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E-raamat: Statistical Methods for Materials Science: The Data Science of Microstructure Characterization

Edited by (Purdue University, ECE and Biomedical Engineering, ), Edited by (Carnegie Mellon University, Materials Science and Engineering Department, Pittsburgh, Pennsylvania, USA), Edited by (Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio, USA), Edited by
  • Formaat: 536 pages
  • Ilmumisaeg: 13-Feb-2019
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781498738217
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Statistical Methods for Materials Science: The Data Science of Microstructure CharacterizationSuurem pilt
  • Formaat: 536 pages
  • Ilmumisaeg: 13-Feb-2019
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781498738217
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Data analytics has become an integral part of materials science. This book provides the practical tools and fundamentals needed for researchers in materials science to understand how to analyze large datasets using statistical methods, especially inverse methods applied to microstructure characterization. It contains valuable guidance on essential topics such as denoising and data modeling. Additionally, the analysis and applications section addresses compressed sensing methods, stochastic models, extreme estimation, and approaches to pattern detection.

Preface xvii
About the Editors xix
Contributors xxi
I Introduction 1(12)
1 Materials Science vs. Data Science
3(10)
Jeffrey P. Simmons
Lawrence F. Drummy
Charles A. Bouman
Marc De Graef
II Emerging Data Science in Microstructure Characterization 13(68)
2 Emerging Digital Data Capabilities
17(10)
Stephen Mick
2.1 Introduction
17(2)
2.2 Benefits of Large Data Volumes
19(2)
2.3 Challenges of Large Data Volumes
21(1)
2.4 Emerging Techniques
22(3)
2.4.1 Multi-Instrument Coordination
23(1)
2.4.2 Upstream Data Analysis
23(1)
2.4.3 Data Mining
24(1)
2.4.4 Data Curation
24(1)
2.5 Conclusions
25(2)
3 Cultural Differences
27(20)
Mary Comer
Charles A. Bouman
Jeffrey P. Simmons
3.1 What Makes Modern Image Processing So Modern?
27(1)
3.2 Language of Image Processing
28(11)
3.2.1 Notational Differences
28(1)
3.2.1.1 Sets
28(1)
3.2.1.2 Operations on Sets
29(1)
3.2.1.3 Computations on Sets
31(1)
3.2.2 Bayesian Probability and Image Processing
32(1)
3.2.2.1 Modern Probability and Sets
33(1)
3.2.2.2 Foundational Rules of Modern Probability
33(1)
3.2.2.3 Mathematical Constructs
35(1)
3.2.2.4 Bayesian Probability in Image Processing
36(3)
3.3 Language of Materials Science
39(7)
3.3.1 Thermodynamic Phases
39(3)
3.3.2 Free Energies
42(4)
3.4 Concluding Remarks
46(1)
4 Forward Modeling
47(16)
Marc De Graef
4.1 What Is Forward Modeling?
47(4)
4.1.1 What Are the Unknowns in Materials Characterization?
47(2)
4.1.2 A Schematic Description of Forward Modeling
49(2)
4.2 A Brief Overview of Electron Scattering Modalities
51(1)
4.3 Case Studies
52(10)
4.3.1 Electron Backscatter Diffraction
52(1)
4.3.1.1 BSE Monte Carlo Simulations
52(1)
4.3.1.2 Dynamical Scattering Simulations
54(1)
4.3.1.3 Detector Parameters
55(1)
4.3.2 Lorentz Vector Field Electron Tomography
56(1)
4.3.2.1 Lorentz Forward Model
56(1)
4.3.2.2 Electron Wave Phase Shift Computations
57(1)
4.3.2.3 Example Lorentz Image Simulation
61(1)
4.4 Summary
62(1)
5 Inverse Problems and Sensing
63(18)
Charles A. Bouman
5.1 Introduction
63(1)
5.2 Traditional Approaches to Inversion
63(4)
5.3 Bayesian and Regularized Approaches to Inversion
67(4)
