TWO-DIMENSIONAL X-RAY DIFFRACTION

Transcription

1 TWO-DIMENSIONAL X-RAY DIFFRACTION BOB B. HE GQ WILEY

2 ,. "'! :~! CONTENTS~\.-.~..). Preface 1. Introduction 1.1 X-Ray Technology and Its Brief History, 1.2 Geometry of Crystals, Crystal Lattice and Symmetry, Lattice Directions and Planes, Atomic Arrangement in Crystal Structure, Imperfections in Crystal Structure, Principles of X-Ray Diffraction, Bragg Law, Diffraction Patterns, Reciprocal Space and Diffraction, Reciprocal Lattice, The Ewald Sphere, Diffraction Cone and Diffraction Vector Cone, Two-Dimensional X-Ray Diffraction, Diffraction Pattern Measured by Area Detector, Two-Dimensional X-Ray Diffraction System and Major Components, Summary, 23 References, 25 xiii 1

3 vi CONTENTS 2. Geometry Conventions 2.1 Introduction, Comparison Between XRD 2 and Conventional XRD, Diffraction Space and Laboratory Coordinates, Diffraction Cones in Laboratory Coordinates, Diffraction Vector Cones in Laboratory Coordinates, Detector Space and Detector Geometry, Ideal Detector for Diffraction Pattern in 31> Space, Diffraction Cones and Conic Sections with Flat 2D Detectors, Detector Position in the Laboratory System, Pixel Position in Diffraction Space-Flat Detector, Pixel Position in Diffraction Space-Curved Detector, Sample Space and Goniometer Geometry, Sample Rotations and Translations in Eulerian Geometry, Variation of Goniometer Geometry, Transformation from Diffraction Space to Sample Space, Summary of XRD 2 Geometry, 49 References, X-Ray Source and Optics 3.1 X-Ray Generation and Characteristics, X-Ray Spectrum and Characteristic Lines, Focal Spot and Takeoff Angle, Focal Spot Brightness and Profile, Absorption and Fluorescence, X-Ray Optics, Liouville's Theorem and Fundamentals, X-Ray Optics in a Conventional Diffractometer, X-Ray Optics in Two-Dimensional Diffractometer, The ~-Filter, Crystal Monochromator, Multilayer Mirrors, Pinhole Collimator, Capillary Optics, 79 References, X-Ray Detectors 4.1 History of X-Ray Detection Technology, Point Detectors in Conventional Diffractometers, Proportional Counters,

4 CONTENTS vii 4.3 Characteristics of Point Detectors, Counting Statistics, Detective Quantum Efficiency and Energy Range, Detector Linearity and Maximum Count Rate, Energy Resolution, Detection Limit and Dynamic Range, Line Detectors, Geometry of Line Detectors, Types of Line Detectors, Characteristics of Line Detectors, Characteristics of Area Detectors, Geometry of Area Detectors, Spatial Resolution of Area Detectors, Types of Area Detectors, Mu1tiwire Proportional Counter, Image Plate, CCD Detector, Microgap Detector, Comparison of Area Detectors, 127 References, Goniometer and Sample Stages Goniometer and Sample Position, Introduction, Two-Circle Base Goniometer, Sample Stages, Sequence of the Goniometer Axes, Goniometer Accuracy, Sphere of Confusion, Angular Accuracy and Precision, Sample Alignment and Visualization Systems, Environment Stages, Domed High Temperature Stage, Temperature Stage Calibration, 146 References, Data Treatment Introduction, Nonuniform Response Correction, Calibration Source, Nonuniform Response Correction Algorithms, Spatial Correction, Fiducial Plate and Detector Plane, 156

