Fundamentals of powder diffraction and structural characterization of materials /

Fundamentals of powder diffraction and structural characterization of materials /

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Bibliographic Details
Author / Creator:Pecharsky, Vitalij K.
Imprint:New York : Springer, [2005]
Description:1 online resource (xxiii, 713 p.) : ill.
Language:English
Subject:
X-rays -- Diffraction -- Measurement.
Powders -- Optical properties -- Measurement.
X-ray crystallography.
Powders -- Optical properties -- Measurement.
X-ray crystallography.
X-rays -- Diffraction -- Measurement.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/8874943
Hidden Bibliographic Details
Other authors / contributors:Zavalij, Peter Y.
ISBN:0387241477 (softcover)
9780387241470 (softcover)
0387245677 (e-book)
9780387245676 (e-book)
6611334602
9786611334604
Notes:Originally published: Boston : Kluwer Academic Publishers, c2003.
Includes bibliographical references and index.
Other form:Print version: Pecharsky, Vitalij K. Fundamentals of powder diffraction and structural characterization of materials. New York : Springer, [2005] 0387241477 9780387241470
Table of Contents:
  • Preface
  • 1.. Fundamentals of Crystalline State
  • 1.1. Introduction
  • 1.2. Crystalline state
  • 1.3. Crystal lattice and crystal structure
  • 1.3.1. Shape of the unit cell
  • 1.3.2. Content of the unit cell
  • 1.3.3. Asymmetric part of the unit cell
  • 1.4. Symmetry operations and symmetry elements
  • 1.5. Finite symmetry elements
  • 1.5.1. One-fold rotation axis and center of inversion
  • 1.5.2. Two-fold rotation axis and mirror plane
  • 1.5.3. Three-fold rotation axis and three-fold inversion axis
  • 1.5.4. Four-fold rotation axis and four-fold inversion axis
  • 1.5.5. Six-fold rotation axis and six-fold inversion axis
  • 1.6. Interaction of symmetry elements
  • 1.6.1. Symmetry groups
  • 1.6.2. Generalization of interactions between finite symmetry elements
  • 1.7. Fundamentals of group theory
  • 1.8. Crystal systems
  • 1.9. Stereographic projections
  • 1.10. Crystallographic point groups
  • 1.11. Laue classes
  • 1.12. Selection of a unit cell and Bravais lattices
  • 1.13. Infinite symmetry elements
  • 1.13.1. Glide planes
  • 1.13.2. Screw axes
  • 1.13.3. Interaction of infinite symmetry elements
  • 1.14. Crystallographic planes, directions and indices
  • 1.14.1. Indices of planes
  • 1.14.2. Lattice directions and indices
  • 1.15. Reciprocal lattice
  • 1.16. Crystallographic space groups
  • 1.16.1. Relationships between space and point groups
  • 1.16.2. Full international symbols of crystallographic space groups
  • 1.16.3. Visualization of space group symmetry in three dimensions
  • 1.16.4. Space groups in nature
  • 1.17. International Tables for Crystallography
  • 1.18. Equivalent positions
  • 1.18.1. General and special equivalent positions
  • 1.18.2. Special sites with points located on mirror planes
  • 1.18.3. Special sites with points located on rotation or inversion axes
  • 1.18.4. Special sites with points located on centers of inversion
  • 1.19. Symbolic description of symmetry operations
  • 1.19.1. Finite symmetry operations
  • 1.19.2. Infinite symmetry operations
