1 Present State of Electron Backscatter Diffraction and
Prospective Developments ..................................... 1
Robert A. Schwarzer, David P. Field, Brent L. Adams, Mukul
Kumar, and Adam J. Schwartz
1.1 Introduction ............................................ 1
1.2 Generation and Interpretation of Electron Backscatter
Diffraction Patterns .................................... 2
1.3 Experimental Set-Up of an EBSD System ................... 3
1.4 The Components of an Automated EBSD System .............. 4
1.4.1 The Pattern Acquisition Device ................... 4
1.4.2 Mechanical Stage and Digital Beam Scanning ....... 5
1.5 Spatial Resolution ...................................... 7
1.6 SEM Specifications for Good EBSD Performance ............ 9
1.7 The Radon or Hough Transformation for Band
Localization ........................................... 11
1.8 Indexing ............................................... 12
1.9 Fast EBSD .............................................. 13
1.10 Ion Blocking Patterns .................................. 15
1.11 Conclusions ............................................ 19
2 Dynamical Simulation of Electron Backscatter Diffraction
Patterns .................................................... 21
Aimo Winkelmann
2.1 Introduction ........................................... 21
2.2 Model of Electron Backscatter Diffraction .............. 21
2.3 Dynamical Electron Diffraction in EBSD ................. 22
2.3.1 Dynamical Electron Diffraction in EBSD .......... 22
2.3.2 Dynamical Electron Diffraction in EBSD .......... 23
2.3.3 Dynamical Electron Diffraction in EBSD .......... 24
2.4 Applications ........................................... 25
2.4.1 A Real-Space View of EBSD ....................... 25
2.4.2 Full Scale Simulation of EBSD Patterns .......... 27
2.4.3 The Influence of the Energy Spectrum of the
Backscattered Electrons ......................... 28
2.4.4 Dynamical Effects of Anisotropic
Backscattering .................................. 30
2.5 Summary ................................................ 32
3 Representations of Texture .................................. 35
Jeremy K. Mason and Christopher A. Schuh
3.1 Introduction ........................................... 35
3.2 Rotations and Orientations ............................. 36
3.2.1 Defining a Rotation ............................. 36
3.2.2 Defining an Orientation ......................... 37
3.3 Pole Figures ........................................... 38
3.4 Discrete Orientations .................................. 40
3.4.1 Axis-Angle Parameters ........................... 41
3.4.2 Rodrigues Vectors ............................... 42
3.4.3 Quaternions ..................................... 42
3.4.4 Euler Angles .................................... 45
3.5 Orientation Distribution Functions ..................... 46
3.5.1 Circular Harmonics .............................. 46
3.5.2 Spherical Harmonics ............................. 47
3.5.3 Hyperspherical Harmonics ........................ 48
3.5.4 Generalized Spherical Harmonics ................. 49
3.5.5 Symmetrized Harmonics ........................... 49
3.6 Conclusion ............................................. 50
4 Energy Filtering in EBSD .................................... 53
Alwyn Eades, Andrew Deal, Abhishek Bhattacharyya, and
Tejpal Hooghan
4.1 Introduction ........................................... 53
4.2 Background ............................................. 53
4.3 Energy Filters ......................................... 54
4.4 Operating the Filter ................................... 56
4.5 Early Results .......................................... 57
4.6 Patterns at Different Energies ......................... 60
4.7 Localization of the Signal ............................. 61
4.8 Future Energy Filters in EBSD .......................... 62
4.9 Summary and Conclusions ................................ 62
5 Spherical Kikuchi Maps and Other Rarities ................... 65
Austin P. Day
5.1 Introduction ........................................... 65
5.2 Electron Backscatter Patterns .......................... 65
5.3 Spherical Kikuchi Maps ................................. 65
5.4 EBSP Detectors ......................................... 65
5.5 EBSP Imaging and Uniformity ............................ 68
5.6 EBSP Simulation ........................................ 68
5.7 Spherical Kikuchi Maps from EBSPs ...................... 68
