Electron Backscatter Diffraction in Materials Science (eBook)

Adam J. Schwartz is the Deputy Division Leader for Condensed Matter and High Pressure Physics in the Physics and Advanced Technologies Directorate. Dr. Schwartz joined LLNL as a post-doctoral research associate to investigate the systematics of displacive phase transformations after receiving his PhD from the University of Pittsburgh in 1991. His areas of interests focus on structure-propoerty-processing relations, aging and phase transformations in actinides; influence of microstructure and impurities on high-strain rate deformation behavior, texture and texture gradients in materials, intercrystalline defects and the role of grain boundary character distribution in materials, conventional and high resolution transmission electron microscopy, and electron backscatter diffraction. Dr. Schwartz has authored over 50 publications and has one patent. Mukul Kumar joined as a staff scientist in the Materials Science and Technology Division in 1998 after completing a stint as a post-doctoral fellow at Johns Hopkins University. Prior to that, he received his PhD from the University of Cincinnati, where he was an Oak Ridge Institute for Science and Engineering Fellow and also received the ASM International Arthur Focke Award for his dissertation work. His areas of interest include the relationship between properties and microstructures, particularly as related to extreme environments encountered in turbine jet engine and nuclear reactor environments and high strain rate and pressure conditions; defect analysis using conventional transmission electron microscopy; and electron backscatter diffraction. Kumar has authored over 70 publications and has two patents.

Contents 5
Contributors 14
1 Present State of Electron Backscatter Diffraction and Prospective Developments 22
1.1 Introduction 22
1.2 Generation and Interpretation of Electron Backscatter Diffraction Patterns 23
1.3 Experimental Set-Up of an EBSD System 24
1.4 The Components of an Automated EBSD System 25
1.4.1 The Pattern Acquisition Device 25
1.4.2 Mechanical Stage and Digital Beam Scanning 26
1.5 Spatial Resolution 28
1.6 SEM Specifications for Good EBSD Performance 30
1.7 The Radon or Hough Transformation for Band Localization 31
1.8 Indexing indexing 33
1.9 Fast EBSD Fast EBSD 34
1.10 Ion Blocking Patterns 36
1.11 Conclusions 40
References 40
2 Dynamical Simulation of Electron Backscatter Diffraction Patterns 42
2.1 Introduction 42
2.2 Model of Electron Backscatter Diffraction 42
2.3 Dynamical Electron Diffraction in EBSD 43
2.3.1 Using the Reciprocity Principle 43
2.3.2 Bloch Wave Formalism 44
2.3.3 Inclusion of the Backscattering Process 45
2.4 Applications 46
2.4.1 A Real-Space View of EBSD 46
2.4.2 Full Scale Simulation of EBSD Patterns 48
2.4.3 The Influence of the Energy Spectrum of the Backscattered Electrons 49
2.4.4 Dynamical Effects of Anisotropic Backscattering 51
2.5 Summary 53
References 53
3 Representations of Texture 55
3.1 Introduction 55
3.2 Rotations and Orientations 56
3.2.1 Defining a Rotation 56
3.2.2 Defining an Orientation 57
3.3 Pole Figures 58
3.4 Discrete Orientations 60
3.4.1 Axis-Angle Parameters 61
3.4.2 Rodrigues Vectors 62
3.4.3 Quaternions 62
3.4.4 Euler Angles 65
3.5 Orientation Distribution Functions 66
3.5.1 Circular Harmonics 66
3.5.2 Spherical Harmonics 67
3.5.3 Hyperspherical Harmonics 68
3.5.4 Generalized Spherical Harmonics 69
3.5.5 Symmetrized Harmonics 69
3.6 Conclusion 70
References 71
4 Energy Filtering in EBSD 72
4.1 Introduction 72
4.2 Background 72
4.3 Energy Filters 73
4.4 Operating the Filter 75
4.5 Early Results 76
4.6 Patterns at Different Energies 79
4.7 Localization of the Signal 80
4.8 Future Energy Filters in EBSD 81
4.9 Summary and Conclusions 81
References 82
5 Spherical Kikuchi Maps and Other Rarities 83
5.1 Introduction 83
