Diffraction Analysis of the Microstructure of Materials (Springer Series in Materials Science Vol.68) (2004. XXVI, 552 p. w. 240 figs.)

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Diffraction Analysis of the Microstructure of Materials (Springer Series in Materials Science Vol.68) (2004. XXVI, 552 p. w. 240 figs.)

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Full Description


Overview of diffraction methods applied to the analysis of the microstructure of materials. Since crystallite size and the presence of lattice defects have a decisive influence on the properties of many engineering materials, information about this microstructure is of vital importance in developing and assessing materials for practical applications. The most powerful and usually non-destructive evaluation techniques available are X-ray and neutron diffraction. The book details, among other things, diffraction-line broadening methods for determining crystallite size and atomic-scale strain due, e.g. to dislocations, and methods for the analysis of residual (macroscale) stress. The book assumes only a basic knowledge of solid-state physics and supplies readers sufficient information to apply the methods themselves.

Table of Contents

Part I Retrospective on Line-Broadening Analysis
1 Line Profile Analysis: A Historical Overview
J.I. Langford 3 (14)
1.1 Early Years 3 (1)
1.2 Bertram E. Warren (1902-1991) 4 (1)
1.3 Arthur J.C. Wilson (1914-1995) 5 (1)
1.4 The Parrish Diffractometer 6 (1)
1.5 Williamson-Hall Plot 6 (1)
1.6 Fourier Methods 7 (1)
1.7 Variance Method 8 (1)
1.8 Further Development of Fourier 8 (2)
Methods
1.9 Powder Pattern Fitting 10 (1)
1.10 Whole Powder Patterns Modelling 11 (1)
References 11 (6)
Part II Analysis of the Full Diffraction Pattern
2 Convolution Based Profile Fitting
A. Kern, A.A. Coelho, R.W. Chearg 17 (34)
2.1 Introduction 17 (2)
2.2 Convolution Based Profile Fitting 19 (10)
2.2.1 General Considerations 19 (2)
2.2.2 Numerical Procedures of 21 (1)
Convolution Based Profile Fitting
2.2.3 The Wavelength Distribution in 21 (5)
Laboratory Diffractometers
2.2.4 Examples 26 (3)
2.3 Fundamental Parameters Approach 29 (17)
2.3.1 General Considerations to FPA 29 (2)
2.3.2 Applicability of the FPA 31 (1)
2.3.3 Diffractometer Configurations and 31 (1)
Their Geometrical Aberrations
2.3.4 Geometric Instrument Aberrations 32 (10)
2.3.5 Examples 42 (4)
2.4 Convolution Based Profile Fitting 46 (2)
versus Analytical Profile Fitting
2.4.1 Quality of Fit 46 (1)
2.4.2 Number of Fit Parameters Required 47 (1)
2.5 Conclusions 48 (1)
References 49 (2)
3 Whole Powder Pattern Modelling: Theory and
Applications
P. Scardi, M. Leoni 51 (42)
3.1 Introduction 51 (4)
3.2 Theoretical Basis of WPPF and WPPM 55 (20)
3.2.1 Basic Expressions for the 55 (2)
Diffracted Intensity from a Defected
Material
3.2.2 Line Profile Components 57 (15)
3.2.3 WPPM and WPPF 72 (3)
3.3 Experimental 75 (1)
3.4 Application of WPPM 75 (10)
3.4.1 WPPM Results for Ball-Milled Ni 75 (10)
Powders