5.4 Why Does Bayesian Estimation Work?
71(4)
5.5 Model-Based Reconstruction
75(2)
5.6 Successes and Opportunities of Bayesian Inversion
77(4)
III Inverse Methods for Analysis of Data 81(62)
6 Model-Based Iterative Reconstruction for Electron Tomography
85(26)
Singanallur Venkatakrishnan
Lawrence F. Drummy
6.1 Introduction
85(1)
6.2 Model-Based Iterative Reconstruction
86(2)
6.3 High-Angle Annular Dark-Field STEM Tomography
88(8)
6.3.1 HAADF-STEM Forward Model
88(2)
6.3.2 Prior Model
90(1)
6.3.3 Cost Function Formulation and Optimization Algorithm
91(2)
6.3.4 Experimental Results
93(1)
6.3.4.1 Simulated Dataset
93(1)
6.3.4.2 Experimental Dataset
95(1)
6.4 Bright-Field Electron Tomography
96(11)
6.4.1 BF-TEM Forward Model and Cost Function Formulation
97(1)
6.4.1.1 Generalized Huber Functions for Anomaly Modeling
98(1)
6.4.1.2 MBIR Cost Formulation
100(1)
6.4.2 Results
100(1)
6.4.2.1 Simulated Dataset
101(1)
6.4.2.2 Real Dataset
105(2)
6.5 Future Directions
107(1)
6.6 Conclusion
108(3)
7 Statistical Reconstruction and Heterogeneity Characterization in 3-D Biological Macromolecular Complexes
111(16)
Qiu Wang
Peter C. Doerschuk
7.1 Introduction
111(2)
7.2 Statistical 3-D Signal Reconstruction of Macromolecular Complexes
113(7)
7.2.1 Introduction
113(1)
7.2.2 Statistical Model
113(2)
7.2.3 Relationship between the Moments of the Weights and the Moments of the Electron Scattering Intensity
115(1)
7.2.4 Estimation Criterion
115(1)
7.2.4.1 q as a Function of oc, oV, oQ
116(1)
7.2.4.2 c, V, and Q as a Function of oc, oV, oQ
116(1)
7.2.4.3 c as a Function of V, Q, oc, oV, oQ
117(1)
7.2.4.4 V as a Function of a, Q, oa, oV, oQ
117(1)
7.2.4.5 Q as a Function of V, c, oc, oV, oQ
118(1)
7.2.5 Relationship with Other Results
118(1)
7.2.6 Algorithm
118(1)
7.2.7 Performance
118(1)
7.2.8 Estimation of the a priori Probability Distribution on the Nuisance Parameters
119(1)
7.2.9 Pre- and Post-Processing
119(1)
7.3 Biological Examples
120(3)
7.3.1 Flock House Virus (FHV)
120(1)
7.3.2 Nudaurelia Capensis (ω Virus (NωV)
121(1)
7.3.3 Summary
122(1)
7.4 Discussion
123(2)
7.4.1 Challenges and Future Directions
123(2)
7.5 Conclusion
125(2)
8 Object Tracking through Image Sequences
127(16)
Song Wang
Hongkai Yu
Youjie Zhou
Jeffrey P. Simmons
Craig Przybyla
8.1 Tracking and Kalman Filters
128(1)
8.2 Fiber Tracking Using the Kalman Filter
129(4)
8.2.1 Fiber Detection
130(1)
8.2.2 Model Parameters
131(1)
8.2.3 Multiple Fiber Association
131(2)
8.3 Tracking Performance Evaluation
133(3)
8.4 Testing Data and Sparse Sampling
136(1)
8.5 Experiment Results
137(4)
8.6 Other Tracking Methods
141(1)
8.7 Summary
141(2)
IV Structure Formation in Materials 143(58)
9 Grain Boundary Characteristics
147(16)
Hossein Beladi
Gregory S. Rohrer
9.1 Introduction
147(1)
9.2 Grain Boundary Representation
148(1)
9.2.1 The Crystallographic Lattice Misorientation
148(1)
9.2.2 Grain Boundary Plane Orientation
148(1)
9.3 Representation of the GBCD
149(2)
9.4 Measurement of the Grain Boundary Plane Distribution
151(1)
9.4.1 The Relative Grain Boundary Character Distribution
151(1)
