Physical methods for materials characterisation [2nd ed.] 9780750308083, 0750308087

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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

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To our wives Ann & Gillian

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‘‘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 Preface 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 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 3 Vacuum systems 3.1 Introduction 3.2 Kinetic theory of gases 3.3 Production of vacuum 3.4 Vacuum pumps

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3.5 3.6 3.7 3.8

Pressure measurement Leak detection Specimen handling References

4

Diffraction 4.1 Electromagnetic radiation 4.2 Photons 4.3 X-ray diffraction 4.4 Electron diffraction 4.5 References

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

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

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

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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

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 Appendix 1

List of symbols used in book

Appendix 2.1

Commonly used conversion factors

Appendix 2.2

Wavelength of selected radiation sources

Appendix 3

Physical constants

Appendix 4

Acronyms for techniques

Appendix 5

Electron structure of elements

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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.

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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.

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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

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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

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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.

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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

Optical

Absorption and other properties mainly of the individual ions

High refractive index, absorption different in solid or gas

Conduction by Insulator electron transport

Opaque, with similar properties in liquid state

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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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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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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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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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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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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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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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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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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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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1.8

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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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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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

m
3 m
2 m
1 m0

J J m
1 J m
2 J m
3

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 ½m
3  0-dimensional: 0 ¼ v ¼ P 1-dimensional: 1 ¼ d ¼ L=V ¼ ½m
2  ð1:1Þ P 2-dimensional: 2 ¼ b ¼ A=V ¼ ½m
1  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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density and specific energy gives a bulk microstructural energy with the unit of an energy density (J m
3 ) 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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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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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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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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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

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 10
14 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 10
4 m would result in an inadequate spatial resolution and we do not require radiation less than about 10
10 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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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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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 expð
tÞ

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 10
2 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 expð
xÞ

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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2.2.2

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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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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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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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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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 mg
1 cm
2 ) in carbon and a

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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 mg
1 cm
2 ) 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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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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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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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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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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Figure 2.15. The heating effect of a 10 keV, 5  10
9 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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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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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 cm
1 ) to 1 mm (wave number 10 cm
1 ) 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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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 (10
12 to 10
9 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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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 ( 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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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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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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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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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 10
2 Pa and, indeed, with the addition of sophisticated analytical attachments such as windowless spectrometers there is now a trend to achieve pressures of 10
5 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 10
7 to 10
9 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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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

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  10
4 

ð3:9Þ

Thus if a specimen is examined in a vacuum of 5  10
4 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 10
8 to 10
9 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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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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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 10
6 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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3.3.2

Medium to high vacuum (10
2 to 10
5 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 (10
6 to 10
9 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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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 10
1 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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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 1–10
2 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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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 10
2 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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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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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 10
2 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 10
1 to 10
9 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 10
1 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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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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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,