambiguous value. Thus a plot of the difference/sum of the two signals as a function of surface tilt gives a single line for each value of working distance. Calculated values for the BSE detector are shown in figure 6.15(d) for different working distances. Maximum sensitivity occurs for small working distances but saturates at low tilt angles. A surface oriented with the normal not in the plane of opposite quadrupoles, allows evaluation of the component of tilt in one plane. The other component
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Figure 6.15. Schematic diagrams showing (a) the geometry for detecting the BSE using a quadrupole detector; (b) the BSE signal captured to each detector with sample orientation; (c) calculated intensity recorded by a single detector as a function of working distance for a range of surface tilts between 0 and 808; (d) calculated normalised BSE signal for detectors 1 and 2 as a function of tilt angle for working distance between 5 and 40 mm; (e) stereographic representation of the components of a surface normal, P (Doig et al (1987)) (reproduced by permission of the Institute of Physics).
requires a similar measurement from the other pair of poles (figure 6.15(c)). For a surface normal P, the angular component is determined from the BSE signal for poles 1 and 2 and the angular component from poles 3 and 4 of the detector. The direction of P is evaluated from the signals
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Figure 6.16. Quantitative backscattered electron images in the SEM: (a) image of a machine turned surface and (b) reconstructed topographic image of the surface (Doig et al (1987)) (reproduced by permission of the Institute of Physics).
detected by each of the four poles and the relevant calibration curve (figure 6.15(d)), which is established by direct calibration on a flat surface tilted a known amount for the detector parameters used to record the signal. Mapping of a surface and storing each signal allows surface topography to be established by using the experimental calibration. An example obtained from a machine-turned surface is shown in figure 6.16: the conventional BSE topographic image is shown in figure 6.16(a) and the reconstructed quantitative image in figure 6.16(b). Provided a specimen is insulated, then absorbed electrons can be collected and the signal displayed (figure 6.8(d)) (Shmoda (1969)). Since this electron current is the difference between the incident electron beam current and the
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sum of the secondary and backscattered electrons, then the image shows contrast reversed compared with a backscattered electron image. The resolution of the image is limited by the signal-to-noise ratio to be typically no better than 20 nm. A range of other imaging modes can be achieved in the SEM for specific applications including cathode luminescence (Cusano (1964)), voltage contrast (Nathrop (1972)), electron and magnetic field contrast (Joy and Jakobuvics (1968)) and induced conductivity. Although subject to more specific applications they serve to illustrate the potential of this commonly used and widely available instrument. Cathodoluminescence is the emission of light when a specimen is excited by an incident beam of electrons (Thornton (1968) and Walmsley and Lang (1987)). Under these circumstances, the equilibrium atomic configuration is achieved when excited electrons relax to their original energy state emitting, as light, some of the energy transferred from the primary electron beam. Although cathodoluminescent phosphors emit up to 10% of the absorbed energy many materials, including polymers and glasses, are weak emitters. However, the decay time can be between 1010 and 102 s depending upon the particular material. In the SEM the photons (light) passes directly into a light pipe where they enter a photomultiplier and are converted to an electrical signal that can be amplified. Unfortunately no bias can be applied so that the collection efficiency is low. The critical element in the design of the detector is coupling with the specimen and to achieve this with high sensitivity an ellipsoidal mirror is placed over the specimen at one focus (Van Essen (1974)). The light emitted by the specimen is reflected to a second focus where the light pipe is positioned, thereby increasing collection efficiency by up to two orders of magnitude. Cathodoluminescence is applied to a range of materials but has particular benefits for semiconductors. The latter materials are characterised by a filled valence electron band and an empty conduction band, the two being separated by a band gap of forbidden states of defined energy. In CdS the gap is 2.4 eV, while silicon has a gap of only 1.1 eV so that if no bias voltage is applied to the specimen to sweep the electron–hole pairs apart the electron and hole may recombine. This excess energy is released as a photon and the radiation is sharply peaked at specific energies and is characteristic of the composition. Thus spectra of cathodoluminescence provide a useful and powerful tool characterising semiconductor materials (Cullis et al (1985)) and minerals (figure 6.17). Certainly it has developed as a standard technique for investigating minerals and ceramics (Marfurien (1979), Gotze (1998) and Gotze and Magnus (1997)). The distinct cathodoluminescence properties of minerals such as diamond, sphalerite (sulphides), apatite (phosphates) etc, affords rapid identification of these different mineral constituents. This extends to ceramics, glasses, refractory materials and biomaterials where the technique has been used for identification of phase distributions (Watt et al (1998) and Budd et al (2000)).
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Figure 6.17. A comparison of the microstructure of a mineral using (a) reflected light and (b) cathodoluminescence (reproduced by permission of Taylor and Francis).
Domains within a ferromagnetic specimen can be observed in the SEM due to small variations in the surface magnetic field near the surface which deflect secondary electrons, due to the Lorentz force of the magnetic field. Two contrast mechanisms are used to provide magnetic domain images (Booker (1970), Fathers et al (1973) and Newbury and Yakowitz (1973)). The first results from magnetic fields outside the specimen, between the adjacent domains. These are of sufficient magnitude in some materials to change the trajectory of secondary electrons and the associated change in collection efficiency produces the domain contrast. In the second case the trajectories of electrons scattered within the specimen are modified by the magnetic domain field. Here the change of trajectory in the direction of the collector is important so that only the magnetisation component perpendicular to the specimen collector line produces the contrast. Indeed it is possible to establish a measure of the magnetisation direction. This contrast is developed when the specimen is tilted away from the normal to the incident electron beam. Figure 6.18 shows an example of magnetic domains imaged in polycrystalline cobalt. Typically a rather low beam voltage, 5 keV, is used since magnetic contrast is sensitive to both secondary electron collector geometry and to the voltage applied to the collector grid, disappearing when the voltage is insufficient. Resolution of typically 100 nm is achieved. When a semiconducting device is swept by an electron beam, local subsurface conducting currents are generated within the specimen (Hirsch (1985)). Under these circumstances voltages are produced at inhomogeneities within the specimen which cause small variations in the positions of the band edges relative to the Fermi level. The mechanism by which these voltages develop is identical to that operating when a p–i–n junction is used in a photovoltaic cell (figure 6.19). Here band bending is shown and where electron–hole pairs are created on the right hand side (p type) these electrons diffuse to the potential discontinuity and are attracted to the opposite side
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Figure 6.18. Magnetic domains imaged at 5 keV in cobalt (courtesy JEOL UK).
by the inherent field; holes cannot cross the discontinuity due to the presence of the field. The reverse applies for electron–hole pairs approaching from the opposite side so that both sets of carriers charge the specimen positively on the right hand side. The additional induced field results in a potential difference that can be observed in the external current. The largest voltage developed is the diffusion potential of the discontinuity, VD . Saturation is reached when the charge collected for the volume within a carrier diffusion length (D1 )1=2 (where D is the diffusion constant, e =kT, and 1 the minority
Figure 6.19. Specimen voltages developed due to gradient of impurity concentration in a semiconductor device.
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carrier life time) exceeds the internal field. This contrast mode has a resolution determined by the diffusion carrier length and variations in voltage at different points on the specimen reflect changes in mobility, lifetime and impurity concentration. Output voltages down to 106 V can be detected from semiconductive devices within the noise constraints. Certainly using electron beam induced current (EBIC) contrast in the SEM makes it possible to resolve individual dislocations and other defects in semiconductors and ceramics and to determine their electronic properties (Cullis et al (1985)). The phenomenological theory of EBIC dislocation contrast in semiconducting materials has been described by Donolato (1983) where the incident electron beam energy excites a volume in the semiconductor where electron–hole pairs are generated. The carriers diffuse from this volume and an electrical barrier such as a surface Schottky contact will attract carriers of one sign to collect an EBIC current. This is reduced by extra recombination via defects. Wilshaw and Booker (1985) and Holt (1987) described EBIC contrast using the model of a dislocation as a line of acceptance. The ability to interface energy dispersive and wavelength dispersive spectrometers to the SEM provides a method of detecting and quantifying characteristic X-ray emissions. Thus chemical compositions within the overall microstructure of materials can be established. However, in the case of the environmental scanning electron microscope, account has to be taken of the atmosphere present for the particular investigation since the X-ray counts can be reduced as a consequence of photon–gas interactions (Bilde-Sorensen and Appell (1996). In order to reduce these contributions, a practical solution is to use a gaseous environment with a low atomic mass number (Stowe and Robinson (1997)). However, X-ray microanalysis is discussed further in section 6.3 of this chapter. In addition it is now usual to use computers both to control and operate the instruments and to process the images. The latter will be considered more fully in chapter 8.
6.3 6.3.1
Electron probe microanalysis Introduction
The electron probe microanalyser developed in 1951 by Castaing (1954, 1960a,b) provides an ability to detect and quantify the characteristic Xrays emitted when electrons interact with a bulk specimen. These interactions have been described and discussed in chapter 2. Indeed current generation instruments embrace a medium performance scanning electron microscope together with spectrometers to detect and discriminate the emitted X-rays. Thus electron probe microanalysis of microstructural features in bulk specimens is a diagnostic technique for determining chemical composition to a spatial resolution of between 0.1 and 1 mm corresponding to an analysed
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volume of 1021 m3 to 1018 m3 (Cosslett and Duncumb (1956), Castaing (1960a,b), Marton (1969), Goldstein (1969), Beaman and Isasi (1972), Poole and Martin (1969), Martin and Poole (1971), Duncumb and Shields (1963), Reed (1975) and Duncumb (1966, 1979)). The principal features of these instruments are (i) an electron optical system forming an incident electron beam of between 0.1 and 1 mm diameter, (ii) a specimen translation stage, (iii) optical and electron optical imaging, (iv) X-ray detectors and (v) computers to control and process data. The success of the electron probe microanalyser in providing information on the chemical composition within the microstructure of bulk materials led Duncumb (1979), over 20 years ago, to mount an X-ray spectrometer on a transmission electron microscope to obtain from the same area of a thin foil specimen, chemical, structural and high resolution visual information. This idea of a combination of instrumentation has developed rapidly into the high resolution microanalytical scanning transmission electron microscopes currently available where electron beams with accelerating voltages between 100 and 400 keV can be focused down to 2 nm diameter on the specimen surface. These systems are discussed fully later in this chapter. These microanalytical techniques rely on efficient detection and discrimination of X-rays emitted from a specimen bombarded with high energy electrons (figures 2.6). The emitted X-radiation may be divided into two components: (a) characteristic X-rays related to the constituent elements and (b) continuous background X-radiation produced by electrons decelerated within the specimen. The characteristic X-rays emitted by a specific element may be identified from either wavelength, , or characteristic energy, E, since E ¼ hc=
ð6:21Þ
where h is the Planck constant and c is the velocity of light. Although this forms the basis of techniques which use characteristic X-rays for microanalysis, other less widely adopted methods require either a measure of the energy distribution of electrons which have interacted with the specimen or a quantitative evaluation of the lattice spacing using the high resolution lattice imaging. 6.3.2
Electron probe microanalyser
This instrument was the forerunner of all present day systems which combine electron optics and X-ray detection and remains in widespread use (Castaing (1954, 1960), Cosslett and Duncumb (1956), Goldstein (1969), Beaman and Isasi (1972), Poole and Martin (1969), Martin and Poole (1971), Duncumb and Shields (1963), Reed (1975), Duncumb (1979), Jacobs (1974) and Salter (1979)). The design of the electron probe microanalyser (EPMA) has to accommodate the low efficiency of X-ray production and, therefore,
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ðaÞ
Figure 6.20. Schematic diagram showing the main features of (a) an electron probe microanalyser and (b) the mini-lens (courtesy JEOL UK).
must collect a large fraction of the emitted X-rays (figure 6.20). The condenser lens system selected allows the electron beam current to be controlled over a wide range typically 1012 to 105 A. Moreover, modern instruments are provided with a liner tube that allows the pole pieces and deflection coils to be positioned outside the vacuum to ensure a clean vacuum system and thereby minimise contamination of the specimen analysed. To enable microanalysis and imaging to be carried out at the same working distance and to facilitate a large working space around the specimen for interfacing detectors, a mini-lens for the objective is used. The various designs of ‘mini-lenses’ all have a large magnetic field distribution coupled with a
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short spectrometer-to-specimen working distance and a minimum spherical aberration coefficient to ensure that a fine electron probe of high current density is produced. Moreover, the small-sized pole piece contributes to reducing the magnetic hysteresis, providing a stable optical axis. Various designs of commercial instruments have been produced to optimise X-ray yield which is further improved by using LaB6 or field emission electron sources in place of a tungsten thermal filament. The EPMA is fitted with a high quality light microscope to inspect the specimen and select the particular microstructural features to be investigated. The instrument is usually operated as a medium resolution, 10 nm, scanning electron microscope, enabling the specimen to be imaged using backscattered electrons, secondary electrons or specimen current. However, the emphasis in the design is placed upon the quality of the X-ray detection system. The specimen may be moved mechanically relative to the electron beam in the x, y (traverse) and z (height) directions using encoded motor stage drives. The electron beam is focused to 0.5 mm diameter on the specimen and scan coils deflect the beam either in a scanning raster or allow fine adjustment of the static probe position. The specimen stage also carries pure element standards. Most instruments have mechanical or computer based systems to enable the operator to pre-select microanalysis positions on both the specimen and the standards. Certainly, computer control reduces operator interaction to achieve compositional analysis from identified microstructural features. The magnitude of the angle at which X-rays are collected is an important parameter which becomes of increasing importance for low atomic number element microanalysis; it should be high to reduce the absorption path in a specimen (figure 6.21). Generally instruments have the maximum
Figure 6.21. Absorption path for X-rays emerging from a specimen.
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take-off angle consistent with overall performance and access of other electron and X-ray detector systems. The emergent X-rays are detected using both wavelength crystal and energy dispersive spectrometers. A typical combination is to have up to four wavelength- and one energy-dispersive spectrometer. The wavelength-dispersive spectrometers are usually linear focusing and contain exchangeable crystals, a slit which is variable to control the incident X-rays, and a detector. The combination of detectors is selected to allow a range of elements to be analysed simultaneously to reduce errors in the finally evaluated chemical composition of a particular feature. The spectrometers and microscope operate either within the same high vacuum or they are separated by X-ray transmissive windows. In addition to point counting on selected features, the X-ray output can be used to provide an image of the characteristic X-rays emitted from a particular element and this can be displayed on a cathode ray tube or captured digitally in the computer. As the electron beam is scanned in a raster over the specimen, the characteristic X-rays ‘map’ the distribution of the selected element. By simply changing the characteristic X-ray detected, distribution maps for each element present may be obtained and compared with the optical or electron image. The method of display has been extended to include digital scan generators to control the electron beam position and the information at each location is stored digitally in a computer memory. This can be displayed continuously on a video monitor, where a given image can have, for example, up to sixteen different intensity levels with each level corresponding to either a particular colour or grey scale level. 6.3.3
X-ray spectrometers
An important part of any microanalysis technique is the detection of characteristic X-rays emitted from the specimen (figure 6.22), using one of essentially three types of detector: (a) the wavelength dispersive crystal spectrometer, (b) the gas flow proportional counter and (c) the energy dispersive solid state spectrometer (Beaman and Isasi (1972), Jacobs (1974), Salter (1979) and Chandler (1977)). Each detector has advantages and limitations but may be used with any form of electron optical column provided certain geometrical conditions are satisfied. However, since these spectrometers are an essential feature of the EPMA it is appropriate to discuss these here. Wavelength dispersive crystal spectrometer When electrons interact with a specimen X-rays are produced. A narrow cone of emitted X-rays are detected by the wavelength dispersive spectrometer which contains a diffracting crystal of finite size (figure 6.22(a)) typically 25 mm 10 mm. The spectrometer crystal is curved and diffracts
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Figure 6.22. Wavelength dispersive crystal spectrometer: (a) collection of X-rays by spectrometer; generated X-rays have a range of wavelengths, , but only one is selectively diffracted to the detector; (b) the constant take-off angle and change of crystal and detector position required to retain a focused condition (courtesy Institute of Materials).
X-rays of selected wavelength, defined by the Bragg equation. Thus, from the lattice spacing of the diffracting crystal, d, and the angle of incidence, , the wavelength of the diffracted characteristic X-rays entering the spectrometer can be calculated. The crystal has to be rotated until a position of maximum intensity is obtained to identify the wavelength of the emitted characteristic X-rays. The detecting crystal, bent or ground to a given radius, focuses the diverging beam of X-rays emitted by the specimen at different points on the spectrometer (Rowland) circle. To maintain focus it is free to move as the angle of the crystal is changed relative to the direction of the X-ray beam (figure 6.22(b)). The range of wavelengths that an individual crystal can focus depends upon the angle through which it can be rotated. A crystal with a particular lattice spacing is selected to cover a range of a few tenths of a nanometre of wavelength, which corresponds to the characteristic X-rays emitted from a limited number of elements in the Periodic Table. Therefore spectrometers have to contain a number of crystals of different lattice spacing so that
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Table 6.4. Crystals used in wavelength dispersive spectrometers.
Crystal Lithium fluoride (LiF) Germanium (Ge) Sodium chloride (NaCl) Ethylene diamine tartrate (EDT) Pentaerythritol (PET) Ammonia dihydrogen phosphate (ADP) Ortho-phthalate potassium hydrogen (KAP) Ortho-phthalate rubidium hydrogen (RAP) Gypsum Stearate (STE) Laurate (LAU) Cerotate (CER) ML1 (W-Si multilayer) ML2 (Ni-C multilayer)
Diffracting planes ðhkl)
Wavelength range (nm)
Atomic number range for K radiation
200 111 200 020 001 101
0.1–0.38 0.11–0.60 0.09–0.53 0.14–0.83 0.14–0.83 0.18–1.03
19–35 16–34 16–37 14–22 14–22 12–21
001
0.34–2.5
11–14
001
0.2–1.8
11–14
020 – – – – –
0.26–1.5 2.5–8.5 4.0–13.5 2.5–11.9
11–14 5–8 6–9 4–7 4–7 4–7
the wavelength range covers as large a number of elements as possible. Crystals commonly used in wavelength dispersive spectrometers, together with the ranges of elements each cover, are listed in table 6.4. After selective diffraction, X-rays of a particular wavelength are collimated and pass to a detector, usually a proportional counter. The detector collimator slit is positioned perpendicular to the direction of the emitted X-rays at the focus point on the Rowland circle to eliminate scattered X-rays and electrons and improve the peak-to-background ratio and the wavelength resolution of the detected X-rays. Gas flow proportional counter A typical proportional counter comprises a gas-filled cylinder with an axial anode wire (figure 6.23). An X-ray photon entering the counter ionises a gas molecule, producing an electron–ion pair, and the anode attracts the electron. This electron gains sufficient energy to ionise other molecules and produce an avalanche of electrons travelling to the anode wire to give electrical pulses with an amplitude proportional to the energy of the X-ray photon. It is by this method that intensity of the characteristic X-ray beam emitted from the specimen, which is related to the concentration of the element analysed, is converted to a proportional number of electrical pulses. Such
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Figure 6.23. Gas-flow, proportional counter used as a detector with a crystal spectrometer.
gas-flow proportional counters (figure 6.23), are used to detect emitted characteristic X-rays directly by increasing the size of the detector to accept a greater solid angle of all characteristic X-rays emitted from the specimen. Since each X-ray generates a voltage pulse with an amplitude inversely proportional to the X-ray wavelength, several elements will produce a range of pulse amplitudes in the detector and these can be displayed simultaneously. Energy dispersive solid state spectrometer Fitzgerald et al (1968) were the first to describe the use of a solid state X-ray detector on an EPMA. Although these early detectors had poor resolution, this improved rapidly to the present stage where they meet the requirements for undertaking X-ray microanalysis. Indeed solid state, energy dispersive spectrometers overcome a limitation of wavelength dispersive spectrometers since they are able to detect and display simultaneously all the characteristic X-rays emitted from a specimen (Beaman and Isasi (1972), Jacobs (1974), Statham (1982) and Goodhew and Chescoe (1981)). The schematic arrangement for energy dispersive X-ray spectrometer systems is shown in figure 6.24. The X-rays emitted by the specimen pass into a standard spectrometer through a beryllium window where they are collected by a solid state detector. In most cases this detector is a silicon crystal, typically of an area about 300 mm2 , into which a layer of lithium has been diffused. This produces a semiconducting layer which is clamped between two metal electrodes and a bias voltage applied. X-rays that pass through the beryllium window produce electron–hole pairs in the semiconductor and the number of electron–hole pairs, N , is related to the X-ray energy, E, by N ¼ E=E1
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Figure 6.24. Energy dispersive spectrometer where the X-rays enter the detector via a thin Be window and produce electron–hole pairs within the semiconductor crystal. A typical energy spectrum obtained from a general area of a ferritic stainless steel is shown (courtesy Institute of Materials).
where E1 is the energy required to produce an electron–hole pair in the detector material; for silicon this is 3.8 eV. The detector will work efficiently if it is maintained at liquid nitrogen temperature, 77 K, and does not become contaminated with hydrocarbons from the vacuum system. It is for this reason that a beryllium window is placed between the specimen and the silicon detector. Unfortunately the window has the effect of preventing, or considerably reducing, X-rays of certain energies from reaching the detector. This effectively limits this design of spectrometer to detecting X-rays produced from elements of atomic number greater than 11. However, for electron optical instruments with better vacuums designs of solid state spectrometers exist where the window is either replaced by a Mylar ‘thin’ window or removed altogether, thereby increasing the range of elements that can be detected to include the important low atomic number elements carbon, oxygen and nitrogen. The electron–hole pairs created in the silicon drift to the bias plates cause a current to be produced in the semiconducting detector, which incorporates a dead layer, which is then amplified before passing into a
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multichannel analyser, where it is operated on by the data system to produce a spectrum of counts as a function of energy. A typical spectrum is reproduced as figure 6.24. This has been recorded from a ferritic stainless steel and displays X-ray intensity as a function of X-ray energy over the range 0–10 keV showing peaks from the major alloying elements, chromium, iron and nickel, in the 5–8 keV region. The latter three elements each produce peaks from the K and K transitions with an intensity ratio between the K and K of approximately 7 : 1. Often overlapping peaks occur and in this example the chromium K peak coincides with the manganese K peak position. However, with modern data systems it is possible to deconvolute the relative contributions for each element. A new class of energy dispersive detectors have become available, referred to as silicon-drift detectors (Struder et al (1999)). These use sideward depletion of a thin silicon crystal 300 nm thick to which is applied an electric field parallel to the detector surface. These spectrometers can operate at temperatures of about 250 K so that cooling can be achieved using a Peltier electrical system. These have the advantage of a shorter pulse shaping time and a much larger active area of up to 50 mm2 . Despite the higher operating temperatures a resolution of about 140 eV can be achieved with count rates of 3 105 s1 . The relative performance of wavelength and energy dispersive spectrometers Table 6.5 compares the capabilities of wavelength and energy dispersive spectrometers. However, before proceeding there are three factors related to spectrometer performance that require further discussion: (i) resolution, (ii) efficiency and (iii) sensitivity. Resolution The natural energy width of an X-ray peak is of the order of 2 eV measured at half the maximum of the peak intensity (FWHM). It is essential that a spectrometer discriminates between characteristic X-ray peaks with similar wavelengths or energies and in this respect the wavelength dispersive spectrometer is superior to the energy dispersive spectrometer by about an order of magnitude. The measured peak width from an energy dispersive spectrometer is 150 eV for Mn K or 2.5% of the peak energy compared with 2.3 eV which is about 0.039% of the peak energy for the wavelength dispersive spectrometer. This degradation in width has been described by Goldstein and colleagues (1984) as a combination of a statistical distribution in the final number of charge carriers created by capturing photons of a single energy due to the discrete nature of the counting process and an uncertainty introduced by the thermal noise in the amplification process. The distribution of the number of charge carriers by a single photon energy is reasonably described by a Gaussian distribution where the
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Table 6.5. Relative strengths and weaknesses of solid state detectors and crystal spectrometers based on Chandler (1977) and Flewitt and Wild (1985). Energy dispersive spectrometer Strengths No X-ray focusing required.
Wavelength-dispersive crystal
High resolution: good spatial separation of X-ray lines.
High sensitivity: high solid angle possible with up to 100% detector efficiency.
Quantification: a small dead-time, X-ray count proportional to elemental content, therefore good for trace elements.
No diffraction interference from higher order peaks.
Good peak-to-background ratio: gives high sensitivity for trace elements.
Simple mechanical design. High count rate detectability allows smaller Sensitive to low atomic number elements electron probes and less specimen damage. with suitable choice of crystals. Complete elemental spectrum displayed, rapid qualitative analysis and no error from specimen or instrumental changes. Weaknesses Inferior energy resolution.
Mechanical system introducing possible errors between measurements.
Operates at cryogenic temperatures (77 K). Occasional compromise necessary in electron-optical system.
One element at a time analysed; need for multiple spectrometers.
Need to isolate the crystal detector using a Be window which absorbs low energy emissions, with high vacuum and window-less detector, poor sensitivity for low atomic number elements.
Possible interference from high order diffraction lines. Peak and background must be measured separately.
Non-discriminating to X-ray sources, stray signals from remote areas, high background. Quantification: poor accuracy at very low concentrations.
FWHM can be calculated by quadrature addition of the two sources of noise: FWHM / ðC12 E þ N22 Þ1=2
ð6:23Þ
where C1 is the uncertainty in the formation of a charge carrier given by C1 ¼ 2:35(F E)1=2 , F is the Fano constant, E the energy and N2 is the
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Figure 6.25. (a) Si(Li) energy resolution, including intrinsic and electronic noise effects as a function of energy (adapted from Woldseth (1973)). (b) Redistribution of peak counts for Mn K with 150 eV resolution peak (reproduced by permission of JEOL UK Ltd).
FWHM of the electronic noise of amplification. Figure 6.25 provides values calculated by Woldseth (1973) of the observed FWHM as a function of energy for different contributions of electronic noise together with a typical Mn K peak with 150 eV resolution. Even if the noise were totally eliminated, the theoretical energy resolution limit still exceeds 100 eV for Fe K at 6.4 keV. Figure 6.26(a) shows a spectrum obtained from flakes of MoS2 in an electron probe microanalyser at 30 keV with an electron beam of 1 mm diameter using a PET crystal in a wavelength dispersive spectrometer, (table 6.4). The S K peak ( ¼ 0.5373 nm) is resolved even though separated by a wavelength difference of only 0.0034 nm from the Mo L peak ð ¼ 0.5407 nm). By comparison the X-ray energy dispersive spectrum (figure 6.26(b)) is unresolved since the characteristic energy peaks for S K (E ¼ 2:307 keV) and Mo L (E ¼ 2:293 keV) are separated by only 0.014 keV. However, if the energy range selected for the total spectrum is sufficient then both the Mo K and the Mo L peaks can be interrogated, confirming the presence of molybdenum. As a consequence of the relatively poor energy resolution ð150 eV for Mn K ) use of energy dispersive spectrometers for microanalysis of certain specimens, particularly if they contain transition elements, can be open to misinterpretation. An example of this is for steels where the commonly occurring elements of chromium and manganese can be unresolved. To overcome these disadvantages it is necessary to adopt sophisticated computer-based deconvolution procedures (Reed (1975)). Efficiency Detection efficiency, defined as the ratio of X-rays counted to those collected, depends upon the X-ray energy. Over a significant range of X-ray energies
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Figure 6.26. Flake of Mo2 S examined in an electron microprobe analyser at 30 keV: (a) wavelength-dispersive spectrum; (b) energy-dispersive spectrum showing the Mo K peak in addition to Mo L peak.
3150 keV, for the energy dispersive spectrometer this is almost 100%. However, at lower energies, absorption of X-rays by the beryllium window, the gold contact layer and the p-type silicon dead layer sets a practical lower value of 1 keV (figure 6.24). This restricts microanalysis to those elements with atomic numbers greater than about eleven. Spectra can be obtained from the important elements below this, such as oxygen,
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nitrogen and carbon, using windowless spectrometers, but poor counting statistics limit accuracy and minimise the detection limit. By comparison, a wavelength dispersive crystal spectrometer is not subject to the same restrictions and by correct selection of crystals all elements can be detected and evaluated (table 6.4). Sensitivity The sensitivity of energy dispersive spectrometers relative to wavelength dispersive spectrometers depends upon the characteristics of each X-ray optical system, the analysis conditions selected and the type of specimen. The design of the energy dispersive spectrometer allows it to be positioned close to the specimen and there is an associated increase in the solid angle for X-ray collection and thereby the X-ray count rate. This enables a lower electron signal to be used to produce the same magnitude characteristic Xray signal and this allows analysis from smaller volumes of material with the related advantages of reduced specimen damage and increased spatial resolution. Unfortunately, simply using a faster counting rate does not necessarily increase the sensitivity of mass detection, which depends upon the integrated number of X-ray counts within the measured peak compared with those in the attendant background.
6.3.4
Specimen preparation
The condition of the specimen surface is of prime importance in EPMA because this technique is essentially a surface analysis. The preparation of the specimen presents several potential problems: (a) embedding of polishing compounds, (b) the removal of second phase material, (c) the development of relief, (d) the rounding of edges during lapping, (e) surface smearing, (f ) nonflat surfaces and (g), closely related to (f ) scratches. Metallographic preparation procedures are used for both the specimen to be analysed and the pure element comparison standards (Goldstein (1969) and Beaman and Isasi (1972)); the specimen has to be flat with no rounding of the edges to ensure geometry is retained. Light etching may be necessary to remove mechanically flowed surface layers for some materials (section 3.2) and this has advantages when locating particular microstructural features under the optical microscope. However, etching can produce surface films which introduce misleading results, so the use of ‘film forming’ etchants should be avoided. Surface roughness, whether caused by residual scratches, porosity or ‘excessive’ etching, can modify the characteristic X-ray yield and introduce errors into quantitative chemical analyses. Similar problems arise if contamination forms on the specimen surface during the period the microanalysis is undertaken in the EPMA. Such contamination by hydrocarbon molecules from within the vacuum
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system is particularly disconcerting when attempting carbon analysis, and can be minimised by using a cold-finger maintained at 77 K to condense vacuum products. Specimens with low electrical/thermal conductivity have to be coated with a conducting medium which may introduce analytical errors. These problems can be reduced by minimising the coating thickness and selecting a coating material with an X-ray emission characteristic that does not interfere with the X-ray spectrum of interest. For many materials, evaporated films of copper, gold, aluminium and carbon of between 10 and 20 nm thickness are appropriate. 6.3.5
Spatial resolution
The interaction of the incident electron beam with the bulk specimen effects scattering that defines the resolution of the microanalysis. In chapter 2 and later in this chapter we show that this scattering can be described experimentally, analytically and by Monte Carlo calculations (figure 6.27). The magnitude of the scattering depends upon the mean atomic number of the phase to be analysed and the incident electron beam conditions. Figure 6.27 shows a Monte Carlo calculation of the electron trajectories and the corresponding X-ray excitations. It must be remembered that there is a minimum energy or excitation potential to effect K, L and M X-ray spectra and this increases with atomic number. For a given element the excitation potential increases on passing from M to L to K lines. The intensity, I, of a characteristic X-ray emission by the electron beam increases with both beam current, i, and the over-voltage: the amount by which the voltage, V0 , of the incident electrons exceeds the critical value for excitation VE . This intensity, I, is given by Jonssan (1927) as I ¼ iC ðV0 VE Þn
ð6:24Þ
where C is a constant dependent upon atomic number and X-ray spectra series and n is approximately 1.67 for V=VE 3; as voltage increases, n tends to unity. The intensity I of the continuous background emission at wavelengths between 0.1 and 0.128 nm is approximately (Kulenkampff (1922)) I ¼ ðZ=2 ÞðaV b=Þ þ ðNx Z2 =2 Þ
ð6:25Þ
where a, b and Nx are constants and Z is the mean atomic number for the specimen. Thus the background intensity at a fixed value of and Z is directly proportional to the electron beam voltage and it is desirable to operate the EPMA with a large over-voltage to increase peak-to-background ratio. However, since over-voltage increases electron penetration into the specimen and correspondingly reduces spatial resolution, operating conditions are selected for 2<(V=VE )<5. Mulvey (1967) shows that the
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312 Electron sources Figure 6.27. Monte Carlo simulated interaction of a 0.2 mm diameter beam with a hypothetical 1 mm diameter hemispherical TaC inclusion in a NiCr matrix. (a) Electron trajectories, 15 keV; (b) electron trajectories, 30 keV; (c) Ta M X-rays at 30 keV (reproduced by permission of Plenum Press).
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theoretical maximum electron probe current im is 8=3
2=3
im ¼ ð32 =16Þi ½eV=kTðBD =Cs Þ
ð6:26Þ
where i is electron source brightness, V is the applied voltage, kT is the thermal energy of the electron, BD the diameter of the incident electron beam and Cs the spherical aberration coefficient. The maximum useful count rate for energy dispersive spectrometer systems operating at about optimum resolution is approximately 2 to 3 103 c s1 over the entire energy range whereas for wavelength dispersive spectrometers set to a specific element, count rates in excess of 5 104 c s1 can be accepted without a loss of resolution. Thus it is important to select an electron probe of a size to optimise the overall analysis. Using a heated tungsten filament, the probe current varies as (beam diameter)8=3 (equation (6.26)), so that at 20 keV incident electron beams of diameter 0.2 to 2 mm produce a current which is typically in the range 1010 to 106 A. Thus it is important to select the electron beam conditions to optimise the currents received by the detector and that depends upon the type of detector used. For the bulk specimens used in the EPMA, spectral resolution of the chemical analysis does not improve for electron beams of diameter of much less than 1 mm, since the volume of X-ray production is controlled by electron scattering and penetration rather than probe size (figure 6.27). Here the electron trajectories and the region of X-ray production at the high voltage exceeds 1 mm or four times the incident probe diameter. In such cases, the analysis can be optimised by increasing the electron beam current to 10 nA and using wavelength dispersive spectrometers, where the benefit of the higher count rate and energy resolution is invoked. 6.3.6
Spectrum treatment
One of the more difficult steps, particularly for the lower resolution energy dispersive spectrometers, is the separation of characteristic peaks within the spectrum from the background. This is essential to quantify the peak intensity and the Bremsstrahlung radiation from the specimen. Goodhew and Chescoe (1981) summarised the factors that affect the measurement of these parameters (figure 6.28), which are discussed fully by Reed (1975). Statham (1976, 1977) has reviewed the techniques available for spectrum treatment and points to the important fact that there is no need to use a technique more sophisticated than that which gives an error of similar magnitude to the statistical uncertainty in the data. There are spurious peaks in energy dispersive spectra, including silicon escape peaks at an energy of 1740 eV below each major peak, sum peaks at an energy equal to the addition of two major peaks and system peaks derived from the specimen holder and/or the instrument (figure 6.28). These particular peaks can be considered by processing in the computer
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Figure 6.28. Energy dispersive spectra characteristics. (a) Spurious peak: (i) sum peaks (S) corresponding to Al þ Al, Al þ Si and Si þ Si together with an escape peak (E) from Fe K and copper peaks from the system; (b) three main types of peak overlap, small amounts of Na in presence of Mg, Mo L in presence of S K and Mn in presence of Fe and Cr; (c) Characteristic background where in addition the shape may be noisy and contain absorption edges contribution to major peaks (after Goodhew and Chescoe (1981)) (reproduced by permission of Pergamon Press).
software or can be minimised by the design of the instrument. Specifically for energy dispersive analysis, peak overlap occurs for the transition elements where, for example, the K peak of each element overlaps almost completely with the K peak of the element below. A further problem is encountered when the K peak of a lighter element almost coincides with
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the L peak of a heavier element. The background which has to be subtracted from each peak to give the characteristic intensity is nonlinear and the statistical scatter from the small number of counts in each channel of the spectrum makes it difficult to quantify to the required accuracy. However, commercial electron microprobe analysis systems usually have software packages to undertake the deconvolution of peaks to a greater or lesser degree of accuracy. 6.3.7
Quantitative analysis
To achieve a quantitative X-ray microanalysis the measured X-ray intensities have to be converted into weight percentages for the elements of concern (Beaman and Isasi (1972), Martin and Poole (1971), Duncumb (1979), Ziebold and Ogilvie (1964), Sweatman and Long (1969), Scott (1974), Reed (1974) and Haworth (1979)). Essentially two approaches can be adopted, one based on homogeneous standards of known composition relating to the alloy system to be measured and the other, a theoretical approach, based on pure element standards and calculated corrections. Each depends upon a comparison between the intensity, IA , of characteristic X-rays emitted from an element A within the specimen and the intensity from 0 , where the a pure element, or well characterised compound standard, IðAÞ prime indicates the measured intensity of X-radiation. The weight fraction is established by calculating the number of X-ray quanta produced per electron using an approximate proportional relationship between the intensity ratio and the weight fraction, CA , for an element A: 0 ¼ ðZAFÞCA IA =IðAÞ
ð6:27Þ
where Z is the atomic number, A is the absorption and F the fluorescence correction. A similar relationship is valid for each element present. An alternative approach particularly suited to microanalysis using an energy dispersive spectrometer, where all wavelengths are measured instantaneously, depends upon measurement of the ratios IA : IB : IC for all elements present. Here it is assumed that the measured concentrations sum to a known value, usually 100%, and for this it is necessary to calibrate the system for excitation and detection efficiency in addition to the ZAF correction. However, the overall accuracy for this method is less when the ratio K is measured for each element. Irrespective of the method used to calculate the composition, CA , the accuracy ultimately depends upon correct measurement of the emitted X-ray intensity. Thus it becomes necessary to accommodate background X-radiation, nonlinear response in the measuring system, e.g. dead-time losses and other sources of error. Figure 6.29 shows an X-ray peak containing Np counts with a background of Nb counts. When the number of counts in a peak is large relative to the background the counting error, SN is equal to (Np )1=2 .
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Figure 6.29. Schematic diagram defining the X-ray counts in the characteristic peak and in the associated background.
Since this error is independent of counting time it is beneficial to record a fixed number of counts, rather than operate for a fixed microanalysis period. In a series of n trial runs the standard error, I , is defined by X ðxi xÞ2 =ðn 1Þ ð6:28Þ 2i ¼ i
If exceeds N an experimental error exists which could arise from, for example, drift in the counter voltage. If the background count Nb is a significant proportion of the total then the standard counting error is N ¼ ðNp þ Nb Þ1=2 =ðNp Nb Þ:
ð6:29Þ
For small concentrations such as trace impurities, Np tends to Nb and therefore it is necessary to establish Nb accurately to minimise errors, and various procedures are adopted to ensure that contributions to Nb are evaluated correctly. In the theoretical procedure for calculating the elemental composition based on pure standards it is necessary to calculate corrections for the atomic number Z, the absorption A, and fluorescence F. Atomic number The number of K shell ionisation events which occur per electron for an element A in a two component system, AB, over part of the electron path, dx, is dnK ¼ fðQK N0 XAÞ=ZA g dx
ð6:30Þ
where QK is the ionisation cross-section for K radiation from the element A, N0 is the Avogadro number, is the density, ZA is the atomic weight and X is
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the mass concentration of element A. Ionisation occurs in the energy range E0 to Ec where E0 is the incident electron energy and Ec the minimum excitation energy. The total number of ionisation events per electron for component A is given by ð Ec ð QK =ðdE=dxÞÞ dE ð6:31Þ nK ¼ ðN0 X=ZA Þ E0
where dE/dx is the loss of energy per unit path length. The stopping power determining the depth of penetration of electrons into the specimen, S , is given by 1 (dE/dx). The ratio for intensities of K radiation generated by element A in an alloy and a pure element standard gives the atomic number correction Z: ð E0 ð E0 ðQE =SAB dEÞ= RA ðQk =SAB dE : ð6:32Þ Z ¼ RAB Ex
Ex
The numerator describes the production of characteristic X-rays from element A in the specimen and the denominator the production of these Xrays from the standard. Thus, the correction factor for each element analysed may be calculated. Values for R, the backscattered loss factor, lie in the range 0.5 to 1.0 and tend to unity as the atomic number decreases and the accelerating voltage approaches the ionisation potential. Absorption correction The absorption correction has been expressed in the analytical form (Philibert (1963)) ð6:33Þ AX ¼ ð1 þ hÞ½ð1 þ =Þð1 þ hi ð1 þ =ÞÞ1 P P 2 where h ¼ 1:2 ai ZA =ð di Zi Þ , a is the atomic concentration, ZA the atomic weight and Z the atomic number, ¼ ð = )A þ B þ þ i cosec ð is the take-off angle), is the linear absorption coefficient, is the density and is the cross-section for electron absorption given by Duncumb and Shields (1963) as ¼ 2:39 105 =ðE01:5 Ec1:5 Þ
ð6:34Þ
where E0 and Ec are defined above. The success of this and other absorption corrections has been reviewed by Poole and Thomas (1961–2); current values for absorption coefficients are tabulated by Heinrich (1972). For elements with atomic numbers of less than 11 and when detecting longer wavelengths, these data are less reliable and measurements due to Henke et al (1967) provide better results, whilst for boron, carbon, nitrogen and oxygen data by Ruste and Gantois (1975), Love et al (1974) and Love and Scott (1987) are more appropriate.
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Fluorescence correction A fluorescence correction is necessary when either the characteristic Xradiation or part of the continuous spectrum excited by the electron beam from one species of atom is sufficient to excite a characteristic emission from a second series. A fluorescence correction has been derived for K lines excited by K lines which gives an intensity ratio, If =IA , of the fluorescent intensity, If , to that of the primary radiation, IA . These intensities are corrected for absorption on emerging from the specimen (Reed (1974)): If =IA ¼ XB ½0:5WKB ððrA 1Þ=rA ÞðAA =AB ÞðA =B Þð AB = BB Þ
ð6:35Þ
where ¼ ½lnðð1 þ uÞ=uÞ þ lnðð1 þ yÞ=yÞ, XB is the weight fraction of element B, WKB is the K shell fluorescent yield of element B, rA is the K absorption edge jump ratio of element A, A and B are the wavelengths of the absorption edges of elements A and B, B is the mass absorption coefficient element A for K X-radiation from B which is equivalent to the linear absorption coefficient divided by the density, and B is the mass absorption coefficient of elements B for K radiation from element B. u and y are given by u ¼ ð A = B Þ cosec y ¼ = B
ð6:36Þ ð6:37Þ
Various modifications to equation (6.37) have been proposed by Reed (1974) to allow for multicomponent systems and K and L radiations but essentially the form remains the same. ZAF correction For current generation electron probe microanalysis systems the complete correction to achieve a quantitative analysis is referred to as ZAF correction. This is usually carried out online with the instrument using small computers, and a range of software is available and developments have been made to accommodate all significant elements in the analysed specimen into these programs. These computer controlled systems reduce operator time and effort by enabling control of the instrument as well as providing a means of storing and processing the acquired data. The specimen stage is usually controlled together with the wavelength and energy dispersive spectrometers. To maintain correct microanalysis conditions, there is monitoring and regulation of the electron beam current and accelerating voltage together with the counter and timer system to allow reproducible results to be achieved. An empirical method developed by Ziebold and Ogilvie (1964) uses specimens of a known composition to establish a calibration curve given by the hyperbolic relationship: ð1 KA Þ=KA ¼ aA ð1 XA Þ=XA
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ð6:38Þ
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or XA =KA ¼ CA þ ð1 CA ÞXA : A linear relationship is established between XA =KA and XA for binary alloy systems so that the factor CA is a constant established from a regression fit to a series of experimental analyses of standard alloys. An extension of the procedure to a multicomponent system is possible if it is assumed that CA is a weighted mean of C-values corresponding to each of the n elements present in the specimen. This has the general form X CA ¼ CA Xi =ð1 XA Þ ð6:39Þ Unfortunately this technique is often limited by a lack of availability of suitable standard alloys. 6.3.8
Light element analysis
For many materials that are to be examined in the EPMA a knowledge of the lighter elements, atomic number less than 11, is often extremely important. Recently progress has been made in extending the range of the EPMA to elements below sodium in the Periodic Table where the principal problems are related to the long wavelength of the characteristic X-ray emission, which leads to absorption losses in the detector windows and energy discrimination limitations. Moreover, there is a high level of absorption experienced by soft <1 keV X-rays in the specimen together with interaction with the multiplicity of L and M lines from heavier elements that interfere with the X-ray peak of interest (Heinrich (1972)). To accommodate these difficulties various procedures have been evolved to enable correction and quantification. Indeed Love et al (1974) appraised a series of procedures, examined the construction of the models, and provide guidance on the suitability of their application. More recently however, Love and Scott (1987) have described how improved instrumentation and developments in wavelength dispersive spectrometers assist quantitative analysis of these elements (Philibert (1963), Spiller (1981), Henke (1981), Nicolosi and Jenkins (1983) and Nicolosi et al (1986)). Conventionally, salts of phthalic acid, KAP, RAP and TAP, with an interplanar spacing, 2d, of about 2.6 nm (table 6.4) are used to analyse the K radiation from N, F and O. However, for lower energies, pseudo-crystals are used which comprise layers of heavy metal cations separated by chains of organic acid, where the cations provide the diffracting layer and the size of the organic chain controls the interplanar spacing. Of these, the most widely used is lead stearate with an interplanar spacing equal to 10 nm, although lead laurate and melessate (7 and 16 nm respectively) are also used. However, multilayer devices are now available that consist of alternate layers of high and low atomic number elements deposited by sputtering on to
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Table 6.6. Minimum detectable limits in wt% with different analysing crystals. X-ray
Specimen
TAP
Pb laurate
Pb stearate
ML1
ML2
CK NK OK
SiC Si3 N4 Al2 O3
– – 0.019
0.04 0.07 0.015
0.025 0.075 0.017
0.03 0.03 0.005
0.009 0.095 0.008
a smooth substrate. The diffraction efficiency for these is optimised by appropriate selection of the deposited elements and essentially any desired interplanar spacing can be achieved. Moreover, they are robust and the diffraction efficiency does not degrade with time. Typical multilayers are a tungsten silicon combination (ML1) with 2d equal to 6.09 nm and a nickel carbon multilayer (ML2) with 2d equal to 9.32 nm which are used mainly for nitrogen and carbon respectively (table 6.4). In table 6.6 we show the minimum detectable limits calculated by Love and Scott (1987) for carbon, nitrogen and oxygen from measurements in SiC, Si3 N4 and Al2 O3 for these multilayer systems compared with more conventional crystals. These multilayer devices show significant improvements in detection sensitivity over the more conventional crystals. Although the resolution achieved from these multilayers is still insufficient for chemical bonding studies, it is adequate for quantitative analysis. 6.3.9
Applications
The applications of the electron microprobe microanalysis are wide-ranging and information obtained divides into two broad categories: (a) qualitative analysis usually presented as X-ray maps which allow the spatial relationship of the elemental distribution to be compared with that of the microstructure and (b) quantitative analysis where point counts are retrieved from predefined positions within the microstructure. Indeed it is the computing power of the current generation instruments that provides hardware and specimen stage control as a prerequisite for mapping large areas of specimen and this is supported by the appropriate software for the data manipulation. Technological advances in recent years have exploited grey level contrast differences between different parts of the image permit quantification and classification of features within it; this is discussed more fully in chapter 8. Morever, the computing power is now such that full quantitative analysis of selected locations can be undertaken online. Figure 6.30(a) shows a backscattered electron image of a section of a boiler furnace tube fabricated from a nominal 214%Cr–1%Mo low alloy ferritic steel. This image shows the bore of the tube covered by an oxide layer following a period of service. Microanalysis of these bore deposits was carried out using a commercially available instrument fitted with four
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Figure 6.30. (a) Backscattered electron image of bore deposits in a boiler division wall tube (Chastell (1990)); (b) Wavelength dispersive microanalysis in the EPMA showing the concentrations of Fe, P, Mn, Ni, Cu, Zn and Ca in bore deposits; accelerating voltage of 15 keV and an electron beam current of 0.05 mA (courtesy D Chastell).
wavelength dispersive spectrometers and an energy dispersive spectrometer. Figure 6.30(b) shows the results of a wavelength dispersive analysis of the area, giving the distribution of the elements within the bore deposit. This reveals elements within the protective magnetite layer that arise from contamination by the boiler water. The effect of these deposits is to reduce the heat transfer coefficient which can lead to significant overheating problems and on-load corrosion. The convenience and speed of use of the energy dispersive spectrometer makes it an ideal technique for the semi-quantitative analysis of different areas on an uneven specimen. Figure 6.31 is a typical example showing how the technique is applied to an Inconel 800 alloy oxidised at a high temperature of 1070 K where, on cooling, stresses in the system cause the
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Figure 6.31. Compositions of oxides and metal in an Inconel 800 alloy annealed and oxidised at a temperature of 1070 K obtained using an energy dispersive spectrometer (reproduced by permission of JEOL UK Ltd).
oxide to spall from the substrate. Point analyses have been obtained from five different regions and the energy dispersive spectrum is reproduced for each point and compared with the secondary electron image. Clearly the outer oxide is rich in chromium and titanium, below which is a chromium oxide, and a nickel-rich layer is encountered below this. At the base all elements from the alloy are detected, but there is an additional large peak from aluminium indicating the presence of an aluminium oxide. Since the discovery of new high-superconducting-temperature oxides, considerable effort has been devoted to identifying the superconducting phases (Bednortz and Muller (1986)). An example is described by Takahashi et al (1989a,b) where electron probe microanalysis has been used to identify
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Figure 6.32. A backscattered electron composition contrast image and the corresponding X-ray images for Ba L , Y L , Cu K and O K of a Y–Ba–Cu–O superconducting specimen (Takahashi et al (1989b)) (reproduced by permission of JEOL UK Ltd).
and establish the distribution of the superconducting phase in Y–Ba–Cu–O specimens. Here, the Cu–O bond is known to be an important superconducting parameter to characterise, and this can be examined with respect to peak shape and position. Figure 6.32 shows the backscattered electron image which contains composition, atomic number contrast, together with elemental distribution maps for Ba–L , Y–L , Cu–K and O–K for the Y–Ba–Cu– O specimens. The darker areas in the backscattered image correspond with the Cu and O rich phase, whereas the lighter areas show a homogeneous distribution of Ba, Y, Cr and O and this is the superconducting phase. By comparison it is possible to establish information regarding the chemical bond from a given oxygen wavelength dispersive intensity profile
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Figure 6.33. A comparison of the O K peaks obtained using a TAP crystal [10 keV, 0.07 A] from (a) Cu2 O, (b) CuO and (c) Y–Ba–Cu–O superconducting material showing that the bonding in the light phase (figure 6.31 is CuO(G) and the dark phase (M) is YBa2 Cu3 O67 (Takahashi (1989b)) (reproduced by permission of JEOL UK Ltd).
so that the chemical form of the oxides may be classified as A2 O, AO, A2 O3 etc. (Takahashi et al (1989b)). Figures 6.33(a) and (b) show the O K peak profiles obtained from Cu2 O and CuO and these are compared with that obtained from Y–Ba–Cu–O. This latter oxygen profile matches closely with that obtained in figure 6.33(b) for CuO. Moreover, the peak obtained from the lighter phase in figure 6.32 corresponds with the peak shape and position of the perovskite structure so that this particular phase is probably YBa2 Cu3 O67 . These applications show that the EPMA is not simply an instrument for obtaining a chemical analysis from a very small volume of specimen. Advances in the technology, coupled with the interfacing with a computer, have resulted in a very flexible, highly automated instrument with the ability to manipulate the data and present formats that provide more interpreted information than simple X-ray images or point analyses.
6.4 6.4.1
Transmission electron microscopy Introduction
One of the most powerful instruments for investigating the microstructure of materials is the transmission electron microscope. This enables the fine-scale microstructure to the nanoscale to be examined in specimens sufficiently thin
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to facilitate transmission of a beam of electrons without a great loss of intensity. The maximum transmittable thickness depends upon the atomic number of the material, but typically this thickness lies in the range 250–500 nm. However, the higher the electron energy, the better the transmission through the specimen and this has led to the construction of instruments with accelerating voltages in the range 100 keV to 3 MeV (Loretto et al (1988), Williams et al (1999) and Vincent and Cherns (1988)). However, it is necessary to optimise the information retrieved with respect to the size, complexity and cost of the instruments and this has resulted in current generation instruments of major use having accelerating voltages that lie in the range 120–400 keV. These allow observations down to atomic level and, in addition, many instruments have the capability to undertake analysis, both physical and chemical, on micro-areas of the specimen so that in section 6.5 of this chapter we address the extension of the transmission electron microscope, the scanning transmission electron microscope and the associated ability to undertake chemical analysis. Indeed, some of the distinctions between instruments are now becoming somewhat arbitrary, since, for example, many of the commercially available instruments are designed to operate in either the conventional or scanning modes. Although with the earlier designs of instruments in these categories the compromise to achieve both operating modes introduced limitations to the performance, this is becoming a less obvious restriction. Despite this, there remains a need for some dedicated instruments with maximum performance in specific areas of work. 6.4.2
Transmission electron microscope
The main features of a conventional transmission electron microscope are shown in figure 6.34 and, by comparison, it is obvious that many aspects are common with the SEM. The evacuated column contains the electron source, usually a tungsten filament or LaB6 crystal, together with an assembly of condenser, objective and projector lenses (Agar (1973), Orloff (1989) and Cosslett (1970)). Although the conditions for electron sources, set out in chapters 2 and 4, apply to the transmission electron microscope, for high and ultra-high resolutions, <0.5 nm, the field emission or extended Schottky emission cathodes are preferred. Orloff (1989) has reviewed the properties of various emission cathodes and considers that the performance of the thermal field emission cathode compares unfavourably with both the cold and extended Schottky emission cathodes because of the associated noise; these cathodes are preferred electron sources for ultra-high resolution instruments. The design of current generation instruments gives particular attention to producing a clean, high-vacuum system using, in many cases, ion pumps to minimise specimen contamination. The instrument shown in figure 6.34(a) has a five-lens illumination system and there is a trend to
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Figure 6.34. Schematic diagram of a typical transmission electron microscope (courtesy JEOL UK Ltd).
increasing the number of lenses to optimise the overall performance of the instrument and maximise the flexibility and ease of operation by, for example, eliminating image rotation with increasing magnification. On leaving the source, electrons are formed into a crossover and this demagnified source image is projected on to the specimen by two condenser lenses. The first condenser forms a demagnified image of about 1 mm diameter, that is projected on to the specimen by a second condenser lens with a magnification
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Figure 6.34. (b) The corresponding ray diagram. The double condenser system is shown in detail. The beam divergence 2 and the spot size are controlled by varying the strength of the condenser lens C2 . The maximum value of 2 is D=L obtained when the beam source is imaged on the specimen. The advantage of a double condenser is that it produces a small spot size (reproduced by permission of JEOL UK Ltd).
of about two. The final illumination spot on the specimen is typically as small as 2 mm, which is sufficient to fill the viewing screen at the highest magnifications. The current density of the electron beam incident on the specimen depends upon filament characteristics and the divergence angle (Grundy and Jones (1976) and Gronsky (1980)). Typically the condenser aperture and the operating divergence angle would be 400 mm diameter and 103 rad respectively for a 100 keV instrument. This second lens gives both fine control over the area illuminated, to minimise contamination to neighbouring areas, and a beam of low divergence for an equivalent amount of defocusing. A smaller value of reduces the effective electron source size and increases the coherence length of the beam, which increases the contrast and resolution of the images and diffraction patterns. On passing through a thin foil specimen, the electrons enter the objective lens whose design and aberrations critically affect the performance of the microscope. The coherent Bragg diffracted beams leaving the specimen form an
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intermediate low magnification image I1 (figure 6.34(b)). The intermediate lens produces a second intermediate image I2 which is magnified at the viewing screen by the final projector lens. The viewing screen comprises a metal plate coated with a zinc phosphor which scintillates when interacting with the electrons. The image is focused at the screen by varying the focal length of the objective lens, and the magnification is changed by altering the excitation of the two projector lenses. Some instruments have an additional projector lens to extend the magnification range. The image is recorded using a photographic camera or a digitised recording system located below the viewing chamber. Specimens, in the form of 3 mm diameter discs, are introduced into the microscope chamber via an airlock and the specimen stage affords x and y together with z movement. The latter is necessary for effective use of fully eucentric goniometer stages which allow specimens to be tilted without image movement, defocusing or a change in magnification. This form of operation is essential to allow the correct imaging modes to be established and the images interrogated. Computers control, display and evaluate the information produced by these microscopes. Modern instruments allow the operating conditions to be displayed, including the operating mode, accelerating voltage, beam size, magnification, etc. Moreover, there is often provision for self-diagnosis of the status, a convenient function for the maintenance and servicing of the instrument (see chapter 5). 6.4.3
Theory of image formation
One of the important properties of a lens is that it forms a Fraunhofer diffraction pattern of an object at a finite distance (chapter 4). Using, for convenience, a ray diagram to indicate the wave optical process, as described in chapter 4, the mathematical description of image formation for transmission electron microscopy is compared in figure 6.35. From Abbe´’s theory the diffraction pattern in the back focal plane of the objective lens maps the Fourier transform of the specimen. The maximum image information is
Figure 6.35. Comparison of the ray diagram and the mathematical description of the image formation process (courtesy Institute of Materials).
