Handbook of X-Ray Analysis of Polycrystalline Materials

Back-Reflection Cameras.- 2-4c. Nomogram for Setting Cameras for Express Recording.- 2-5. Ionization Recording.- 2-5a. Radiation Detectors.- 2-5b. Absorption of X-Rays in Geiger Counters.- 2-5c. Efficiencies of Counters.- 2-6. Selective Filters.- 2-7. Characteristics of Monochromator Crystals.- 2-7a. Reflections and Properties of Monochromator Crystals.- 2-7b. Reflectivity of Monochromator Crystals.- 2-7c. Optimal Thickness of Monochromator Crystal for Use in Transmission.- 2-7d. Properties of Plane Monochromator Crystals.- 2-7e. Reflection Angles for Bent Monochromator Crystals.- 2-8. Parameters for Use with Bent Quartz Crystals.- 2-9. Measurement of Diffraction Lines on Patterns.- 2-9a. Determination of Bragg Angles for a Flat Film.- 2-9b. Correction for Deviation of Camera Diameter from Standard.- 2-9c. Correction for Specimen Thickness.- 2-9d. Correction for Eccentricity of Specimen in Camera.- 2-10. Intensity Measurements.- 2-10a. Number of Counts Needed to Give a Specified Probable Error.- 2-10b. Statistical Error of Count.- 2-10c. Correction for Particle Size, Fixed Specimen.- 2-10d. Correction for Particle Size, Rotating Specimen.- 2-10e. Correction for Lost Counts.- 2-11. Doublet Splittings.- 2-12. Data for Calculations on Laue Patterns.- 2-12a. Net for Calculations on Back-Reflection Patterns.- 2-12b. Net for Calculations on Transmission Patterns.- 2-12c. Accessory Table for Constructing the Projection of the Crystal from the Laue Pattern.- 2-13. Determination of Orientation for Large Crystals in Polycrystalline Materials.- 3. Indexing of X-Ray Patterns.- 3-1. Accessory Tables.- 3-1a. Some Composite Trigonometric Functions.- 3-1b. Values of 1/d2.- 3-1c. Values of n? and lg (n?/2).- 3-1d. Values of ?, ?/2, ?2/4, lg (?2/4), and (?/2)?n.- 3-2. Space-Group Symbols.- 3-3. Tables of Absences for Determining X-Ray Groups.- Cubic System.- 3-4. Schemes for X-Ray Patterns.- 3-5. Quadratic Forms.- 3-6. Graphs for Indexing X-Ray Patterns.- 3-7. Graphs for Determining Whether a Material is Cubic.- 3-8. Limiting Values for Sums of the Squares of Indices for Various Unit-Cell Volumes and Radiations.- Tetragonal System.- 3-9. Schemes for X-Ray Patterns.- 3-10. Quadratic Forms.- 3-11. Values of (a/c)2l2.- 3-12. Analytic Method of Indexing X-Ray Patterns.- 3-13. Graphs for Indexing X-Ray Patterns.- Hexagonal System.- 3-14. Schemes for X-Ray Patterns.- 3-15. Quadratic Forms.- 3-16. Analytic Method of Indexing for the Hexagonal and Trigonal Systems.- 3-17. Graphs for Indexing X-Ray Patterns.- 3-18. Relations between Indices in Indexing for the Hexagonal, Trigonal, and Orthohexagonal Systems.- Trigonal System.- 3-19. Quadratic Forms.- 3-20. Values of (2 cos ?)/(1 + cos ?) = 1 - tg2 (?/2).- 3-21. Relation of ? to c/a for the Trigonal System.- 3-22. Relation of Sum of the Squares of the Indices to ? for Fixed Cell Volume.- 3-23. Graphs for Indexing X-Ray Patterns.- Orthorhombic System.- 3-24. Analytic Method of Indexing X-Ray Patterns.- 3-25. Graphs for Indexing X-Ray Patterns.- Lower Systems.- 3-26. Graphical Method of Indexing X-Ray Patterns.- 3-27. Use of the Theory of Homology in Indexing Patterns for Crystals of Low Symmetry.- 4. Line Intensities on X-Ray Patterns.- 4-1. Some Formulas for Line Intensities.- 4-2. Values of e4?3/2m2c4.- Angular Intensity Factors.- 4-3. Product of the Polarization, Lorentz, and Geometric Factors for Patterns Recorded without Monochromators.- 4-3a. Debye Patterns in Cylindrical Cameras.- 4-3b. Recording on Flat Film.- 4-3c. Reflection from a Monocrystal.- 4-4. Product of the Polarization, Lorentz, and Geometric Factors for Symmetrical Recording with a Monochromator.- 4-5. Some Trigonometric Functions.- Atomic Intensity Factors.- 4-6. Accessory Table for Calculating Atomic Factors.- 4-7. Atomic Scattering Factors for Atoms and Ions.- 4-8. Correction for Anomalous Dispersion.- 4-8a. Values of ?fk?.- 4-8b. Values of ?fk?.- 4-8c. Values of ?K for Some Elements.