INTRODUCTION (James A．Ibers and Walter C．Hamilton) 1
Purpose and Scope of the Tables 1
Acknowledgments 1
1．X-RAY WAVELENGTHS (J．A．Bearden) 3
1．1．Comments on the Tables (James A．Ibers and Walter C．Hamilton) 5
Table 1．1A．X-ray Wavelengths in A Units and in keV Arranged by Atomic Number 6
Table 1．1B．X-ray Wavelengths and Absorption Edges in A Units and in keV in Order of Increasing Wavelength 20
2．ABSORPTION AND SCATTERING 45
2．1．X-ray Cross Sections and Attenuation Coefficients (J．H．Hubbell，W．H．McMaster，N．Kerr Del Grande，and J．H．Mallett) 47
2．1．1．Introduction 47
2．1．2．Sources of Information 47
2．1．2．1．Experimental Attenuation Coefficient Data 47
2．1．2．2．Experimental Photoeffect Data 48
2．1．2．3．Theoretical Photoeffect Data 48
2．1．2．4．Theoretical Coherent Scattering Data 48
2．1．2．5．Theoretical Incoherent Scattering Data 48
2．1．3．Compilation Procedure 48
2．1．3．1．Synthesis of Photoeffect Cross Sections from th Experimental and Theoretical Input Information 48
2．1．3．2．Photoeffect Data Fitting 49
2．1．4．Uncertainty of the Compilation Values 50
Table 2．1A．Wavelengths and Energies Used for Tables 2．1B and 2．1C 54
Table 2．1B．Total Cross Section (σ) in 10-24 cm2 per Atom for Selected X-ray Wavelengths 55
Table 2．1C．Mass Attenuation Coefficients (μ/ρ) in cm2 g-1 61
2．1 References 67
2．2 Atomic Scattering Factors for X-rays (Don T．Cromer and J．T．Waber) 71
Table 2．2A．Mean Atomic Scattering Factors in Electrons for Free Atoms and Chemically Significant Ions 72
Table 2．2B．Coefficients for Analytical Approximation to the Scattering Factors of Table 2．2A 99
Table 2．2C．Spherical Bonded Hydrogen Atom Scattering Factor 102
Table 2．2D．Orbital Scattering Factors for Unfilled p，d，and f Orbitals for Atoms and Ions 103
2．2．References 147
2．3．Dispersion Effects 148
2．3．1．Dispersion Corrections for X-ray Atomic Scattering Factors (Don T．Cromer) 148
Table 2．3．1．Real and Imaginary Dispersion Corrections for Atomic Scattering Factors 149
2．3．2．Dispersion Corrections and Crystal Structure Analyses (James A．Ibers) 148
Table 2．3．2．Reciprocal Lattice Points Equivalent under the Operations of a Given Noncentrosymmetric Point Group 151
2．3．References 151
2．4．Scattering Factors for the Diffraction of Electrons by Crystalline Solids (P．A．Doyle and J．M．Cowley) 152
2．4．1．Elastic Scattering from a Perfect Crystal 152
2．4．2．Atomic Scattering Factors 152
2．4．3．Approximations of Restricted Validity 153
2．4．4．Relativistic Effects 154
2．4．5．Absorption Effects 154
2．4．6．Tables of Atomic Scattering Amplitudes for Electrons 154
Table 2．4．6A．Atomic Scattering Amplitudes in A for Electrons for Neutral Atoms 155
Table 2．4．6B．Atomic Scattering Amplitudes in A for Electrons for Ionized Atoms 164
Table 2．4．6C．Parameters Useful in Electron Diffraction as a Function of Accelerating Voltage，E 174
2．4．References 175
2．5．Complex Scattering Factors for the Diffraction of Electrons by Gases (R．A．Bonham and Lothar Schafer) 176
2．5．1．Introduction 176
2．5．2．Complex Atomic Scattering Factors for Electrons 176
2．5．2．1．Elastic Scattering Factors for Atoms 176
2．5．2．2．Elastic Scattering Factors for Ions 177
2．5．2．3．Total Inelastic Scattering Factors 178
2．5．2．4．Corrections for Defects in the Theory of Atomic Scattering 178
2．5．3．Molecular Scattering Factors for Electrons 178
Table 2．5A．Partial Wave Elastic Scattering Factors for Neutral Atoms 181
Table 2．5B．Partial Wave Ionic Scattering Factors 257
Table 2．5C．Inelastic Scattering Factors 258
Table 2．5D．Inelastic Scattering Factors for He and Ne 268
2．5．References 269
2．6．neutron Scattering Amplitudes for Elements and Isotopes (G．E．Bacon) 270
Table 2．6．Neutron Nuclear Scattering Data for Elements and Isotopes 270
2．6．References 271
3．ANGLE SETTINGS FOR FOUR-CIRCLE DIFFRACTOMETERS (Walter C．Hamilton) 273
3．1．Introduction 275
3．2．Definitions 276
3．2．1．The Diffractometer 276
3．2．2．Coordinate Systems 276
3．2．2．1．Diffractometer-Fixed Axis System 277
3．2．2．2．Crystal-Fixed Orthonormal System 277
3．2．2．3．The Direct Crystal Axes 277
3．2．2．4．The Reciprocal Crystal Axes 277
3．2．2．5．Coordinates of a Reciprocal Vector 277
3．2．2．6．Crystal Rotation 277
3．2．2．7．The Orientation Matrix 277
3．3．Calculation of Setting Angles 278
3．3．1．General Solution 278
Table 3．3．1．Various Settings for Observing a Reflection on a Four-Circle Diffractometer 278
3．3．2．Rotation Around the Diffraction Vector 278
3．3．3．Computational Aspects 279