5.2 Electron Backscatter Patterns 83
5.3 Spherical Kikuchi Maps 83
5.4 EBSP Detectors 83
5.5 EBSP Imaging and Uniformity 86
5.6 EBSP Simulation 86
5.7 Spherical Kikuchi Maps from EBSPs 86
5.8 Kikuchi Band Profiles 90
5.9 Spherical Kikuchi Map Inversion 92
5.10 Uses for Spherical Kikuchi Maps 93
5.11 Colour Orientation Contrast Images 94
5.12 STEM in the SEM 94
5.13 Unusual Features in EBSPs 95
References 97
6 Application of Electron Backscatter Diffraction to Phase Identification 99
6.1 Introduction 99
6.2 Considerations for Phase ID with EBSD 100
6.3 Case Studies 102
6.3.1 Simultaneous EBSD/EDS Phase Discrimination 103
6.3.2 Distinguishing ' and '' in Ni Superalloys 104
6.3.3 Volume Fraction Determination in a Multiphase Alloy 107
References 112
7 Phase Identification Through Symmetry Determination in EBSD Patterns 114
7.1 Introduction 114
7.2 Basis of the Phase Identification Method 114
7.3 Determination of the Crystal Unit Cell 115
7.4 Discovering the Lattice Symmetry 117
7.5 Re-Indexing the Pattern According to the Discovered Crystal Class 118
7.6 Examples 119
7.6.1 Case 1, A Cubic Crystal 119
7.6.2 Case 2, A Hexagonal Crystal 121
7.6.3 Case 3, A Trigonal Crystal 121
7.7 Discussion 123
References 124
8 Three-Dimensional Orientation Microscopy by Serial Sectioning and EBSD-Based Orientation Mappingin a FIB-SEM 125
8.1 Introduction 125
8.2 The Geometrical Set-Up for 3D Characterisation in a FIB-SEM 126
8.3 Automatic 3D Orientation Microscopy 129
8.4 Software for 3D Data Analysis 129
8.5 Application Examples 130
8.5.1 The 3D Microstructure and Crystallography of Pearlite Colonies 130
8.5.2 Microstructure of ''Nanocrystalline'' NiCo Deposits 131
8.6 Discussion 135
8.6.1 Accuracy and Application Limits 135
8.6.2 Materials Issues 136
8.7 Conclusions 136
References 137
9 Collection, Processing, and Analysis of Three-Dimensional EBSD Data Sets 139
9.1 Introduction 139
9.2 Data Collection 139
9.3 Processing Strategies 140
9.3.1 Registration and Alignment of Sections 140
9.3.2 Segmentation of Grains 142
9.3.3 Clean-Up Routines 143
9.3.3.1 Filtering of Low Quality Data 143
9.3.3.2 Removal of Small Grains 145
9.3.3.3 Additional Data Processing Possibilities 145
9.4 Analysis Capabilities 145
9.4.1 Morphological Descriptors 145
9.4.1.1 Grain Size and Volume 145
9.4.1.2 Grain Shape 146
9.4.1.3 Number of Neighbors 147
9.4.1.4 Correlations Between Parameters 148
9.4.2 Crystallographic Descriptors 149
9.4.2.1 Classical Measurements 149
9.4.2.2 Fundamentally 3D Measurements 150
9.5 Summary 151
References 152
10 3D Reconstruction of Digital Microstructures 154
10.1 Motivation 154
10.2 Background 154
10.2.1 2D--3D Inference 154
10.2.2 3D Polycrystal Microstructure Generation 155
10.3 Data Collection and Analysis 155
10.3.1 Data Sources 155
10.3.2 Identifying Features 156
10.3.3 Statistical Description of Features 156
10.4 Methods for 3D Structure Inference 156
10.4.1 Monte Carlo-Based Histogram Fitting 158
10.4.2 Observation-Based Domain Constraint 160
10.5 Generation of 3D Structure 161
10.5.1 Packing of Ellipsoids 162
10.5.2 Relaxation of Boundaries 164
10.6 Quality Analysis 164
10.6.1 Size Distribution Comparison 164
10.6.2 Shape Distribution Comparison 164
10.6.3 Neighborhood Comparison 166
10.6.4 Boundary Structure Comparison 166
10.7 Thoughts on Current Conditions and Future Work 166
References 167
11 Direct 3D Simulation of Plastic Flow from EBSD Data 169
11.1 Introduction 169
11.2 Material and Microstructural Model 170
11.2.1 Three-Dimensional Microstructure Generation 171
11.2.2 Micromechanical Model 172
11.2.3 Finite Element Model 173
11.3 Simulation Results 173
11.4 Directions for Further Computational Development 176
11.5 Conclusions 179
References 180
12 First-Order Microstructure Sensitive Design Based on Volume Fractions and Elementary Bounds 182
12.1 Introduction 182
12.2 Quantification of Microstructure 183
