Texture Analysis in Materials Science (eBook)

Mathematical Methods

H.-J. Bunge (Autor)

eBook Download: PDF

2013 | 1. Auflage
614 Seiten
Elsevier Science (Verlag)
978-1-4832-7839-1 (ISBN)

Infos

Texture Analysis in Materials Science Mathematical Methods focuses on the methodologies, processes, techniques, and mathematical aids in the orientation distribution of crystallites. The manuscript first offers information on the orientation of individual crystallites and orientation distributions. Topics include properties and representations of rotations, orientation distance, and ambiguity of rotation as a consequence of crystal and specimen symmetry. The book also takes a look at expansion of orientation distribution functions in series of generalized spherical harmonics, fiber textures, and methods not based on the series expansion. The publication reviews special distribution functions, texture transformation, and system of programs for the texture analysis of sheets of cubic materials. The text also ponders on the estimation of errors, texture analysis, and physical properties of polycrystalline materials. Topics include comparison of experimental and recalculated pole figures; indetermination error for incomplete pole figures; and determination of the texture coefficients from anisotropie polycrystal properties. The manuscript is a dependable reference for readers interested in the use of mathematical aids in the orientation distribution of crystallites.

Inhalt

Front Cover 1
Texture Analysis in Materials Science: Mathematical Methods 4
Copyright Page 5
Table of Contents 10
Preface 6
Preface to the English Edition 7
List of Symbols Used 16
Chapter 1. Introduction 22
Chapter 2. Orientation of Individual Crystallites 24
2.1. Various Representations of a Rotation 24
2.2. Some Properties of Rotations 57
2.3. Ambiguity of Rotation as a Consequence of Crystal and Specimen Symmetry 57
2.4. Orientation Distance 59
2.5. Orientation for Rotational Symmetry 60
Chapter 3. Orientation Distributions 63
Chapter 4. Expansion of Orientation Distribution Functions in Series of Generalized Spherical Harmonics (Three-dimensional Textures) 68
4.1. Determination of the Coefficients Clµv 70
4.2. The General Axis Distribution Functions A(h,y) 74
4.3. The Angular Distribution Function Why (T) 94
4.4. Determination of the Coefficients Clµv by the Method of Least Squares 99
4.5. Measures of Accuracy 100
4.6. Truncation Error 103
4.7. Determination of the Coefficients Clµv from Incompletely Measured Pole Figures 106
4.8. Texture Index 109
4.9. Ambiguity of the Solution 111
4.10. Comparison with ROE'S Terminology 118
4.11. The Role of the Centre of Inversion 121
Chapter 5. Fibre Textures 140
5.1. Determination of the Coefficients Clµ 142
5.2. The General Axis Distribution Function A(h F) 143
5.3. Determination of the Coefficients Clµ According to the Least Squares Method 150
5.4. Measures of Accuracy 151
5.5. Truncation Error 153
5.6. Determination of the Coefficients Clµ from Incompletely Measured Pole Figures 156
5.7. Texture Index 158
5.8. The Approximation Condition for Fibre Textures 159
5.9. Calculation of the Function .(F, ß) for Various Crystal Symmetries 161
5.10. The Role of the Centre of Inversion 163
Chapter 6. Methods not Based on the Series Expansion 175
6.1. The Method of PERLWITZ, LÜCKE and PITSCH 175
6.2. The Method of JETTER, MCHARGUE and WILLIAMS 178
6.3. The Method of RUER and BARO 182
6.4. The Method of IMHOF 188
Chapter 7. Special Distribution Functions 190
7.1. Ideal Orientations 190
7.2. Cone and Ring Fibre Textures 194
7.3. 'Spherical' Textures 197
7.4. Fibre Axes 197
7.5. Line and Surface Textures (Dimension of a Texture) 199
7.6. Zero Regions 200
7.7. Gaussian Distributions 201
7.8. Polynomial Approximation (Angular Resolving Power) 204
Chapter 8. Texture Transformation 209
Chapter 9. A System of Programs for the Texture Analysis of Sheets of Cubic Materials 215
9.1. The Subroutines 216
9.2. The Mainline Programs 221
9.3. The Library Program 221
9.4. Calculation Times and Storage Requirements 225
9.5. Supplementary Programs 225
9.6. A Numerical Example 226
9.7. Listings of the ODF and Library Programs 232
Chapter 10. Estimation of the Errors 233
10.1. A Reliability Criterion for Pole Figures of Materials with Cubic Symmetry 234
10.2. The Error Curve /.Fvl/ 235
10.3. The Error Curve /.Clµv/ 238
10.4. Error Estimation According to the HARRIS Relation 239
10.5. Comparison of Experimental and Recalculated Pole Figures 239
10.6. Negative Values 242
10.7. Estimation of the Truncation Error by Extrapolation 242
10.8. The Integration Error 243
10.9. The Statistical Error 245
10.10. The Indetermination Error for Incomplete Pole Figures 246
Chapter 11. Some Results of Texture Analysis 247
11.1. Three-dimensional Orientation Distribution Functions (ODF) 247
11.2. Fibre Textures 289
Chapter 12. Orientation Distribution Functions of Other Structural Elements 300
12.1. Orientation Distribution Functions of the Grain Surfaces 300
12.2. Orientation Distribution Functions of the Grain Boundaries 302
12.3. Orientation Distribution Functions of the Grain Edges 311
Chapter 13. Physical Properties of Polycrystalline Materials 315
13.1. Physical Properties of Single Crystals 315
13.2. The Problem of Averaging 320
13.3. The Calculation of the Simple Mean Valued E 323
13.4. Average Values of Special Properties 329
13.5. Determination of the Texture Coefficients from Anisotropic Polycrystal Properties 361
13.6. Determination of Single Crystal Properties from Polycrystal Measurements 363
13.7. Textures With Equal Physical Properties 364
13.8. Physical Meaning of the Coefficients Clµv 369
Chapter 14. Mathematical Aids 372
14.1. Generalized Spherical Harmonics 372
14.2. Spherical Surface Harmonics 377
14.3. FOURIER Expansion of the .lmn(F) 380
14.4. CLEBSCH—GORDAN Coefficients 383
14.5. Symmetric Generalized Spherical Harmonics 384
14.6. Symmetric Spherical Surface Harmonics 397
14.7. The Symmetric Functions of the Various Symmetry Groups 399
14.8. CLEBSCH—GORDAN Coefficients for Symmetric Functions 422
Chapter 15. Numerical Tables 425
References 426
Appendix 1: Tables 9.2—9.14 442
Appendix 2: Listings of the ODF and Library Programs 460
Appendix 3: Tables for Chapter 15 476
15.1. FOURIER Coefficients 477
15.2. Symmetry Coefficients Blmµ 522
15.3. Generalized LEGENDRE Functions Plmn(F) 540
15.4. Cubic Surface Harmonics klµ(Fß) 548
15.5. Cubic Generalized Spherical Harmonics 554
Appendix 4: Graphic Representations 582
A4.1. The Generalized LEGENDRE Functions .lmn(F) 583
A4.2. Cubic Spherical Harmonics klu(Fß) 588
A4.3. Cubic Generalized Spherical Harmonics 589
Subject Index 606

Produkt-Details

• Erscheint lt. Verlag: 3.9.2013
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Chemie
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Mineralogie / Paläontologie
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 1-4832-7839-5 / 1483278395
• ISBN-13: 978-1-4832-7839-1 / 9781483278391