INTRODUCTION (James A．Ibers and Walter C．Hamilton)

Purpose and Scope of the Tables

Acknowledgments

1．X-RAY WAVELENGTHS (J．A．Bearden)

1．1．Comments on the Tables (James A．Ibers and Walter C．Hamilton)

Table 1．1A．X-ray Wavelengths in A Units and in keV Arranged by Atomic Number

Table 1．1B．X-ray Wavelengths and Absorption Edges in A Units and in keV in Order of Increasing Wavelength

2．ABSORPTION AND SCATTERING

2．1．X-ray Cross Sections and Attenuation Coefficients (J．H．Hubbell，W．H．McMaster，N．Kerr Del Grande，and J．H．Mallett)

2．1．1．Introduction

2．1．2．Sources of Information

2．1．2．1．Experimental Attenuation Coefficient Data

2．1．2．2．Experimental Photoeffect Data

2．1．2．3．Theoretical Photoeffect Data

2．1．2．4．Theoretical Coherent Scattering Data

2．1．2．5．Theoretical Incoherent Scattering Data

2．1．3．Compilation Procedure

2．1．3．1．Synthesis of Photoeffect Cross Sections from th Experimental and Theoretical Input Information

2．1．3．2．Photoeffect Data Fitting

2．1．4．Uncertainty of the Compilation Values

Table 2．1A．Wavelengths and Energies Used for Tables 2．1B and 2．1C

Table 2．1B．Total Cross Section (σ) in 10-24 cm2 per Atom for Selected X-ray Wavelengths

Table 2．1C．Mass Attenuation Coefficients (μ/ρ) in cm2 g-1

2．1 References

2．2 Atomic Scattering Factors for X-rays (Don T．Cromer and J．T．Waber)

Table 2．2A．Mean Atomic Scattering Factors in Electrons for Free Atoms and Chemically Significant Ions

Table 2．2B．Coefficients for Analytical Approximation to the Scattering Factors of Table 2．2A

Table 2．2C．Spherical Bonded Hydrogen Atom Scattering Factor

Table 2．2D．Orbital Scattering Factors for Unfilled p，d，and f Orbitals for Atoms and Ions

2．2．References

2．3．Dispersion Effects

2．3．1．Dispersion Corrections for X-ray Atomic Scattering Factors (Don T．Cromer)

Table 2．3．1．Real and Imaginary Dispersion Corrections for Atomic Scattering Factors

2．3．2．Dispersion Corrections and Crystal Structure Analyses (James A．Ibers)

Table 2．3．2．Reciprocal Lattice Points Equivalent under the Operations of a Given Noncentrosymmetric Point Group

2．3．References

2．4．Scattering Factors for the Diffraction of Electrons by Crystalline Solids (P．A．Doyle and J．M．Cowley)

2．4．1．Elastic Scattering from a Perfect Crystal

2．4．2．Atomic Scattering Factors

2．4．3．Approximations of Restricted Validity

2．4．4．Relativistic Effects

2．4．5．Absorption Effects

2．4．6．Tables of Atomic Scattering Amplitudes for Electrons

Table 2．4．6A．Atomic Scattering Amplitudes in A for Electrons for Neutral Atoms

Table 2．4．6B．Atomic Scattering Amplitudes in A for Electrons for Ionized Atoms

Table 2．4．6C．Parameters Useful in Electron Diffraction as a Function of Accelerating Voltage，E

2．4．References

2．5．Complex Scattering Factors for the Diffraction of Electrons by Gases (R．A．Bonham and Lothar Schafer)

2．5．1．Introduction

2．5．2．Complex Atomic Scattering Factors for Electrons

2．5．2．1．Elastic Scattering Factors for Atoms

2．5．2．2．Elastic Scattering Factors for Ions

2．5．2．3．Total Inelastic Scattering Factors

2．5．2．4．Corrections for Defects in the Theory of Atomic Scattering

2．5．3．Molecular Scattering Factors for Electrons

Table 2．5A．Partial Wave Elastic Scattering Factors for Neutral Atoms

Table 2．5B．Partial Wave Ionic Scattering Factors

Table 2．5C．Inelastic Scattering Factors

Table 2．5D．Inelastic Scattering Factors for He and Ne

2．5．References

2．6．neutron Scattering Amplitudes for Elements and Isotopes (G．E．Bacon)

Table 2．6．Neutron Nuclear Scattering Data for Elements and Isotopes

2．6．References

3．ANGLE SETTINGS FOR FOUR-CIRCLE DIFFRACTOMETERS (Walter C．Hamilton)

3．1．Introduction

3．2．Definitions

3．2．1．The Diffractometer

3．2．2．Coordinate Systems

3．2．2．1．Diffractometer-Fixed Axis System

3．2．2．2．Crystal-Fixed Orthonormal System

3．2．2．3．The Direct Crystal Axes

3．2．2．4．The Reciprocal Crystal Axes

3．2．2．5．Coordinates of a Reciprocal Vector

3．2．2．6．Crystal Rotation

3．2．2．7．The Orientation Matrix

3．3．Calculation of Setting Angles

3．3．1．General Solution

Table 3．3．1．Various Settings for Observing a Reflection on a Four-Circle Diffractometer