5.8 Kikuchi Band Profiles .................................. 72
5.9 Spherical Kikuchi Map Inversion ........................ 74
5.10 Uses for Spherical Kikuchi Maps ........................ 75
5.11 Colour Orientation Contrast Images ..................... 76
5.12 STEM in the SEM ........................................ 76
5.13 Unusual Features in EBSPs .............................. 77
6 Application of Electron Backscatter Diffraction to Phase
Identification .............................................. 81
Bassem El-Dasher and Andrew Deal
6.1 Introduction ........................................... 81
6.2 Considerations for Phase ID with EBSD .................. 82
6.3 Case Studies ........................................... 84
6.3.1 Simultaneous EBSD/EDS Phase Discrimination ...... 85
6.3.2 Distinguishing γ and γ' in Ni Superalloys ....... 86
6.3.3 Volume Fraction Determination in a Multiphase
Alloy ........................................... 89
7 Phase Identification Through Symmetry Determination
in EBSD Patterns ............................................ 97
David J. Dingley and S.I. Wright
7.1 Introduction ........................................... 97
7.2 Basis of the Phase Identification Method ............... 97
7.3 Determination of the Crystal Unit Cell ................. 98
7.4 Discovering the Lattice Symmetry ...................... 100
7.5 Re-Indexing the Pattern According to the Discovered
Crystal Class ......................................... 101
7.6 Examples .............................................. 102
7.6.1 Case 1, A Cubic Crystal ........................ 102
7.6.2 Case 2, A Hexagonal Crystal .................... 104
7.6.3 Case 3, A Trigonal Crystal ..................... 104
7.7 Discussion ............................................ 106
8 Three-Dimensional Orientation Microscopy by Serial
Sectioning and EBSD-Based Orientation Mapping in a
FIB-SEM .................................................... 109
Stefan Zaefferer and Stuart I. Wright
8.1 Introduction .......................................... 109
8.2 The Geometrical Set-Up for 3D Characterisation in
a FIB-SEM ............................................. 110
8.3 Automatic 3D Orientation Microscopy ................... 113
8.4 Software for 3D Data Analysis ......................... 113
8.5 Application Examples .................................. 114
8.5.1 The 3D Microstructure and Crystallography of
Pearlite Colonies .............................. 114
8.5.2 Microstructure of "Nanocrystalline" NiCo
Deposits ....................................... 115
8.6 Discussion ............................................ 119
8.6.1 Accuracy and Application Limits ................ 119
8.6.2 Materials Issues ............................... 120
8.7 Conclusions ........................................... 120
9 Collection, Processing, and Analysis of Three-Dimensional
EBSD Data Sets ............................................. 123
Michael A. Groeber, David J. Rowenhorst, and Michael
D. Uchic
9.1 Introduction .......................................... 123
9.2 Data Collection ....................................... 123
9.3 Processing Strategies ................................. 124
9.3.1 Registration and Alignment of Sections ......... 124
9.3.2 Segmentation of Grains ......................... 126
9.3.3 Clean-Up Routines .............................. 127
9.4 Analysis Capabilities ................................. 129
9.4.1 Morphological Descriptors ...................... 129
9.4.2 Crystallographic Descriptors ................... 133
9.5 Summary ............................................... 135
10 3D Reconstruction of Digital Microstructures ............... 139
Stephen D. Sintay, Michael A. Groeber, and Anthony
D. Rollett
10.1 Motivation ............................................ 139
10.2 Background ............................................ 139
10.2.1 2D-3D Inference ................................ 139
10.2.2 3D Polycrystal Microstructure Generation ....... 140
10.3 Data Collection and Analysis .......................... 140
10.3.1 Data Sources ................................... 140
10.3.2 Identifying Features ........................... 141
10.3.3 Statistical Description of Features ............ 141
10.4 Methods for 3D Structure Inference .................... 141
10.4.1 Monte Carlo-Based Histogram Fitting ............ 143
10.4.2 Observation-Based Domain Constraint ............ 145