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obtained by an inverse Fourier transform which occurs where diffraction patterns fall within the imaging aperture; this is achieved only for a perfect objective lens of infinite aperture. Electron optical instruments introduce modifications to the amplitude and phase because of the finite aperture size and lens aberrations of the intensity distribution in the back focal plane. The phase distortion of a beam located at q from the optical axis is described by Xq ¼ ðCs 4 q4 þ z0 ð22 q2 ÞÞ=2
ð6:40Þ
where Cs is the spherical aberration coefficient, z0 the extent of defocus of the objective and is the wavelength (Gronsky (1980)). The spatial information contained within a particular beam at qi is transferred to the image when the phase factor, exp(iX(qi )), is about unity and the variation in this term over all reciprocal space, the transfer function, provides a measure of the imaging capabilities of the objective lens (Lenz (1971)). Diffraction spectra are modified by the contrast transfer function before the inverse transformation to the image plane (figure 6.35). It is the determination of the transfer functions which assists the interpretation of images produced in the transmission electron microscope defining the resolution of the system. For a parallel incident electron beam, the diffracted beams leaving the specimen are focused in the back focal plane of the objective lens; the diffraction pattern is imaged if the back focal plane is projected on to the viewing screen by reducing the excitation of the first projector lens (figure 6.36) (see chapter 4). Interchangeable objective apertures, typically 50 mm to 200 mm diameter, are positioned close to the back focal plane of the objective lens to enhance image contrast. If an objective aperture intercepts all the diffracted beams and allows only the direct beam to pass, deficiency contrast occurs and a bright field image is formed (figures 6.37(a) and (b)). In addition, the objective aperture can be used to select a single diffracted beam (figure 6.38(a)), to produce a dark field image. If this is produced by tilting the incident electron beam, the astigmatism in the image is reduced (figure 6.38(b)). The kinematic contrast theory (Hirsch et al (1965), Ball (1971), Loretto and Smallman (1975) and Thomas and Goringe (1979) and Gronsky (1980)) is used to explain and predict image contrast when the intensity scattered into the diffracted beam is small so that re-diffraction of weakly diffracted beams may be neglected. For this theory, the specimen is considered to be a perfect crystal that contains a column whose axis is the direction of the diffracted beam and this is divided into layers perpendicular to this direction. The amplitude at the bottom of the column from each layer is calculated assuming that each acts as a Fresnel zone. The total amplitude is the sum of these contributions over the thickness of the crystal, t (figure 6.39). The amplitude of the diffracted beam, g , for an incident amplitude
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Figure 6.36. Ray diagrams in a transmission electron microscope for diffraction conditions where the back focal plane of the objective lens and screen are conjugate.
Figure 6.37. (a) Bright field imaging where the objective aperture is positioned to allow the direct beam to form the final image. (b) Typical bright field image of interphase VC carbide precipitation in a low alloy 12%Cr–12%Mo–14%V steel.
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Figure 6.38. (a) Dark field imaging where the illumination is tilted to select a given diffracted beam. (b) Dark field image showing distribution of interphase carbide precipitates as figure 6.37(b).
0 equal to unity, is g
¼ ði g Þ
ðt expð2isz dzÞ
ð6:41Þ
0
where g is the extinction distance for the operating diffracted beam g, i is the root of 1, z is depth (see figure 6.39), and g ¼ Vc cos =F
ð6:42Þ
where Vc is the unit cell volume, is the wavelength of electrons, F is the structure factor for diffraction for atom i, and s is the deviation parameter
Figure 6.39. The parameters used to calculate the amplitude of the diffracted beam on the bottom surface of foil. The column considered is at a distance x from a screw dislocation, which is at a depth y below the surface of a foil of thickness t.
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Figure 6.40. Ewald sphere construction in reciprocal space showing incident and scattered wave vectors k0 and ki and the relationship between the beam direction, the diffraction vector g and the deviation parameter s.
(figure 6.40). If s is not a function of the depth, z, then: ¼ ði= g Þðsin ts=sÞ exp½ðitsÞ
ð6:43Þ
jg j2 ¼ Ig ¼ ð2 = g2 Þðsin2 ts=2 s2 Þ:
ð6:44Þ
g
and
For s equal to zero, this equation reduces to ðt= g )2 and for t > g = the diffracted beam intensity, Ig , exceeds the incident electron beam intensity. Despite this restriction, this provides a simple and helpful theory for evaluating the contrast observed in electron micrographs. From this equation it is possible to calculate the variation of intensity for the direct and diffracted beam at the bottom of a thin foil specimen. For example, the weak-beam technique, discussed later, uses very large values for s and the kinematic theory gives reasonable predictions of the experimental observations. For a crystal lattice defect such as a dislocation, the displacement R of a unit cell from the lattice position is established and the amplitude, g , is given by: ðt expf2iðsZ þ g Rg dz: ð6:45Þ g ¼ ði= g Þ 0
If R is calculated using isotropic elasticity theory, then for a screw dislocation positioned at a depth y below the surface of the foil (figure 6.39), the displacement at the point P in the column is simplified to be given by R ¼ ðb=2Þftan1 ðz yÞ=xg
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expf2iðsz þ ðg b=2ÞÞ tan1 ½z y=x dzg:
ð6:47Þ
thus: g
¼ ði= g Þ
ðt 0
Solving equation (6.47) for columns of material located either side of the dislocation enables a profile of intensity to be obtained and the contrast intensity for a dislocation to be described through the foil. These simplifying assumptions allow the theory to be used to establish an ‘invisibility criterion’ which allows the Burgers vector of a dislocation, b, to be determined by comparing the respective expressions for g for perfect and imperfect crystal; the only difference is that the term g R ¼ 0 defines a condition for the dislocation to be invisible. For an elastically isotropic crystal, displacements associated with a screw dislocation are in the direction of b and the invisibility criterion reveals crystal planes that contain b are not tilted, therefore electrons are diffracted as if the dislocation was absent. For an edge dislocation, these displacements are more complex and consequently conditions for invisibility are more restrictive such that both g b and g b ^ u must be zero for invisibility where u is a vector along the dislocation line. For a dislocation of mixed character, isotropic elasticity theory predicts that some contrast will always be observed. The two-beam dynamical theory of image contrast (Howie (1965), Antis and Cockayne (1979) and Cowley (1981)) addresses re-diffraction of both acted beams, thereby coupling both 0 and g . The equations describing the variation with depth of the diffracted and the transmitted amplitude are d
0 =dz
¼ i
d g =dz ¼ i
þ ðig = g Þ expð2iszÞ
ð6:48Þ
þ ði0 = g Þ expð2iszÞ
ð6:49Þ
0 = g g = g
where all the symbols have been defined and 0 has dimensions of length and is proportional to the atomic scattering amplitude for zero angle, and relates to the refractive index of the crystal. By comparing experimental electron images within the foil specimens with images computed from this theory, modifications have been used where terms involving extinction distances are replaced by complex quantities to improve agreement with observed images. The need for these corrections arises because some electrons are scattered outside the diffraction aperture and these do not contribute to the image. This leads to the useful form of the two-beam dynamical (equations (6.48) and (6.49)) for an imperfect crystal: d 0g =dz ¼ i 0g ð1= g Þ þ ði= g0 Þ d 0g =dz
¼
i 0g fð1= g Þ
þ
ði= g0 Þg
þ
2i 0g fs
þ gðdR=dzÞg:
ð6:50Þ ð6:51Þ
The primes indicate that different phase factors are used in the expressions for the amplitudes. From these coupled differential equations, the displacement term gðdR=dzÞ in which dR=dz describes tilting of the diffraction
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plane and locally changes the effective value of s . The image contrast depends on both s and gðdR=dzÞ so that, when gðdR=dzÞ is zero, a defect is invisible and, when s is large, then gðdR=dzÞ has to be large to achieve adequate contrast. For examining the majority of materials in the transmission electron microscope, the simple approximations to the dynamical theory described above are usually sufficient to interpret the images produced. Certainly for resolutions >1 nm, crystal thickness 10–100 nm, accelerating voltages 100– 200 keV and with selection of the specimen orientation, the two-beam approximation affords a qualitative interpretation of images derived from metals, semiconductors and materials with small unit cells. The image intensity varies strongly and sinusoidally with specimen thickness and changes rapidly with orientation when the incident electron beam direction is close to the Bragg angle for the major crystal lattice planes. The strain fields associated with dislocations and other defects produce characteristic contrast that is rigorously addressed. However, Cowley (1986a) correctly points out that these relatively simple assumptions are insufficient in many cases to exploit the full potential of present generation electron microscopes where resolutions below 0.2 nm can be achieved routinely. As a consequence, he reviews the principles of image formation that allow a more complete understanding of the image contrast features observed under high resolution conditions, or with unconventional electron optics, and the reader is commended to this review for such specialist applications. 6.4.4
Specimen preparation
The types of specimens examined in a conventional transmission electron instrument are usually either replicas or thin foils (Brammar and Dewey (1966), Goodhew (1972) and Titchmarsh and Williams (1981)). In the former case, after polishing a bulk specimen, as for light microscopy (chapter 3) the surface is etched to reveal the required metallographic detail and produce surface relief. The surface is overlaid with either a cellulose acetate or similar film to replicate this relief and this stripped replica can be coated by evaporation with carbon and the relief, and thereby image contrast, enhanced by shadowing with a heavy metal such as gold or platinum. The acetate film is removed with a solvating reagent, leaving a positive replica of the surface (figure 6.41(a)). This technique is now usually restricted to specialist applications where foil preparation is precluded. However, procedures that extract precipitates, such as carbides from steel specimens, offer the ability to provide information about the size, shape and distribution of these phases (figure 6.41(b)). Extraction replicas are being used extensively for undertaking chemical analysis of precipitates (Doig et al (1986)).
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Figure 6.41. (a) Replica showing faulted substructure within an 1 plate of an aged Cu– 40%Zn alloy. (b) Carbides extracted from a 1%Cr–12%Mo steel.
The principal methods for preparing electron-transparent foils from bulk specimens are: (i) electrothinning; (ii) ultra-microtomy; (iii) chemical thinning; (iv) cleavage; (v) solvent casting; (vi) ion bombardment. The most widely used of these is electrothinning, which is usually based upon jetting an electrolyte on to a prepared disc of material up to about 500 nm thickness within the current and voltage range that gives rise to polishing (figure 5.4) (Titchmarsh and Williams (1981) and McG.Tegart (1959)). A number of automatic electrolytic thinning systems are available commercially based on this method where a light detection system is used to indicate when penetration of the foil has occurred. Moreover, these techniques and the electrolytes appropriate for use with a range of materials have been subject to extensive reviews (Brammar and Dewey (1966), Goodhew (1972) and McG.Tegart (1959)). When electro-thinning is impractical, ultramicrotomy provides a method for preparing suitable electron-transparent specimens. The technique, reviewed by Glauert and Phillips (1965), is used routinely for biological specimens and is appropriate for wood, bone, textile fibres and polymeric materials. Amorphous polymers can be cut on an ultramicrotome with a glass or diamond knife if the temperature is reduced to below the glass transition temperature (Vesely (1989)). Crystalline polymers are more difficult to prepare and cutting properties are improved by chemical staining, for example with osmium tetroxide (Kanig (1974)). An alternative procedure for polymeric materials is to dissolve in a solvent and cast this on to a glass slide. After the solvent has evaporated, the resulting film is coated with a thin layer of carbon. Indeed, this specimen can be melted and re-crystallised before stripping from the glass slide in water. The technique, although subject to limitations, can be used to study the crystallography of polymeric materials (Veseley (1989)). A number of materials that are difficult to prepare by other techniques, such as silica,
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germanium and magnesium oxide (Goodhew (1972)), can be prepared as foils by chemical etching techniques. Generally, however, difficulties are encountered in producing foils with large, uniformly thin areas. For a range of ceramics and semiconducting materials, ion bombardment is used to thin the specimens (Cowley (1986b), Flewitt (1970) and MacMillan and Flewitt (1975)). In this technique, the surface of the material is bombarded with ions of an inert gas, usually argon. Although applied successfully to a range of materials, including oxides, carbides, nitrides, ceramics, glasses and metals, the total time required to produce the final foil is usually greater by at least a factor of five compared with electrochemical procedures. Moreover, care has to be exercised to ensure crystal lattice defects are not introduced into the specimen. However, this technique, although slow, has the advantage that it is very controllable and produces a highly reliable and reproducible foil. In addition, it is relatively easy to progressively remove material and check the suitability of the foil for examination at each intermediate stage. Thus, it can be used, for example, if there is a need to retain the geometry of a specific feature, such as a void or a creep cavity in a metal (Lonsdale and Flewitt (1978a)). Indeed, this technique enables special requirements for examining specimens to be addressed, such as cross-sections of small, 1 mm diameter, Nb/20–40%Zr wires (Thompson and Flewitt (1971)) irradiated foils (Seitzman et al (1989)) and ceramic film interfaces (Endemir and Cheng (1989)). A major development in the preparation of transmission electron microscopy specimens has been the introduction of the focused ion beam (FIB) technique (Barber (1995)). Field emission ion guns (see section 7.5.1) have been developed with intense beams capable of being focused to less than 20 nm diameter (Kirk (1989) and Overwijk (1993)). These focused ion beams can be used to machine specimens from all types of material. They are fast (a foil specimen can be produced in less than 2 h), precise, the exact location can be specified and can be used in awkward positions—for example, specimens can be cut from surfaces and edges. The technique is illustrated in figure 6.42. Initially a thin metallic layer may be laid down, although this is not always necessary. The metallic layer is built up by passing a gas over the surface that is a compound of the metal to be deposited while the ion beam is rastered over the area to be covered. Two slots are then cut, defining the sides of the specimen, which are typically 100 nm thick. Cuts are then made down the sides and along the base to produce a transmission electron microscope (TEM) specimen approximately 20 mm 10 mm 0.1 mm. The whole unit is then removed from the FIB system and transferred to a TEM. Another typical application is described by Lozano-Perez et al (2001) who used this technique to prepare specimens through cracks in an austenitic stainless steel. In this approach it was possible to retain a thicker frame to the specimen and, thereby, provide support at all stages of preparation and observation. Certainly focused ion beam
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Figure 6.42. A TEM specimen prepared using a focused ion beam (FIB) and viewed in the scanning electron microscope (courtesy of FEI Ltd).
bombardment is widely used in semiconductor device manufacture where quality control and early fault finding depend upon site-specific thinning of a specimen and fast preparation. With these benefits several suspect locations can be prepared in one operation and indeed can be controlled. There are also examples where precision polishing can be combined with this method of preparation (Anderson and Klepeis (1997)). 6.4.5
Images in the conventional electron microscope
Bright field and dark field images are the basic mode for viewing crystalline specimens in the transmission electron microscope. They provide the essential microstructural information from a specimen prior to having to resort to more specialist imaging or operating techniques. Although these images can be obtained over the complete range of accelerating voltages, we address here the range that covers both the conventional and medium
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Figure 6.43. Bright field dislocation images in a quenched 0 phase Cu–9%Au–40%Zn alloy shown in (a) together with the corresponding computed image (b) (Flewitt and Wild (1985)) (reproduced with permission of Institute of Metals).
voltage instruments up to 400 keV; high voltage, typically 1 MeV, microscopy is considered separately. Under bright field contrast conditions, dislocations can be observed in a range of materials because they produce crystal lattice displacements that produce images, typically 20 nm wide (figure 6.43(a)). The extent of this contrast corresponds to the local elastic strain field. The visibility criteria for dislocations (section 6.4.3) enable the Burgers vector for different dislocations to be established: if g b ¼ 0, a screw dislocation will be invisible and, in addition, if g b ^ u also equals zero, an edge dislocation will be invisible. These invisibility criteria are widely used, but their limitations require more sophisticated techniques for interpreting dislocation and dislocation loop contrast (France and Loretto (1968), Head et al (1973) and Goringe (1975)). Indeed, the only reliable method of interpreting contrast from a bright field image of a dislocation is to compare that observed with an image computed for the experimental conditions used. Computer techniques (Head et al (1973) and Bullough et al (1971)) accommodate anisotropy in the elastic properties of the material, and the example shown in figure 6.43 is for a superdislocation image where the partial dislocations are separated by antiphase boundary in the ordered 0 phase (B2) of a Cu–9%Au–40%Zn alloy (Flewitt and Wild (1985)). Centred dark field images are produced using a selected diffraction beam to form the image. Figure 6.44 is an example where NiFe2 O4 spinel
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Figure 6.44. Centred dark field images (g ¼ ½220spinel ) showing bright spinel precipitates in dark NiO matrix: [001] beam direction. Heat treated for 1800 s at (A) 973 K; (B) 1073 K; (C) 1123 K; (D) 1173 K (Summerfelt and Carter (1989)) (reproduced by permission of Elsevier Science Publishers).
precipitates are preferentially imaged in a bulk (Ni0:9 Fe0:1 )O material (Summerfelt and Carter (1989)). Here four centred dark field images are formed using the (220) spinel diffraction spot with the electron beam oriented nearly parallel to the [001] direction. The specimen has been tilted a few degrees from the pole to excite only the 220 or 220 systematic row of diffraction spots. The spinel precipitates have a lattice parameter which is almost double that of the NiO matrix. Thus, although the two diffraction patterns are almost identical, the spinel diffraction spots are separated by half the distance of those derived from the NiO. These images assist in the interpretation of the precipitate morphology (figure 6.44); the square point of the precipitate image is the arm that has grown in the [001] direction
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Figure 6.45. Various image conditions used for extrinsic and intrinsic stacking faults and precipitates in a (Co0:78 Fe0:22 )3 V alloy aged at 1073 K for 8 h: (a) Bright field, g ¼ ½200; (b) Dark field, g ¼ ½200; (c) Dark field, g ¼ ½200VC showing VC precipitates on extrinsic stacking fault; (d) Superlattice dark field image, g ¼ ½100, showing thermal antiphase boundaries and stacking faults (Braski et al (1982)) (reproduced by permission of Pergamon Press).
and is bounded by the (110) and (110) planes which are edge-on in the projection. An investigation of the microstructure developed in a (Co0:78 Fe0:22 )3 V alloy with an LI2 ordered crystal structure when imaged with bright and dark field conditions shows (Braski et al (1982)) intrinsic and extrinsic stacking faults incorporated into the antiphase boundary (APB) network (figure 6.45). The intrinsic stacking faults have a relatively high APB energy and interact strongly with thermal APBs, whereas the reverse is the case for extrinsic faults. Detailed analysis, using a range of imaging conditions, reveals VC carbide precipitates that have punched out a=2 h110i dislocations into the matrix and these, in turn, dissociate. The first dissociation is to Frank and Shockley partial dislocations. The Frank partial climbs from the particle creating an extrinsic stacking fault which grows by cooperative, repeated VC precipitation and climb of the Frank partial. The second mechanism involves dissociation into Shockley partials. Precipitation-free intrinsic stacking faults result from subsequent glide of the outer partial, dragged along by the interaction with the coarsening APBs. Ageing of the metastable phase in the niobium 25–40% zirconium alloy system (Flewitt (1974a,b)) at temperatures below the monotectoid, produces precipitates of 0 (hcp) phase distributed uniformly in the (bcc) matrix (figure 6.46(a)). The 0 precipitates plates are coherent with the matrix, but differences between the lattice parameters of the product and
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Figure 6.46. Precipitation in metastable phase niobium–zirconium alloy. (a) Fine distribution of 0 plates on aging at 573 K. (b) Detail of coherency strain contrast for 0 precipitates and schematic diagram showing atom displacements normal to 0 plate interface. (c) Modulated spinodal structure ðNb þ Zr ) produced on ageing at 973 K. (d) Loss of coherency of the spinodal decomposition product giving networks of interfacial dislocations between Nb and Zr phases. Interfacial dislocation networks in plane of the foil [100] showing Moire´ fringes (M) and dislocation networks (D) (Flewitt (1974a,b)) (reproduced by permission of Pergamon Press).
parent phases produce an elastic distortion in the matrix immediate to their interface. As shown in figure 6.46(b), a column of crystal adjacent to the precipitate is distorted and diffracts differently from an equivalent undistorted crystal. In the direction parallel to the electron beam, the crystal is oriented such that sets of vertical lattice planes satisfy the Bragg equation (figure 6.46(b)). Under these conditions, the misfit vector is equivalent to the operating diffraction vector, and planes through the centre line of these precipitates are undistorted, resulting in a line of no contrast perpendicular to this direction in the image.
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Figure 6.47. Bright field image of Guinier–Preston zones in an Al–15%Ag alloy imaged by precipitate structure factor contrast (courtesy G W Lorimer).
Above the monotectoid temperature, the metastable phase transforms by spinodal decomposition into two bcc phases, one rich in zirconium, Zr , and one rich in niobium, Nb (figure 6.46(c)). The contrast observed in the electron microscope for spinodal decomposition has been analysed using the kinematical theory. Since niobium, atomic number 40, and zirconium, atomic number 41, are adjacent to each other in the Periodic Table, the major contribution to contrast is from lattice parameter differences associated with small composition fluctuations which give a phase displacement of the diffracted electrons. Contrast is enhanced by preferential thinning of the zirconium-rich phase during foil preparation by electropolishing. As ageing continues, coherency is lost between the two phases and distinct interfaces develop which contain dislocations. Although dislocations, D, in these interfaces are imaged in figure 6.46(d), there is additional contrast information at, for example, M. The latter arises because the parent and product crystals are each bcc in structure and superimposed so that Moire´ fringes, M, arise from interference between the directly transmitted and the doubly diffracted beams. The spacing between the fringes is given by (Laird and Aaronson (1967)): DM ¼ d1 d2 ½d12 d22 d1 d2 cos 0 1=2
ð6:52Þ
where d1 and d2 are spacings of the lattice planes imaged for the parent and product phases and 0 is the angle of rotation. Figure 6.47 shows Guinier–Preston (GP) zones in an aluminium base alloy imaged using structure factor contrast (Nicholson and Nutting (1961)). The structure factor, F, contains information related to the atomic species and their position in the unit cell (see chapter 4) such that X ð fn expð2ig rn ÞÞ ð6:53Þ F¼ n
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where fn is atomic scattering factor and rn is the position vector of the nth atom in the unit cell. A variation in F produces a change in the extinction distance, g F 1 , so that the extinction distance within the crystal containing a GP zone differs from that for the matrix, and thickness fringes at the edge of a foil are displaced in those columns of foil that contain GP zones. This contrast mechanism allows these small, coherent precipitates with lattice parameters similar to the matrix to be imaged when they cannot be viewed using either strain or orientation contrast. 6.4.6
High-resolution images
An extension to conventional transmission electron microscopy has been to seek to increase the resolution of the images produced and, in addition, to achieve this for higher voltage conditions. The first high resolution images were achieved by Allpress et al (1969) to give intensity peaks that correspond with the atom positions in two-dimensional lattices. High-resolution images from crystalline materials requires the highest possible structural resolution as defined by the first zero of the plane contrast transfer function at optimum focus (Scherzer (1947 and 1970), Erickson and Klug (1971) and Herrmann (1978)). Thus it is necessary to have the smallest possible values for the objective lens focal length and aberration coefficients and the maximum mechanical stability for the microscope. This has led to the use of top entry stages and miniaturisation of the objective lens pole pieces. If the transmitted beam and one diffracted beam from a very thin area of a foil are selected using the objective aperture of a microscope fitted with a high resolving power objective lens, a periodic fringe pattern is formed by phase interference between the two beams. Under carefully controlled conditions, the periodicity of the fringes in the image corresponds with the spacing of crystal lattice planes in the specimen. Figure 6.48 shows such a Cu–Zn–Al alloy image where the structure of the martensite phase is designated 18R, which corresponds to an 18-plane repeat distance for close packed planes with a stacking sequence a b c b c a c a b (Perkins et al (1989)). These lattice images reveal the presence of fine substructural faults in the 18R martensite which have a 2H structure. This lattice image has been obtained using the (2, 0, 8), (2, 0, 14) (2, 0, 20) and (2, 0, 26) diffraction spots in a selected area diffraction pattern that has a [010]18R zone axis and reveals the stacking sequence of the close packed planes. The fringes are spaced at 0.43 nm in the faulted regions compared with 0.65 nm for the 18R matrix. Comparing these fringes with the calculated interplanar spacings shows that the distance between two successive black fringes in the matrix involves three atomic layers of (0, 0, 18) planes, while in the structural faults it represents two close packed planes. Thus, it is possible to deduce that these are not simple random stacking faults in the 18R structure but, rather, thin slices of a distinctly different crystal with a 2H type of structure. When the specimen
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Figure 6.48. One-dimensional lattice image showing the fine structure of an 18R martensite plate in Cu–14.6%Zn–16.1%Al alloy obtained by using the (2,0,8), (2,0,14), (2,0,20) and (2,0,26) diffraction beams. The lattice fringe spacing in the 18R matrix is 0.65 nm, while that in the thin faulted regions is 0.43 nm, indicating a 2H structure (Perkins et al (1989)) (reproduced by permission of Elsevier Science Publishers).
thickness is several times the precipitate diameter and the lattice images show significant deviations from periodicity, then correspondence between the specimen and the image can no longer be assumed. Direct lattice images should always be compared with computed images for quantitative measurements of either the precipitate crystal structure or the matrix strain. It has always been a goal of electron microscopy to obtain genuine atomic resolution images. Although possible for a number of years for some crystalline complex oxides with a large unit cell, it is only more recently, with the availability of the higher voltage (up to 400 keV), high-resolution instruments, that the stringent conditions required to produce such images in a range of materials, including semiconductors, has become possible. Silicon has a diamond cubic crystal structure where the nearest atom neighbours, at 0, 0, 0 and 14, 14, 14, are 0.235 nm apart. For the main low index projections, the most closely spaced columns of atoms are 0.219 nm in the h111i projection, 0.191 nm in h100i and 0.136 nm in the h111i. Figure 6.49 shows a high-resolution image of a h110i projection after enhancement by photographic averaging compared with the projected atomic structure (Hutchinson et al (1986)). Figure 6.50(a) provides another example of a high-resolution image, in this case the interface between silicon and a continuous layer of A-type CoSi2 fabricated by high-dose cobalt ion implantation. Prominent (200) fringes are visible in the CoSi2 which agree well with the simulations shown in figure 6.50(b). Along the (200) rows of fringes, there is a shift to the left on passing from the Si into the CoSi2 , which is consistent with the predictions of a sevenfold model (De Jong and Bulle-Lieuwma (1990)); sevenfold refers to the number of silicon atoms that surround the interfacial metal atom. Figure 6.51 shows two grain boundaries imaged under high resolution (Turan and Knowles (1995).
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Figure 6.49. High-resolution electron micrograph (200 keV) of h110i lattice image of silicon after enhancement by photographic averaging. The inset shows the projected atomic structure (Hutchinson et al (1986)) (reproduced by permission of JEOL UK Ltd).
Figure 6.50. (a) High resolution electron microscopy image (250 keV; defocus, 50 nm) of a CoSi2 (A)/Si(111) interface for an ion implanted material. There is a shift of the (200) fringes when crossing the interface. (b) Corresponding computer simulated images (De Jong and Bulle–Lieuwma (1990)) (reproduced by permission of Taylor and Francis Ltd).
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Figure 6.51. Two grain boundaries between two -Si3 N4 grains imaged under high resolution (Turan and Knowles (1995)). (a) shows an asymetrical high-tilt-angle grain boundary with the electron beam direction close to [011] while (b) shows a low-angle grain boundary with the electron beam direction close to [211] (reproduced by permission of Blackwell Science Publications).
Figure 6.51(a) shows an asymmetrical high-tilt-angle grain boundary while figure 6.51(b) reveals a low angle grain boundary between two -Si3 N4 grains. For complex oxides and nitrides of this type with large unit cells it is only with higher voltage (up to 400 keV) and high-resolution instruments that the stringent conditions required to produce workable images have been achieved. The contrast of electron microscope images changes with small differences of focus for the objective lens of the microscope with the resolution at the atomic scale. This change of image contrast is described by the phase contrast function (Scherzer (1949)). The phase of the waves leaving the specimen at a given scattering angle is shifted by the spherical aberration of the imaging lens. This contribution is usually compensated by underfocusing the image. The phase angle is given by ¼ f=2gfðCS 4 Þ ð2f 2 Þg
ð6:54Þ
where CS is the spherical aberration coefficient, f the defocus and the electron scattering angle. However, in the case of a lens with CS equal to zero the intensity distribution at the crystal exit face is projected on to the image plane where f is zero. At the present time CS of zero cannot be achieved for the electron beams that are scattered with a large angle.
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However, various approaches have been, and are being, invoked to approximate and achieve this condition (Hashimoto (1999)). The approaches centre upon the disturbance introduced by spherical aberration and defocus on image contrast which can be eliminated by assuming the phase of the contrast transfer function equals 2m so that: f ¼ mð2d 2 =Þ þ ðCS 2 =2d 2 Þ
ð6:55Þ
where the lattice spacing d ¼ /2 and m ¼ 0; 1; 2; . . . . When expressed as a plot of f versus CS , the combination of values of CS and f at any point can give rise to an image without any spherical aberration. The value of CS in equation (6.55) is based on the term of third order. It has been confirmed that the term of the fourth order does not have a significant effect on beams which are diffracted by crystal planes with a spacing 0.1 nm (Cowley (1986)). Significant steps have been taken to develop a spherical aberration correction for a STEM instrument (Lupini et al (2001)). The essential components of the CS corrected STEM are (i) improved ways of diagnosing the aberrations including all parasitic aberrations up to the fifth order, (ii) the flexibility to null second and fourth order aberrations and (iii) improved electrical and mechanical stability of both the corrector and the microscope. Hence it is possible to achieve the precision for 0.1 nm resolution. This forms the basis of the next generation of high-resolution instruments being developed in the US and UK. An alternative way of correcting lens aberration is to use the holographic method. Here the specimen is illuminated by an electron beam and part of the beam is scattered by the specimen and the remainder of the beam does not interact. As shown in figure 6.52, when these beams are brought together at a detector an interference pattern or hologram is recorded. This contains information about the phase and the amplitude of the electron beam diffracted by the specimen. A beam of light is then used to reconstruct the three-dimensional image of the specimen from the hologram and this image can be corrected for aberrations optically (Tonomura (1993)). As shown in figure 6.52(a), the interference pattern can be formed when a bi-prism is positioned behind the objective lens. Here electron beams pass either side of a central filament of 1 mm diameter which is maintained at a positive voltage and overlap in the lower plane. If a parallel electron beam is incident on the bi-prism, interference fringes are formed in the region of overlap. When a specimen is placed in one of these two beams a hologram is formed. An alternative way of producing the hologram is shown in figure 6.52(b) where a crystal film is used as the beam splitter (Tonomura (1994)). Overall, with the use of coherent field emission sources electron holography allows a resolution approaching 0.1 nm to be obtained. Certainly electric and magnetic field distributions have been achieved such that individual vortices in high-temperature superconductors have been imaged.
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Figure 6.52. Schematic showing electron hologram formation with (a) an electron bi-prism and (b) a single crystalline film. In both cases the object is the black arrow. In (a) an electron lens (not shown) focuses the electron beam which is effectively split by the filament. The object and reference beams are recombined by the electric fields in the bi-prism. In (b) the beam is split by Bragg diffraction in the crystal and the beams recombined by an electron lens. The resulting information contains holographic information about both the crystal and the object.
In weak beam microscopy, a high resolution, a dark field image is formed with a reflection that is weakly excited: the deviation parameter, s, is large (Cockayne (1973a,b) and Stobbs (1975)). This specialist technique is an extension of the conventional matrix strain field condition, s ¼ 0, the image width formed by strain field contrast is large and can be used since, as the value of s is increased, the image width decreases and, at large values of s, it approaches the true width of the feature. Although weak beam microscopy is used to decrease the image width of precipitates, it is of particular value when observing dislocations, since under these conditions the image width corresponds to that of the dislocation core. An example of the use of weak beam imaging is the examination of the dislocation structure generated in deformed single crystals of Ni3 (Al,Ti) (Korner (1988)). Figure 6.53 shows the unit dislocations of a half-loop of the superlattice dislocation with a Burgers vector b ¼ a ½101 imaged in a foil with the normal parallel to the beam direction of [010]. Contrast analysis reveals segments P and C to be dissociated on the primary (111) and cube (010) planes respectively. A
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Figure 6.53. A weak beam micrograph of a Ni3 (AeTi) alloy (010) foil with g ¼ 202 showing a superlattice dislocation with a transition from the (111) plane, segment P, on to the (010) plane, segment C (Korner (1988)) (reproduced by permission of Taylor and Francis Ltd).
mixed dislocation segment, C, oriented at approximately 608 is deduced from the projected direction of the oscillatory dislocation line. This provides an example of cross-slip from octahedral (111) on to (010) cube planes and is consistent with computer simulations. 6.4.7
Surface electron microscopy
Apart from the methods of producing images discussed so far, the transmission electron microscope offers several other possible ways of obtaining information about materials. Indeed, it is possible to obtain surface information, but here the approach depends upon the particular detail required (Smith (1986), Cowley (1986a) and Yagi (1987)). At a free surface the bulk periodic interatomic potential no longer exists, since the forces on the surface atoms are no longer symmetrical, so that surface atoms are displaced from their ideal crystal lattice positions to form relaxed and reconstructed surfaces. Thus, defects together with surface relaxation can contribute significantly to surface processes of chemisorption, epitaxial growth and oxidation and, therefore, it becomes important to obtain the maximum information about these surfaces. Surface profile imaging To obtain surface profile images, the electron microscope is operated in the same mode as that for high resolution with a large objective aperture
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Figure 6.54. Schematic diagram illustrating the technique used to form surface images: (a) lens–specimen configuration; (b) specimen in side view; (c) specimen in plan view (Smith et al (1989)) (reproduced by permission of Elsevier Science Publishers).
(figure 6.54) (Smith (1985), Marks (1984) and Smith et al (1989)). The specimen is thinned and aligned with a low index zone axis parallel to the incident electron beam direction and the images are obtained at the optimum lens defocus, to display the surface profile at the resolution limit for the instrument. Details of surface topography are obtained under these conditions but it is important to support image interpretation with computer simulation. This technique can be applied to a range of materials, although metals are more difficult to image because of the small spacing between projections of adjacent atom columns which are typically less than about 0.2 nm, even for low index zone axis projections (Bonzel and Ferrer (1982) and Smith and Marks (1985)). Cleaning semiconductor surfaces for profile imaging can be undertaken in the electron microscope either by heating under an ultra-high vacuum (<107 Pa) (Sinclair et al (1981)) or in a less controlled way by focusing the electron beam to effect evaporation of the surface layers (Lu and Smith (1987)). Figure 6.55 shows the results obtained for a CdTe semiconductor based upon the h110i projections. The predominant CdTe surfaces are (111) which are long and flat with a significant number of the surface layers having a twin orientation relationship with the bulk crystal (figure 6.55(a)). For (001) surface profiles, an unusual 3 periodicity has been observed occasionally (figure 6.51(b)), whereas for (110) surfaces a
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Figure 6.55. Profile images from [110] CdTe recorded at 400 keV: (a) (111) surface with twinning (arrowed); (b) 3 reconstruction on (001) surface; (c) one-to-one reconstruction on (110) surface (Smith et al (1989)) (reproduced by permission of Elsevier Science Publishers).
characteristic chevron appearance is produced by rotation of the outermost CdTe atom pair (figure 6.55(c)). However, both are predicted by computer image simulations (Smith et al (1989)). Reflection imaging In this technique, the electron beam is incident on the specimen surface at a glancing angle (figure 6.56), where electrons are inelastically scattered by atoms at, or just below, the surface and these are used to provide the image of the surface (Halliday (1965)). To achieve this, the electron gun of the microscope is tilted so that the electron beam is incident at an angle 1 to the specimen surface and the scattered electron signal is directed along the microscope axis at an angle 2 . The signal intensity is maximised at the expense of excessive image foreshortening if glancing incidence is employed and 1 equals 2 . This technique is helpful to image dislocations which interact with the free surface. Peng and Cowley (1989) have used the Bethe´ multi-beam dynamical theory (Bethe´ (1930)) to describe the wave function, ðrÞ, above the specimen surface: X RðhÞ expðiKh rÞ ðrÞ ¼ expðiK0 rÞ þ h
h i X0 ¼ expðiK0 rÞ þ RðhÞ expðiKh rÞ þ RðsÞ expðiKs rÞ
ð6:56Þ
where K0 , Kh and Ks are the wave vectors, RðsÞ and RðhÞ are the reflection coefficients, the summation is over all the reflected beams in vacuum and the prime on the summation indicates omission of the term for specular reflection which is usually selected to form the reflection electron images.
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Figure 6.56. Schematic ray diagram showing the main features of a reflection electron microscope.
The images are foreshortened by factors up to fifty times, depending on the particular diffraction conditions selected. The specimen surfaces have to be very flat due to the sensitivity of the reflected beam amplitude to deviations from perfect surfaces. The specularly reflected beam wave function is s
¼ RðsÞ expðiKs rÞ ¼ jRðsÞj expðis Þ expðiKs rÞ
ð6:57Þ
where s is the phase factor of the specularly reflected beam amplitude. As for dark field transmission electron images, reflected image contrast arises from variations in the amplitude of diffraction from the crystal lattice due to local strains and distortions of the crystals, compositional changes and coherent interface effects which introduce differences of optical path length for the electron beams (Cowley (1986b)). For reflection from a perfect surface jRðsÞj and s are constant over all the surface. Figure 6.57 is a reflection electron micrograph of a dislocation imaged from a platinum surface (Peng and Cowley (1989)). This screw dislocation is associated with a surface step one atom high and fine axial symmetry and meets the (111) surface plane of the plane of the specimen normally. The Burgers vector of this dislocation is b ¼ a=3 ½111 which is not common for bulk crystals; however, this type of dislocation is favoured energetically due to the free surface interaction.
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Figure 6.57. Reflection electron microscope image from Pt(111) surface, showing a screw dislocation emerging at the surface (Peng and Cowley (1989)) (reproduced by permission of Elsevier Science Publishers).
Low-energy electron microscopy Low-energy electron microscopy combines low-energy electron diffraction and imaging of surfaces using electron energies up to 150 eV (Bauer and Telieps (1987), Bauer et al (1989), Mundschau et al (1990) and Mundschau (1990)). This technique has only recently come to prominence due to the ability to provide the necessary ultra-high vacuum. A typical low-energy electron microscope is shown schematically in figure 6.58 where the source provides electrons accelerated at voltages up to 20 keV. The focused electrons are deflected by a non-focusing magnetic sector and enter a cathode lens where they decelerate to energies of between 0.1 and 150 eV prior to interacting with the specimen where low energy diffraction occurs. These diffracted electrons are re-accelerated within the cathode lens up to 20 keV. The successful operation of the instrument depends upon the fact that focusing is undertaken at high energies using conventional electron optics and the electrons decelerate and re-accelerate near to the specimen surface; this removes the difficulty of focusing low-energy electrons. The reflected electrons are redeflected within the magnetic sector and then enter the imaging column containing transfer and projector lenses. The projected image is amplified by a channel plate image intensifier and the final image is formed on a phosphorescent screen. The advantage of this technique is that the specimen is
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Figure 6.58. Schematic diagram illustrating the main components of a low-energy electron microscope.
not limited by size or thickness and can be heated by electron bombardment from the backside or cooled to liquid nitrogen temperatures. Instead of using the electron gun a light source can be used to produce photoelectrons from the surface which can then be focused using the same electron optics to form a photoemission image on the viewing screen. Figure 6.59 shows features associated with in-situ epitaxial growth of copper on a {110} orientation molybdenum single crystal substrate. The low-energy electron micrograph obtained at 3 eV contains dark lines which correspond to monatomic steps on the surface. The bright areas are covered with a single monolayer of copper which is pseudomorphic with the substrate. Dark areas reveal a second monolayer of copper which has grown between the atomic steps and by this stage the copper achieves a fcc structure. Clearly this provides a powerful addition to the surface imaging techniques. Photoemission electron microscopy The photoemission electron microscope (PEEM) enables polished surfaces to be studied at elevated temperatures. The image is formed by electron emission from the surface as a result of excitation by ultraviolet light, ion bombardment, electron bombardment or heating with or without an activator coating on the specimen. This technique has been reviewed by Eicher (1967), Mollenstedt and Lenz (1963) and Wegmann (1970). The contrast in the image is produced by differences in the electron emission
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Figure 6.59. Low-energy electron image of the growth of copper on a molybdenum substrate with a {110} surface plane (Mundschau (1990)) (reproduced by permission of Rollston Gordon Communications).
across the specimen surface and this is enhanced by differential contrast using electronic signal processing. The operating principle is shown in figure 6.60 where the specimen is maintained at a high negative potential, 40 keV, with reference to an anode plate that faces the specimen surface. More usually it is either an ion gun or ultraviolet light that is reflected on to the specimen surface from a polished anode plate to effect electron emission. These electrons are accelerated by the applied field and pass via the anode aperture into a three-stage electron microscope, thereby allowing photoemission images to be produced on a viewing screen with resolutions of the order of 10 nm. The vacuum for these microscopes is typically 105 Pa and because of this clean environment the specimen can be heated both to effect electron emission and to enable dynamic experiments to be undertaken. An example of the application of this type of electron microscopy is the progressive development of a diffusion bonding in mild steel undertaken at 1263 K (figure 6.61) (Taylor (1983)). The high orientation contrast that can be achieved between the prior austenite grains and the planar boundary interface is evident. At this stage the boundary interface is discontinuous with selective grain growth across it in certain places. 6.4.8
Magnetic domain images
Electrons which interact with the magnetic field, B, of a thin section of magnetic material are subject to Lorentz force, L, given by L ¼ eðv ^ BÞ
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Figure 6.60. Schematic diagram showing the components of a photoemission electron microscope (PEEM).
Figure 6.61. Diffusion bond developed in a mild steel to mild steel interface heated at 1263 K in the photoemission electron microscope (Taylor and Pollard (1982)) (courtesy of Taylor and Pollard).
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Figure 6.62. Electron ray diagrams showing the two modes of imaging in Lorentz transmission electron microscopy: (a) Fresnel and (b) Foucault.
where v is the velocity of an electron within the beam and e is the charge (Wade (1968) and Grundy (1971)). As a consequence of this Lorentz force, the electron beam is deflected through a scattering angle 104 rad, which is smaller than a typical Bragg angle 102 rad. There are two modes of imaging in Lorentz transmission electron microscopy, the Fresnel and the Foucault (Tsuno et al (1989)) (see section 6.4.10). In the Fresnel mode shown in figure 6.62 the image is obtained simply by defocusing the objective lens of the microscope such that the image plane, the broken line, is focused on to the imaging screen; the intensity distribution of electrons on this plane is also given. However, in the Foucault mode, half the electrons are eliminated by the objective aperture at the back focal plane, whereas the direct beam is split by the deflection of electrons in each domain. Magnetic domain contrast for a cobalt foil (figure 6.63) is achieved by defocusing the objective lens and taking the distribution of electron intensity at a distance either above or below the specimen as the object. Such Lorentz microscopy provides the magnetisation distribution within several types of boundary surrounding each magnetic domain (Grundy (1971) and Taylor (1983)). 6.4.9
High-voltage electron microscopy
The conventional transmission electron microscope has been extended by increasing the accelerating voltage of the electrons to above 500 keV (Jouffrey (1975) and Madden and Fisher (1982)). Thus high voltage electron
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Figure 6.63. A Lorentz electron micrograph of cylindrical ‘bubble’ domains in a cobalt thin foil (courtesy P J Grundy).
microscopy (HVEM) allows quantitative image and diffraction information to be obtained from thicker specimens. The variation in penetration with voltage is almost linear for low density materials, but changes to a thickness versus (voltage)1=2 relationship for elements in the transition region of the Periodic Table (Johnson (1975)) (figure 6.64). The ability to examine ‘thick’ specimens is useful in those instances where there is a need to contain specific features within the foil section, for example the distribution of cavities or voids, arising from creep deformation, in the 1 mm to 0.1 mm size range, and to correlate these with other microstructural features. In addition to the increased penetration, use of higher voltages reduces the spherical and chromatic aberrations (Dupouy (1973)). Thus the theoretical resolution limit of the microscope is reduced to about 0.06 nm for a highperformance 3 MeV microscope. This provides another important advantage since high-resolution dark field images can be produced by simply displacing the objective aperture to produce images using the appropriate diffracted
Figure 6.64. The variation of penetration with accelerating voltage for silicon ðZ ¼ 14Þ and stainless steel ðZ ¼ 26Þ.
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Figure 6.65. High voltage electron microscopy. (a) Dislocation in a specimen of stainless steel imaged at 2 MeV. (b) Corresponding image to (a) at 1 MeV where separation of dislocations at D is no longer achieved. (c) Stacking faults in silicon examined at 2 MeV (Dupouy (1973)).
beam. Figures 6.65(a) and (b) show the same region of a stainless steel specimen where the first image was obtained at 2 MeV and the second at 1 MeV. The difference in quality between the two images is immediately evident by comparing, for example, the two dislocations, D, which are resolved only at 2 MeV. Another example of the quality of the images that can be achieved is shown in figure 6.65(c), where stacking faults in silicon are imaged at 2 MeV. Despite these advantages associated with both image quality and the ability to view thicker foil sections, the benefits to the understanding of materials have not been advanced in proportion to the effort and cost associated with high-voltage electron microscopy. The major contributions have been a result of the ability to observe more extensive microstructural features such as shear bands produced by explosive deformation of steel
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(Wittman et al (1990)) or in situ experiments. In the case of the latter, examples are radiation damage (Loretto and Loretto (1989) and Vetrano et al (1989)) deformation of materials in situ (Messerschmidt and Appel (1989) and Rozenak (1990)) and studying the influences of different environmental conditions (Humphrey et al (1985)). The latter has been aided by the larger working space available in these instruments, enabling a range of specialist stages with environmental cells to be constructed. It has to be recognised that there remains a demand for such in situ specialist experiments (Kastner and Messerschmidt (1999)). 6.4.10
Scanning transmission electron microscopy
An important advance in electron optical instrumentation has been the development over the past thirty years of the scanning transmission electron microscope (STEM). The instrumentation was developed along two separate and unrelated lines; the first produced a dedicated instrument of the type devised by Crewe (Crewe (1968) and Crewe et al (1968)) and the second extended existing conventional transmission electron microscopes (Cowley (1969)). By strict definition the former is a STEM instrument and is dedicated to providing high spatial resolution scanning transmission images. The latter is a conventional transmission electron microscope fitted with scan coils in the illumination system with the specimen located at the centre of the objective lens, which is then used as a third condenser to form a small diameter electron probe ð2 nm) and an electron detector is placed below the specimen to record the transmitted image. Both instruments, but perhaps particularly the latter, have profoundly influenced the understanding of microstructures by providing the opportunity to interface various electron and X-ray detectors so that high-resolution chemical information may be obtained to a similar spatial resolution (Carpenter (1982)). We will therefore consider this type of electron microscopy in two parts: first the formation of images and second the methods of undertaking chemical analysis to a high spatial resolution when interfacing energy dispersive Xray spectrometers. 6.4.11
STEM imaging
The reciprocity theorem allows a comparison of the images formed in the conventional transmission and STEM instruments (figures 6.66(a) and (b)). This theorem states: ‘If a signal is detected at point A when a source is placed at point B, then the same signal in amplitude and phase will be detected as B if a source is placed at A’. Replacing the electron source and condenser of the conventional microscope in figure 6.66(a) by a detector, and the photographic plate by an electron source, gives a STEM optical system (figure 6.66(b)). Since the electron paths are identical for both the
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Figure 6.66. Ray diagrams for (a) conventional and (b) scanning transmission electron microscopy illustrating the reciprocity principle. (c) Formation of a convergent-beam diffraction pattern in the detector plane of a STEM instrument showing the position of the bright field detector aperture.
