Fundamentals of Powder Diffraction and Structural Characterization of Materials

ISBN-10: 0387095780

ISBN-13: 9780387095783

Edition: 2nd 2009

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Description: This textbook provides an in-depth introduction to the theories and applications of the powder diffraction method for structure determination. The emphasis is placed on powder diffraction data collected using conventional x-ray sources, which remain primary tools for thousands of researchers and students in their daily experimental work.

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Book details

Edition: 2nd
Copyright year: 2009
Publisher: Springer
Publication date: 11/26/2008
Binding: Paperback
Pages: 744
Size: 6.00" wide x 9.25" long x 1.50" tall
Weight: 2.332
Language: English

Fundamentals of Crystalline State and Crystal Lattice
Crystalline State
Crystal Lattice and Unit Cell
Shape of the Unit Cell
Crystallographic Planes, Directions, and Indices
Crystallographic Planes
Crystallographic Directions
Reciprocal Lattice
Additional Reading
Problems
Finite Symmetry Elements and Crystallographic Point Groups
Content of the Unit Cell
Asymmetric Part of the Unit Cell
Symmetry Operations and Symmetry Elements
Finite Symmetry Elements
Onefold Rotation Axis and Center of Inversion
Twofold Rotation Axis and Mirror Plane
Threefold Rotation Axis and Threefold Inversion Axis
Fourfold Rotation Axis and Fourfold Inversion Axis
Sixfold Rotation Axis and Sixfold Inversion Axis
Interaction of Symmetry Elements
Generalization of Interactions Between Finite Symmetry Elements
Symmetry Groups
Fundamentals of Group Theory
Crystal Systems
Stereographic Projection
Crystallographic Point Groups
Laue Classes
Selection of a Unit Cell and Bravais Lattices
Additional Reading
Problems
Infinite Symmetry Elements and Crystallographic Space Groups
Glide Planes
Screw Axes
Interaction of Infinite Symmetry Elements
Crystallographic Space Groups
Relationships Between Point Groups and Space Groups
Full International Symbols of Crystallographic Space Groups
Visualization of Space-Group Symmetry in Three Dimensions
Space Groups in Nature
International Tables for Crystallography
Equivalent Positions (Sites)
General and Special Equivalent Positions
Special Sites with Points Located on Mirror Planes
Special Sites with Points Located on Rotation and Inversions Axes
Special Sites with Points Located on Centers of Inversion
Additional Reading
Problems
Formalization of Symmetry
Symbolic Representation of Symmetry
Finite Symmetry Operations
Infinite Symmetry Operations
Algebraic Treatment of Symmetry Operations
Transformation of Coordinates of a Point
Rotational Transformations of Vectors
Translational Transformations of Vectors
Combined Symmetrical Transformations of Vectors
Augmentation of Matrices
Algebraic Representation of Crystallographic Symmetry
Interaction of Symmetry Operations
Additional Reading
Problems
Nonconventional Symmetry
Commensurate Modulation
Incommensurate Modulation
Composite Crystals
Symmetry of Modulated Structures
Quasicrystals
Additional Reading
Problems
Properties, Sources, and Detection of Radiation
Nature of X-Rays
Production of X-Rays
Conventional Sealed X-Ray Sources
Continuous and Characteristic X-Ray Spectra
Rotating Anode X-Ray Sources
Synchrotron Radiation Sources
Other Types of Radiation
Detection of X-Rays
Detector Efficiency, Linearity, Proportionality and Resolution
Classification of Detectors
Point Detectors
Line and Area Detectors
Additional Reading
Problems
Fundamentals of Diffraction
Scattering by Electrons, Atoms and Lattices
Scattering by Electrons
Scattering by Atoms and Atomic Scattering Factor
Scattering by Lattices
Geometry of Diffraction by Lattices
Laue Equations
Braggs' Law
Reciprocal Lattice and Ewald's Sphere
Additional Reading
Problems
The Powder Diffraction Pattern
Origin of the Powder Diffraction Pattern
Representation of Powder Diffraction Patterns
Understanding of Powder Diffraction Patterns
Positions of Powder Diffraction Peaks
Peak Positions as a Function of Unit Cell Dimensions
Other Factors Affecting Peak Positions
Shapes of Powder Diffraction Peaks
Peak-Shape Functions
Peak Asymmetry
Intensity of Powder Diffraction Peaks
Integrated Intensity
Scale Factor
Multiplicity Factor
Lorentz-Polarization Factor
Absorption Factor
Preferred Orientation
Extinction Factor
Additional Reading
Problems
Structure Factor
Structure Amplitude
Population Factor
Temperature Factor (Atomic Displacement Factor)
Atomic Scattering Factor
Phase Angle
Effects of Symmetry on the Structure Amplitude
Friedel Pairs and Friedel's Law
Friedel's Law and Multiplicity Factor
Systematic Absences
Lattice Centering
Glide Planes
Screw Axes
Space Groups and Systematic Absences
Additional Reading
