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Fundamentals of Crystalline State and Crystal Lattice | |
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Crystalline State | |
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Crystal Lattice and Unit Cell | |
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Shape of the Unit Cell | |
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Crystallographic Planes, Directions, and Indices | |
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Crystallographic Planes | |
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Crystallographic Directions | |
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Reciprocal Lattice | |
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Additional Reading | |
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Problems | |
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Finite Symmetry Elements and Crystallographic Point Groups | |
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Content of the Unit Cell | |
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Asymmetric Part of the Unit Cell | |
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Symmetry Operations and Symmetry Elements | |
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Finite Symmetry Elements | |
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Onefold Rotation Axis and Center of Inversion | |
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Twofold Rotation Axis and Mirror Plane | |
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Threefold Rotation Axis and Threefold Inversion Axis | |
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Fourfold Rotation Axis and Fourfold Inversion Axis | |
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Sixfold Rotation Axis and Sixfold Inversion Axis | |
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Interaction of Symmetry Elements | |
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Generalization of Interactions Between Finite Symmetry Elements | |
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Symmetry Groups | |
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Fundamentals of Group Theory | |
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Crystal Systems | |
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Stereographic Projection | |
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Crystallographic Point Groups | |
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Laue Classes | |
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Selection of a Unit Cell and Bravais Lattices | |
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Additional Reading | |
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Problems | |
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Infinite Symmetry Elements and Crystallographic Space Groups | |
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Glide Planes | |
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Screw Axes | |
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Interaction of Infinite Symmetry Elements | |
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Crystallographic Space Groups | |
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Relationships Between Point Groups and Space Groups | |
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Full International Symbols of Crystallographic Space Groups | |
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Visualization of Space-Group Symmetry in Three Dimensions | |
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Space Groups in Nature | |
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International Tables for Crystallography | |
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Equivalent Positions (Sites) | |
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General and Special Equivalent Positions | |
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Special Sites with Points Located on Mirror Planes | |
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Special Sites with Points Located on Rotation and Inversions Axes | |
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Special Sites with Points Located on Centers of Inversion | |
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Additional Reading | |
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Problems | |
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Formalization of Symmetry | |
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Symbolic Representation of Symmetry | |
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Finite Symmetry Operations | |
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Infinite Symmetry Operations | |
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Algebraic Treatment of Symmetry Operations | |
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Transformation of Coordinates of a Point | |
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Rotational Transformations of Vectors | |
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Translational Transformations of Vectors | |
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Combined Symmetrical Transformations of Vectors | |
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Augmentation of Matrices | |
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Algebraic Representation of Crystallographic Symmetry | |
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Interaction of Symmetry Operations | |
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Additional Reading | |
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Problems | |
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Nonconventional Symmetry | |
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Commensurate Modulation | |
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Incommensurate Modulation | |
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Composite Crystals | |
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Symmetry of Modulated Structures | |
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Quasicrystals | |
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Additional Reading | |
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Problems | |
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Properties, Sources, and Detection of Radiation | |
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Nature of X-Rays | |
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Production of X-Rays | |
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Conventional Sealed X-Ray Sources | |
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Continuous and Characteristic X-Ray Spectra | |
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Rotating Anode X-Ray Sources | |
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Synchrotron Radiation Sources | |
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Other Types of Radiation | |
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Detection of X-Rays | |
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Detector Efficiency, Linearity, Proportionality and Resolution | |
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Classification of Detectors | |
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Point Detectors | |
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Line and Area Detectors | |
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Additional Reading | |
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Problems | |
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Fundamentals of Diffraction | |
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Scattering by Electrons, Atoms and Lattices | |
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Scattering by Electrons | |
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Scattering by Atoms and Atomic Scattering Factor | |
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Scattering by Lattices | |
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Geometry of Diffraction by Lattices | |
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Laue Equations | |
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Braggs' Law | |
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Reciprocal Lattice and Ewald's Sphere | |
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Additional Reading | |
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Problems | |
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The Powder Diffraction Pattern | |
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Origin of the Powder Diffraction Pattern | |
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Representation of Powder Diffraction Patterns | |
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Understanding of Powder Diffraction Patterns | |
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Positions of Powder Diffraction Peaks | |
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Peak Positions as a Function of Unit Cell Dimensions | |
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Other Factors Affecting Peak Positions | |
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Shapes of Powder Diffraction Peaks | |
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Peak-Shape Functions | |
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Peak Asymmetry | |
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Intensity of Powder Diffraction Peaks | |
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Integrated Intensity | |
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Scale Factor | |