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instruments then, from the reciprocity theorem, the images should be identical, with a resolution determined approximately by the direction of the incident electron beam. Therefore, in the STEM system shown in figure 6.66(c), the incident beam in the specimen has a convergence defined by the objective aperture. For each point of the incident beam, a diffraction pattern is produced on the detector plane. As discussed in chapter 4, this is a convergent beam diffraction pattern where for a very thin crystal the central beam and each diffraction spot form a circular disc of uniform intensity; for thicker crystals these contain complicated intensity modulations. Certainly the intensity distribution in these convergent beam patterns contains a considerable amount of information on the local atomic arrangements within the region of the excited crystal. If a small aperture is placed to contain the central spot of the convergent beam pattern, a bright field image is produced. As shown by Cowley (1986a), for a STEM point source, the wave incident on the specimen is given by Fourier transform of the objective lens transfer function 0 ðrÞ
¼ cðrÞ þ isðrÞ ¼ FT fAðuÞ exp½i 0 ðuÞg
ð6:59Þ
where r and u are two-dimensional vectors in real space, is the phase factor in the lens transform function, AðuÞ is the lens aperture function and FT is the Fourier transform operator. The latter terms combine to give the spread functions for amplitudes in coherent images. For a thin foil specimen the transmission function is q(r R), where R is the translation of the specimen relative to the incident beam, or vice versa, and the wave amplitude on the detector plane, R ðuÞ is given by R ðuÞ
¼ ½QðuÞ expð2iu RÞ½AðuÞ exp½i ðuÞ
ð6:60Þ
where QðuÞ is the Fourier transform of qðuÞ the phase object approximation transmission function and the intensity distribution is IR ðuÞ which equals j R ðuÞj2 . The image signal, JðRÞ, corresponding to beam position, R is ð ð6:61Þ JðRÞ ¼ IR ðuÞDðuÞ du where DðuÞ describes the detector aperture. In the limit for a very small axial detector, DðuÞ is replaced by ðuÞ and equation (6.61) becomes JðRÞ ¼ jqðRÞ tðRÞj2
ð6:62Þ
which is equivalent to plane-wave illumination in the conventional transmission electron microscope. As the electron detector diameter is increased, the signal strength increases but unfortunately although small electron beam diameters are used in the STEM there is still a limitation arising from the small number of electrons present. This results in the need to discriminate the image
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signal from that of the background. If there are N electrons reaching an image point, the statistical fluctuation will be N 1=2 and to detect this the signal-to-noise ratio N=N 1=2 should be >100/1. Practically this limits the resolution for a thermal tungsten filament source to 7 nm whereas for a brighter field emission source 0.2 nm can be attained (see chapter 5). Unfortunately, the bright field phase contrast term for a thin specimen passes through a maximum and decreases to zero as the collector aperture size approaches the objective aperture size. For thin specimens the secondorder bright field amplitude contrast increases continually with collector aperture size. Thus, the collector aperture size and defocus to give the optimum image contrast and resolution can be established for each type of specimen. The reader is referred to the papers of Cowley (1986b) and Cowley and Au (1976) for a complete mathematical description of image formation in the STEM mode of operation. An effective way to align instruments to obtain routinely the optimum resolution for high-resolution imaging is to use the Ronchigram (Cowley (1986c)) and (Rodenburg and Lupini (1999)). In figure 6.66(c) the electron probe is the beam cross-over focused at the specimen plane. The detectors are positioned at the bottom where the convergent beam electron diffraction pattern is formed. The Ronchigram, also known as the Gabor hologram, is simply the disc of undiffracted electrons that are formed at the centre of this pattern. Aberrations in the probe forming optics complicate the Ronchigram. Spherical aberration causes high-angle electron beams to be brought to a focus higher up the column. When the probe forming lens is underfocused the Ronchigram has two regions: (i) a central portion where the shadow image is reversed and (ii) an outer region where the image is not reversed because adjacent beams cross above the specimen plane. The presence of misalignment or astigmatism in the optics of the STEM will distort the symmetry of this pattern. Adjusting the electron optics to produce a flat Ronchigram so that the intensity is distributed equally across the region ensures that every electron has passed through one point in the specimen. This procedure means that a perfect focus condition is achieved. Aberrations usually prevent this ideal condition, but by approximating to a flat Ronchigram allows optimum performance of the instrument to be achieved (Rodenburg and Macak (2002)). In a dedicated STEM instrument as proposed by Crewe (1968) (figure 6.67), a field emission electron source produces a high brightness beam of 0.3 nm diameter with a current of 1011 A. The specimen chamber is evacuated by ion-getter pumps to better than 5 106 Pa. The electron current that strikes an annular detector modulates the intensity and it is that which provides the image on a synchronously scanned display unit. Moreover, a signal can be obtained from electrons that have lost energy as well as from those which pass through a hole in the annular detector with no energy loss. These three signals or any linear combination can be used
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Figure 6.67. Scanning transmission electron microscopy: the dedicated instrument is shown, giving detail of the field emission electron gun and the first and second condenser assembly.
to create an ‘image’. To image individual atoms, the annular detector can be set to collect these electrons that are elastically scattered from collisions with the nucleus to reveal atom positions. Moreover, since the probability of elastic scattering is proportional to atomic number, Z 3=2 , the signal increases for heavier atoms so that they can be visualised on a low atomic number substrate. The more widely used of the two types of scanning transmission electron microscopes is the extension to the conventional transmission electron microscope, since it is favoured for overall flexibility of operation. The instrument is, however, quite complex, and represents a compromise between the design requirements for maximum resolution imaging, diffraction performance and elemental microanalysis. As discussed below, it is to achieve the latter that the design has been progressively changed to optimise performance. Figure 6.68 shows a STEM micrograph of a superalloy with a distribution of 0 ordered fcc precipitates in a phase, fcc, matrix. It has to be remembered that in general the conventional transmission microscope provides images from larger, useful areas and the resolution is better than for the corresponding bright field STEM image. The STEM images are generally more noisy because the electron collection efficiency is low. Effort is now being directed to two areas to improve image quality: one is the use of multiple bright field detectors to improve the spatial resolution and contrast, and the other is to provide more accurate digital intensity measurement. In general, for imaging defects such as dislocations in
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Figure 6.68. Scanning transmission electron micrograph showing ordered 0 precipitates in a matrix for the superalloy IN738.
crystals, the STEM offers a greater variety of possibilities than conventional microscopy. An example of the steps being taken to achieve very high spatial resolution for nano structural imaging coupled with detailed spectroscopic analytical capabilities is the Super STEM, which has been commissioned as a national facility in the UK. This instrument takes advantage of two main developments, one in the area of spectrometry and the other aberration correction. As described previously there have been progressive improvements so that it is possible to produce electron energy loss spectra that are comparable with the results of X-ray absorption spectra over a wide range of energy loss, from about 1 eV to more than 1 keV (Krivanek et al (1987) and McMillan et al (1992)). In addition, by invoking the beam aberration correction system developed by Krivanek et al (1997) combined with computer controlled multiple focusing it is possible to produce electron probes that can achieve resolutions of 0.1 nm or less. At present the SuperSTEM has yet to demonstrate its potential and, indeed, the contribution it should be able to make to the imaging of chemical analyses of materials at the nanoscale. However, in developing this as a central high-cost facility, advantage is being taken of computer interaction via the Web to provide interaction and use by a wide number of users at various geographical locations. In the case of beam-sensitive materials, such as polymers, it is possible to use the strengths of the STEM to great advantage. It is very difficult to obtain images of undamaged polymers in the transmission electron microscope because those electrons which interact with the specimen are highly ionising and destroy the chemical bond. The free radicals formed accelerate the process of molecular decomposition of the polymer so that significant changes to the microstructure arise (Vesely (1988)). The major processes are loss of side groups, crosslinking, chain scission and the formation of new compounds more resistant to damage by the electron beam than the
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Figure 6.69. The dependence of the diffracted intensity on the electron dose for polyethylene irradiated with 100 keV electrons: a change in the former is a measure of loss of crystallinity.
original polymer. Indeed it is possible to measure the loss of crystallinity, for example in polyethylene, from the change in the diffracted beam intensity for a given electron dose (Veseley (1983, 1984)) (figure 6.69). The point at which the diffracted intensity falls to 37% of the initial intensity is the critical dose which is a characteristic value for a given polymer specimen thickness, temperature and accelerating voltage, and varies from 50 Cm2 to 500 Cm2 . In the scanning transmission electron microscope, the beam is focused to a small electron diameter by the condenser lenses and highly excited objective lens, and is scanned across the specimen so that it is possible to work with a low beam current density. It is this ability to control the electron beam, locate it accurately on the specimen without damaging surrounding areas and record at low current densities that makes the technique so well suited for evaluating the microstructures of beam-sensitive materials (Vesely (1984) and Finch and Vesely (1987)). In figure 6.70(a) and (b), we compare STEM and CTEM images obtained from a highdensity polyethylene spherulite which shows substantial morphological changes due to beam damage when using the conventional imaging mode (Vesely (1983)). Differential phase contrast (DPC) is a quantitative method of producing magnetic domain images (Chapman (1984) and Tsuno (1988)) which has the advantage of characterising recording materials and permanent magnets (Chapman et al (1983)). As shown in figure 6.62(a) a split detector is placed on the diffraction plane, which is transferred from the objective
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Figure 6.70. A spherulite of high-density polyethylene is shown, (a) in scanning transmission and (b) in conventional transmission electron microscopy modes. Substantial morphological changes due to beam damage are visible in the latter micrograph (Vesely (1983)).
back focal plane to the plane below the projector lens by the imaging lens system. If the incident electrons are parallel to the microscope axis, electrons passing through domains with one direction of magnetisation intersected by one half of the detector, A, and those through the other domains by the other half, B. Since in STEM the convergent electrons are incident in the specimen, producing a small probe where the deflection angle for electrons is smaller than the convergent angle of the incident electrons. Thus the split of electrons of the back focal plane is smaller than the radius of the convergent disc. The difference signal provides the resultant domain structure image. The contrast of the subtracted signal is proportional to the magnetisation and this provides a measure of the magnetisation rotation around the domain wall. Figure 6.71 shows differential phase contrast images revealing the sub-domain structure observed on a large grain size specimen of 6.06% Si–Fe annealed at 1200 8C for 1 h. The Fresnel and Foucault micrographs are shown in figures 6.71(a) and (b) respectively. 6.4.12
Contrast analysis
In recent years both the Fresnel method and high angle annular dark field imaging in the STEM instrument have been used to investigate local composition distributions, such as grain boundary composition in materials, thereby making use of the high spatial resolution these techniques offer. Fresnel contrast Ozakaya et al (1993) applied Fresnel contrast to characterise the distribution of tin at high angle grain boundaries in an Al–0.09 wt%Sn alloy aged at a
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Figure 6.71 Sub-domain structure observed in a large grain size specimen of 6.06%Si–Fe annealed at 12008C for 1 h (a) Fresnel micrograph, (b) Foucault micrograph.
temperature of 473 K. A through focal Fresnel series of data for a high angle boundary are shown for three thicknesses of foil in figure 6.72(a)–(c), with the boundary being nearest to edge in figure 6.72(b). The segregation is localised as revealed from this series which shows (i) a thin dark absorption line in the mean focus images and (ii) absorption enhanced double dark fringes in the under focused images. Here the contrast is affected by the magnitude and form of the potential changes associated with the segregation of the tin and the retained rigid body displacements for the boundary as well as the different absorption behaviour of aluminium and tin. By matching these contrast profiles with those obtained from image simulations it is possible to obtain a measure of the width, 0.3–0.8 nm, and magnitude of the segregated tin, 2.0 wt% profile at the boundary. Atomic number contrast Atomic number or Z-contrast images, unlike conventional phase-contrast images, are incoherent and thereby allow columns of different atomic number atoms to be distinguished and located directly from the image (figure 6.73) (Browning et al (1995) and Pennycook and Boatner (1988)). If supported by using maximum entropy image analysis techniques it is possible to deduce atom positions accurately (Gull and Daniell (1978)). This provides a valuable tool since two columns separated below the resolution limit will image as a single, bright feature, that can be deconvolved into the constituents by image analysis. The technique was originally used with
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Figure 6.72. Fresnel profiles of a grain boundary in Al–0.09 wt% Sn for three thicknesses (contrast levels and the defocus in nm are given on the profiles) (Ozakaya et al (1995)) (reproduced by permission of Blackwell Science Publications).
dedicated ultra-high vacuum STEM instruments but it is now within the capability of FEG–TEM instruments. In practice Z-contrast images are formed by collecting high angle scattered electrons from the foil specimen on to an annular detector and synchronously displaying the integrated output while the incident electron beam is scanned across the specimen (figure 6.74) (McGibbon et al (1996)). At high angles in the range 75– 150 mrad the detected intensity is mainly the result of thermal diffuse scattering. Lateral coherence between atomic columns in a specimen are averaged by detecting over a large angle range and coherence between atoms in a given column is reduced by thermal vibrations to residual correlations between near neighbours. Since these latter correlations are a second-order effect, each atom can be considered as scattering independently with a crosssection close to a dependence of Z 2 . It is this mass section that forms an
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Figure 6.73. Schematic diagram of the detector arrangement in a dedicated STEM showing that the atomic resolution Z-contrast image and atomic resolution electron energy loss spectrum can be acquired simultaneously.
object function that is strongly peaked at the position of the atom. Hence for a specimen where there is little or no dynamic diffraction the detected density is a convolution of this object function with the electron beam intensity profile. The small width of the object function, which is 0.02 nm, gives a spatial resolution limited by the incident electron beam size of about 0.2 nm. Therefore as the electron beam is scanned over the specimen an atomic resolution compositional map is generated where the intensity depends upon the atomic number of the atoms from which the columns are compared. Following this procedure a Z-contrast image for a symmetric [001] tilt boundary (36.88) in SrTiO3 is shown in figure 6.74(a). The brighter spots within the image correspond to the lighter TiO columns (Z ¼ 22 for Ti and Z ¼ 8 for O); the pure O columns are not visible. Maximum entropy image processing is used to deconvolute the positions and intensities of the Sr and Ti atoms in each column. Figure 6.74(b) shows the corresponding grain boundary structural model for this 36.88
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Figure 6.74. (a) Z-contrast image of 36.88 symmetric tilt grain boundary in SrTiO3 compared with (b) the maximum entropy image providing scattering intensities and coordinates of the Sr and Ti atomic columns directly from the image (McGibbon et al (1996)). (c) Grain boundary structural model for a 36.88 symmetric grain boundary in SrTiO3 where the grain boundary structural units are shown outlined. (d) A comparison of (i) Ti L2;3 -edge and (ii) O K-edge spectra acquired from the bulk and boundary of a SrTiO3 bicrystal, showing that the octahedral Ti–O coordination is maintained across the boundary (McGibbon et al (1996)) (reproduced by permision of the Materials Research Society).
symmetric grain boundary. Figure 6.74(c) shows the corresponding energy loss spectra. Therefore this technique has the potential for establishing the position and type of atoms distributed within a specific microstructural feature.
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372 6.4.13
Electron sources Analytical transmission electron microscopy
The scanning transmission electron microscope (STEM) has provided the basis for considerable advance in the application of electron optical techniques by affording high spatial resolution chemical microanalysis for characterising the microstructure of materials. This has been achieved by interfacing an energy dispersive X-ray spectrometer (figure 6.75) to the microscope, thereby allowing the local composition within the foil specimens to be determined to a resolution approaching that of the transmission image (Goodhew and Chescow (1981), Chandler (1977), Goldstein (1979), Zaluzec (1979), Carpenter (1982), Newbury and Williams (2000) and Doig and Flewitt (1984)). This uses the ability of the STEM to form small-diameter, <10 mm, high-intensity electron beams. Of the two basic types of scanning transmission electron microscopes described in section 6.4.10, that most widely used for this application is the extension to the conventional
Figure 6.75. Schematic diagram of a scanning transmission electron microscope interfaced with an energy dispersive spectrometer for undertaking high spatial resolution chemical analysis.
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transmission electron microscope since it has a greater overall flexibility of operation. Certainly as an analytical transmission electron microscope this instrument is complex and represents a compromise between the design requirements for high-resolution imaging, performance and elemental analysis. An earlier technique using a wavelength dispersive spectrometer interfaced to a conventional transmission electron microscope was restricted in application by the limited spatial resolution (Duncumb (1966)). Since that time there has been a progressive development in the instrumentation effecting improvements in the detection limits, spatial resolution and reliability of the systems. Among the most important developments is the ability to use higher brightness field emission sources, better vacuum systems to reduce contamination, higher accelerating voltages for better specimen penetration, smaller electron beam diameters, and improved X-ray detection systems. The instrument development has continued along two somewhat separate paths. The intermediate voltage 300–400 keV CTEM/STEM system has evolved as a convenient method for higher spatial resolution, bright field imaging where the higher voltage allows thicker, more realistic specimens to be analysed. However, the dedicated STEM with a field emission source at conventional voltages, 100 keV, such as those produced by Thermo VG Scientific (VG Series of instruments), provides the tool for achieving highest spatial resolution chemical analysis. As described for the electron microprobe analysis and the energy dispersive spectrometers in chapter 5, computer systems are used with the analytical electron microscopes to control the microscope and analysis system, acquire data and process that data online. It is now possible to undertake quantitative high resolution (<2 nm) X-ray mapping (XRM) (Williams (1998) and Williams et al (1999)). To achieve this two energy dispersive spectrometers are used to give a large solid angle of X-ray collection of about 0.5 Sr. This provides maps of the distribution of elements within the microstructure of thin foil specimens. Spatial resolution and detectability Spatial resolution and the minimum quantity of an element detectable are interrelated in microanalysis since any improvement in spatial resolution is balanced by a corresponding decrease on the detectability limit. This is because at the higher spatial resolution the analysed volume is smaller and the signal intensity is reduced so that the acquired energy dispersive X-ray spectrum will be more noisy and the small peaks arising from low concentration of elements will be less readily detected. Unfortunately the understanding of spatial resolution in analytical electron microscopy has not been helped by the lack of an accepted definition (Williams (1988)). Spatial resolution is a combination of the diameter of the electron beam at the surface of the specimen (figure 6.76(a)) and the spreading of this beam as it passes through the thickness of the specimen. The first
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Figure 6.76. STEM-EDS X-ray microanalysis: (a) interaction of an electron probe with a thin foil; (b) section along A–B in (a) showing the volume of foil from which X-rays are generated together with the cylinder section (dotted) within which 90% of the X-ray events occur.
quantitative description of spatial resolution was given by Goldstein et al (1977) in terms of the spatial extent of an elastically scattered electron beam emerging from the bottom surface of a foil specimen. More recently resolution has been related to the diameter of a cylindrical volume, parallel to the axis of the incident electron probe, within which an arbitrarily selected, fixed proportion (usually 90%) of characteristic X-ray events occur (figures 6.76(a) and (b)). Descriptions of electron scattering and therefore spatial resolution of microanalysis in thin foils have been achieved using analytical approximations and Monte Carlo methods of calculation Joy (1995).
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However, there remain some discrepancies in the numerical values obtained between various workers (Hall et al (1981), Stephenson et al (1981), Kyser (1979) and Doig et al (1981, 1982)) that originate from differences in the input parameters and calculation method. Unfortunately, these Monte Carlo procedures involve lengthy computation times and, as such, are not usually so readily available online to most operators undertaking microanalysis. In view of this, the simple analytical approximation to describe the electron intensity distribution within an elastically scattered electron beam was developed based on a statistical calculation of electron scattering behaviour in the foil (Doig et al (1981, 1982)). Indeed, such an approach is not dissimilar to that adopted in the Monte Carlo procedure (Kyser (1979)) and the predicted beam spreading is in good agreement with the various methods (figure 6.77(a)). Regardless of the particular description of spatial resolution, it is generally agreed that scattering of the electron within the foil increases with atomic number, material density and foil thickness, and decreases with increasing electron accelerating voltage (figure 6.77(b)). Moreover the spatial resolution degrades as the incident electron beam diameter is increased. More recently Hainton and Vesely (1991) have used the novel technique of examining the irradiation damage zone in a polymeric material by ultraviolet light excitation (figure 6.77(c)). This provides a direct measure of the region from which X-ray excitation can occur. In most cases it is necessary to undertake microanalyses on specific features or regions within the microstructure which extend throughout the foil volume and are not confined simply to the exit surface. Therefore the volume distribution of incident electron beam intensity is required to establish the emitted X-ray intensity (figures 6.76(a) and (b)). The measured characteristic X-ray intensity derived from a given microstructural feature, I 0 , is a convolution of the volume electron flux intensity, IðVÞ, and the solute composition, XðVÞ, distributions within the total sampled region of the foil (Doig et al (1981)), ð 0 ð6:63Þ I ¼ C IðVÞ XðVÞ dV V
where C is a constant which describes efficiency of X-ray generation, emission and detection for the particular element of interest. The analytical expression for the electron intensity distribution within the foil, IðVÞ, is Iðr; tÞ ¼ Ie fð2B2D þ 0 t3 Þg1 expfr2 =ð2B2D þ 0 t3 Þg
ð6:64Þ
for a total incident electron flux of Ie where Iðr; tÞ is the electron flux at a distance r from the centre of the electron beam and depth t in the foil, BD is a measure of incident electron beam diameter, D(FWHM) ¼ 2.35BD , and 0 defines the electron scattering characteristic of the foil material: 0 ¼ ð4Z=E0 Þ2 ð =A500Þ:
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ð6:65Þ
376
Electron sources
Figure 6.77. (a) Results of electron beam scattering calculated using analysis by Doig et al (1981b) (dotted lines) superimposed on results from Monte Carlo calculations (Kyser (1979)). (b) Spatial resolution of STEM X-ray microanalysis in thin foils for a range of elements as a function of electron accelerating voltage (foil thickness 200 nm and incident electron probe diameter 5 nm). (c) Polymeric material subjected to 100 keV electrons revealing electron scattered region by ultraviolet excitation (courtesy Hainton and Vesely).
Here Z, A and are atomic number, atomic weight and density of the material and E0 is the electron accelerating voltage in eV; is given in units of nm1 . The objective of a microanalysis experiment is to optimise the measurement of I 0 in equation (6.63) for the particular microstructural feature defined by the term XðVÞ. This can be achieved by controlling the term IðVÞ, or rather Iðr; tÞ (equation (6.64)). Here, electron flux, Ie , is related to the electron source current, I0 the incident probe size, d, and the recording time for data acquisition, , such that (Beaman and Isasi (1972) and Doig and Flewitt (1983(a)) 8=3
Ie ¼ C0 I0 BD
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ð6:66Þ
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where C0 is a constant dependent on the geometry and design of the individual microscope illumination system. This or similar analysis procedures allows the experimental variables of electron beam diameter, foil thickness and electron accelerating voltage to be examined and their influence on IðvÞ to be considered and the microanalysis conditions optimised (Doig and Flewitt (1983a, 1983b and 1983c)). If we consider either a precipitate with a diameter sufficiently small so that it is contained within the cross-section of a thin foil or a segregation of an element to a grain boundary, the detectability of the particular element being analysed for these microstructural features in the X-ray spectrum is determined by the number of the characteristic X-ray quanta contained in the peak, Np , compared with those in the background of the spectrum Nb , figure 6.29, (Doig and Flewitt (1983, 1984)). Detection of the X-ray peak requires the magnitude to exceed the error in its estimation such that Np > ðNp þ Nb Þ1=2 þ ðNb Þ1=2 :
ð6:67Þ
For a given electron source the total incident electron flux, Ie , is related to the incident probe size, BD as given by equation (6.64). The total emitted X-ray intensity increases with electron diameter and the background X-ray intensity in a recorded spectrum is proportional to the electron beam current, Ie , the foil thickness, t, and the total recording time, , such that 8=3
Nb ¼ C0 BD t
ð6:68Þ
0
where C is a constant for a particular X-ray energy and illumination system which characterises the ‘effective’ electron intensity for X-ray generation and detection. The number of counts in the X-ray peak, Np , for the element contained in a localised microstructural feature, such as a small precipitate or segregation to a grain boundary, is given by the volume integral: ð 8=3 0 IðVÞ XðVÞ dV ð6:69Þ Np ¼ K RBD V
where R is the characteristic X-ray peak-to-background ratio obtained from a homogeneous specimen of unit composition and V is the foil volume. The inequality in equation (6.67) defines the condition for detecting a characteristic X-ray energy peak from the segregated species in a recorded X-ray spectrum. Nb and Np are calculated from equations (6.68) and (6.69) for given values of foil thickness, t, and material, , spectrum recording time, , electron probe size, BD , electron accelerating voltage, E0 , ‘effective’ electron intensity, K 0 , and composition distribution XðVÞ to give the conditions for detecting the local composition for a particular element within these microstructural features. For a particular microstructural feature, the volume integral component of equation (6.69) decreases with increasing incident electron beam diameter
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Electron sources
Figure 6.78. Schematic diagram showing the influence of sampling electron probe size on the detectability in the recorded X-ray spectrum of segregations to small microstructures contained within a thin foil.
since a smaller proportion of the total electron flux interacts with the feature. Conversely, the total electron current increases rapidly (equation (6.66)), such that the total electron flux that interacts with the feature tends to increase. Therefore, these two competing effects define a range of electron beam diameter over which the inequality in equation (6.66) is satisfied such that the intensity of characteristic X-rays emitted from the element measured at the feature will be detected in the recorded spectrum. Clearly for very small features the inequality will never be satisfied since the volume integral term (equation (6.69)) tends to zero and the element cannot be detected. The overall behaviour is shown schematically in figure 6.78 where the electron beam diameter range for detection is given as a function of the characteristic dimension of the particular microstructural feature analysed: the diameter of an embedded precipitate or the width of a grain boundary segregation profile. For small incident electron beams the overall X-ray count rate is low such that statistical noise in the recorded spectrum precludes detection, whereas for large beams the volume integral term decreases and the measured Np =Nb is reduced to a level below that where the increasing statistical confidence in the data compensates. The form of the curve defining the bound for detectability displays a minimum which provides a measure of the ultimate sensitivity for microanalysis. Quantitative analysis As discussed in section 6.3.7, classical electron microprobe analysis of bulk specimens considers all the ZAF factors to obtain a quantitative evaluation
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of the local chemical composition. In the case of the analytical electron microscope we use specimens which are sufficiently thin to allow electron transmission. Under these conditions few of the electrons are backscattered and, indeed, they lose only a small proportion of their energy within the specimen. Therefore the characteristic X-ray intensity, IA , emitted from the thin specimen is given by (Goldstein (1979)) IA ¼ const: XA WA QA A t=ZA
ð6:70Þ
where XA is the concentration of element A, WA is the fluorescence yield for element A, A is the absorption of element A, QA is the ionisation crosssection (the probability per unit path length of an electron of a given energy effecting ionisation in a particular K, L or M shell for the atom A), t is the specimen thickness and ZA is the atomic weight of element A. If the specimen is infinitely thin the effects of absorption and fluorescence will be negligible and the generated X-ray intensity approximates to that leaving the specimen. A number of methods have been developed for quantitative chemical analysis of thin specimens (Duncumb (1968), Philbert and Tixier (1968), Nasir (1972) and Tixier (1979)). However, from equation (6.70) the composition of the analysed volume is derived by measuring the emitted intensity, IA , and calculating the constant and other terms; this is not easily achieved. Moreover, the specimen thickness can vary from one position to another on the foil specimen and it is not easy to measure this value continually. Several investigators (Philbert and Tixier (1968), Nasir (1972), Tixier (1979) and Cliff and Lorimer (1975)) proposed the analysis is undertaken based upon the intensity ratio of two elements in the foil measured simultaneously and related directly to the mass concentration ratio. This is now referred to as the Cliff–Lorimer method and here the ratio of two characteristic X-ray intensities, IA =IB , is related to the corresponding weight fraction ratio, XA =XB , by XA =XB ¼ KAB IA =IB
ð6:71Þ
where KAB is a constant at a given accelerating voltage which is independent of P both specimen thickness and composition. A normalisation procedure, Xn ¼ 1, is used to convert the weight fractions into weight ratios. Further equations similar to the above account for the intensity ratio of any other elements giving rise to detected peaks so that the approach can be extended to multi-component systems. The accuracy of this ratio method depends upon the calibration of the KAB values which can be established either experimentally or by calculation. It is unnecessary to establish KAB values for all elemental pair combinations since it is practice to relate each element to a reference, such as silicon. The relationship between K factors and KAB factors is given by KAB ¼ KASi =KBSi ¼ KA =KB
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ð6:72Þ
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Electron sources
Figure 6.79. (a) Comparison of measured K factors for K lines relative to Si (Wood et al (1981)). (b) Experimental KAFe factors for K lines (Wood et al (1981)) for a 120 keV operating potential ðSÞ direct (kÞ indirect. (c) Experimental KAFe factors for L lines (Wood et al (1981) (kÞ (1984)) (120 keV) and Goldstein et al (1979) (100 keV) (Þ. Below a characteristic X-ray energy of 3.2 keV, the KAFe factor is calculated by using the intensity ratio of the L and L lines of element A (reproduced by permission of Plenum Press).
Although silicon provides an appropriate basis for ceramics and semiconductors, for metals it is more helpful to display the K factors by reference to iron. Figure 6.79(a)–(c) show the KASi and KAFe experimental factors obtained by Wood et al (1981) at an accelerating voltage of 120 KeV. For the iron base, homogeneous alloys are relatively easy to obtain enabling direct determination of KAFe : when no convenient alloy is available indirect methods are required. For example to obtain KAFe , KAB is measured from
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an alloy A–B and KAFe is derived using the measured KBFe factor so that: KAFe ¼ KAB =KBFe :
ð6:73Þ
Figure 6.79(c) has corresponding values for the L series lines. The thin specimen criterion neglects effects of X-ray absorption and fluorescence, unfortunately, this is not always possible and Goldstein et al (1979) offer a correction of KAB for the preferential absorption of X-rays from elements A and B: ð1 B expð B = B Þ cosec dt ð6:74Þ KAB ¼ KAB=TF ð 10 A expð A = A Þ cosec dt 0
where KAB=TF is the absolute value of KAB when there is no absorption or fluorescence; therefore it is of zero thickness, AB is the depth distribution of X-ray production from element A or B as a function of mass thickness ð t) and mAB = AB is the mass absorption coefficient for X-rays from element A or B in the specimen and is the take-off angle. X-ray absorption is important for thin foils when considering X-ray emission from elements of atomic number approaching 11 and/or thick specimens. To a first approximation absorption is accommodated by assuming that the average X-ray path is half the foil thickness: I ¼ I0 expð t=ð2 cosec ÞÞ
ð6:75Þ
where the terms have been defined previously. Assuming an X-ray travels an average distance equal to t=2 cosec , where t is the thickness from the specimen surface, the observed intensity ratio IA =IB compared with an infinitely thin specimen becomes IA =IB ¼ fI0A =I0B g expðð A B Þ t=ð2 cosec ÞÞ
ð6:76Þ
where mA and mB are the mass absorption coefficients. An iterative method is necessary to deduce a mean value of the density, , for the specimen. Therefore, it is important to measure the foil thickness at the position where the microanalysis is undertaken. Following an analysis by Philibert and Tixier (1968) for the specimen fluorescence correction, Nockolds et al (1979) derived an analysis using the model shown in figure 6.80(a) where X-ray generation is assumed uniform through the specimen along the line of the incident beam. Here the ratio of fluorescence intensity I A to the primary intensity IA is given by I A =IA ¼ XB WB ððrA 1Þ=rA ÞZA =ZB ð = ÞAB ðEcA =EcB Þ ðln E0 =EcB Þ=ðln E0 =EcA Þ t=2½0:932 lnð B = B Þ t sec
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ð6:77Þ
382
Electron sources
Figure 6.80. Analytical electron microscopy effects of foil thickness comparing: (a) uncorrected and fluorescence-corrected data as a function of thickness for a Fe–10.5 wt% Cr alloy; (b) the fluorescence correction predicted by the model of Nockold et al (1979) and that of Philibert and Tixier (1968) for a Fe–10 wt% Cr alloy as a function of thickness [100 keV] (reproduced by permission of Plenum Press).
where WB is the fluorescence yield of element B, rA is the absorption edge jump ratio of element A, ð = )AB and ð = )B are the mass absorption coefficients of X-rays from element B in element A and the specimen, ZA and ZB are the atomic weight of elements A and B and EcA , EcB are the critical
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383
excitation energies for the characteristic radiation of A and B. Nockold et al (1979) and later Twigg et al (1981) showed that equation (6.77) provides the basis for correcting data, for example a specimen of Fe–10.5 wt%Cr up to a thickness in excess of 600 nm (figure 6.80(b)). Foil thickness measurement It is important to achieve a rigorous microanalysis to measure the thickness of the foil specimen to accommodate absorption corrections. A number of techniques have been developed to determine the thickness of thin foil specimens, including the use of thickness fringes (Edington (1976)), trace analysis and parallax measurements (Hirsch et al (1965) and Chester (1985)) and convergent beam diffraction. The periodicity of extinction con tours is a maximum at the exact Bragg condition, s ¼ B , and equals the extinction distance g . In a bright-field image a light and dark sequence of fringes occurs at integral values of t=g and the extinction distance can be calculated provided the structure factor is known. For some commonly used materials, values can be obtained from tables. Measurements must be made at the exact Bragg condition because the observed extinction distance g is a function of the deviation parameter. The measurement of extinction fringe spacing gives the foil thickness to an accuracy of 15–20%. The projected width of a crystallographically characterised planar feature, X, such as a slip trace, precipitate or stacking fault (figure 6.81(a)), passing through a foil to intersect the top and bottom surfaces, can be used to determine the thickness. A similar technique involves using parallax separation of objects located on the top and bottom surface of foils. Gold particles evaporated on to both surfaces of a foil are suitable for parallax measurements (Wood et al (1981)), carried out by stereo-microscopy on micrographs obtained with a few degrees of tilt between exposures. This technique has been extended to contamination features (figure 6.81(b)), introduced on to the foil surfaces during their examination (Lorimer et al (1975)) where the thickness, d , is given by: d ¼ X=M tan
ð6:78Þ
where is the angle between the feature and the foil surface and M is the magnification. The major error with this and all trace techniques is establishing the tilt of the foil since a departure of 58 from the horizontal can lead to an error of between 5% and 10% in the calculated thickness, and this approaches 50% for a 158 departure. The convergent beam electron diffraction method (Kelly et al (1975)) relies on the two-beam solution of the dynamical equations which describe the diffracted intensity as a function of deviation parameter at given values of t and g . The positions of the minima are described by ðsi =ni Þ2 ¼ ð1=g2 Þð1=ni Þ2 þ ð1=t Þ2
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ð6:79Þ
384
Electron sources
Figure 6.81. The measurement of foil thickness, d , from (a) a trace of projected width, (b) surface features such as contamination spots formed on an untilted foil and the same foil tilted through an angle, .
where si is the deviation parameter at the ith minimum, and ni are integers which correspond to the ‘order’ of the minima. Equation (6.79) is defined for ni > t=g , and the order of the minimum closest to s ¼ Oðn1 Þ is the next integer above t=g . There is an analogous equation for the maxima in the intensity profile: ðsi =xk Þ2 ¼ ð1=g Þð1=xk Þ2 þ ð1=tÞ2
ð6:80Þ
where the constant xk is defined by xk ¼ tan xk . Equations (6.79) and (6.80) define the same straight line and a plot of ðsi =ni ; xk Þ2 against ð1=ni ; xk Þ2 yields values of g from the gradient and t from the intercept. The distances to be measured are L0 from the centre of the diffracted beam profile to the centre of the transmitted beam and L1 , L2 , L3 and L4 from the centre of the diffracted beam profile to each of the successive minima. These distances are indicated in figure 6.82, which shows the 220 intensity
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385
Figure 6.82. Determination of specimen thickness by measuring the distances of successive minima from the centre of the transmitted beam in the convergent beam electron diffraction method (Kelly et al (1975)) (reproduced by permission of Taylor and Francis Ltd).
profile of a silicon crystal taken at an approximately two-beam condition. si is then given by (=d 2 ) (Li =L0 ) where is the incident beam wavelength and d is the spacing of the reflected planes. For further details of the analytical procedure, the constants xk , the nature of the extremum which always occurs at s ¼ 0 and the sequence of extreme, values of ni and xk expected at various thickness, the reader is referred to the original paper of Kelly et al (1975) and to the very complete description given by Allen (1981). Ecob (1986) has addressed the errors associated with this method and, apart from measurement errors, these can arise from multi-beam scattering and anomalous absorption, because neither is incorporated into the two-beam, zero absorption equations on which the method is based. However, it is shown that these difficulties can be circumvented for the purpose of quantitative electron microscopical analysis of microstructure by recording all the required convergent beam diffraction patterns under identical conditions, and by measuring the effective extinction distance for the given conditions using a preliminary analysis of at least three patterns recorded at widely varying foil thickness. Subject to a judgement on the required accuracy of the foil thickness determinations, the latter can then be made relatively easily. Specimen preparation In principle there is no need to adopt special specimen preparation procedures for undertaking analytical electron microscopy. The choice remains between thin foils and extraction replicas. The latter have found increasing application for measuring the composition of a phase such as a small precipitate, without any contribution from the adjacent matrix. In the case of larger precipitates such as carbides encountered in high speed steels that are of dimensions greater than the specimen thickness, ion thinning is often preferred to electrolytic thinning (Thompson et al (1976)) (figure 6.83(a)), to ensure that preferential thinning of a particular phase does not occur. However, in the case of foil specimens, surface oxide films and
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Electron sources
Figure 6.83. Specimen preparation for the analytical electron microscope. (a) Thickness variations in a foil containing a second phase thinned electrolytically and ion thinned. (b) Variation of X-ray intensity ratio with foil thickness in an Al–6%Zn–2%Mg– 1.3%Cu alloy (l, Zn/A1; k, Cu/A1) 60 keV. (c) Schematic diagram showing calculated variation in X-ray intensity with foil thickness, b, for a surface enriched layer of constant thickness, a.
segregation of one constituent to the surfaces have been observed which can distort a chemical analysis. This is particularly relevant in figures 6.83(b) and (c) where a series of measurements were made at points transversing thickness variation extending from the edge towards the thick section of a uniform composition foil with an overall wedge shape (Karagoz et al (1989)). Sources of error In addition to errors arising from the difficulties described above there are further potential errors in analytical electron microscopy produced within the illumination system, the specimen and the post specimen system. We
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Figure 6.84. Sources of an analytical electron microscope illumination system artefacts are hard X-rays and uncollimated electrons. Hard X-rays that penetrate the C2 aperture can fluoresce the specimen. Stray electrons poorly collimated or circumventing the final C2 aperture generate spurious X-rays (reproduced by permission of Plenum Press).
intend here to alert the reader to these and offer sufficient caution without describing the complete detail. However, the reader is referred to descriptions by Williams et al (1986), Goodhew and Chescoe (1981) and Hren (1986) for further detail. (i) Illumination systems. The major problems arise from the need to ensure that the electron beam selects the feature of interest in the microstructure and the X-rays generated are exclusive to this region. As shown in figure 6.84, spurious X-rays arise from either uncollimated primary electrons or Bremsstrahlung X-radiation which are usually minimised by the use of appropriate apertures and shielding within the microscope column. However, it is important to ensure extraneous X-rays are not generated and the test undertaken is usually referred to as the ‘hole-count’. Here the incident electron beam is positioned on a hole in the specimen to establish if a specimenderived energy dispersive spectrum is detected. However, this has to be undertaken with care using a specimen with a low energy L line excitation, <5 keV, and a high energy K line excitation >20 KeV. The source of the spurious X-rays can be established from the L=K ratio; a high ratio is derived from electron excitation and a low ratio from X-ray excitation.
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(ii) Specimen. The limitations which must be imposed on an appropriate thin specimen for microanalysis are more rigorous than required for imaging because of the conflicting needs for achieving image contrast and precise microanalysis. Although we have addressed these when considering the preparation of specimens, it is appropriate to consider the effects of contamination. Contamination is present because of the presence of conical carbonaceous deposits which as we have shown can be used to advantage in determining the thickness of a foil specimen (figure 6.81). However, this is undesirable since carbonaceous deposits absorb the lowenergy X-rays preferentially with respect to those of higher energy, increase the X-ray background, and thereby reduce signal-to-background ratio and further spread the incident electron beam to degrade the resolution of the microanalysis. The major sources of the contamination arise either directly from the microscope vacuum system, which has to be as ‘clean’ as possible, or from the specimen. It is the latter that is controlled by the user and indeed a series of precautions should be adopted including pre-pumping the specimens in a separate vacuum system to remove undesirable contamination carried from the preparation stage. (iii) Post specimen. Post specimen contributions arise in the analytical electron microscope because electrons are transmitted and scattered in both the forward and backward directions. As a consequence, incident high-energy electrons can be backscattered into the microscope specimen chamber where interaction can generate X-rays from the cold trap, upper pole piece and spectrometer collimator. This is eliminated by the use of appropriate shielding; similar precautions have to be taken for transmitted electrons. In addition, tilting the specimen to optimise the microstructural feature of interest for imaging and microanalysis can effect fluorescence induced by continuum radiation emitted from the specimen; this depends critically upon the shape, thickness and microstructure of the specimen together with the energy and intensity distribution of the Bremsstrahlung X-rays. Applications In general the application of high spatial resolution chemical analysis has been directed to providing information from extremely small features within the microstructure of materials. Such applications usually involve features smaller than the diameter of the measuring electron beam. One application is measuring the compositions of second phases, another is establishing local solute distributions associated with either grain boundaries or interphase boundaries. In each case because either second phase precipitates can be very small, or the solute composition changes at and adjacent to boundaries are limited to distances of monolayers or a few atomic distances, the spatial resolution due to beam broadening is invariably
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insufficient to enable direct measurement of absolute concentration. Therefore models using Fourier analysis procedures have been developed which allow the true compositions to be deconvoluted from measured values (Rapperport (1969)). For this both Monte Carlo calculations and analytical models can be used to describe the beam broadening (Williams (1988), Goldstein et al (1977), Doig et al (1981), Hall et al (1981), Stephenson et al (1981) and Kyser (1979)). However, the analytical approach (Doig et al (1981)) has the advantage of allowing these calculations to be undertaken using a small computer and as such they can be conducted interactively during the course of making the chemical analysis measurements. One particular application is the identification and measurement of the chemical composition of carbide precipitates in steels. Figure 6.85(a) shows an extraction replica of carbide precipitates which constitutes part of the microstructure of a 214%Cr–1%Mo ferritic steel. These carbide precipitates are distributed on prior boundaries, on lath boundaries and within laths (Stevens and Flewitt (1986)). It has been possible to produce characteristic X-ray spectra from the various carbide types so that it is possible to use the technique of ‘fingerprinting’ to identify a given type of carbide based upon the X-ray spectrum produced (Doig et al (1982), Hippsley (1981) and Titchmarsh (1979)) (figure 6.85(b)). Despite some variation in the relative amounts of the principal elements, iron, molybdenum and chromium it is possible to assign the carbides types M2 X, MC3 , M7 C3 , M23 C6 and M6 C (figure 6.85(b)). In this particular steel, phosphorus was identified to be segregated to the M6 C carbide precipitates at the grain boundaries. Care has to be taken with the interpretation of the phospphorus peak, P/K radiation (2.014 to 2.015 keV), in the presence of molybdenum since it can be attributed to Mo LL radiation (2.013 keV). Using a full least squares analysis procedure such as the Link RTS/2FLS for establishing the shape of the L and K series spectrum profiles, and provided adequate care is taken in acquiring the calibration spectra, it is possible to deconvolute the P K and the Mo LL peak profiles. However, to have the necessary confidence in the evaluation of the P K peak it is important that sufficient X-ray counts are accumulated to reduce statistical errors to acceptable values. The second example relates to the development of chromium depletions at the grain boundaries of a Type 316 austenitic stainless steel as a result of neutron irradiation. Here the benefits of the high spatial resolution instruments using analysing electron probes of 1 nm diameter are evident. Chromium profiles have been determined in relation to the position of grain boundaries in these steels. The results show a chromium depleted region adjacent to the grain boundary (figure 6.86), and an increase in concentration at the position of the grain boundary. However, in this case, unlike similar depletions in thermally sensitised steels (Doig and Flewitt (1988)), there is no carbide precipitate formed at the grain boundaries for these irradiated materials (Titchmarsh and Dumbill (1996)). These
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Figure 6.85. (a) Extraction replica from a low alloy ferritic steel showing carbide precipitates. (b) Energy dispersive spectra, characteristic of the principal carbide types, obtained from X-ray microanalysis of carbon extraction replicas of the type shown in (a) (reproduced by permission of the Institute of Materials).
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Figure 6.86. Experimental measurements of Cr concentration at two boundaries in neutron-irradiated stainless steels. Each profile clearly demonstrates the presence of a depletion profile adjacent to but not at the boundary, in addition to segregation at the boundary (Titchmarsh and Dunbill (1996)).
measurements made using this high-resolution capability of the STEM–EDS X-ray microanalysis system require further interpretation if the true composition profile is to be derived. The true composition profile is limited by the spatial resolution even for such a small, focused electron probe. The exact form of the grain boundary segregation profile has to be derived using appropriate deconvolution procedures of the type described by Doig et al (1981) and Carter et al (1994). Another example is the case of electrostatic bonding, which is a fast and reliable method of producing a strong bond between ionic conducting glasses and a semiconductor or metal. It is possible to investigate the nature of the bond. In the case of an electrostatic bond formed between silicon and a Pyrex glass the silicon is the anode and the glass is the cathode. The mobile cations move in the glass towards the cathode so that a cationdepleted layer is formed at the interface (Lepienski et al (1993)). This interface has been revealed in bright field transmission electron images (figure 6.87(a)), where a bright layer C 0.5–1.7 mm thick is visible in the glass adjacent to the glass–silicon interface (Van Helvoort et al (2001)). A dark line D is present in this layer C, located 0.2 mm from the edge of the layer with the bulk glass. Energy dispersive X-ray microanalysis (figure 6.87(b)–(d)) shows that the layer C is depleted in sodium and there is a local increase in potassium at position D. These distributions of sodium
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(a)
(b)
(c)
(d)
Figure 6.87. The band formed between Pyrex glass and silicon: (a) bright field transmission electron micrograph of band formed at 623 K at 1000 V for 60 s followed by 623 K at 1000 V and 60 s (Barscale 500 nm), (b) energy dispersive spectrum of region E, (c) detail of sodium peak in (b), and (d) the potassium peak for regions B1, C, D and E (Van Helvoort et al (2001)).
and potassium are consistent with the proposed mechanism of movement of these elements during the bonding process (Carlson et al (1974)). A valuable extension of this high spatial resolution technique is highresolution X-ray mapping which can be applied, for example, to examine localised segregation to grain boundaries (Newbury and William (2000)).
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Figure 6.88 (a) X-ray map of copper on boundaries in Al–4 wt% Cu. (b) Cu composition profile across a grain boundary in (a) (Williams et al (1999)).
This has been applied by Williams et al (1999) to the segregation of copper to the grain boundaries in an aluminium alloy (figure 6.88). Figure 6.88(a) shows the copper distribution at several grain boundaries in a thin foil of Al–4 wt% Cu. The colour scale can be converted to a percentage of copper using look-up tables. The data are then integrated from several pixels across a defined grain boundary in the image. From this information it is possible to obtain the copper composition profile associated with the particular grain boundary (figure 6.88(b)). As a consequence it is possible to obtain similar profiles that correspond to different positions on a given grain boundary and also for all grain boundaries that have been interrogated in the image of figure 6.87(a). Maps of this type provide a powerful method for examining the distribution of elements within the overall microstructure of a material to a very high spatial resolution and to low levels of detection, <100 atoms, in the analysed volume.
6.5 6.5.1
Electron energy-loss spectrometry Introduction
Electron energy losses occur when electrons are reflected or scattered from a solid and they were originally investigated by Rudberg (1927). During the intervening 75 years this has been followed by many theoretical and experimental developments (Hillier and Baker (1944), Egerton (1975, 1978), Joy and Maher (1978) and Joy (1979)) that have resulted in electron energy-loss spectrometry (EELS) becoming a useful analytical tool. Indeed
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Figure 6.89. A schematic diagram of typical electron energy-loss spectrum showing the main characteristic features.
there has been an increasing interest in EELS because of the interest in high spatial resolution X-ray microanalysis for low atomic number elements. This is particularly important for steels which contain interstitial elements C, N, O and B which contribute significantly to the physical and chemical properties of these materials. An energy-loss spectrometer can be interfaced easily to most commercial STEM instruments, thus complementing the chemical analysis system. 6.5.2
Energy loss processes
We will now examine how the various inelastic interactions of electrons with a specimen produce an energy-loss spectrum which has the characteristic features shown schematically in figure 6.89. This typical spectrum contains three clearly identifiable energy regions, where there is no loss, low loss and core loss of momentum and energy. No losses This energy region contains the zero-loss peak. The incident electron beam has a finite width because it has an energy spread, and the electron spectrometer has an energy resolution so that electrons with an energy difference less than this are not separated. The zero-loss peak contains contributions from electrons that are not scattered on passing through the specimen, elastically scattered electrons and those electrons that generated a phonon excitation.
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Low losses This energy region extends over a range from the edge of the zero-loss peak to about 50 eV and contains the plasmon loss peak. Here the energy losses are a result of electrostatic interactions with the electrons. The energy loss structures are a consequence of either the excitation or ionisation of electrons from various bound states. Moreover there are the plasmon excitations that occur in metals, because they have ‘free’ electrons excited by fast incident electrons. The frequency of the plasmon oscillation is proportional to the root of the number of free electrons per unit volume of plasma. As a consequence, the plasmon energy loss has the potential for providing an identification of a material; unfortunately all metals and alloys have plasmon peaks of a similar electron energy. With careful calibration (Williams and Edington (1976)) it is possible to measure changes in composition from small shifts in the plasmon peak position. Core losses It is in this energy region, extending 50 eV upwards, that the energy losses arise from the inelastic interactions with the inner atomic shells of the specimen atoms whereas the background intensity results from valence shell excitations. This produces the characteristic edges used for elemental analysis. The energy and momentum distribution of high energy electrons (30–200 keV) which have interacted with a foil specimen is measured (figure 6.90), to provide information on local chemical composition (Carpenter (1982), Isaacson (1978), Egerton (1989), Egerton and Cheng (1987) and Joy (1987)). Since momentum is a vector quantity a complete description of the interaction requires a knowledge of both the energy change, E, and the angular displacement (figure 6.90) (Isaacson (1978) and Egerton (1989)). Therefore, the signal IðEÞ detected at some energy loss E by a spectrometer collecting electrons scattered through angles up to is given by IðEÞ ¼ INð; E; E0 Þ
ð6:81Þ
where I is the intensity of the incident electron beam of energy E0 , N is the number of atoms in the irradiated area, is an efficiency factor and is the interaction cross-section. The latter represents the probability that any incident electron suffers an energy loss E as it is being scattered into a solid angle less than (figure 6.90). A minimum energy Ek is needed to ionize a particular inner shell of an atom such that for E > Ek a finite cross-section of ionisation exists to increase IðEÞ when this condition is satisfied. This will produce a discontinuity or ‘edge’ in the spectrum at Ek . Since the energy Ek approximates to the binding energy of the particular atom shell ionized, it uniquely characterises the atom and a single measure of the energy loss identifies the element.
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Figure 6.90. Energy loss spectroscopy illustrating the incident electron beam convergence angle , the scattering angle and the spectrometer acceptance angle .
Any energy loss by an electron of E > Ek causes ionisation so that the edge could extend from Ek to E0 . Since the cross-section falls as E r , where r 4, the inner shell edge approximates to a triangle in the spectrum and for K-shell ionisations this is observed experimentally. For L shells the situation is more complex since additional energy terms arise from the angular momentum associated with the 2p orbitals. This increases the apparent energy required to ionize the atom, giving a delayed maximum edge of the type observed in the L23 shell edge from silicon and other elements in the first row of the Periodic Table (figure 6.91(a)(b)). For elemental analysis both the energy and the shape of the edge in the spectrum are used. Table 6.7 lists the energies, E, and the types of K and L edges commonly encountered in the loss range 50–2000 eV (Joy (1981)). The background is substantial under the edges to be measured in the energy loss spectrum. The cross-section term, , in equation (6.81) contains contributions from other interactions together with the required edges that
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Figure 6.91. Electron energy loss spectra: (a) K ionisation edge of energy EK in a transmission energy loss spectrum. After the edge the intensity decreases as approximately E r , where r 4. (b) Experimental L23 edge recorded from silicon at 100 keV in STEM mode with ¼ 7.5 mrad and resolution of 5 eV.
combine to produce a signal: IðEÞ ¼ ICE r
ð6:82Þ
where C and r are constants for limited ranges of a spectrum whose values depend upon E, and the material. Indeed, it is the magnitude of this background relative to that of an identified peak (figures 6.92(a) and (b)), that make peak deconvolution procedures necessary for quantitative evaluation of elemental concentration (Collet et al (1981)).
Table 6.7. Energies EK and types of edge in loss range 50 to 2000 eV. Element
Z
EK (eV)
Element
Z
EL23 (eV)
Li Be B C N O F Ne Na Mg A1 Si
3 4 5 6 7 8 9 10 11 12 13 14
55 110 188 284 400 532 684 865 1075 1305 1510 1832
A1 Si P S C1 Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn
1313 1414 1515 1616 1717 1818 1919 2020 2121 2222 2323 2424 2525 2626 2727 2828 2929 3030
73 100 136 165 202 250 296 348 405 459 517 580 645 714 786 863 941 1031
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Figure 6.92. Energy loss spectra. (a) Spectrum from 20 nm thick carbon including zero-loss and plasmon peaks. Gain change makes edge visible. (b) Spectrum from TiS2 together with computer-modelled background fit to AE r (Collett et al (1981)) (courtesy Institute of Materials).
6.5.3
Instrumentation
In practice an electron energy-loss analyser and the associated electronics can be interfaced to a conventional electron microscope operating in the energy range 30–400 keV (Loretto et al (1988)). The magnetic prism analyser (see chapter 7) positioned below the specimen focuses electrons leaving the object point of the system to an image point. Electrons with an energy E0 diverging from the object point are deflected through an angle of /2 before being focused at the image point, I, whereas those of a different energy, E0 E, are brought to a point focus at a position displaced by a distance x from I to form a line dispersion. Three parameters define the performance of this design of spectrometer, the dispersion E=x, the
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Figure 6.93. Basic layout of analyser for electron energy-loss spectrometer. Electrons leaving object point from the specimen in the transmission electron microscope are deflected through /2 by a magnetic field and form a dispersed line image at the position of the detector slit. Dispersion E=x is typically a few mm/eV.
solid angle acceptance = 2 and the energy resolution. For rays of energy difference E and separation x in the image plane (figure 6.93), the dispersion, D, of the spectrometer is given by D ¼ 2R=E0 ¼ E=x
ð6:83Þ
where R is the radius of the electron path through the spectrometer. The minimum energy difference selected by the acceptance slit of width, d0 , at the image point prior to the detector is given by E ¼ d0 =D0 :
ð6:84Þ
It is this which limits the energy resolution of the system which for 100 keV incident electrons allow an energy resolution of typically 1–2 eV to be achieved for an acceptance angle of 10 m rad. The electrons emerging from the slit are detected by a scintillator–photomultiplier or an array of solid-state diodes and are collected either serially or in parallel (Krivanek 1989). Parallel detection electron energy-loss spectrometers based upon solid state detectors have improved detection efficiency by at least two
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orders of magnitude compared with the serial detection spectrometers. This increases detection limits, reduces damage to radiation sensitive materials, improves collection of extended energy loss fine structure and increases speed of data acquisition. It is now the practice to store the spectrum in a multi-channel analyser and process it within the computer. 6.5.4
Quantitative analysis
Figure 6.94 shows an energy loss spectrum acquired from a Type 304 stainless steel, where the gain has been increased for the high loss regions (Collet et al (1981)). The chromium and iron edges are easily identified, whereas nickel edges are less pronounced. The background under each peak has to be subtracted, using equation (6.82), to fit to the background shape at a position before the edge position, thus from equation (6.81) N ¼ Ik I:
ð6:85Þ
In practice the edge integral, the area under peak, can be obtained for an energy window, E, so that N ¼ Ik ð; Þ=Ip ð; Þ
ð6:86Þ
where the variables and indicate that the integral and the cross-section relate to scattering angles up to and energy losses in the window Ek to Ek þ . For quantitative microanalysis I is conventionally replaced by I0 ð; Þ, the integral in the energy window under the zero-loss peak, , for the acceptance angle . This allows backscattering and plasmon scattering in the specimen and integral counts from the element being analysed to be
Figure 6.94. Type 304 stainless steel spectrum where gain and energy scale have been changed at higher losses: L edges have larger gain (dotted lines indicate schematic background extrapolation) (Collet et al (1981)) (courtesy Institute of Materials).
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evaluated directly from the spectrum. However, when undertaking a microanalysis, elemental ratios are usually required such that NA =NB ¼ IKA ðp BB Þ=IKB ðp ZA A Þ
ð6:87Þ
giving mass concentration ratios XA XB ¼ ðZA NA =t Þ=ðZB NB =t Þ ¼ ðZA NA Þ=ðZB NB Þ
ð6:88Þ
where t is the specimen thickness, is specimen density and ZA is the atomic weight of element A. These relationships are functionally identical to the ‘K factor’ formulation used for STEM–EDX X-ray microanalysis (section 6.4.11). Although there is a need to improve the accuracy of quantitative analysis, this technique offers a potentially powerful procedure for undertaking quantitative measurements for low atomic number elements in thin foil specimens. The adoption of sub-nanometre electron probes enables high spatial resolution microanalyses to be undertaken where the chemical composition change is at the atomic level. Here the process, as with the energy dispersive X-ray spectrometer, is carried out by sequential point-to-point analyses across the selected microstructural feature. For this, the improved performance of the parallel array electron energy loss spectrometers is invoked. Figure 6.95(a) shows part of an energy-loss spectrum from a grain boundary in phase Zr–2.50 wt% Nb containing a 1000 ppm iron which has segregated under the influence of neutron irradiation. The Fe L2;3 edge at a loss energy of 700 eV is caused by the transitions from the full 2p states to the empty states in the bands in the 4s and 3d atomic levels (figure 6.95(b)). The transitions are dominated by the 3d states as they are more localised and have larger matrix elements than the 4s states. The so-called white lines are also present in the spectrum and these relate to the spin–orbit splitting in the 2p states; the L3 and L2 lines from the 2p3=2 and 2p1=2 states respectively (Dray et al (1995)). As described by Okamato et al (1992) the white lines vary systematically across the series of transition elements to provide a measure of the number of holes in the d-band (figure 6.96). To quantify these data two procedures can be adopted: (a) the Pearson ratio which is the ratio of the total white line counts to the background and (b) the ratio of the intensities of the L3 =L2 peaks in the two white lines. Provided these ratios are determined in a prescribed manner (Dray et al (1995) and Dray and Brown (1999)), normalisation against the transition series (figure 6.97), provides an estimate of the number of electrons in the d-band of electrons. Oxidation of the iron increases with the Pearson ratio because electrons are transferred from the iron. Figure 6.98 shows that the quantitative use of this technique involves extensive numerical simulation of the background counts in the spectra under the white lines so that an appropriate measure of the white line intensity can be obtained. Hence, by use of reference spectra obtained from known intermetallic compounds of Fe, Zr and Nb, the
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Figure 6.95. (a) Spectrum from an – phase grain boundary in Zr–2.5 wt% Nb alloy containing 1000 ppm Fe. The feature arising at 710 eV is due to segregated iron. (STEM in spot mode, channel width 0.83 eV, acquisition time, 90s). (b) The origin of the white lines in transition elements. Electrons from 2p states are promoted into the empty 3d bands. In the solid, the sharp atomic levels are broadened into bands, but the 3d bands are narrow by comparison with the 4s band, and give rise to sharp features in the density of states and thus in the energy loss spectrum. The 4s band contributes a relatively featureless continuum, arising under white lines (Dray et al (1995)).
segregated iron has been shown to be in an anionic state as a result of a gain of about two electrons. This state resembles iron in ZrNbFe alloys. By this means it is possible to consider both the composition and chemical state of species segregated to the grain boundaries (Brown et al (1995)). This
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Figure 6.96. The variation of white line intensity across the first series of transition metals (Okamoto et al (1992)).
