High Energy Electron Diffraction and Microscopy

by L.M. Peng, S.L. Dudarev, M.J. Whelan

Overview

High Energy Electron Diffraction and Microscopy provides a comprehensive introduction to high energy electron diffraction and elastic and inelastic scattering of high energy electrons, with particular emphasis on applications to modern electron microscopy. Starting from a survey of fundamental phenomena, the authors introduce the most important concepts underlying modern understanding of high energy electron diffraction. Dynamical diffraction in transmission (THEED) and reflection (RHEED) geometries is treated using a general matrix theory, where computer programs and worked examples are provided to illustrate the concepts and to familiarize the reader with practical applications. Diffuse and inelastic scattering and coherence effects are treated comprehensively both as a perturbation of elastic scattering and within the general multiple scattering quantum mechanical framework of the density matrix method. Among the highlights are the treatment of resonance diffraction of electrons, HOLZ diffraction, the formation of Kikuchi bands and lines and ring patterns, and application of diffraction to monitoring of growing surfaces. Useful practical data are summarised in tables including those of electron scattering factors for all the neutral atoms and many ions, and the temperature dependent Debye-Waller factors given for over 100 elemental crystals and compounds.

Product Details

ISBN-13:	9780198500742
Publisher:	Oxford University Press
Publication date:	03/11/2004
Series:	Monographs on the Physics and Chemistry of Materials , #61
Pages:	558
Product dimensions:	9.21(w) x 6.14(h) x 1.19(d)

