Book description
This book introduces and details the key facets of Combined Analysis - an x-ray and/or neutron scattering methodology which combines structural, textural, stress, microstructural, phase, layer, or other relevant variable or property analyses in a single approach. The text starts with basic theories related to diffraction by polycrystals and some of the most common combined analysis instrumental set-ups are detailed. Also discussed are microstructures of powder diffraction profiles; quantitative phase analysis from the Rietveld analysis; residual stress analysis for isotropic and anisotropic materials; specular x-ray reflectivity, and the various associated models.
Table of contents
- Cover
- Title Page
- Copyright
- Introduction
- Acknowledgements
-
Chapter 1: Some Basic Notions About Powder Diffraction
- 1.1. Crystallite, grain, polycrystal and powder
- 1.2. Bragg's law and harmonic reflections
- 1.3. Geometric conditions of diffraction, Ewald sphere
- 1.4. Imperfect powders
- 1.5. Main diffraction line profile components
- 1.6. Peak profile parameters
-
1.7. Modeling of the diffraction peaks
- 1.7.1. Why do we need modeling?
-
1.7.2. Modeling of a powder diffraction pattern
- 1.7.2.1. Decomposition of the diagram (individual adjustment of the peaks)
- 1.7.2.2. Profile refinement with cell constraint (whole pattern fitting)
-
1.7.2.3. Peak-shape functions for constant wavelength instruments
- 1.7.2.3.1. Gaussian
- 1.7.2.3.2. Lorentzian and modified Lorentzian (Pearson VII)
- 1.7.2.3.3. Voigt
- 1.7.2.3.4. Pseudo-Voigt
- 1.7.2.3.5. Split Pearson VII [TOR 86]
- 1.7.2.3.6. Variable pseudo-Voigt
- 1.7.2.3.7. Parameterized pseudo-Voigt [THO 87]
- 1.7.2.3.8. Anisotropic variable pseudo-Voigt [LEB 97]
- 1.7.2.3.9. Anisotropic variable Pearson VII [LEB 97]
- 1.7.2.3.10. Anisotropic parameterised pseudo-Voigt [STE 99]
- 1.7.2.4. Peak-shape functions for TOF neutrons
- 1.8. Experimental geometry
- 1.9. Intensity calibration (flat-field)
- 1.10. Standard samples
- 1.11. Probed thickness (penetration depth)
-
Chapter 2: Structure Refinement by Diffraction Profile Adjustment (Rietveld Method)
- 2.1. Principle of the Rietveld method
- 2.2. Rietveld-based codes
-
2.3. Parameter modeling
- 2.3.1. Background modeling
- 2.3.2. Structure factor
- 2.3.3. Crystallites’ preferred orientation (texture) corrections
- 2.3.4. Peak asymmetry
-
2.3.5. Peak displacements
- 2.3.5.1. Zero-shift
- 2.3.5.2. Debye-Scherrer geometry
- 2.3.5.3. Flat plate, θ-2θ Bragg-Brentano symmetric geometry
- 2.3.5.4. Flat plate at fixed sample angle ω, asymmetric geometry
- 2.3.5.5. Flat plate transmission geometry
- 2.3.5.6. Sample excentricity (Bragg-Brentano geometry)
- 2.3.5.7. Sample transparency
- 2.3.5.8. Sample planarity (Bragg-Brentano geometry)
- 2.3.6. Lorentz-polarization correction
- 2.3.7. Volume, absorption, thickness corrections
- 2.3.8. Localization corrections
- 2.3.9. Microabsorption/roughness corrections
- 2.3.10. Wavelength
- 2.4. Crystal structure databases
- 2.5. Reliability factors in profile refinements
- 2.6. Parameter exactness
- 2.7. The Le Bail method
- 2.8. Refinement procedures
- 2.9. Refinement strategy
- 2.10. Structural determination by diffraction
- Chapter 3: Automatic Indexing of Powder Diagrams
-
Chapter 4: Quantitative Texture Analysis
-
4.1. Classic texture analysis
- 4.1.1. Qualitative aspects of texture analysis
- 4.1.2. Effects on diffraction diagrams
- 4.1.3. Limitations of classic diagrams
- 4.1.4. The Lotgering factor
- 4.1.5. Representations of textures: pole figures
- 4.1.6. Localization of crystallographic directions from pole figures
- 4.1.7. Texture types
- 4.2. Orientation distribution (OD) or orientation distribution function (ODF)
- 4.3. Distribution density and normalization
- 4.4. Direct and normalized pole figures
- 4.5. Reduced pole figures
- 4.6. Fundamental equation of quantitative texture analysis
-
4.7. Resolution of the fundamental equation
- 4.7.1. ODF and OD
- 4.7.2. Generalized spherical harmonics
- 4.7.3. Vector method [RUE 76, RUE 77, VAD 81]
- 4.7.4. Williams-Imhof-Matthies-Vinel (WIMV) method [WIL 68, IMH 82, MAT 82]
- 4.7.5. Arbitrarily-defined cells (ABC) method [PAW 93]
- 4.7.6. Entropy maximization method [SCH 88, SCH 91a, SCH 91b]
- 4.7.7. Component method [HEL 98]
- 4.7.8. Exponential harmonics [VAN 91]
- 4.7.9. Radon transform and Fourier analysis
