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Large-angle convergent-beam electron diffraction (LACBED) : applications to crystal defects PDF

433 Pages·2002·17.4 MB·English
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Monograph of the French Society of Microscopies LARGE-ANGLE CONVERGENT-BEAM ELECTRON DIFFRACTION (LACBED) Applications to crystal defects Jean Paul MORNIROLI Professor in the Ecole Nationale cle Chimie de Lille Laboratoire de Métallurgie et Génie des Matériaux UMR CNRS 8517 Université des Sciences et Technologies de Lille SFµ, Paris Copyright © 2002 Société Française des Microscopies Cover illustration: image processing of a LACBED pattern from a Σ25 coincidence grain boundary. Silicon specimen. Courtesy of J.L. Maurice La loi dull mars 1957 n’autorisant, aux termes de l’alinéa 2 at 3 de I’article4l, que les “copies ou reproductions réservées à rusage privé du copiste et non destinées à une utilisation collective” et que lea analyses et courtes citations dans un but d’exemple at d’illustration, “toute representation et reproduction integrale ou partielle faite sans le consentement de Vauteur ou de ses ayants droil ou ayants cause, est illicite” (alinéa 1er de Article 40). Cette représentation ou reproduction, par quelque procéde que ce soit, constlimerait donc une contrefaçon sanctionnée par les articles 425 et suivants on Code Pénal. Sociétié Française des Microscopies Case 243 (UPMC) - Bâtiment C 9 Quai Saint Bernard - 75005 PARIS Copyright © 2002 Société Française des Microscopies, Paris ISBN : 2-901483-05-4 Copyright © 2002 Société Française des Microscopies PREFACE Electrons are indeed incredible particles! They are not only responsible for the cohesion and the properties of condensed matter but furthermore, they are easily produced, accelerated and, when aimed at a specimen, they interact strongly with it and are scattered, yielding a wealth of information on its organisation at the atomic scale. As they are charged particles, electric and magnetic fields deflect them and it becomes possible to construct devices that act on an electron beam in the same way that a glass lens acts on light. The consequences of all this are enormous; in particular, electron micro- scopes can be designed, with which we can observe the diffraction pattern associated with the illuminated specimen, in which case we are in Fourier space and we can also observe a magnified image of the specimen, in direct space. The technique of convergent-beam electron diffraction has brought enormous benefits to structural studies. By replacing an inci- dent beam that is close to being a plane wave by a beam converging strongly on the specimen, the diffraction spots becomes disks; the diffraction information, more spread out in Fourier space, is hence more complete. Largeangle convergent-beam electron diffraction, a natural development, is the ideal form of the technique for the micro- scopist. The specimen is moved away from the plane conjugate to the recording plane, in which information about both the image and the diffraction pattern is then seen: the two spaces, direct and recip- rocal, are both present on the screen of the microscope. We can eas- ily imagine the resulting attractiveness of this method. A few years ago, during meetings of the Council of the French Society for Microscopies, I suggested that the Society should publish a series of monographs on microscopy. Each monograph should be written by an active specialist of the technique with a strong peda- gogic aspect, in order to interest both beginners and experienced microscopists. Jean-Paul Morniroli is the first author of this series. He has gone far beyond these modest aims and written a textbook that contains an extremely thorough account of the techniques of large-angle convergent- i Copyright © 2002 Société Française des Microscopies beam diffraction and explains in detail the various microscope operating modes. That first monograph in French as well as the present English ver- sion will serve as a reference for forthcoming books. Jean-Paul