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Combined Analysis

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

  1. Cover
  2. Title Page
  3. Copyright
  4. Introduction
  5. Acknowledgements
  6. Chapter 1: Some Basic Notions About Powder Diffraction
    1. 1.1. Crystallite, grain, polycrystal and powder
    2. 1.2. Bragg's law and harmonic reflections
      1. 1.2.1. Bragg's law
      2. 1.2.2. Monochromator
      3. 1.2.3. Harmonic radiation components
    3. 1.3. Geometric conditions of diffraction, Ewald sphere
    4. 1.4. Imperfect powders
    5. 1.5. Main diffraction line profile components
      1. 1.5.1. Origin of g(x)
        1. 1.5.1.1. Laboratory x-rays
        2. 1.5.1.2. Synchrotron x-rays
        3. 1.5.1.3. Constant wavelength neutrons
        4. 1.5.1.4. Time of flight neutrons
        5. 1.5.1.5. Constant-wavelength instrument resolution examples
      2. 1.5.2. Origin of f(x)
      3. 1.5.3. Deconvolution-extraction of f(x) and g(x)
    6. 1.6. Peak profile parameters
    7. 1.7. Modeling of the diffraction peaks
      1. 1.7.1. Why do we need modeling?
      2. 1.7.2. Modeling of a powder diffraction pattern
        1. 1.7.2.1. Decomposition of the diagram (individual adjustment of the peaks)
        2. 1.7.2.2. Profile refinement with cell constraint (whole pattern fitting)
        3. 1.7.2.3. Peak-shape functions for constant wavelength instruments
          1. 1.7.2.3.1. Gaussian
          2. 1.7.2.3.2. Lorentzian and modified Lorentzian (Pearson VII)
          3. 1.7.2.3.3. Voigt
          4. 1.7.2.3.4. Pseudo-Voigt
          5. 1.7.2.3.5. Split Pearson VII [TOR 86]
          6. 1.7.2.3.6. Variable pseudo-Voigt
          7. 1.7.2.3.7. Parameterized pseudo-Voigt [THO 87]
          8. 1.7.2.3.8. Anisotropic variable pseudo-Voigt [LEB 97]
          9. 1.7.2.3.9. Anisotropic variable Pearson VII [LEB 97]
          10. 1.7.2.3.10. Anisotropic parameterised pseudo-Voigt [STE 99]
        4. 1.7.2.4. Peak-shape functions for TOF neutrons
          1. 1.7.2.4.1. Convolution of Gaussian and rising and falling exponentials
          2. 1.7.2.4.2. Convolution of pseudo-Voigt and back-to-back exponentials
          3. 1.7.2.4.3. Moderator pulse shape function
          4. 1.7.2.4.4. Convolution of PV with the Ikeda-Carpenter pulse function
    8. 1.8. Experimental geometry
      1. 1.8.1. Curved Position Sensitive detector, asymmetric reflection geometry
      2. 1.8.2. CCD or image plate detector, transmission geometry
      3. 1.8.3. Curved-Area Position-Sensitive detector, transmission geometry
    9. 1.9. Intensity calibration (flat-field)
      1. 1.9.1. Counts and intensity
        1. 1.9.1.1. Monitored incident intensity
        2. 1.9.1.2. Counting statistics
          1. 1.9.1.2.1. Poisson statistics
          2. 1.9.1.2.2. Zero-background peak and best precision
          3. 1.9.1.2.3. Detection limit
          4. 1.9.1.2.4. Presence of background under peaks
      2. 1.9.2. Flat-field
      3. 1.9.3. PSD detector
      4. 1.9.4. CAPS detector
    10. 1.10. Standard samples
      1. 1.10.1. Laboratory x-ray standards
      2. 1.10.2. Neutron texture standards
        1. 1.10.2.1. International round-robin calcite standard
        2. 1.10.2.2. Belemnite rostrum calcite standard
    11. 1.11. Probed thickness (penetration depth)
  7. Chapter 2: Structure Refinement by Diffraction Profile Adjustment (Rietveld Method)
    1. 2.1. Principle of the Rietveld method
    2. 2.2. Rietveld-based codes
    3. 2.3. Parameter modeling
      1. 2.3.1. Background modeling
        1. 2.3.1.1. Background components
        2. 2.3.1.2. Empirical approaches
          1. 2.3.1.2.1. mth order polynomial function
          2. 2.3.1.2.2. Fourier series
          3. 2.3.1.2.3. Interpolation
          4. 2.3.1.2.4. 2D detectors
