Elements of X-Ray Diffraction

Preface xvii Properties of X-Rays 1(30) Introduction 1(1) Electromagnetic Radiation 2(2) The Continuous Spectrum 4(3) The Characteristic Spectrum 7(4) Absorption 11(7) Filters 18(1) Production of X-Rays 19(8) Gas Tubes 20(1) Filament Tubes 20(2) Focal Spot 22(1) Power Rating 23(1) Rotating-Anode Tubes 23(1) Microfocus Tubes 23(1) Pulsed (Or Flash) Tubes 24(1) Miniature Tubes 24(1) High Voltage Tubes and Linear Accelerators 24(1) Synchrotron Radiation 24(3) Detection of X-Rays 27(1) Safety Precautions 27(4) Electric Shock 27(1) Radiation Hazard 27(1) Problems 28(3) Geometry of Crystals 31(58) Introduction 31(1) Lattices 31(4) Designation of Points, Lines, and Planes 35(3) Reciprocal Lattice 38(2) Symmetry 40(3) Crystal Systems 43(4) Primitive and Nonprimitive Cells 47(4) Indexing in the Hexagonal System 51(1) Crystal Structure 52(11) Atom Sizes and Coordination 63(2) Crystal Shape 65(1) Crystal Defects 66(4) Annealing Twins 67(2) Deformation Twins 69(1) General 70(1) The Stereographic Projection 70(19) Problems 85(4) Diffraction I: Geometry 89(34) Introduction 89(1) Diffraction 90(5) Bragg's Law 95(1) Laue's Equations 96(2) Reciprocal Lattice and Diffraction 98(3) Diffraction Directions 101(2) X-Ray Spectroscopy 103(3) Diffraction Methods 106(12) Laue Method 107(6) Powder Method 113(5) Experimental Visualization of the Reciprocal Lattice 118(2) Diffraction Under Nonideal Conditions 120(3) Problems 122(1) Diffraction II: Intensities Diffraction II: Intensities 123(44) Introduction 123(1) Scattering by an Electron 124(4) Scattering by an Atom 128(3) Scattering by a Unit Cell 131(6) Some Useful Relations 137(1) Structure-Factor Calculations 138(6) Application To Polycrystal Diffraction 144(1) Multiplicity Factor 145(1) Lorentz Factor 145(5) Absorption Factor 150(4) Hull/Debye-Scherrer Camera 150(2) Diffractometer 152(2) Temperature Factor 154(3) Intensities of Diffraction Peaks From Polycrystalline Samples 157(2) Hull/Debye-Scherrer Camera 157(1) Diffractometer 158(1) Qualifications 158(1) Examples of Intensity Calculations 159(3) Reciprocal Space and Diffracted Intensities 162(2) Measurement of X-Ray Intensity 164(3) Problems 165(2) Diffraction III: Real Samples 167(18) Introduction 167(1) Crystallite Size 167(4) Interference Function 171(3) Strain 174(3) Perfect Crystals 177(5) Amorphous and Partially Crystalline Samples 182(3) Problems 183(2) Diffractometer Measurements 185(50) Introduction 185(1) General Features 186(8) X-Ray Optics 194(4) Detectors (General) 198(4) Counting Losses 198(2) Counting Efficiency 200(1) Energy Resolution 201(1) Proportional Counters 202(4) Geiger Counters 206(1) Scintillation Detectors 207(1) Semiconductor Detectors 208(3) Pulse-Height Analysis 211(4) Pulse-Height Discriminator 212(1) Single-Channel Pulse-Height Analyzer 213(2) Multichannel Pulse-Height Analyzer 215(1) Special Kinds of Diffractometry 215(3) Energy-Dispersive Diffractometry 216(1) Position-Sensitive Diffractometry 217(1) Scalers 218(4) Ratemeters 222(3) Monochromatic Operation 225(6) Monochromating Crystal 225(4) Balanced Filters 229(2) Determination of Diffraction Peak Positions 231(4) Problems 234(1) Powder Photographs 235(28) Introduction 235(1) Hull/Debye-Scherrer Method 236(3) Specimen Preparation 239(1) Film and Other Detection Media 240(3) Fluorescent Screens 240(1) Photographic Film 241(1) Image Plates 241(2) Film Loading 243(2) Cameras For Special Conditions 245(1) High-Temperature Cameras 245(1) Low-Temperature Cameras 246(1) High-Pressure Cameras 246(1) Seemann-Bohlin Camera 246(2) Back-Reflection Focusing Cameras 248(3) Pinhole Photographs 251(4) Microbeams and Microcameras 255(1) Choice of Radiation 255(1) Background Radiation 256(2) Crystal Monochromators 