12.3 Microstructure Sensitive Design Framework 183
12.4 Property Closures 185
References 188
13 Second-Order Microstructure Sensitive Design Using 2-Point Spatial Correlations 189
13.1 Introduction 189
13.2 Definition and Properties of the 2-Point Correlation Functions 190
13.2.1 Boundary Conditions 191
13.2.2 Properties of the 2-Point Functions 191
13.2.3 Visualization of the 2-Point Functions 191
13.2.4 Metrics from 2-Point Correlations 192
13.2.5 Collecting 2-Point Correlations from Material Samples 192
13.3 Structure Property Relations 193
13.3.1 Localization Tensors 194
13.3.1.1 Spectral Form 195
13.3.1.2 Calibration Techniques 195
13.3.2 Effective Tensors 196
13.4 Microstructure Design 198
References 199
14 Combinatorial Materials Science and EBSD: A High Throughput Experimentation Tool 201
14.1 Introduction 201
14.2 Introduction to Combinatorial Methods 201
14.2.1 High Throughput EBSD Screening 202
14.2.1.1 Analysis of Chemical Libraries 202
14.2.1.2 Microstructural Gradients 205
14.2.2 Informatics and Data 206
14.3 Summary 208
References 210
15 Grain Boundary Networks 212
15.1 Introduction 212
15.2 Measurement and Classification of Local Network Elements 213
15.2.1 General Definitions for Single Boundaries 213
15.2.2 Structures with More than One Boundary 214
15.3 Geometry of the Network Structure 215
15.3.1 Percolation Measures of the Grain Boundary Network 216
15.3.2 Crystallographic Constraints 217
15.4 Microstructure-Property Connections 219
15.4.1 Composite Averaging vs. Percolation Theory 220
15.4.2 Crystallographic Correlations 222
15.5 Conclusions and Future Outlook 222
References 224
16 Measurement of the Five-Parameter Grain Boundary Distribution from Planar Sections 226
16.1 Introduction: Grain Boundary Planes and Properties 226
16.2 Serial Sectioning 227
16.3 Single-Surface Trace Analysis 227
16.4 Five-Parameter Stereological Analysis 229
16.4.1 Parameterization and Discretization of the Space of Grain Boundary Types 229
16.4.2 Measurement of the Grain Boundary Characterization Distribution 230
16.4.3 Performance of the Stereological Analysis 232
16.4.4 Comparison GBCDs Measured Stereologically and by Serial Sectioning in the Dual Beam FIB 234
16.5 Examples of Five-Parameter Analyses 235
References 239
17 Strain Mapping Using Electron Backscatter Diffraction 241
17.1 Introduction 241
17.1.1 The Need for Local Strain Assessment 241
17.1.2 Competing Strain Mapping Techniques 241
17.1.3 Review of Applications of EBSD to Analysis of Elastic Strains 242
17.2 Cross-Correlation-Based Analysis of EBSD Patterns 244
17.2.1 Geometry: Linking Pattern Shifts to Strain 244
17.2.2 Pattern Shift Measurement 245
17.2.3 Sensitivity Analysis 247
17.2.4 Illustrative Applications 249
17.3 Concluding Remarks 257
References 257
18 Mapping and Assessing Plastic Deformation Using EBSD 260
18.1 Plastic Deformation Effects on the EBSD Pattern and Orientation Map 260
18.2 Pattern Rotation Approaches 262
18.2.1 Mapping Orientations and Misorientations 262
18.2.2 Average Misorientation Approaches 264
18.2.3 Measurement and Calculation of GND Densities 267
References 271
19 Analysis of Deformation Structures in FCC Materials Using EBSD and TEM Techniques 272
19.1 Introduction 272
19.2 Orientation Noise in EBSD Data 273
19.2.1 A Quantitative Description of Orientation Noise 274
19.2.2 Postprocessing Orientation Filtering Operations 275
19.3 Quantitative TEMEBSD Comparison 277
19.4 Heterogeneity in Microstructural Refinement 279
19.4.1 Analysis of Local Heterogeneity 280
19.4.2 Potential for Analysis of Large-Scale Heterogeneities 281
19.5 Summary and Conclusions 282
References 283
20 Application of EBSD Methods to Severe Plastic Deformation (SPD) and Related Processing Methods 285
20.1 Introduction 285
20.2 Microstructures During the Initial ECAP Pass 286
20.3 Microstructures Developed by Machining 290
20.4 Grain Refinement During FSP 292