10.5 Generation of 3D Structure ............................ 147
10.5.1 Packing of Ellipsoids .......................... 147
10.5.2 Relaxation of Boundaries ....................... 149
10.6 Quality Analysis ...................................... 149
10.6.1 Size Distribution Comparison ................... 149
10.6.2 Shape Distribution Comparison .................. 149
10.6.3 Neighborhood Comparison ........................ 151
10.6.4 Boundary Structure Comparison .................. 151
10.7 Thoughts on Current Conditions and Future Work ........ 151
11 Direct 3D Simulation of Plastic Flow from EBSD Data ........ 155
Nathan R. Barton, Joel V. Bernier, Ricardo A. Lebensohn,
and Anthony D. Rollett
11.1 Introduction .......................................... 155
11.2 Material and Microstructural Model .................... 156
11.2.1 Three-Dimensional Microstructure Generation .... 157
11.2.2 Micromechanical Model .......................... 158
11.2.3 Finite Element Model ........................... 159
11.3 Simulation Results .................................... 159
11.4 Directions for Further Computational Development ...... 162
11.5 Conclusions ........................................... 165
12 First-Order Microstructure Sensitive Design Based on
Volume Fractions and Elementary Bounds ..................... 169
Surya R. Kalidindi, David T. Fullwood, and Brent L. Adams
12.1 Introduction .......................................... 169
12.2 Quantification of Microstructure ...................... 170
12.3 Microstructure Sensitive Design Framework ............. 170
12.4 Property Closures ..................................... 172
13 Second-Order Microstructure Sensitive Design Using
2-Point Spatial Correlations ............................... 177
David T. Fullwood, Surya R. Kalidindi, and Brent L. Adams
13.1 Introduction .......................................... 177
13.2 Definition and Properties of the 2-Point Correlation
Functions ............................................. 178
13.2.1 Boundary Conditions ............................ 179
13.2.2 Properties of the 2-Point Functions ............ 179
13.2.3 Visualization of the 2-Point Functions ......... 179
13.2.4 Metrics from 2-Point Correlations .............. 180
13.2.5 Collecting 2-Point Correlations from Material
Samples ........................................ 180
13.3 Structure Property Relations .......................... 181
13.3.1 Localization Tensors ........................... 182
13.3.2 Effective Tensors .............................. 184
13.4 Microstructure Design ................................. 186
14 Combinatorial Materials Science and EBSD: A High
Throughput Experimentation Tool ............................ 189
Krishna Rajan
14.1 Introduction .......................................... 189
14.2 Introduction to Combinatorial Methods ................. 189
14.2.1 High Throughput EBSD Screening ................. 190
14.2.2 Informatics and Data ........................... 194
14.3 Summary ............................................... 196
15 Grain Boundary Networks .................................... 201
Bryan W. Reed and Christopher A. Schuh
15.1 Introduction .......................................... 201
15.2 Measurement and Classification of Local Network
Elements .............................................. 202
15.2.1 General Definitions for Single Boundaries ...... 202
15.2.2 Structures with More than One Boundary ......... 203
15.3 Geometry of the Network Structure ..................... 204
15.3.1 Percolation Measures of the Grain Boundary
Network ........................................ 205
15.3.2 Crystallographic Constraints ................... 206
15.4 Microstructure-Property Connections ................... 208
15.4.1 Composite Averaging vs. Percolation Theory ..... 209
15.4.2 Crystallographic Correlations .................. 211
15.5 Conclusions and Future Outlook ........................ 212
16 Measurement of the Five-Parameter Grain Boundary
Distribution from Planar Sections .......................... 215
Gregory S. Rohrer and Valerie Randle
16.1 Introduction: Grain Boundary Planes and Properties .... 215
16.2 Serial Sectioning ..................................... 216
16.3 Single-Surface Trace Analysis ......................... 217
16.4 Five-Parameter Stereological Analysis ................. 218
16.4.1 Parameterization and Discretization of the
Space of Grain Boundary Types .................. 218
16.4.2 Measurement of the Grain Boundary