About the Author

Peking University

EURATOM/UKAEA Fusion Association, Culham Science Centre, Oxfordshire

Oxford University

Table of Contents

1	Basic concepts of high-energy electron diffraction	1
1.1	Introduction	1
1.2	The interaction between high-energy electrons and a solid	2
1.3	Elastic and inelastic scattering, and the complex potential	3
1.4	The amplitude and the differential cross-section of scattering of electrons	4
1.5	Elastic scattering by a time-independent potential--the one-body Schrodinger equation	6
1.6	Selected area electron diffraction (SAED), convergentbeam electron diffraction (CBED), and Kikuchi patterns	8
1.7	Scattering by time-dependent fluctuations of the potential	11
1.8	Damping of coherence in inelastic scattering and the validity of the optical potential	14
1.9	Relativistic corrections	17
1.10	Probability current density and conservation of probability	18
1.11	Correlation between theory and experiment	19
1.12	Summary	21
2	Kinematic theory	24
2.1	Introduction	24
2.2	Kinematic and quasi-kinematic diffraction theory	25
2.2.1	Kinematic diffraction	25
2.2.2	Quasi-kinematic diffraction	27
2.3	Scattering by a single atom	27
2.4	Amplitude of scattering by an assemblage of atoms	33
2.5	Diffraction by single crystals	36
2.6	Diffraction by a gas, an amorphous solid, and a liquid	42
2.7	Diffraction by polycrystals and textures	45
2.8	Fluctuation microscopy	48
2.9	Summary	52
3	Dynamical theory I. General theory	54
3.1	Introduction	54
3.2	Role of symmetry in dynamical diffraction	55
3.3	Forward and backward scattering	59
3.4	The multislice method	60
3.5	The general matrix method	63
3.5.1	Fundamental equations	64
3.5.2	The dispersion surface	65
3.5.3	Translation properties of Bloch waves	66
3.5.4	Boundary conditions and formal solutions	69
3.6	Summary	74
4	Dynamical theory II. Transmission high-energy electron diffraction	75
4.1	Introduction	75
4.2	Diffraction geometry	75
4.3	Basic concepts and the treatment of ZOLZ diffraction	79
4.3.1	Basic equations and Bloch waves	79
4.3.2	Bound and free Bloch waves	81
4.3.3	Dispersion surfaces and band structure	84
4.3.4	Excitation of Bloch waves	86
4.3.5	Two and few Bloch wave approximations	90
4.3.6	Propagation of Bloch waves	96
4.3.7	Effects of absorption	97
4.4	The general treatment of THEED and HOLZ diffraction	98
4.4.1	Kinematic geometry of HOLZ diffraction	98
4.4.2	Formation of a HOLZ ring	98
4.4.3	Distribution of intensity in HOLZ patterns	102
4.4.4	General treatment of HOLZ diffraction	107
4.5	Summary	115
5	Dynamical theory III. Reflection high-energy electron diffraction	117
5.1	Introduction	117
5.2	Surface structure notation and RHEED geometry	118
5.2.1	The nature of the surface	118
5.2.2	The five surface nets	119
5.2.3	The relation between the surface mesh and the substrate mesh	119
5.2.4	Surface reciprocal lattice rods	121
5.3	RHEED theory	123
5.3.1	The THEED approach to RHEED	123
5.3.2	The semi-reciprocal formulation	126
5.3.3	The Green's function approach	130
5.3.4	The Bloch wave method	138
5.4	Worked examples	159
5.4.1	RHEED from the surface of a metal: the Ag(001) surface	160
5.4.2	RHEED from a surface of an ionic crystal: the NiO(001) and UO[subscript 2](111) surfaces	164
5.5	RHEED from growing surfaces: intensity oscillations	175
5.6	Summary	185
6	Resonance effects in transmission and reflection high-energy electron diffraction	186
6.1	The origin of resonances	186
6.2	Transmission resonance diffraction of high-energy electrons	187
6.2.1	The geometry of transmission resonance diffraction	188
6.2.2	Transmission resonance: a formal solution	191
6.2.3	Transmission resonance: diffraction via tightly bound states	193
6.3	Resonance diffraction from a crystal surface	200
6.3.1	The geometry of surface resonance scattering	202
6.3.2	The two-rod approximation	204
6.3.3	Resonance scattering via a surface state	208
6.3.4	Resonance diffraction via localized bulk states	213
6.3.5	Interference between resonance and potential scattering	217
6.3.6	The time delay of the incident electron in the resonance state	223
6.4	Summary	227
7	Diffuse and inelastic scattering--Elementary processes	228
7.1	Diffuse and inelastic scattering	228
7.2	The distorted wave Born approximation	230
7.3	Diffuse scattering by point defects	235
7.4	The Van Hove dynamic form factor	241
7.5	Thermal diffuse scattering	246
7.6	Electron energy losses	251
7.6.1	Plasmons	254
7.6.2	Ionization of inner electronic shells	256
7.6.3	The extended energy loss fine structure (EXELFS)	259
7.7	Summary	263
8	Diffuse and inelastic scattering--Multiple scattering effects	264
8.1	Introduction	264
8.2	Breakdown of the DWBA and the optical potential model	266
8.3	Diffraction and multiple incoherent scattering of electrons	268
8.4	Kinetic equation for the density matrix	269
8.5	Loss of coherence due to multiple scattering by plasmons	274