- Structure Factors.- 4-9. Accessory Table for Calculating Structure Factors,.- 4-10. Nomogram for Calculating Structure Factors.- 4-11. Array of Atoms in Some Types of Crystal Structure.- 4-12. Structure Factors for Some Cubic Space Groups.- 4-13. Structure Factors for Some Cubic Structure Types.- 4-14. Structure Factors for Some Tetragonal Space Groups.- 4-15. Structure Factors for Some Hexagonal Space Groups.- 4-16. Structure Factors for Some Hexagonal Structure Types.- 4-17. The Temperature Factor.- 4-17a. Debye's function.- 4-17b. Values of the Temperature Factor for Various B and ?.- 4-17c. The Functions e?x and lg e?x.- 4-17d. Values of B? in the Expression for the Temperature Factor.- 4-18. Multiplicity Factors for the Various Crystal Systems.- Absorption Factors.- 4-19. Absorption Factors for Cylindrical Specimens.- 4-19a. Absolute Values for Homogeneous Specimens.- 4-19b. Relative Values for Homogeneous Specimens.- 4-19c. Absolute Values for Powder Specimens Attached to Fibers.- 4-20. Absorption Factors for Plane Specimens.- 4-21. Absorption Factors for Spherical Specimens.- 4-21a. Absolute Values.- 4-21b. Relative Values.- 4-22. Absorption Factors for Powder Mixed with Binder.- 2: Some Special Problems and Methods in X-Ray Structure Analysis.- 5. Phase Analysis.- 5-1. Methods.- 5-1a. Qualitative Methods.- 5-1b. Quantitative Methods Involving Intensity Measurement.- 5-2. Crystal Structures of Elements and Compounds.- 5-3. Interplanar Distances and Line Intensities for Elements and Compounds.- 5-4. Tables for Phase Analysis of Isomorphous Compounds.- 5-4a. Cubic System.- 5-4b. Tetragonal System.- 5-4c. Hexagonal System.- 5-5. Method of Homologous Pairs.- 5-5a. Homologous Pairs for Determining Austenite in Steels.- 5-5b. Homologous Pairs for Quantitative Analysis of Two-Phase Brasses.- 5-5c. Homologous Pairs for Analysis of Oxides on Steel.- 5-6. Method of Superposition.- 5-7. Conversion of Weight Percent to Atomic Percent.- 6. Precision Measurement of Lattice Constants.- 6-1. Aspects of Precision Methods of Measuring Lattice Constants.- 6-1a. Asymmetric Recording.- 6-1b. Recording at Large Distances in Divergent Beams.- 6-1c. Use of a Standard.- 6-1d. Graphical Extrapolation.- 6-1e. Combined Graphical Extrapolation and Calculation.- 6-1f. Analytic Least-Squares Method.- 6-1g. Method Not Involving Use of a Standard.- 6-1h. Aspects of Precision Determination by Ionization Methods.- 6-2. Choice of Method in Precision Determinations.- 6-2a. Methods of Measurement.- 6-2b. Choice of Method.- 6-3. Choice of Radiation for Cubic Crystals.- 6-4. Choice of Radiation for Tetragonal Crystals.- 6-5. Choice of Radiation for Hexagonal and Trigonal Crystals.- 6-6. Choice of Conditions for Certain Materials.- 6-7. Tables for Determining Lattice Constants of Cubic Substances.- 6-7a. Use of Copper Radiation.- 6-7b. Use of Nickel Radiation.- 6-7c. Use of Cobalt Radiation.- 6-7d. Use of Iron Radiation.- 6-7e. Use of Chromium Radiation.- 6-8. Extrapolation Functions.- 6-8a. Function cos2?.- 6-8b. Function ½(cos2?)/sin ? + (cos2?)/?].- 6-8c. Function ? tg ?.- 6-9. Lattice Constants of Some Standard Substances.- 6-10. Bragg Angles for Some Standard Substances.- 6-10a. NaCl.- 6-10b. Ag.- 6-10c. Au.- 6-10d. Polycrystalline Quartz.- 6-10e. Monocrystalline Quartz.- 6-10f. Some Lines of Al, Cr, Au, Ag, and W.- 6-11. Factors for Reducing sin2? to a Single Wavelength.- 6-12. Correction for Refraction.- 6-13. Linear-Expansion Coefficients for Some Metals, Alloys, and Other Materials.- 7. Determination of Macroscopic Stresses.- 7-1. Some Formulas for Stress Determination.- 7-2. Accessory Table for Determining Stresses in Iron, Copper, Aluminum, and Alloys of These.- 7-3. Stresses Producing a Line Shift of 0.1 mm for Various Materials and Conditions.- 7-4. Accessory Function for Calculating Macroscopic Stresses in Iron from Patterns Taken with Cobalt Radiation.- 7-5. Values of Constants in Stress-Determination Relations.