Characterization Distribution .................. 219
16.4.3 Performance of the Stereological Analysis ...... 221
16.4.4 Comparison GBCDs Measured Stereologically
and by Serial Sectioning in the Dual Beam FIB .. 223
16.5 Examples of Five-Parameter Analyses ................... 224
17 Strain Mapping Using Electron Backscatter Diffraction ...... 231
Angus J. Wilkinson, David J. Dingley, and Graham Meaden
17.1 Introduction .......................................... 231
17.1.1 The Need for Local Strain Assessment ........... 231
17.1.2 Competing Strain Mapping Techniques ............ 231
17.1.3 Review of Applications of EBSD to Analysis of
Elastic Strains ................................ 232
17.2 Cross-Correlation-Based Analysis of EBSD Patterns ..... 234
17.2.1 Geometry: Linking Pattern Shifts to Strain ..... 234
17.2.2 Pattern Shift Measurement ...................... 235
17.2.3 Sensitivity Analysis ........................... 237
17.2.4 Illustrative Applications ...................... 239
17.3 Concluding Remarks .................................... 247
18 Mapping and Assessing Plastic Deformation Using EBSD ....... 251
Luke N. Brewer, David P. Field, and Colin C. Merriman
18.1 Plastic Deformation Effects on the EBSD Pattern and
Orientation Map ............................................ 251
18.2 Pattern Rotation Approaches ........................... 253
18.2.1 Mapping Orientations and Misorientations ....... 253
18.2.2 Average Misorientation Approaches .............. 255
18.2.3 Measurement and Calculation of GND Densities ... 258
19 Analysis of Deformation Structures in FCC Materials
Using EBSD and ТЕМ Techniques .............................. 263
Oleg V. Mishin, Andrew Godfrey, and Dorte Juul Jensen
19.1 Introduction .......................................... 263
19.2 Orientation Noise in EBSD Data ........................ 265
19.2.1 A Quantitative Description of Orientation
Noise .......................................... 265
19.2.2 Postprocessing Orientation Filtering
Operations ..................................... 266
19.3 Quantitative TEM-EBSD Comparison ...................... 268
19.4 Heterogeneity in Microstractural Refinement ........... 271
19.4.1 Analysis of Local Heterogeneity ................ 271
19.4.2 Potential for Analysis of Large-Scale
Heterogeneities ................................ 272
19.5 Summary and Conclusions ............................... 273
20 Application of EBSD Methods to Severe Plastic Deformation
(SPD) and Related Processing Methods ....................... 277
Terry R. McNelley, Alexandre P. Zhilyaev, Srinivasan
Swaminathan, Jianqing Su, and E. Sarath Menon
20.1 Introduction .......................................... 277
20.2 Microstructures During the Initial ECAP Pass .......... 278
20.3 Microstructures Developed by Machining ................ 282
20.4 Grain Refinement During FSP ........................... 284
20.5 Conclusions ........................................... 288
21 Applications of EBSD to Microstructural Control in
Friction Stir Welding/Processing ........................... 291
Sergey Mironov, Yutaka S. Sato, and Hiroyuki Kokawa
21.1 Introduction .......................................... 291
21.2 Brief Explanations of FSW/P Terminology ............... 292
21.3 Microstructural Evolution ............................. 292
21.4 Material Flow ......................................... 296
21.5 Structure-Properties Relationship ..................... 298
21.6 Summary and Future Outlook ............................ 299
22 Characterization of Shear Localization and Shock Damage
with EBSD .................................................. 301
John F. Bingert, Veronica Livescu, and Ellen K. Cerreta
22.1 Introduction .......................................... 301
22.2 Shear Localization .................................... 302
22.2.1 Constrained Shear in Pure Fe—Shear Zone
Geometry ....................................... 302
22.2.2 Constrained Shear in Pure Fe—Texture
Development .................................... 306
22.2.3 Effect of Morphology on Grain Instability in
Cu ............................................. 307
22.3 Shock Loading Damage in Tantalum ...................... 309
22.3.1 Effect of Shock Duration on Incipient Spall
Structure ...................................... 310
22.3.2 Effect of Pressure on Incipient Spall
Structure ...................................... 313
22.4 Conclusions ........................................... 313