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Multiplicity Factor | |
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Lorentz-Polarization Factor | |
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Absorption Factor | |
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Preferred Orientation | |
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Extinction Factor | |
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Additional Reading | |
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Problems | |
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Structure Factor | |
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Structure Amplitude | |
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Population Factor | |
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Temperature Factor (Atomic Displacement Factor) | |
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Atomic Scattering Factor | |
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Phase Angle | |
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Effects of Symmetry on the Structure Amplitude | |
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Friedel Pairs and Friedel's Law | |
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Friedel's Law and Multiplicity Factor | |
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Systematic Absences | |
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Lattice Centering | |
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Glide Planes | |
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Screw Axes | |
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Space Groups and Systematic Absences | |
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Additional Reading | |
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Problems | |
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Solving the Crystal Structure | |
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Fourier Transformation | |
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Phase Problem | |
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Patterson Technique | |
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Direct Methods | |
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Structure Solution from Powder Diffraction Data | |
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Total Scattering Analysis Using Pair Distribution Function | |
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Additional Reading | |
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Problems | |
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Powder Diffractometry | |
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Brief History of the Powder Diffraction Method | |
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Beam Conditioning in Powder Diffractometry | |
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Collimation | |
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Monochromatization | |
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Principles of Goniometer Design in Powder Diffractometry | |
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Goniostats with Strip and Point Detectors | |
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Goniostats with Area Detectors | |
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Nonambient Powder Diffractometry | |
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Variable Temperature Powder Diffractometry | |
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Principles of Variable Pressure Powder Diffractometry | |
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Powder Diffractometry in High Magnetic Fields | |
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Additional Reading | |
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Problems | |
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Collecting Quality Powder Diffraction Data | |
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Sample Preparation | |
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Powder Requirements and Powder Preparation | |
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Powder Mounting | |
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Sample Size | |
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Sample Thickness and Uniformity | |
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Sample Positioning | |
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Effects of Sample Preparation on Powder Diffraction Data | |
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Data Acquisition | |
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Wavelength | |
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Monochromatization | |
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Incident Beam Aperture | |
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Diffracted Beam Aperture | |
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Variable Aperture | |
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Power Settings | |
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Classification of Powder Diffraction Experiments | |
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Step Scan | |
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Continuous Scan | |
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Scan Range | |
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Quality of Experimental Data | |
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Quality of Intensity Measurements | |
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Factors Affecting Resolution | |
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Additional Reading | |
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Problems | |
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Preliminary Data Processing and Phase Analysis | |
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Interpretation of Powder Diffraction Data | |
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Preliminary Data Processing | |
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Background | |
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Smoothing | |
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K�<sub>2</sub> Stripping | |
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Peak Search | |
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Profile Fitting | |
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Phase Identification and Quantitative Analysis | |
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Crystallographic Databases | |
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Phase Identification | |
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Quantitative Analysis | |
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Phase Contents from Rietveld Refinement | |
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Determination of Amorphous Content or Degree of Crystallinity | |
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Additional Reading | |
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Problems | |
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Determination and Refinement of the Unit Cell | |
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The Indexing Problem | |
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Known Versus Unknown Unit Cell Dimensions | |
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Indexing: Known Unit Cell | |
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High Symmetry Indexing Example | |
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Other Crystal Systems | |
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Reliability of Indexing | |
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The F<sub>N</sub> Figure of Merit | |
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The M<sub>20</sub> (M<sub>N</sub>) Figure of Merit | |
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Introduction to Ab Initio Indexing | |
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Cubic Crystal System | |
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Primitive Cubic Unit Cell: LaB<sub>6</sub> | |
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Body-Centered Cubic Unit Cell: U<sub>3</sub>Ni<sub>6</sub>Si<sub>2</sub> | |
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Tetragonal and Hexagonal Crystal Systems | |
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Indexing Example: LaNi<sub>4.85</sub>Sn<sub>0.15</sub> | |
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Automatic Ab Initio Indexing Algorithms | |
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Indexing in Direct Space | |
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Indexing in Reciprocal Space | |
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Unit Cell Reduction Algorithms | |
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Delaunay-Ito Transformation | |
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Niggli Reduction | |
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Automatic Ab Initio Indexing: Computer Codes | |
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TREOR | |
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DICVOL | |
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ITO | |
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Selecting a Solution | |
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Ab Initio Indexing Examples | |
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Hexagonal Indexing: LaNi<sub>4.85</sub>Sn<sub>0.15</sub> | |