3.5 Comparison between TEM and WPPM Data 85 (3)
3.6 Conclusions 88 (1)
References 89 (4)
4 Full Profile Analysis of X-ray Diffraction
Patterns for Investigation of Nanocrystalline
Systems
S.V. Tsybulya, S.V. Cherepanova, G.N. 93 (32)
Kryukova
4.1 The peculiarities of Structural 94 (3)
Analysis of Nanocrystalline Materials
4.2 Crystal Structure Refinement Using 97 (5)
the Modified Rietveld Method
4.3 Microstructure Modelling and Full 102(7)
Powder Pattern Simulation Using the
Kakinoki-Komura Method
4.3.1 The Choice of the Simulation 102(1)
Algorithm
4.3.2 The Theory of Scattering by a 1D 103(4)
Disordered Crystal
4.3.3 Disorders of the First and Second 107(2)
Types: A Generalized Algorithm for
Microstrain Account
4.4 Program Description 109(1)
4.5 Simulation of the XRD Patterns of 110(10)
Nanocrystalline Materials: Some Examples
4.5.1 Filamentary Carbons 110(2)
4.5.2 Metallic Cobalt 112(5)
4.5.3 Metastable In-Ni Alloys 117(3)
4.6 Conclusion 120(1)
References 121(4)
5 Crystallite Size and Residual Strain/Stress
Modeling in Rietveld Refinement
D. Balzar, N.C. Popa 125(22)
5.1 Introduction 125(1)
5.2 Modeling of the Crystallite-Size 126(10)
Broadened Line Profile in Rietveld
Refinement
5.2.1 Background 126(2)
5.2.2 The Crystallite-Size Broadened 128(1)
Line Profile and Size Distribution
5.2.3 Application to the Lognormal Size 128(1)
Distribution: Isotropic Case
5.2.4 Determination of the Distribution 129(2)
Parameters
5.2.5 The Analytical Approximation for 131(1)
Φ(χ)
5.2.6 Limitations of the Common 132(1)
Analytical Approximations of the
Size-Broadened Profile
5.2.7 The Anisotropic Crystallite Shape 132(1)
5.2.8 Application to Two Cubic Ceria 133(2)
Samples
5.2.9 Conclusion 135(1)
5.3 Modeling of Residual Strain/Stress in 136(8)
Rietveld Refinement
5.3.1 Background 136(1)
5.3.2 The Measured Strain, the Average 137(2)
Strain and Stress Tensors
5.3.3 The Strain Expansion in 139(2)
Generalized Spherical Harmonics
5.3.4 The Selection Rules for All Laue 141(1)
Classes
5.3.5 Determination of Average Strain 142(1)
and Stress Tensors
5.3.6 Conclusion 143(1)
5.4 Concluding Remarks 144(1)
References 144(3)
6 The Quantitative Determination of the
Crystalline and the Amorphous Content by the
Rietveld Method: Application to Glass
Ceramics with Different Absorption
Coefficients
A.F. Gualtieri, A. Guagliardi, A. Iseppi 147(20)
6.1 Introduction 148(3)
6.2 Experimental 151(5)
6.2.1 Sample Selection and Preparation 151(3)
6.2.2 Calculation of the Linear 154(1)
Absorption Coefficient
6.2.3 Data Collection for the QPA 154(1)
6.2.4 Rietveld Refinements 155(1)
6.3 Results and Discussion 156(7)
6.4 Conclusions and Future Perspectives 163(1)
References 163(4)
7 Quantitative Analysis of Amorphous Fraction
In the Study of the Microstructure of
Semi-crystalline Materials
P. Riello 167(20)
7.1 Introduction 167(1)
7.2 A Short Historical Introduction to 168(3)
the Standardless Quantitative Methods
7.3 A Rietveld Based Solution 171(6)
7.4 Examples 177(6)
7.4.1 Example 1: Study of a Supported 177(4)
Metal Catalyst