20.5 Conclusions 296
References 296
21 Applications of EBSD to Microstructural Control in Friction Stir Welding/Processing 298
21.1 Introduction 298
21.2 Brief Explanations of FSW/P Terminology 299
21.3 Microstructural Evolution 299
21.4 Material Flow 303
21.5 Structure-Properties Relationship 305
21.6 Summary and Future Outlook 306
References 306
22 Characterization of Shear Localization and Shock Damage with EBSD 308
22.1 Introduction 308
22.2 Shear Localization 309
22.2.1 Constrained Shear in Pure Fe---Shear Zone Geometry 309
22.2.2 Constrained Shear in Pure Fe---Texture Development 313
22.2.3 Effect of Morphology on Grain Instability in Cu 314
22.3 Shock Loading Damage in Tantalum 316
22.3.1 Effect of Shock Duration on Incipient Spall Structure 317
22.3.2 Effect of Pressure on Incipient Spall Structure 320
22.4 Conclusions 320
References 321
23 Texture Separation for 0 / 0 Titanium Alloys 323
23.1 Introduction 323
23.2 Microstructure Microstructure of / Titanium / Titanium Alloys 323
23.3 Texture of Ti-6Al-4V Ti-6Al-4V 324
23.3.1 Separation of Primary and Secondary Alpha secondary alpha Texture texture 325
23.3.2 EBSD + BSE Imaging Technique 325
23.3.3 EBSD or XRD + Heat Treatment Technique 326
23.4 Texture Separation Using EBSD + EDS EDS Technique 326
23.4.1 Procedures for the EBSD/ EDS EDS 326
23.4.2 Microstructure Microstructure Observations 327
23.4.3 Chemical Composition Maps ( EDS EDS ) 327
23.5 Industrial Application: Controlling Texture texture During Hot-Rolling hot rolling of Ti-6Al-4V Ti-6Al-4V 328
23.5.1 Microstructure Microstructure Evolution 329
23.5.2 Overall Texture Evolution 329
23.5.3 Primary-Alpha ( 0 p ) Textures 330
23.5.4 Secondary-Alpha (0 s ) Texture texture 331
23.6 Conclusions 332
References 332
24 A Review of In Situ EBSD Studies 334
24.1 Introduction 334
24.2 In Situ Postmortem Experiments 335
24.3 Deformation Stage Experiments 336
24.4 Heating Stage Experiments 337
24.4.1 Phase Transformation 337
24.4.2 Recrystallization and Grain Growth 338
24.5 Combined Heating and Tensile Stage Experiments 340
24.6 Conclusions 340
References 341
25 Electron Backscatter Diffraction in Low Vacuum Conditions 343
25.1 Introduction 343
25.2 Considerations for Low Vacuum EBSD 344
25.3 Example Applications 345
25.3.1 Microstructural Analysis of AlN-TiB 2 Ceramic Composite 345
25.3.2 Characterization of CaHPO 4 02H 2 O Single Crystals 346
References 348
26 EBSD in the Earth Sciences: Applications, Common Practice, and Challenges 349
26.1 Development of EBSD in Earth Sciences 349
26.2 Current Practice, Capabilities, and Limitations 350
26.2.1 Range of Materials and Preparation 350
26.2.2 Speed of Data Collection 351
26.2.3 Spatial Resolution 351
26.2.4 Misindexing 352
26.2.5 Polyphase Samples 354
26.3 Application of EBSD in Earth Sciences 355
26.3.1 Rock Deformation and Solid Earth Geophysics 356
26.3.2 Metamorphic Processes 359
26.3.3 Meteorites 360
26.3.4 Other Areas 360
26.4 Conclusions 361
References 361
27 Orientation Imaging Microscopy in Research on High Temperature Oxidation 365
27.1 Introduction 365
27.2 High Temperature Oxidation 366
27.3 Experimental Procedure 367
27.3.1 Oxidation of Samples and Oxide Formation 367
27.3.2 Sample Preparation and Geometry in OIM 368
27.3.3 Microstructure and Texture Measurement 369
27.3.4 Oxidation of Low Carbon Steel 369
27.3.4.1 Microstructure Investigation by OIM 370
27.3.4.2 Phase Analysis 370
27.4 Results and Discussion 372
27.4.1 Grain Growth in Iron Oxide 372
27.4.1.1 Grain Growth of Wüstite 372
27.4.1.2 Grain Growth of Magnetite 373
27.4.1.3 Grain Growth of Hematite 375
27.4.2 Effect of the Oxidation Process on Microstructure 375
27.4.3 Oxidation of Pure Iron 377
27.4.3.1 Effects of Substrate Deformation and Texture on Oxidation 377
27.4.3.2 Structure of Interfaces 381
27.5 Cracks and Defects 388
27.6 Conclusion 393
References 396
Index 396