  • 1.20. Algebraic treatment of symmetry operations
  • 1.20.1. Transformations of coordinates of a point
  • 1.20.2. Rotational transformations of vectors
  • 1.20.3. Translational transformations of vectors
  • 1.20.4. Combined symmetrical transformations of vectors
  • 1.20.5. Augmented matrices
  • 1.20.6. Algebraic representation of crystallographic symmetry
  • 1.20.7. Interactions between symmetry operations
  • 1.21. Non-conventional symmetry
  • 1.21.1. Commensurate modulation
  • 1.21.2. Incommensurate modulation
  • 1.21.3. Quasicrystals
  • 1.22. Additional reading
  • 1.23. Problems
  • 2.. Fundamentals of Diffraction
  • 2.1. Introduction
  • 2.2. Properties and sources of radiation
  • 2.2.1. Nature and properties of x-rays
  • 2.2.2. Production of x-rays
  • 2.2.3. Conventional sealed x-ray sources
  • 2.2.4. Continuous and characteristic x-ray spectra
  • 2.2.5. Rotating anode x-ray sources
  • 2.2.6. Synchrotron radiation sources
  • 2.2.7. Other types of radiation
  • 2.3. Collimation and monochromatization
  • 2.3.1. Angular divergence and collimation
  • 2.3.2. Monochromatization
  • 2.4. Detection of x-rays
  • 2.4.1. Detector efficiency, linearity, proportionality and resolution
  • 2.4.2. Classification of detectors
  • 2.4.3. Point detectors
  • 2.4.4. Line and area detectors
  • 2.5. Scattering by electrons, atoms and lattices
  • 2.5.1. Scattering by electrons
  • 2.5.2. Scattering by atoms and scattering factor
  • 2.5.3. Scattering by lattices
  • 2.6. Geometry of diffraction by lattices
  • 2.6.1. Laue equations and Braggs' law
  • 2.6.2. Reciprocal lattice and Ewald's sphere
  • 2.7. Origin of the powder diffraction pattern
  • 2.7.1. Representation of powder diffraction patterns
  • 2.7.2. Understanding of powder diffraction patterns
  • 2.8. Positions of powder diffraction peaks
  • 2.8.1. Peak positions as a function of unit cell dimensions
  • 2.8.2. Other factors affecting peak positions
  • 2.9. Shapes of powder diffraction peaks
  • 2.9.1. Peak shape functions
  • 2.9.2. Peak asymmetry
  • 2.10. Intensity of powder diffraction peaks
  • 2.10.1. Integrated intensity
  • 2.10.2. Scale factor
  • 2.10.3. Multiplicity factor
  • 2.10.4. Lorentz-polarization factor
  • 2.10.5. Absorption factor
  • 2.10.6. Preferred orientation
  • 2.10.7. Extinction factor
  • 2.11. Structure factor
  • 2.11.1. Structure amplitude
  • 2.11.2. Population factor
  • 2.11.3. Temperature factor
  • 2.11.4. Atomic scattering factor
  • 2.11.5. Phase angle
  • 2.12. Effects of symmetry on the structure amplitude
  • 2.12.1. Friedel pairs and Friedel's law
  • 2.12.2. Friedel's law and multiplicity factor
  • 2.12.3. Systematic absences
  • 2.12.4. Space groups and systematic absences
  • 2.13. Fourier transformation
  • 2.14. Phase problem
  • 2.14.1. Patterson technique
  • 2.14.2. Direct methods
  • 2.14.3. Structure solution from powder diffraction data
  • 2.15. Additional reading
  • 2.16. Problems
  • 3.. Experimental Techniques
  • 3.1. Introduction
  • 3.2. Brief history of the powder diffraction method
  • 3.3. Powder diffractometers
  • 3.3.1. Principles of goniometer design in powder diffractometry
  • 3.3.2. Goniostats with point detectors
  • 3.3.3. Goniostats with area detectors
  • 3.4. Safety