3．3．2．Rotation Around the Diffraction Vector

3．3．3．Computational Aspects

3．4．Determination of U，the Orientation Matrix

3．4．1．Determination of U from Three Reflections

3．4．2．Determination of U from Two Reflections

3．4．3．Least-Squares Refinement of Cell Constants and Orientation Angles

3．5．Measurement Procedures

Table 3．5A．Translational Errors for Various Crystal Settings

Table 3．5B．Equivalent Crystal Setting Angles for Crystal Alignment on a Four-Circle Diffractometer

3．References

4．TESTS FOR STATISTICAL SIGNIFICANCE (Walter C．Hamilton)

4．1．Introduction

4．2．Tests of the R-Factor Ratio，R

Table 4．2．Significance Points for the R-Factor Ratio，R

4．3．Tests for the Consistency of Weights

4．3．1．Tests on S，the Standard Deviation of the Observation of Unit Weight

4．3．2．Normal Probability Plots

Table 4．3．2A．Percentage Points xi of the Cumulative Normal Distribution Function

Table 4．3．2B．Expected Values ξ(i/n) of Ranked Normal Deviates

Table 4．3．2C．Expected Values ξ(i/n) of Ranked Normal Deviates Compared with Approximate Values

Table 4．3．2D．Expected Values of ith Ranked Moduli of Normal Deviates in Samples of Size n

Table 4．3．2E．Expected Values of Extreme Ranked Moduli of Normal Deviates

4．References

5．THERMAL-MOTION ANALYSIS USING BRAGG DIFFRACTION DATA (C．K．Johnson and H．A．Levy)

5．1．Introduction

5．2．Thermal Motion of Independent Atoms

5．2．1．The Gaussian Density Function Model

5．2．2．Properties of the Dispersion Matrix

5．2．2．1．Mean-Square Displacement

5．2．2．2．Probability Ellipsoids

5．2．2．3．Positive-Definite Matrix

5．2．2．4．Transformation Properties

5．2．2．5．Principal Axis Transformation

5．2．2．6．Cartesian Coordinate Systems and the Reporting of Results

5．2．2．7．Contraction and Expansion

5．2．3．Expansions based on the Gaussian Model

5．2．3．1．Gram-Charlier Series Expansion

5．2．3．2．Cumulant Expansion

5．2．4．Models based on Curvilinear Density Functions

5．2．4．1．Density Functions on a Circle

5．2．4．2．Density Functions on a Sphere

5．2．4．3．The Quasi-Gaussian Approximation

5．3．Thermal Motion of a Rigid Body

5．3．1．Rigid Motions

5．3．2．The 6-Space of rotation and Translation

5．3．3．The Center of Reaction

5．3．4．Trace-of-S and Geometrical-Arrangement Singularities

5．3．5．Non-Intersecting Screw Axes

5．4．Correction of Interatomic Distances and Angles

5．4．1．The Rigid-Body Model

5．4．2．The Riding Model

5．5．Site Symmetry Restrictions on Thermal-Motion Tensor Coefficients

Table 5．5A．Site Symmetry Table

Table 5．5B．Symmetry Restrictions of Coefficients in Second-Order Tensors

Table 5．5C．Symmetry Restrictions on Coefficients in Third-Rank Symmetric Polar Tensors

Table 5．5D．Symmetry Restrictions on Coefficients in Fourth-Rank Symmetric Polar Tensors

Table 5．5E．Symmetry Restrictions on Coefficients in Second-Rank Axial Tensors

5．References

6．DIRECT METHODS FOR STRUCTURE DETERMINATION：ORIGIN SPECIFICATION，NORMALIZED STRUCTURE FACTORS，FORMULAS，AND THE SYMBOLIC-ADDITION PROCEDURE FOR PHASE DETERMINATION (J．Karle)

6．1．Origin Specification

6．1．1．Centrosymmetric Space Groups

6．1．2．Noncentrosymmetric Space Groups

6．1．3．Application

Table 6．1A．Seminvariant Vector，Modulus，and Phases for the Conventionally Primitive Centrosymmetric Space Groups

Table 6．1B．Seminvariant Vector，Modulus，and Phases for the Conventionally Centered Centrosymmetric Space Groups

Table 6．1C．Seminvariant Vector，Modulus，and Phases for the Conventionally Primitive Noncentrosymmetric Space Groups

Table 6．1D．Seminvariant Vector，Modulus，and Phases for the Conventionally Centered Noncentrosymmetric Space Groups

Table 6．1E．Examples of Sets of Phases and Values for Origin Specification in Noncentrosymmetric Space Groups

6．2．Normalized Structure Factors

Table 6．2．Selected Statistical Properties of Normalized Structure-Factor Magnitudes

6．3．Phase-Determining Formulas

6．3．1．Introduction

6．3．2．Centrosymmetric Crystals

6．3．3．Noncentrosymmetric Crystals

6．3．4．Auxiliary Phase-Determining Formulas

6．4．Symbolic-Addition Procedure for Phase Determination：X-ray and Neutron Diffraction

6．4．1．Introduction

6．4．2．Centrosymmetric Crystals

6．4．3．Noncentrosymmetric Crystals

6．References

7．SUBJECT INDEX FOR VOLUMES Ⅰ，Ⅱ，Ⅲ，AND Ⅳ