Figure 6.97. Schematic diagram of the separation of the white line features from the continuum (Okamoto et al (1992)).
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Figure 6.98. (a) The L3 =L2 intensity ratio and the ratio of intensity in the white lines to that in the continuum, ‘Pearson ratio’, (b) for iron in various intermetallic compounds and (bottom row in each diagram) for iron segregated to – phase boundaries. The vertical line in each box is the mean, and separate r.m.s. deviations for readings above and below the mean are shown. Scatter bands are shown where there are significant outliers, particularly for segregated iron. The arrow shows a value for pure metallic iron.
general approach has been applied to the investigation of segregation of nitrogen to planar defects in diamond (Fallon et al (1995)), radiationinduced boron segregation in Ni3 Al (Muller and Silcox (1995)) and phosphorus segregation into grain boundaries in a Fe–0.4 wt% P alloy (Ozakaya et al (1995)).
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Figure 6.99. (a) Electron energy-loss spectrum from within an iron grain and from a phosphorus-containing grain boundary. The difference between the two spectra indicates that the presence of phosphorus in the grain boundary causes about half an electron per boundary atom to be transferred to the iron. (b) Electron energy-loss spectrum from an iron grain and from a pure grain boundary that has no phosphorus. The difference between the two spectra now shows no transfer of electrons to the iron (Ozakaya et al (1995)) (published by permission of Blackwell Science Publishers).
In the latter case figure 6.99(a) shows the L2;3 edges obtained from a grain boundary and the matrix of a Fe–0.4 wt% P alloy after a furnace cool from a temperature of 1273 K. Spectra are shown which are corrected for thickness changes across the grain boundary, so that the difference between these spectra relates directly to an increase in a shell filling by electrons at the boundary. In the spatial difference method, two spectra are recorded, one from an
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Figure 6.100. Schematic diagram showing the basis of the spatial difference technique. With a beam located at points A and B, the measured intensities are IA and IB , respectively. When properly scaled by factor f , IB is used to model the background of IA . The spatial difference is shown as Id .
area including the interface and the second displaced from the interface (figure 6.100) (Bruley et al (1994)). The latter spectrum provides a reference to model the energy dependent background of the first spectrum. After subtracting a smooth power law curve from both these spectra fitted in the region preceding the edge, the numerical difference between the two is obtained by subtracting a scaled version of the latter spectrum from that of the former. The difference spectrum provides the detail of the information associated with the interface. This technique can be applied to a range of metal, ceramic and metal– ceramic systems with the advantages that (i) apparent noise produced by detector channel to channel gain variations is removed, (ii) the resultant signal intensities and accuracies are limited only by counting statistics and (iii) surface artifact differences are removed. From figure 6.99(a) and (b) it is possible to establish the approximate magnitude of the charge transfer since the ratio of the area under the stripped Fe L2;3 edge, compared with a
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window taken after an edge, is a direct function of d-shell occupancy (Okamoto et al (1992)). The iron in the grain boundary has fewer holes in the d-shell than the matrix iron, since the d-shell is related to the electron transferred from the phosphorus to the iron. Assuming six electrons in the d-shell this gives four holes which translates to about 4/8 or a half an electron transfer. Use of a calibration curve established by Okamoto et al (1992) gives 0.4 of an electron transfer. As a consequence it is clear that this technique offers a powerful way for establishing the chemical state of segregated species at grain boundaries and interfaces. An extension of the electron energy-loss technique is elemental mapping based upon images of atoms formed by the inelastically scattered electrons. Hashimoto (1980) proposed that a sector-type energy spectrometer positioned under an atom resolution electron microscope would produce characteristic images of atoms using the selected electron energy spectrum (Putilin et al (1993)). This resulted in a three-stage electron lens microscope positioned behind the sector analyser as shown in figure 6.101. Unfortunately
Figure 6.101. Schematic of a three-stage electron lens microscope positioned behind the sector analyser.
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with this imaging condition the magnification of the images in the horizontal and vertical directions is different so that the resultant images are distorted. Subsequently a commercial system with an image distortion correction system using quadrupole and sextupole magnetic lenses has been developed (Krivenek et al (1995)). The system made by the Gatan Company produced core-loss electron images; this is the Gatan image filter system known as GIF. With this system maps can be formed by imaging with electrons that have lost energy corresponding to inner-shell ionisation energies characteristic of particular elements. Figure 6.102(a) shows chromium and iron energy selected images obtained from a region of -ferrite in a duplex stainless steel (figure 6.102(b)). For this, three energy window maps were formed using the pre-edge images to calculate a power law background which has been subtracted from the post-edge image (Yamada et al (2001)). Overall
(a)
(b)
Figure 6.102. (a) Cr and Fe energy selected images obtained from a region of -ferrite in a duplex stainless steel using the energy windows shown in (b) (Yamada et al (2001)).
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this technique has the advantage that distribution images can be produced to a nanometre scale resolution with a short acquisition time (Krivanek et al (1995) and Hofer et al (1997)). 6.5.5
Extended fine structure
Frequently fine oscillatory modulations are observed on the high energy side of an electron energy loss edge. The effect is analogous with the extended absorption fine structure EXAFS observed in association with the X-ray absorption edge and this is used to provide structural detail of a material (Wong (1986) and Joy (1987)), (figure 6.89(a)). This corresponding effect in electron energy loss spectra is referred to as extended energy-loss fine structure (EXELFS). These are oscillations which are theoretically understood to be a final state electron effect arising from the interference between the outgoing ionized electromagnetic wave (figure 6.103(b)) and that fraction of this wave that is backscattered from the neighbouring atoms. The interference that is either constructive or destructive reflects the net phase shift of the backscattered electron in the vicinity of the central excited atom. Therefore, it provides information on the atomic environment of the excited atom. The interference will be constructive when the returning wave is in phase with the outgoing wave such that 2ð2d=Þ þ
¼ 2n
ð6:89Þ
where d is the interatomic spacing, is the wavelength, is the phase shift and n is an integer. Thus the modulations observed in the electron
Figure 6.103. Schematic representation of an EXAFS event. The excited electronic state is centred about the A atom. The full circles represent the crests of the outgoing part of the electronic state. The surrounding B atoms backscatter the outgoing part as shown by broken circles. Constructive interference is represented in (a) and destructive interference in (b) (courtesy North Holland Publishing Company).
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energy-loss edge will be non-periodic but periodic in k-space (Leapman and Cosslett (1976)). Extended fine structure modulations provide a means of estimating nearest atom neighbour distances in both crystalline and amorphous materials to an accuracy of about 0.01 nm. Therefore it provides a method for examining the structure of amphorous materials that cannot be achieved by diffraction techniques (Joy (1987)). 6.5.6
Reflection electron energy-loss spectroscopy
When low-energy electrons escape from the surface a proportion will lose energy by being inelastically scattered. The amount of energy lost by the
Figure 6.104. Reflection electron loss spectroscopy from a plasma vapour deposited diamond. The secondary electron image: (a) with points P1, P2 and P3 indicating the positions for the diamond, graphite and amorphous carbon loss spectra shown in (b) together with phase maps generated for diamond (c) and graphite (d) (results obtained at VG Scientific).
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electron during these collisions is dependent on the particular element being analysed and the crystallography of the phase. Thus the low kinetic energy side of a peak will contain structure that is characteristic of the crystallographic phase of the material. Reflection electron energy-loss spectroscopy can be used to distinguish between the different phases of carbon when the Auger KLL peak shows no detectable position shift. Figure 6.104 demonstrates the capability when using a specimen of plasma vapour deposited diamond (Kuo et al (2000)). Figure 6.104(a) shows the secondary electron image of the surface with the positions for the REELS spectra indicated by points P1, P2 and P3. In the REELS spectra in figure 6.104(b), P1 is from a diamond particle, P2 is from a graphite region and P3 is from an amorphous carbon region. Phase maps can be generated by selecting a loss peak characteristic of each phase while rastering across the surface. Figures 6.104(c) and (d) show maps for diamond and graphite respectively.
6.6
Auger electron spectroscopy
Auger spectroscopy was briefly described in chapter 2 but will be treated in more detail here and more extensive treatments are given elsewhere (Briggs and Seah (1990), Rivie`re (1990), Chang (1974), Carlson (1975), Watts and Wolstenholme (2003) and Watts (1990b). Figure 6.105 schematically illustrates the electron energy levels of an atom and the stages involved in the production of an Auger electron. An Auger electron is ejected from the surface following ionisation of an atom by the removal of an inner shell electron. This results from rearrangement of the atom with an electron from an outer shell falling into the hole created by the initial ionisation process and the energy released being transferred to an electron in an outer electron shell. If it has sufficient energy to overcome its binding energy and the work function of the surface, this electron may be ejected. It is referred to as an Auger electron after Pierre Auger who first discovered it in 1925 while studying cosmic ray collisions. The Auger electron has an energy given by EAuger ¼ EK1 ðZÞ EL1 ðZÞ EL2;3 ðZÞ
ð6:90Þ
where EK1 ðZÞ, EL1 ðZÞ and EL2;3 ðZÞ are electron binding energies of the K1 , L1 and L2;3 electron shells in the atom and is the work function. Equation (6.90) is a simplification because the atom will be in an ionised state during the transfer of energy between electron shells, thereby increasing the binding energy of the outer shell electrons. The situation is equivalent to increasing the atomic number of the atom. One modification made to the binding energy levels to obtain a more accurate value for the Auger energy was proposed by Chung and Jenkins (1970) an equation of the form which
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Figure 6.105. Schematic of Auger process.
gave EAuger ¼ EA ðZÞ 12 ½EB ðZÞ þ EB ðZ þ 1Þ 12 ½EC ðZÞ þ EC ðZ þ 1Þ
ð6:91Þ
where Ei is the binding energy of the ith level in atom of atomic number Z and Ei ðZ þ 1Þ is that in an element of atomic number Z þ 1. This equation predicts Auger energies to within values that are accurate for analytical purposes but is not theoretically correct even though it has been used by Coghlan and Clausing (1973) to produce calculated values of Auger electron energies. A more physically correct expression is ext EAuger ¼ EA ðZÞ EB ðZÞ EC ðZÞ Fn½BC :x þ Rins x þ Rx
ð6:92Þ
where Fn½BC : x is the energy of interaction between the holes in B and C in the final atomic state x and Rx are relaxation energies. The reader is referred to Rivie`re (1990) for a more complete description. 6.6.1
Nomenclature
It is customary to use the X-ray symbol for the electron energy level to identify the Auger electron. Each level involved in the Auger process is used to describe the Auger electron. Thus a KL1 L2;3 Auger electron would result from ionisation of the K shell, rearrangement of the atom by an electron from the L1 shell falling into the hole created and an electron from the L2;3 shell being ejected. The X-ray and spectroscopic notations, giving the X-ray suffices, X-ray levels and spectroscopic levels for the
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Table 6.8. X-ray and spectroscopic notations. Quantum numbers n
l
j
X-ray suffix
X-ray level
Spectroscopic level
1 2 2 2 3 3 3 3 3
0 0 1 1 0 1 1 2 2
1/2 1/2 1/2 3/2 1/2 1/2 3/2 3/2 5/2
1 1 2 3 1 2 3 4 5
K L1 L2 L3 M1 M2 M3 M4 M5
1s1=2 2s1=2 2p1=2 2p3=2 3s1=2 3p1=2 3p3=2 3d3=2 3d5=2
various quantum numbers are given in table 6.8. The total angular momentum of the electron will influence the energy of the Auger electron by determining the energy of the electron shells. There are two ways in which the total angular momentum can be derived. In the first the individual spin moment (s) of each electron can be added to the individual orbital momentum (l) to give a individual angular momentum ( j) and these can then be summed to give a total angular momentum (J). This is known as j–j coupling and describes the situation for atoms of atomic number greater than about 80. The second method sums all individual spin moments, s, to give a total spin momentum (S), to sum all the individual orbital momentums to give a total orbital momentum (L) and to add these together to give a total angular momentum J ¼ jL þ Sj. This is referred to as L–S coupling and describes the situation for atoms with atomic number below about 20. Atoms between atomic number 20 and 80 are best described by summing momenta, a method that combines these two approaches and is referred to as intermediate coupling. The classification giving the L–S, L, S, J and the intermediate coupling terms are shown in tables 6.9 and 6.10 and the change from L–S to j–j coupling is shown in figure 6.106. For L–S coupling the L–S term is added to the end of the X-ray symbols, thus for atoms of atomic number 3 to 20 one may see KL1 , L2;3 (2S þ 1L). For atoms with atomic numbers greater than 20 where j–j coupling pertains then J is also included, thus one sees KL1 , L2;3 (2S þ 1LJ). 6.6.2
Instrumentation
Auger spectroscopy developed from LEED systems because there was a need to determine the chemical composition of the surface being studied. At the same time it was recognised that instrumentation that produced LEED patterns could also be used to obtain Auger spectra and hence analyse the
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Electron sources Table 6.9. Classification in extreme L–S coupling. Electron
Configuration
L
S
Term
(KL1 L1 ) (KL2 L2;3 )
2s0 2p6 2s1 2p5
(KL2;3 L2;3 )
2s2 2p4
0 1 1 1 0 {1 2 2
0 0 1 1 0 1 0 0
1S 1P 3P 3P 1S 3P } 1D 1D
Forbidden.
surface. It was realised (Palmberg and Rhodin (1968) and Harris (1968)) that by modifying the potentials on the LEED system shown in figure 4.89 in the manner shown in figure 6.107 that an Auger spectrum could be produced. The electron beam is incident on to the specimen surface in the same manner as for LEED except that somewhat higher energies are used; in early systems this energy would be typically 2–3 keV. The secondary electrons pass through the first grid, which, like the fourth grid, has the function of shielding the specimen from high potential fields. The second and/or third grids now have a large slowly varying potential applied to them. Only electrons with energy greater than that applied to the grid can pass through it, through the fourth grid and be collected by the fluorescent screen. As the potential is swept from zero to the primary electron energy Ep , Auger peaks appear as points of inflection on this current versus energy curve which are not easily detected and measured. To aid peak detection the spectrum is differentiated, dI/dE gives NðEÞ as a function of energy Table 6.10. Classification in intermediate coupling. L–S
Term
2s0 2p6 2s1 2p5
1s 1p 3p
2s2 2p4
1s 3P
1D
Forbidden.
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L
S
J
IC term
0 1 1 1 1 0 1 {1 1 2
0 0 1 1 1 0 1 1 1 0
0 1 0 1 2 0 0 1 2 2
1
S0 P1 3 P0 3 P1 3 P2 1 S0 3 P0 3 P1 } 3 P2 1 D2 1
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Figure 6.106. Addition of electron spin and orbital momenta as a function of atomic number. L–S coupling dominates at low atomic number (<20) while j–j coupling occurs above atomic number 80.
and here the Auger peaks are revealed on a large slowly varying background. To remove the background the spectrum is differentiated once again to give dNðEÞ=dE ¼ d2 I=dE 2 . Differentiation was achieved in the early spectrometers by applying a small sinusoidal potential to the second and/or third grids. The collected signal was then processed by a lock-in amplifier which could be tuned to the first or second harmonics in the signal; for small sinusoidal potentials, using a Taylor expansion, the first harmonic is proportional to dI/dE and the second harmonic to d2 I=dE 2 .
Figure 6.107. Schematic of modification of LEED system to detect AES.
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Figure 6.108. Schematic diagram of cylindrical mirror Auger analyser.
It was soon realised that this was an important analytical technique, not just an aid to LEED, and attention was focused to improve the sensitivity and speed of collection. Palmberg et al (1968) suggested that a cylindrical mirror analyser (CMA) could be used to detect Auger electrons. The basic principles suggested are now incorporated in these systems (figure 6.108), where an electron gun, housed between two concentric cylinders, provides electrons to bombard the surface normally. Secondary electrons passing through a slit in the inner cylinder, are deflected by a negative potential applied to the outer cylinder, and pass through an exit slit on to an electron multiplier where they are detected. For any given potential applied to the outer cylinder only electrons with specific energy will pass through the exit slit. A spectrum is built up by sweeping the outer cylinder potential (figure 6.109). These analysers have a high transmission function and spectra are displayed on an oscilloscope. They are very useful for the kinetic studies such as trace element diffusion to surfaces. However, the energy resolution is a percentage of the Auger energy and E=E normally varies from 0.1 to 0.6%, giving a relatively poor energy resolution for Auger electrons >100 eV. While these developments had been taking place chemists had been developing the technique of X-ray photoelectron spectroscopy (XPS) described in chapter 5 where a surface is bombarded with X-ray photons, usually from aluminium or magnesium, to determine the energy of photoemitted electrons. This required an accurate electron energy analyser of the type shown in figure 6.110, which employs hemispherical analysers (HSA). Electrons enter through a slit on one side, are deflected by a negative potential applied to the outer hemisphere, and pass though a slit on the other side where they are detected by an electron multiplier. By retarding the electrons prior to the entrance slit a spectrum can be obtained with
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Figure 6.109. Differentiation of collected current to give Auger peaks: (a) is the primary signal and (b) is the differential signal.
fixed energy resolution over its entire range. Typically energy resolution of 0.1–0.2 eV is standard. Unfortunately the transmission of electrons through these analysers is much reduced compared with the CMA, but in recent years lens systems have been developed to focus more electrons on to the entrance slit and multiplate detectors have increased detection rates to the extent that the hemispherical analyser (HSA) is now the most
Figure 6.110. Schematic diagram of hemispherical analyser which has a negative potential applied to the outer hemisphere.
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Figure 6.111. Schematic of Auger spectrometer using a hemispherical analyser.
commonly encountered Auger detection system. Figure 6.111 is a schematic diagram of a modern Auger spectrometer with a fine spot field emission electron gun. This produces a high-intensity beam of electrons with energies from 1 to 25 keV focused on to a specimen to give a spatial resolution of a few nanometres in both secondary electron image and Auger mapping mode. The secondary electrons are focused on to the entrance slit of an HSA with detection by multichannel electron plates. 6.6.3
Energy resolution
Auger spectra are normally recorded in the range 0–1000 eV as shown in figure 6.112. This range, occasionally extended to 2000 eV, contains peaks from all elements, except hydrogen and helium, in the Periodic Table. Energies of Auger electrons for elements as a function of atomic number are given in figure 6.113 and from tables of this type it can be deduced that the spectrum in figure 6.112 contains LMM Auger transitions from titanium at 387 and 418 eV, from nickel at 716, 783 and 848 eV and KLL transitions from carbon at 272 eV, nitrogen at 379 eV and oxygen at 503 eV. The improvement in energy resolution from the CMA to the HSA is demonstrated in figure 6.114. In this instance a spectrum was recorded from a chromium metal surface in the energy range 460–600 eV using a retarding field analyser (a), a cylindrical mirror analyser (CMA) (b) and a hemispherical analyser (HSA) (c). The retarding field analyser produces only three broad peaks which are considerably sharpened using the CMA while the HSA contains much resolved fine structure.
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Figure 6.112. Auger spectra from chromium carbide particle (Wild (1981)) (reproduced with permission of Pergamon Press).
6.6.4
Chemical effects
The HSA allows Auger spectroscopy to detect chemical state changes on a much greater scale than the CMA. When two elements combine to form a compound, changes occur in the electron binding energies of the individual atoms. In addition, new orbitals may be formed that share electrons from each atom and these may take part in the Auger process, producing new peaks. Consider the theoretical electron binding energies of an atom in the neutral state and the charged state shown schematically in figure 6.115. If electron shells 1, 2 and 3 each change energy by an amount E1 , E2 and E3 then the resultant shift in Auger electron energy is given by Eshift ¼ E1 E2 E3 :
ð6:93Þ
Shifts in Auger peak positions are comparable with shifts in XPS, but they can be larger or smaller depending on the specific changes in electron binding energies. Figure 6.116 gives two examples of the chemical effects that can be observed in Auger spectra. The first (figure 6.116(a)) involves low-energy MVV transitions in transition metals on oxidation (Wild (1976)); for example the Auger spectrum of metallic iron contains a single peak at 45 eV. Moreover, the spectrum from the oxidised iron contains
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Figure 6.113. Energies of Auger peaks.
two peaks on either side of the original at 52 and 38 eV, produced by sharing of electrons between iron and oxygen, and hence an extra electron shell that is able to partake in the Auger process is created. Similar effects are observed when chromium and manganese combine with oxygen. The second example (figure 6.116(b)) shows the change in the carbon KLL transition in the energy region 220–280 eV for a series of carbides (Chang (1974)) which allows carbides to be identified from their fingerprint. In both these examples the spectra were recorded at relatively low electron kinetic energies. The shifts involved in these spectra are of the order of 5 eV, which are easily detected using both CMAs and HSAs; the resolution of 0.5% using a CMA means that the energy resolution in the region of 50 eV is 0.25 eV. However, the energy resolution in CMAs degrades to 4 eV at 800 eV and chemical effects in this region are difficult to detect using a CMA—the HSA is preferred. AES has been used here to provide chemical state information with good spatial resolution from a superalloy coating (Heard et al (2000)). AES spectra obtained from various points on the sample revealed the
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Figure 6.114. Energy resolution with different types of Auger analysers: (a) retarding field, (b) cylindrical mirror and (c) hemispherical (Wild (1981)) (reproduced with permission of Pergamon Press).
presence of aluminium, chromium, titanium, nickel, cobalt, oxygen and nitrogen. A secondary electron image of the sample is shown in figure 6.117, together with titanium and aluminium AES maps. The secondary electron image, figure 6.117(a), shows a structure of light and dark phases which are aligned along crystallographic directions. Spectra from the dark phases
Figure 6.115. Schematic diagram showing the chemical effects in Auger electrons for the neutral and charged states.
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Figure 6.116. Chemical effects involving valence electrons (a) MVV transitions in iron, chromium and manganese in the metal and oxidised state and (b) the carbon KLL transition in various carbides (Wild (1981)) (reproduced with permission of Pergamon Press).
show that there are two types: one containing nitrogen and aluminium, and the other containing nitrogen and titanium with some carbon and nickel. The nitrogen KLL peak is found at 380–390 eV kinetic energy in the AES spectrum. The detailed spectra shown in figure 6.118 indicate that the exact location of the nitrogen peak is dependent upon the position of the beam for analysis; the peak in the aluminium phase is at 383 eV, and that in the titanium phase is at 388 eV. This chemical shift can be utilised to distinguish between nitrogen bound to aluminium, and that bound to titanium. The chemical shift in the nitrogen peak has been utilised to give the images shown in figures 6.117(d) and (e). The upper image was recorded with a peak position of 388 eV, and backgrounds of 379 and 400 eV, while the lower image was recorded with a peak position of 383 eV and backgrounds of 374 and 396 eV. The energy resolution of the electron detector on this instrument is
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Figure 6.117. Auger images of coated superalloy: (a) secondary electron image, together with Auger maps of (b) titanium, (c) aluminium, (d) nitrogen at 388 eV energy, marking nitrogen associated with titanium, (e) nitrogen at 383 eV energy, marking nitrogen associated with aluminium (Heard et al (2000)).
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Figure 6.118. Nitrogen Auger peaks from two areas of the coated superalloy sample corresponding with maps shown in figure 6.117(d) and (e): (a) titanium rich region, (b) aluminium rich region.
given by E=E ¼ 200, so that a FWHM peak width of 2 eV is obtained at an energy of 400 eV. This is sufficient to resolve the shift in the nitrogen peak for aluminium nitride and titanium nitride. When taken in association with the aluminium and titanium maps, they show very clearly the presence of separate aluminium nitride and titanium nitride phases.
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425
Quantitative AES
In principal it should be possible to obtain quantitative analyses by considering the probabilities of the various processes involved in producing an Auger electron. Good quantitative results have not been produced with this approach but it gives an insight into the basis behind the interpretation of Auger spectra. The probability that an Auger electron will be produced when a single electron is incident on a surface is n ¼ NRð1 WÞQð Þ cosec
ð6:94Þ
where N is the number of atoms per cm2 , R is the backscattering factor, W is the probability of photon production, Q is the ionisation cross-section and is the angle of incidence of the electron. The probability that a photon will be produced, W, and therefore an Auger electron is not produced is W ¼ ð1 þ aZ 4 Þ1
ð6:95Þ
where Z is the atomic number and a is a constant which is 1:12 106 for K shell ionisation and 6:4 107 for L shell ionisation. For atoms of low atomic number aZ 4 is large, hence W is small and Auger production is favoured but as the atomic number increases so W approaches unity and photon production starts to dominate. The backscatter factor varies with both electron energy and atomic number (Worthington and Tomlin (1956)). Figure 6.119 shows the change in the backscatter factor R as a function of the critical ionisation energy, Ec , divided by the primary beam energy, Ep , for elements of atomic number, 6, 13, 22 and 29. R decreases as Ec =Ep and atomic number increases and this is the reason why heavy elements appear bright in backscattered
Figure 6.119. Backscattering of electrons as a factor of the critical ion ejection energy normalised to the incident electron beam energy.
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Figure 6.120. Ionisation cross-sections, Q, as a function of Ep =Ec .
scanning electron images. The ionisation cross-section (Bishop and Rivie`re (1969)) is described by an equation of the form 2e2 bEp lnð4Ec =Ep Þ 2 ð6:96Þ QEc ¼ 1:65 þ 2:35 expð1 ðEc =Ep ÞÞ Ec and is plotted against Ep =Ec in figure 6.120. The ionisation probability increases rapidly to a maximum at about Ep =Ec equal to 3 and thereafter decreases relatively slowly. Thus the ideal primary beam energy is three times the ionisation energy. However, to obtain good Auger electron yield over a range of elements the primary beam energy is maintained at least three times that of the maximum ionisation potential so that typically electron beam energies of between 3 and 10 keV are employed. 6.6.6
Determination of atomic concentration
In practice Auger spectroscopy is made quantitative by using known standards to obtain sensitivity factors (Davis et al (1976), McGuire (1979) and Sekine et al (1982)). Using a known electron beam current the Auger signal is measured relative to the signal from a standard and the sensitivity of the element relative to the standard then gives the sensitivity factor. A spectrum from the unknown material is then obtained, the peaks are identified and the appropriate sensitivity factor applied to give the
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Figure 6.121. Auger sensitivity factors as a function of atomic number for 5 keV incident electrons.
concentration, Xx of element x Xx ¼ P
Ix =Ix1 1 a ¼ A;B Ia =Ia
ð6:97Þ
where Ix and Ix1 are the intensities from the element in the unknown material and the intensity from a pure specimen of that material and Ia and Ia1 the summation of the intensities of all elements detected and the intensities of those elements in the pure state respectively. Sensitivity factors can be obtained from published data produced by other workers or equipment manufacturers and this reduces the need to obtain data from pure specimens in the spectrometer. Figure 6.121 shows sensitivity factors for incident electrons of 5 keV as a function of atomic number. Since the sensitivities of useful peaks do not change by more than a factor of 50 over the entire Periodic Table relatively accurate quantitative determinations can be obtained. Further improvements can be obtained if sensitivity factors are measured within a given system since the factor for the element in the specific environment can be obtained. The method described above has limitations since it relies on the fact that the specimen is homogeneous, which is frequently not the case. If a thin monolayer of segregant such as sulphur exists on top of a nickel matrix, the composition determined will be very different from that same quantity of sulphur being uniformly distributed within the top five atom layers. Seah (1980) has published an equation to
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Electron sources
determine the amount of segregant A coating matrix B. X IB ¼ IB1 exp tA =A ðEB Þ cos
ð6:98Þ
where IB and IB1 are the signals from the layer and a pure specimen of the layer element respectively, A is the mean free path of the electron in A, tA is the layer thickness and is the angle of the electron beam relative to the surface normal. However, it has to be first ascertained that the element is indeed segregated to the surface and not a large concentration within the matrix by measuring the peak heights of Auger peaks at low and high kinetic energies. Those at low kinetic energies, 50–200 eV, have lower escape depths, 1–2 nm, than those at high kinetic energies, 700–1000 eV, where escape depths tend to be nearer 5 nm. Thus if the segregant is present as an atomically thin surface layer the low kinetic energy peak height will be enhanced relative to the high kinetic energy peak height. By comparing spectra from the unknown surface with a standard homogeneous specimen, the make-up of the surface can be determined and the correct quantitative procedure adopted. 6.6.7
Scanning auger microscopy (SAM)
So far we have considered only the analytical aspects of Auger spectroscopy that are related to the surface nature of the technique. However, many features of the process are similar to the scanning electron microscopy (SEM) and indeed the most modern Auger analysers are beginning to resemble these instruments and, indeed, SEMs are being constructed to allow Auger analysis in addition to the many other features. The Auger process does not require the incident ionising radiation to be defined with any degree of accuracy, it simply has to be capable of ionising the surface atom. It must therefore have an energy that will give a high yield of Auger electrons in the 0–1000 eV region. Thus electron beam energies of 3–30 keV are employed. Manufacturers of scanning electron microscopes now produce versions to ultra-high vacuum (UHV) standards and use field emission sources to give a spatial resolution of a few nanometres. The high beam current from these sources can be used to obtain spectra from small areas. By scanning the electron beam over the surface while positioning the analyser on a major Auger peak from a detected element, a map of the occurrence of that element over the surface can be produced. Because the electron energy does not have to be precisely defined, the design effort is concentrated on producing a finely focused beam which can be deflected and rastered over the surface being studied. At present electron beams with a diameter of 10–20 nm are common and these are used to produce a secondary electron image (SEI) of the surface being analysed. In the schematic diagram of the CMA analyser (figure 6.108), the incident electron
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Figure 6.122. Secondary electron image of a grain boundary in an Fe–3wt%Ni alloy heat treated to produce grain boundary segregation and containing cavities (b) tin Auger element map from region (a) showing tin segregation to cavities (Wild (1977)).
gun is normal to the surface being analysed with the advantage that topographical effects and shadowing are reduced to a minimum. This is particularly useful since Auger spectroscopy is frequently used to analyse rough surfaces, such as fracture faces. By scanning the electron beam over the surface while positioning the analyser on a major Auger peak from a detected element, a map of the occurrence of that element over the surface can be produced. Unlike element maps from energy dispersive X-ray analysers (EDX) the spatial resolution of the map is essentially the same as the secondary electron image because the electron mean free path is <5 nm compared with 1–5 mm for the EDX peaks with the result that the Auger element maps have a spatial resolution of less than 10 nm. Invariably rough surfaces are studied using Auger analysers and topographic effects can be severe, and although minimised by using a normal incidence electron source different parts of the surface yield different total currents due to a range of factors including surface roughness effects or grain boundary orientation differences. To eliminate this it is customary to raster the incident electron beam over the surface while detecting two energies on either side of the peak being mapped, and then normalising the signal from the peak using these two additional signals to obtain a mean background. An example of the mapping procedure in scanning Auger spectroscopy is shown in figure 6.122 (Wild (1997)) which demonstrates element mapping with 100 nm spatial resolution. Figure 6.122(a) shows the secondary electron image from the surface of an Fe–3 wt%Ni alloy fractured in UHV. Grain boundaries have been exposed which contain cavities varying in size from 0.1 to 1 mm. The heat treatment given to this material has caused tin to segregate to the cavity surface as shown by the tin element map (figure 6.122(b)). Maps of this type demonstrate that Auger spectroscopy can yield information with high spatial resolution.
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430 6.6.8
Electron sources Depth information
There are three basic ways in which Auger spectroscopy is used to obtain depth information. Outer 10 nm—electron escape depth Since low energy Auger electrons have a shorter escape depth than high energy Auger electrons, by detecting changes in the peak heights of these electrons the variation of a particular element with depth can be determined. This method can be improved by changing the angle of incidence of the electron beam since a beam normal to the surface will excite deeper atoms than a beam at glancing angle. Outer 1000 nm—depth profiling This is the most frequently adopted method of obtaining depth information using Auger spectroscopy. The procedure is first to obtain a spectrum from the surface, then to remove a fixed number of atom layers by ion bombardment and to repeat the analysis until the desired depth has been reached. From these spectra the variation of composition with depth can be determined. This method has been automated using dedicated data systems, where elements to be profiled are first determined and windows established around each major peak. The data system then measures each peak, switches on the ion beam for a fixed period, remeasures the peaks and so on. This method can be used to obtain several depth profiles from positions only a few micrometres apart, e.g. a grain boundary and a grain centre. The technique is limited to depth profiles of the order of 1–2 mm because mixing of surface atoms, caused by the ion bombardment, results in a depth resolution that is approximately 10% of the depth profiled. Thus after 1 mm has been profiled, an interface one atom layer thick would be smeared over 1000 atom layers and as a result would not be detected. The technique is capable of some very impressive results. Figure 6.123 shows the depth profile through a series of very thin layers of gallium arsenide and gallium arsenide doped with aluminium deposited on gallium arsenide. It is also possible to use the edge of the crater formed during a depth profile to obtain a composition profile (Van Oostram (1979)). The crater edge slopes uniformly from the surface to the crater bottom at a shallow angle, and by recording spectra at points along the crater edge a depth profile can be built up. This method has advantages over conventional profiling in that elements not profiled in the original depth profiling can be revisited but it does require an analyser with a good spatial resolution. Thick layers and hidden boundaries Thick layers, with perhaps very thin internal interfaces, can be studied by taper sectioning. Two approaches to taper sectioning are employed. The
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Figure 6.123. Auger depth profile through a series of thin semiconducting layers (reproduced by permission of Perkin-Elmer Ltd.).
specimen can simply be mounted at a shallow angle and polished metallographically to produce a smooth surface through the layer as shown in figure 6.124(a). Alternatively a crater can be formed in the surface by polishing using a rotating ball of known diameter (Walls et al (1979)). This produces a crater with the depth, z, as a function of distance, x, from the edge given by: z ¼ t R þ ½R2 ðD xÞ2 1=2
ð6:99Þ 2
where t, D and R are as defined in figure 6.124(b) and d ¼ D =8R. These sections are washed to remove the polishing material, cleaned in isopropanol, dried and introduced to the analyser. The surface is given a light etch using the ion bombardment gun to remove any contamination and air-formed oxide and the Auger analyser is then used in its high spatial resolution mode to scan along the taper section or the ball crater. This
Figure 6.124. Taper sectioning (a) and ball cratering (b) to enable the composition of the underlying layer to be established.
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Figure 6.125. A secondary electron image of a ball crater on a specimen containing layers of InP, 10 nm thick, separated from layers of GaInAs, 30 nm thick, showing that the layers are readily resolved (courtesy M Razeghi) (reproduced with permission of The American Vacuum Society).
method gives better results than using EDX to determine the composition because the EDX technique analyses from a volume at least 1 mm in diameter whereas the Auger analyser detects the surface atoms over a lateral resolution of a few tens of nanometres. Figure 6.125 shows the crater formed in a material which was made up of layers of indium phosphide, 10 nm thick, separated by layers of GaInAs, 30 nm thick (Razeghi and Duchemin (1983)). The layers are resolved, each layer appearing as a circle, allowing analysis to be performed across the interface. 6.6.9
Special methods for undertaking Auger analysis
Here we provide a series of examples of how special techniques have been developed to allow Auger analysis to be undertaken to effect. Segregation and surface oxidation Auger spectroscopy was designed to give rapid analysis of a surface and is ideally suited to the study of processes that require fast measurements such as segregation, volatilisation, oxidation and corrosion. If a transition metal is heated in a vacuum, certain trace impurity elements such as sulphur, phosphorus and carbon will diffuse to the surface. These elements will affect the way in which the surface reacts to corrosive gases such as oxygen. In figure 6.126 the surface composition of a stainless steel has been monitored as a function of time exposed to a low pressure of oxygen (Wild (1977)). Initially the surface has a layer of segregated sulphur with the major alloying element iron, the other element, detected in large quantities. When exposed to oxygen, the surface does not become immediately oxidised because the oxygen reacts with the sulphur to form
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Figure 6.126. Surface composition of stainless steel as a function of time exposed to 105 Pa of oxygen (Wild (1977)) (reproduced with permission of Pergamon Press).
SO2 , which is released into the environment. Gradually the sulphur is removed and only when the sulphur arrival rate has fallen to a low level does the surface form an oxide. The oxide that first forms is the thermodynamically stable chromium oxide Cr2 O3 . However, manganese, present in the alloy to 1–2 wt% rapidly diffuses to the oxide surface and forms the spinel oxide MnCr2 O4 . The speed of acquisition of this technique allows the quantitative determination of the surface composition at all stages of oxidation. Internal interfaces Metals, alloys and other materials are made up of grains and the interface between these grains is responsible for the mechanical and often the corrosion resistance of the material. Frequently, elements segregate to these grain boundaries where they may weaken the interface. Surface techniques are used to characterise these boundaries by exposing them in the analytical chamber. Many metals and alloys have a brittle/ductile transition at temperatures between room temperature and that of liquid nitrogen and it is possible to fracture these alloys by impact following cooling to 77 K. Other alloys, particularly the nickel-based superalloys and the austenitic
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Figure 6.127. Effect of air exposure on a monolayer of tin on an iron matrix (Seah (1975)) (reproduced with permission of North-Holland Publishing Company).
stainless steels remain ductile at these temperatures and special techniques must be applied to expose grain boundaries in these materials. The effect of air exposure on grain boundary composition It might be thought possible that a material could be fractured outside the spectrometer to expose the grain boundary which could then be introduced and analysed. This would have many advantages for the operator since there would be no need to incorporate a fracture stage in the already crowded analysis region. Unfortunately this is not possible because the surface chemistry is dramatically altered by exposure to relatively small amounts of air. This was demonstrated by Seah (1975) in an experiment where a monolayer of tin was deposited on to a surface of iron and then exposed to air at a pressure of 160 kPa. Figure 6.127 shows the spectrum recorded after the tin had been deposited and Auger MNN transitions from tin are present at 430 and 440 eV together with the LMM transitions from iron at 595, 650 and 703 eV. Exposure to air shows the tin peaks have almost disappeared and only iron and oxygen peaks are present to any significant intensity; clearly it is essential to undertake fracture in the vacuum of the Auger system. Impact fracture Impact fracture is the most widely used method of exposing grain boundary surfaces in the spectrometer. The specimen is introduced to the impact stage via a special port and prior to fracture is positioned across the anvil
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Figure 6.128. A typical impact fracture stage (a) general view, (b) cross-section.
(figure 6.128). It is cooled by passing liquid nitrogen through the block until the specimen temperature has fallen below the ductile–brittle transition when it is fractured by applying an impact force to one half, which then falls into a holder and is transferred on to the spectrometer stage for examination. An impact fracture surface from a specimen of 2.25%Cr–1%Mo ferritic steel is shown in figure 6.129(a), where fracture has occurred almost entirely along grain boundaries. A spectrum from the surface of a grain (figure 6.129(b)) shows peaks from the alloy constituents but, in addition, peaks occur at 120 eV from the LMM transition in phosphorus, at 272 eV from the KLL transition in carbon and at 180 and 220 eV from MNN transitions in molybdenum. This particular cast has received a heat treatment which has allowed sulphur, carbon and molybdenum, all present in the bulk in small quantities, to segregate to the grain boundaries where the carbon and molybdenum have combined to form a carbide, which can be identified from the carbon Auger ‘fingerprint’, and the phosphorus is present as a single atom layer of phosphorus. Phosphorus segregation can weaken the material by reducing the strength of the grain boundary. Tensile fracture Nickel-based superalloys are ductile at 77 K and will not fracture in an intergranular manner in a standard impact stage but they can be fractured
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Figure 6.129. An impact surface from a 2.25%Cr–%1Mo steel (a) together with an Auger spectrum (b) for a given grain boundary surface.
by straining in tension. It is necessary, however, to weaken the boundary in some way before the specimen is fractured. The most common method used is to hydrogen-charge the specimen by immersing in dilute sulphuric acid and cathodically charging using a current of 50 mA cm2 at approximately 343 K for periods of 1 to 7 days. The hydrogen diffuses into the alloy and segregates to grain boundaries, and if the specimen is fractured shortly after hydrogen charging, so that the hydrogen has not had time to diffuse away, it will invariably fracture, with a significant proportion of the fracture being intergranular. The intergranular region is usually confined to a region within 200 to 300 mm from the outer edge of the specimen. A tensile fracture stage is shown in figure 6.130, where the hydrogencharged specimen is transferred from the introduction probe to the fixed and movable jaws of the tensile stage and fractured using a slow strain rate of approximately 0.001 mm s1 and the stress–strain curve is
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Figure 6.130. A typical tensile fracture stage used for fracturing specimens that are not suitable for impact fracture.
recorded using a load cell. Following fracture the specimen is transferred back to the introduction probe, which then moves the specimen on to the analysis stage. Figure 6.131 shows the tensile fractured surface for Inconel 600 alloy (Allen and Wild (1986)) hydrogen-charged to effect intergranular fracture. Metal/oxide interfaces Segregation of elements to the interface between two dissimilar materials may influence the mode of bonding or, if one or more of the layers is growing, the kinetics of growth. One such interface is between a metal and its oxide, where segregation of elements such as sulphur may react at the interface and cause the oxide-to-metal bond to be weakened and silicon segregation can have a protective effect by reducing the cation diffusion rate. Unfortunately, this particular interface is one of the most difficult to access. Depth profiling is only partially successful because the oxide thickness is normally greater than 1 mm and the resolution of this technique tends to be
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Figure 6.131. Tensile fracture of Inconel 600 following hydrogen charging to reveal intergranular fracture facets.
10% of the profiled depth with the result that layers with a thickness less than 100 nm tend not to be detected. Ball cratering and taper sectioning have problems caused by the difference in hardness of the metal and the oxide which results in the metal being smeared over the oxide. One method that has met with some success in exposing the oxide/metal interface on steels involves sputter ion plating (figure 6.132) (Coad and Wild (1983)). In this method the metal with its oxide is exposed to a plasma of an inert gas such as argon to clean the outer oxide surface. Then a metal such as nickel or molybdenum is evaporated on to the surface and the plasma bombardment
Figure 6.132. Schematic of sputter ion plating method (Wild (1985)) (reproduced with permission of Pergamon Press).
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Figure 6.133. Oxide (a) and metal (b) sides of the oxide/metal interface on 20%Cr– 25%Ni–Nb stainless steel exposed to CO2 at 1123 K for 100 h (Wild (1985)) (reproduced with permission of Pergamon Press).
causes the plated metal to be buried into the oxide surface, resulting in a very strong bond. The whole process is undertaken at a temperature of about 500 K. On cooling the sides and ends are cut away and the stresses set up between the plating metal and the oxide cause the plating metal to pull away, bringing with it the oxide. Figure 6.133 shows the two sides of the metal/oxide interface from a specimen of 20%Cr–25%Ni–Nb stabilised stainless steel oxidised in CO2 gas at 1123 K for 100 h (Wild (1985)). The grains in the metal are readily identified from the grooves and the oxide has pulled away from the metal taking with it ridges of oxide from within the grain boundaries. Element maps of the surfaces show that the metal side is enriched in chromium and silicon at the grain boundaries but in iron at the grain centre, while the oxide side shows that the silicon enrichment is confined to the grain centre (figure 6.134). Argon ion depth profiling through the centre of a grain positioned on the oxide side indicates that the silica layer is of the order of 20 nm thick. Depth profiling through the oxide (see figure 5.74) indicates that the oxide which forms on this steel in these conditions is an outer layer of spinel oxide below which is a layer of
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Figure 6.134. Auger element maps from the oxide/metal interface on 20%Cr–25%Ni–Nb stainless steel exposed to CO2 at 923 K for 12 000 h (Wild (1985)) (reproduced with permission of Pergamon Press).
rhombohedral Cr2 O3 , while the metal/oxide interface studies show that a layer of SiO2 only a few tens of nanometres thick exists.
6.7
References
Agar A W 1973 The basic principles of electron microscopy in Principles and Practices of Electron Microscopy ed A M Glauert (Amsterdam: North-Holland) ch 1 Allen G C and Wild R K 1986 Phil. Mag. 54 L37 Allen M 1981 Phil. Mag. 43A 325 Allpress J G, Sanders J and Wadsley D W 1969 Acta Cryst. B25 1156 Anderson R and Klepeis S J 1997 Electron Microsc. IV MRS Sympos. Proc. 480 187 MRS (Pittsburg)
Copyright © 2003 IOP Publishing Ltd.
References
441
Antis G R and Cockayne D J 1979 Acta Cryst. A35 511 Arnal F, Verdies P and Vincesini P-D 1969 C R Acad. Sci. Paris 268 1526 Auger P 1925 J. Phys. Radium 6 205 Ball C J 1971 Introduction to the Theory of Diffraction (Oxford: Pergamon Press) Barber D J 1995 Micros and Analysis May 5 Bauer E and Telieps W 1987 Low energy electron microscopy in Scanning Microscopy Suppl. 1 (Chicago: AMF O’Hare) p 99 Bauer E, Mundschau M, Swiech W and Telieps W 1989 Ultramicroscopy 31 49 Beaman R and Isasi J A 1972 Electron Beam Microanalysis ASTM Special Tech. Pub 506 Bednortz J G and Mu¨ller K A 1986 Z. Phys. B64 189 Bethe´ H 1930 Ann. Physik 5 325 Bilde-Sorensen J B and Appell C C 1996 Energy Dispersive X-ray Spectrometry in the ESEM Proc. SCANDEM 96 4 Bishop H E and Rivie`re J C 1969 J. Appl. Phys. 40 1740 Bonzel H P and Ferrer S 1982 Surf. Sci. 118 L263 Booker G R 1970 Modern Diffraction and Imaging Techniques in Materials Science ed S Amelincx, R Gevers, G Remant and J Van Landuyt (Amsterdam: North-Holland) Bowen D K and Hall C R 1975 Microscopy of Materials; Modern Imaging Methods using Electron, X-ray and Ion Beams (London: Macmillan) Brammar I S and Dewey M A P 1966 Specimen Preparation for Electron Metallography (New York: Elsevier) Braski D N, Carpenter R W and Bentley J 1982 Acta Metall. 30 799 Briggs D A and Seah M P 1990 Practical Surface Analysis by Auger and X-ray Photoelectron Spectroscopy (Chichester: Wiley) Brown L M, Walsh C A, Dray A and Bleloch A L 1995 Microsc. Microanal. Microstruct. 6 121 Browning N D, Pennycook S J, Chisholm M F, McGibbon M M and McGibbon A J 1995 Interface Sci. 2 397 Bruley J, Brydson R, Mo`llejans H, Gutekunst G, Mader W, Knauss D and Ro`hle M 1994 J. Mater. Res. 9 2574 Budd D, Hammes U and Ward W B 2000 J. Sedimentary Res. 70 217 Bullough R, Maher D M and Perrin R C 1971 Phys. Status Solidi 43 689 Carlson T A 1975 Photoelectron and Auger Spectroscopy (New York: Plenum Press) Carlson D E, Hang K W and Stockdale G F 1974 J. Am. Ceram Soc. 57 295 Carpenter R W 1982 Ultramicroscopy 8 79 Carter R D, Damcoff D L, Atzmon M, Was G S, Bruemmer S and Kernitz E A 1994 J. Nucl. Mat. 211 70 Castaing R 1960 Electron probe microanalysis in Advances in Electronics and Electron Physics ed L Marton vol 13 (New York: Academic Press) p 117 Castaing R 1960 Adv. Electron. Electron Phys. 13 317 Castaing R 1954 Doctoral Thesis (Paris: University of Paris) English translation by D B Wittery Rept. No. WAL 142/59-7, Dept. of Army, Dec. 1955 Catto K J and Smith K C A 1973 J. Microscopy 98 1619 Chandler J A 1977 X-ray microanalysis in the electron microscope in Practical Methods in Electron Microscopy ed A M Glauert (Amsterdam: North-Holland) Chang C C 1974 in Characterisation of Solid Surfaces ed P F Kane and G R Larrabee (New York: Plenum Press)
Copyright © 2003 IOP Publishing Ltd.
442
Electron sources
Chapman J N 1984 J. Phys. D: Appl. Phys. 17 623 Chapman J N, Morrison G R, Jakubovics J P and Taylor R A 1983 Institute of Physics Conference Series 68 p 197 Chastell D J and Flewitt P E J 1979 J. Mat. Sci. Eng. 23 153 Chester R J 1985 Metallography 18 161 Chung M F and Jenkins L H 1970 Surf. Sci. 21 253 Cliff G and Lorimer G W 1975 J. Microscopy 103 203 Coad P and Wild R K 1983 Appl. Surf. Sci. 14 321 Cockayne D J H 1973 J. Microscopy 98 116 Cockayne D J H 1973 in Understanding Materials ed C J Humphreys Marney Pub (London: Institute of Metals) p 51 Collet S A, Browne L M and Jacobs M H 1981 Electron Energy Loss Spectroscopy in Quantitative Microanalysis with High Spatial Resolution (London: Metals Society) Cosslett V E 1970 IEE Reviews 117 1489 Cosslett V E and Duncumb P 1956 Nature 177 1172 Cowley J M 1969 Appl. Phys. Lett. 15 58 Cowley J M 1981 Diffraction Physics (Amsterdam: North-Holland) Cowley J M 1986a Prog. Surf. Sci. 21 209 Cowley J M 1986b Principles of image formation in Principles of Analytical Electron Microscopy ed D C Joy, A D Romig and J I Goldstein (New York and London: Plenum Press) Cowley J M and Au A Y 1976 Scanning Electron Microscopy 1976 ed O Johain (Chicago: IITRC) 1 377 Cowley J M and Moodie A F 1957 Proc. Phys. Soc. 70 505 Crewe A V, Wall J and Walter L M 1968 J. Appl. Phys. 39 5861 Crewe A V 1968 Science 154 729 Cullis A G, Chew N G, Hutchinson J L, Irvine S J C and Geuss 1985 Microscopy of Semiconducting Materials (Bristol: Institute of Physics) Cusano D A 1964 Solid State Comm. 2 353 Danilatos G D 1988 Foundations of Electron Scanning Microscopy (Sydney: Academic Press) Davis L E, MacDonald N C, Palmberg P W, Riach G E and Weber R E 1976 Handbook of Auger Electron Spectroscopy (Minnesota: Physical Electronic Industries Inc) De Jong A F and Bulle-Lieuwma C W T 1990 Phil. Mag. 62 183 Doig P and Flewitt P E J 1983a Met. Trans. 14A 1943 Doig P and Flewitt P E J 1983b J. Microscopy 130 377 Doig P and Flewitt P E J 1983c Micron Microscopia Acta 14 225 Doig P and Flewitt P E J 1984 J. de Physique 45 2-38 Doig P and Flewitt P E J 1987 Met. Trans. 18A 399 Doig P and Flewitt P E J 1988 Analytical Electron Microscopy (London: Institute of Metals) Doig P, Lonsdale D and Flewitt P E J 1981a Electron Distributions in STEM-EDS X-ray Microanalysis of Thin Foils in ‘Quantitative Microanalysis with High Spatial Resolution’ (London: Metals Society) 277 p 41 Doig P, Lonsdale D and Flewitt P E J 1981b Metall. Trans. 12A 1277 Doig P, Lonsdale D and Flewitt P E J 1982 Scripta Met. 16 1201 Doig P, Lonsdale D and Flewitt P E J 1986 Metal Sci. 16 335
Copyright © 2003 IOP Publishing Ltd.
References
443
Doig P, Williams S H and Flewitt P E J 1987 Electron Microscopy and Analysis Institute of Physics Conference Series 90 p 193 (Bristol: Institute of Physics) Donolato C 1983 J. Appl. Phys. 54 1314 Dray A, Walsh C C and Brown L M 1995 Report for Ontario Hydro Duncumb P 1966 Precipitation studies with EMMA in Electron Microprobe ed T D McKinley, K F J Heinrich and D B Wittery (New York: Wiley) Duncumb P 1979 J. Microsccopy 117 165 Duncumb P and Shields P K 1963 Brit J. Appl. Phys. 14 617 Duncumb P 1968 J. de Microscopic 7 581 Dupouy G 1973 Endeavour 32 66 Ecob R 1986 Script Met. 20 1001 Edington J W 1976 Practical Electron Microscopy in Materials Science vol 3 Philips Tech. Library (London: Macmillan) Eicher E 1967 High Temperature High Resolution Metallography ed H I Aaronson and G S Ansell (New York: Gordon and Breach) p 167 Egerton R F and Cheng S C 1987 Ultramicroscopy 21 231 Egerton R F 1975 Phil. Mag. 31 199 Egerton R F 1978 Ultramicroscopy 3 39 Egerton R F 1989 Ultramicroscopy 28 215 Endemir A and Cheng C C 1989 Ultramicroscopy 29 268 Erickson H P and Klug A 1971 Phil. Trans. Roy. Soc. London B261 1 Fallon P J, Brown L M, Barry J C and Bruley J 1995 Phil. Mag. 72 21 Fathers D J, Jakubovics J P, Joy D C, Newbury D E and Yakowitz H 1973 Phys. Stat. Solidi A20 535 Finch D S and Vesely D 1987 Polymers 28 675 Fitgerald A, Kiel J M and Heinrich K F J 1968 Science 159 528 Flewitt P E J 1970 Recent Advances in Electron Microscopy Specimen Preparation (London: Edwards) p 10 Flewitt P E J 1974a Acta Met. 22 47 Flewitt P E J 1974b Acta Met. 22 65 Flewitt P E J and Wild R K 1985 Microstructural Characterisation of Materials and Alloys (London: Institute of Metals) France L K and Loretto M H 1968 Proc. Roy. Soc. A307 83 Glauert A M and Phillips R 1965 Techniques for Electron Microscopy ed D H Kay (Oxford: Blackwall Scientific Publications) Goldstein J I 1969 Electron probe analysis in metallurgy in Interpolation and Extrapolation in Electron Probe Microanalysis ed A J Tousimis and L Marton (New York: Academic Press) Goldstein J I 1979 Principles of thin film X-ray microanalysis in Introduction to Analytical Electron Microscopy ed J J Hren, J I Goldstein and D C Joy (New York: Plenum Press) Goldstein J I, Costley J L, Lorimer G W and Reed S J B 1977 Proc. Workshop on Analytical Electron Microscopy SEM 1 (Chicago: IITRI) Goldstein J I, Newbury D E, Echlin P, Joy D C, Fiori C and Lifshin E 1984 Scanning Electron Microscopy and X-ray Microanalysis (New York: Plenum Press) Goodhew P J 1972 Specimen Preparation in Materials Science (Amsterdam: NorthHolland) Goodhew P J and Chescoe D 1981 Micron 11 153
Copyright © 2003 IOP Publishing Ltd.