  • 3.4.1. Radiation quantities and terms
  • 3.4.2. Biological effects of ionizing radiation
  • 3.4.3. Exposure limits
  • 3.4.4. Radiation hazards of analytical x-ray systems
  • 3.4.5. Hazard control measures for analytical x-ray systems
  • 3.5. Sample preparation
  • 3.5.1. Powder requirements and powder preparation
  • 3.5.2. Powder mounting
  • 3.5.3. Sample size
  • 3.5.4. Sample thickness and uniformity
  • 3.5.5. Positioning the sample with respect to the goniometer axis
  • 3.5.6. Effects of sample preparation on powder diffraction data
  • 3.6. Data acquisition
  • 3.6.1. Wavelength selection
  • 3.6.2. Monochromatization
  • 3.6.3. Incident beam aperture
  • 3.6.4. Diffracted beam aperture
  • 3.6.5. Variable aperture
  • 3.6.6. Power settings
  • 3.6.7. Classification of powder diffraction experiments
  • 3.6.8. Step scan
  • 3.6.9. Continuous scan
  • 3.6.10. Scan range
  • 3.7. Quality of experimental data
  • 3.7.1. Quality of intensity measurements
  • 3.7.2. Factors affecting resolution
  • 3.8. Additional reading
  • 3.9. Problems
  • 4.. Preliminary Data Processing and Phase Analysis
  • 4.1. Introduction
  • 4.2. Interpretation of powder diffraction data
  • 4.3. Preliminary data processing
  • 4.3.1. Background
  • 4.3.2. Smoothing
  • 4.3.3. K[alpha subscript 2] stripping
  • 4.3.4. Peak search
  • 4.3.5. Profile fitting
  • 4.4. Phase identification and analysis
  • 4.4.1. Crystallographic databases
  • 4.4.2. Phase identification and qualitative analysis
  • 4.4.3. Quantitative analysis
  • 4.5. Additional reading
  • 4.6. Problems
  • 5.. Unit Cell Determination and Refinement
  • 5.1. Introduction
  • 5.2. The indexing problem
  • 5.3. Known versus unknown unit cell dimensions
  • 5.4. Indexing: known unit cell
  • 5.4.1. High symmetry indexing example
  • 5.4.2. Other crystal systems
  • 5.5. Reliability of indexing
  • 5.5.1. The F[subscript N] figure of merit
  • 5.5.2. The M[subscript 20] figure of merit
  • 5.6. Introduction to ab initio indexing
  • 5.7. Cubic crystal system
  • 5.7.1. Primitive cubic unit cell: LaB[subscript 6]
  • 5.7.2. Body-centered cubic unit cell: U[subscript 3]Ni[subscript 6]Si[subscript 2]
  • 5.8. Tetragonal and hexagonal crystal systems
  • 5.8.1. Indexing example: LaNi[subscript 4.85]Sn[subscript 0.15]
  • 5.9. Automatic ab initio indexing algorithms
  • 5.9.1. Trial-and-error method
  • 5.9.2. Zone search method
  • 5.10. Unit cell reduction algorithms
  • 5.10.1. Delaunay-Ito reduction
  • 5.10.2. Niggli reduction
  • 5.11. Automatic ab initio indexing: computer codes
  • 5.11.1. TREOR
  • 5.11.2. DICVOL
  • 5.11.3. ITO
  • 5.11.4. Selecting a solution
  • 5.12. Ab initio indexing examples
  • 5.12.1. Hexagonal indexing: LaNi[subscript 4.85]Sn[subscript 0.15]
  • 5.12.2. Monoclinic indexing: (CH[subscript 3]NH[subscript 3])[subscript 2]Mo[subscript 7]O[subscript 22]
  • 5.12.3. Triclinic indexing: Fe[subscript 7](PO[subscript 4])[subscript 6]
  • 5.13. Precise lattice parameters and linear least squares
  • 5.13.1. Linear least squares
  • 5.13.2. Precise lattice parameters from linear least squares
  • 5.14. Epilogue
  • 5.15. Additional reading
  • 5.16. Problems
  • 6.. Crystal Structure Determination
  • 6.1. Introduction
