X-RAY DIFFRACTIO N B. E. WARREN

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1 X-RAY DIFFRACTIO N B. E. WARREN

2

3 Chapter 1 X-Ray Scattering by Atom s 1.1 Classical scattering by a free electron Polarization by scattering Scattering from several centers, complex representation Scattering by an atom 7 Chapter 2 Crystal Axes and the Reciprocal Lattic e 2.1 Crystal axes The crystallographic planes hkl Reciprocal vectors and the reciprocal lattice The sphere of reflection Spacing formulae The 14 Bravais lattices Transforming axes and indices 2 4 Chapter 3 Diffraction by a Small Crystal 3.1 Intensity from a small crystal The 3 Laue equations Structure factor for a Bragg reflection Effect of temperature vibration on the intensity from a small crystal 3 5 Chapter 4 The Integrated Intensit y 4.1 Integrated intensity from a small single crystal The extended face imperfect crystal The integrated intensity for a powder sample 4 7 Chapter 5 The Powder Method 5.1 Powder patterns by film recording Diffractometer recording of power patterns Analysis of a cubic powder pattern by diffractomete r recording Analysis of a hexagonal powder pattern 62

4 5.5 Analysis of orthorhombic powder patterns Precision axial length measurements 6 7 Chapter 6 The Laue Method 6.1 The transmission Laue pattern The back reflection Laue pattern 7 7 Chapter 7 The Rotation Method 7.1 The simple rotation pattern Indexing of rotation patterns The Weissenberg pattern Fiber diagrams as rotation patterns 92 Chapter 8 The Use of Space Groups in Structure Determinatio n 8.1 The space group Cmcm Space group methods applied to Uranium 100 Chapter 9 Fourier Series Methods in Structure Determinations 9.1 Representation by Fourier series Fourier series representation of the electron density The Patterson function 11 2 Chapter 10 Scattering by Noncrystalline Forms of Matter 10.1 The general scattering equation for a random orientation Gas of polyatomic molecules Application to a crystalline powder Liquid or amorphous solid with one kind of atom Application to a simple liquid Convergence factor and termination errors Fourier inversion with the Beevers-Lipson strips Approximate method for sample with more than one kin d of atom Exact method for an amorphous sample with more tha n one kind of atom 135

5 10.10 Amorphous scattering from a flat-faced diffractometer sample Multiple scattering from amorphous samples 14 5 Chapter 11 The Effect of Temperature Vibration on X-Ray Diffraction 11.1 Introduction Long wavelength elastic waves in a cubic crystal Restrictions due to the lattice nature and finite size of the sample Intensity from a cubic crystal with one atom per cell The first-order temperature diffuse scattering The second-order temperature diffuse scattering The measurement of temperature diffuse scattering Interpretation of temperature diffuse scattering measurements Determination of the interatomic force constants fro m temperature scattering Evaluation of 2M Temperature diffuse scattering for cubic powder patterns Existence of an inversion temperature for the diffus e scattering 20 1 Chapter 12 X-Ray Studies of Order-Disorder 12.1 Introduction Long-range order in binary compositions Antiphase domains Short-range order diffuse intensity Effect of temperature vibration on short-range orde r intensities Size effect in disordered binary compositions Experimental measurements of short-range order intensity 24 5 Chapter 13 Diffraction by Imperfect Crystals 13.1 Particle size broadening Corrections for instrumental broadening Powder pattern power theorem Small coherent domains and strains 264

6 13.5 Effects of deformation and twin faulting in FCC metals Effects of deformation and twin faulting in HCP metals Effect of deformation and twin faults in BCC metals General remarks 31 2 Chapter 14 Perfect Crystal Theory 14.1 Introduction The Darwin treatment for Bragg reflection Bragg reflection for a thick crystal with negligible absorption Width of a Bragg reflection Extinction Bragg reflection when the reflecting power is small Bragg reflection with absorption The symmetrical Laue case and the Borrmann effect Asymmetric Bragg reflection 34 8 Appendix I The Kinematical Integrated Intensity By Fresnel Diffraction 35 9 Appendix II Wavelengths (in Angstroms) of Som e Characteristic Emission Lines and Absorption Edges Appendix III Mass Absorption Coefficients p m of the Elements (Z = 1 to 83) For a Selection of Wavelengths 36 6 Appendix IV Atomic Scattering Factors 36 9 Appendix V Dispersion Corrections fo r Atomic Scattering Factors 37 2 Appendix VI Compton-Scattering Intensities 1;,,,/R wit h Exchange Terms Based on Hartree-Fock Wave Functions 37 4 Index 377

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