444
Electron sources
Goringe M J 1975 Diffraction Contrast from Imperfect Crystals in Electron Microscopy in Materials Science ed E Reudl and U Valdre´ (Brussels: Commission of European Communities) Gotze J 1998 Cathode Luminescence in Geosciences ed M Pagel, V Barbin, P Blanc and D Ohrenstetten (Berlin: Springer) Gotze J and Magnus M 1997 Europ. J. Minerals 9 1207) Gronsky R 1980 Direct imaging of grain boundaries in Grain Boundary Structure and Kinetics (Ohio: ASM) Grundy P J 1971 IEE Trans. Magn. 7 483 Grundy P J and Jones G A 1976 Electron Microscopy in the Study of Materials (London: Edward Arnold) Gull S T and Daniell G J 1978 Nature 272 616 Hall E L, Imeson D and Vander Sande J B 1981 Phil. Mag. A 43 1569 Halliday J S 1965 Techniques in Electron Microscopy ed D H Kay (Oxford: Blackwall Scientific Publications) Harris L A 1968 J. Appl. Phys. 39 4862 Hashimoto H 1980 Japanese Patent Application S-55-183575 Hashimoto H 1999 Topics in Electron Diffraction and Microscopy of Materials ed P B Hirsh (Bristol: IOP Publishing) Haworth C W 1979 Quantitative microanalysis in Electron Microscopy and Microanalysis of Crystalline Materials ed J A Belk (London: Applied Science) Head A K, Humble P, Clarebrough L M, Morton A J and Forward C T 1973 Computed Electron Micrographs and Defect Identification (Amsterdam: NorthHolland) Heard P J, Day J C C and Wild R K 2000 Microscopy and Analysis May p 9 Hearle J W S 1972 Introduction to scanning electron microscopy in The Use of the Scanning Electron Microscope ed J W S Hearle, J T Sparrow and P M Cross (Oxford: Pergamon) Heinrich K F J 1972 Anal. Chem. 44 350 Henke B L 1981 Low Energy X-ray Diagnostics ed D T Attwood and B L Henke (New York: Institute of Physics) p 85 Henke B L, Elgin R L, Lent R E and Ledingham R B 1967 Norelco Reporter 14 1121 Herrmann K 1978 J. Phys. E 11 1075 Hillier J and Baker R F 1944 J. Appl. Phys. 15 663 Hippsley C A 1981 Metal Science 15 137 Hirsch P B, Howie A, Nicholson R B, Pashley D W and Whelan M J 1965 Electron Microscopy of Thin Crystals (London: Butterworths) Hirsch P B 1985 Mat. Sci. Technol. 1 666 Hofer F, Grogger W, Kothleitner G and Warbichler P 1997 Ultramicroscopy 67 83 Holt D B 1987 Electron Microscopy and Analysis 1987 Conference Series 90 (Bristol: Institute of Physics) p 289 Howie A 1965 Techniques for Electron Microscopy ed D H Kay (Oxford: Blackwell Scientific Publications) Hren J J 1986 Principle of Analytical Electron Microscopy (London: Plenum Press) Humphrey C J, Bergholz W, Butler J, Gai P L, Hardy G J, Jenkins M L, Salisbury I G, Smith B C and Spence J C H 1985 In.t Symp. on In-situ Experiments with HVEM Osaka Hutchinson J, Honda T and Boyes E 1986 JEOL News 24E 9
Copyright © 2003 IOP Publishing Ltd.
References
445
Isaacson M 1978 Proc. 11th Annual SEM Symposium (Chicago) Jacobs M H 1974 Energy and wavelength dispersive X-ray microanalysis in Advances in Analysis of Microstructural Features by Electron Beam Techniques (London: Metals Society) Jenkins F E and White H E 1951 Fundamentals of Optics Interscience (New York: McGraw-Hill) Johnson W 1975 Metals and Materials Feb 21 Jonssan A 1927 Inst. Physik 43 845 Jouffrey G 1975 High Voltage Electron Microscopy up to 3.1 MV in Electron Microscopy in Materials Science ed E Reundl and U Valdre´ (Brussels: Commission of European Communities) p 981 Joy D C 1974 The choices of electron sources for analysis in Advances in Analyser of Microstructural Features by Electron Beam Techniques (London: Metals Society/Institute of Physics) Joy D C 1979 Introduction to Analytical Electron Microscopy ed J J Hren, J I Goldstein and D C Joy (New York: Plenum Press) p 223 Joy D C 1981 Electron Energy Loss Spectroscopy in Quantitative Microanalysis with High Spatial Resolution (London: Metals Society) p 277 Joy D C 1987 Principles of Analytical Electron Microscopy ed D C Joy, A D Romiy and J I Goldstein (New York: Plenum Press) p 277 Joy D C 1995 Monte Carlo Modelling for Electron Microscopy and Microanalysis (Oxford: Oxford University Press) Joy D C and Maher D M 1978 Ultramicroscopy 3 39 Joy D C and Jakobuvics J P 1968 Phil. Mag. 17 61 Kanig G 1974 Kunststoffe 64 470 Karagoz S, Lien I, Bischoff E and Fischmeisten H F 1989 Met. Trans. 20A 2696 Kastner G and Messerschmidt U 1999 JEOL News 34 24 Kelly P M, Jostsons A, Blake R G and Napier J G 1975 Phys. Stat. Solidi 31 771 Kirk E 1989 Microscopy of Semiconducting Materials: Proc. Royal Micros Soc. (Bristol: Institute of Physics) 15 831 Korner A 1988 Phil. Mag. 58A 507 Krivanek O L 1989 Ultramicroscopy 28 118 Krivanek O L, Gubbens A J, Meyer N and Meyer C E 1992 Proc. EMSA Boston Electron Micro Soc. America 2 1994 Krivanek O L, Kundmann M K and Kunoto K 1995 J. Microscopy 180 277 Krivanek O L, Ahn CC and Keeney R B 1987 Ultramicroscopy 22 103 Krivanek O L, Dellby N, Spence A J H, Camps R A and Brown L M 1997 Institute of Physics International Conference Series 153 p 35 Kulenkampff H 1922 Ann. Physik 69 549 Kuo M-T, May P W, Gun A, Ashfold M N R and Wild R K 2000 Diamond Relat Mater. 9 1222 Kyser D F 1979 Monte Carlo simulation in analytical electron microscopy in Introduction to Analytical Electron Microscopy ed J J Hren, J I Goldstein and D C Joy (New York: Plenum Press) p 199 Laird C and Aaronson H I 1967 Acta Met. 15 73 Leapman R O and Cosslett J E 1976 J. Phys. D: Appl. Phys. L29 Lebiedzik J, Lebiedzik J, Edwards R and Phillips B 1979 Scanning Electron Microscopy (Illinois: AMF O’Hare) p 61
Copyright © 2003 IOP Publishing Ltd.
446
Electron sources
Lenz F A 1971 Transfer of image information in The Electron Microscope in Electron Microscopy in Materials Sciences ed U Valdre´ (London: Academic Press) p 541 Lepienski C M, Giacometti J A, Leal-Ferreira G L, Fisive F L and Achete C A 1993 J. Non Crystalline Solids 159 204 Lonsdale D and Flewitt P E J 1978a Mat. Sci. Eng. 32 167 Lonsdale D and Flewitt P E J 1978b Met. Trans. 9A 1619 Loretto D and Loretto M H 1989 Phil. Mag. 60A 597 Loretto M H and Smallman R E 1975 Defect Analysis in Electron Microscopy (London: Chapman and Hall) Loretto M H, Chen Z and Burbery A J 1988 in EMAG 87 Analytical Electron Microscopy ed G W Lorimer (London: Institute of Metals) p 31 Lorimer G W, Cliff G and Clarke N J 1975 Developments in Electron Microscopy and Analysis ed J A Venables (New York: Academic Press) p 153 Love G, Cox M G C and Scott V D 1974 J. Phys. D 7 2131 Love G and Scott V D 1987 Electron Microscopy and Analysis Institute of Physics Conference Series 90 p 349 (Bristol: Institute of Physics) Lozano-Perez S, Huang Y, Lanford and R Titchmarsh J M 2001 Electron Microsc and Analysis IOP Conference Series 168 191 Lu P and Smith D J 1987 Phys. Rev. Letters 59 2217 Lupini A R, Krivanek O L, Delby N, Nellist P D and Pennycook S J 2001 Electron Microscopy and Analysis Institute of Physics Conference Series 168 p 31 (Bristol: IOP Publishing) McMillan D, Fallon P J, Ito Y and McGibbon A J 1992 in Electron Microscopy Proc. Enrem 92 Granada, Spain 1 p 103 MacMillan J and Flewitt P E J 1975 Micron 6 141 Madden P K and Fisher S B 1982 Phys. Stat. Solidi A69 569 Marfurien A S 1979 Spectroscopy Luminescence and Radiation Centres in Minerals (Berlin: Springer) Marks L D 1984 Surf. Sci. 139 281 Martin P M and Poole D M 1971 Met. Rev. 15 19 Marton L 1969 Survey of microanalysis in Interpolation and Extrapolation in Electron Probe Microanalysis ed A J Tousimis and L Marton (New York: Academic Press) McG.Tegart W J 1959 Electrolytic Thinning and Chemical Polishing of Metals (London: Pergamon Press) McGibbon M M, Browning N D, McGibbon A J and Pennycook S J 1996 Phil. Mag. A 73 625 McGuire G E 1979 Auger Electron Spectroscopy Reference Manual (New York: Plenum Press) Messerschmidt U and Appel F 1989 Mat. Sci. Eng. A113 409 Messier P and Vitale T 1993 Microscopy Res. Tech. 25 374 Mollenstedt G and Lenz F 1963 Adv. Electron. Electron Phys. 18 (New York: Academic Press) p 251 Muller D A and Silcox J 1995 Phil. Mag. 71 1375 Mulvey T 1967 Focusing of Charged Particles vol 1 ed A Septier (London: Academic Press) p 469 Mundschau M 1990 Microscopy and Analysis 19 29 Mundschau M, Bauer E, Telieps W and Swiech W 1990 Phil. Mag. A 61 257 Napchan E 2001 Microscopy and Analysis Jan p 9
Copyright © 2003 IOP Publishing Ltd.
References
447
Nasir M J 1972 Proc. 5th European Cong Electron Microscopy (London: Institute of Physics) Nathrop D C 1972 Applications to solid-state electronics in The Use of the Scanning Electron Microscope ed J W S Hearle, J T Sparrow and P M Cross (Oxford: Pergamon) Newbury D J and Yakowitz H 1973 Proc. 19th AIP Conference on Magnetism Boston Newbury D J and Williams D B 2000 Acta. Met. 48 323 Nicholson R B and Nutting J 1961 Acta Met. 9 210 Nicolosi J A and Jenkins R 1983 Norelco Reporter 31 1 Nicolosi J A, Goven J P, Merol D and Jenkins R 1986 Optical Eng. 25 964 Nockold C, Nasir M J, Cliff G and Lorimer G W 1979 Electron Microsc. Anal. Inst. of Physics Series No 52 (Bristol: IOP) Nonoka S 1982 Proc. 19th Int. Congress Electron Microscopy Hamburg 1 385 Oatley C W 1972 The Scanning Electron Microscope Part 1, The Instrument (Cambridge: University Press) Oatley C W, Nixon W C and Pease R F W 1965 Scanning Electron Microscopy, Advances in Electronics and Electron Physics vol 21 ed L Martin (New York: Academic Press) Okamato J K, Pearson D H, Ahn C C and Fultz B 1992 in Transmission Electron Energy Loss Spectroscopy in Materials Science ed M M Disko, C C Ahn and B Fultz (Warrendale, PA: TMS) Orloff J 1989 Ultramicroscopy 28 88 Overwijk M 1993 J. Vac. Sci. Tech. 21B 2021 Ozakaya D, Stobbs W M and Brown L M 1993 Electron Microscopy and Analysis Series (Bristol: IOP Publishing) 138 413 Ozakaya D, Yann J, Brown L M and Flewitt P E J 1995 J Microsc. 180 300 Palmberg P W and Rhodin T N 1968 J. Appl. Phys. 39 2425 Palmberg P W, Bohn G K and Tracy J C 1968 Appl. Phys. Lett. 15 254 Peng L M and Cowley J M 1989 Ultramicroscopy 29 135 Pennycook S J and Boatner L A 1988 Nature 336 565 Perkins J, Adachi K and Yamashita T 1989 Ultramicroscopy 30 217 Philbert J 1963 X-ray Optics and Microanalysis 3rd Symp. Stanford (New York: Academic Press) Philbert J and Tixier R 1968 Br. J. Appl. Phys. 1 685 Poole M D and Martin P M 1969 Met. Rev. 14 61 Poole D M and Thomas P M 1961–2 J. Inst. Met. 90 228 Putilin S N, Antipov E V, Chinaissen O and Ho H R O 1993 Nature 363 56 Rapperport E J 1969 A technique to increase electron probe resolution in Electron Probe Microanalysis ed A J Tousimis and L Marton Advances in Electronics and Electron Physics Supplement 6 (New York: Academic Press) p 117 Razeghi M and Duchemin J P 1983 J. Vac. Sci. Technol. B1 262 Reed S J B 1974 The accuracy of matrix corrections in Advances in Analysis of Microstructural Features by Electron Beam Techniques (London: Metals Society) Reed S J B 1975 Electron Microprobe Analysis (Cambridge: Cambridge University Press) Reimer L and Niemietz A 1985 Ultramicroscopy 16 161 Remer L and Krefting E R 1976 NBS Special Pub. 460 45 Rivie`re J C 1990 Surface Analytical Techniques (Oxford: Clarendon Press) Rodenburg J M and Lupini A R 1999 Proc. EMAG 1999 Institute of Physics Conference Series 161 p 339 Rodenburg J M and Macak E B 2002 Micros and Analysis July p 5
Copyright © 2003 IOP Publishing Ltd.
448
Electron sources
Roever E W and Cosper D R 1996 Scanning 18 500 Rozenak P 1990 Mat. Sci. Eng. A128 91 Rudberg E 1927 Svenska Vet. Akad. Handl. 7 1 Ruste J and Gantois M 1975 J. Phys. D: Appl. Phys. 8 872 Salter W J M 1979 Instrumentation in electron probe microanalysis in Electron Microscopy and Microanalysis of Crystalline Materials ed J A Belk (London: Applied Science) Scherzer O 1947 Optik 2 114 Scherzer O 1949 J. Appl. Phys. 20 20 Scherzer O 1970 Ber. Bunsenges Phys. Chem. 74 1154 Scott V D 1974 Electron probe microanalysis using soft X-rays in Advances in Analysis of Microstructural Features by Electron Beam Techniques (London: Metals Society) Seah M P 1975 Surf. Sci. 53 168 Seah M P 1980 J. Vac. Sci. Technol. 17 16 Seitzman L E, Wang L M, Griffin R D, Komissarov A P, Kulcinski G L and Dodd L A 1989 Ultramicroscopy 29 291 Sekine T, Nagasawa Y, Kudoh M, Sakai Y, Parkes A S, Geller J D, Mogami A and Hirota H 1982 Handbook of Auger Electron Spectroscopy (Tokyo: JEOL Inc) Shmoda G 1969 Behaviour of electrics in a specimen in electron probe microanalyzers in Advance in Electronics and Electron Physic’ ed A J Tousimis and L Martin (New York: Academic Press) Sinclair R, Yamashita T and Pouce G A 1981 Nature 290 386 Smith D J 1985 J. Vacuum Sci. Tech. B3 1563 Smith D J 1986 Surf. Sci. 178 462 Smith D J and Marks L D 1985 Ultramicroscopy 16 101 Smith D J, Glaisher R W, Lu P and McCartney M R 1989 Ultramicroscopy 29 123 Smith K C A 1956 PhD Dissertation (Cambridge: University of Cambridge) Smith R F, Doig P and Flewitt P E J 1984 Eng. Fract. Mech. 19 653 Spiller E 1981 Low Energy X-ray Diagnostics ed D T Attwood and B L Henke (New York: Institute of Physics) p 124 Statham P J 1976 X-ray Spectroscopy 5 16 Statham P J 1977 Analyt. Chem. 49 2149 Statham P J 1982 Ultramicroscopy 8 309 Stephenson T A, Loretto M H and Jones I P 1981 Beam spreading in thin foils in Quantitative Microanalysis with High Spatial Resolution (London: Metals Society) 277 p 53 Stevens R A and Flewitt P E J 1986 Acta Met. 34 849 Stobbs W M 1975 The weak beam technique in Electron Microscopy in Materials Science ed E Reundl and U Valdre´ (Brussels: Commission of European Communities) Stowe S J and Robinson V N E 1997 Scanning 20 57 Struder L, Meidinger N, Stotten D, Kemmer J, Lechner P, Leuttenegger P, Soltan H, Eggert P, Rohde M and Schulein T 1999 Micros and Microanalysis 4 622 Summerfelt S R and Carter C B 1989 Ultramicroscopy 30 150 Sweatman T R and Long T V P 1969 J. Petrology 36 322 Takahashi H, Okumura T and Seo Y 1989a J. Jpn. Inst. Metals 153 349 Takahashi H, Kondo Y, Okumura T and Seo Y 1989b Jeol News 27E 2 Taylor D S and Pollard G 1982 Metallography 15 225 Taylor R A 1983 J. Magn. Mag. Mat. 31-34 999 Thomas G and Goringe M J 1979 Transmission Electron Microscopy of Materials (New York: Wiley)
Copyright © 2003 IOP Publishing Ltd.
References
449
Thompson S J and Flewitt P E J 1971 Metallography Thompson M N, Doig P, Edington J W and Flewitt P E J 1976 Phil. Mag. 35 1537 Thornton P R 1968 Scanning Electron Microscopy (London: Chapman and Hall) Tiab D and Donaldson E C 1996 Petrophysics; Theory and Practice (Houston: Gulf Pub. Co.) Titchmarsh J M 1979 UKAEA Harwell Internal Rep AERE R9661 Titchmarsh J M and Dunbill S 1996 J. Nucl. Mat. 227 203 Titchmarsh J M and Williams T M 1981 Quantitative Analysis with High Spatial Resolution (London: Metals Society) p 223 Tixier R 1979 Electron Probe Micronalyser of Thin Samples in Microbeam Analysis— Biology ed C Lechene and R Warner (London: Academic Press) Tonomura A 1993 Electron Microscopy (Heidelberg: Springer) Tonamura A 1994 Physics World March p 39 Tsuno K 1988 Rev. Solid State Sci. 2 623 Tsuno K, Inove M and Ueno K 1989 Mat. Sci. Eng. B3 403 Turan S and Knowles K M 1995 J. Microscopy 177 287 Twigg M E, Loretto M H and Fraser H L 1981 Phil. Mag. 43 1587 Van Essen C G 1974 J. Phys. E 7 48 Van Essen C G 1979 Scanning electron microscope in Electron Microscopy and Microanalysis of Crystalline Materials ed J A Belk (London: Applied Science) Van Helvoort A T J, Knowles K M Boothroyd C and Fermier J A 2001 Electron Micro and Analysis (Bristol: IOP publications) p 541 Van Oostram A 1979 Surf. Sci. 89 615 Vesely D 1983 Shell Polymers 7 54 Vesely D 1984 Ultramicroscopy 14 279 Vesely D 1988 Encyclopedia of Materials Science and Engineering ed R W Cahn (Oxford: Pergamon Press) Vesely D 1989 Encyclopedia of Materials Science and Engineering vol 1 ed R W Cahn (location: publisher?) p 404 Vesely D, Low A and Bevis M 1976 Developments in Electron Microscopy ed J A Venables (London: Academic Press) p 333 Vetrano J, Berch M W, Robertson I M and Kirk M A 1989 Met. Trans. 20A 2673 Vincent R and Chearns D 1988 in EMAG 87 Analytical Electron Microscopy ed G W Lorimer (London: Institute of Metals) p 37 Wade R H 1968 J. Phys. Colloque C2 Supplement 2-3 29 95 Walls J M, Hall D D and Sykes D E 1979 Surf. Interface Anal. 1 204 Walmsley J C and Lang A R 1987 Electron Microscopy and Analysis Institute of Physics Series 90 p 281 (Bristol: IOP Publishing) Watt G R, Wright P, Galloway S and McLean C 1998 Geochimica Cosmochimica Acta 61 433 Watts J F 1990 Microscopy and Analysis January 25 Watts J F 1990 An Introduction to Surface Analysis by Electron Spectroscopy (Oxford: Oxford University Press) Watts J F and Wolstenholme J 2003 An Introduction to Surface Analysis by XPS and AES (Chichester: John Wiley & Sons) Wegmann L 1970 Res. Dev. 21 20 Wells O C 1974 Scanning Electron Microscopy (New York: McGraw-Hill) Wild R K 1976 Vacuum 26 441
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Wild R K 1977 Corrosion Sci. 17 87 Wild R K 1981 Vacuum 31 183 Wild R K 1985 Spectrochimica Acta 40B 827 Wild R K 1997 Materials World May 389 Williams D B 1998 Microchimica Acta (suppl) 15 49 Williams D B, Carpenter D T and Keast V J 1999 Microscopy and Analysis Sept p 19 Williams D B 1988 Analytical Electron Microscopy ed G W Lorimer (London: Institute of Metals) p 1 Williams D B, Goldstein J I and Fiori C E 1986 Principles of Analytical Electron Microscopy (London: Plenum Press) Williams D and Edington J 1976 J. Microscopy 108 113 Wilshaw P R and Booker G R 1985 Microscopy of Semiconducting Materials Conference Series (Bristol: Institute of Physics) p 329 Wittman C L, Mayers M A and Pate H 1990 Met. Trans. 21 707 Woldseth P 1973 X-ray Energy Spectrometry (California: Kevex Corporation) Wong J 1986 Mater. Sci. Eng. 80 107 Wood J E, Williams D B and Goldstein J I 1981 Quantitative Microanalyser with High Spatial Resolution (London: Metals Society) Book 277 Wood J E, Williams D B and Goldstein J I 1984 J. Microsc. 133 255 Worthington C R and Tomlin S G 1956 Proc. Phys. Soc. A69 401 Yagi K 1987 J. Appl. Cryst. 20 147 Yamada T Tichmash, J M Dunin-Borkowski R E and Lozano-Perez S 2001 Electron Microscopy and Analysis (Bristol: IOP Publishing) 168 179 Yoshimura N, Hirano H and Etoh T 1983 Vacuum 33 391 Zaluzec N J 1979 Quantitative X-ray microanalysis: instrumental considerations and applications to materials science in Introduction to Analytical Electron Microscopy ed J J Hren, J I Goldstein and D C Joy (New York: Plenum Press) Ziebold T O and Ogilvie R E 1964 Anal. Chem. 36 322
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Chapter 7 Atom/ion sources 7.1
Introduction
In this chapter we describe the analytical information that can be obtained by using ions to probe the material surface. Since ions have a mass which is several orders of magnitude greater than either electrons or photons, the potential for damage using even the lightest ion, the hydrogen ion or proton, is considerable. However, ions with very low kinetic energy can be reflected from a surface without displacing any of the surface atoms from their lattice positions so that it is possible to probe a surface with ions while causing little or no surface damage. This method of probing a surface is known as ion scattering spectroscopy (ISS). In addition, because an ion cannot penetrate into a surface without causing damage, this technique detects only the outermost atoms in the material and is the most surface-sensitive of those currently available. In general, though, ions are used to dislodge surface atoms, which are ejected as neutral atoms and atom clusters, positive or negative ions and ion clusters together with electrons. These ejected ions are mass-analysed to identify the clusters using secondary ion mass spectroscopy (SIMS). The large number of neutral atoms ejected when the surface is bombarded can be ionised after ejection and detected by the technique of sputtered neutral mass spectroscopy (SNMS). Ions and electrons can be induced to leave a surface by applying a large electromagnetic field and this involves the use of methods to promote electron tunnelling. Here we will also address techniques which employ this method to desorb and analyse surface atoms such as the atom probe, field ion microscopy (FIM) and field emission microscopy (FEM). In the case of the first two of these techniques ions are not used as a probe but are ejected, albeit by very high potential fields, and the concept of using ions to study a surface is maintained. Electron tunnelling is also fundamental to the technique of scanning probe microscopy (SPM) and so this relatively new, but rapidly developing, technique has been included here. Finally the technique of proton-induced X-ray emission (PIXE) is described although it could equally have been described in previous chapters.
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7.2 7.2.1
Atom/ion sources
Ion scattering spectroscopy Theory
Ion scattering spectroscopy began to be developed in the 1950s when Brunee (1957) demonstrated that alkali ions incident on molybdenum surfaces showed maximum energies predicted for single, binary elastic collisions. Rubin (1959) studied MeV ion scattering and Panin (1962) the mid-energy range before Smith (1967, 1971) demonstrated that scattering of low-energy ions, below 1 keV, gave more detailed information. Since that time the theory has been developed fully by Heiland (1982) who showed that a low-energy noble gas ion beam of mass M1 and energy E0 incident on a surface consisting of atoms of mass M2 will be elastically reflected and following scattering will have an energy E1 (figure 7.1). If is the angle between the incident ion direction and the reflected direction, then if the incident ion mass is less than the mass of the surface atom (i.e. M2 =M1 > 1) the relationship between the energy of the incident ion, E0 , and reflected ion, E1 , is given by cos þ ððM1 =M2 Þ2 sin2 Þ1=2 2 E1 ¼ E0 : ð7:1Þ M1 =M2 þ 1 If the incident ion mass, M1 , exceeds the mass of the surface atom, M2 , then the relationship between incident and reflected energies becomes cos ððM1 =M2 Þ2 sin2 Þ1=2 2 E0 : ð7:2Þ E1 ¼ M1 =M2 þ 1
Figure 7.1. Impact of an incident ion of energy, E0 , with a material surface.
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Figure 7.2. The relationship between E0 and E1 for low-energy ions of He, Ne and Ar incident on a surface (Baun (1982)) (reproduced with permission of North-Holland Publishing Company).
However, when equals /2 degrees this equation reduces to E1 ¼
M2 M1 E M2 þ M 1 0
ð7:3Þ
which may be rearranged to give the mass of the surface atom, M2 M2 ¼ M1
E1 þ E0 : E1 E0
ð7:4Þ
Thus by measuring E1 and knowing M1 and E0 , the mass of the target atom, M2 , can readily be determined. For a given scattering angle the energy relationship E1 =E0 can be calculated for various inert gas ions (Baun (1982)). Figure 7.2 shows this relationship for an angle ¼ 1388 for Ar, Ne, and two isotopes of helium. 7.2.2
Instrumentation
The instrumentation for studying elastically scattered ions is remarkable simple. The elastically scattered ions are detected using either a system that scatters ions through /2 or the commercially available hemispherical electrostatic energy analysers (HSAs) or cylindrical mirror analysers (CMAs) similar to those designed for Auger analysis. A typical arrangement is shown schematically in figure 7.3 where a collimated beam of ions from any one of the types of ion sources available (see SIMS section) produces a
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Figure 7.3. Instrumentation used for ion scattering spectroscopy (ISS).
parallel, monoenergetic well-defined beam of ions. The ion beam is then arranged to be incident on the specimen surface at any desired angle, L , by mounting it on a target that is capable of being rotated about an axis normal to the plane of the incident and scattered beams. The scattered beam enters an electrostatic analyser where potentials on the hemispheres allow detection using a channeltron electron multiplier. A spectrum is generated by sweeping the analyser voltage potential. A CMA may replace the HSA and this would operate as in Auger spectrometers (see chapter 6) with the exception that a positive potential is applied to the outer cylinder to deflect the positive ions. Occasionally a double pass CMA is used to give better energy resolution. Alternative approaches use either a magnetic sector or a time-of-flight analyser in place of the electrostatic hemispherical or cylindrical mirror analysers. A backscattered spectrum obtained by bombarding a surface of tantalum pentoxide with 1.5 keV 20 Neþ ions (Honig and Harrington (1973)) (figure 7.4) illustrates many of the features of ISS. A broad peak is observed at the lower energies which is the result of the incident ion beam sputtering surface atoms from the tantalum pentoxide. At higher energies a broad region, which results from inelastic collisions of the incident ion beam with the lattice, the intensity of this background increases with energy since inelastic collisions in which a small amount of energy is lost are more probable than those in which a large amount of energy is transferred. At higher energies the elastically scattered peak resulting from tantalum atoms scattering the neon ions can be seen at E2 =E1 ¼ 0.8. The neon source has 3 Heþ present as a contaminant and this produces a peak at E2 =E1 ¼ 0.7 as a result of collisions with oxygen. A second spectrum in which Neþ ions of only 300 eV are incident on a surface of nickel on to which chlorine, bromine and iodine have been adsorbed is reproduced in figure 7.5 (Brongersma and Mul (1973)). The scattering angle in this experiment was /2 so the simplified equation (7.3) may be used to
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Figure 7.4. The backscattered ion spectrum obtained by bombarding 1.5 keV neon ions on to tantalum pentoxide (Honig and Harrington (1973)) (reproduced with permission of Elsevier Sequoia).
predict E2 =E1 . In this spectrum the proportion of inelastic scattering is much less and as a consequence elastically scattered neon ions are present from 35 Cl, 37 Cl, Ni, Br and I at 83, 91, 146, 181 and 221eV respectively, which compares with values of 82, 90, 146, 179 and 219 eV predicted by equation (7.3). 7.2.3
Quantification
The quantitative aspects of ISS have been considered by Niehus and Bauer (1975) who show that a single-collision model describes the process reasonably well but that peak height is not a linear function of coverage because of inelastic scattering contributions. In addition, for helium ions the top two atom layers take part in the collision process whereas for oxygen ions, with energies less than 500 eV, only the top atom layer need be considered. Therefore it is difficult to obtain quantitative data from surfaces using this technique unless the specifically prepared standards are used. This view contrasts with the approach adopted by Smith (1971), who reports two experiments to accommodate these limitations. In the first, Heþ ions are used to probe an oxidised aluminium foil; spectra from the oxidised surface and the aluminium substrate are shown in figure 7.6. The Al peak height from the substrate was assumed to represent 100% and was compared with the peak height of Al in
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Figure 7.5. A backscattered energy spectrum of Neþ ions scattered over 908 by a halogenated nickel surface. The energy of the incident ions is 300 eV. The spectrum is essentially a mass spectrum having its best resolution for the light elements (after Brongersma and Mul (1973)) (reproduced with permission of North-Holland Publishing Company).
Figure 7.6. Heþ ion scattering spectra from a thin film of Al2 O3 compared with pure aluminium (Smith (1971)) (reproduced with permission of North-Holland Publishing Company).
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Figure 7.7. Energy spectrum of Heþ (1 keV) backscattered from ZnO annealed at 550 8C. The solid curve is the spectrum after sputtering and is mainly Zn while after annealing the specimen is covered with a monolayer of Na (Brongersma and Buck (1978)) (reproduced with permission of North-Holland Publishing Company).
the Al2 O3 of the oxidised surface: a correct ratio of 2.5 was obtained. In a second experiment the nickel and gold concentrations in binary alloys determined by ISS were compared with wavelength dispersive X-ray analysis (WDX) measurements (figure 7.7). Agreement is good, especially when recognising that the WDX analysis is a bulk measurement compared with the single-surface atom layer result from the ISS analysis.
7.3
Rutherford backscattering
Ion scattering spectroscopy, which has been reviewed by Mackintosh (1974), is concerned with the elastic scattering of ions from surface atoms. As the energy of the incident ion beam increases, the ions penetrate into the material and in doing so they will lose energy due to inelastic collisions. In this case some ions may be elastically scattered from the surface while the ions that have lost energy may be elastically scattered by atoms in the bulk or may lose energy during collisions. By measuring the energy and intensity of the backscattered ions it is possible to identify the position and concentration of the impurity atoms. In 1909 Rutherford established that alpha particles consisted of doubly-charged helium atoms. Rutherford backscattering experiments involve bombarding a surface with these alpha particles and determining the energy and number of particles scattered in the backward direction after colliding with atoms in the near surface of the material. The technique is known as Rutherford backscattering (RBS), and ion scattering spectroscopy (ISS) is really a special case of RBS although the term RBS is normally
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taken to include ion beam interactions in which the energy of the incident beam is greater than 10 keV. 7.3.1
Theory
The energy, E1 , of an ion of mass M1 scattered by a surface atom of mass M2 in a direction to the incident ion which has energy E0 is given by " # M1 sin 2 1=2 M1 cos 2 M1 1 1þ : ð7:5Þ E1 ¼ E 0 þ M2 M2 M2 The value of the ratio E1 =E0 becomes smaller for target materials of low atomic number elements composed of high atomic number elements. Indeed alpha particles will not be scattered in the back direction by either hydrogen or helium and so only atoms with atomic numbers from beryllium upwards can be detected. However, helium and hydrogen can be detected by placing a detector in the forward direction. The separation in the energy of the backscattered particles from adjacent elements in the Periodic Table is usually sufficient to allow low atomic number elements such as C, N, O etc. to be resolved but this is not possible for elements such as Fe and Ni when present at the same depth in a specimen. Figure 7.8 shows an RBS spectrum recorded from a Si3 N4:1 O1:4 H layer when bombarded with 2 MeV alpha particles. The backscatter yield increases with atomic number, approximately proportional to the square of the atomic number, as illustrated in figure 7.9, indicating that RBS is two orders of magnitude more sensitive to heavy elements than light.
Figure 7.8. Rutherford backscatter (RBS) spectrum recorded from a Si3 N4:1 O1:4 H layer when bombarded with 2 MeV alpha particles (courtesy Dr T Schreiber).
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Figure 7.9. Relative backscattering yield of selected elements for 2 MeV He2þ ions.
When a particle travels through a material it loses energy as a result of glancing collisions with the target atoms. Thus backscattered ions from deep within the target emerge with less energy than ions backscattered from the surface. The ratio of energy loss to two-dimensional atom density for a given material is known as the stopping cross-section. Empirical values of stopping cross-sections are normally used and a polynomial equation, together with a table of coefficients, allows stopping power to be calculated for a wide range of elements and energies. Figure 7.10 illustrates how
Figure 7.10. Example illustrating how the backscattering and stopping power are used to identify element and position in TaSi layers of 230 mm and 590 mm (courtesy T Schrieber).
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ion backscattering and stopping power are used to identify an element and position (Schreiber (2001)). Here 2.2 MeV He2þ ions have been used to probe two silicon substrates with layers of TaSi, 230 and 590 nm thick respectively. The tantalum near the surface scatters at almost the incident energy of 2.2 MeV whereas the silicon at the surface scatters ions at 1.3 MeV. Scattered ions from deeper in the film lose energy and the deepest ions scattered from Ta in the 230 nm thick sample are scattered with an energy of 1.9 MeV, whereas those from the 590 nm thick sample have an energy of 1.7 MeV. The silicon spectrum exhibits a step which corresponds to the outer TaSi layer and the step is 0.2 MeV wide for the 230 nm thick sample and 0.5 MeV for the 590 nm thick sample. Ions which have penetrated below the surface will lose energy (E0 E0 ) and the elastically scattered ions will also lose energy (E1 E1 ) in reaching the surface. The rate of energy loss is given by the stopping power Sp and the energy E1 emerging from the surface following scattering at a depth x below the surface is given by ð r1 ¼ x sec 1 ð0 2 Sp ðEÞ dr C Sp ðEÞ dr ð7:6Þ E1 ¼ E 0 r2 ¼ x sec 2
0
where r1 and r2 are the distances of the incoming and outgoing particle trajectories and 1 and 2 are the angles between the surface normal and the ingoing and outgoing particle directions. C is given by M1 cos M1 cos 2 M2 M1 2 1=2 C¼ þ þ : ð7:7Þ M 2 þ M1 M 1 þ M2 M1 þ M 2 The number of particles scattered is directly related to the number of particles in the specimen material, thus by measuring the flux of backscattered ions the concentration of that element in the target can be determined. To a first approximation the ratio of the number of counts in an impurity peak, Ii , to the number in one channel of the substrate spectrum, Is , is given by Ii Zi2 Ni ¼ Is Zs2 Ns
E0
E02 ð r1 ¼ x sec 1 0
2
ð7:8Þ
Sp ðEÞ dr
where Zi and Zs are the atomic numbers of the incident and target atoms respectively, Ni is the number of impurity atoms and Ns is the number of substrate atoms contributing to the selected channel and the other terms are as defined above. The stopping power Sp contributes to equations (7.6) and (7.7) and must be determined from look-up tables which have been produced for most ions and energies (Williamson et al (1966) and Northcliffe and Schilling (1970)).
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461
Instrumentation
RBS instruments require a source of He2þ ions at an energy of 2 MeV and a detector to measure the energy of the backscattered ions. A schematic diagram of a typical RBS instrument is shown in figure 7.11. A source of Heþ ions is produced either in a duoplasmatron or by ionising He atoms in an electromagnetic field produced by a radio frequency source. Conversion of the Heþ to He is achieved by passing Heþ through a hot alkali metal vapour such as rubidium. The negatively charged helium ions are then inserted into a tandem accelerator which converts the He to He2þ with an energy 2 MeV. This source is then focused, deflected to remove unwanted neutrals and He2þ ions, and then focused on to the specimen. The energies of the particles that recoil into the detector are measured using surface barrier silicon detectors. Since these devices are essentially diodes, they are often called semiconductor diode detectors. The high energy charged particles produce electron–hole pairs in the semiconducting material. Backscattered ions are detected by either a fixed or mobile detector which is operated with an electrical potential, typically 4 keV, between the front and back surfaces. In the resulting electric field, the electron–hole pairs produce a current proportional to the energy of the charged particle.
Figure 7.11. A schematic of a typical RBS instrument showing production of Heþþ ions, focusing and detection.
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462 7.3.3
Atom/ion sources Applications
The technique although not widely used is simple to apply, non-destructive and rapid. It can be used to determine the amount and distribution of elements in thin layers on substrates. It is also possible to determine the amount and depth of a layer of foreign atoms if the identity of that layer is known, in which case the depth and concentration can be determined by applying equation (7.8). For example, measures of the amount of silver on glass (Anders (1966)), gold on silicon (Thompson et al (1969)) and lead/ mercury and silver/antimony mixtures on steel (Rubin et al (1957)) have been reported. Peisach and Poole (1966) and Brown and Mackintosh (1973) have shown that thicknesses ranging from 10 to 100 mg cm2 of alumina films on aluminium may be measured. An example of the use of Rutherford backscattering to determine the amount of an impurity in a bulk specimen is given in figure 7.12. This shows two RBS spectra recorded from a single crystal of silicon implanted with arsenic. One spectrum has been recorded with the beam in the direction of a major axis of silicon while in the other the beam is aligned randomly. The backscattered signal from the silicon is much reduced when in the direction of a major axis because the incident beam is steered down the axial channel, greatly reducing the probability of collisions with silicon atoms. By contrast the As signal is the same size in both spectra showing that this atom occupies interstitial rather than substitutional sites in the crystal. The silicon surface peak shows that in the near surface region the crystal is heavily damaged, as the height of the Si signal is close to that for random alignment.
Figure 7.12. RBS spectra from a silicon single crystal implanted with As recorded with the beam aligned as in channelled and a random direction (courtesy AEA Technology).
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Secondary ion mass spectroscopy
7.4
463
Proton backscattering
Ion scattering spectroscopy relies on incident ions being reflected by the surface atom layers while Rutherford backscattering detects both the intensity and energy of ions scattered from the surface and from within the bulk. Ions that have penetrated into the bulk and are scattered in the backward direction emerge from the surface with an intensity that varies with angle as a result of channelling within the bulk. Single crystals can be studied with low-mass ions such as protons; in proton scattering a beam of protons with an energy range from 20 to 100 keV is fired at a single-crystal specimen. The protons penetrate some hundred atom layers into the material and a fraction are scattered in the back direction, and it is these that are detected to give information concerning the crystallographic structure of the material. Unfortunately this particular form of ion scattering spectroscopy is highly damaging to the specimen. 7.4.1
Instrumentation
A schematic diagram of a proton scattering microscope is shown in figure 4.52 where a beam of high-energy protons is fired into the single crystal to be studied. As the protons penetrate the crystal those scattered in the direction of close packed planes tend to be blocked, while those scattered in directions where there are relatively few atoms escape from the crystal. The protons can be detected by either a fluorescent screen or a photographic emulsion. The image will have the symmetry determined by the crystal structure so that information on the crystallographic nature of the thin surface layers of materials is obtained. In practice the beam of protons is produced in an ion gun into which hydrogen is bled. The protons are produced by a cold cathode discharge and represent approximately a third of the ions produced with the other two þ thirds being Hþ 2 and H3 ions. The total ion beam is accelerated and focused before passing through a deflection system to remove the neutrals and unwanted ions. The focused beam of protons, approximately 0.5 mm wide and of 20 keV energy, is then incident on the specimen which is capable of being rotated about two mutually orthogonal axes. The specimen is maintained under vacuum, but because the technique samples approximately the top one hundred atom planes an ultra-high vacuum is not needed. The backscattered ions can be recorded on a photographic plate giving what is known as a blocking pattern or the intensity can be quantitatively measured as for the Rutherford backscattering example shown in figure 7.12.
7.5
Secondary ion mass spectroscopy
Ion scattering spectroscopy is a technique where a specimen surface is bombarded with ions of a particular species and as the energy and momentum
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Figure 7.13. The basic ion impact and ejection processes that occur when a primary beam of ions interacts with a surface.
of these ions increases there is a likelihood that they will penetrate further into the surface, knocking atoms from their normal lattice positions that are then ejected from the material. At all energies there will be a proportion of incident ions scattered from the surface but the fraction decreases with increasing energy, and it is these ions scattered from the matrix that form the basis of secondary ion mass spectroscopy (SIMS) (Benninghoven et al (1987)). The technique has gained widespread acceptance as a tool for studying surfaces because it has high sensitivity, can give chemical state information, and in recent years has been used to produce ion images with high spatial resolution. When a beam of ions is incident on the surface of a material the considerable momentum is sufficient to break the atom bonds and translate surface atoms a considerable distance into the bulk. The various processes are summarized in figure 7.13. Here the displaced atoms may cause other atoms and atom clusters to be dislodged from their normal positions and a fraction of these will be ejected from the surface and into the containing vacuum. The bulk of the atoms and atom clusters are ejected in the neutral state, but some will be ionised while others will have a negative charge. At the same time electrons are emitted from the surface. The ionised atoms and particles are detected in SIMS while the neutral atoms are collected in the technique of sputtered neutral mass spectroscopy (SNMS) to be described in the next section. Both the electrons and the ions emitted from the surface can be used to obtain images. A schematic of the basic equipment required to obtain SIMS
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Figure 7.14. A schematic diagram showing the SIMS system with computer control.
information is shown in figure 7.14 where ions from a suitable source are arranged to be incident on the surface being studied. The ejected ions and ion clusters are first separated using a filter, usually an electrostatic deflection system to remove unwanted neutrals, electrons and ions of the opposite polarity to that being detected. They are then detected using either magnetic sector analysers, quadrupole mass spectrometers or time-of-flight mass spectrometers. Since most of the ion guns can be used with any combination of analyser and detector, ion guns and analysers will be discussed separately. 7.5.1
Ion guns
The production of a good ion source is essential if an acceptable SIMS spectrum is to be obtained and here we consider the more commonly encountered types of ion sources. Some of these are not used in SIMS but are used elsewhere, for example in the production of clean surfaces or sputter depth profiles in AES and XPS (see chapter 6). There are four basic methods used to produce a beam of ions. Electron The simplest and most basic (Von Ardenne (1962)) ion source is where a beam of electrons from a hot filament is allowed to collide with a gas, causing a fraction of the gas atoms to be ionised, and these are extracted using a high potential field. A typical source of this type was developed by Nielsen (1957) and gas enters the chamber through the axis of the hot
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Figure 7.15. A schematic diagram of an electron bombardment ion gun (Nielsen (1957)) (reproduced with permission of Deutscher Verlag).
filament with the chamber negatively charged to draw electrons from the filament sides and so ionise the maximum fraction of gas atoms. This type of source produces a beam that is very diffuse and has a maximum intensity of about 100 mA at 1 keV (figure 7.15). Plasma A frequently used source in SIMS instruments is where gas atoms are ionised by the formation of a plasma in the ionisation chamber (Ball et al (1972) and Nier (1947)); one such source is the Penning ion gun (figure 7.16 (a)). Here an inert gas enters a chamber where a combination of high electrostatic and
Figure 7.16. A schematic diagram of (a) Penning ion gun.
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Figure 7.16. (b) Duoplasmatron ion gun; A, anode; C, magnet coil; E, extraction electrode; F, filament cathode; G, gas feed; IE, intermediate electrode; M, magnetic yoke (Septier (1967)) (reproduced with permission of Academic Press). (c) Saddle field ion gun.
magnetic fields produce a plasma. The ions are extracted from the plasma by applying a high potential between the plasma source and the exit slit. The gun may contain some focusing electrodes to confine the emerging beam. Probably the most widely used plasma source in SIMS is known as the Duoplasmatron (Von Ardenne (1962)) (figure 7.16(b)), where a gas enters between the filament electrodes. A low voltage arc created between the cathode and the anode is confined to the axis by an opening in the intermediate electrode and the magnetic field. This creates a plasma from the filament to the
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Figure 7.17. A schematic diagram of a radio frequency ion gun: 1, anode; 2, extraction electrode; 3, final acceleration electrode; 4, divergence diaphragm; 5, insulating tube; 6, deflection plates; E1 , E2 , electrodes of immersion lens; G, einzel lens (Slodzian (1964)) (reproduced with permission of The Commission des Publications Franc¸aise de Physique).
anode along the axis of the gun and the ions are extracted from the plasma by applying a potential to the electrode E. This type of ion source can produce a focused ion beam of diameter ranging from 1 to 100 mm. A third type of ion gun, more commonly used to produce ion beams for cleaning, thinning or depth profiling, is known as the saddle field source. This gun (figure 7.17(c)), allows the inert gas to enter through a port at the back and a high potential is applied to two tungsten electrodes to create the plasma. The electron paths follow a figure-of-eight pattern and ionised atoms are accelerated towards the cathode, which is the body of the gun containing an exit on one side through which the ions emerge. Ions impinge on the internal surface and sputter away the wall of the gun during operation so the choice of construction material is important. Radio-frequency Radio-frequency (RF) ion sources have been reviewed by Blanc and Degeilh (1961) and this type is often used to produce a beam of positive ions for SIMS instruments. Figure 7.17 shows schematically the RF ion source used in the CAMECA IMS 300 microscope. A radio-frequency source operates in the region of 100 MHz with about 50 W power which capacitatively induces an
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electric field in the chamber. Electrons in the gas are accelerated by the field and result in the gas being ionised. The experimental arrangement is for a copper ring to surround a glass or other non-conducting vessel into which the inert gas is leaked to a pressure in the region of 104 Pa. The ions are extracted, collimated and accelerated in the normal manner. A drawback to this type of ion gun is that the energy spread of the emitted ions is very large, extending over several hundred eV. Liquid metal ion Liquid metal ion guns are highly specialised but capable of producing a very narrow defined ion beam (Prewett and Jeffries (1980) and Waugh et al (1984a,b)). Beam diameters of a few hundred nm have been routinely achieved so that it is used extensively in scanning SIMS (SSIMS) instruments. In operation liquid metal is allowed to flow, from a reservoir, over the surface of a needle with a fine tip (figure 7.18). Metals with a melting point close to room temperature, such as gallium, are normally used to provide the source. A high negative voltage, frequently 10 keV but in some
Figure 7.18. A schematic diagram of a liquid metal ion gun. Liquid metal flows from the reservoir to the tip.
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cases as high as 50 keV, is applied to the extractor electrode to produce a high field around the tip which causes the liquid metal to be drawn into a cusp, and the ions are extracted by field emission. This produces a source with a very high brightness that can be focused to very small diameters while retaining a significant beam current. 7.5.2
Filters and detectors
The performance and operation of filters and detectors used in secondary ion mass spectrometry has been reviewed by Benninghoven et al (1987) and only a very brief description of the various methods of ion detection will be given here. The Wien filter Most high quality SIMS instruments incorporate a filter between the ion gun and the specimen to remove unwanted ions and neutrals. The most frequently used filter, the Wien filter (Wein (1902)), combines an electrostatic and a magnetic field as shown schematically in figure 7.19. Here the forces along the axis balance for particles of velocity v when 1=2 eVi E ¼ ð7:9Þ v¼ M B where V is the particle potential, M the mass number, e the electron charge, E the electrostatic field and B the magnetic field. In practice E and B are chosen such that the desired ions follow a trajectory that is slightly different from the axis of the filter and the direction of the ions from the ion gun. This, as well as removing unwanted ions, allows the neutral species to be removed since they will continue in the direction that they entered the filter.
Figure 7.19. The principles of the Wein filter (Wein (1902)).
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Magnetic and electrostatic sector The magnetic sector analyser was one of the first types to be used to massanalyse particles, particularly in mass spectrometers, where the objective was to identify gas atoms. Here ions of mass M, charge e and velocity v enter the entrance slit of the analyser (figure 7.20), and are deflected by a magnetic field B. The radius, R, followed by the ion is then given by R¼
Mv2 : eVi B
ð7:10Þ
Only ions with a specific velocity and charge emerge through the exit slit for any given magnetic field; a spectrum could be generated by varying either B or more practically v. In some instruments the ion velocities are retarded prior to reaching the analyser so that all ions entering the analyser have the same charge-to-mass ratio and the magnetic field may be kept constant. Ions may also be analysed by using an electrostatic field in a manner exactly analogous to the magnetic sector analysers. A specific mass and charge will be deflected by an electrostatic field to pass through the exit slit of the analysers provided the outer hemisphere is negatively charged relative to the inner. In this case the relationship between the kinetic energy E, the deflecting potential Vi and the mean radius R is given by E¼
Mv2 2eVi ¼ : R R
ð7:11Þ
A spectrum can once again be generated by varying either E or Vi and with these analysers both methods are frequently used.
Figure 7.20. The magnetic sector analyser.
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Figure 7.21. The double focusing analyser which combines a magnetic sector analyser shown in figure 7.20 with an electrostatic analyser.
The mass resolution in both the magnetic sector and electrostatic mass spectrometers is degraded by chromatic aberration terms. However, the aberration is such that by combining a magnetic sector analyser with an electrostatic analyser these aberrations can be cancelled out at least to a first approximation. Figure 7.21 shows a double focusing ion analyser of this type. Quadrupole The quadrupole mass analyser is probably the most popular detector used in SIMS instruments (Dayton et al (1954) and Paul and Steinwedel (1953)) because it has a reasonable mass range, can handle large ion currents, is simple to construct and can be relatively compact. The transmission of ions is comparable with a magnetic sector analyser but considerably less than a time-of-flight detector. It contains hyperbolic cylinders positioned along the axis of the ion trajectory (figure 7.22), and a combined DC, VDC , and AC, VAC with frequency, !, and time, , potential is applied to the cylinders in such a way that equal and opposite potentials of the form V ¼ ðVDC þ VAC cos !Þ are applied to adjacent cylinders. The motion of ions of mass M and charge e are described by d2 x 2ex þ ðVDC þ VAC cos !Þ ¼0 2 d Mr20
ð7:12Þ
d2 y 2ey ðVDC þ VAC cos !Þ ¼0 2 d Mr20
ð7:13Þ
where x, y and r0 are defined in figure 7.22. Thus ions with the correct mass and charge are accelerated in an oscillatory manner such that they emerge at
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Figure 7.22. Principles involved in the quadrupole mass analyser.
the exit where they can be detected; all other ions are accelerated into the walls and lost. In practice the field produced by these hyperbolic cylinders can be approximated by circular rods where rrod ¼ 1:16r0 and r0: As a consequence quadrupole analysers are more usually constructed by using four rods positioned as shown in figure 7.23. Time-of-flight The time-of-flight (TOF) mass spectrometer distinguishes between ions of different mass by detecting the time an ion takes to travel a fixed distance when accelerated by a given field (Chait and Standing (1981) and Harrington (1960)). A pulsed beam of ions is incident on the surface being analysed, the ions ejected from a pulse are then accelerated, allowed to travel down a drift
Figure 7.23. Schematic diagram of the quadrupole mass detector.
