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Tables of Contents for Defect and Microstructure Analysis by Diffraction
Chapter/Section Title
Page #
Page Count
List of contributors
xvii
Abbreviations
xx
Introduction to defect and microstructure analysis or the analysis of real structure
1
16
Jaroslav Fiala
Robert L. Snyder
Introduction
1
1
What is real structure?
2
2
X-ray diffraction analysis of real structure
4
4
Restoring physical patterns from observed values
8
2
Conclusions
10
1
References
10
7
Part I. Fundamentals of defect analysis by diffraction
17
314
Some applications of the kinematical theory of X-ray diffraction
19
10
Hans Bradaczek
Introduction
19
1
The basis of the kinematical theory
19
2
Bragg's law
21
1
Direct methods of phase determination
22
2
Particle size effect
24
1
Convolution square root
25
1
Influence of the periodic elements (atoms, clusters)
26
1
General epilogue
27
1
References
28
1
Profile fitting and analytical functions
29
12
Stefano Enzo
Liliana Schiffini
Historical presentation of the theoretical framework
29
2
The selection and the mathematical properties of the line shape function
31
5
The use of line shape parameters in practical cases
36
3
Conclusions
39
1
References
40
1
Effects of instrument function, crystallite size, and strain on reflection profiles
41
18
V. Honkimaki
P. Suortti
Introduction
41
1
Total pattern
42
1
Instrument function
43
2
Modeling of background
45
7
Crystallite size and strain
52
2
Anisotropic strain and particle size
54
2
Summary
56
1
References
56
3
Spherical harmonics
56
3
Use of pattern decomposition or simulation to study microstructure: theoretical considerations
59
23
J. Ian Langford
Introduction
59
4
Diffraction effects due to crystallite or domain size
63
5
Diffraction effects due to structural `mistakes'
68
2
Interpretation of apparent strain
70
2
Characterization of microstructure
72
4
References
76
6
Analytical functions commonly used to model powder diffraction line profiles
77
2
Apparent and `true' size of crystallites or domains from the integral breadth
79
3
Classical treatment of line profiles influenced by strain, small size, and stacking faults
82
12
C.R. Houska
R. Kuzel
Introduction
82
1
Classical treatment
83
9
Discussion
92
1
References
93
1
Voigt function model in diffraction-line broadening analysis
94
33
Davor Balzar
List of symbols
94
1
Introduction
95
2
Diffraction-line broadening
97
11
Size--strain analysis
108
15
Concluding remarks
123
1
References
124
3
X-ray analysis of precipitation-related crystals with dislocation substructure
127
14
R.I. Barabash
References
140
1
Analytic functions describing line profiles influenced by size distribution, strain, and stacking faults
141
24
C.R. Houska
R. Kuzel
Introduction
141
6
Correlated dislocations
147
3
Analytic profiles
150
1
General analytic method
151
8
Discussion
159
1
References
160
5
Appendix 1
161
2
Appendix 2. Krivoglaz expansion of strain
163
1
Appendix 3. Column distances, conversions, units
163
2
The dislocation-based model of strain broadening in X-ray line profile analysis
165
35
T. Ungar
Introduction
165
2
The theory of strain broadening
167
12
Experimental aspects
179
2
Single-profile measurements and results
181
1
Two-profile analysis of the dislocation structure
182
8
The analysis of small grain specimens
190
5
Conclusions
195
1
References
196
4
Diffraction-line broadening analysis of dislocation configurations
200
14
A.C. Vermeulen
R. Delhez
Th.H. de Keijser
E.J. Mittemeijer
Introduction
200
1
Integral breadths and Fourier coefficients: previous work
200
1
Theory of diffraction-line broadening by dislocations
201
4
How to deal with eqn (8)
205
2
[111] Fibre-textured f.c.c metal layers plastically deformed by thermal stresses
207
2
Practical example: aluminium layers
209
3
Summary
212
1
References
213
1
Diffraction-line broadening analysis of strain fields in crystalline solids
214
20
J.G.M. van Berkum
R. Delhez
Th.H. de Keijser
E.J. Mittemeijer
Introduction
214
1
Basic considerations and scope of the chapter
214
3
Line profile description
217
1
Line profile decomposition: resolving size and strain
218
4
Line profile synthesis and matching: refining microstructure parameters
222
4
Order dependence of line broadening: evaluation of line profile decomposition methods
226
2
Line profile syntheses and matching: practical example
228
3
Summary
231
1
References
232
2
Paracrystallinity
234
13
Hans Bradaczek
Introduction
234
1
The basic idea
234
4
The real paracrystal
238
1
Computer simulation of paracrystals
239
6
Summary
245
1
References
245
2
The model of the paracrystal and its application to polymers
247
17
W. Wilke
Introduction
247
1
Ideal paracrystal
248
2
Scattering intensity of ideal paracrystals
250
4
Examples of application of the method to polymers
254
8
Some remarks about paracrystal models for the interpretation of small-angle scattering
262
1
References
262
2
Effect of planar defects in crystals on the position and profile of powder diffraction lines
264
54
A.I. Ustinov
Introduction
264
1
Equation for intensity calculation and common law of X-ray scattering crystals with planar defects
265
4
Planar defects in body-centered cubic (body-centered tetragonal and body-centered rhombohedral) lattices
269
16
Planar defects in crystals with face-centered cubic lattices
285
14
Planar defects in hexagonal close-packed crystals
299
10
One-dimensionally disordered crystals with long periods
309
6
Conclusions
315
1
References
316
2
Effect of stacking disorder on the profile of the powder diffraction line
318
13
Z. Weiss
P. Capkova
Introduction
318
1
Translation stacking faults
318
2
Diffraction patterns
320
2
Results of calculations
322
6
References
328
3
Part II. Experimental techniques
331
34
Crystallite statistics and accuracy in powder diffraction intensity measurements
333
13
Deane K. Smith
Introduction
333
2
Intensity measurement
335
1
Crystallite statistics
336
2
Crystallite statistics in diffractometer geometry
338
5
Crystallite statistics for other instruments
343
1
Summary
344
1
References
345
1
Reciprocal space mapping and ultra-high resolution diffraction of polycrystalline materials
346
19
Paul F. Fewster
Norman L. Andrew
Introduction
346
1
Why high resolution?