9.4.2 The Relative Grain Boundary Planes Energy Distribution
152(1)
9.5 Grain Boundary Plane Anisotropy
152(1)
9.6 Influence of Parameters on the GBCD
153(5)
9.6.1 Intrinsic Parameters
154(1)
9.6.1.1 Alloy Composition
154(1)
9.6.1.2 Crystal Structure
155(1)
9.6.2 Extrinsic Parameters
155(1)
9.6.2.1 Solidification
155(1)
9.6.2.2 Thermomechanical Processing
156(1)
9.6.2.3 Thin Film
157(1)
9.6.2.4 Magnetic Field
157(1)
9.6.2.5 Transformation Path
158(1)
9.7 Grain Boundary Network
158(3)
9.7.1 Grain Boundary Correlation Number
158(1)
9.7.2 Percolation Model
159(1)
9.7.3 Homology Metrics
160(1)
9.8 Summary and Current Challenges
161(2)
10 Interface Science and the Formation of Structure
163(20)
Ming Tang
Jian Luo
10.1 Introduction
163(1)
10.2 Effect of Interface Energy on Triple Junction Geometry
163(5)
10.3 Effect of Energy Anisotropy on Crystal Shape
168(3)
10.4 Effect of Interface Energy on Wetting
171(3)
10.4.1 Interface Wetting
171(2)
10.4.2 Triple-Junction Wetting
173(1)
10.5 Changes Due to Thermodynamic State Variables
174(7)
10.5.1 Variation of Interfacial Energy with Thermodynamic State Variables
174(2)
10.5.2 Interface Complexions and Transitions: Thermodynamics
176(3)
10.5.3 Effects of Complexion Transitions on Microstructure Formation and Evolution: The Kinetic Aspect
179(2)
10.6 Summary
181(2)
11 Hierarchical Assembled Structures from Nanoparticles
183(18)
Dhriti Nepal
Sushil Kanel
Lawrence F. Drummy
11.1 Fundamentals of Nanostructure Assembly
183(1)
11.2 Light Scattering and Surface Plasmons
183(7)
11.2.1 Plasmon Coupling
185(2)
11.2.2 Plasmon-Exciton Coupling
187(2)
11.2.3 Assembly of NPs, Thermodynamics, DLVO Theory, and Extended DLVO
189(1)
11.3 Directed Assembly and Self-Assembly of NPs
190(6)
11.3.1 Assemblies in Solution
191(4)
11.3.2 Assemblies on Surfaces
195(1)
11.4 Complex Architectures for Metamaterials
196(1)
11.5 Future Opportunities
197(9)
11.5.1 Tomography
197(2)
11.5.2 Scanning Transmission Electron Microscopy/Electron Energy Loss Spectroscopy (STEM/EELS)
199(1)
11.5.3 In-Situ Characterization
199(1)
11.5.4 Summary
199(2)
V Microstructure 201(118)
12 Estimating Orientation Statistics
205(18)
Stephen R. Niezgoda
12.1 Orientations and Orientation Distributions
206(2)
12.1.1 Formal Definition of the ODF
206(1)
12.1.2 Metrics on the ODF
207(1)
12.2 Non-Parametric Estimation
208(5)
12.2.1 Generalized Spherical Harmonics for the Estimation of Mesoscale ODFs
209(1)
12.2.2 Spatial Statistics of Orientations
210(3)
12.3 Parametric Estimation of Orientation Distributions
213(5)
12.3.1 Bingham and Von Mises Fisher Distributions
214(1)
12.3.2 Symmetrized Probability Distributions
215(2)
12.3.3 EM-ML Algorithm for Parameter Estimation
217(1)
12.4 Brief Discussion and Conclusions
218(1)
12.5 Appendix A: Quaternion Representation of Orientations
219(1)
12.6 Appendix B: Bunge-Euler Angles
220(2)
12.7 Appendix C: Useful Properties of Generalized Spherical Harmonics
222(1)
13 Representation of Stochastic Microstructures
223(18)
Stephen R. Niezgoda
13.1 Overview
223(1)
13.2 Interpreting Microstructure as a Stochastic Process
224(4)
13.2.1 Brief Review of the Terminology and Notation of Stochastic Processes