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Figure 7.24. Schematic diagram of the time-of-flight SIMS instrument showing: primary ion source, pulsed 908 deflector, bunching system, alignment and raster plates, einzel lens, specimen, secondary ion lens, alignment plates, single stage reflector, post-acceleration optics, channel plate and scintillator, photomultiplier.
tube, and the different times taken for them to reach the detector produces a spectrum. The ions will have different velocities because they have the same kinetic energy after the acceleration phase but different masses. Hence they separate as they drift along the tube with the ions of lowest mass arriving first at the detector and those of highest mass arriving last. The time, , taken to reach the detector is given by M 1=2 L ð7:14Þ ¼ 2NeVi where L is the length of the flight tube, M is the mass, e the electronic charge, Vi the accelerating voltage and N the number of charges on the ion. In many modern instruments (figure 7.24), the ions travel down a drift tube and are then reflected back and detected after passing down the tube twice. This has advantages in that ions with the same mass, but different velocities prior to the acceleration phase, arrive at the detector at the same time thereby increasing the mass resolution of the analyser. Similar systems in which an electrostatic mass analyser has been combined with two drift tubes are also used (Poschenrieder (1972)). The incident ion beam is first passed through a mass separator such as a Wien filter or electrostatic sector to improve the quality of the incident beam, define the energy spread more accurately, and remove neutrals and impurities. The transmission of ions using a TOF detector can be as high as 10% and when this is combined with the fact that all the secondary ions from one pulse are simultaneously detected these detectors have a practical sensitivity that is 105 times that of
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a quadrupole mass analyser. The mass range is simply determined by the TOF of the species, and in principle can be as large as desired with masses up to 10 000 amu having been detected. It is ideally suited to SIMS studies in the static mode where it is necessary to determine the surface composition with minimum surface damage and only small quantities of secondary ions are available for detection. Compared with the magnetic sector and quadrupole analysers is its ability to detect ions of very high mass number. In principle an ion of any mass can be detected if the time between initial ion pulses is made sufficiently long. However, it is not suited to the dynamic SIMS measurements used to obtain a depth profile because the number of ions arriving at the detector is too great. 7.5.3
Static and dynamic SIMS
Mention has been made of static and dynamic SIMS and some explanation is required. SIMS is a destructive analytical technique with high sensitivity which can be used to determine the composition and chemical state of the atoms at a surface with little surface modification. This is possible because in practice such a small fraction of surface atoms can be removed that the surface remains essentially undisturbed and the probability that an incoming ion will encounter a region already disturbed by an ion impact is low. When SIMS is used in this way it is known as static SIMS. The criterion for SIMS to be regarded as static or dynamic was originally defined by Benninghoven (1970) who stated that if a surface of area A is covered by a number of ion impacts, each disturbing an area a, then static SIMS can be applied if P ðaÞ=A 1. In practice this can be referred to the fraction of the surface layer that is removed during an experiment. If <0.01 of a monolayer is removed then the static regime is said to be operating, but if more is removed it is said to be dynamic. It should be stressed that the same type of surface damage occurs in both regimes, and only the degree of total damage is different. Static SIMS is used to identify atoms situated in the top surface layers, whereas dynamic SIMS is used to obtain depth distributions of specific atoms. Static SIMS Although this technique is essentially non-damaging in that only a few percent of the surface atoms are disturbed, the individual events cause much disruption. An energetic ion incident on the surface will collide with surface atoms causing them to impinge on other atoms, resulting in a cascade of atoms, ions and electrons. Some of these will be scattered in the backward direction towards the surface and may escape forming a plasma of atoms, ions and electrons. The ions can then be mass-analysed to produce a SIMS spectrum. The spectrum will contain mass fragments
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from the surface molecules, but in many cases these fragments will have been broken down to such an extent that it is often difficult to identify the original molecule. G-SIMS Gilmore and Seah (2000, 2003) have developed a gentle SIMS method, described by the acronym G-SIMS. This is used to identify the original molecules and ion fragments from the static SIMS spectrum which contains a number of low mass fragments. It works on the principle that the cascade produced by high-energy low-mass ions is characterised by a higher surface plasma temperature, whereas low-energy high-mass ions produce a lower surface plasma temperature. Experimentally two spectra are obtained from the same surface using two different ion sources, for example caesium and argon. These could be chosen because in the unified cascade gradient plot (Gilmore and Seah (2000)) these ions generate spectra that are well separated in terms of the extent of fragmentation that they cause. The G-SIMS spectrum is calculated by multiplying an existing spectrum Nx , by the factor Fx13 . This forms a G-SIMS spectrum with intensities Ix given by Ix ¼ Mx Nx Fx13
ð7:15Þ
where Mx is the linear mass which is included as a first-order term to correct for the discrimination of intensities of the peaks at high mass. The term Fx is obtained by recording spectra from the same ion at different energies, say argon at 4 and 10 keV. The technique has been successfully applied to a range of polymers and more recently to biological materials. Figure 7.25 shows the static SIMS spectrum, obtained using 10 keV caesium, of the polyamino acid, poly-L-lysine. This contains many low-mass fragments and very few high-mass fragments that make identification of the original material very difficult. In contrast the G-SIMS spectrum, obtained using 10 keV caesium and argon ions, shows the poly-L-lysine clusters at 84.1 and 271.2 amu. There is also an intense bromide double peak which is present because the polyamino acid was supplied as a salt. 7.5.4
Detection limits
A major advantage that SIMS has over most other techniques is a high level of sensitivity whereby parts per million are detected routinely with a part per billion capability for many elements. Unfortunately, the sensitivity for detection varies with atomic number and the sign of the charge on the ion. Figure 7.26 shows the relative ion yield for most elements in the Periodic Table for both the positive and negative ions. The yields vary over five orders of magnitude and differences of several orders of magnitude occur between elements adjacent to one another in the Periodic Table. In the
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Figure 7.25. The spectra from poly-L-lysine: (a) 10 keV caesium static SIMS (poly-L-lysine has a repeat unit of mass 128 amu where there is no peak), (b) G-SIMS spectrum using 10 keV caesium and argon (structures of poly-L-lysine occur at 84.1 and 271.2 amu) (Gilmore and Seah (2003)).
positive SIMS mode the best sensitivity is obtained for elements with the highest yields such as Be, B, Mg, Al, Si, Na, Ca while relatively poor yields are obtained for C, S, As etc. In the case of negative SIMS the situation is reversed for many elements; in particular C, S and As have fairly high yields whereas Be and Ca have low yields. It is therefore important, when identifying a surface species, to know the specific elements to be detected and record the correct ion species or alternatively to always record both positive and negative spectra. The typical spectrum reproduced in figure 7.27, which is a spectrum recorded from the surface of a chromium nickel superalloy, illustrates many of the pitfalls and advantages of SIMS. In addition to the peaks from iron, chromium and nickel a large peak is observed from aluminium at 23 atomic mass units (amu) but this element
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Figure 7.26. Relative ion yields as a function of atomic number.
is present in relatively small quantities on the surface; the high yield of this element is responsible for this height. Although figure 7.26 gives the relative secondary ion yields for pure elements, the yield will be different if the element is combined with one or more elements in a compound. For example, combination with oxygen will generally enhance the positive yield of an element and it is often common practice to bleed a small amount of oxygen on to the surface being analysed to enhance the spectrum. This is an acceptable procedure if the intention is simply to detect the presence of
Figure 7.27. A typical SIMS spectrum displayed as counts per second in a linear manner as a function of atomic mass units.
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Figure 7.28. Comparison of SIMS and EPMA composition determinations for a series of steel standards showing the direct correlation (Allen et al (1989)) (reproduced with permission of The Institute of Materials).
trace contaminants, but extreme care should be exercised if the intention is to obtain either chemical state or a quantitative analysis. 7.5.5
Quantification
Quantification of SIMS spectra is not straightforward due to the very large variations in ion yield (see figure 7.26) and the change in yield of elements when they form compounds. Therefore it is necessary to use well characterised standards that closely mirror both the composition and chemical state of the specimen. For example, if a series of stainless steels is to be studied then it is reasonable to use a few alloys with differing iron, chromium and nickel ratios to determine sensitivity factors for these elements and thereby determine the composition of other similar alloys (Allen et al (1989)). In such a study the weight percent determined using SIMS was compared with the weight percent determined using EPMA (figure 7.28), where a straight line with a slope of 1.045 and an intercept of 0.005 indicates good agreement between the two methods. However, the sensitivity values determined from this system cannot necessarily be used to quantify SIMS spectra obtained from another alloy system containing these elements: for example, the composition of the oxide formed on these steels could not be determined. 7.5.6
Imaging
Images can be obtained within a secondary ion microprobe in one of a number of ways, because as the ion beam bombards the specimen surface
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Figure 7.29. Schematic diagrams illustrating the methods used to produce a SIMS image: (a) the ion-optical method used in the CAMECA IMS-3f (reproduced by permission of CAMECA), (b) the scanning ion system.
it ejects electrons, and positive and negative ions may all be utilised to produce images containing different information. The incident ion beam can be focused to a small spot and rastered over the surface while either the electrons, the total ion current or individual ion species are detected. Alternatively the surface can be flooded with ions and then the optics used to obtain an image in real time. Both methods, shown schematically in figure 7.29, are capable of producing images with spatial resolution less than 20 nm. Figure 7.29(a) is for the CAMECA IMS-3f ion microscope (Bernius et al (1986)) which operates in a manner analogous to the optical microscope. The specimen is flooded with an argon ion beam which can be a wide beam from a Duoplasmatron source. The ions are focused on to a contrast aperture and form a real image at the entrance to a double focusing electrostatic and magnetic analyser before the energy and mass-selected ions reach the fluorescent screen. This instrument produces images with a resolution of the order of 0.5 mm (figure 7.30). This example shows two secondary ion images from a steel specimen doped with C and N and recorded using a CAMECA IMS-3f microscope. Image (a) is the 56 Feþ 2 image while image (b) is the negative 26 CN image. Figure 7.29(b) is a schematic diagram of a scanning ion microscope in which a fine-focused beam of ions is rastered over the surface and the ejected electrons and ions are detected.
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Figure 7.30. Secondary ion images from a steel specimen doped with C and N recorded using 26 a CAMECA IMS-3f ion microscope (a) 56 Feþ 2 image and (b) CN image (reproduced by permission of CAMECA).
Early instruments used inert gas ions from a duoplasmatron source (Drummond and Long (1967)) which are capable of producing ion beams with spot sizes down to 2 mm. In 1980 the first liquid metal sources were developed (Prewett and Jefferies (1980)) and these have been improved to give spot sizes of less than 100 nm. The field emission liquid metal ion source produces a beam of ions from the tip, which are focused and deflected to remove unwanted neutrals and ions and impinged on the surface. The beam is rastered using X and Y deflection plates. Channeltrons are placed close to the specimen and by suitable biasing these can be used to detect the total ejected electron or ion current. To detect and obtain images from specific ions the ions are first deflected through 908 to remove unwanted atom and ion species before entering a quadrupole mass spectrometer. A conventional SIMS spectrum of the surface can be obtained or the spectrometer can detect selected ion peaks while the ion gun is rastered to give a spatial distribution of the ions over the surface. Images obtained by using the incident ion beam to eject secondary electrons show variations in contrast compared with those excited using an incident electron beam. Figure 7.31 shows two images of the cross-section of a semiconductor device containing copper. The top image (a) is an ion-induced secondary electron image while the lower image (b) is an electron-induced secondary electron image of the type produced in a SEM instrument (Young and Moore (2002)). The ioninduced image provides additional information as a result of channelling of the incident ions producing secondary electrons that then form an image in which the grain structure in the copper is clearly visible. Figure 7.32 shows an example from the study of the cross-section of a printed paper specimen. Here an ion-induced secondary electron image (a) shows the topographic features across the paper while ion maps from aluminium
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Figure 7.31. Two images of the cross-section of a semiconductor device containing copper. The top image (a) is an ion-induced secondary electron image while the lower image (b) is an electron-induced secondary electron image of the type produced in a SEM instrument (Young and Moore (2002)).
(b), calcium (c), potassium (d) and sodium (e) show the distribution of these elements throughout the sample. SIMS detects ionised mass clusters and it is common for such clusters from fragments with different elemental composition to have the same mass, making positive identification of the cluster difficult. This is particularly so for low-mass ions and fragments where carbon–hydrogen combinations are common. In such cases it is often possible to use different isotopes of the element to arrive at a positive identification. This method has been used to identify the presence of boron in a C–Mn steel where the boron is present in the bulk to less than 5 ppm (Jones et al (2002)). Boron has two isotopes with masses at 10 and 11 daltons with a ratio of approximately 1 : 4
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Figure 7.32. The cross-section from a printed paper sample. Here an ion induced secondary electron image (a) shows the topographic features across the paper while ion maps from aluminium (b), calcium (c), potassium (d) and sodium (e) show the distribution of these elements throughout the sample.
respectively. By recording a SIMS spectrum in the low-mass region the presence of boron can be inferred both from the position and ratio of the peaks, which can then be used to map the location of the boron. Figure 7.33(a) shows the ion-induced secondary electron image for a Si-killed C– Mn steel plate containing 4 ppm of boron. Figure 7.33(b) shows the spectrum recorded in the boron region with the two peaks at the expected positions and intensity. The peaks at 10 and 11 daltons were then used to map the surface
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Figure 7.33. Ion-induced secondary electron image of a steel plate containing 4 ppm boron together with SIMS spectrum (b) and elemental distribution maps obtained at the same magnification (c)–(f ). Maps (c) and (d) are for 10 B and 11 B, respectively (Jones et al (2002)).
and an exact match is observed between the images in (c) for 10 amu and in (d) for 11 amu, in contrast to a map for silicon shown in (e). 7.5.7
Depth profiling
Ion bombardment removes material from a specimen surface and thereby provides a method for producing depth profiles through that surface. A typical
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Figure 7.34. A SIMS composition depth profile through layers of SiO2 , Si and SiNx deposited on a glass substrate (reproduced by permission of CAMECA).
SIMS depth profile from a SiO2 , Si and SiNx layered deposit on a glass substrate is reproduced in figure 7.34. The standard procedure is to collect the ions from predetermined elements while the surface is being bombarded with ions. The total etch rate from the surface is established from previous calibrations using standards with known thicknesses of surface layers, such as Ta2 O5 on tantalum. However, care has to be exercised when using calibrated etch rates from one system to determine layer thicknesses on another, simply because etch rates can vary by up to an order of magnitude. The peak intensity is then plotted as a function of time or depth. No attempt is normally made to quantify SIMS depth profiles because the range of sensitivities between elements is so great when crossing interfaces. The potential for depth profiling is greater if a small spot ion source can be used. Thus the liquid metal ion guns can produce depth profiles from small areas while profiling at a very fast rate. An additional practical advantage is that the small well-defined crater produced readily identifies the location of the depth profile so that, if required, the profile can be measured in adjacent regions with little risk of
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overlap. When obtaining a depth profile care must be exercised to ensure that the detected signal emanates from the centre of the crater and does not include any signal from the crater sides. The high sensitivity of certain elements can cause effects to be masked if a signal is detected from the edges. A procedure known as gating is used to ensure that only ions from the centre of the profiled area enter the spectrometer. Ions from the crater edges would have to enter the input aperture of the spectrometer at a different angle from those at the centre. By choosing the focusing conditions it is possible to ensure that only those ions within a specific range enter the spectrometer. The degree of gating can usually be chosen and a compromise is generally adopted between signal strength and edge effects. 7.5.8
Applications
A major use for SIMS is the detection of low levels of impurities on the surface of a sample. Both time-of-flight SIMS systems and dynamic SIMS systems, which can detect part per billion quantities of certain elements, can be utilised and combined with the depth profiling capability of the ion gun to give a profile through layers where the variation in composition through the layer may change by several orders of magnitude. An example of the application of this technique to detect both bulk elements and low concentrations of elements with good spatial resolution (200 nm) is a study of a chromium–titanium–aluminium superalloy that contains several phases and an outer coating (Heard et al (2000)) (figure 7.35). In this example the area was selected and the incident ion beam rastered while the detector was fixed on specific peaks to determine the spatial distribution of the elements. Figure 7.35(a) shows the ion-induced secondary electron image while element maps are shown in figure 7.35(b) for Al, (c) for Cr, (d) for Ti, (e) for Co, (f ) for Ni, (g) for Nb and (h) for Y. This shows the good spatial resolution since the total image is only 200 mm square and areas with a size of 1 mm are clearly resolved. The SIMS maps indicate the different phases that are present in the bulk and the outer layer. The coating contains aluminium-rich particles while the bulk has some titanium-rich particles. The trace element yttrium is concentrated in thin layers of the outer surface. 7.5.9
Focused ion bombardment
Ion beam instruments have been developed to the state where high-intensity well-focused beams can be used to machine cross-sections through materials and subsequently chemically analyse their microstructure. Major applications are in the semiconductor industry where the procedure is used to study problems with devices, and the ion beam can be accurately located on the region of interest such as a device failure (Abramo and Wasielewski (1997) and Verkleij (1998)). Figure 7.36 shows a cross-section though a
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Figure 7.35. SIMS element maps recorded from a chromium–titanium–aluminium superalloy containing small concentrations of impurity elements: (a) ion-induced secondary electron image and ion maps of (b) Al, (c) Cr, (d) Ti, (e) Co, (f ) Ni, (g) Nb and (h) Y (Heard et al (2000)).
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Figure 7.36. A cross-section though a pair of transistors imaged at high magnification using a transmission electron microscope (courtesy of FEI Ltd).
pair of transistors imaged at high magnification in a transimisson electron microscope. The ion beams are used, together with electron beams and gas inputs, to lay down a metallic layer on top of surfaces that need to be accurately preserved or to repair a semiconductor device where there may have been a conductivity failure (Young et al (1990), Lipp et al (1996) and Hooghan et al (1999)). Another application of fast ion beams which is becoming increasingly popular is the production of transmission electron microscope specimens (Sheng et al (1997) and Pantel et al (1997)). Advantages of this procedure are that the TEM specimen is obtained from exactly the desired location, many specimens can be produced from a single sample and from a small volume, and the specimen may cross oxides, metals, glasses and ceramics with little or no variation in specimen thickness. Figure 7.37 shows a TEM specimen cut from a semiconductor device and ready to be transferred to the electron microscope grid. This has been prepared by making two parallel cuts closely spaced, usually 100 nm apart, to define the sample. This is then released by making further cuts along the base and the two side to produce a TEM specimen with approximate dimensions 10 mm 10 mm 0.1 mm. Figure 7.38 shows a TEM specimen cut from a Ti/TiO2 sample. Figure 7.38(a) is a low-magnification image showing the protective metal laid down before the specimen was cut, the thin 1 mm layer of TiO2 and the metal substrate. The high-resolution image (b) and the selected area diffraction patterns (c)–(f ) correspond to zones (1)–(4) respectively (Gueneau et al (2003)).
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Figure 7.37. A transmission electron microscope specimen cut from a semiconductor device and ready to be transferred to the electron microscope grid (courtesy of FEI Ltd).
7.6
Sputtered neutral mass spectroscopy
When a surface is bombarded by energetic ions the atom clusters that are ejected from the surface are in both the ionised and neutral states. Secondary ion mass spectroscopy (SIMS) is used to detect and analyse the ionised species. The technique of sputtered neutral mass spectroscopy (SNMS) (Mu¨ller et al (1985), Lipinski et al (1985), Wilson et al (1989) and Oechsner and Stumpe (1977)) has been developed to detect and analyse the neutral atoms and atom clusters that are rejected by SIMS. 7.6.1
Theory
When an ion, normally an inert gas ion such as argon, with energy in the range 1–10 keV strikes a material surface the majority of the particles ejected are in the neutral state but a few (<10%) are either negatively or positively ionised. Whereas the intensity of the ionised particles is strongly dependent on the atom species, the neutral atom concentrations are closely related to the surface composition so that if they can be ionised after sputtering and detected and mass-analysed in a similar manner to that used in SIMS a quantitative surface analysis can be obtained. The difficulty with the technique lies in ionising a sufficient fraction of the neutral particles so that an appropriate signal can be obtained. Several methods that have been used to effect ionisation, including electron bombardment, ion bombardment, plasma discharge and photon ionisation using lasers. 7.6.2
Instrumentation
Commercial instruments are now available which operate by using an ion gun to sputter particles from the surface and then post-ionise the neutral
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Figure 7.38. A TEM specimen cut from a Ti/TiO2 sample (a) is a low magnification image showing the protective metal laid down before the specimen was cut, the thin 1 mm layer of TiO2 and the metal substrate. The high-resolution image (b) and the selected area diffraction patterns (c)–(f ) correspond to regions (1)–(4) respectively in (b) (Gueneau et al (2003)).
particles using a plasma discharge (figure 7.39). The specimen is placed at the end of the probe where it is screened from the plasma by a metal grid. The specimen is bombarded by high-energy ions with energies up to 10 keV from a gun angled at 608 to the surface. Ejected neutral particles and ions enter the plasma which is produced by applying a radio frequency field to the chamber which contains argon gas at a pressure of 102 to 103 Pa. To increase the probability that the neutral particles will be ionised a magnetic field is applied to the chamber designed to cause the electrons generated in
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Figure 7.39. A schematic diagram of the experimental arrangement for sputter neutral mass spectrometry (SNMS) (Muller et al (1985)) (reproduced with permission of The American Vacuum Society).
the plasma to describe a circular path. Sputtering of the specimen by the plasma is prevented by applying a suitable electrical bias and the postionised neutral particles are extracted from the plasma using an electrostatic lens system positioned prior to the quadrupole mass spectrometer. The form of the SNMS spectrum shown in figure 7.40 recorded from the surface of stainless steel can be compared with the SIMS spectrum from the same material (figure 7.27). In particular, the SNMS spectrum contains peaks
Figure 7.40. A SNMS spectrum obtained from the surface of an austenitic stainless steel.
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with intensities that approximate to the concentration of the element in the matrix whereas the SIMS spectrum does not. For example, there is no significant peak at atomic mass unit 24 in figure 7.40, indicating that the concentration of sodium at the surface is very low. 7.6.3
Quantification
While the yield from SNMS is similar for all elements there are variations between atoms and it is necessary to use sensitivity factors in order to obtain good quantification. If the signal from a standard Y, which has a fractional concentration CðYÞ in the bulk, is compared with a specimen X with a fractional concentration CðXÞ and the intensity of the signals from X and Y are IðXÞ and IðYÞ respectively then CðXÞ=CðYÞ ¼ fIðXÞ=IðYÞgfSf ðYÞ=Sf ðXÞg
ð7:16Þ
where Sf ðYÞ and Sf ðXÞ are the sensitivity factors for Y and X respectively. Relative sensitivity factors in general differ by factors of 1 to 3 between
Figure 7.41. Sensitivity factors relative to iron DA;Fe in SNMS for some of the common elements (Lipinski et al (1985)) (reproduced with permission of The American Vacuum Society).
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Figure 7.42. A depth composition profile obtained using SNMS through two thin (5 nm) layers of aluminium and silver sandwiched between SnO2 (reproduced by permission of Leybold-Hereas).
elements, although in some cases it may be as high as 10. The sensitivity factors for the major elements in an austenitic stainless steel relative to iron are reproduced in figure 7.41. 7.6.4
Applications
A major use of SIMS is to obtain depth composition profiles through the surface of a material. SNMS is also ideally suited to this type of investigation but it has the additional advantage that quantitative composition with depth can be obtained. Figure 7.42 shows a depth profile through a specimen which consisted of two thin (5 nm thick) layers of aluminium and silver sandwiched between tin oxide. Here the quantification was achieved by applying sensitivity factors, obtained from standard specimens, to the raw data. No normalisation was applied and yet the tin and oxygen concentrations are in the correct proportion for SnO2 . The aluminium and silver layers are well resolved although the concentration is reduced to close to 70 at% due to atom mixing over the thin layers.
7.7
Field ion microscopy
This section headed field ion microscopy really encompasses two other techniques, field emission microscopy and the atom probe (Muller (1956,
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1960) and Gomer (1961)). Historically the subject developed from field emission microscopy where high potentials were used to exceed the work function and thereby effectively pull electrons from a sharp tip made from the material being studied (Muller (1936)). This was later developed to use gas ions to image the surface in the field ion microscope (Muller (1951)) and the individual atoms were analysed using a TOF mass spectrometer combined with an FIM (Muller et al (1968)). The reader is directed to a brief but instructive review by Kane (1974) and a book based on a short course on field ion microscopy by Hren and Ranganathan (1968). 7.7.1
Electron tunnelling and field emission
Electrons are normally only emitted from a metal surface if the material is heated to a sufficiently high temperature to allow the electrons to gain sufficient energy to overcome the work function barrier and escape. This involves the electrons acquiring a few electron volts. If an external field is applied, and the material from which the electrons are being emitted is made the cathode, the external barrier is effectively reduced and the electrons have to acquire less thermal energy to escape. This is the principle that is employed in all electron microscopes to produce a beam of electrons (see chapter 6, section 6.2). However, if the field is increased to a very high level, in the region of 10–50 MV cm1 , then the height and the width of the barrier reduces to be comparable with the wavelength of the electron (figure 7.43). In this situation there is a finite probability that an electron may cross the barrier although it may not have sufficient energy to climb the potential barrier. Thus electrons may be emitted without the need for heating, a phenomenon known as electron tunnelling. Once the other side of the barrier, the high potential field accelerates the electrons away. This effect is known as field emission and is the basic principle of field emission microscopy (FEM) and scanning tunnelling microscopy (STM) described in the next section.
Figure 7.43. The effect of an external field on the barrier to electron escape from an atom in a surface (a) without or (b) with an external field applied.
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Field emission microscope
The design of the field emission microscope is shown in figure 7.44 where the basic problem to be overcome is the production of the very high field necessary to cause field emission. It is solved by making use of the fact that there is an increase in surface fields in regions of high curvature. The electrostatic field, F, at a surface of a free sphere of radius r is given by F ¼ V=r
ð7:16Þ
where V is the applied potential. A field of the desired magnitude is obtained by using a tip with a radius that is approximately 100 nm and a potential of a few tens of keV. To produce tips with such diameters is not straightforward. However, these specimens are produced from the bulk material as very sharp needles using a combination of mechanical, chemical and/or electrochemical methods. Indeed these techniques have now been developed to the stage where these methods can be applied to irradiated materials in an active cell environment using remote handling techniques (Miller et al (1989)). Once the electrons have been emitted they are accelerated on to a fluorescent screen placed a few centimetres from the tip and which is the anode for the instrument. The electrons essentially travel in straight lines from the tip and so produce a magnified image of the work function distribution over the tip surface. The magnification obtained is approximately one million times. A work function distribution is obtained because as the work function changes so the width of the potential barrier varies and the probability of electron tunnelling alters. The work function changes with the crystallography of the material and thus a field emission pattern reveals crystallographic
Figure 7.44. Schematic diagram for the field emission microscope (FEM) showing details of the cathode tip that forms the specimen.
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Figure 7.45. A field emission pattern obtained from a single crystal of tungsten.
symmetry. A typical field emission pattern is reproduced in figure 7.45 from the surface of clean tungsten. It is difficult to obtain field emission patterns with spatial resolution better than 2 nm and there are other effects such as thermal atom vibrations that may further degrade the spatial resolution. 7.7.3
Field ion microscope
The spatial resolution of the FEM is improved if particles of greater mass than the electrons are used (Good and Muller (1956)); Muller used ions to give a significant resolution improvement. Here, instead of the tip being negatively charged it is made the anode and an imaging gas is admitted to the system. Gas atoms very close to the tip become ionised by a process that is similar to electron tunnelling. The high potential field produces a relatively narrow potential barrier, although it raises rather than depresses the height. Electrons from the gas atoms tunnel into the tip. The ionised atom is ejected and then accelerated on to the fluorescent screen to produce an image. Again the probability that an electron will tunnel is determined by the work function and thus the image is a work function map. Early field ion microscopes used hydrogen as an imaging gas but it was subsequently realised that helium, at a pressure of 101 to 10 4 Pa, which is less easily polarised, offers better spatial resolution. Using helium as an imaging gas with a tip of radius 100 nm, a spatial resolution of 0.2 nm is obtained and it is possible to image individual atoms. The image is degraded by thermal vibration effects and improvements are gained by cooling the specimen to reduce the atom vibrations. Figure 7.46 shows the field ion image from tungsten showing the {110} and {001} planes. It should be noted that not all atoms have the same probability for ionisation: atoms on irregularities and protrusions will have a higher local field and are likely to be removed first. This results in the tip becoming progressively smoother and then layers of atoms are removed sequentially. Figure 7.47 shows this effect where a tungsten tip had been bombarded by
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Figure 7.46. A field ion image recorded from a single crystal of tungsten in the h1 10i orientation revealing {110} and {001} planes (courtesy J M Walls).
Figure 7.47. Field ion images recorded from a tungsten single crystal with a damaged surface (a) and after removal of (b) 6, (c) 15 and (d) 35 atom layers by field evaporation (courtesy J M Walls).
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argon ions which caused the surface to be damaged and the symmetry destroyed (Walls (1979)). Field ion micrograph (a) shows the surface following bombardment while images (b), (c) and (d) are recorded after 6, 15 and 35 atom layers had been removed by field evaporation. The crystalline nature of the tungsten is revealed as the damaged layers are removed. Clearly the condition of the specimen has to be recognised before interpreting these images. 7.7.4
Atom probe
A development of the field ion microscope occurred in 1968 when Muller and his colleagues added a time-of-flight (TOF) detector (Muller (1973) and Muller et al (1968)). Figure 7.48 is a schematic diagram of an atom probe that shows the field ion microscope together with the TOF mass analyser. The specimen tip, which can be cooled to liquid helium temperatures, is on the left-hand side. Close to this is a gas inlet to admit the imaging gas. The imaging plates, which in this instrument may be a channel-plate image converter to give much improved light levels, has a small aperture to allow specific field evaporated and imaging gases to pass through. These then pass through a hole in the angled viewing mirror and are focused on to the drift tube of the TOF mass analyser. Individual atoms are made to pass through the aperture in the channel plates by first obtaining an image of the tip on the channel plates, the desired atom is then selected and the tip angled so that the atom lies over the hole. The field is then pulsed and the mass to charge ratio (M=n) of the field evaporated ion is given by M=n ¼ 2eðVi þ Vp Þ 2 =L
ð7:18Þ
where e is the electronic charge, Vi is the imaging voltage, Vp is the pulsed voltage, the time taken for the ion to travel down the drift tube and L is
Figure 7.48. Schematic diagram of the time-of-flight atom probe.
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Figure 7.49. Spectra recorded using the time-of-flight SIMS in the atom probe. (a) Peaks resulting from evaporation of Mo and (b) a similar spectrum obtained with He gas.
the length of the drift tube. The design has been further improved by incorporating an energy analyser into the TOF probe (Poschenreider and Oetjen (1972)). This can give a mass resolution (M=M) for 10% half height separation of 1/1000. The TOF mass spectrum from a molybdenum tip evaporating in UHV and in a helium imaging gas is reproduced in figure 7.49. The spectrum (a) simply shows peaks resulting from the evaporation of molybdenum and indicates that there are many isotopes of molybdenum, while spectrum (b) which was obtained with the helium gas shows that the helium is combining with the molybdenum to form MoHe2þ þ Mo2 Heþ and Mo3 Heþ . Cerezo et al (1988, 1989) developed a position-sensitive detector that has been combined with a TOF mass spectrometer in the atom probe field ion microscope to produce an instrument where both chemical identity and spatial information are derived for individual ions evaporated from the surface of the specimen. A state of the art position sensitive instrument is shown schematically in figure 7.50 (Blavette et al (1993)). In this instrument, for each pulse to remove ions, all ions are mass analysed and their position determined from the position of the ion impacts on the detector with a magnification of G ¼ L=bR, where L is the length of the flight path, R is the tip radius and b is a factor, close to 2, related to the position of the projection point. A three-dimensional representation is produced of the location of all atoms within a cylinder of diameter da which is equal to d=G. This
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Figure 7.50. Schematic diagram of the tomographic atom probe. The coordinates of atoms on the surface of a sample are deduced from the position of each ion impact on the detector, which corresponds to the intensity distribution on the position sensitive detector. The magnification is G ¼ L=bR (Blavette (1993)).
method has been used to investigate the grain boundary composition in a nickel-based superalloy (Letellier (1994)). In this study grain boundaries in the nickel-based alloy, Astroloy, were imaged. This alloy has a grain size of approximately 40 mm but the imaging atom probe can only detect a cylinder of about 10 nm in diameter and it is necessary to identify a grain
Figure 7.51. Grain boundaries in a nickel-based superalloy, Astroloy, imaged using a tomographic atom probe showing the spatial distribution of Al þ Ti, Cr, Mo and B (þC) in the vicinity of a serrated grain boundary. During analysis two – 0 and one 0 – 0 boundary were crossed (after Letellier et al (1994)).
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boundary within a prepared specimen tip. This is done by prior examination of the tip in a transmission electron microscope (TEM). The specimen is then transferred to the imaging atom probe. Figure 7.51 shows the spatial distributions of Al þ Ti, Cr, Mo and B in the vicinity of a serrated grain boundary in this alloy. The total depth that was probed in this study was 120 nm, during which two different types of grain boundary were crossed, two – 0 interphase boundaries and one 0 – 0 grain boundary in this ordered phase.
7.8
Scanning probe microscopy
Scanning probe microscopes (SPM) are a specialised group of instruments that have been developed over the past 20 years to measure surface properties. They differ from most of the imaging techniques described in this book in that the spatial resolution that can be obtained is determined by the size of the probe being used and not the wavelength of the interaction. The historical development, together with descriptions of the major developments in the field, has been given by Wickramasinghe (2000). It is interesting to note that the concept of scanning probe microscopy was described by Synge (1928, 1932) who proposed using a small aperture at the end of a glass tip which would be raster scanned over an illuminated surface. He even suggested piezoelectric scanning but the idea was not seriously taken up until Binnig et al (1982) demonstrated with scanning tunnelling microscopy that a probe would image with sub-nanometer resolution on conducting surfaces. Later the atomic force microscope (AFM) was developed to image non-conducting surfaces (Binnig et al (1986)). Both instruments measure surface properties in all three dimensions, x, y and z, with spatial resolutions for x and y typically 0.1 nm for STM and 2–10 nm for AFM, and for the z direction 0.01 nm for STM and 0.1 nm for AFM. Both types of instrument operate by bringing a fine sharp probe into close proximity with the surface, but in STM the tip does not touch the surface. Rather it maintains a constant tunnelling current between the probe and the surface. In AFM the tip contacts the surface and maintains a constant but very small force. STM, while having better resolution than AFM, is limited to studying conducting materials whereas the AFM can probe all types of materials. Both techniques are limited to examining specimens that have height variations of less than 10 mm. 7.8.1
Scanning tunnelling microscopy
The scanning tunnelling microscope (STM) was the first of the surface probes to be developed (Binnig and Rohrer (1982) and Gerber and Weibel (1982)) . It is capable of giving information on the distribution of single atoms on a conducting surface in a simple, elegant and relatively inexpensive manner. Moreover with lateral resolution of 0.1 nm and vertical resolution of
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Figure 7.52. Schematic diagram showing the operation of the scanning tunnelling microscope (STM) (courtesy JEOL). (a) The basic principle, (b) control and acquisition electronics.
0.01 nm and can readily resolve individual atoms. The principle of the technique (figure 7.52), is based upon a sharp tip, usually made from tungsten or platinum/iridium, brought into close proximity (0.5 to 1 nm) with the surface to be studied. At this distance the electron wave functions of the tip and the surface overlap leading to a finite probability that an electron from the surface can tunnel through the potential barrier to the tip and vice versa, depending on the potential applied between the tip and the surface. Thus it is based upon the well established phenomenon of electron tunnelling. The current that flows depends on the distance, d, between the tip and the surface, the tunnel barrier height between the tip and the surface, , and the potential between the surface and the tip, Vi , and is given by I/
Vi exp½Cd1=2 d
ð7:19Þ
where C ¼ 10:25 eV1=2 nm1 , Vi is usually a few millivolts to a few volts, is of the order of a few eV and d is 0.5 nm which produces a current of a few nanoamps. Instrumentation The instrumentation required to achieve scanning tunnelling images is relatively simple and inexpensive. The microscope operates by bringing the tip close to the surface, <1 nm, to obtain a given current I. The tip or the
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specimen is then slowly rastered in the x and y directions while maintaining the current I constant. This requires the tip to be moved in the z direction as it is rastered over regions of surface topography. A feedback loop is set up to maintain I constant and hence to determine changes in z. The design of the instrument has to accommodate vibration, temperature changes and the position of the tip. Early instruments were large and included elaborated damping devices, but as the technique has developed it has become clear that the vibration problems are less severe if the STM is made as small as possible. This has advantages in that small STM devices can be incorporated into existing analytical instruments and STMs have now been added to scanning electron microscopes, LEED and Auger spectrometers (Iwatsuki and Kitamura (1990)). Positioning of the tip is difficult and achieved in two stages. First a coarse drive is used to bring the tip within a millimetre of the surface and the fine drive takes it to within a nanometre. Even so there is the real probability that the tip may be driven into the specimen and sophisticated control and feedback currents are needed to reduce the likelihood of damage (figure 7.52(b)). Applications The STM is ideally suited to the study of surfaces in UHV but works nearly as well at atmospheric pressure because the number of gas atoms in the space between the tip and the surface is not sufficient to significantly affect the tunnelling of electrons. An example of the STM’s capabilities is the solution of the superlattice that exists on the surface of silicon. The (111) surface contains a superlattice that is seven times larger than the lattice spacing in both the x and y directions. The Si (111) images in figure 7.53 show visible contrast changes between the corner and centre adatoms in the 7 7 unit cell. They also contrast STM with AFM images (see next section) of the same surface (Erlandsson et al (1996)). The figure compares (a) an AFM image and (b) empty-state and (c) filled-state STM images. The grey scales in the images correspond to a height difference of 0.1 nm. The STM images were recorded with tip voltages of 2 V and þ2.2 V, respectively, and a constant current of 0.1 nA. The AFM image has been low-pass filtered using a 3 3 convolution filter while the STM images show unfiltered data. The crosssections through the four non-equivalent adatoms show that the centre adatoms appear 0.013 nm higher than the corner adatoms. The 7 7 unit cell is outlined in the filled-state STM image. The faulted and unfaulted halves correspond to the left and right side, respectively. A comparison with STM data obtained at different bias voltage and ab-initio calculations show that the a.c.-mode AFM contrast does not correspond to variations in true atom positions. Rather, these data suggest that the contrast is due to either a variation in the chemical reactivity of the adatoms or to a tip-induced atomic-relaxation effect that reflects the stiffness of the surface lattice. The
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Figure 7.53. Comparison between Si (111) SPM images showing contrast between the corner and centre adatoms in the 7 7 unit cell: (a) an AFM image and (b) empty-state and (c) filled-state STM images (Erlandsson et al (1996)).
example shown in figure 7.53 was obtained from a similar surface from which the LEED pattern shown in figure 4.90 was obtained. It should be noted that while the STM image shown here indicates that the surface contains many defects, the LEED pattern suggests a perfect structure (Tear (1990)). However, it was with the advent of this technique that the 7 7 superlattice structure of oxygen on silicon was finally confirmed (Binnig and Rohrer (1983) and Trump et al (1987)). STM data can also be displayed in the form of an isometric projection where a three-dimensional image is obtained. An example of this type of display is given in figure 7.54 which was taken from
Figure 7.54. Highly oriented pyrolytic graphite image, showing near the step edge (courtesy JEOL).
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pffiffiffi pffiffiffi 3 3 construction
Scanning probe microscopy 505 pffiffiffi pffiffiffi highly oriented pyrolytic graphite and shows a 3 3 construction near the step edge (Iwatsuki and Kitamura (1990)). The technique is also ideally suited to the study of adsorption and desorption. Surface steps mapped and the growth of these steps followed as atoms adsorb on to the surface. There is also the potential for chemical state information to be obtained from the STM, since when elements combine to form compounds charge transfer takes place and one element will become positive and the other negative. This results in a larger tunnelling current from atoms of one element than the other. Which element will produce the largest current will be determined by the sign of the charge on the atom and the sign of the potential between the tip and the surface. In the case of gallium arsenide it is possible to distinguish between gallium and arsenic atoms in the surface by switching the polarity of the applied potential (Feenstra et al (1987)). While the STM has atomic spatial resolution it can also be used to map surface contours in a much coarser way and has been used to determine, for example, the surface flatness of mirrors etc. Currently effort is being devoted to the interpretation of the images because of the need to correctly predict the origin of the signal due to the weighted nature of the joint local density of states of the tip and the specimen (Binnig and Rohrer (1987)). However, in addition there are many applications that have been developed leading to specific instruments such as the atomic force microscope (Albrecht and Quate (1987)) and the magnetic force microscope (Saenz et al (1987)). 7.8.2
Atomic force microscopy
The atomic force microscope (AFM) also employs a sharp tip to probe the surface under investigation. However, in this case the tip is placed at the end of a long cantilever with a low spring constant (1 Nm2 ) and the tip brought into physical contact with the surface. The experimental arrangement for the atomic force microscope is shown in figure 7.55. The tip is placed at the end of a long cantilever and the force on the tip is determined by measuring the deflection of the cantilever. In early instruments the cantilever deflection was measured using a tunnelling sensor but this has been replaced by a laser probe (Ruger and Hansma (1990)). The instrument can then be operated in one of two modes: (i) constant force mode, (ii) tapping mode. Constant force mode In the constant force mode the force between the tip and the specimen is kept constant by forcing the tip against the sample (Rugar and Hansma (1990)). Either the probe can be scanned over the sample or the specimen rastered while the tip is maintained stationary. A piezoelectric scanner is used to keep the force constant and a laser beam, reflecting from the back of the
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Figure 7.55. The experimental arrangement for the atomic force microscope.
cantilever on to a photo diode, detects probe motion. Signals are fed into the electronic interface and computer to control the feedback system to keep the force constant while recording motion in the x, y and z directions. Figure 7.56 shows three AFM images recorded from the surface of very flat titanium oxide that illustrates the lateral spatial resolution capability of this technique. Figure 7.56(a) shows the regular square lattice over a region 7.5 nm 7.5 nm while (b) shows a larger area with a distorted square lattice and (c) shows a surface region with defects within an ordered structure. The raw images, taken in contact mode in air, were filtered with inverse Fourier transform to enhance the ordered structure (Cacciafesta et al (2002)). Unlike the STM technique there is physical contact between the specimen and probe in AFM and a likelihood that the specimen can become damaged as the probe or sample are rastered causing a loss of resolution. This would be particularly severe for materials such as polymers. To reduce this threat and to improve lateral resolution, AFM systems have been modified to operate in a tapping mode. Tapping mode In this mode of operation, shown schematically in figure 7.57, the probe is lightly tapped against the sample (McClelland et al (1987)). This has the effect of reducing the lateral shear forces and thus reducing the sample damage. This mode of operation is particularly suited to soft samples such as polymers and the use of SPM techniques in biological applications has been reviewed by Miles (2003). However, recent papers (Antognozzi et al (2002)) have shown that AFM, when operated in a surface liquid film, can have comparable resolution to that obtained by tapping mode AFM. In the example shown in figure 7.58 DNA fragments were deposited on to mica from a diluted buffer. The images were taken in air with shear force control (a) and with tapping mode (b). The DNA molecules appear
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Figure 7.56. AFM images recorded from the surface of very flat titanium oxide: (a) the regular square lattice over a region 7.5 nm 7.5 nm, (b) a larger area with a distorted square lattice and (c) a surface region with defects within an ordered structure. The grey scale range is typically 0 (dark) to 0.5 nm (light) (Cacciafesta et al (2002)).
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Figure 7.57. Schematic diagram of tapping force mode AFM.
equilibrated on the surface and well distributed. The measurement of the contour length confirms the estimated length of the fragments to be around 1.5 mm. A qualitative comparison of the two images does not highlight significant differences between the two techniques. Applications of AFM AFM in both constant force and tapping mode can be used to give high resolution three-dimensional images of the specimen topography. However, by replacing the standard probe by specially modified tips, and
Figure 7.58. DNA fragments deposited on to mica from a diluted buffer. The images were taken in air with shear force control (a) and with tapping mode (b) (Antognozzi et al (2002)).
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Figure 7.59. Some applications of AFM.
with minor operating modifications, many additional physical properties of the surface can be determined with the same high lateral spatial resolution. Some of these are illustrated schematically in figure 7.59 and include the following: (i) Micro-thermal analysis. The scanning thermal probe was developed prior to the AFM in order to profile insulating surfaces (Williams and Wickramasinghe (1986)). In this mode the displacement of the tip, which is a thermal sensor or thermocouple, is measured as it is heated in contact with the specimen. A constant current is passed through the tip, which then heats to an equilibrium temperature. As the tip approaches the specimen
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it cools due to heat transfer. The tip temperature is then used to control the tip–sample spacing. This method can give valuable information on the thermal properties of the surface (Price et al (1998) and Majumdar (2000)). (ii) Electrostatic force microscopy and surface potential imaging. Electrostatic force microscopy (EFM) is used to map the vertical (z) gradient of the electric field between the tip and the specimen versus x and y. To do this an a.c. voltage is applied between the tip and the specimen and the induced force measured. The field due to trapped charges is often sufficient to generate contrast in an EFM image but if not a field can be induced by applying a voltage between the tip and the specimen. Surface potential (SP) imaging maps the electrostatic potential on the specimen surface with or without a voltage applied (Martin et al (1988) and Williams (2000)). (iii) Magnetic force microscopy. In magnetic force microscopy (MFM) the cantilever tip is replaced or coated with a magnetic material such as iron or nickel, and the magnetic force between the tip and the specimen is used to determine the magnetic features on the specimen surface. The magnetic domain distribution can then be obtained simultaneously with the topographical image. This form of AFM is frequently used to characterize magnetic recording devices (Hartmann (2000)). (iv) Lateral force microscopy and chemical force microscopy. Lateral force microscopy (LFM) identifies and maps relative differences in surface frictional characteristics. It is one of several techniques developed as extensions to the basic topographical mapping capabilities of SPM. LFM is particularly useful for differentiating materials by considering the surfaces. Applications include identifying transitions between different components in polymer blends, composites and other materials. The chemical force microscope (CFM) is a modification of LFM where the tip is functionalised with one chemical species and scanned over a specimen to detect adhesion differences between the species on the tip and those on the surface. Frisbie et al (1994) changed the chemical species on the tip between scans of the same surface, causing the lateral force image of the surface to invert (figure 7.60). There are many more applications and modifications of the basic scanning probe microscopes which are too numerous to cover in this book. However, a few of the applications are listed in table 7.1 compiled from Wickramasinghe (2000). 7.8.3
Photonic force microscopy
Although AFM has the capability to image with atomic resolution and can produce images using very low forces, there still remain restrictions regarding the type of specimens that can be imaged. For example, it is impossible, using
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Figure 7.60. Lateral force image of the surface obtained with two chemical species on the tip causing the image to invert (Frisbie (1994)). Table 7.1. Some scanning probe techniques. Technique
Application
Reference
Scanning tunneling microscope
Atomic resolution of conducting surfaces
Binnig et al (1982)
Scanning near-field optical microscope
50 nm lateral resolution of optical images
Lewis et al (1984), Pohl et al (1984)
Scanning thermal microscope 50 nm lateral resolution of thermal images
Williams and Wickramasinghe (1986)
Atomic force microscope
Atomic resolution of conducting and non-conducting surfaces
Binnig et al (1986)
Scanning attractive force microscope
5 nm lateral resolution non-contact images of surfaces
Martin et al (1987)
Magnetic force microscope
100 nm lateral resolution of magnetic surfaces
Martin and Wickramasinghe (1987)
Electrostatic force microscope
Detection of charge distribution
Martin et al (1988)
Ballistic electron emission microscope
Probing Schottky barriers on Kaiser and Bell (1988) a nanometre scale
Absorption microscope/ spectroscope
1 nm lateral resolution absorption images/spectroscopy
Weaver and Wickramasinghe (1991)
Scanning chemical potential microscope
Atomic scale images of chemical potential variation
Williams and Wickramasinghe (1990)
Photovoltage STM
Photovoltage images on nanometre scale
Hamers and Markert (1990)
Kelvin probe microscope
Contact potential Nonnenmacher (1991) measurements on 10 nm scale
Apertureless near-field microscope
Optical microscopy at 1 nm resolution
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Figure 7.61. Schematic diagram of the photonic force microscope (PFM).
a mechanical cantilever, to obtain three-dimensional images within a cell and there is still the potential for damage. A microscope has been developed by the European Molecular Biology Laboratory (EMBL) which uses a probe with no mechanical connection. This instrument, known as the photonic force microscope (PFM), shown schematically in figure 7.61, replaces the mechanical cantilever with the three-dimensional trapping potential of a laser beam focus. This is achieved by using a nano or micrometre steel particle such as a latex, glass or metal bead as the tip which is trapped by the laser focus. The bead acts as a Brownian particle in a potential well and its position distribution is described by the Boltzmann equation. The PFM instrument is based on an inverted optical microscope and a Nb : YVO4 laser, which is not absorbed by water or biological material, is coupled into the microscope using scanning laser microscopy techniques. A dichroic mirror focuses the light on to a quadrant photo diode and the difference between the left and right halves of the diode provides the x, the difference between the top and bottom halves of the diode provides the y and the sum signal the z position. This instrument has high spatial resolution in three dimensions (Pralle et al (1998, 1999) and Florin et al (1998). Figure 7.62 shows a three-dimensional map of the potential from a biological cell.
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Figure 7.62. The three-dimensional map of the potential from a biological cell using the photonic microscope (Pralle et al (1999)).
7.9
Particle induced X-ray emission
Bombardment of a material by electrons or other charged particles produces an emission of X-rays. This is the result of ionisation of atoms which then rearrange, emitting a photon (X-ray fluorescence) (Watt and Grime (1987), Johannsson and Campbell (1988), Grime and Watt (1988), Folkmann et al (1974), Johannsson and Johannsson (1976) and Campbell et al (1981)). The most frequently encountered application of X-ray fluorescence is when it is stimulated by electron bombardment (chapter 6, section 6.3.7) but it is also possible to obtain a chemical analysis by bombarding with charged particles and detecting the X-rays emitted. The method, while having many drawbacks when compared with electron bombardment, does have the advantage of a high sensitivity. 7.9.1
Instrumentation
The principles involved in particle-induced X-ray emission (PIXE) are similar to energy dispersive X-ray (EDX) analysis discussed in chapter 6. A typical instrumental layout for PIXE analysis is shown in figure 7.63. A beam of charged particles is arranged to be incident on the specimen, usually inclined at 458 to the incident beam, and the X-rays emitted pass through a thin Mylar window to a silicon detector. In some cases the
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Figure 7.63. Schematic diagram of a typical proton induced X-ray emission (PIXE) system (Johannsson and Johannsson (1976)) (reproduced with permission of Wiley).
window is dispensed with, allowing detection of elements of low atomic number, while in other systems the silicon detector is replaced by a gas proportional counter. The particle beam of protons is produced using a Van de Graaff accelerator, but any particle source will suffice. This is, of course, one of the drawbacks to the technique. It is necessary to have an intense high energy source of charged particles and while many such sources exist around the world not every laboratory can possess one. The beam is then passed through a diffuser foil and collimators which select the central fraction of the diffused beam. Other approaches to produce a homogeneous beam involve magnetic sweeping (Cahill (1973)) or sweeping a well focused beam over the collimator entrance (Johannsson et al (1972)). The beam enters the analytical chamber and impinges on the target placed at 458 to the incident beam. The specimen, approximately 50 mm 50 mm, is loaded through a vacuum airlock and normally several specimens are loaded at one instant and changed automatically thus maintaining a good vacuum in the chamber. The chamber is constructed of materials which give negligible spurious radiation. Aluminium has been used for this purpose since it produces low energy characteristic Xrays although it does give rise to an intense radiation when stopping a proton beam. The X-ray detector is usually placed normally to the incident beam and as close to the specimen as possible; distances of less than 2 cm have been achieved. Lithium drifted silicon detectors are used to detect the
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Figure 7.64. A PIXE spectrum from an Al2 O3 -based catalyst, showing peaks from low to high atom number elements (courtesy AEA Technology).
X-rays (chapter 6) but in certain instances wavelength dispersive systems have been employed with their much better energy resolution, but these operate with much smaller solid angles than the energy dispersive type and a scan procedure is required (see chapter 6). PIXE has been obtained using a range of types of incident particles. The most common source is the proton but -particles, deuterium and oxygen ions have all been used. A typical spectrum containing peaks from the K , K , obtained by bombarding a specimen of Al2 O3 -based catalyst with protons, is shown in figure 7.64. This spectrum contains X-rays of elements at the low end of the Periodic Table such as aluminium and potassium and L X-rays for the heavier elements such as rhodium, platinum and lead. 7.9.2
Sensitivity and spatial resolution
One advantage that PIXE has is that it can detect trace elements present in amounts several orders of magnitude lower than are detectable by EDX. This is because electron-stimulated X-ray fluorescence produces a large background of Bremsstrahlung radiation which effectively limits the detection by this technique to 104 . Particle-induced X-ray emission does not produce this large Bremsstrahlung background and as a result detection levels in the region of 106 are common. Figure 7.65 shows the minimum detectable concentrations as a function of atomic number for proton bombardment at energies of 1 and 3 MeV. The detection sensitivity achieved depends on the type of bombarding particle, the particle energy and the atom being detected.
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Figure 7.65. PIXE minimum detectable concentrations as a function of atomic number (Johannsson and Johannsson (1983)) (reproduced with permission of Wiley).
As with all charged particles the possibility exists of producing a focused beam of charged particles that can be rastered over the surface and hence produce a PIXE microprobe. It is, however, much more difficult to focus a beam of protons than electrons and developments have been slower. Proton beam diameters as small as a few micrometres have been produced (Cookson and Pilling (1970)) and used to obtain spectra with a silicon detector (Peisach et al (1973)). Focused beams have been rastered over the specimen surface to produce two-dimensional X-ray element maps and it is claimed that the resolution should be capable of 1 mm (Horowitz and Grodzins (1975)). 7.9.3
Applications
PIXE is ideally suited to the analysis of thin specimens, or thin layers of powders containing up to twenty different elements, and as a consequence has many potential applications. It has been used extensively to study aerosol specimens in pollution studies, it can detect trace element concentrations in liquid specimens although it is often necessary to dry the specimen first, and it has been used to determine trace element concentrations in biological tissue. In the latter application it has been used to study the effects of toxic pollution from cadmium, mercury and lead poisoning. Thick steel specimens have been studied but a major problem is that the very strong X-ray emission from the iron matrix can mask some of the peaks from trace elements. This is always a problem with materials that contain high concentrations of one element which may have a major peak close to that of the trace element. In such cases careful selection of X-ray absorbers is necessary.
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7.10 Glow discharge spectroscopy Glow discharge spectroscopy (GDS) or glow discharge optical emission spectroscopy (GDOES) is a technique used to determine the elemental composition of bulk samples, the surface of samples and the elemental depth
Figure 7.66. Schematic arrangement for glow discharge optical emission spectroscopy: (a) Grimm source, (b) general layout.