7.4.2 Example 2: Nucleation of Glass 181(2)
Ceramic Materials in the System
Li2O-A12O3-Si02
7.5 Conclusion 183(1)
References 184(3)
Part III Crystallite Size and Shape
8 A Bayesian/Maximum Entropy Method for the
Certification of a Nanocrystallite-Size NIST
Standard Reference Material
N. Armstrong, W. Kalceff, J.P. Cline, J. 187(42)
Bonevich
8.1 Introduction 187(3)
8.2 Nanocrystallite-Size Broadening of 190(5)
X-ray Line Profiles
8.2.1 Size-Broadened Profiles 190(4)
8.2.2 Observed Line Profiles 194(1)
8.3 Developing the Inverse Problem 195(2)
8.3.1 Forward Mapping 195(1)
8.3.2 Inverse Problem 195(2)
8.4 Axioms for Inductive Reasoning 197(2)
8.4.1 Two Basic Axioms 197(1)
8.4.2 Bayes' Theorem 198(1)
8.4.3 Marginalisation or "Integrating 199(1)
Out"
8.5 Developing a "Method" for Determining 199(7)
P(D)
8.5.1 Bayes' Theorem for P(D) 199(1)
8.5.2 Likelihood and Entropy Functions 200(2)
8.5.3 Combining S and L 202(1)
8.5.4 What to Do with a? 202(2)
8.5.5 Determining f (20) 204(1)
8.5.6 Derivation of Langford et al. 205(1)
(2000)
8.6 Analysis of CeO2 X-ray Diffraction 206(17)
Data
8.6.1 XRD Details 206(1)
8.6.2 TEM Details 207(1)
8.6.3 Identifying Specimen Broadening 208(7)
8.6.4 Determining the P(D) Using the 215(6)
Bayesian/MaxEnt Method
8.6.5 TEM Size Distribution 221(1)
8.6.6 Comparison of Methods 222(1)
8.7 Discussion 223(2)
References 225(4)
9 Study of Submicrocrystalline Materials
Diffuse Scattering in Transmitted Wave
U. Kuzel, V. Holy, M. Cernansky, J. Kubena, 229(20)
D. Simek, J. Kub
9.1 Introduction 229(2)
9.2 Theoretical Background 231(4)
9.3 Experimental Setup and Evaluation 235(2)
9.3.1 Determination of the 236(1)
Autocorrelation Function by
Transformation of Measured Data
9.3.2 Evaluation by the Fitting of 236(1)
Measured Data
9.4 Results and Discussion 237(7)
9.5 Conclusions 244(1)
References 245(4)
Part IV Dislocations and Stacking Faults
10 Determining the Dislocation Contrast
Factor for X-ray Line Profile Analysis
N. Armstrong, P. Lynch 249(38)
10.1 Introduction 249(2)
10.2 X-ray Line-Profile Broadening 251(2)
10.2.1 Quantifying the Line-Broadening 251(1)
10.2.2 Quantifying the Dislocation 252(1)
Broadening
10.3 Dislocation Contrast Factors, Chkl 253(9)
10.3.1 Evaluating the Contrast Factor, 253(5)
Chkl
10.3.2 Determining the Dislocation 258(4)
Displacement Fields
10.4 Computing the Contrast Factor, Chkl 262(16)
10.4.1 Chkl Values for fcc Materials 263(8)
10.4.2 Chkl Values for bcc Materials 271(2)
10.4.3 An Unusual Case 273(5)
10.5 Conclusion 278(3)
A Transforming the Elastic Constants and 281(1)
Diffraction Vector
A.1 Transforming the Elastic Constants 281(1)
A.2 Transforming the Diffraction Vector 282(1)
B Determining A, L and D for u(x1,x2) 282(5)
B.1 General Field Equations 282(1)
B.2 Determining the Reduced Elastic 283(1)
Compliances
B.3 Determining the Compliance 284(1)
Polynomial
B.4 Determining the L Matrix 284(1)
B.5 Determining the A kappaα 284(1)
Coefficients
B.6 Determining the Dα, 285(1)
Coefficients
References 285(2)
11 X-ray Peak Broadening Due to Inhomogeneous