- 4.7.10. Orientation space coverage
- 4.8. OD refinement reliability estimators
- 4.9. Inverse pole figures
- 4.10. Texture strength factors
-
4.11. Texture programs
- 4.11.1. Berkeley texture package (BEARTEX)
- 4.11.2. Material analysis using diffraction (MAUD)
- 4.11.3. General structure analysis system (GSAS)
- 4.11.4. Preferred orientation package, Los Alamos (popLA)
- 4.11.5. Texture analysis software (LaboTex)
- 4.11.6. Pole figure interpretation (POFINT)
- 4.11.7. Strong textures (STROTEX and Phiscans)
- 4.11.8. STEREOPOLE
- 4.11.9. MTEX
- 4.12. Limits of the classic texture analysis
-
4.13. Magnetic quantitative texture analysis (MQTA)
- 4.13.1. Magnetization curves and magnetic moment distributions
- 4.13.2. A simple sample holder for MQTA
-
4.13.3. Methodology
- 4.13.3.1. Measured pole figures
- 4.13.3.2. Normalization conditions
- 4.13.3.3. Nuclear part determination
- 4.13.3.4. Normalization conditions of the ODFs
- 4.13.3.5. Absence of external magnetic field
- 4.13.3.6. Application of an external magnetic field
- 4.13.3.7. Magnetic part determination
- 4.13.3.8. Fundamental equations of MQTA
- 4.13.4. From magnetic-scattering to the MODF and magnetic moment distributions
- 4.13.5. One example
- 4.14. Reciprocal space mapping (RSM)
-
4.1. Classic texture analysis
-
Chapter 5: Quantitative Microstructure Analysis
- 5.1. Introduction
- 5.2. Microstructure modeling (classic)
- 5.3. Bertaut-Warren-Averbach approach (Fourier analysis)
- 5.4. Anisotropic broadening: the Popa approach [POP 98]
- 5.5. Stacking and twin faults
- 5.6. Dislocations
- 5.7. Crystallite size distributions
- 5.8. Rietveld approach
- Chapter 6: Quantitative Phase Analysis
- Chapter 7: Residual Strain-Stress Analysis
-
Chapter 8: X-Ray Reflectivity
- 8.1. Introduction
- 8.2. X-rays and neutrons refractive index
- 8.3. The critical angle of reflection
- 8.4. Fresnel formalism (specular reflectivity)
- 8.5. Surface roughness
- 8.6. Matrix formalism (specular reflectivity)
- 8.7. Born approximation
- 8.8. Electron density profile
- 8.9. Multilayer reflectivity curves
- 8.10. Instrumental corrections
-
Chapter 9: Combined Structure-Texture-Microstructure-Stress-Phase Reflectivity Analysis
- 9.1. Initial queries
- 9.2. Implementation
- 9.3. Experimental set-up
- 9.4. Instrument calibration
- 9.5. Refinement strategy
-
9.6. Examples
- 9.6.1. QTA of single-phased materials
- 9.6.2. QTA and isotropic QMA
- 9.6.3. Anisotropic crystallite shape, texture, cell parameters, and thickness
- 9.6.4. Layering, isotropic shape, microstrains, texture, and structure
- 9.6.5. Phase and texture
- 9.6.6. Texture of modulated structures
- 9.6.7. Texture, residual stresses and layering
- 9.6.8. Texture and structure
-
Chapter 10: Macroscopic Anisotropic Properties
- 10.1. Aniso- and isotropic samples and properties
-
10.2. Macroscopic/microscopic properties
- 10.2.1. TM and T tensors
-
10.2.2. Microscopic properties
- 10.2.2.1. Classifications of properties
- 10.2.2.2. Extensive and intensive variables
- 10.2.2.3. Work element of conjugated variables
- 10.2.2.4. Generalized thermodynamics
- 10.2.2.5. Thermal properties
- 10.2.2.6. Electric and optical properties
- 10.2.2.7. Magnetic properties
- 10.2.2.8. Mechanical properties
- 10.2.2.9. ThermoElectric (TE) properties
- 10.2.2.10. ThermoMechanic (TMe) properties
- 10.2.2.11. ElectroMechanic (EMe) properties
- 10.2.2.12. MagnetoMechanic (MMe) properties
- 10.2.2.13. MagnetoElectric (ME) properties
- 10.2.2.14. MagnetoOptic (MO) effects and magnetic birefringence
- 10.2.2.15. Mechano-Optic (MeO) properties
- 10.2.2.16. Atomic diffusion
- 10.2.2.17. PiezoMagnetoElectric (PME) properties
- 10.2.2.18. Multiferroics
-
10.2.3. Macroscopic properties anisotropy and modeling
- 10.2.3.1. Averaging of tensors
- 10.2.3.2. Heat capacity
- 10.2.3.3. Thermal expansion
- 10.2.3.4. Electric polarization
- 10.2.3.5. Mechanical properties
- 10.2.3.6. Bulk acoustic waves from OD and Ciℓmn
- 10.2.3.7. Thermoelectric properties
- 10.2.3.8. Magnetization in oriented easy-plane ErMn4Fe8C
- 10.2.3.9. Dielectric constant
- Bibliography
- Glossary
- Abbreviations
- Mathematical Operators
- Index
Product information
- Title: Combined Analysis
- Author(s):
- Release date: July 2010
- Publisher(s): Wiley
- ISBN: 9781848211988
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