224(1)
13.2.2 The Microstructure Process
225(1)
13.2.3 Statistics of the Microstructure Function
226(2)
13.3 Microstructure Descriptors
228(6)
13.3.1 Metrics from the Two-Point Correlations and Characteristic Length Scales
228(2)
13.3.2 Other Microstructure Descriptors
230(1)
13.3.2.1 Surface Correlation Function
230(1)
13.3.2.2 Chord Length Distributions and Lineal Path Functions
230(1)
13.3.2.3 Topological Invariants
231(3)
13.4 Reduced Order Descriptions and Relational Statistics
234(5)
13.5 Closing Thoughts
239(2)
14 Computer Vision for Microstructure Representation
241(18)
Brian DeCost
Elizabeth Holm
14.1 Introduction
241(2)
14.2 A Brief Tour of Computer Vision
243(9)
14.2.1 Texture Features
243(2)
14.2.2 Midlevel: Local Features
245(1)
14.2.2.1 Feature Localization Techniques
246(1)
14.2.2.2 Alternate Pattern Descriptors
247(1)
14.2.2.3 Alternate Image Encoding Methods
248(1)
14.2.3 Deep Learning
249(3)
14.3 Materials Applications
252(3)
14.3.1 Microstructure Characterization
252(1)
14.3.1.1 GLCM and Wavelet Features
252(1)
14.3.1.2 EM/MPM Texture-Based Segmentation
253(1)
14.3.1.3 Characterizing Two-Phase Microstructures
253(1)
14.3.1.4 Midlevel Features
253(2)
14.3.2 Deep Features
255(1)
14.3.3 Microstructure Generation
255(1)
14.4 Outlook and Call for Standardization
255(1)
14.5 Acknowledgments
256(3)
15 Topological Analysis of Local Structure
259(16)
Emanuel Lazar
David Srolovitz
15.1 Introduction
259(4)
15.1.1 Local Structure in Atomic Systems
259(1)
15.1.2 Conventional Characterization Approaches
260(1)
15.1.3 Voronoi Analysis
261(2)
15.2 Voronoi Topology Structure Analysis
263(6)
15.2.1 Topology Basics
263(1)
15.2.2 Voronoi Topology
264(1)
15.2.3 Recording Voronoi Topology
265(1)
15.2.4 Topological Instability and Families of Topologies
266(1)
15.2.5 Determination of Families of Topologies
267(1)
15.2.6 Ambiguous Topologies and Their Disambiguation
268(1)
15.2.7 Alloys
269(1)
15.3 Applications
269(4)
15.3.1 Defect Identification in High-Temperature Crystals
270(1)
15.3.2 Melting
271(2)
15.3.3 Grain Boundary Characterization
273(1)
15.4 Automation through Software
273(2)
16 Markov Random Fields for Microstructure Simulation
275(16)
Veera Sundararaghavan
16.1 Introduction
275(1)
16.2 Microstructures as Random Fields
276(6)
16.2.1 Spatial Sampling
277(2)
16.2.2 Temporal Sampling
279(1)
16.2.3 3D Optimization
280(2)
16.3 Examples
282(7)
16.3.1 Example 1: 2D Synthesis of an Aluminum Alloy AA3002 Representing the Rolling Plane
282(2)
16.3.2 3D Reconstruction: A Polycrystal and a Lamellar Composite
284(1)
16.3.3 3D Reconstruction of a Two-Phase Composite
284(2)
16.3.4 Spatio-Temporal Sampling (2D + time) of Grain Growth
286(2)
16.3.5 Microstructure Embedding in CAD Models
288(1)
16.4 Conclusion
289(1)
16.5 Acknowledgments
290(1)
17 Distance Measures for Microstructures
291(14)
Patrick Callahan
17.1 Introduction
291(1)
17.2 Moment Invariants and the Shape Quotient
292(1)
17.3 Distances
293(3)
17.3.1 Hellinger Distance
294(1)
17.3.2 Histogram Intersection Distance
295(1)
17.3.3 X2 Distance
295(1)
17.3.4 Jeffrey Divergence