Dislocation Distributions
I. Groma, A. Borbely 287(22)
11.1 Introduction 287(2)
11.2 Properties of the Fourier Transform 289(5)
of Intensity Distribution Induced by
Dislocations
11.3 Peak Broadening Due to Narrow 294(1)
Dislocation Dipoles
11.4 Asymptotic Properties of the 295(2)
Intensity Distribution
11.5 Evaluation Procedure 297(4)
11.6 Influence of the Finite Coherent 301(3)
Domain Size
11.7 Conclusions 304(2)
References 306(3)
12 Determination of Non-uniform Dislocation
Distributions In Polycrystalline Materials
J.-D. Kamminga, L.J. Seijbel, R. Delhez 309(24)
12.1 Introduction 309(2)
12.2 Theory 311(6)
12.2.1 Background 311(2)
12.2.2 Analysis for Different Kinds of 313(4)
Polycrystalline Specimens
12.3 Experimental Illustrations 317(10)
12.3.1 Al Layers 317(6)
12.3.2 Ni Layers 323(4)
12.4 Discussion 327(2)
12.5 Conclusions 329(1)
References 330(3)
13 Line Profile Fitting: The Case of fcc
Crystals Containing Stacking Faults
A.I. Ustinov, L.O. Olikhovska, N.M. 333(30)
Budarina, F. Bernard
13.1 Introduction 333(1)
13.2 Influence of Stacking Faults on XRD 334(15)
Powder Peak Profiles
13.2.1 Description of the Structures 334(4)
Containing Stacking Faults
13.2.2 Calculation Procedure for the 338(1)
Intensity Scattered by a Single-Crystal
13.2.3 Calculation Procedure for the 339(2)
Intensity Scattered by a Powder
13.2.4 Intrinsic Stacking Faults (hh) 341(2)
13.2.5 Extrinsic Stacking Faults (hc'h) 343(1)
13.2.6 Twin Stacking Faults (h) 344(3)
13.2.7 Determination of the Dominant 347(2)
Type of SF from the XRD Powder Diagram
13.3 Simulation Procedure for "Real" XRD 349(4)
Powder Peak Profiles
13.4 Defect and Microstructure Analysis 353(5)
of Ball-Milled Cu Powders XRD
13.4.1 Preparation and Characterization 353(1)
of the Powders
13.4.2 Full Profile Fitting 354(4)
13.5 Conclusion 358(1)
References 359(4)
Part V Grain Interaction
14 Diffraction Elastic Constants and Stress
Factors; Grain Interaction and Stress In
Macroscopically Elastically Anisotropic
Solids; The Case of Thin Films
U. Welzel, M. Leoni, E.J. Mittemeijer 363(28)
14.1 Introduction 363(3)
14.2 Theoretical Background 366(7)
14.2.1 Frames of Reference 366(1)
14.2.2 Euler Angles and the 367(1)
Crystallographic Orientation
Distribution Function (ODF)
14.2.3 Calculation of Averages of 368(1)
Tensors
14.2.4 Mechanical Elastic Constants 369(1)
14.2.5 Diffraction Elastic Constants 370(1)
and Stress Factors
14.2.6 Principle of Diffraction Stress 371(1)
Analysis
14.2.7 Effective Grain Interaction 371(2)
14.3 Direction-Dependent Grain Interaction 373(13)
14.3.1 The Vook-Witt Model 374(3)
14.3.2 Recent Developments 377(9)
14.4 Surface Anisotropy as a Special Case 386(2)
of Direction Dependent Grain Interaction
14.5 Conclusion 388(1)
References 389(2)
15 Interaction between Phases In Co-deforming
Two-Phase Materials: The Role of Dislocation
Arrangements
R.E. Bolmoro, H.-G. Brokmeier, J.W. 391(22)
Signorelli, A. Fourty, M.A. Bertinetti
15.1 Introduction 391(1)
15.2 Grain Interaction Assessment 392(10)
15.2.1 Strain Interaction 392(4)