258(1) Guinier Cameras [G.13, G.17] 258(1) Measurement of Line Position 259(1) Measurement of Line Intensity 260(3) Problems 261(2) Laue Photographs 263(12) Introduction 263(1) Cameras 264(4) Transmission Camera 264(1) Back-Reflection Camera 265(1) General 266(2) Specimens and Holders 268(2) Collimators 270(2) The Shapes of Laue Spots 272(3) Problems 273(2) Phase Identification By X-Ray Diffraction 275(20) Introduction 275(1) Basic Principles 276(1) Powder Diffraction File 276(3) Hanawalt Method 277(2) Fink Method 279(1) Procedure 279(1) Identification of Single Phase Samples 280(2) Identification of Phases in Mixtures 282(6) Computerized Search-Match 288(3) Practical Difficulties 291(4) Problems 293(2) Determination of Crystal Structure 295(36) Introduction 295(2) Preliminary Treatment of Data 297(2) Indexing Patterns of Cubic Crystals 299(3) Indexing Patterns of Noncubic Crystals 302(4) Tetragonal System 303(1) Hexagonal System 303(2) Orthorhombic System 305(1) Monoclinic and Triclinic Systems 306(1) General 306(1) The Effect of Cell Distortion on the Powder Pattern 306(2) Determination of the Number of Atoms in a Unit Cell 308(1) Determination of Atom Positions 309(2) Example of Structure Determination 311(4) Order-Disorder Determination 315(1) Long-Range Order 315(11) Short-Range Order and Clustering 326(5) Problems 328(3) Phase-Diagram Determination 331(16) Introduction 331(1) General Principles 332(5) Solid Solutions 337(3) Determination of Solvus Curves (Disappearing-Phase Method) 340(2) Determination of Solvus Curves (Parametric Method) 342(5) Problems 345(2) Quantitative Phase Analysis 347(16) Introduction 347(1) Chemical Analysis by Parameter Measurement 347(1) Basic Principles of Multiphase Quantitative Analysis 348(1) External Standard Method 349(2) Direct Comparison Method 351(4) Internal Standard Method 355(3) Other Methods 358(1) Practical Difficulties 359(4) Problems 361(2) Precise Parameter Measurements 363(22) Introduction 363(2) Diffractometers 365(4) Hull/Debye-Scherrer Cameras 369(5) Back-Reflection Focusing Cameras 374(1) Pinhole Cameras 374(1) Example 375(1) Cohen's Method 376(6) Cubic System 377(5) General 382(3) Problems 383(2) Structure of Polycrystalline Aggregates 385(50) Introduction 385(1) Crystal Size and Quality 386(1) Grain Size 386(2) Crystallite Size 388(2) Crystal Quality (Microstrain) 390(6) Depth of X-Ray Penetration 396(3) Size and Strain Separation 399(3) Crystal Orientation 402(1) General 402(5) Fiber Texture 403(1) Sheet Texture 404(1) Pole Figures 404(3) The Texture of Wire (Area Detector Method) 407(4) The Texture of Sheet (Diffractometer Methods) 411(12) Transmission Methods 412(4) Reflection Methods 416(3) Plotting the Pole Figure 419(4) The Texture of Wire (Diffractometer Method) 423(4) Inverse Pole Figures 427(2) Orientation Distribution Functions 429(2) Amorphous and Semi-Amorphous Solids 431(1) Summary 431(4) Problems 432(3) Stress Measurement 435(36) Introduction 435(1) Applied Stress and Residual Stress 436(3) General Principles 439(4) Elasticity 443(3) Biaxial and Triaxial Stress Analysis 446(4) Diffractometer Method 450(9) Measurement of Line Position 454(1) Specimen Preparation 455(1) Measurement of Stress as a Function of Depth 455(1) Variant Techniques 456(1) Special Diffractometers 457(2) Photographic or Area Detector Method 459(4) Calibration 463(2) Precision and Accuracy 465(2) Precision 465(1) Accuracy 466(1) Practical Difficulties 467(4) Large Grain Size 467(1) Preferred Orientation 467(1) Plastic Deformation 468(1) Problems 469(2) Orientation of Single Crystals 471 Introduction 471 Back-Reflection Laue Method 471 Transmission Laue Method 487 Diffractometer Method 490 Setting a Crystal in a Required Orientation 496 Problems 500