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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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| |
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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 | |
| |
| |
| |
| 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> | |
| |
| |
| |
| Full Pattern Decomposition | |
| |
| |
| |
| Solving the Crystal Structure | |
| |
| |
| |
| Rietveld Refinement | |
| |
| |
| |
| Empirical Methods of Solving Crystal Structures | |
| |
| |
| |
| Crystal Structure of Gd<sub>5</sub>Ge<sub>4</sub> | |
| |
| |
| |
| Crystal Structure of Gd<sub>5</sub>Si<sub>4</sub> | |
| |
| |
| |
| Crystal Structure of Gd<sub>5</sub>Si<sub>2</sub>Ge<sub>2</sub> | |
| |
| |
| |
| 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> | |
| |
| |
| |
| Gd<sub>5</sub>Ge<sub>4</sub> | |
| |
| |
| |
| Gd<sub>5</sub>Si<sub>4</sub> | |
| |
| |
| |
| Gd<sub>5</sub>Si<sub>2</sub>Ge<sub>2</sub> | |
| |
| |
| |
| Structure-Property Relationships | |
| |
| |
| |
| Crystal Structure of NiMnO<sub>2</sub>(OH) | |
| |
| |
| |
| Observed Structure Factors from Experimental Data | |
| |
| |
| |
| Solving the Crystal Structure | |
| |
| |
| |
| A Few Notes About Using GSAS | |
| |
| |
| |
| Completion of the Model and Rietveld Refinement | |
| |
| |
| |
| Initial Refinement Steps | |
| |
| |
| |
| Where Is Mn and Where Is Ni? | |
| |
| |
| |
| Finalizing the Refinement of the Model Without Hydrogen | |
| |
| |
| |
| Locating Hydrogen | |
| |
| |
| |
| Combined Rietveld Refinement | |
| |
| |
| |
| Crystal Structure of tma V<sub>3</sub>O<sub>7</sub> | |
| |
| |
| |
| Observed Structure Factors | |
| |
| |
| |
| Solving the Crystal Structure | |
| |
| |
| |
| Completion of the Model and Rietveld Refinement | |
| |
| |
| |
| Unrestrained Rietveld Refinement | |
| |
| |
| |
| Rietveld Refinement with Restraints | |
| |
| |
| |
| Crystal Structure of ma<sub>2</sub>Mo<sub>7</sub>O<sub>22</sub> | |
| |
| |
| |
| Possible Model of the Crystal Structure | |
| |
| |
| |
| Rietveld Refinement and Completion of the Model | |
| |
| |
| |
| Crystal Structure of Mn<sub>7</sub>(OH)<sub>3</sub>(VO<sub>4</sub>)<sub>4</sub> | |
| |
| |
| |
| Solving the Crystal Structure | |
| |
| |
| |
| Rietveld Refinement | |
| |
| |
| |
| Determining Chemical Composition | |
| |
| |
| |
| Crystal Structure of FePO<sub>4</sub> | |
| |
| |
| |
| Building and Optimizing the Model of the Crystal Structure | |
| |
| |
| |
| Rietveld Refinement | |
| |
| |
| |
| Crystal Structure of Acetaminophen, C<sub>8</sub>H<sub>9</sub>NO<sub>2</sub> | |
| |
| |
| |
| Ab Initio Indexing and Le Bail Fitting | |
| |
| |
| |
| Solving the Crystal Structure | |
| |
| |
| |
| Creating a Model | |
| |
| |
| |
| Optimizing the Model (Solving the Structure) | |
| |
| |
| |
| Restrained Rietveld Refinement | |
| |
| |
| |
| Chapters 15-25: Additional Reading | |
| |
| |
| |
| Chapters 15-25: Problems | |
| |
| |
| Index | |