295(1)
17.3.5 Kolmogorov-Smirnov Distance
295(1)
17.3.6 Earth Mover's Distance
295(1)
17.3.7 Quadratic-Form Distance
296(1)
17.4 IN100 Experimental and Synthetic Microstructures
296(8)
17.4.1 Volume
297(1)
17.4.2 Grain Morphology
298(1)
17.4.2.1 Moment Invariant n3
298(1)
17.4.2.2 Shape Quotient
301(1)
17.4.2.3 Volume and Morphology
301(1)
17.4.3 Developing a Criterion for Microstructure Comparison
302(2)
17.5 Summary
304(1)
18 Industrial Applications
305(14)
David Furrer
David B. Brough
Ryan Noraas
18.1 Introduction
305(1)
18.2 Microstructural Characterization
305(2)
18.3 Microstructural Characterization Examples
307(5)
18.4 Future State in Microstructural Characterization
312(6)
18.5 Conclusion
318(1)
VI Anomalies 319(38)
19 Anomaly Testing
323(16)
James Theiler
19.1 Introduction
323(4)
19.1.1 Anomaly Testing as Triage
323(1)
19.1.2 Anomalies Drawn from a Uniform Distribution
324(1)
19.1.2.1 Nonuniform Distributions of Anomalousness
325(1)
19.1.3 Anomalies as Pixels in Spectral Imagery
325(1)
19.1.3.1 Global and Local Anomaly Detectors
326(1)
19.1.3.2 Regression Framework
327(1)
19.2 Evaluation
327(1)
19.3 Periphery
328(2)
19.4 Subspace
330(1)
19.5 Kernels
331(3)
19.5.1 Kernel Density Estimation
331(1)
19.5.2 Feature Space Interpretation: The "Kernel Trick"
331(3)
19.6 Change
334(3)
19.6.1 Subtraction-Based Approaches to Anomalous Change Detection
334(2)
19.6.2 Distribution-Based Approaches to Anomalous Change Detection
336(1)
19.6.3 Further Comments on Anomalous Change Detection
337(1)
19.7 Conclusion
337(2)
20 Anomalies in Microstructures
339(18)
Stephen Bricker
Craig Przybyla
Jeffrey P. Simmons
Russel Hardie
20.1 Introduction
339(1)
20.2 Features of the Local Fiber Microstructure
339(11)
20.2.1 Orientation Field
341(1)
20.2.1.1 Description of the Orientation Field
341(1)
20.2.1.2 Computational Simplification of the Orientation Field
343(1)
20.2.1.3 Color Visualization of the Orientation
344(1)
20.2.2 Orientation Gradient Field
345(1)
20.2.2.1 Geometric Simplifications of the Orientation Gradient
346(1)
20.2.2.2 Color Visualization of the Orientation Gradient
347(1)
20.2.3 Estimation of the Orientation Gradient Field
348(2)
20.3 Anomaly Detection
350(4)
20.3.1 Gaussian Mixture Modeling
350(1)
20.3.2 Anomalies of the Microstructure
351(3)
20.4 Conclusion
354(3)
VII Sparse Methods 357(82)
21 Denoising Methods with Applications to Microscopy
361(26)
Rebecca Willett
21.1 Introduction
361(2)
21.1.1 Organization of
Chapter
363(1)
21.2 Image and Noise Models
363(4)
21.2.1 Noise Models
363(1)
21.2.2 Gaussian Noise Model
363(1)
21.2.3 Poisson Noise Model
364(2)
21.2.4 Image Models
366(1)
21.3 Maximum Likelihood Estimation
367(5)
21.3.1 Tikhonov Regularization
367(2)
21.3.2 Sparsity and Wavelet Denoising
369(1)
21.3.3 Total Variation
370(2)
21.4 Kernel Denoising Methods
372(5)
21.4.1 Linear Smoothing
372(1)
21.4.2 Ideal Weights
373(1)
21.4.3 Bilateral Filters
374(1)
21.4.4 Nonlocal Means (NLM)
375(2)
21.5 Patch-Based Methods
377(5)
21.5.1 Principal Components Analysis
378(1)
21.5.2 Nonlocal PCA
379(2)
21.5.3 BM3D
381(1)
21.6 Examples
382(2)