        3. 2.3.1.3. Physical approaches
      2. 2.3.2. Structure factor
        1. 2.3.2.1. Structure factor expression
          1. 2.3.2.1.1. Usual three-dimensional definition
          2. 2.3.2.1.2. Higher-space representation
        2. 2.3.2.2. Scattering factors
          1. 2.3.2.2.1. X-ray scattering factors
          2. 2.3.2.2.2. Neutron scattering factors
          3. 2.3.2.2.3. Electron scattering factors
        3. 2.3.2.3. Site occupation factors
        4. 2.3.2.4. Atomic positions
        5. 2.3.2.5. Thermal vibrations and temperature factors
          1. 2.3.2.5.1. Isotropic
          2. 2.3.2.5.2. Anisotropic
          3. 2.3.2.5.3. Negative thermal displacement parameters
          4. 2.3.2.5.4. Debye temperature to temperature factors
      3. 2.3.3. Crystallites’ preferred orientation (texture) corrections
        1. 2.3.3.1. Original Rietveld and March approaches
        2. 2.3.3.2. March−Dollase approach
        3. 2.3.3.3. Modified March−Dollase approach
        4. 2.3.3.4. Donnet−Jouanneaux function
        5. 2.3.3.5. Arbitrary texture correction
        6. 2.3.3.6. Remarks
      4. 2.3.4. Peak asymmetry
        1. 2.3.4.1. Rietveld’s correction [RIE 69]
        2. 2.3.4.2. Howard’s correction [HOW 82]
        3. 2.3.4.3. Finger, Cox and Jephcoat’s correction [FIN 94]
        4. 2.3.4.4. Bérar-Baldinozzi correction [BER 93]
        5. 2.3.4.5. TOF neutrons
      5. 2.3.5. Peak displacements
        1. 2.3.5.1. Zero-shift
        2. 2.3.5.2. Debye-Scherrer geometry
        3. 2.3.5.3. Flat plate, θ-2θ Bragg-Brentano symmetric geometry
        4. 2.3.5.4. Flat plate at fixed sample angle ω, asymmetric geometry
        5. 2.3.5.5. Flat plate transmission geometry
        6. 2.3.5.6. Sample excentricity (Bragg-Brentano geometry)
        7. 2.3.5.7. Sample transparency
        8. 2.3.5.8. Sample planarity (Bragg-Brentano geometry)
      6. 2.3.6. Lorentz-polarization correction
        1. 2.3.6.1. Series of flat co-planar monochromators
        2. 2.3.6.2. Powder diffraction
          1. 2.3.6.2.1. Bragg-Brentano geometry
          2. 2.3.6.2.2. 2D detector and polarized beams
        3. 2.3.6.3. Time of flight neutrons
        4. 2.3.6.4. General remark
      7. 2.3.7. Volume, absorption, thickness corrections
        1. 2.3.7.1. Schulz geometry, point detector, thin layered structure
        2. 2.3.7.2. Schulz geometry, CPS detector, thin layered structure
        3. 2.3.7.3. Transmission geometry, 2D detectors, flat sample
      8. 2.3.8. Localization corrections
        1. 2.3.8.1. Schulz reflection geometry, CPS detector
        2. 2.3.8.2. Debye-Scherrer transmission geometry, 2D detectors
        3. 2.3.8.3. Debye-Scherrer transmission geometry, CAPS detectors
      9. 2.3.9. Microabsorption/roughness corrections
        1. 2.3.9.1. Sparks model, Bragg-Brentano
        2. 2.3.9.2. Suortti model, Bragg-Brentano
        3. 2.3.9.3. Pitschke model, Bragg-Brentano
        4. 2.3.9.4. Sidey model, Bragg-Brentano
      10. 2.3.10. Wavelength
    4. 2.4. Crystal structure databases
    5. 2.5. Reliability factors in profile refinements
    6. 2.6. Parameter exactness
    7. 2.7. The Le Bail method
    8. 2.8. Refinement procedures
      1. 2.8.1. Least squares
      2. 2.8.2. Genetic or evolutionary algorithms
      3. 2.8.3. Derivative difference minimization (DDM)
      4. 2.8.4. Simulatedannealing g
    9. 2.9. Refinement strategy
    10. 2.10. Structural determination by diffraction
      1. 2.10.1. The phase problem in diffraction
      2. 2.10.2. Patterson function
      3. 2.10.3. Direct methods
      4. 2.10.4. Direct space methods
      5. 2.10.5. Fourier difference map
      6. 2.10.6. Extension to aperiodic structures
        1. 2.10.6.1. Introduction