5 viii CONTENTS 6.4 Detector Position Accuracy and Calibration, Detector Position Tolerance, Detector Position Calibration, Frame Integration, Definition of Frame Integration, Algorithm of Frame Integration, Lorentz, Polarization, and Absorption Corrections, Lorentz, Polarization, Air Scatter and Be-Window Absorption, Sample Absorption, Combined Intensity Correction, 188 References, Phase Identification 7.1 Introduction, Relative Intensity, Multiplicity Factor, Electron and Atomic Scattering, Structure Factor, Attenuation Factors, Geometry and Resolution, Detector Distance and Resolution, Defocusing Effect, Transmission Mode Diffraction, Sampling Statistics, Effective Sampling Volume, Angular Window, Virtual Oscillation, Sample Oscillation, Preferred Orientation Effect, Relative Intensity with Texture, Intensity Correction on Fiber Texture, 211 References, Texture Analysis 8.1 Introduction, Pole Density and Pole Figure, Fundamental Equations, Pole Figure Angles, Pole Density, Data Collection Strategy, Single Scan,

6 CONTENTS ix 8.5 Texture Data Process, (} Integration, Absorption Correction, Pole Figure Interpolation, Pole Figure Symmetry, Pole Figure Normalization, Orientation Distribution Function, Eulerian Angles and Space, ODF Calculation, Calculated Pole Figures From ODF, Fiber Texture, Pole Figures of Fiber Texture, ODF of Fiber Texture, Other Advantages of XRD 2 for Texture, Orientation Relationship, Direct Observation of Texture, 245 References, Stress Measurement 9.1 Introduction, Stress, Strain, Elasticity and Hooke's Law, X-Ray Elasticity Constants and Anisotropy Factor, Residual Stresses, Principle of X-Ray Stress Analysis, Strain and Bragg Law, Strain Measurement, Stress Measurement, Stress Measurement Without d 0, t/j-tilt and Goniometer, Sin 2 t/j Method with Area Detector, Theory of Stress Analysis with XRD 2, D Fundamental Equation for Stress Measurement, Relationship Between Conventional Theory and 2D Theory, D Equations for Various Stress States, True Stress-Free Latticed-Spacing, Diffraction Cone Distortion Simulation, Process of Stress Measurement with XRD 2, Instrument Requirements and Configurations, Data Collection Strategy, Data Integration and Peak Evaluation,

7 x CONTENTS 9.5 Experimental Examples, Comparison Between 2D Method and Conventional Method, Virtual Oscillation for Stress Measurement, 305 Stress Mapping on Weldment, 307 Residual Stresses in Thin Films, 310 Residual Stress Measurement with Multiple {hkl} Rings, Gage Repeatability and Reproducibility Study, 316 Appendix 9.A Calculation of Principal Stresses from the General Stress Tensor, 320 Appendix 9.B Parameters for Stress Measurement, 323 References, Small-Angle X-Ray Scattering 10.1 Introduction, Principle of Small-Angle Scattering, General Equation and Parameters in SAXS, X-Ray Source and Optics for SAXS, D SAXS Systems, SAXS Attachments, Dedicated SAXS System, Detector Correction and System Calibration, Data Collection and Integration, Application Examples, Particles in Solutions, Scanning SAXS and Transmission Measurement, Some Innovations in 2D SAXS, Simultaneous Measurements of Transmission and SAXS, Vertical SAXS System, 346 References, Combinatorial Screening 11.1 Introduction, Combinatorial Chemistry, Combinatorial Screening, XRD 2 Systems for Combinatorial Screening, Combinatorial Screening in Reflection Geometry, Retractable Knife-Edge, Combinatorial Screening in Transmission Geometry, Combined Screening with XRD 2 and Raman,

8 CONTENTS xi 12. Quantitative Analysis Percent Crystallinity, Introduction, Comparison of Conventional XRD and XRD 2, Scatter Correction, Internal and External Methods, Full Method, Crystal Size, Introduction, Line Broadening for Crystallite Size, y-profile Analysis for Crystallite Size, Retained Austenite, 387 References, Innovation and Future Development Introduction, Scanning Line Detector for XRD 2, Working Principle, Advantages of Scanning Line Detector, Three-Dimensional Detector, The Third Dimension of a Detector, Geometry of Three-Dimensional Detector, Three-Dimensional Detector and Reciprocal Space, Pixel Direct Diffraction Analysis, Concept, Pixel Diffraction Vector and Pixel Count, PDD Analysis in Phase-ID, Texture, and Stress, 404 References, 406 Appendix A. Values of Commonly Used Parameters 407 Appendix B. Symbols 412 Index 419