8.6	Diffraction of diffusely scattered electrons: the formation of Kikuchi lines and bands	282
8.7	Kikuchi patterns in electron backscattering	287
8.8	Multiple diffuse scattering: an exact solution of the backscattering problem	290
8.9	Electron channelling patterns and channelling imaging of crystal defects	296
8.10	Diffraction effects in inner-shell ionization, X-ray, and Auger electron production	304
8.11	Summary	310
9	Crystal and diffraction symmetry	311
9.1	Introduction	311
9.2	Representation of symmetry	312
9.3	The reciprocity principle	313
9.4	Symmetry elements and their identification	314
9.5	Diffraction symmetry--a formal derivation	318
9.5.1	Basic solutions and relations	318
9.5.2	Effect of the space group symmetry	320
9.5.3	Diffraction groups and the symmetry of CBED patterns	323
9.5.4	Derivation of the fundamental symmetry relations	326
9.6	Crystal point group determination	330
9.7	Crystal space group determination	332
9.7.1	Formation of G-M lines	333
9.7.2	Identification of G-M lines	336
9.7.3	Space group determination	337
9.8	Automated identification of CBED pattern symmetry	337
9.8.1	Genetic algorithm--basic concepts and implementation	339
9.8.2	Identification of CBED pattern symmetry	344
9.9	Summary	348
10	Perturbation methods and tensor theory	350
10.1	Introduction	350
10.2	Perturbation treatment of a periodic structure	353
10.2.1	Bloch waves, left-hand, and right-hand eigenvectors	354
10.2.2	Non-degenerate perturbation theory	355
10.2.3	First-order perturbation	356
10.2.4	Second-order perturbation	357
10.3	Tensor THEED	358
10.4	Direct inversion of THEED data	362
10.4.1	Inversion of crystal structure factors	364
10.4.2	Inversion of atomic coordinates	370
10.5	Perturbation methods for non-periodic structures	379
10.5.1	The DWBA treatment of diffraction by a non-periodic structure	379
10.6	Tensor RHEED and the direct inversion of a surface structure	383
10.7	Summary	386
11	Digital electron micrograph recording and basic processing	388
11.1	Introduction	388
11.2	Basic features of CCDs	389
11.3	A basic model of an SSC camera	390
11.4	Main characteristics of an SSC camera	391
11.4.1	The overall gain	391
11.4.2	Resolution and the point spread function	393
11.4.3	The detection quantum efficiency	395
11.5	The sampling theorem	398
11.6	Discrete and fast Fourier transform	399
11.6.1	Discrete Fourier transform	399
11.6.2	Fast Fourier transform (FFT)	401
11.7	Restoration of images	402
11.7.1	Generation of data points in reciprocal space	402
11.7.2	Generation of data points in real space	404
11.8	Summary	404
12	Image formation and the retrieval of the electron wave function	406
12.1	Introduction	406
12.2	Electron source and coherence	406
12.2.1	Partial coherence and the complex degree of coherence	406
12.2.2	Temporal coherence	408
12.2.3	Spatial coherence	410
12.3	Image formation in an electron microscope	412
12.3.1	Transmission cross-coefficient (TCC) for coherent illumination	413
12.3.2	The TCC for incoherent illumination	415
12.3.3	The TCC for a partially coherent illumination	417
12.4	Exit electron wave function retrieval	418
12.4.1	Linear image retrieval	419
12.4.2	Non-linear image retrieval	424
12.5	Summary	426
13	The atomic scattering factor and the optical potential	427
13.1	Introduction	427
13.2	The optical potential	429
13.3	The averaged potential	432
13.3.1	Thermally averaged potential	432
13.3.2	Electron atomic scattering factor	433
13.3.3	Temperature factor	434
13.4	The absorptive potential	437
13.5	Computation of the complex structure factor	440
13.5.1	A worked example: strontium titanate	441
13.6	Analytical representation of atomic scattering factors	443
13.6.1	The parameterization of the elastic atomic scattering factor for electrons	444
13.6.2	Parameterization of the absorptive atomic scattering factor	446
13.7	Analytical expressions for the optical potential of atoms and crystals	447
13.8	Summary	449
14	Temperature-dependent Debye-Waller factors	454
14.1	Introduction and definitions	454
14.2	Debye-Waller factors of elemental crystals	456
14.3	Debye-Waller factors of cubic compounds	458
14.4	Summary	460
A	Some useful mathematical relations	470
A.1	Fourier transformation	470
A.2	The Dirac delta function	470
A.3	The Kronecker delta symbol	471
A.4	Some useful integrals	472
B	Green's functions	473
C	FORTRAN listing of RHEED routines	477
C.1	A FORTRAN routine for the calculation of U[subscript G](z)	477
C.1.1	The input file for the calculation of U[subscript G](z)	477
C.1.2	FORTRAN routine for calculating U[subscript G](z)	477
C.2	A FORTRAN routine for dynamical RHEED calculations	481
C.2.1	Example input data file for dynamical RHEED calculations	482
C.2.2	A FORTRAN routine for dynamical RHEED calculations	482
D	Parameterization of the electron atomic scattering factor	490
D.1	The parameterization algorithm	490
D.2	The absorptive atomic scattering factor	496
	References	501
	Subject Index	531