3．4．Determination of U，the Orientation Matrix 280
3．4．1．Determination of U from Three Reflections 280
3．4．2．Determination of U from Two Reflections 280
3．4．3．Least-Squares Refinement of Cell Constants and Orientation Angles 280
3．5．Measurement Procedures 282
Table 3．5A．Translational Errors for Various Crystal Settings 282
Table 3．5B．Equivalent Crystal Setting Angles for Crystal Alignment on a Four-Circle Diffractometer 283
3．References 284
4．TESTS FOR STATISTICAL SIGNIFICANCE (Walter C．Hamilton) 285
4．1．Introduction 287
4．2．Tests of the R-Factor Ratio，R 288
Table 4．2．Significance Points for the R-Factor Ratio，R 289
4．3．Tests for the Consistency of Weights 293
4．3．1．Tests on S，the Standard Deviation of the Observation of Unit Weight 293
4．3．2．Normal Probability Plots 293
Table 4．3．2A．Percentage Points xi of the Cumulative Normal Distribution Function 295
Table 4．3．2B．Expected Values ξ(i/n) of Ranked Normal Deviates 296
Table 4．3．2C．Expected Values ξ(i/n) of Ranked Normal Deviates Compared with Approximate Values 301
Table 4．3．2D．Expected Values of ith Ranked Moduli of Normal Deviates in Samples of Size n 302
Table 4．3．2E．Expected Values of Extreme Ranked Moduli of Normal Deviates 306
4．References 310
5．THERMAL-MOTION ANALYSIS USING BRAGG DIFFRACTION DATA (C．K．Johnson and H．A．Levy) 311
5．1．Introduction 313
5．2．Thermal Motion of Independent Atoms 314
5．2．1．The Gaussian Density Function Model 314
5．2．2．Properties of the Dispersion Matrix 314
5．2．2．1．Mean-Square Displacement 314
5．2．2．2．Probability Ellipsoids 314
5．2．2．3．Positive-Definite Matrix 315
5．2．2．4．Transformation Properties 315
5．2．2．5．Principal Axis Transformation 315
5．2．2．6．Cartesian Coordinate Systems and the Reporting of Results 315
5．2．2．7．Contraction and Expansion 316
5．2．3．Expansions based on the Gaussian Model 316
5．2．3．1．Gram-Charlier Series Expansion 316
5．2．3．2．Cumulant Expansion 317
5．2．4．Models based on Curvilinear Density Functions 317
5．2．4．1．Density Functions on a Circle 317
5．2．4．2．Density Functions on a Sphere 318
5．2．4．3．The Quasi-Gaussian Approximation 319
5．3．Thermal Motion of a Rigid Body 320
5．3．1．Rigid Motions 320
5．3．2．The 6-Space of rotation and Translation 320
5．3．3．The Center of Reaction 321
5．3．4．Trace-of-S and Geometrical-Arrangement Singularities 321
5．3．5．Non-Intersecting Screw Axes 321
5．4．Correction of Interatomic Distances and Angles 323
5．4．1．The Rigid-Body Model 323
5．4．2．The Riding Model 323
5．5．Site Symmetry Restrictions on Thermal-Motion Tensor Coefficients 324
Table 5．5A．Site Symmetry Table 325
Table 5．5B．Symmetry Restrictions of Coefficients in Second-Order Tensors 328
Table 5．5C．Symmetry Restrictions on Coefficients in Third-Rank Symmetric Polar Tensors 329
Table 5．5D．Symmetry Restrictions on Coefficients in Fourth-Rank Symmetric Polar Tensors 331
Table 5．5E．Symmetry Restrictions on Coefficients in Second-Rank Axial Tensors 332
5．References 335
6．DIRECT METHODS FOR STRUCTURE DETERMINATION：ORIGIN SPECIFICATION，NORMALIZED STRUCTURE FACTORS，FORMULAS，AND THE SYMBOLIC-ADDITION PROCEDURE FOR PHASE DETERMINATION (J．Karle) 337
6．1．Origin Specification 339
6．1．1．Centrosymmetric Space Groups 339
6．1．2．Noncentrosymmetric Space Groups 341
6．1．3．Application 344
Table 6．1A．Seminvariant Vector，Modulus，and Phases for the Conventionally Primitive Centrosymmetric Space Groups 340
Table 6．1B．Seminvariant Vector，Modulus，and Phases for the Conventionally Centered Centrosymmetric Space Groups 341
Table 6．1C．Seminvariant Vector，Modulus，and Phases for the Conventionally Primitive Noncentrosymmetric Space Groups 342
Table 6．1D．Seminvariant Vector，Modulus，and Phases for the Conventionally Centered Noncentrosymmetric Space Groups 345
Table 6．1E．Examples of Sets of Phases and Values for Origin Specification in Noncentrosymmetric Space Groups 347
6．2．Normalized Structure Factors 350
Table 6．2．Selected Statistical Properties of Normalized Structure-Factor Magnitudes 351
6．3．Phase-Determining Formulas 352
6．3．1．Introduction 352
6．3．2．Centrosymmetric Crystals 352
6．3．3．Noncentrosymmetric Crystals 353
6．3．4．Auxiliary Phase-Determining Formulas 353
6．4．Symbolic-Addition Procedure for Phase Determination：X-ray and Neutron Diffraction 355
6．4．1．Introduction 355
6．4．2．Centrosymmetric Crystals 355
6．4．3．Noncentrosymmetric Crystals 356
6．References 358
7．SUBJECT INDEX FOR VOLUMES Ⅰ，Ⅱ，Ⅲ，AND Ⅳ 359