- 7-6. Correction for Relation between ?x and ?y.- 7-7. Correction for Film Movement.- 7-8. Nomogram for Determining Stresses.- 8. Determination of Crystallite and Block Sizes, of Microstresses, and of Lattice Distortion.- 8-1. Determination of Crystallite Sizes.- 8-1a. From Size and Number of Spots on Pattern.- 8-1b. Table for Determining Block Sizes from Line Intensities.- 8-2. Measurement of Crystallite and Block Sizes from Line Intensities.- 8-3. X-Ray Determination of Dislocation Densities.- 8-4. Geometric Broadening of Lines on X-Ray Patterns.- 8-5. Correction for Heterochromatic Radiation.- 8-6. Physical Line Broadening.- 8-7. Separation of the Effects of Block Size and of Microstresses.- 8-8. Microstress Anisotropy Factor.- 8-9. Block-Shape Constant.- 8-10. Determination of True Width and Shape of Lines from Fourier Series.- 8-10a. A cos 2?tx.- 8-10b. A sin 2?tx.- 8-10c. Tables for Determining Positions of Peaks.- 8-11. Determination of Dynamic Lattice Distortions and Characteristic Temperatures.- 8-12. Determination of Static Lattice Distortions of Atomic Scale.- 9. Determination of Preferred Orientations (Textures).- 9-1. The Wulff Net.- 9-2. The Polar Net.- 9-3. Standard Projections of Crystals.- 9-4. Angles between Atomic Planes.- 9-4a. Cubic System.- 9-4b. Tetragonal System.- 9-4c. Hexagonal System.- 9-5. Nets for Constructing Polar Figures for a Flat Film.- 9-6. Net for Constructing Polar Figures When an Axial Camera is Used.- 9-7. Correction for Absorption in Ionization Recording.- 10. Diffuse Scattering of X-Rays and Small-Angle Scattering.- 10-1. Some Formulas for the Diffuse-Scattering Intensity.- 10-2. Values of s(?) for Various Radiations.- 10-3. Polarization Factor for Diffuse Scattering.- 10-4. Angular Intensity Factors.- 10-5. Incoherent-Scattering Intensity.- 10-6. Relativistic Correction for Incoherent Scattering.- 10-7. Values of q for Particles of Various Shapes.- 10-8. Scattering Functions for Systems of Homogeneous Particles.- 10-8a. Spherical Particles (General Values).- 10-8b. Spherical Particles (Maxima and Minima).- 10-8c. Ellipsoid of Rotation.- 10-8d. Particles in the Form of Cylinders.- 10-8e. Particles in the Form of Cylinders of Small Diameter.- 10-8f. Particles in the Form of Elliptic Cylinders.- 10-8g. Particles in the Form of Discs.- 10-8h. Particles in the Form of Rectangular Prisms.- 10-9. Graph for Determining Radii of Gyration of Particles.- 10-10. Scattering by Inhomogeneous Systems of Particles.- 10-10a. System of Spherical Particles.- 10-10b. Scattering Function for a System of Spherical Particles Separated by Gaps.- 10-10c. Scattering Function for a System of Spherical Particles of Various Radii.- 10-10d. System of Particles with a Linear Structure.- 10-10e. Short-Range Order in Particle Disposition.- 10-11. Scattering Curves for Various Particle-Size Distributions.- 10-12. The Collimator Effect.- 10-12a. Effect of the Collimator on the Scattering Function.- 10-12b. Effect of the Collimator on the Turning Points in the Scattering Function.- 10-12c. Choice of Collimator.- 11. Electron Diffraction.- 11-1. Some Formulas for Electron Diffraction.- 11-2. Relation of Electron Wavelength to Applied Voltage.- 11-3. ? Correction in Precision Interplanar Distance Measurements.- 11-4. Universal Atomic-Scattering Function for Electrons.- 11-5. Atomic Scattering Factors for Electrons.- 11-5a. Scattering by Light Atoms.- 11-5b. Scattering by Atoms of Medium and High Atomic Numbers.- 11-5c. Scattering by Ions.- 11-6. Symmetry of Point Patterns.- 12. Neutron Diffraction.- 12-1. Some Formulas for Neutron Diffraction.- 12-2. Characteristics of Neutrons of Various Energies.- 12-3. Properties of X-Rays and Neutrons.- 12-4. Neutron Scattering by Isotopes.- 12-5. Neutron Absorption.- 12-6. Nuclear and Magnetic Scattering Amplitudes for Neutrons.- 12-7. Form Factors for Magnetic Scattering for Atoms and Ions.- 12-8. Effective Neutron-Scattering Cross Sections for Metals and Alloys.- Literature Cited.