  • 6.2. Ab initio methods of structure solution
  • 6.2.1. Conventional reciprocal space techniques
  • 6.2.2. Conventional direct space techniques
  • 6.2.3. Unconventional reciprocal and direct space strategies
  • 6.2.4. Validation and completion of the model
  • 6.3. The content of the unit cell
  • 6.4. Pearson's classification
  • 6.5. Structure factors from powder diffraction data
  • 6.6. Non-linear least squares
  • 6.7. Figures of merit in full pattern decomposition
  • 6.8. Structure solution from powder data
  • 6.9. Crystal structure of LaNi[subscript 4.85]Sn[subscript 0.15]
  • 6.10. Crystal structure of CeRhGe[subscript 3] from x-ray data
  • 6.11. Crystal structure of CeRhGe[subscript 3] from neutron data
  • 6.12. Crystal structure of Nd[subscript 5]Si[subscript 4]
  • 6.13. Crystal structure of NiMnO[subscript 2](OH)
  • 6.14. Crystal structure of tmaV[subscript 3]O[subscript 7]
  • 6.15. Crystal structure of ma[subscript 2]Mo[subscript 7]O[subscript 22]
  • 6.16. Crystal structure of Mn[subscript 7](OH)[subscript 3](VO[subscript 4])[subscript 4]
  • 6.17. Crystal structure of FePO[subscript 4]
  • 6.18. Empirical methods of solving crystal structures
  • 6.18.1. Crystal structure of Gd[subscript 5]Ge[subscript 4]
  • 6.18.2. Crystal structure of Gd[subscript 5]Si[subscript 4]
  • 6.18.3. Crystal structure of Gd[subscript 5]Si[subscript 2]Ge[subscript 2]
  • 6.19. Additional reading
  • 6.20. Problems
  • 7.. Crystal Structure Refinement
  • 7.1. Introduction
  • 7.2. The Rietveld method
  • 7.2.1. Rietveld method basics
  • 7.2.2. Classes of Rietveld parameters
  • 7.2.3. Figures of merit and quality of refinement
  • 7.2.4. Termination of Rietveld refinement
  • 7.3. Rietveld refinement of LaNi[subscript 4.85]Sn[subscript 0.15]
  • 7.3.1. Scale factor and profile parameters
  • 7.3.2. Overall atomic displacement parameter
  • 7.3.3. Individual parameters, free and constrained variables
  • 7.3.4. Anisotropic atomic displacement parameters
  • 7.3.5. Multiple phase refinement
  • 7.3.6. Refinement results
  • 7.3.7. Different radiation
  • 7.3.8. Combined refinement using different diffraction data
  • 7.4. Rietveld refinement of CeRhGe[subscript 3]
  • 7.4.1. Refinement using x-ray diffraction data
  • 7.4.2. Refinement using neutron diffraction data
  • 7.5. Rietveld refinement of Nd[subscript 5]Si[subscript 4]
  • 7.6. Rietveld refinement using GSAS
  • 7.7. Completion of the model and Rietveld refinement of NiMnO[subscript 2](OH)
  • 7.8. Completion of the model and Rietveld refinement of tmaV[subscript 3]O[subscript 7]
  • 7.9. Rietveld refinement and completion of the ma[subscript 2]Mo[subscript 7]O[subscript 22] structure
  • 7.10. Rietveld refinement of Mn[subscript 7](OH)[subscript 3](VO[subscript 4])[subscript 4]
  • 7.11. Rietveld refinement of the monoclinic FePO[subscript 4]
  • 7.12. Rietveld refinement of Gd[subscript 5]Ge[subscript 4], Gd[subscript 5]Si[subscript 4] and Gd[subscript 5]Si[subscript 2]Ge[subscript 2]
  • 7.12.1. Gd[subscript 5]Ge[subscript 4]
  • 7.12.2. Gd[subscript 5]Si[subscript 4]
  • 7.12.3. Gd[subscript 5]Si[subscript 2]Ge[subscript 2]
  • 7.13. Epilogue
  • 7.14. Additional reading
  • 7.15. Problems
  • Index

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