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profile from the surface into the sample. It is a sensitive technique but cannot provide any lateral information. For bulk analysis the technique assumes that the sample is homogeneous and for surface analysis that there is no significant variation in composition across the surface. The technique has been reviewed by Marcus (1993), Bengtson (1985) and Bengtson et al (1991) for metals and by Baude et al (2000) for environmental materials. The sample to be analysed is placed in an inert gas environment, usually argon. The argon gas is then ionised by applying either a high d.c. voltage or by a radio-frequency (RF) field. The ionised argon atoms are then accelerated onto the sample by making the sample the cathode in the case of metals or by placing the sample in contact with the cathode in the case of non-metals. The argon ions impinging on the sample surface cause atoms on the surface to be ejected into the argon plasma. The atoms are themselves excited by inelastic collisions with electrons or other species. When these atoms relax they emit photons with characteristic wavelengths. This optical emission is detected and measured both for wavelength and intensity. The technique is quantified by reference to a standard sample. The experimental arrangement for GDOES is shown schematically in figure 7.66. Part (a) shows the glow discharge source. This is of the Grimm type which is the most commonly used source (Grimm (1968)). The Grimm source may be operated in either the d.c. mode, in which case a discharge current of 5 to 200 mA and voltage of 400 to 2000 V would be used, or in RF mode when frequencies between 3 and 41 MHz are employed. The optical emission from the Grimm source is then focused onto a grating
Figure 7.67. GDOES depth profile through a zinc–iron coating on a steel substrate.
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and the diffracted light is detected using a combination of simultaneous spectroscopy with sequential spectroscopy (figure 7.66(b)). Most GDOES instruments utilise photomultiplier tubes for signal detection with multiple tubes located around the Rowland circle and a movable photomultiplier to traverse the Rowland circle for sequential measurements. GDOES is capable of detecting most elements with a sensitivity varying from 105 to 103 . Figure 7.67 shows a depth profile obtained from a zinc–iron coating applied to a steel substrate with depth profiles recorded for Zn, Al, Mn and P.
7.11 References Abramo M and Wasielewski R 1997 FIB for Failure Analysis Semicond. International, 133 Ahlberg M, Akselsson R, Bruce D and Lorenzen J 1975 Nucl. Instrum. Meth. 123 385 Albrecht T R and Quate C F 1987 J. Appl. Phys. 62 2599 Allen G C, Sparry R P and Wild R K 1989 Mat. Sci. Tech. 5 560 Anders O U 1966 Anal. Chem. 38 1442 Antognozzi M, Szczelkun M D, Round A N and Miles M J 2002 Single Mol. 3, 105 Ball D J, Buck T M, MacNair D and Weatley G H 1972 Surf. Sci. 30 69 Baude S, Broekaert J A C, Delfosse D, Jakubowski N, Fuechtjohann L, Orellana-Velado N G, Pereiro R and Sanz-Medel A 2000 J. Anal. At. Spectra. 15 1516 Baun W L 1982 Appl. Surf. Sci. 13 198 Bengtson A 1985 Spectrochim. Acta 40B 631 Bengtson A, Eklund A and Saric A 1991 J. Anal. At. Spectrum 5 563 Benninghoven A 1970 Chem. Phys. Lett. 6 616 Benninghoven A, Rudenauer F G and Werner H W 1987 Secondary Ion Mass Spectrometry (New York: Wiley) Bernius M T, Ling Y C and Morrison G H 1986 J. Appl. Phys. 59 3332 Binnig G and Roher H 1982 Phys. Acta 55 726 Binnig G and Roher H 1983 Phys. Rev. Lett. 50 120 Binnig G and Roher H 1987 Angew Chem. Int. Ed. English 26 606 Binnig G, Rohrer H, Gerber Ch and Weibel E 1982 Phys. Rev. Lett. 49 57 Binnig G, Quate C F and Gerber Ch 1986 Phys. Rev. Lett. 56 930 Blanc D and Degeilh A 1961 J. Phys. Rad. 22 230 Blavette D, Deconihout B, Bostel A, Sarrau J M, Bouet M and Menand A 1993 Rev. Sci. Instrum. 64, 2911 Brongersma H H and Buck T M 1978 Nucl. Instrum. Meth. 149 569 Brongersma H H and Mul P M 1973 Surf. Sci. 35 393 Brown F and Mackintosh W D 1973 J. Electrochem Soc. 120 1096 Brunnee C 1957 Z. Phys. 147 161 Cacciafesta P, Hallam K R, Oyedepo C A, Humphries A D L, Miles M J and Jandt K D 2002 Chem. Mater. 14, 777 Cahill T A 1973 University of California at Davis Report UCD-CNL-162 (Davis: California) Campbell J L, Russell S B, Faiq S, Schulte C W, Ollerhead R W and Gingerich R R 1981 Nucl. Instrum. Meth. 181 285 Cerezo A, Godfrey T J and Smith G D W 1988 Rev. Sci. Instrum. 59 862
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Atom/ion sources
Cerezo A, Godfrey T J, Grovenor C R M, Hetherington M G, Hoyle R M, Jakubovics J P, Liddle J A, Smith G D W and Worrall G M 1989 J. Microscopy 154 215 Chait B T and Standing K G 1981 Int. J. Mass Spectrum Ion Phys. 40 185 Cookson J A and Pilling F D 1970 Report AERE-R 6300 (Harwell: Atomic Energy Research Establishment) Dayton I E, Shoemaker F C and Hozey R F 1954 Rev. Sci. Instrum. 25 485 Drummond I and Long J V P 1967 Nature 215 950 Erlandsson R, Olsson L and Ma˚rtensson P 1996 Phys. Rev. B 54 R8309 Feenstra R M, Stroscio J A, Tersoff J and Fein A P 1987 Phys. Rev. Lett. 58 1192 Folkmann F, Gaarde C, Huus T and Kemp K 1974 Nucl. Instrum. Meth. 116 487 Florin E-L, Pralle A, Stelzer E H K and HØrber J H K 1998 Applied Phys. A 66 S75 Frisbie C D, Rozsnyai A, Noy A, Wrighton MS and Lieber C M 1994 Science 265 2071 Gerber B R and Weibel E 1982 Phys. Rev. Lett. 49 57 Gilmore I S and Seah M P 2000 Appl. Surf. Sci. 161 465 Gilmore I S and Seah M P 2003 Appl. Surf. Sci. 203–204C 548 Gomer R 1961 Field Emission and Field Ionisation (Oxford: Oxford University Press) Good R H and Muller E W 1956 Field Emission in Encyclopedia of Physics ed S Flugge vol 21 (Berlin: Springer) p 176 Grime G W and Watt F ed 1988 First Int. Conf. on Nuclear Microprobe Technology and Applications: Nucl. Instrum Meth. Phys. Res. B 30 Grimm W 1968 Spectrochim. Acta 23B 443 Gueneau de Mussy J P, Langelaan G, Decerf J, Delplancke J L 2003 Scripta Materialia 48 23 Hamers R J and Markert K 1990 Phys. Rev. Lett. 64 1051 Harrington D B 1960 in Encyclopedia of Spectroscopy ed C F Clark (New York: Reinhold) Hartmann U 2000 A Rev. Mater. Sci. (In Press) Heard P J, Day J C C and Wild R K 2000 Micros and Analysis May p 9 Heiland W 1982 Appl. Surf. Sci. 13 282 Honig R E and Harrington W L 1973 Thin Solid Films 19 43 Hooghan K N, Wills K S, Rodriguez P A and O’Connell S 1999 Integrated circuit device repair using FIB system: tips, tricks, and strategies in Proc. 25th International Symposium for Testing and Failure Analysis (ISTFA 99) (ASM International, Materials Park, Ohio) p 247 Horowitz P and Grodzins L 1975 Science 189 795 Hren J J and Ranagathan S ed 1968 Field Ion Microscopy (New York: Plenum Press) Iwatsuki M and Kitamura S 1990 JEOL News 28E 25 Johannsson T B, Akselsson R and Johannsson S A E 1972 Adv. X-ray Anal. 15 373 Johannsson S A E and Campbell J R 1988 PIXE: A Novel Technique for Elemental Analysis (Chichester: Wiley) Johannsson S A E and Johannsson T B 1976 Nucl. Instrum. Meth. 137 473 Jones R B, Younes C M, Heard P J, Wild R K and Flewitt P E J 2002 Acta Mater. 50 4395 Kaiser W J and Bell L D 1988 Phys. Rev. Lett. 60 1406 Kane P F 1974 Field Ion Microscopy in Characterisation of Solid Surfaces ed P F Kane and G R Larrabee (New York: Plenum Press) Letellier L, Guttmann M and Blavette D 1994 Phil. Mag. Lett. 70 189 Lewis A, Isaacson M, Harootunian A and Muray A 1984 Ultramicroscopy 13 227 Lipinsky D, Jede R, Ganschow O and Benninghoven A 1985 J. Vac. Sci. Technol. A3 2007
Copyright © 2003 IOP Publishing Ltd.
References
521
Lipp S, Frey L, Lehrer C, Demm E, Pauthner S and Ryssel H 1996 Microelectron. Reliab. 36 1779 Mackintosh W D 1974 Rutherford scattering in Characterisation of Solid Surfaces ed P F Kane and G R Larrabee (New York: Plenum Press) McClelland G M, Erlandsson R and Chiang S 1987 Review of Progress in Quantitative Nondestructive Evaluation vol 6B ed D O Thompson and D E Chimenti (New York: Plenum Press) p 307 Majumdar A 2000 Ann. Rev. Mater. Sci. (In Press) Marcus R K 1993 Glow Discharge Spectroscopies (London: Plenum) Martin Y, Williams C C and Wickramasinghe H K 1987 J. Appl. Phys. 61 4723 Martin Y and Wickramasinghe H K 1987 Appl. Phys. Lett. 50 1455 Martin Y, Rugar D and Wickramasinghe H K 1988 Appl. Phys. Lett. 52 244 Martin Y, Abraham D W and Wickramasinghe H K 1988 Appl. Phys. Lett. 52 1103 Miles M J 2003 Materials Today February p 39 Miller M K, Hetherington M G and Buvlze M G 1989 Met. Trans. 20A 1651 Muller E W 1936 Phys. Z. 37 838 Muller E W 1951 Z. Physik 131 136 Muller E W 1956 Field emission microscopy in Physical Methods in Chemical Analysis ed W G Bel vol III (New York: Academic Press) p 135 Muller E W 1960 Adv. Elect. Electron Phys. 13 83 Muller E W 1973 Laboratory Practice 22 408 Muller E W, Panitz J A and McLane S B 1968 Rev. Sci. Instrum. 39 83 Mu¨ller K H Seifert K and Wilmers M 1985 J. Vac. Sci. Technol. A 3 1367 Niehus H and Bauer E 1975 Surf. Sci. 47 222 Nielsen K O 1957 Nucl. Instrum. Meth. 1 289 Nier A O 1947 Rev. Sci. Instrum. 18 398 Nonnenmacher M, O’Boyle M P and Wickramasinghe H K 1991 Appl. Phys. Lett. 58 2921 Northcliffe L C and Schilling R F 1970 Nuclear Data Tables 7 233 Oechsner H and Stumpe E 1977 Appl. Phys. 14 43 Panin H V 1962 Sov. Phys. JETP 15 215 Pantel R, Auvert G and Mascarin G 1997 Microelec. Eng. 37/38 49 Paul W and Steinwedel H 1953 Z. Naturforsch. 8A 448 Peisach M, Newton D A, Peck P F and Pierce T B 1973 J. Radioanal. Chem. 16 445 Peisach M and Poole D O 1966 Anal. Chem. 38 1345 Pohl D W, Denk W and Lanz M 1984 Appl. Phys. Lett. 44 651 Poschenreider W P 1972 Int. J. Mass Spectrum Ion Phys. 9 357 Poschenreider W P and Oetjen G H 1972 J. Vac. Sci. Technol 9 212 Pralle A, Florin E-L, Stelzer E H K and HØrber J H K 1998 Appl. Phys. A 66 S7 Pralle A, Florin E-L, Stelzer E H K and HØrber J H K 1999 Microscopy Res. Tech. 44 378 Prewett P D and Jefferies D K 1980 Int. Phys. Conf. Ser. 54 316 Price D M, Reading M, Caswell A, Hammiche and Pollock H M 1998 Microscopy Anal. May Rubin S 1959 Nucl. Instrum. Meth. 5 177 Rubin S, Passell T O and Bailey L E 1957 Anal. Chem. 29 736 Rugar D and Hansma P 1990 Physics Today 43 23 Saenz J J, Garcia N, Grtter P, Meyer E, Heinzelmann H, Rosenthaler L, Hidber H R and Gntherodt H J 1987 J. Appl. Phys. 62 4293
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Atom/ion sources
Septier A 1967 Focusing of Charged Particles vol 2 ed A Septier (New York: Academic Press) Schreiber T 2001 Unaxis Materials Feb p 8 Sheng T T, Goh G P, Tung C H and Wang L F 1997 J. Vac. Sci. Technol. B 15 610 Slodzian 1964 Ann. Phys. 9 591 Smith D P 1967 J. Appl. Phys. 38 Smith D P 1971 Surf. Sci. 25 171 Synge E H 1928 Phil. Mag. 6 356; 1932 13 297 Tear S P 1990 Microscopy and Analysis 19 7 Thompson D A, Barber H D and Mackintosh W D 1969 Appl. Phys. Lett. 14 102 Trump R M, Hamers R J and Demuth J E 1987 Science 304 234 Verkleij D 1998 Microelectron. Reliab. 38 869 Von Ardenne M 1962 Tabellen zur Angewandten Physik B und I (Berlin: VEB Deutscher Verlag der Wissenschaften) Walls J M 1979 Thin Solid Films 57 201 Watt F and Grime G W 1987 Principles and Applications of High Energy Microbeams (Bristol: Adam Hilger) Waugh A R, Bayly A R and Anderson K 1984 Vacuum 34 103 Waugh A R, Bayly A R and Anderson K 1984b Secondary Ion Mass Spectrometry: SIMSIV ed A Benninghoven, J Okana, R Shimizu and Werner (New York: Springer) p 138 Weaver J M R and Wickramasinghe H K 1991 J. Vac. Sci. Technol. B 9 1652 Wein W H 1902 Ann. Phys. 8 260 Wickramasinghe H K 2000 Acta Mater. 48 347 Williams C C 2000 Ann. Rev. Mater. Sci. (In Press) Williams C C and Wickramasinghe H K 1986 Appl. Phys. Lett. 49 1587 Williams C C and Wickramasinghe H K 1990 Nature 344 317 Williamson C F, Boujot J P and Picard J 1966 Tables of Range and Stopping Power of Chemical Elements for Charged Particles of Energy 0.05 to 500 MeV Centre D’Etudes Nucle´aires de Saclay Report CEA- R3042 Wilson R, Van den Berg J A and Vickerman J C 1989 Surf. Interface Anal. 14 393 Young R J, Cleaver J R A and Ahmed H 1990 Microelec. Eng. 11, 409 Young R J and Moore M V 2002 DUAL-BEAM (FIB-SEM) SYSTEM) Zenhausern F, Martin Y and Wickramasinghe H K 1994 Appl. Phys. Lett. 65 1623
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Chapter 8 Application of computers 8.1
Introduction
We have referred frequently throughout the various chapters of this book to the significant use of computers for the examination and quantification of the microstructure of materials. Figure 8.1 shows schematically the various ways a computer can be interfaced with an instrument that is used to evaluate microstructure. We do not propose to provide either a detailed or a comprehensive review of computer systems and processing techniques, but rather the purpose is to give a simple overview of some of the underlying philosophy adopted in the application of computers to microstructural investigation techniques and their evaluation. This can be addressed by considering the major areas where computers can be and are applied: (i) instrument control, (ii) instruction, (iii) data acquisition and storage, (iv) data processing and image analysis, (v) image quantification, (vi) data bases, (vii) expert
Figure 8.1. A schematic arrangement demonstrating the various ways in which a computer can be interfaced with an instrument to evaluate the microstructure of materials.
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systems and (viii) simulation. Since it is extremely difficult to provide a comprehensive coverage of these selected topics, each will be addressed by reference to specific examples which we hope will make the reader aware of the potential to be attained from computer systems.
8.2
Instrument control
When a computer is interfaced to an instrument, such as an electron microscope, the basis of the approach is to reduce the effort of building electronics for digital applications by using a ready-made central processing unit with ancillary random access memory as the main building block. This enables the system to be extended simply by adding interfaces and rewriting the program that controls the central processing unit. Depending upon the application, the central processing unit can range from a simple desk-top microcomputer up to a large capacity computer. However, the choice of the computer depends on the ease of constructing suitable interfaces. As pointed out by Statham (1982) interfacing an instrument with a computer involves translation between the digital logic circuits in the computer and the analogue signals, usually voltages and currents, of the instrument. The output from a digital to analogue converter (DAC) can be buffered with a suitable amplifier to give computer control of lens current, beam deflection or spectrometer energy selection if interfaced with, for example, a scanning electron microscope fitted with an energy dispersive spectrometer. In such applications it may be necessary to control the stability and definition of the lens current to be as high as 1 part in 106 and this would require a 20 bit DAC. Apart from the need for a stable, low drift electronic system, manipulation of 20 bits increases the complexity of the interface. With current generation instruments described in this book such as optical and electron microscopes, Auger spectrometers, scanning probe instruments and X-ray diffractometers, the functions of each instrument can be controlled from either a central processing unit or a dedicated processor. Thus the operating functions of the instrument can be interrogated and programmed for control. This has the advantage of both improved and easier operation of the instruments and repeatability of performance. For example, in the case of an X-ray diffractometer all the specimen detail can be entered, the angular ranges for the analysis can be specified and the operating conditions selected via the keyboard. In the case of the various electron optical instruments, the use of dedicated processors enables instrument and recording conditions to be filed and the instrument functions to be selected via the keyboard, thereby allowing those conditions adopted by the operator to be retrieved and used for future investigations. The computer can be used to perform a complete experiment, freeing the operator from repeated laborious operations. For example, an image of
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the surface being interrogated can be obtained, and the operator identifies regions of interest which are then stored electronically. The computer can then be programmed to move the incident electron beam to specific points, acquire spectra over desired energy ranges, switch on ion guns to remove material before obtaining further spectra at the specific points and so on. The computer can also be used to monitor the image at intervals to detect any sample drift and move the specimen back into alignment. Such a process of input of commands, comments and interrogation of operating conditions increases the flexibility of instrument usage and effects ultimately easier, more rapid and reliable use by the operator. The caution that has to be recognised here, and indeed with all computer systems, is that familiarity with the computer system has to be achieved in addition to a knowledge of the particular physical technique and detail of the instrument being used.
8.3
Computer aided instruction
One of the problems associated with many of the instruments described in the preceding chapters of this book is that they are complex. As a consequence the operator is faced with the need to acquire skills to operate the instrument, often without being able to appreciate readily the implications of the actions being undertaken. Training and instruction has traditionally required the presence of an experienced and suitably qualified operator to supervise the novice and acquire data of the required pedigree. This approach in turn safeguards the instrument from inadvertent damage. In some areas of microscopy progress is now being made to address the issue of providing appropriate training via computer aided systems. For example, Goldstein (1992) developed software which simulates various types of optical microscopy imaging systems. It provides teaching aids for specific light microscopy techniques described in chapter 5 of this book, such as bright field and phase contrast microscopy. Extensions to this approach have been developed; one example is the interactive microscope laboratory (Baggott and Watson (1997)) which provides a laboratory work bench for use by school children that contains a microscopic field of view, shade box, note book and tool box. However, the principles can be adopted more widely. In the case of the instruments described in the preceding chapters of this book, the approach needs to be refined. It is not readily obvious why a smaller beam size in any of the various electron microscopes, including the electron microprobe analyser, inevitably reduces the beam current. The great advantage of a computer training model is that it is interactive with the user thereby providing an effective and powerful tool. One example has been described by Cox (1989) where use is made of a graphical simulation to assist instruction: a beneficial extension of the use of text alone. In the
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Figure 8.2. Computer aided training for the operation of a transmission electron microscope (em TUTOR). (a) The imaging system for the three-lens microscope. (b) The objective lens detail (Cox (1989)) (reproduced by permission of the Institute of Physics).
program described by Cox (1989) the imaging component (figures 8.2(a) and (b)) presents a ray diagram of the complete imaging system for a transmission electron microscope with three imaging lenses. The prescribing instruction changes the magnification from the low range to the selected area magnification and intermediate stages and image inversions are displayed together with the corresponding ray paths. Moreover, it is possible to select the diffraction operating range with the option of switching to an enlarged view of the objective lens to present ray diagrams up to the first image at the position of the selected area aperture (figure 8.2(b)). As part of the operator interaction it is possible to insert different sizes of objective and selected area aperture and observe their contribution to both the image and diffraction pattern. Such instruction can be undertaken either remotely from the instrument or online, thereby linking the operator’s theoretical understanding with the operational implications and requirements. To operate a scanning electron microscope also requires considerable experience and understanding of the instrument, which includes the fact that these instruments are now more usually software driven. As a consequence the operator needs specialist training to ensure the instrument achieves the required performance. To facilitate this Holburn et al (2000) have developed a virtual scanning electron microscope, or rather software that simulates the scanning electron microscope and emulates both the behaviour and user interface. This enables training and instruction for the complete operation including specimen insertion, operations such as magnification, brightness, contrast and astigmatism correction. This provides a realistic simulation of the operation of this instrument. Such a virtual system can be, and has
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been used for interacting with manuals, training in microscope operation and demonstration of the facilities and capabilities of the scanning electron microscope. Such computer-based training programs and methods provide a powerful and essential way forward for the future training and instruction on complex, high cost instruments.
8.4
Data acquisition
The images produced by the various microscopes and instruments described in this book, and the data associated with the electronic signals generated as a consequence of electromagnetic radiation interaction with a specimen, contain information which has to be quantified if it is to be of practical use. For a computer system the data has to be in digital form so that even for a simple optical microscope it is necessary to insert an opto-electronic device to convert light to an electrical signal which can then be digitised. It is this simple numerical data that is stored in the memory of a computer so that it can be processed subsequently (Barsanti et al (1990)). It is important to remember that a weakness of automated systems of this type is they do not explore the processes by which the data is derived and, as a consequence, the acquisition and subsequent processing can often be a compromise to achieve rapid data capture and processing at the expense of precision and accuracy (Leapman et al (1984). Figure 8.3 shows a typical system of a scanning optical microscope (chapter 5) connected via a parallel interface to a mini computer, a mass storage unit, an optical scanning digitiser and an image processing unit (Barsanti et al (1990)). It would not help to acquire an overall, averaged
Figure 8.3. Schematic diagram of hardware for digital image processing.
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image since this would not correlate with point-by-point brightness variations in that image. Therefore it is necessary, at the stage when the image is acquired, to measure this point-by-point variation. To effect this invokes an acquisition system which divides the image into small adjacent areas, where the smaller the area discriminated makes it possible for the measured light intensity variation to be more precise (Barsanti et al (1990)). Since a light microscope is a two-dimensional, non-casual linear system, an increase in the intensity of a point source introduces a proportional increase in the intensity of the spot image and two-point sources produce an image where they combine by addition. A point spread function is the image obtained from the object which in this case is a light source (Painter (1965)). Therefore an object transmitting light may be considered to be a two-dimensional distribution of weighted point sources and as a consequence the image is the sum of the point spread functions having the same weight as the point sources in the original object. If the microscope is space invariant then the image, gðx; yÞ, is a convolution of the object, f ðx; yÞ, and the point spread function, hðx; yÞ, of the microscope (Barsanti et al (1990)) then gðx; yÞ ¼ f ðx; yÞhðx; yÞ:
ð8:1Þ
If the illumination is coherent the convolution is related to the complex amplitude of the electromagnetic waves, whereas for incoherent illumination it has to be based upon the intensity (Castleman (1979) and Golay (1969)). Digitisation can be effected by considering two nonlinear, non-reversible operators; sampling, S, and quantisation, Cq (Painter (1965)), described by Fði; jÞ ¼ SfCq ½ f ðx; yÞg:
ð8:2Þ
Sampling and quantisation divide equally in the spatial domain. The spatial sampling is achieved by either moving a spot of light incident on the object along a given path and then measuring the total light intensity (Castleman (1979)) or illuminating the total image and measuring the light from one point at a time (Benedetti et al (1976, 1983)). Quantisation transforms a continuous range of either brightness or intensity values into a range of integer numbers. One example where computers have been used to enhance image quality is the use of aberration correction in electron optics (Batson et al (2002)). A new transmission electron microscope has been constructed which combines seven major optical elements, adding three octopole and four quadrupole lenses to the electron microscope. Computer measurement of the optical aberrations and control of the lenses are essential to achieve optimum performance. The optical performance is measured using a TV camera to view a ‘shadow map’ of randomly structured test samples, which is then analysed by the computer to produce corrections for the coils. With this correction the transmission electron microscope can achieve a resolution of about 0.075 nm compared with the previous resolution of 0.2 nm. Figure 8.4 shows the
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Figure 8.4. A transmission electron image of a sample of Si70 Ge30 viewed in the [110] projection, in which the dumbbell spacing is 0.135 nm without aberration correction (a) and with aberration correction (b).
performance of this transmission electron microscope without aberration correction (a) and with aberration correction (b) for a sample of Si70 Ge30 viewed in the [110] projection, in which the dumbbell spacing is 0.135 nm. Video images, such as the output of a scanning electron microscope, can be captured and stored using a video digitiser which converts the analogue video signal into a digital picture for storage in the computer memory (Saxton (1978)). Irrespective of the source, a monochrome digitised image is stored as an array of pixels each with a particular grey value: if colour images have to be stored then there is an additional requirement to include the red, green and blue components (Hayes (1989)). A typical framestore with 512 512 pixels has 256 grey levels. This is perhaps most easily compared with a typical size and quality of a monochrome television image which is 512 512 pixels, but with only 128 grey levels. The larger the number of bits (up to 12 bits represents 4096 grey levels) the greater the storage capacity so that more than one image can be stored and this provides a greater range of operations to be undertaken, i.e. Fourier pairs, edge maps or to use pseudocolour and look-up tables to aid interpretation. The limitations associated with the use of the standard mini computer, for the purposes of image storage and display, have been reduced by the use of framestores (figure 8.5). In essence a digital framestore comprises a block of digital computer memory that has been configured to handle image data. Indeed it can hold complete video images and often each image frame can be supplemented by overlay planes of graphical and alphanumeric data which can be added by the operator. A framestore usually has at least two parts for data transfer. The first is interfaced to the host computer to allow images to be written to the framestore and the second allows the data to be read at high speed; images may be read at standard
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Figure 8.5. A schematic arrangement for a digital framestore computer system.
television rates via the display. The rate at which the image can be transferred to the framestore using the computer port is determined by the host computer system and the type of interface. There is often a third port for effecting noise reduction in the image using a high-speed arithmetic unit. This allows either calculation of the average of a selected number of incoming image frames or recursive filtering of the image data continuously (Smith (1982) and Rosenfeld and Kak (1967)). Moreover, for interactive operation a cursor system is often provided to select regions of interest within the image.
8.5
Data processing and analysis
Whatever the acquisition and storage system, the image is stored in an ordered numerical form. Therefore the image becomes a matrix whose element, the pixel, corresponds to the smallest quantized detail. In this form a digital image can be processed algebraically to improve image quality and allow analysis of optical and morphological detail. Current processing techniques can be grouped into noise reduction, image enhancement and feature extraction and these functions can be performed using point, local and global algebraic operations (Barsanti et al (1990), Saxton (1978), Andrew et al (1970) and Goodman (1968)). Point operations are used where a value of each pixel obtained from the T function transformation is applied to the previous value of the pixel according to Gði; jÞ ¼ T½Fði; jÞ
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ð8:3Þ
Data processing and analysis
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Figure 8.6. The use of a logarithmic transfer function to expand the region of rapidly changing contrast in the original image (after Russ (1990)).
where Fði; jÞ is given by equation (8.2). Typical applications of these operations are histogram modifications. If the brightness values of the image extend over only a small proportion of the total range, the image contrast can be increased by substituting additional brightness values. The original and new images are related by the transfer function which can take a prescribed form. An example of this is the use of the logarithmic gamma function for photographic film. However, of more general help is the histogram equalisation method where an equal number of pixels in the finally produced image are assigned a grey level. Under these circumstances the transfer function can be determined from the brightness histogram of the initial image to establish the range of expansion so that in figure 8.6 the contrast in the rapidly changing region is expanded. These operations can be used interactively with look-up tables so that it is not necessary to operate on the original image to effect the transformation. Local operations Local operations are introduced where a new value of a pixel is a linear or nonlinear combination of the neighbouring pixels. For a linear combination the operation is a digital convolution, which involves running a 3 3 matrix, H, mask over the image (Rosenfeld and Kak (1967), Lohmann et al (1967) and Brown and Lohmanns (1966)). For each pass of the mask over the image the products of the corresponding pixels are calculated and a value for the sum of the products is assigned to the central pixel such that XX ð8:4Þ Gðm; nÞ ¼ Fðm s; n t0 ÞHðs; t0 Þ
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where t0 is a fixed threshold which degrades high frequencies which arise from noise. In the case of nonlinear combinations, instead of the product of the two matrices, a nonlinear law has to be used. Typical applications of these operations are enhancement and filtering of images. Global operations are used where the new value of a pixel is a function of those values of all the pixels that constitute the complete image (Rosenfeld and Kak (1967)). These transforms have the mathematical form XX Gðm; nÞ ¼ Fði; jÞAði; j; m; nÞ ð8:5Þ where Aði; j; m; nÞ is the kernel of the transform and Fði; jÞ is given by equation (8.2). 8.5.1
Spatial domain
Noise reduction The various devices which produce images have a contribution from noise to the digitised data introducing variations to individual pixels which are not spatially correlated. Noise can be either random, referred to as stochastic, or periodic. Random noise is commonly encountered and can be addressed in the simplest form by averaging together many acquired images. However, in general, individual pixels are significantly in error with respect to their neighbouring pixels and their contribution to the overall image. Such marked but random differences provide a basis for formulating many of the algorithms available for reducing noise in a single image (Castleman (1979), Rosenfeld and Kak (1982) and Pratt (1978)). Generally noise in an image has a higher spatial frequency spectrum than the normal image components simply because there is no spatial correlation. Simple low-pass spatial filters can be very effective in achieving noise smoothing (figure 8.7(a)). Unfortunately when applied without discrimination filtering techniques produce an out-of-focus image; reducing high spatial frequencies from the images leads blurring of edges and lines. This contribution is derived when an image is processed according to Gði; jÞ ¼ Gði; jÞ
ð8:6Þ
this is valid if ½8E ðA þ B þ C þ D þ E þ F þ G þ H þ IÞ > c where the pixels A to I are those comprising the 3 3 matrix of those in the neighbourhood of the value examined (figure 8.7(b)). For all other conditions then Gði; jÞ ¼ Fði; jÞ: ð8:7Þ It is possible to reduce deterministic errors in images such as a non-uniform field illumination and the shading introduced by variations in either the
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Figure 8.7. The basis for digital image processing (Barsanti et al (1990)): (a) A typical mask used for smoothing data. (b) Nomenclature of a 3 3 matrix of pixels. (c) Numerical example demonstrating the difference between the median value (1) and the mean value (10). (d) A typical mask used in an enhancement operation. (e) A typical mask used for edge detection.
illumination or the sensitivity of the specimen response. To achieve this, use is made of the algebraic operation of producing an output image that is the pixel by pixel quotient of two input images. Another nonlinear technique, median filtering, makes use of an algorithm which substitutes the value for the pixel being examined with the median value of those in the fixed neighbourhood (Frieden (1981)). The difference is due to the fact that the pixel values are not redistributed; only significantly noisy values for pixels are eliminated (figure 8.7(c)). Image enhancement Image enhancement by edge sharpening can be effected by using the simple H mask, kernel of multiplying factors, to act as a high-pass filter (figure 8.7(d)). This is a Laplacian operator, a non-directional second derivative that gives a zero result on any uniform or smoothly varying region of an image, but the change is large at edges, lines or points. When applied to an image these features are enhanced and areas of more uniform contrast are suppressed. A similar result can be achieved by subtracting from the original image an out-of-focus image obtained from a convolution of the original image and a low-pass filtered image. Edge enhancement is important when images are to be analysed to establish, for example, the volume fraction of the phases present or in high-resolution electron microscopy when evaluating atomic resolution images prior to more extensive processing or image analysis. Another defect encountered in an image is poor contrast, so that it becomes difficult to discern fine detail within the image. Poor contrast
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generally results from a reduced or nonlinear brightness range in the image. It is possible to improve the discrimination of the image detail by undertaking operations on the grey level histogram; unfortunately these procedures usually increase quantisation errors. Another technique used to improve the quality of monochrome image is to adopt pseudocolour mapping where each grey level is mapped on to an individual colour. This fact has a psychophysical motivation, since the human eye discriminates about 20 to 30 grey levels, whereas for the same conditions of light it can perceive hundreds of colours. As a consequence pseudocolour mapping is often adopted to provide a further contrast enhancement to an image (Cox and Sheppard (1983)). 8.5.2
Frequency domain
In addition to the discrete representation of an image by a consideration of individual pixels and their spatially related neighbours, an image may be described continuously. It is the latter approach provides the other main class of image processing which takes place in the frequency domain. This introduces the area of transform processing based upon, for example, the Fourier transform or other frequency transforms such as the Hadamand, cosine etc. (Smith (1982), Russ (1984, 1990), Russ and Russ (1986) and Levialdi (1982)). More usually, for ease of operation, the processing adopts the fast Fourier transform and is used to remove periodic noise, blurring and other artifacts that are present in the original image. An image may be described by a two-dimensional brightness function, f ðx; yÞ, such that ð1 ð1 f ðx; yÞ exp ½2iðux þ vyÞ dy dx ð8:8Þ Fðu; vÞ ¼ 1
1
where Fðu; vÞ is the Fourier transform of f ðx; yÞ, u and v are the spatial frequencies in the x and y directions respectively. The application of frequency domain processing is enhanced by the use of the fast Fourier transform. The computed fast Fourier transform of an image is essentially a power spectrum or diffraction pattern since the Fourier description of the image f ðx; yÞ is a linear combination of elementary periodic patterns, each component being weighted by the complex weighting function Fðu; vÞ which is the spectrum of f ðx; yÞ. This provides the ability to obtain information about both the image and the performance of the system that has been used to acquire that image. It is possible to obtain the latter information from optical diffraction systems but use of the fast Fourier transform enables processing to be computed on line. It is important to recognise that the continuous image f ðx; yÞ has to be sampled at more than twice the highest spatial frequency, otherwise moire´ fringes are introduced. The latter are produced when under-sampling the image and arise from aliasing contributions.
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An advantage of processing the transformed image is that it makes it easier to undertake convolutions since it becomes appropriate to multiply the transform of the image by the transform of the operator pixel by pixel. A convolution can be written, generally, as gðx; yÞ ¼
m X n X
hði; jÞf ðx i; y jÞ
ð8:9Þ
i¼1 j¼1
where f ðxyÞ is the original image, hðm; nÞ is the kernel and gðx; yÞ is the final image. If we consider frequency space this reduces to Gðu; vÞ ¼ Hðu; vÞFðu; vÞ
ð8:10Þ
where F, H and G are the frequency transforms of the image, kernel and the final image; the derived image can be obtained from the inverse transform. The function H, on the other hand, can be obtained from both calculation and measurement. If the original image is blurred or contains defects due to the acquisition system it can be measured directly using a point source image, otherwise the function is calculated from the image. In frequency space it is possible to smooth an image by multiplying the magnitude of the Fðu; vÞ function by a filter H. The filter in this case would comprise a circular symmetrical array of values decreasing with radius from U ¼ 0 to V ¼ 0. This suppresses the higher frequency information in the transform so that when retransformed to the spatial domain the image is smoothed. Irrespective of the type of transform used, all periodic arrangements in the image are mapped to the new image so that intensity variations in the image are transferred. Thus it is possible to separate repetitive and nonrepetitive information. Indeed for certain images it is possible to produce images equivalent to frequency space transforms by superposition, an approach adopted to remove the noise and enhance the periodic image of single atoms obtained in high resolution transmission electron micrographs of type shown in figure 6.49. 8.5.3
Feature extraction
Features are primitive characteristics or attributes of an image and to measure them it is necessary to distinguish them from the parent image. This can be defined either with respect to the pixel image or a specified boundary (figure 8.8). However, some features of the image like pixel brightness and object edges are natural, whereas others are artificial since they arise as a result of specific operations on the image, for example manipulation of grey level histograms. If edge extraction is the basis of a feature examination then the algorithms used have to contain two logical steps. The first increases high-contrast regions and the second extracts the feature by applying a threshold operation. By comparison linear extraction techniques introduce
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Figure 8.8. The feature shown can be defined either by the pixels or the specified boundary.
random noise and increase high frequencies due to contributions from both the image edges and stochastic noise (figure 8.7(e)). As a consequence it is better to use nonlinear combinations of the pixels before undertaking this particular thresholding operation. Under these conditions operators like Gradient Gði; jÞ ¼ jðA þ B þ CÞ ðG þ H þ IÞj þ jðA þ D þ GÞ ðC þ F þ HÞj ð8:11Þ where A to I are defined in figure 8.7(b), and Sobel sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½ðC þ 2F þ IÞ ðA þ 2D þ GÞ2 þ Gði; jÞ ¼ ½ðA þ 2B þ CÞ ðG þ 2H þ IÞ2
ð8:12Þ
are used very effectively (Saxton (1987), Saxton et al (1979), Hormann et al (1978), Yokato et al (1981), Erasmus et al (1980) and Hashimoto (1986)). Each of these edge detection operators are gradient operators since the magnitude of the response is to the steepest gradient in brightness of the image. Figure 8.9 shows the application of a Sobel operator to a part of an image where the values of 0 to 9 assigned to each pixel provide a measure of brightness. An extension of this approach is to substitute a thresholding operator with the additive coefficient in L module arithmetic Gði; jÞ ¼ ½Gði; jÞ þ L=2 mod ðLÞ
ð8:13Þ
which makes possible edge enhancement as a consequence of three-dimensional lateral illumination (Gualtieri (1982)). For a more comprehensive consideration the reader is referred to Russ (1990). To increase the ability to extract features it is possible to manipulate or edit the binary image. Most editing operations are performed in the digital
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Sobel Direction
Figure 8.9. Application of a Sobel operator to a portion of an image to provide edge enhancement (Russ (1990)) (reproduced by permission of Plenum Press).
images, where the spatial arrangement of the pixels is analysed either manually or using more complex routines. The latter leads to processes which combine images: for example, various X-ray elemental distribution and image maps obtained using the electron microprobe analyser based on Boolean logic operators (Russ and Russ (1986)) or local neighbour operations which dilate and erode images (Levialdi (1982)); the later process leads to skeletonisation (Russ (1984)). The skeleton of a feature is a medial axis transform and consists of the lines of pixels that define the midline of the feature. If the feature has projections these are revealed and retained in the skeleton and provide a method for describing the amount of branching. However, as shown in figure 8.10, it is possible to define other topological parameters of a feature such as links, nodes and ends. In this respect skeletonisation is a useful tool in providing a quantitative measure of microstructural specific features such as the grain size of a material. Certainly it is possible to establish the ASTM grain size number, d, directly from a skeletonized image d ¼ f½loge ðn =2Þ 1=½a loge z2
ð8:14Þ
where a is the image area and n the number of nodes. This technique has advantages since even in poorly prepared micrographs the grain boundary triple points can be identified because they usually etch preferentially. 8.5.4
Spectral manipulation
Many techniques described in the earlier chapters of this book utilise instruments that acquire a spectrum that takes the form of a number of counts
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Figure 8.10. A feature showing the skeleton and the main topological features: (a) branches, (b) ends, (c) nodes and (d) links.
versus a parameter such as energy. Such a spectrum will have been converted into two columns of numbers, counts and energy, which are then stored in the computer. The counts would frequently be in the form of an intensity which is converted to counts using an analogue-to-digital converter. The computer can then be used to apply algorithms to the data to perform a number of useful manipulations. In particular the data may be smoothed by the use of a Savitsky–Golay approximation or differentiated to detect regions of inflection on slowly varying backgrounds. Peaks from different elements in a spectrum may overlap with one another and here peak fitting routines may be applied to separate out the peaks from the several elements. Figure 8.11 shows a peak fit for an Auger spectrum in the energy range 460 to 535 eV where there is overlap between peaks from oxygen and chromium. Here a background is first subtracted and a number and position of likely peaks is input. The computer then iterates by varying the area, width and position of the peaks to give the best fit judged by a least-squares approach (Chatfield (1983)). The operator may restrict the degrees of freedom given to the computer by fixing either the width and/or position of the peaks, although this may result in a poor ultimate fit. Once the peak fit is complete the individual peak areas may be stored for subsequent use in quantification. A powerful and potential consideration for the analyses of data lies in the application of a range of statistical procedures. One example is the use of multivariate analysis (Hair et al (1983)) which allows the exploration of the relationship between the categorical independent variables and the dependent variables. This has been applied to Auger electron spectroscopy data acquired from the intergranular fracture facets of a 3.5 wt.% Ni ferritic steel. Here the microanalyses were undertaken on a number of matched intergranular fracture facets that were enriched or depleted in elements
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Figure 8.11. Peak fit in an Auger spectrum recorded from a stainless steel surface in the energy range 475–550 eV to extract the oxygen and chromium peaks.
such as nickel, phosphorus and tin. In this case the categorical variables are the time at which the measurement was made and the particular grain boundary facet, and the dependent variables are the specific elements analysed. Figure 8.12 shows the bivariate data for these three elements together with the derived correlation coefficients. In the case of phosphorus and tin there is a small negative correlation coefficient whereas the correlation between phosphorus and nickel is small and positive. A larger and positive correlation exists between nickel and tin. Flewitt et al (2002) demonstrate that these statistical correlations are consistent with previous experimental measurement and theoretical predictions. Various other applications of the use of multivariate statistical procedures have been described (Titchmarsh and Dunbill (1996) and Knowles and Titchmarsh (1997)). 8.5.5
Parallel data processing
An important feature of computers is their use to improve data collection, particularly the ability to collect from different sources simultaneously. Many of the analytical instruments described in the preceding chapters record signals from specimens by detecting electrons, photons or ions in a single energy channel during a particular time interval. Much saving in data acquisition times, together with a reduction in the dose of particles received at any plane on a surface, can be realised by collecting several signals in parallel. Characteristic X-rays, elastically scattered electrons, backscattered electrons, the current flowing from the specimen to ground and the
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Figure 8.12. Derived bivariate data for P, Sn and Ni together with derived correlation coefficients (Flewitt et al (2002)).
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total secondary electron yield can be used both individually and in combination to deduce crystallographic, chemical and topographic information. The pseudo-parallel image acquisition and multi-spectral analysis has been applied (i) to reduce the effects of surface topography (Prutton et al (1983)) and the effects on Auger yields of variations in backscattering factors due to changes in subsurface composition, (ii) to identify edge artifacts and to separate them from surface chemical composition variations (El Gomati et al (1988)) and unexpected surface phases (Prutton and El Gomati (1988)), (iii) to produce accurate quantitative Auger maps of the distribution of each chemical element in the surface of the specimen (Walker (1988)), (iv) to correct for artifacts arising from the curvature of the spectrum where there is no Auger peak (El Gomati and Walker (1988)), (v) to produce maps of the magnetisation vector in the surface of a ferromagnetic specimen (Browning et al (1990)) and (vi) to analyse SIMS images of surfaces (Bright et al (1988)). These demonstrations of the power of multi-spectral analysis methods are described in more detail by Prutton et al (1991) who have given them the generic title, multi-spectra Auger microscopy or MULSAM. Figure 8.13 shows the arrangement of the specimen and detectors in the MULSAM instrument at York University. It contains a set of four quadrants of Si p–n junctions that act as backscattered electron detectors (1), a Si(Li)
Figure 8.13. A schematic diagram of the multi-spectral Auger microscope (MULSAM) (reproduced by permission of John Wiley and Sons).
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Figure 8.14. A multi-spectral set (7 band) on Au/Si. The central vertical line of the Au overlay pattern is 1 mm wide. Beam energy 18 keV; beam current 1 nA. The images are 128 pixels square (Prutton et al (1991)) (reproduced by permission of John Wiley and Sons).
X-ray detector (2), a channeltron detecting very energetic scattered electrons (3), a 15-channel multistrip double channel plate detector (4), a channeltron to form the conventional SEM signal (5) and the specimen absorption current channel (6). The various signals from these detectors are used to form a set of 23 images. The power of the multiple acquisition is demonstrated in figure 8.14 where a set of seven simultaneous images obtained from an Au overlay pattern on an Si substrate are shown. SEM, sample current, ‘elastic’ channeltron, summed CHA strips at 100 eV kinetic energy and three of the BSE images are shown. The collection and disc-filing time for this set of images was 25 min. The histogram beside each image shows the intensity distribution in that image. The anticipated anti-correlation between the SEM and sample current images is very clear. The remaining images are correlated as might be expected.
8.6
Image quantification
The widespread availability of computers provides the capability to quantify images on a more routine basis. Indeed it is now possible with the present computing capability to use the procedures described in section 8.4 to quantify images; previously they have been too time-consuming to apply,
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apart from special applications. The range of image analysis systems, dedicated computers, now commercially available extends from those which have extensive computing capacity and can be operated flexibly to cover a wide range of applications to small systems either undertaking limited but general measurement or configured to undertake specific, defined measurements. Although the quantification of the microstructure of materials represents a considerable field we propose to restrict our considerations to an introduction of (i) image measurement, (ii) stereology and (iii) a consideration of fractal analysis. 8.6.1
Image measurement
When undertaking measurements on a defined image reference area it is possible to establish either global or individual feature measurements. A typical global measurement for a given microstructure is the area fraction, which is the area proportion of features embraced by the total selected pixel representation (Cruz-Orive and Werbel (1981)). The extension of this is to determine the number of features, such as second phase precipitates, to effect this. It is necessary to correct for those features that intersect the image frame to ensure that an unbiased total number of features per unit area of the image is counted (figure 8.15). One method to achieve this is to count all features contained completely in the frame and intersect one side; a feature intersecting two sides is not counted. A computing approach to this is to introduce an internal guard frame so that features that lie within this frame, but do not intersect any portion of the image frame, are measured and counted. Thus the reference area is the guard frame which should occupy an area which is about a quarter of the total image frame. Unfortunately this reduces the area and resolution of the images. Other methods for counting features are based upon image brightness so that the Sobel or gradient
Figure 8.15. Counting features within a defined image frame and the incorporation of a computer selected guard frame.
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operator, described in section 8.5.3, can be used to determine the orientation of the gradient which can be coded as brightness in a grey scale image. A histogram of the image represents the directions of the gradients in the image which determine either the mean or degree of preferred orientation which can arise, for example, from illumination or preparation in optical light microscopy. More usually there is a need to establish the detail of particular features contained within the overall image so that the main measurements required are (i) size, (ii) shape, (iii) position, (iv) brightness, and for each of these there are various parameters that can be measured or derived (DeHoff and Rhines (1968), Underwood (1970) Weibel (1979) and Hare et al (1982)). Size The simplest method of establishing the size of a feature is to count the number of pixels within the image; the area within the boundary. In addition to area it is necessary to be able to establish other parameters such as perimeter, length, breadth and width of the individual features (figure 8.16), since from these it is possible to derive parameters. For example, another estimate of the length of the 1 plate in a Cu-44% Zn alloy shown in figure 8.16 (see also figure 5.5) is available from the perimeter; the length is approximately half the perimeter. However, as the width becomes larger it is possible to establish length from the perimeter and area, assuming a constant width. Moreover in this particular case from the breadth and length it is possible to evaluate the included angle between the two plates, an essential input to establishing the habit plane of the plates (see figure 4.27). Clearly the image analysis method described in section 8.5 enables
Figure 8.16. A feature (1 plate in a phase matrix of a Cu–Zn alloy) shows the main size features area, length, breadth and width.
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these measurements to be made routinely using computer based systems (Shapiro (1978)). Shape Shape is an important description in recognising, selecting and characterising features (Pesce Defino et al (1990) and Exner and Hongardy (1988)) but unfortunately in practice this is a difficult parameter to establish. Shape factors tend to be dimensionless numbers and are usually obtained by combining size parameters in various ways. Probably the most widely used shape parameter is form factor, FF : FF ¼ 4A=r2p
ð8:15Þ
where A is the area and rp is the perimeter. The form factor for a circle is 1 and since any other shape has a greater perimeter for a given area the form factor establishes this; a square has a form factor of 0.785. Other factors such as roundness, aspect ratio, convexivity, solidity and extent are also used as descriptions of shape. An alternative approach to establishing shape is using spectral or harmonic analysis of the outline of the feature (figure 8.17) (Pesce Defino et al (1990), Exner and Hongardy (1988), Lestrel (1974), Flook (1982), Barth and Sun (1985) and Ehrlicl and Wernberg (1970)). A Fourier analysis is then carried out on the outline so that the magnitude of the radius vector is the summation of the terms shown in figure 8.17.
Figure 8.17. The feature profile plotted as a function of () where ¼ a0 þ a1 cos þ b1 sin þ a2 sin2 (Russ (1990)) (reproduced by permission of Plenum Press).
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Position Measurement of the position of a feature within the total image can be with respect to a global coordinate system or relative to other objects in units of length. This is often described by the coordinates of the centroid of the feature; the position at which the moment of the feature is minimised. The centroid is determined by integrating the moment of the feature about any coordinate axes and dividing by the area. Clearly this is best achieved by a pixel-based representation. Having established the position of a given feature it is frequently necessary and constructive to consider the interrelationship of this feature with other features within the image. One approach to measuring feature spacing and alignment has been described by Russ (1990) and is based upon use of a linear Hough transform. Atomic resolution transmission electron micrographs, such as figure 6.49, usually show alignment of atoms where the individual atom images are fuzzy so that it is difficult to establish spacing. The Hough transform reduces each line of atoms to a single point so that it becomes easier to locate the maximum in the brightness and determine the mean and standard deviation on the atom spacing. This enables small changes in the lattice parameter adjacent to specific crystallographic features to be evaluated. Brightness In addition to the pixel and boundary representations described, it is important to be able to use the grey scale data contained within the image to interrogate features. Unfortunately these particular data are not so readily usable for feature analysis within images. However, in some cases pronounced brightness and therefore image density information does allow brightness to be converted to optical density and stored. An example is the interpretation of electron diffraction patterns (figures 4.60 and 4.61), where the diffraction spot features are identified and from this the angular and interspot distances are measured. Thus it becomes possible to provide a solution to the patterns. 8.6.2
Stereology
Stereology describes the relationship between the two-dimensional measurements obtained from images and the three-dimensional structure from which many are derived (DeHoff and Rhines (1968), Underwood (1970) Weibel (1979) and Rhines and DeHoff (1986)). This is an important interrelationship for many of the microstructural images that are produced by the techniques described in the earlier chapters of this book. It is certainly not the intention to provide anything but a superficial consideration here and the reader is referred to the specific references on stereological interpretation (DeHoff and Rhines (1968), Underwood (1970) and Weibel (1979)) which are based
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Figure 8.18. Stereological examples of (a) plane-section image, (b) projection image and (c) finite section (Russ (1990)) (reproduced by permission of Plenum Press).
upon the mathematical concepts of geometrical probability. The broad types of measurement, global and feature, are described in section 8.5.1. Figure 8.18 sets out various two-dimensional images that would require stereological interpretations. The approach originates from that adopted by the metallographer who typically examines plane surfaces polished on bulk specimens; but this applies to any technique that provides two-dimensional image features. On many occasions it is necessary to determine the size of a three-dimensional phase from two-dimensional measurements, an example being the simple case of a distribution of spheres, typical for example of cavities or pores or precipitates of ordered 0 encountered in nickel-base superalloys. Figure 8.19 shows the size distribution of circular sections produced by randomly sectioning a sphere. This produces a frequency distribution (figure 8.19); large circles are produced when approaching the equatorial diameter. Although for this simple geometry it is not necessary to invoke computer techniques it is obvious that departures from this require performing large numbers of two-dimensional measurements and more complicated three-dimensional conversions where computer procedures are essential. When considering a distribution of spheres of a range of sizes, a frequency histogram of the size of the observed twodimensional circular sections is obtained which is a combination of several size distributions. However, it is possible to determine the coefficients that relate the number of circular features, N, in size class, i, due to random sectioning of spheres in size class j which is given by X ij NVj ð8:16Þ Ni ¼
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Figure 8.19. The determination of the size distribution of spheres from two-dimensional measurements (a) the circle distributions from intersectioning a sphere (b) the frequency distribution of circle sizes of random sectioning a sphere (Russ (1990)) (reproduced by permission of Plenum Press).
where NV is the total number of objects per unit volume. This matrix can be inverted to obtain the matrix, which can be stored and used to derive the true size distribution of the spherical features. 8.6.3
Three-dimensional images
Of the various methods and techniques described in this book only a few such as transmission electron microscopy or ultrasound microscopy provide an opportunity to interrogate the internal structure of the material directly. Even under these circumstances two-dimensional images are viewed. More generally, as described in the previous section, serial sections are invoked and these are then used to reconstruct the three-dimensional image. The principal distinction that has to be addressed for these images when serial section reconstruction is used is if the sections are continuous in space or separated by intervening gaps. In the case of elemental distribution maps (see section 7.5) if a single element is being monitored and the brightness is proportional to the concentration, the information is organised into voxels. These are volume elements comparable with pixels in the two-dimensional images. There are some cases where voxel images can be obtained directly, but these are usually the exception. Certainly
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tomographic reconstruction is one method that allows this (Herman (1980)) but more usually several section images are collected which represent planes through the three-dimensional body. However, these planes are usually separated by more than the lateral spacing of a pixel in each image, so that information in the intervening space is lost (Baba et al (1984)). As a consequence the three-dimensional reconstruction requires interpolation between planes. Such interpolation is undertaken readily if the structures vary gradually in size and position through the stacked images. Unfortunately it is more likely that the slices are spaced so that significant information is contained in the intervening space that is not interrogated. To match the objects or boundaries in the sequential slices it is necessary to examine the size, colour, density, shape and position of the objects in the images. Hence a one-to-one matching is not obvious and it is the start and finish and branching of solids, surfaces, interfaces and linear structures that need to be described unambiguously. Sometimes it is possible to interpolate the position of either an end or branch, figure 8.10, between two image planes by considering the shape of the object in the third dimension. It is only if the size or position of the objects in several images changes smoothly can an extrapolation be undertaken with confidence. Often this procedure is undertaken on isolated features selected by the operator. Although full three-dimensional modelling of objects including ends and branches (figure 8.10) can be undertaken using a range of procedures, the complexity of the problem demands substantial computing capability including the use of CAD/CAM systems and algorithms (Wang et al (1983), Fuchs et al (1982), Mayhew and Gundersen (1996), Gundersen and Jensen (1987), Mayhew (1997) and Reed and Howard (1999)). If by comparison the image planes are uniformly spaced and this is equal to, or less than, the pixel resolution, then combining images into a voxel element is possible. This approach provides a basis for a continuous model to describe sharp end and branches within the image. There are various ways to display the information: (i) features cannot be viewed directly unless part of the features are assumed transparent, (ii) any cutting surface, usually a plane, allows an image of features within that plane to be produced, (iii) use of a wire-frame stereo display with the advantages of obtaining density data and (iv) transparency or gel displays where each voxel is assigned a value of a measured property such as colour, composition etc. and these can be inverted to display a transparency coefficient. As a specific example for confocal microscopy the light in the transmission mode (section 5.5.2) passes through the same points on the specimen twice. A series of images for each section can be combined using the measured density of each plane. These images can then be used to show the three-dimensional arrangement of the image by rotating the entire voxel array. Computer simulations have been used to examine the interrelationship between the two- and three-dimensional distributions of grains in materials
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Figure 8.20. Computer two-dimensional image obtained from a regular distribution of equal size polyhedral grains (Crocker et al (1987)).