Morniroli is to be congratulated on having set the standard so high. Richard Portier ENSC Paris ii Copyright © 2002 Société Française des Microscopies ACKNOWLEDGEMENTS I make a point of addressing especial thanks to Paul-Henri ALBAREDE, Jeanne AYACHE, David BIRD, Daniel CAILLARD, David CHERNS, Patrick CORDER, Brigitte DECAMPS, Nathalie DOUKHAN, Jo6l FAURE, Denis GRATIAS, Christian JAGER, Wolfgang JAGER, Elzbieta JEZIERSKA, Danielle LAUB, Jean-Luc MAURICE, Jean-Pierre MICHEL, Maria Louisa NO, Jaime PONS, Richard FORTIER, Sophie POULAT, Alastair PRESTON, Louisette PRIESTER, Abdelkrim RED- JAIMIA, Pedro RODRIGUEZ, Pierre STADELMANN, John STEEDS and Michiyoshi TANAKA. They entrusted me with specimens and fur- nished several of the documents used to illustrate this monograph. I also thank very warmly the students involved in the LACBED studies of dislocations and grain boundaries. The contributions of Francis GAILLOT, Agnés LECLERE, Olivier RICHARD, Françoise STRZELCZYK and Philippe VERMAUT were particularly appreciated. During these last few years, many fruitful cooperations have been established with colleagues from Lille and with microscopists in France and elsewhere. They represent a major contribution to this monograph for they gave me the opportunity of observing a very wide range of specimens and brought me into contact with a variety of research fields connected with structure and microstructure. Their role is warmly acknowledged. Paul-Henri ALBAREDE deserves particular thanks. He developed the tripod method used to prepare flat specimens with nearly con- stant thickness by mechanical polishing. Such specimens are per- fectly adapted to CBED and LACBED experiments. Many of the high-quality patterns shown in this book were obtained from speci- mens he prepared for me. Patrick CORDER, Paul-Henri ALBAREDE and Richard PORTER accepted the arduous task of proofreading the original French draft of the manuscript. Their remarks, comments, corrections and sug- gestions were invaluable. It is a sad duty to mention the name of Mike STOBBS, deeply regret- ted by the electron microscopy community. He showed me how to iii Copyright © 2002 Société Française des Microscopies obtain my first CBED pattern. That was in 1986, during a stay in Cambridge where my initial goal was to learn how to pratice high res- olution electron rnicroscopy! My predilection for reciprocal space began there. I am very indebted to John STEEDS, David CHERNS and Roger VINCENT, who have shared their extensive knowledge and experi- ence of CBED and LACBED with me. David CHERNS’s contribution to the characterization of dislocations by LACBED was a major step for- ward and doubtless triggered the development of this technique. I appreciated very much the work we did together on the characteriza- tion of partial dislocations and grain boundary dislocations. Many thanks to John SPENCE and Jin Min ZUO. They welcomed me in their laboratory in Tempe, where I learned a great deal about energy filtering and quantitative electron diffraction. It was Richard PORTIER who launched the idea that the French Society of Microscopies, of which he was then President, should pub- lish a series of monographs on microscopy. I thank him particularly for having encouraged me to embark on this first monograph, which, I hope, will be followed by numerous others. Richard PORTIER has always supported and encouraged convergent-beam electron diffrac- tion. He was one of the few French pioneers involved in CBED in the early eighties. Most of the experiments were performed on the CM30 Philips transmission electron microscope of the Centre Commun de Microscopie Electronique (CCME) de l’Université des Sciences et Technologies de Lille. Many thanks to the CCME team for providing excellent facilities for LACBED experiments. I am very grateful to the Head of the Laboratoire de Métallurgie Physique et Genie des Mat6riaux, Jacques FOCT, for his confidence and support. Since my arrival in his laboratory in 1989, he has always encouraged me to follow this field of reseach. The idea of