        2. 2.10.6.2. Superspace formalism principle
  8. Chapter 3: Automatic Indexing of Powder Diagrams
    1. 3.1. Principle
    2. 3.2. Dichotomy approach
    3. 3.3. Criterions for quality
  9. Chapter 4: Quantitative Texture Analysis
    1. 4.1. Classic texture analysis
      1. 4.1.1. Qualitative aspects of texture analysis
      2. 4.1.2. Effects on diffraction diagrams
        1. 4.1.2.1. θ-2θ diagrams
        2. 4.1.2.2. Asymmetric diagrams
        3. 4.1.2.3. ω-scans: rocking curves
      3. 4.1.3. Limitations of classic diagrams
        1. 4.1.3.1. θ-2θ diagrams
        2. 4.1.3.2. Asymmetric diagrams
        3. 4.1.3.3. Rocking curves
      4. 4.1.4. The Lotgering factor
      5. 4.1.5. Representations of textures: pole figures
        1. 4.1.5.1. Pole Sphere
        2. 4.1.5.2. Equal-angular projection: stereographic projection
        3. 4.1.5.3. Equal-area projection: Lambert projection
        4. 4.1.5.4. Pole figures
        5. 4.1.5.5. Coverage of pole figures and scanning strategies
          1. 4.1.5.5.1. Using point detectors
          2. 4.1.5.5.2. Using 1D detectors
          3. 4.1.5.5.3. Using 2D CAPS detectors
          4. 4.1.5.5.4. Pole figure coverage
      6. 4.1.6. Localization of crystallographic directions from pole figures
        1. 4.1.6.1. Normal diffraction and pole figures
        2. 4.1.6.2. Grains, crystallites and crystallographic planes
        3. 4.1.6.3. Single texture component
        4. 4.1.6.4. Multiple texture component
        5. 4.1.6.5. Pole figures and (hkℓ) multiplicity
        6. 4.1.6.6. A real example
      7. 4.1.7. Texture types
        1. 4.1.7.1. Curie groups (limit groups)
        2. 4.1.7.2. Random texture
        3. 4.1.7.3. Planar textures
        4. 4.1.7.4. Fiber textures
        5. 4.1.7.5. 3D textures
          1. 4.1.7.5.1. 3D texture
          2. 4.1.7.5.2. Single crystal texture
    2. 4.2. Orientation distribution (OD) or orientation distribution function (ODF)
      1. 4.2.1. Pole figures and orientation spaces
        1. 4.2.1.1. Pole figures and orientation of planes
        2. 4.2.1.2. Mathematical expression of diffraction pole figures
      2. 4.2.2. The orientation space
      3. 4.2.3. Euler angle conventions
      4. 4.2.4. Orientations and pole figures
      5. 4.2.5. Choice for the sample co-ordinate system KA
      6. 4.2.6. Pole figure, crystal, texture and sample symmetries
      7. 4.2.7. Orientation distance
    3. 4.3. Distribution density and normalization
    4. 4.4. Direct and normalized pole figures
      1. 4.4.1. Direct experimental pole figures
      2. 4.4.2. Normalized pole figures
        1. 4.4.2.1. Direct normalization
        2. 4.4.2.2. Normalization refinement
    5. 4.5. Reduced pole figures
    6. 4.6. Fundamental equation of quantitative texture analysis
      1. 4.6.1. Fundamental equation
      2. 4.6.2. Typical OD components
        1. 4.6.2.1. Random OD and random part: FON
        2. 4.6.2.2. Isolated components
        3. 4.6.2.3. Cyclic components
      3. 4.6.3. OD plotting
        1. 4.6.3.1. 2D plots
        2. 4.6.3.2. 3D plot
      4. 4.6.4. Finding an orientation component in the OD
    7. 4.7. Resolution of the fundamental equation
      1. 4.7.1. ODF and OD
      2. 4.7.2. Generalized spherical harmonics
        1. 4.7.2.1. Principle
        2. 4.7.2.2. Normal diffraction and positivity of f(g)
          1. 4.7.2.2.1. Complete, even and odd ODFs
          2. 4.7.2.2.2. Positivity method
          3. 4.7.2.2.3. "GHOST" and quadratic methods
        3. 4.7.2.3. Least-squares refinement
      3. 4.7.3. Vector method [RUE 76, RUE 77, VAD 81]
      4. 4.7.4. Williams-Imhof-Matthies-Vinel (WIMV) method [WIL 68, IMH 82, MAT 82]
        1. 4.7.4.1. Regular WIMV
        2. 4.7.4.2. Extended WIMV (E-WIMV)