(Crocker et al (1987)). Figure 8.20 shows a computed random two-dimensional section obtained from a three-dimensional uniform distribution of polyhedral grains. In general, computing procedures offer the potential for the stereological interpretation of images and if combined with adequate pattern recognition procedures could provide rapid and true interpretation of two-dimensional images. True three-dimensional images can be produced using incident sources such as X-rays and then tomographic techniques used to reconstruct the images. These approaches are based upon fundamental theory developed by Radon (1917). Although originally applied in the medical field it has increasingly found applications for interrogating materials more generally. This has led to various considerations including microtomography (Sasov (1987), Cazaux (1993) and Sasov and Van Dyke (1998)). As an example figure 8.21 shows an X-ray shadow image of a block of composite material,
Figure 8.21. Shadow X-ray image of composite material (a), reconstructed cross-section (b) and partial reconstruction of fibre welding (c).
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fibre reinforced plastic foam. The reconstructed cross-section (figure 8.21(b)) reveals the periodic fibre structure and figure 8.21(c) provides more detail of the foam and fibre structure. 8.6.4
Fractal analysis
The concept of fractals (fractal, Latin for irregular) in evaluating irregular shapes has been developed mainly as a consequence of the increasing availability of computer graphics. Essentially it provides a basis for examining the geometry of objects which are irregular on a fine scale so that classical geometrical and mathematical procedures cannot be applied. As a consequence fractal geometry offers a tool to study highly irregular surfaces typical of those encountered in fracture (Mandlebrot (1967) and Dauskardt et al (1990)) and indeed microstructural features in general (Hornbogen (1989) and Mandlebrot (1983)). The definition of the fractal dimension is difficult and has been probably best summarized by Mandlebrot (1967). From a recognised mathematical approach a set of points exhibit fractal behaviour when the fractal dimension is non-integer (Von Koch (1906)) having fractional values between those of the intuitive topological dimensions. An example of the fractal character of a system is the measurement of the length of continental coast lines (Richardson (1961)) where the length measured depends upon the measuring scale. An operational definition for the fractal behaviour of a set of points is given by the Richardson structured walk method which is analogous to walking a pair of dividers with a fixed span along any given boundary line and counting the number of steps. Mandlebrot (1967) observed that the length of a coastline depends on the basis of measurement since as the scale of the interrogation becomes finer so the length increases, almost without limit. This led Mandlebrot to conclude that shapes similar to coastlines lie ‘between dimensions’ so that they are not one-, two- or three-dimensional but rather they have a fractal, non-integral, dimension. Under these circumstances Euclidean geometry is no longer appropriate. The simplest example of fractals are those identical at each scale or level. Mandlebrot (1967) modelled a shape, such as a coastline, by choosing an initiator, a straight line, and applied a generator to introduce the appropriate irregularity into the line (figure 8.22(a)). The generator shown is based on dividing the line into three equal parts and then extending the length by displacing the centre part along two sides of an equilateral triangle. The resulting line is now 4/3 times the length of the initiator. Applying the generator and repeating this procedure for each individual new length increases the total length again by 4/3 and produces a further, but smaller, irregularity. By applying this recursive process to a triangle as the initiator results in a Koch curve or ‘snow flake’ (figure 8.22(b)).
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Figure 8.22. (a) Fractal initiator and generator which when applied in (b) to the sides of a triangle produce the so-called Koch snow flake.
Mandlebrot (1967) defines the fractal dimension DF in terms of the number of parts of an object generated, N, and the similarity ratio 1=r which is used to divide the initiator such that DF ¼ log N= logð1=rÞ:
ð8:17Þ
For the Kock snow flake shown in figure 8.22(b), N equals 4 and 1=r is 1/3 such that D equals 1.26. Moreover a relationship exists between the observed surface area, AS , and the scale, E (Hornbogen (1989)). AS ¼ C0 E 2 DF
ð8:18Þ
where C0 is a constant. This leads to the conclusion that the area of a given rough surface has meaning only if the scale is defined. In addition, surfaces can be characterized by the angular distribution of the linear segments along the profile to give a measure of the angular deflection; the average deviation of the segment normals from a predefined reference direction. Such an approach is appropriate to the analysis of, for example, a crack path or a fracture surface profile. Fracture surface topography derived from optical micrographs or scanning electron micrographs can be simulated using defined distributions of segments to represent the microstructural dimension. As shown by
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Figure 8.23. Model used to simulate fracture profiles using normal distributions of segment lengths with mean, standard deviation and angular deviation. The model incorporates (a) a single distribution of segment lengths for macroroughness ðPðLÞ ¼ 1=2m Þ1=2 exp½ðL MÞ2 =2m Þ and (b) a second smaller distribution to represent the superimposed microroughness (reproduced by permission of Plenum Press).
Dauskardt et al (1990) the model incorporates known distributions of interconnected segment lengths selected to describe the macro and microscopic roughness of the fracture surface figure 8.23. Macro-roughness is simulated by a normal distribution of segmented lengths with a defined mean and standard deviation (figure 8.23(a)). Computer code generates a digitized profile by selecting segmented lengths and connecting at fixed
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Table 8.1. Comparison of fractal dimensions and validity ranges for fractal behaviour with characteristic microstructural and fractographic dimensions (Dauskardt et al (1990)). Size range and (mean value) (mm)
Range of fractal value (mm)
Fractal dimension (DF )
Feature mode
Structural feature
AISI 1008 Steel: Transgranular cleavage
grain size cleavage steps
10 to 75(28) 2 to 15(15)
15 to 75 1 to 15
1.08 1.02
particle spacing slip steps grain size grain boundary particle spacing grain boundary slip steps
6 to 50(20) 0.8 to 4(1) 20 to 150(56) 6 to 15(10)
5 to 150 0.6 to 5 35 to 200 6 to 20
1.18 1.06 1.26 1.09
0.8 to 4(1)
0.6 to 5
1.06
50 to 200(100) 1 to 31 50 to 200 2 to 70 250 to 440(300)
80 to 1000 0.6 to 80 80 to 1000 0.6 to 80 200 to 1000
1.01 1.08 1.06 1.12 1.04
5 to 100(19) 0.4 to 3(1)
10 to 200 0.6 to 9
1.14 1.08
Mn-Steel: Microvoid coalescence Intergranular fracture
A533B Steel: Quasicleavage (196 8C) (H charged) Ductile intergranular (H attacked)
grain size ‘flag segments’ grain size ‘flat segments’ banded structure and fissures grain size methane bubble size
angles, to the horizontal, to establish independently the contribution to fractal dimension. Micro-roughness, on the other hand, is derived by imposing a second normal distribution of segment lengths with a smaller mean and standard deviation (figure 8.23(b)). The simulated profiles can then be analysed using a procedure similar to that for measuring true surface profile. Table 8.1 shows the microstructural and fractographic dimensions for five distinct fracture morphologies (Dauskardt et al (1990)). For transgranular cleavage, brittle and ductile intergranular cracking quasicleavage and microvoid coalescence fracture mechanisms. Fractal character is not a singular mode but good correlation exists between the extent of fractal behaviour and several key microstructural and fractographic features over a wide range of dimensions appropriate to the size distribution of those features. Fractal analysis has been applied to the characterisation of fracture surfaces in ferritic steels where the relationship between the fractal dimension, DF , and the material microstructure has been investigated (Spain
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Figure 8.24. Impact toughness as a function of fractal dimension by means of slit island analysis for steel tempered at different temperatures (Huang et al (1990)).
(1998)). However, determination of the fractal dimension is not straightforward and several methods have been devised to achieve this end including the slit island method (Pande et al (1987)), the vertical section method (Mandelbrot et al (1984)) and secondary electron line scanning (Huang et al (1989)). The fractal dimension has been plotted against materials properties in a number of studies. Charpy impact energy plotted against fractal dimensional increment shows that the fractal dimension decreases with increasing impact energy (Mandelbrot et al (1984)) but the fractal dimension is shown to increase with tempering temperature or impact toughness (Huang et al (1989)). Huang et al (1990) demonstrated that the method of measurement determined the nature of the correlation between fractal dimension and material property. They used the slit island method in which they measured both the islands within lakes and lakes containing islands to obtain a converging correlation. Figure 8.24 shows the impact toughness as a function of fractal dimension for steel tempered at different temperatures. Despite these problems, resulting from measurement methods, it is generally agreed that fractal analysis offers a way forward for characterising fracture surfaces. Indeed fractal analysis has been applied to the study of both transgranular and intergranular fracture (Zhang and Lung (1989) and Shu et al (1993)) where models have been developed which demonstrate a correlation between fractal dimension and material property (Shi et al (1997)). As discussed in the first chapter of this book, fractal analysis may provide the way forward for the quantitative evaluation of microstructures of materials that have been difficult to accommodate by more conventional procedures (Hornbogen (1989)). For example a material that is recrystallized the grain boundaries tend to be planar with minimum curvature, but containing steps and dislocations and as a consequence the fractal dimension, DF ,
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Figure 8.25. Schematic grain structure in a recrystallised material: (a) non-fractal, (b) fractal (Dauskardt et al (1990)) (reproduced by permission of Pergamon Press).
lies close to a value of equation 8.18 (figure 8.25). Certainly in this condition there is a valid interrelationship between the grain boundary and the feature density and spacing.
8.7
Data bases
As local computing power grows it is inevitable that these systems become routine tools and therefore many programs, generic sub-routines and data bases are now being produced. The capacity of computers to store and retrieve large quantities of data makes them well suited for storing data bases. As discussed in chapter 4 one method for quantitative analysis of the microstructure of materials is using X-ray diffraction techniques based upon the measurement of the interplanar spacings of crystalline phases so that they can be identified from the position and the relative intensities of the peaks in the diffraction patterns. Since the data are characteristic of the crystalline material, for a given incident X-radiation, files have been assembled as a result of the cooperative effort of a large number of investigators (Barrett and Massalski (1966)). Indeed the powder data file was initiated by Hanawalt, Rinn and Frevel (Hanawalt et al (1938)) and has over the intervening years been expanded and continuously updated (Sagel (1958), Powder Diffraction File (1969–74) and National Bureau of Standards (1973, 1978)). This has culminated in a version that is issued annually by the International Centre for Diffraction Data (1988). This particular data base was a precursor to the computer data bases now available in other areas but readily transferred to a computer system. The existence of this data base is the main tool available
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Figure 8.26. A comparison between the X-ray diffraction trace obtained from an extracted carbide precipitate and the stored data base.
for characterising materials by X-ray diffraction. Indeed it is now possible to have this base on a mini computer interfaced directly with an X-ray diffractometer so that a direct comparison with the X-ray diffraction pattern from the unknown can be compared and rapidly identified. Figure 8.26 shows a comparison between a carbide precipitate extracted from a low-alloy ferritic steel and that stored in the data base. Obviously the advantage of the computer data base lies in the large amount of standard data that can be stored and the fact that it can be rapidly interrogated and sorted on a simple comparative basis such as matching the diffraction angular position and intensity of the eight most intense diffraction peaks. Recently initiatives have been taken to share both data bases and the general programs available in the area of electron microscopy and microanalysis by establishing jointly a public domain software library with the Electron Microscopy Centre at the Argonne National Laboratory (USA) and the Bulletin of the Electron Microscopy Society of America (EMSA) (Zaluzec (1989a,b). The purpose of this particular library is to make available, to the scientific community working in the non-commercial public domain, software useful to researches worldwide. Access to this information is free of charge to users of a range of computer hardware who can access the software data base for that research using conventional telecommunication protocols. The Electron Microscopy and Microanalysis Public Domain Library is an interactive library where users access a central computer to view selected files, abstracts, documentation and source code listings of programs and data which the user community has contributed to the public domain. Clearly this approach
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adopted in electron microscopy provides a way forward that can be adopted at various levels, international, national or simply institutional for accumulating data bases. Clearly it heralds an approach of collaboration in the scientific community that is developing rapidly via the ability to communicate through the vehicle of the World Wide Web.
8.8
Data transfer
As mentioned earlier, computers are used for processing captured data by adopting routines from a built-in set of options for peak synthesis, background subtraction, peak area measurement, quantification, smoothing, differentiation etc. However, operators and analysts process these data on a remote computer using customised programs where encoded data in the capture computer is in a form suitable for transmission and then decode it into the form required in the receiving computer. Instrument manufacturers’ data formats all differ and this may be the case even between models from the same manufacturer. The operator is rarely given access to the format, making it very difficult to work on the data other than by using the dedicated computer. A standard format is therefore required for transferring data which would be incorporated in each instruments software. Dench et al (1988) developed at the National Physical Laboratory, as part of a VAMAS sponsored programme, a prototype data transfer format. This has since been improved and as a work programme within the British Standards Institute and the International Standards Organisation under ISO/TC201/SC3 has been approved as the internationally recognised standard for data transfer (ISO 14976 (1998)). This format transfers data via parallel or serial interfaces and is suitable for a range of techniques described in this book including AES, EDX, FABMS, ISS, SIMS, SNMS, UPS, XPS, XRF and similar analytical methods. It covers transfer of spectra, element maps, depth profiles and sequences of data resulting from a variety of experiments.
8.9
Expert systems
Many of the techniques described in this book have reached a stage where they can be used routinely to obtain quantitative data about the microstructure of materials. Indeed manufacturers provide computer data handling systems for processing the output data from various systems. This leads us to consider the benefits to be achieved from an Expert system either as a simple assistance to a non-expert or as a complete diagnostic tool. For those less familiar with this particular computing term the British Computer Society defines an Expert system as ‘the embodiment within a computer of a knowledge-based component from an expert skill in such a
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form that the system can offer intelligent advice or take an intelligent decision about the processing function. A desirable additional characteristic, which many consider to be fundamental, is the capability of the system to justify a line of reasoning directly to the user. The style adopted to attain these characteristics is rule-based programming. There are three major parts to any Expert system: (i) a knowledge and data base, (ii) a computer program or inference engine and (iii) an interface with the user (Jacobs et al (1985, 1986)). Moreover the system should allow the user and the computer to interact, leading to an output of advice to the user. Indeed in some sophisticated systems an explanation module is included which allows the user to challenge the conclusions reached by the system and interrogate the basis leading to the conclusion achieved (Gevanter (1983)). Expert systems differ from more conventional computer programs because the knowledge relevant to the problem and methods for using this knowledge are interwoven so that it becomes difficult to change the program. In Expert systems the various components are separated, the knowledge base, from information about the current problem, input data and each from the methods inference engine. These divisions are adopted so that it is possible to invoke simple modifications. Indeed an Expert system shell is simply a complete system but with the knowledge base empty. However, such a shell provides a readily available base for producing a specific Expert system. In Expert systems it is not necessary to specify the strategy for turning the statement of the problem into a computable form since this is achieved by the existing computer program or inference engine. However it is essential for the specified problem to be compatible with the specific notation of this central program since this can influence the effectiveness of the finally produced Expert system for a given application (Alty and Coombs (1984)). There are now many software houses producing programs that form the basic building blocks of an Expert system and as a result there has been an increase in interest to develop Expert systems. Baker et al (1990) have addressed the requirements for an Expert system for use in electron spectroscopy. This system allows the main information to be extracted from spectra, but in addition also secondary features are considered so that by inclusion of appropriate physical interpretative rules it is possible to quantify and interpret the surface structure and the depth distribution of elements within specimens. The availability and completion of data bases is an essential input to these Expert systems. Thus the Expert system will also advise a non-expert user how to obtain additional information from the surface of a specimen. To assist in providing the correct input to the Expert system shell Baker et al (1990) considered other relevant Expert systems drawn mainly from the medical and biological fields where developments have been more advanced (Engelmore and Terry (1979), Wong (1984), Johnson (1981), Baas and Bourne (1984) and Gorbov et al (1977)). If the
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Expert system is to meet the needs of the user, it is necessary that the shell is configured so that rules can be added or deleted; rules are used intelligently to reach conclusions, and the system can be run in real time and indeed be extendable in all directions. Thus the input requires validated rules and programs that represent the state of knowledge at the time of formulation and the output for the user will be the concentration and distribution of elements with depth into the specimen together with an estimate of the confidence for each value. A route to achieve this output is given in the flow diagram (figure 8.27) where each step requires a logic argument to be applied, and to achieve
Figure 8.27. A flow diagram leading to the output for an electron spectroscopy measurement (Baker et al (1990)) (Courtesy J Castle).
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Figure 8.28. Rules/algorithms incorporated in ‘QUASES’ software (i) to estimate in depth distribution of atoms (ii) determine the total amount of substance within the surface region of a solids, (iii) the decay length and (iv) the morphology of the surface composition with naometer depth resolution (Tougaard (1987, 1991, 1998)).
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this rules derived by the instrument user have to be applied rigorously. Castle and Baker (1999) have developed a real-time XPS rule set to describe carbon contamination on a specimen surface. By reformulating the carbon contamination rules, a way for constructing a real-life rule set is presented. For example, the carbon 1s signal can be used to determine the thickness of the carbon contamination layer which can then be used to correct the quantification. The development of an Expert system for X-ray photoelectron spectroscopy (XPS) (34th IUVSTA Workshop, 2002, St Malo, France) includes expert knowledge such as the use of shake-up satellites and the Auger parameter to provide chemical state information. Tougaard (1987, 1991, 1998) has developed software incorporating algorithms that permit the determination of in depth information of near surface atoms. The various possibilities are illustrated schematically in figure 8.28. This approach has produced rules/algorithms which are incorporated in ‘QUASES’ software to (i) estimate in depth distribution of atoms (Tougaard (1987)), and to determine (ii) the total amount of substance within the surface region of a solids, (iii) the decay length (Tougaard (1991)) and (iv) the morphology of the surface composition with nanometre depth resolution (Tougaard (1998)). Increasingly Expert systems will assume a greater importance in the application and use of techniques described in this book. One reason for this is that many users frequently require results from a specialist technique where they may have only knowledge of the underlying principles, but the information produced by the technique is essential to solve the specific physical problem. Moreover the growth of Expert systems combined with increased computer capability and access will lead to significant changes in the way the user interacts with the information produced by the sophisticated techniques now available to evaluate the microstructures of materials.
8.10
Computer simulation
When the first edition of this book was published computer simulations of significant value required the use of ‘super computers’ such as the Cray XMP and therefore were not generally available. Within the past ten years the power, speed and memory capacity of personal computers has increased, and is still increasing at such a rate that most computer simulations can be carried out by any dedicated researcher. With appropriate approximations it becomes possible to prepare experiments in the computer to investigate the interatomic forces on atoms and thereby examine the structure of materials. They offer the ability to study a range of problems that will ultimately assist the interpretation of microstructures and their relationship with the mechanical and physical properties described in chapter 1. We will now consider three examples, selected to span a wide range of scale dimensions
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from the nano to the microscale. However, they also provide the link to the various microstructural changes that can be investigated using the techniques described in the previous chapters of this book. These are (i) irradiation damage that leads to changes in the yield strength and fracture toughness, (ii) non-hardening segregation that changes the fracture mode and (iii) a consideration of the fracture mode itself. (i) Neutron irradiation damage. Defect production in metals subjected to fast neutron irradiation from power reactor cores is initiated by displacement cascades. Molecular dynamics (MD) computer simulation provides a powerful means of investigating these events and the atomic mechanisms that lead to defect production and clustering in cascades have been reviewed elsewhere (Bacon and Diaz (1994) and Calder and Bacon (1993)). Two key features of cascade damage have been recognised. First, the number of Frenkel pairs, Np , generated by displacement cascades is calculated to be smaller (20–40) than that predicted by the Norgett, Robinson and Torrens standard formula (Norgett et al (1975)). Second, computer simulation has revealed that many of the self-interstitial atoms created in cascades are in clusters, and the probability of clustering and the size of the largest cluster tends to increase with increasing primary knock-on atom energy and temperature (Kinney et al (1984)). It also found that some of these clusters form as interstitial dislocation loops. In bcc -iron these loops have a perfect Burgers’ vector, b, equal to 1/2 h111i, and they can move conservatively on their glide prism plane. Such ‘glissile’ clusters have a high binding energy and can migrate away from their parent cascades to be absorbed preferentially at sinks such as dislocations and grain boundaries. This provides an explanation as to why some specific microstructure features which arise from cascades cannot be modelled using the conventional rate theory approach based on three-dimensional single defect reaction kinetics. The model size employed is selected to be typically a cube 30a 30a 30a (54 000 atoms) where a is the bcc lattice parameter, or 40a 40a 40a (128 000 atoms). A MD program that can be used is the vectorised MOLDY code modified for the bcc structure. To simulate a cascade, a block is first equilibrated for >10 ps at a temperature of 100 K. After the primary knock-on atom was initiated the crystal is allowed to evolve for 10 ps. The approximations in the model are: (i) heat is not extracted from the cell after the cascade had started, (ii) there is no electron phonon coupling and (iii) the cohesive term in the many-body potential is isotropic and does not include the angular nature of bonding. Examples of visualisations of vacant lattice sites and atoms displaced to interstitial positions during two of the 5 keV and 5 keV overlap simulations are given in figure 8.29 (Gao et al 1996)). The data for the final number of Frenkel pairs as a function of separation, Rpp , for the first sets of overlap conditions at 100 K, are given in figure 8.30. There is a clear trend towards decreasing
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Figure 8.29. Computer generated visualisations of three stages in the evolution of two different simulations of a 5 keV cascade impinging on damage left by prior 5 keV cascade in a crystal at 100 K. The top image is the initial debris consisting of 18 Frenkel pairs. The event on the left results in weak overlap, with Rpp ¼ 7:43a <;, and that on the right involves strong overlap with Rpp ¼ 3:13a <;. Atoms displaced to interstitial sites are shown as large, open spheres and vacant sites are indicated by small solid spheres. The block size is 40a0 40a0 40a0 (Gao et al 1996)).
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Figure 8.30. The total number of Frenkel pairs remaining after the cascade overlap simulations in a crystal at 100 K is plotted as a function of separation parameter Rpp for 5 keV overlap with 5 keV charge. The value of Nf for the initial cascade is given and the equation that fits the data is shown in the inset.
defect numbers as the overlap distance decreases. Here the modelling provides an insight into the development of point defect damage that leads to changes in the yield strength and fracture toughness of pressure vessel steels. These defects can be investigated by high resolution transmission electron microscopy as described in section 6.4.6. (ii) Irradiation-induced segregation. Irradiation-induced segregation mechanisms can be described by inverse Kirkendall models or solute-point-defect complex models (Faulkner et al (1996) and Flewitt and Wild (2001)). Such segregation is recognised to have a significant effect on the non-hardening contributions, see chapter 6, and can lead to a change in the brittle fracture mode from cleavage to intergranular. Solute atoms, point-defects and their complexes are in equilibrium with each other at a given temperature. The complex formed during neutron irradiation is important to solute migration in dilute alloys because (i) the migration of solute interstitial complexes is easier than solute–vacancy complexes and (ii) the interaction of under-sized solute atoms with a self interstitial is stronger than with a vacancy. As a consequence, for solute atoms which have strong interactions with interstitial atoms, for example, phosphorous in steels, the diffusion of solute interstitial complexes should be dominant in neutron irradiation-induced
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Figure 8.31. The grain boundary segregation during neutron irradiation of (a) phosphorus in Fe: 0.072 at. P-C (0,10,100 and 1000 appro C) alloy, and of (b) carbon in Fe: 0.001 at. CP (0 and 720 appm P) alloy as a function of irradiation temperature, predicted by the site competition model (p0 ¼ 1016m002 , R ¼ 10 mm, dose rate ¼ 10008 dpa s01 , dose ¼ 1 dpaÞ.
segregation. An example of the application of this atomic scale modelling is solute segregation in dilute ternary Fe–C–P alloys which takes into account solute–solute competition for segregation sites at the grain boundary. Here solute–interstitial and solute–vacancy complex contributions are treated separately to determine if one is dominant in neutron irradiationinduced non-equilibrium segregation. The predicted grain boundary composition of phosphorous during neutron irradiation from this, the site competition model with different free carbon concentrations, is given in figure 8.31(a) as a function of irradiation temperature. Clearly phosphorous segregation is shown to be suppressed, notably at lower temperatures, due to the competition of free carbon with phosphorous for segregation sites. Carbon segregation is dominant in this alloy and is somewhat influenced by the site competition of phosphorous with carbon in the high-temperature
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range (figure 8.31(b)). This indicates clearly that grain boundary segregation of phosphorous during neutron irradiation in ferritic steels is predicted to be restrained, especially at lower temperatures, by minor changes in free carbon content in the ferritic phase. These grain boundary compositions can be investigated by a range of high-resolution microanalytical techniques including FEG–STEM, EDS and Auger electron sepectroscopy (see sections 6.4.6 and 6.6.6). (iii) Fracture processes. Modelling at the microscale can be used to describe fracture processes that occur in ferritic steels. In addition to cleavage fracture, brittle intergranular fracture can arise if, as described above, certain alloying or impurity elements, mostly from Groups IVB to VIB of the Periodic Table of Elements segregate to grain boundaries (Cottrell (1989) and Hondros and McLean (1995)). Of particular interest is the segregation of phosphorus to grain boundaries which can modify the proportion of intergranular fracture (Flewitt and Wild (2001)). Theoretical, geometrical models (Crocker et al (1999) and Flewitt et al (1998)) have been developed to address crack initiation and propagation in the brittle fracture regime to take account of cleavage and intergranular fracture and contributions from the grain boundary energy. Various threeand two-dimensional models have been developed (Smith et al (2002)). For the three-dimensional models the well known array of tetradidecahedra (14-hedra) filling space has been adopted together with various extensions to these. In the simple applications it is assumed that crystallographic orientations of grains are distributed randomly, only cleavage or brittle grain boundary failure may occur, cleavage is on one of three variants of {100} and fracture facets are as close as possible to being perpendicular to the stress axis. However, to model more complex situations these assumptions are relaxed. In these models a cleavage crack crossing a grain meets, on average, six grain boundaries. Thus propagation of fracture through a polycrystal may also be represented topologically using a simplified model consisting of regular array of parallel hexagonal prisms (Smith et al (2002, 1997)) or, indeed, a random array of parallel polygonal prisms. Such models are intermediate between two and three dimensions and can be effective in tackling selective problems. In order to model the embrittlement of grain boundaries arising from segregation of impurity elements such as phosphorus the relative energies of boundaries have to be considered. In particular a ratio of cleavage to grain boundary fracture energy, a range of grain boundary energies and a possible bias of these energies according to orientation relative to the stress axis have to be introduced. Figure 8.32 shows a perspective view of a fracture surface across twelve complete prismatic grains. The predictions of such models can be compared with the fracture surfaces characterized in materials using scanning electron optical techniques (section 6.2).
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Figure 8.32. The two-dimensional model used in the calculation of the effect of grain boundary embrittlement arising from a change in composition.
In general, multi-scale modelling provides a powerful tool to assist in interpreting the microstructure of materials over the scale range considered in this book.
8.11
Future developments
Various computer developments in the past decade have become available to the user investigating the microstructure of materials. In particular wide area and local area networks for linking computers and peripheral equipment into unified systems have potential considerable benefit, both for greater flexibility of operation and minimising the overall cost. Data can be passed between components of a network quickly and there are several environments for local area networks. Certainly where several computers control instruments within a given laboratory the use of a local area network provides considerable economies through the shared use of disc and other peripheral resources such as printer plotters, hard copy output of image data etc. Such a network can be further integrated into a wide network external to the laboratory, extending further the possibilities of shared resources, transmission of data and indeed communication of data. Unfortunately the manufacturers of many instruments used to investigate the microstructure of materials have established computer systems which are dedicated and stand alone for their particular instrument. Thus they are not well suited to networking; this parochial approach must be considered in the future to ensure systems of appropriate cost and flexibility are provided to the user. An important philosophical consideration that impacts directly on the interpretation of microstructures is set out by Trebbia and Manoubi (1989). They stress that the observer’s eyes and brain are part of the experimental
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interpretation which is in itself dependent upon various factors including preknowledge: the existing comparative data base. With the advent of the ability to process signals and images extensively by computer techniques it offers the capability of bias from both pre-experimental feeling, and processed computer data. Trebbia and Manonbi (1989) cite the drawing by M C Escher entitled ‘Air and Water’ made in 1938 (Escher (1988)) as an illustration of these speculations. Figure 8.33(a) is the original Escher picture which outlines the motifs of
Figure 8.33. (a) Simulation of an experimental measurement and analysis. (b) The interpretation. (c) The true signal. (d) The original 1938 Escher drawing ‘Air and Water’ (Escher (1988)) where the centre line AB from the image from which (a) is taken has the lowest signal-to-noise ratio (Trebbia and Manoubi (1989)) (reproduced by permission of Elsevier Science Publishers).
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both duck and fish which are progressively weakened, repeated and interwoven in such a way that the central line, AB, is the area in the image with the lowest signal-to-noise ratio. They consider figure 8.33 is the result of a measurement which indeed shows some periodicity. If the white areas alone are considered the signal is a fish. It is then possible to process this ‘result’ by filtering, contrast enhancement and other sophisticated computer based procedures to establish the image to be a fish (figure 8.33(b)); unfortunately the true answer could also be a duck (figure 8.33(c)). The problem, therefore, is the need to retrieve a perfectly determined, but unknown property of an object from data values obtained in an experiment. If the experiment is conducted under an appropriate protocol, these values are random variables which can be processed by appropriate statistical methods (Lawless (1982)). If these methods are introduced into computer programs it is possible to reduce the subjective bias in the interpretation by use of these objective procedures. Moreover, statistics can assist in the control of the experimental protocol and the basic hypothesis on a regular basis to allow conclusions to be drawn about the specific unknown at a given level of confidence (Trebbia (1988)).
8.12
References
Alty J L and Coombs M J 1984 Expert Systems Concepts and Examples (Manchester: NCC Publications) p 137 Andrew H C, Pratt W K and Caspari K 1970 Computer Techniques in Image Processing (London: Academic Press) Baas L and Bourne R J 1984 IEEE Transactions on Biomedical Engineering 31 660 Baba N, Naka M, Minamaka Y, Nakamura S, Kino I and Kanaya K 1984 Micron Microsc. Acta 15 221 Bacon D J and Diaz de la Rubia T J 1994 Nucl. Mater. 216 275 Baggott L M and Watson K 1997 Microsc. Anal. 61 67 Baker M B, Castle J E and Ahmad K 1990 Private Communication Barrett C S and Massalski T B 1966 Structure of Metals (London: McGraw-Hill) Barsanti L, Coltelli P, Passarelli V and Gualtieri P 1990 Microsc. Anal. Nov 19 Barth H G and Sun S-T 1985 Anal. Chem. 57 151R Batson P E, Dellby N and Krivanek O L 2002 Nature 418 617 Benedetti P A, Bianchini G and Chiti G 1976 Appl. Optics 15 2554 Benedetti P A, Coltelli P, Evangelista W and Gualtieri P 1983 Atti VI Congresso SIPBAGNCB Bright D S, Newbury D E and Marinenko R B 1988 Microbeam Analysis ed D E Newbury (San Francisco: San Francisco Press) p 18 Brown R B and Lohmanns A W 1966 Appl. Optics 6 967 Browning R, Van Zandt T, Helms C R and Poppa H 1990 J. Electron Spectrosc. Relat. Phenom. 51 321 Calder A F and Bacon D J 1993 J. Nucl. Mater. 207 22 Castle J E and Baker M 1999 J. Electron Spectrosc. Relat. Phenom. 105 245 Castleman K R 1979 Digital Image Processing (New Jersey: Prentice Hall) p 250
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References
571
Cazaux J A 1993 Microsc. Micoanaly. Microstruct. 4 513 Chatfield C 1983 Statistics for Technology (London: Chapman and Hall) Cottrell A H 1989 Mat. Sci. and Tech. 5 11659 Cox G 1989 EMAG-MICRO 1989 Institute of Physics C1989 Conference Series 98 523 Cox I J and Sheppard C J R 1983 Appl. Optics 22 1474 Crocker A G, Elvidge A M and Flewitt P E J 1987 Physica Scripta T19 344 Crocker A G, Smith G E, Flewitt P E J and Moskovic R 1999 Mat. Sci. Forum 294–296 673 Cruz-Orive L M and Werbel E R 1981 J. Microscopy 122 235 Dauskardt R H, Hanbenski F and Richie R O 1990 Acta Metall. 38 143 DeHoff R T and Rhines F N 1968 Quantitative Microscopy (New York: McGraw-Hill) Dench W A, Hazel L B and Seah M P 1988 Surf. Interface Anal. 13 63 Ehrlicl R and Wernberg B 1970 Sediment 40 205 El Gomati M M, Prutton M, Lamb B and Tuppen C G 1988 Surf. Interface Anal. 11 251 El Gomati M M and Walker C G H 1988 Inst. Phys. Conference Series 93 EUREM 88 Proc. 1 277 Engelmore R and Terry A 1979 Proc. IJCAI-79 p 250 Erasmus S T, Holburn D M and Smith K C A 1980 Scanning 3 273 Escher M C 1988 C/o Cordon Alt, Baarn, Holland. (The same drawing used in the ‘Le Monde de la Musique’ (Paris, February 1988) to illustrate J S Bach’s composition in ‘The Art of the Figure’) Exner H E and Hongardy H P 1988 Qualitative Image Analysis of Microstructures (Oberursel, Germany: D G M Information GmbH) Faulkner R G, Song S H and Flewitt P E J 1996 Met. Mat. Trans. 27A 3381 Flewitt P E J, Moskovic R and Wild R K 2002 Surf. Interface Anal. 33 729 Flewitt P E J and Wild R K, 2001 Grain Boundaries: Structure and Composition (Chichester: Wiley) Flewitt P E J, Smith G E, Mosckovic R and Crocker A G 1998 Fracture from Defects ed M W Brown (Warley-EMAS) p 975 Flook A 1982 Particle Size Analysis ed G Stanley-Wood and T Allen (London: Wiley Heyden) Frieden B R 1981 Transformation in Optical Signal Processing SPIE 373 219 Fuchs H, Pizer S M, Tsai L C, Bloomberg S H and Heinz E R 1982 IEEE Comput. Graphics Applic. 2 73 Gao F, Bacon D J, Calder A F, Flewitt P E J and Lewis T A 1996 J. Nucl. Mat. 220 47 Gevanter W B 1983 IEEE Spectrum August p 39 Godby R W, Need R J and Payne M C 1990 Physics World 3 39 Golay M J E 1969 IEEE Trans-Computer C18U 737 Goldstein D J 1992 J. Microscopy 166 185 Goodman J W 1968 Introduction to Fourier Optics (New York: McGraw-Hill) Gorbov L A, Nelyashberg M E and Servov V V 1977 Anal. Chem. Acta 95 75 Gualtieri P 1982 Pixel 1 37 Gundersen H J G and Jensen E B 1987 J. Microscopy 147 229 Hair J F, Anderson L E, Tatham R L and Black W C 1983 Multivariate Data Analysis (New York: Prentice Hall) Hanawalt J D, Rinn H and Frevel L K 1938 Ind. Eng. Chem. Anal. Edition 10 457 Hare T M, Russ J C and Russ J C 1982 Microbeam Analysis (San Francisco: San Francisco Press) Hashimoto H 1986 Electron Microsc. Tech. 2 1
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572
Application of computers
Hayes B 1989 Microsc. Anal. May p 31 Herman G T 1980 Image Reconstruction from Projections (New York: Academic Press) Holburn D M, Robertson R P, Breton B C and Caldwell N H M 2000 Microsc. Anal. Manuals p 5 Hondros E and McLean D 1995 Grain Boundary: Structure and Properties ed G A Chadwick and D A Smith (London: Academic Press) ch 10 p 353 Hormann K H, Krahl D and Rust H P 1978 Ultramicroscopy 3 227 Hornbogen E 1989 Inst. Met. Rev. 34 277 Huang Z H, Tian J F and Wang Z G 1989 Mater. Sci. Eng. A 118 19 Huang Z H, Tian J F and Wang Z G 1990 Scripta Metall 24 967 International Centre for Diffraction Data 1988, 1601 Park Lane, Swarthmore, Pennsylvania, USA ISO 14976 (1998) Surface chemical analysis data transfer format Jacobs D A H, Macqueen J F and Markham G 1986 Expert Systems and some of the Developments in the CEGB CEGB Report TPRD/L/APM 0269/M86 Jacobs D A H, Lyons M J, Macqueen J F and Markham G 1985 Expert Systems and their Applications CEGB Report TPRD/L/AP0228/M85 Johnson P E 1981 Cognitive Science 5 235 Kinney J H, Guinan M W and Munir Z A 1984 J. Nucl. Mater. 122–123 1028 Knowles M K and Titchmarsh J M 1997 Electron Microscopy and Analysis Institute of Physics Conference Series 153 (Bristol: IOP Publications) p 371 Lawless J F 1982 Statistical Models and Methods for Lifetime Data (New York: Wiley) Leapman R D, Fiori C E, Gorlen K E, Gibson C C and Swyt C R 1984 Ultramicroscopy 12 281 Lestrel P E 1974 Year Book of Physical Anthropology 18 140 Levialdi S 1982 Neighbourhood Operators ed R M Haralick Proc. 1982 Nato Advanced Study Institute, Bonas, France F4 (New York: Springer) Lohmann A W, Paris D P and Werlich H W 1967 Appl. Optics 6 1138 Mandlebrot B B 1967 Science 156 636 Mandelbrot B B 1983 The Fractal Geometry of Nature (New York: Freeman) Mandelbrot B B, Passoja D E and Paullay A J 1984 Nature 308 721 Mayhew T M 1997 J. Microscopy 186 153 Mayhew T M and Gundersen H J G 1996 J. Microscopy 188 1 National Bureau of Standards 1973 1978 Crystal Data Determinitive Tables (Washington: NBS) Norgett M J, Robinson M T and Torrens I M 1975 Nucl. Eng. Design 33 50 Painter P F 1965 Modulation, Noise and Spectral Analyses Applied to Information Transmission (New York: McGraw-Hill) Pande C S, Richards L R and Smith S 1987 J. Mater. Sci. Lett. 6 295 Pesce Defino V, Potente F, Vacca E, Lettini T, Ragone P and Ricco R 1990 Microsc. Anal. September p 23 Powder Diffraction File 1969–74 International Tables for X-Ray Crystallography I–IV (Birmingham: Kynoch Press) Pratt W K 1978 Digital Image Processing (New York: John Wiley) Prutton M, Larson L A and Poppa H 1983 J. Appl. Phys. 54 374 Prutton M and El Gomati M M 1988 Surf. Interface Anal. 11 251 Prutton M, Walker C G H, Greenwood J C, Kenny P G, Dee J C, Barkshire I R, Roberts R H and El Gomati M M 1991 Surf. Interface Anal. 17 71
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References
573
Radon J 1917 Berlin Schsische Akad. Wissen. 29 262 Reed M G and Howard C V 1999 J. Microscopy 195 96 Rhines F N and DeHoff R T 1986 Microstructology: Behaviour and Microstructure of Materials (Stuttgart: D Riederer) Richardson L F 1961 General Systems Year Book 6 139 Rosenfeld A and Kak A C 1967 Digital Picture Processing (London: Academic Press) Rosenfeld A and Kak A C 1982 Digital Picture Processing (London: Academic Press) Russ J C 1984 J. Microscopy 136 7 Russ J C 1990 Computer Assisted Microscopy (New York: Plenum Press) Russ J C and Russ J C 1986 Microbeam Analysis ed A D Romig and W F Chambers (San Francisco: San Francisco Press) Sagel K 1958 Tabellen zur Ro¨ntgenstrukturanalyse (Berlin: Springer) Saxton W O 1987 Advanced Course Acquisition and Processing of Scanned Images (London: Institute of Physics) Sasov A and Van Dyke B 1998 Microsc. Anal. March p 21 Sasov A 1987 J. Microscopy 147 169 Saxton W O 1978 Computer Techniques for Image Processing in Electron Microscopy Adv. Electronics and Electron Physics (New York: Academic Press) Saxton W O 1987 Advanced Course Acquisition and Processing of Scanned Images (London: IOP) Saxton W O Pitt T J and Horner M 1979 Ultramicroscopy 4 343 Shapiro S D 1978 Pattern Recognition 10/3 129 Shi D, Jiang J and Lung C 1997 J. Mater. Sci. Tech. 13 495 Shu H, Chen L and Yan Z 1993 J. Phys. D: Appl. Phys. 26 203 Smith G E, Crocker A G, Moskovic R and Flewitt P E J 2002 In Press Smith G E, Crocker A G, Flewitt P E J and Moskovic R 1997 Damaged Failure of Interfaces ed H-O Rossmanith (Rotterdam: Balkema) p 229 Smith K C A 1982 J. Microscopy 127 3 Spain A 1998 MSc Thesis, University of Wales, Swansea Statham P J 1982 Ultramicroscopy 8 302 Titchmarsh J M and Dunbill S 1996 J. Microscopy 184 195 Tougaard S 1987 J. Vac. Sci. Tech. A 5 1275 Tougaard s 1991 Surf. Sci. 244 125 Tougaard S 1998 Surf. Int. Anal. 26 249 Trebbia P and Manoubi T 1989 Ultramicroscopy 28 266 Trebbia P 1988 Ultramicroscopy 24 399 Underwood E E 1970 Quantitative Stereology (Reading, MA: Addison Wesley) Von Koch H 1906 Acta Math. 30 145 Walker C G H 1988 Institute of Physics Conference Series 90 EMAG 87 Proc. 1 277 Wang Y M, Thompson R P, Cobb L and Fitzharris T P 1983 Computers in Biomed. Res. 16 580 Weibel E R 1979 Stereological Methods (London: Academic Press) Wong C M 1984 IEEE Trans. Nucl. Sci. 31 865 Yokato Y, Tomita M, Hashimoto H and Enbloh H 1981 Ultramicroscopy 6 313 Zaluzec N J 1989a Ultramicroscopy 28 283 Zaluzec N J 1989b EMSA Bull. 16, 17 Zhang S and Lung C 1989 J. Phys. D: Appl. Phys. 22 790
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Appendix 1 List of symbols used in book Absorption coefficient Absorption current Absorption edge jump ratio Amplitude Analyser azimuth Angle Angular frequency Area Atomic number Atomic scattering factor Atomic weight Auger parameter Average spacing Average surface area Avogadro’s number Backscatter factor Beam diameter Boltzmann’s constant Brightness Burgers’ vector Collision rate Colour contrast Concentration Concentration Constant Crystallographic direction Current Density Deviation parameter Dimensions Distance (atoms, etc.) Distance (screens, etc.)
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A ra;b A0 ! A Z f ZA A Si as NA R BD k b r Rm Xi X C u, v, w I Sg a , b , c d D
Distance coordinates Efficiency Electric charge density Electric current density Electric flow density Electron charge Electron scattering fact Ellipsometric parameters Energy Extinction distance Extinction distance Fano number Fluorescence current Fluorescence yield Force constant Frequency Gain Impingement rate Ionisation cross-section Kelvin Lattice plane Length Lorentz force Magnetic flux Magnification Mass Matrix factor Matrix factor Multiplicity factor No. of free spaces/unit intensity Number
x, y, z p0 pi J D e 0 and E F F Wk Fc g0 ZA QK;L;M K h, k, l L L B M M F FAB X P Ij N
Optical density Permittivity in vacuum Perturbation Phase angle Phase distortion Planck’s constant Point spread function Polarizer Position dependent phase term Potential Pressure Probability Propagation vector in free space Propagation vector Proportionality constant Radius Reciprocal lattice Reciprocal lattice vector Reflection coefficient Refractive Index Refractive index Resolving power Response of photographic emulsion
"0 " X h hðx; yÞ P0
Scattering cross-section Scattering vector Second Semi angle Sensitivity factor Spherical abberation Spherical and chromatic aberration coefficients Standard deviation Standard error S Stopping Power Vi p Structure factor W Subgrain size Temperature Thickness K1 K0 Time A0 Unit cell r and R Velocity of light Velocity g Volume fraction
Volume
Wave vector Wavelength ni Work function 0
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Q s Sf CS Cc , Cs
m
i Sp F d T t a, b, c c v f V ki
Appendix 2.1 Commonly used conversion factors 1 A˚ (A˚ngstro¨m) ¼ 1010 m 1 dyne ¼ 105 N 1 gauss (G) ¼ 104 Tesla (T) 0 8C ¼ 273.15 K 1 Curie (Ci) ¼ 3.7 1010 s1 107 erg ¼ 6.241 1018 eV ¼ 1 Joule (J) 1 eV ¼ 1.602 1019 Joule (J) 1 calorie ¼ 4.184 Joule (J) e ¼ 2.718 1 mol ¼ 2.24 102 m3 (at STP) 1 mm ¼ 106 m 1 nm ¼ 109 m
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Appendix 2.2 Wavelength of selected radiation sources
Radiation
Wavelength (nm)
Ag K 1 Mo K 1 Cu K 1 Ni K 1 Co K 1 Fe K 1 Cr K 1
0.055936 0.070926 0.154051 0.165784 0.178892 0.193597 0.228962
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Appendix 3 Physical constants Avogadro constant Bohr magneton Boltzmann constant ðR=LA Þ Charge of an electron Compton wavelength of electron (h=me c) proton (h=mp c) neutron (h=mn c) Electron radius Faraday constant Fine structure constant Gas constant Gravitational constant Magnetic moment of electron Magnetic moment of proton Molecular gas constant Nuclear magneton Permeability of a vacuum Permittivity of a vacuum
NA B ¼ e h=2me k e
6:022 1023 mol1 9:274 1024 J T1 1:381 1023 J K1 1:602 1019 C
c cp cn re ¼ 0 e2 =ð4me Þ F ¼ 0 e2 c=2h R G e p R N 0 "0
Planck constant (Planck constant)/2
h h
Rest mass of electron
me
Rest mass of proton
p
Rydberg constant Speed of light in a vacuum Stefan–Boltzmann constant Unified atomic mass unit (12 C)
R1 ¼ 20 me e4 c3 =8h3 c ¼ 25 k4 =15h3 c2 u
2:426 1012 m 1:321 1015 m 1:319 1015 m 2:817 1015 m 9:649 104 C mol1 7:297 103 (1 ¼ 137:0) 8.314 J K1 mol1 6:673 1011 N m2 kg2 9:284 1024 J T1 1:410 1026 J T1 8.314 J K1 mol1 5:051 1027 J T1 4 107 H m1 8:854 1012 F m1 (1=4"0 ¼ 8:988 109 m F1 ) 6:626 1034 J s 1:055 1034 J s ¼ 6.582 1016 eV s 9:11 1031 kg ¼ 0.511 MeV/c2 1:673 1027 kg ¼ 938.3 MeV/c2 1:097 107 m1 2:998 108 m s1 5:670 108 W m2 K4 1:661 1027 kg ¼ 931.5 MeV/c2 1:243 106
Wavelength of a 1 eV photon
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Appendix 4 Acronyms for techniques (Based upon P J Goodhew and J E Castle) (Institute of Physics EMAG 1983; ch 13, p 515) ADES AEM AES AFM APS ARP Atom probe BLE BSE CBD CEMS CFM CIS CL CMR CPAA CTEM CTXM DPC E-2E EBIC EBSD EBSP ECP EDC EDS EDX EEM EFM
Angle dispersed electron spectroscopy Analytical electron microscopy Auger electron spectroscopy Atomic force microscopy Appearance potential spectroscopy Angle resolved photoemission FIM plus time-of-flight mass spectroscopy Bombardment-induced light emission Backscattered electrons Convergent beam diffraction Conversion electron Mo¨ssbauer spectroscopy Chemical force microscopy Constant initial state spectroscopy Cathodoluminescence Contact microradiography Charged particle activation analysis Conventional TEM (¼TEM) Conventional scanning X-ray microscopy Differential phase constrast Electron coincidence spectroscopies Electron beam induced conductivity Electron backscattered diffraction Electron backscattered spectroscopy Electron channelling pattern Energy distribution curve Energy dispersive (X-ray) spectrometry Energy dispersive X-ray analysis Emission electron microscopy Electrostatic force microscopy
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EELS EPMA EPR ESCA ESEM ESD (MS) ESR EXAFS EXELFS FAB (MS) FEED FEG FEM FIB FIM GDOES GDS GIF GSIMS HOLZ HVEM IAES IETS IMP(A) INS IPE ISS Kossel LAMMA LAXS LEED LEELS LEIS LFM LIMA MBE MFM MOLE MS NAA ND NDT NIS NMR
Electron energy loss spectroscopy Electron probe microanalysis Electron paramagnetic resonance Electron spectroscopy for chemical analysis Environmental scanning electron microscope Electron-stimulated desorption mass spectroscopy Electron spin resonance Extended (X-ray) absorption fine structure Extended (electron) energy loss fine structure Fast atom bombardment mass spectroscopy Field emission energy distributions Field emission gun Field emission microscopy Focused ion beam Field ion microscopy Glow discharge optical emission spectroscopy Glow discharge spectroscopy Gatan image filter Gentle secondary ion mass spectroscopy Higher order Laue zone High voltage electron microscopy Ion-induced Auger electron spectroscopy Inelastic electron tunnelling spectroscopy Ion microprobe analysis Ion neutralisation spectroscopy Inverse photoemission Ion scattering spectroscopy Diffraction of electron-excited X-rays Laser microprobe mass analysis Low angle X-ray scattering Low energy electron diffraction Low energy electron loss spectroscopy Low energy ion (back) scattering Lateral force microscopy Laser-induced ion mass analysis Molecular beam epitaxy Magnetic force microscopy Molecular optical laser examiner Mass spectroscopy Neutron activation analysis Neutron diffraction Non-destructive testing Neutron inelastic scattering Nuclear magnetic resonance
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OIM OM PAM PEEM PESM PEYS PFM PIXE PSD(MS) RBS RED REELS REM RHEED SACP SAD SAM SAM SANS SAXS SE SEAM SEM SERS SEXAFS SHEED SIIMS SIMS SIPS SLAM SNMS SOM SOMSEM SPAM SPM STEM STM STXM SXE SXM TCP TEM TL TXRF
Orientation imaging microscopy Optical microscopy Photoacoustic microscopy Photoemission electron microscopy Photoelectron spectro microscopy Photoelectron yield spectroscopy Photonic force microscopy Particle-induced X-ray emission Photon-stimulated desorption mass spectroscopy Rutherford backscattering spectroscopy Reflection electron diffraction Reflection electron energy loss spectroscopy Reflection electron microscopy Reflection high energy electron diffraction Selected area channelling pattern Selected area diffraction Scanning Auger microscopy Scanning acoustic microscopy Small angle neutron scattering Small angle X-ray scattering Secondary electron Scanning electro acoustic microscopy Scanning electron microscopy Surface enhanced Raman scattering Surface EXAFS or synchrotron EXAFS Scanning high energy electron diffraction Secondary ion imaging mass spectroscopy Secondary ion mass spectroscopy Sputter-induced photon spectroscopy Scanning laser acoustic microscopy Sputter neutral mass spectroscopy Scanning optical microscopy SOM in SEM Scanning photo acoustic microscopy Scanning probe microscopy Scanning transmission electron microscopy Scanning tunnelling microscopy Scanning transmission X-ray microscopy Soft X-ray emission Scanning X-ray microscopy Transmission channelling pattern Transmission electron microscopy Thermoluminescence Total X-ray reflection fluorescence spectroscopy
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UPS WF XPS XRD XRF XRM ZAF
Ultraviolet photoelectron spectroscopy Work function X-ray photoelectron spectroscopy X-ray diffraction X-ray fluorescence X-ray microscopy Atomic number, absorption and fluorescence corrections pattern
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Appendix 5 Electron structure of elements
Ele- 1 ment s
Z
1 H 2 He
s
2 p
3 s
p
d
s
1 2 3 5 5 6
1 2 2 2 2 1 2 2
1 2
3 4 5 6 7 8 9 10
Li Be B C N O F Ne
2 2 2 2 2 2 2 2
1 2 2 2 2 2 2 2
1 2 3 4 5 6
11 12 13 14 15 16 17 18
Na Mg Al Si P S Cl A
2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6
1 2 2 2 2 2 2 2
1 2 3 4 5 6
19 20 21 22 23 24 25 26
K Ca Sc Ti V Cr Mn Fe
2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6
2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6
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p
4 d
f
s
p
5 d
f
s
p
6 d
7 f
s
p
Ele- 1 ment s
s
2 p
s
3 p d
s
p
27 28 29 30 31 32 33 34 35 36
Co Ni Cu Zn Ga Ge As Se Br Kr
2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6
2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6
7 8 10 10 10 10 10 10 10 10
2 2 1 2 2 2 2 2 2 2
1 2 3 4 5 6
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
Rb Sr Y Zr Nb Mo Ma Ru Rh Pd Ag Cd In Sn Sb Te I Xe
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
1 2 4 5 6 7 8 10 10 10 10 10 10 10 10 10
55 56 57 58 59 60 61 62 63 64 65 66 67 68 69
Cs Ba La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
Z
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4 d
f
s
p
5 d
f
s
1 2 2 2 1 1 1 1 1
2 3 4 5 6 7 7 8 10 11 12 13
1 2 2 2 2 2 2 2
1 2 3 4 5 6
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
1
1 1
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
p
6 d
7 f
s
p
Ele- 1 ment s
s
2 p
s
p
d
s
p
4 d
f
s
p
5 d
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86
Yb Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102
Fr Ra Ac Th Pa U Np Pu Am Cm Bk Cf E Fm Mv No
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
Z
3
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f
s
p
1 2 3 4 5 6 7 8 10 10 10 10 10 10 10 10
2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2
1 2 3 4 5 6
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
2 3 5 6 7 7 8 10 11 12 13 14
6 d
1 2 1 1
1 1
7 f
s
p
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