346
2
The diffraction equipment
348
2
Conventional methods
350
2
Three-dimensional diffraction in practice
352
3
Practical examples of three-dimensional diffraction
355
7
Summary
362
1
References
363
2
Part III. Macrostress
365
38
X-ray analysis of the inhomogenous stress state
367
36
I. Kraus
N. Ganev
Introduction
367
1
Basic elements of X-ray stress measurement
367
5
The actual residual state of stress in products is inhomogenous
372
4
Stress gradient
376
3
Non-uniform stress problems solved by X-ray at Czech TU in Prague
379
21
Conclusions
400
1
References
401
2
Part IV. Texture
403
130
Texture and structure of polycrystals
405
115
Hans J. Bunge
List of symbols
405
6
Introduction
411
1
Structure of polycrystalline materials
412
3
Correspondence of structure in reciprocal space
415
12
Problems to be considered in texture analysis
427
1
Definition of the texture
428
5
Symmetries of the texture functions
433
3
Statistical relevance of the texture functions
436
2
The texture degree
438
1
Calculation of the ODF from experimental data
438
3
Compatibility of pole figures (measures of error)
441
1
Series expansion
442
4
Special distribution functions
446
2
Experimental methods of texture analysis
448
41
Generalized textural quantities
489
6
Applications of texture analysis
495
18
References
513
7
Texture effects in powder diffraction and their correction by simple empirical functions
520
13
V. Valvoda
Introduction
520
1
Simple texture characterization and correction
521
1
Theory
521
3
Experimental
524
4
Summary
528
2
References
530
3
Part V. Whole-pattern fitting
533
78
Accounting for size and microstrain in whole-powder pattern fitting
535
21
A. Le Bail
List of symbols
535
1
Introduction
535
3
Theory
538
3
WPPF with direct quantitative account for S/M effects
541
3
WPPF with qualitative accounts for S/M effects
544
3
Two experimental illustrations which qualitatively account for S/M in WPPF
547
5
Conclusions
552
1
References
552
4
Modeling of texture in whole-pattern fitting
556
14
Matti Jarvinen
Introduction
556
1
Orientation distribution of grains
556
2
Integrated intensity
558
2
The harmonic model
560
1
Symmetrized harmonics
561
1
Examples
562
1
Further simplifications
563
5
Rietveld method
568
1
Discussion
568
1
References
569
1
A new whole-powder pattern-fitting approach
570
27
P. Scardi
Introduction
570
2
Methodology
572
6
Applications
578
15
Conclusions
593
1
References
594
3
The role of whole-pattern databases in materials science
597
14
Deane K. Smith
Introduction
597
1
The nature of the diffraction pattern
598
3
Defining pattern parameters for a whole-pattern databases
601
2
The role of calculated and simulated patterns in a whole-pattern database
603
1
A database for the analysis of clay minerals
603
3
Uses of the Clay Minerals Database
606
1
Future of whole-pattern databases
606
2
Summary
608
1
References
609
2
Part VI. Restoring physical patterns from the observed variables
611
60
Restoration and preprocessing of physical profiles from measured data
613
39
Marian Cernansky
Introduction
613
2
Preprocessing of data
615
5
Methods of restoration
620
24
Concluding remarks
644
2
References
646
6
Towards higher resolution: a mathematical approach
652
19
Derk Reefman
Introduction to the problem
652
2
The instrument function
654
3
Deconvolution
657
5
Comparison of deconvolution methods
662
3
Applications
665
3
Conclusions
668
1
References
669
2
Part VII. Applications
671
96
Use of pattern decomposition to study microstructure: practical aspects and applications
673
25
Daniel Louer
Introduction
673
1
The problem of line overlap in powder diffraction
674
2
Pattern decomposition
676
4
Instrumental correction
680
3
Examples
683
11
Discussion
694
2
References
696
2
X-ray diffraction broadening effects in mateials characterization
698
30
Giora Kimmel
David Dayan
Introduction
698
1
Techniques and methodology
698
5
Metals and alloys
703
14
Ceramic materials
717
8
Summary and discussion
725
1
References
726
2
Crystal size and disortion parameters in fibres using Wide-Angle X-ray Scattering (WAXS)
728
27
R. Somashekar
Introduction
728
1
Paracrystallinity
729
3
Warren--Averbach method
732
10
Single order method
742
3
Experimental method for some polymer fibres
745
6
Matching of simulated and experimental intensity profiles
751
1
Conclusions
752
1
References
753
2
Pressure-induced profile change of energy-dispersive diffraction using synchrotron radiation
755
12
Takamitsu Yamanaka
Introduction
755
2
High pressure powder diffraction
757
3
Profile change with pressure
760
4
Discussion
764
1
References
765
2
Index
767