15.2.2 Spin Interaction 396(6)
15.3 Results 402(5)
15.3.1 Extruded Al-Cu 404(2)
15.3.2 Extruded Cu-Fe 406(1)
15.3.3 Cu Torsion 407(1)
15.4 Discussion and Conclusions 407(2)
15.4.1 What does Our Model Provide? 407(1)
15.4.2 What Do We Need? 408(1)
References 409(4)
Part VI Surface and Interface Effects
16 Grain Surface Relaxation Effects In Powder
Diffraction
M. Leoni, P. Scardi 413(42)
16.1 Introduction 413(1)
16.2 Surface Relaxation 414(3)
16.3 Surface Relaxation Models in Powder 417(15)
Diffraction
16.3.1 State of the Art 417(5)
16.3.2 Proposed Model of Effective 422(10)
Grain Surface Relaxation
16.4 Experimental Validation: 432(20)
Nanocrystalline Cerium Oxide Powders
16.5 Conclusions 452(1)
References 452(3)
17 Interface Stress In Polycrystalline
Materials
R. Birringer, M. Hoffmann, P. Zimmer 455(18)
17.1 Introduction and Basic Ideas 455(2)
17.2 Theory and Methodology 457(5)
17.3 Experiments and Discussion 462(4)
17.4 Outlook 466(2)
References 468(5)
Part VII Microstructural Gradients; Thin Films
18 Problems Related to X-Ray Stress Analysis
in Thin Films In the Presence of Gradients
and Texture
C. Genzel 473(32)
18.1 Introduction 473(1)
18.2 Residual Stress in Thin Films: Its 474(4)
Origin and Possible Stress States
18.2.1 Extrinsic and Intrinsic Film 474(1)
Stresses
18.2.2 Possible Macrostress States in 475(3)
Thin Films
18.3 Basic Principles of X-Ray Stress 478(7)
Gradient Analysis
18.3.1 Problems Related to Thin Films 478(5)
18.3.2 Concepts in Depth-Resolved 483(2)
Thin-Film X-Ray Residual Stress Analysis
18.4 Problem-Oriented Solutions for 485(14)
Special Cases in Thin-Film XSA
18.4.1 Measurement Techniques Using 485(4)
Grazing and Low Incident Angles
18.4.2 Experimental Techniques Based on 489(5)
Sample Tilt
18.4.3 Residual Stress Depth Profiling 494(5)
by Sample Rotation
18.5 Concluding Remarks 499(2)
References 501(4)
19 Two-Dimensional XRD Profile Modelling in
Imperfect Epitaxial Layers
A. Boulle, O. Masson, R. Guinebretiere, A. 505(22)
Danger
19.1 Introduction 505(1)
19.2 The Sample 506(1)
19.3 XRD Equipment 507(6)
19.3.1 Instrument Description 507(1)
19.3.2 Reciprocal Space Mapping 508(2)
19.3.3 Scans Across Reciprocal Space 510(1)
19.3.4 Instrumental Profile 511(2)
19.4 Profile Modelling 513(11)
19.4.1 Out-of-Plane Profile Modelling 514(2)
19.4.2 In-Plane Modelling 516(8)
19.5 Conclusions 524(1)
References 525(2)
20 Three-Dimensional Reciprocal Space
Mapping: Application to Polycrystalline CVD
Diamond
M. Golshan, D. Lauvdy, P.F. Fenster, M. 527(14)
Moore
20.1 Introduction 527(2)
20.1.1 X-Ray Methods Used for Strain 528(1)
Determination
20.2 Principle of 529(1)
Three-Dimensional-Reciprocal Space
Mapping (3-D RSM)
20.3 Instrumental Requirements for 530(2)
Performing High-Resolution
Reciprocal-Space Mapping
20.4 Studies of Polycrystalline CVD 532(5)
Diamond
20.4.1 Scanning Electron Microscopy 532(1)
20.4.2 Powder Diffraction Studies 533(2)
20.4.3 Three-Dimensional 535(2)
Reciprocal-Space Mapping
20.5 Discussion and Conclusion 537(1)
References 538(3)
Index 541