Problems
Solving the Crystal Structure
Fourier Transformation
Phase Problem
Patterson Technique
Direct Methods
Structure Solution from Powder Diffraction Data
Total Scattering Analysis Using Pair Distribution Function
Additional Reading
Problems
Powder Diffractometry
Brief History of the Powder Diffraction Method
Beam Conditioning in Powder Diffractometry
Collimation
Monochromatization
Principles of Goniometer Design in Powder Diffractometry
Goniostats with Strip and Point Detectors
Goniostats with Area Detectors
Nonambient Powder Diffractometry
Variable Temperature Powder Diffractometry
Principles of Variable Pressure Powder Diffractometry
Powder Diffractometry in High Magnetic Fields
Additional Reading
Problems
Collecting Quality Powder Diffraction Data
Sample Preparation
Powder Requirements and Powder Preparation
Powder Mounting
Sample Size
Sample Thickness and Uniformity
Sample Positioning
Effects of Sample Preparation on Powder Diffraction Data
Data Acquisition
Wavelength
Monochromatization
Incident Beam Aperture
Diffracted Beam Aperture
Variable Aperture
Power Settings
Classification of Powder Diffraction Experiments
Step Scan
Continuous Scan
Scan Range
Quality of Experimental Data
Quality of Intensity Measurements
Factors Affecting Resolution
Additional Reading
Problems
Preliminary Data Processing and Phase Analysis
Interpretation of Powder Diffraction Data
Preliminary Data Processing
Background
Smoothing
K�<sub>2</sub> Stripping
Peak Search
Profile Fitting
Phase Identification and Quantitative Analysis
Crystallographic Databases
Phase Identification
Quantitative Analysis
Phase Contents from Rietveld Refinement
Determination of Amorphous Content or Degree of Crystallinity
Additional Reading
Problems
Determination and Refinement of the Unit Cell
The Indexing Problem
Known Versus Unknown Unit Cell Dimensions
Indexing: Known Unit Cell
High Symmetry Indexing Example
Other Crystal Systems
Reliability of Indexing
The F<sub>N</sub> Figure of Merit
The M<sub>20</sub> (M<sub>N</sub>) Figure of Merit
Introduction to Ab Initio Indexing
Cubic Crystal System
Primitive Cubic Unit Cell: LaB<sub>6</sub>
Body-Centered Cubic Unit Cell: U<sub>3</sub>Ni<sub>6</sub>Si<sub>2</sub>
Tetragonal and Hexagonal Crystal Systems
Indexing Example: LaNi<sub>4.85</sub>Sn<sub>0.15</sub>
Automatic Ab Initio Indexing Algorithms
Indexing in Direct Space
Indexing in Reciprocal Space
Unit Cell Reduction Algorithms
Delaunay-Ito Transformation
Niggli Reduction
Automatic Ab Initio Indexing: Computer Codes
TREOR
DICVOL
ITO
Selecting a Solution
Ab Initio Indexing Examples
Hexagonal Indexing: LaNi<sub>4.85</sub>Sn<sub>0.15</sub>
Monoclinic Indexing: (CH<sub>3</sub>NH<sub>3</sub>)<sub>2</sub>Mo<sub>7</sub>O<sub>22</sub>
Triclinic Indexing: Fe<sub>7</sub>(PO<sub>4</sub>)<sub>6</sub>
Pseudo-Hexagonal Indexing: LiB(C<sub>2</sub>O<sub>4</sub>)<sub>2</sub>
Precise Lattice Parameters and Linear Least Squares
Linear Least Squares
Precise Lattice Parameters from Linear Least Squares
Concluding Remarks
Additional Reading
Problems
Solving Crystal Structure from Powder Diffraction Data
Ab Initio Methods of Structure Solution
Conventional Reciprocal Space Methods
Conventional Direct Space Modeling
Unconventional Direct, Reciprocal, and Dual Space Methods
Validation and Completion of the Model
The Content of the Unit Cell
Pearson's Classification
Finding Structure Factors from Powder Diffraction Data
Nonlinear Least Squares
Quality of Profile Fitting
Visual Assessment of the Quality of Profile Fitting
Figures of Merit
The Rietveld Method
Fundamentals of the Rietveld Method
Classes of Rietveld Refinement Parameters
Restraints, Constraints, and Rigid-Bodies
Figures of Merit and Quality of Rietveld Refinement
Common Problems and How to Deal with Them
Termination of Rietveld Refinement
Concluding Remarks
Additional Reading
Crystal Structure of LaNi<sub>485</sub>Sn<sub>015</sub>
Full Pattern Decomposition
Solving the Crystal Structure
Rietveld Refinement Using Cu K�<sub>1,2</sub> Radiation
Scale Factor and Profile Parameters
Overall Atomic Displacement Parameter
Individual Parameters, Free and Constrained Variables
Anisotropic Atomic Displacement Parameters
Multiple Phase Refinement
Refinement Results
Rietveld Refinement Using Mo K�<sub>1,2</sub> Radiation
Combined Refinement Using Different Sets of Diffraction Data
Crystal Structure of CeRhGe<sub>3</sub>
Full Pattern Decomposition
Solving the Crystal Structure from X-Ray Data
Highest Symmetry Attempt
Low-Symmetry Model
Solving the Crystal Structure from Neutron Data
Rietveld Refinement
X-Ray Data, Correct Low Symmetry Model
X-Ray Data, Wrong High-Symmetry Model
Neutron Data
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
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