21.6.1 Comparison of Linear Gaussian Smoothing, Bilateral Filtering, and Nonlocal Means
382(1)
21.6.2 Examples of Poisson Image Denoising on Simulated Data
382(1)
21.6.3 Application to Electron Microscopy Spectrum Images
382(2)
21.7 Conclusion
384(1)
21.8 Acknowledgments
385(2)
22 Compressed Sensing for Imaging Applications
387(20)
Justin Romberg
22.1 Introduction
387(7)
22.1.1 An Imaging Experiment
387(3)
22.1.2 Mathematical Formulation
390(1)
22.1.2.1 Linear Measurements
390(1)
22.1.2.2 Bases for Discretization and Sparsity
391(1)
22.1.2.3 The Linear Acquisition Model
392(1)
22.1.3 Classical Least Squares Recovery
393(1)
22.2 Principles of Sparse Recovery
394(4)
22.2.1 Sparse Embeddings
395(3)
22.3 Algorithms for Sparse Recovery
398(5)
22.3.1 Orthogonal Matching Pursuit
398(1)
22.3.2 Iterative Hard Thresholding
399(2)
22.3.3 Sparse Recovery Using ti Minimization
401(2)
22.3.4 Beyond Sparsity: Recovery Algorithms for Alternative Structure
403(1)
22.4 Numerical Example: Computed Tomography
403(2)
22.5 Summary
405(2)
23 Dictionary Methods for Compressed Sensing
407(12)
Saiprasad Ravishankar
R. Rao Nadakuditi
23.1 Introduction
407(3)
23.1.1 Synthesis Model and Sparsity Measures
407(1)
23.1.2 Synthesis Sparse Coding
408(1)
23.1.3 Dictionary Learning
408(1)
23.1.4 Why Are There Many Dictionary Learning Algorithms?
408(1)
23.1.5 Compressed Sensing
409(1)
23.1.6 Compressed Sensing with Adaptive Dictionaries
409(1)
23.1.7 Organization
410(1)
23.2 BCS Problem Formulations
410(1)
23.3 BCS Algorithms
411(4)
23.3.1 Dictionary Learning Step for (P0)
411(1)
23.3.1.1 Sparse Coding Step
411(1)
23.3.1.2 Dictionary Atom Update Step
412(1)
23.3.2 Dictionary Learning Step for (P1)
412(1)
23.3.3 Image Update Step
413(1)
23.3.4 Overall Algorithms
413(2)
23.4 Numerical Experiments
415(2)
23.4.1 Framework for Electron Microscopy
415(1)
23.4.2 Results and Discussion
415(2)
23.5 Conclusion
417(2)
24 Sparse Sampling in Microscopy
419(20)
Kurt Larson
Hyrum Anderson
Jason Wheeler
24.1 Motivations for Sparse Sampling in Electron Microscopy
420(1)
24.2 Sparse Sampling and Reconstruction
420(1)
24.3 Sparse Sampling in Transmission Electron Microscopy
421(2)
24.4 Sparse Sampling in Scanning Surface Microscopy
423(1)
24.5 Sparse Sampling in Atomic Force Microscopy
424(1)
24.6 Sparse Sampling in Scanning Electron Microscopy
424(1)
24.7 Compressed Sensing in Multi-Beam Electron Microscopes
424(2)
24.8 Theoretical Analysis for a Multi-Beam CSEM
426(1)
24.9 Potential Embodiments of a Multi-Beam CSEM
427(5)
24.9.1 Concept for Steerable Beams
428(1)
24.9.2 Array of Correlated Steerable Beams
429(1)
24.9.3 Array of Individually Steerable Beams
429(2)
24.9.4 Managing the Electron Budget
431(1)
24.10 Multi-Beam CSEM Speed Estimates
432(2)
24.11 Scientific Challenges in a Multi-Beam CSEM
434(2)
24.12 Engineering Challenges in a Multi-Beam CSEM
436(2)
24.13 Conclusion
438(1)
Appendix 439(6)
A List of Symbols for
Chapters 6, 7, and 13
440(5)
Bibliography 445(56)
Index 501
Jeffrey P. Simmons, Lawrence F. Drummy, Charles A. Bouman, Marc De Graef
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