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Monoclinic Indexing: (CH<sub>3</sub>NH<sub>3</sub>)<sub>2</sub>Mo<sub>7</sub>O<sub>22</sub> | |
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Triclinic Indexing: Fe<sub>7</sub>(PO<sub>4</sub>)<sub>6</sub> | |
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Pseudo-Hexagonal Indexing: LiB(C<sub>2</sub>O<sub>4</sub>)<sub>2</sub> | |
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Precise Lattice Parameters and Linear Least Squares | |
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Linear Least Squares | |
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Precise Lattice Parameters from Linear Least Squares | |
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Concluding Remarks | |
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Additional Reading | |
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Problems | |
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Solving Crystal Structure from Powder Diffraction Data | |
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Ab Initio Methods of Structure Solution | |
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Conventional Reciprocal Space Methods | |
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Conventional Direct Space Modeling | |
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Unconventional Direct, Reciprocal, and Dual Space Methods | |
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Validation and Completion of the Model | |
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The Content of the Unit Cell | |
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Pearson's Classification | |
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Finding Structure Factors from Powder Diffraction Data | |
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Nonlinear Least Squares | |
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Quality of Profile Fitting | |
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Visual Assessment of the Quality of Profile Fitting | |
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Figures of Merit | |
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The Rietveld Method | |
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Fundamentals of the Rietveld Method | |
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Classes of Rietveld Refinement Parameters | |
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Restraints, Constraints, and Rigid-Bodies | |
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Figures of Merit and Quality of Rietveld Refinement | |
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Common Problems and How to Deal with Them | |
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Termination of Rietveld Refinement | |
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Concluding Remarks | |
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Additional Reading | |
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Crystal Structure of LaNi<sub>485</sub>Sn<sub>015</sub> | |
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Full Pattern Decomposition | |
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Solving the Crystal Structure | |
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Rietveld Refinement Using Cu K�<sub>1,2</sub> Radiation | |
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Scale Factor and Profile Parameters | |
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Overall Atomic Displacement Parameter | |
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Individual Parameters, Free and Constrained Variables | |
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Anisotropic Atomic Displacement Parameters | |
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Multiple Phase Refinement | |
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Refinement Results | |
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Rietveld Refinement Using Mo K�<sub>1,2</sub> Radiation | |
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Combined Refinement Using Different Sets of Diffraction Data | |
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Crystal Structure of CeRhGe<sub>3</sub> | |
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Full Pattern Decomposition | |
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Solving the Crystal Structure from X-Ray Data | |
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Highest Symmetry Attempt | |
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Low-Symmetry Model | |
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Solving the Crystal Structure from Neutron Data | |
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Rietveld Refinement | |
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X-Ray Data, Correct Low Symmetry Model | |
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X-Ray Data, Wrong High-Symmetry Model | |
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Neutron Data | |
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Crystal Structure of Nd<sub>5</sub>Si<sub>4</sub> | |
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Full Pattern Decomposition | |
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Solving the Crystal Structure | |
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Rietveld Refinement | |
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Empirical Methods of Solving Crystal Structures | |
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Crystal Structure of Gd<sub>5</sub>Ge<sub>4</sub> | |
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Crystal Structure of Gd<sub>5</sub>Si<sub>4</sub> | |
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Crystal Structure of Gd<sub>5</sub>Si<sub>2</sub>Ge<sub>2</sub> | |
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Rietveld Refinement of Gd<sub>5</sub>Ge<sub>4</sub>,Gd<sub>5</sub>Si<sub>4</sub>, and Gd<sub>5</sub>Si<sub>2</sub>Ge<sub>2</sub> | |
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Gd<sub>5</sub>Ge<sub>4</sub> | |
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Gd<sub>5</sub>Si<sub>4</sub> | |
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Gd<sub>5</sub>Si<sub>2</sub>Ge<sub>2</sub> | |
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Structure-Property Relationships | |
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Crystal Structure of NiMnO<sub>2</sub>(OH) | |
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Observed Structure Factors from Experimental Data | |
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Solving the Crystal Structure | |
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A Few Notes About Using GSAS | |
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Completion of the Model and Rietveld Refinement | |
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Initial Refinement Steps | |
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Where Is Mn and Where Is Ni? | |
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Finalizing the Refinement of the Model Without Hydrogen | |
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Locating Hydrogen | |
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Combined Rietveld Refinement | |
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Crystal Structure of tma V<sub>3</sub>O<sub>7</sub> | |
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Observed Structure Factors | |
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Solving the Crystal Structure | |
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Completion of the Model and Rietveld Refinement | |
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Unrestrained Rietveld Refinement | |
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Rietveld Refinement with Restraints | |
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Crystal Structure of ma<sub>2</sub>Mo<sub>7</sub>O<sub>22</sub> | |
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Possible Model of the Crystal Structure | |
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Rietveld Refinement and Completion of the Model | |
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Crystal Structure of Mn<sub>7</sub>(OH)<sub>3</sub>(VO<sub>4</sub>)<sub>4</sub> | |
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Solving the Crystal Structure | |
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Rietveld Refinement | |
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Determining Chemical Composition | |
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Crystal Structure of FePO<sub>4</sub> | |
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Building and Optimizing the Model of the Crystal Structure | |
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Rietveld Refinement | |
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Crystal Structure of Acetaminophen, C<sub>8</sub>H<sub>9</sub>NO<sub>2</sub> | |
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Ab Initio Indexing and Le Bail Fitting | |
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Solving the Crystal Structure | |
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Creating a Model | |
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Optimizing the Model (Solving the Structure) | |
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Restrained Rietveld Refinement | |
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Chapters 15-25: Additional Reading | |
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Chapters 15-25: Problems | |
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Index | |