preparing an English version of this monograph arose from demands from microscopists unfamiliar with the French lan- guage. It was also a good opportunity to incorporate new and recent developments of the LACBED technique in point defects, antiphase boundaries, trace analysis... But the real point of departure was the proposal by one of my colleagues, Etienne Brbs, to translate the French version into English. I would like to express here my very sin- cere thanks to him for preparing this excellent translation in a rela- tively short period. iv Copyright © 2002 Société Française des Microscopies Peter Hawkes very kindly agreed to read through the manuscript a last time. I must say that without his careful and meticulous correc- tion of the text, this English version could not have been completed so rapidly. I greatly appreciated his help in the final stages of publi- cation. He also made me realise that the English language is full of subtleties. I dedicate this monograph to Céline, Florence and Marie-Annick. They helped me a lot with the English langage and “supported” me in both the French and English meanings of the word, during the writ- ing periods of this monograph. v Copyright © 2002 Société Française des Microscopies CONTENT CONTENT Introduction 1 I - Bragg’s law 5 I.1 - Analogy with the reflection of visible light 5 I.2 - Three-dimensional description of Bragg’s law 6 I.3 - The particular case of electron diffraction 8 II - Formation of the diffraction pattern in the electron microscope 11 II.1 - Electron ray-paths in the objective lens 11 III - Electron diffraction patterns produced by a parallel incident beam 15 III.1 - Diffraction pattern in the two-beam condilions 16 III.1.1 - A set of (hkl) lattice planes is exactly at the Bragg orientation exact two-beam conditions 16 III.1.1.1 - Formation of the diffraction pattern 16 III.1.1.2 - Ewald sphere construction 20 III.1.1.2.1 - Relationship between the Ewald sphere construction and the diffraction pattern 21 III.1.1.2.2 - Peculiarities of the electron diffraction phenomenon 22 III.1.2 - A set of (hkl) lattice planes is close to the Bragg orientation: near two-beam conditions. 23 III.1.2.1 - Formation of the pattern 23 III.1.2.2 - Ewald sphere construction 26 III.1.2.3 - Characterization of the deviation parameter s 26 III.1.3 - Special cases 28 III.1.3.1 - The set parallel incident beam is not directed along the optic axis of the microscope 28 III.1.3.2 - The set of (hkl) lattice planes is parallel to the electron beam 30 III.1.4 - Application: setting (hkl) lattice planes at the exact Bragg orientation 33 III.2 - Diffraction pattern in “multi-beam” conditions 33 III.2.1 - General Case 35 III.2.2 - Special case: [uvw] zone axis pattern (ZAP) 41 IV - Diffraction pattern produced by a convergent incident beam: CBED pattern 41 IV.1 - Diffraction pattern under two-beam conditions 41 IV.1.1 - A single set of (hkl) lattice planes is at the exact Bragg orientation exact two-beam conditions 41 IV.1.1.1 - Formation of the diffraction pattern 41 IV.1.1.2 - Ewald sphere construction 45 IV.1.2 - A set of (hkl) lattice planes is near the Bragg orientation: near two-beam condition 53 vii Copyright © 2002 Société Française des Microscopies CONTENT IV.1.2.1 - Formation of the diffraction pattern 53 IV.1.2.2 - Ewald sphere construction 53 IV.1.3 - Particular case: the set of (hkl) lattice planes is parallel to the optic axis 53 IV.1.4 - The incident beam is tilted with respect to the optic axis 56 IV.1.5 - Application: setting (hkl) lattice planes at the exact Bragg orientation 56 IV.2 - Diffraction pattern under many-beam conditions 58 IV.2.1. - General case 58 IV.2.1 1 - Influence of the convergence semi-angle on the number of diffracted reflections 60 V.2.2 - Particular case: [uvw] zone-axis pattern 61 IV.3 - Influence of the convergence semi-angle on the CBED pattern 65 V - Diffraction pattern produced by a large-angle convergent incident beam Kassel pattern 67 V.1 - Advantage of a large convergence angle 67 V.2 - Kassel patterns 68 V.2.1 - General case 68 V.2.2 - [uvw] zone-axis Kassel pattern 71 V.2.3 - Main characteristics of the Kassel patterns 71 V.2.3.1 - Particular case of a [uvw] zone axis Kassel pattern 78 V.2.4 - Detail of the superimposition of the deficiency and excess lines 78 V.3 - Limiting value of the convergence semi-angle 81 VI - Diffraction pattern produced by a large-angle convergent beam: LACBED patterns 83 VI.1 - Formation of bright- and dark-field LACBED patterns 83 VI.1.1 - Two-beam conditions 83 VI.1.1.1 - Bright-field pattern 86 VI.1.1.2 - Dark-fleld pattern 90 VI.1.2 - [uvw] zone-axis pattern 90 VI.2 - Effect of the specimen height 93 VI.3 - Minimum specimen height 97 VI.4 - Variation of the deviation parameter s 100 VI.5 - Effect of the probe size S 100 VI.6 - Formation of the shadow image 104 VI.6.1 - Size of the illuminated area 106 VI.6.2 - Minimum size of the illuminated area 106 VI.6.3 - Magnification of the shadow image 107 VI.6.4 - Shift of the shadow image in bright- and dark-field LACBED patterns 109 VI.6.5 - Rotation of the shadow image 112 VI.6.6 - Resolution of the shadow image 114 VI.6.7 - Focus of the shadow image and of the line pattern 115 VI.7 - Angular filtering of LACBED patterns 118 VI.8 - Effect of the temperature on LACBED patterns 123 VI.9 - Effect of a specimen tilt 126 VI.10 - Effect of a specimen deformation 126 VI.11 - Effect of a variation of the lattice parameters 131 VI.12 - Effect of the accelerating voltage 133 VI.13 - Effect of the specimen thickness 134 VI 14 - Analogy with bend-contour patterns 136 VI.15 - Analogy with Kikuchi patterns 140 viii Copyright © 2002 Société Française des Microscopies CONTENT VI.15.1 - Indices of the Kikuchi lines 144 VI.15.2 - Properties of Kikuchi lines 144 VI.15.3 -Interest of Kikuchi Iines 148 VII - Diffracted and transmitted intensities 149 VII.1 - Generalities 149 VII.2 - Kinematical theory under two-beam conditions 150 VII.2.1 - Effect of the deviation parameter s on the diffracted intensity I 151 g VII.2.2 - Effect of the thickness t on the diffracted intensity I 153 g VII.3 - Dynamical theory under two-beam conditions 155 VII.3.1 - Effect of the deviation parameter s on the diffracted intensity I 156 g VII.3.2 - Effect of the thickness I on the diffracted intensities I 158 g VII.3.3 - Complementarity of the transmitted and diffracted intensities 158 VII.3.4 - Effect of absorption on the transmitted and diffracted intensities. 159 VII.4 - Comparison of the kinematical and dynamical theories 159 VII.5 - Appearance of the excess and deficiency mes 163 VII.5.1 - Effect of the extinction distance ξ on the excess and g deficiency lines 165 VII.5.2 - Effect of the specimen thickness on the excess and deficiency lines 165 VII.5.2.1 - CBED and Kossel patterns 165 VII.5.2.2 - LACBED patterns 170 VII.5.3 - Angular width of the excess and deficiency lines 170 VII.5.4 - Dynamical and quasi-kinematical lines 171 VII.6 - Dynamical Interactions 173 VII.6.1 - Interactions under two-beam conditions 173 VII.6.1.1 - Parallel incident beam 173 VII.6.1.2 - Convergent Incident beam 173 VII.6.1.3 - Large-angle convergent beam: Kossel patterns 174 VII.6.2 - Many-beam interactions 176 VII.6.2.1 - Three-beam patterns 176 VII 6.2.2 - Multi-beam patterns 177 VII.6.2.3 - LACBED patterns 181 VIII - Experimental methods 185 VIII.1 - Operating principle of magnetic lenses 185 VIII.1.1 - Focused, under-focused and over-focused lenses 187 VIII.1.2 - Condenser-objective lens 187 VIII.1.3 - Description of the “nanoprobe” and “microprobe” modes 188 VIII.2 - General description of the microscope 189 VIII.2.1 - Description of the condenser 192 VIII.2.1.1 - Effect of the first condenser 192 VIII.2.1.2 - Effect of the second condenser 193 VIII 2.1.2.1 - Effect of the aperture of the second condenser 196 Effect of the size of the aperture 196 Effect of the centring of the aperture 198 VIII.2.2 - Angular scanning 198 VIII.2.3 - Complete description of the formation of the image and diffraction pattern 201 ix Copyright © 2002 Société Française des Microscopies

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