23 Texture Separation for α/β Titanium Alloys ................ 317
Ayman A. Salem
23.1 Introduction .......................................... 317
23.2 Microstructure of α/β Titanium Alloys ................. 317
23.3 Texture of Ti-6Al-4V .................................. 318
23.3.1 Separation of Primary and Secondary Alpha
Texture ........................................ 319
23.3.2 EBSD + BSE Imaging Technique ................... 319
23.3.3 EBSD or XRD + Heat Treatment Technique ......... 320
23.4 Texture Separation Using EBSD + EDS Technique ......... 320
23.4.1 Texture Separation Using EBSD + EDS Technique .. 320
23.4.2 Microstructure Observations .................... 321
23.4.3 Chemical Composition Maps (EDS) ................ 321
23.5 Industrial Application: Controlling Texture During
Hot-Rolling of Ti-6A1-4V .............................. 322
23.5.1 Microstructure Evolution ....................... 323
23.5.2 Overall Texture Evolution ...................... 323
23.5.3 Primary-Alpha (ap) Textures .................... 324
23.5.4 Secondary-Alpha (as) Texture ................... 325
23.6 Industrial Application: Controlling Texture During
Hot-Rolling of Ti-6Al-4V .............................. 326
24 A Review of In Situ EBSD Studies ........................... 329
Stuart I. Wright and Matthew M. Nowell
24.1 Introduction .......................................... 329
24.2 In Situ Postmortem Experiments ........................ 330
24.3 Deformation Stage Experiments ......................... 331
24.4 Heating Stage Experiments ............................. 332
24.4.1 Phase Transformation ........................... 332
24.4.2 Recrystallization and Grain Growth ............. 333
24.5 Combined Heating and Tensile Stage Experiments ........ 335
24.6 Conclusions ........................................... 335
25 Electron Backscatter Diffraction in Low Vacuum Conditions .. 339
Bassem S. El-Dasher and Sharon G. Torres
25.1 Introduction .......................................... 339
25.2 Considerations for Low Vacuum EBSD .................... 340
25.3 Example Applications .................................. 341
25.3.1 Microstractural Analysis of AlN-TiB2 Ceramic
Composite ...................................... 341
25.3.2 Characterization of CaHPO4-2H2O Single
Crystals ....................................... 342
26 EBSD in the Earth Sciences: Applications, Common
Practice, and Challenges ................................... 345
David J. Prior, Elisabetta Mariani, and John Wheeler
26.1 Development of EBSD in Earth Sciences ................. 345
26.2 Current Practice, Capabilities, and Limitations ....... 346
26.2.1 Range of Materials and Preparation ............. 346
26.2.2 Speed of Data Collection ....................... 347
26.2.3 Spatial Resolution ............................. 347
26.2.4 Misindexing .................................... 348
26.2.5 Polyphase Samples .............................. 350
26.3 Application of EBSD in Earth Sciences ................. 351
26.3.1 Rock Deformation and Solid Earth Geophysics .... 352
26.3.2 Metamorphic Processes .......................... 355
26.3.3 Meteorites ..................................... 356
26.3.4 Other Areas .................................... 356
26.4 Conclusions ........................................... 357
27 Orientation Imaging Microscopy in Research on High
Temperature Oxidation ...................................... 361
Bae-Kyun Kim and Jerzy A. Szpunar
27.1 Introduction .......................................... 361
27.2 High Temperature Oxidation ............................ 362
27.3 Experimental Procedure ................................ 363
27.3.1 Oxidation of Samples and Oxide Formation ....... 363
27.3.2 Sample Preparation and Geometry in OIM ......... 364
27.3.3 Microstructure and Texture Measurement ......... 365
27.3.4 Oxidation of Low Carbon Steel .................. 365
27.4 Results and Discussion ................................ 368
27.4.1 Grain Growth in Iron Oxide ..................... 368
27.4.2 Effect of the Oxidation Process on
Microstructure ................................. 371
27.4.3 Oxidation of Pure Iron ......................... 373
27.5 Cracks and Defects .................................... 384
27.6 Conclusion ............................................ 390
Index ......................................................... 395
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