      5. 4.7.5. Arbitrarily-defined cells (ABC) method [PAW 93]
      6. 4.7.6. Entropy maximization method [SCH 88, SCH 91a, SCH 91b]
      7. 4.7.7. Component method [HEL 98]
        1. 4.7.7.1. Description
        2. 4.7.7.2. Gaussian components [BUN 69, MAT 87]
        3. 4.7.7.3. Elliptical components [MAT 87]
      8. 4.7.8. Exponential harmonics [VAN 91]
      9. 4.7.9. Radon transform and Fourier analysis
      10. 4.7.10. Orientation space coverage
    8. 4.8. OD refinement reliability estimators
      1. 4.8.1. RP factors
      2. 4.8.2. RPw surface weighted factors
      3. 4.8.3. RB Bragg-like factors
      4. 4.8.4. RBw Bragg-like weighted factors
      5. 4.8.5. Rw weighted factors
      6. 4.8.6. Visual inspection
    9. 4.9. Inverse pole figures
      1. 4.9.1. Definition
      2. 4.9.2. Inverse pole figure sectors
    10. 4.10. Texture strength factors
      1. 4.10.1. Texture index
        1. 4.10.1.1. ODF texture index
        2. 4.10.1.2. Pole figure texture index
      2. 4.10.2. Texture entropy
      3. 4.10.3. Pole figure and ODF strengths
      4. 4.10.4. Correlation between F2 and S
    11. 4.11. Texture programs
      1. 4.11.1. Berkeley texture package (BEARTEX)
      2. 4.11.2. Material analysis using diffraction (MAUD)
      3. 4.11.3. General structure analysis system (GSAS)
      4. 4.11.4. Preferred orientation package, Los Alamos (popLA)
      5. 4.11.5. Texture analysis software (LaboTex)
      6. 4.11.6. Pole figure interpretation (POFINT)
      7. 4.11.7. Strong textures (STROTEX and Phiscans)
      8. 4.11.8. STEREOPOLE
      9. 4.11.9. MTEX
    12. 4.12. Limits of the classic texture analysis
    13. 4.13. Magnetic quantitative texture analysis (MQTA)
      1. 4.13.1. Magnetization curves and magnetic moment distributions
      2. 4.13.2. A simple sample holder for MQTA
      3. 4.13.3. Methodology
        1. 4.13.3.1. Measured pole figures
        2. 4.13.3.2. Normalization conditions
        3. 4.13.3.3. Nuclear part determination
        4. 4.13.3.4. Normalization conditions of the ODFs
        5. 4.13.3.5. Absence of external magnetic field
        6. 4.13.3.6. Application of an external magnetic field
        7. 4.13.3.7. Magnetic part determination
          1. 4.13.3.7.1. Magnetic polarization pole figures
          2. 4.13.3.7.2. Total magnetic-scattering pole figures
        8. 4.13.3.8. Fundamental equations of MQTA
      4. 4.13.4. From magnetic-scattering to the MODF and magnetic moment distributions
      5. 4.13.5. One example
    14. 4.14. Reciprocal space mapping (RSM)
  10. Chapter 5: Quantitative Microstructure Analysis
    1. 5.1. Introduction
    2. 5.2. Microstructure modeling (classic)
      1. 5.2.1. Integral Breadth, FWHM, volume- and area-weighted sizes
        1. 5.2.1.1. Integral breadth and apparent linear size
        2. 5.2.1.2. Area- and volume-weighted sizes
        3. 5.2.1.3. Relationship between FWHM and Gaussian and Lorentzian components of the integral breadth
        4. 5.2.1.4. An expression between Gaussian and Lorentzian integral breadth components
      2. 5.2.2. Scherrer approach
      3. 5.2.3. Stokes and Wilson microstrains
      4. 5.2.4. Williamson-Hall approach
    3. 5.3. Bertaut-Warren-Averbach approach (Fourier analysis)
      1. 5.3.1. Instrumental contribution removal
      2. 5.3.2. Broadening due to crystallite size
      3. 5.3.3. Crystallite size and microdistortion broadening
      4. 5.3.4. Fourier analysis to integral breadths
      5. 5.3.5. Integral breadths to distributions, sizes and microstrains
      6. 5.3.6. Relationships between <RA> and <RV>
    4. 5.4. Anisotropic broadening: the Popa approach [POP 98]
      1. 5.4.1. Anisotropic broadening
      2. 5.4.2. Anisotropic crystallite sizes
      3. 5.4.3. Anisotropic microstrains
    5. 5.5. Stacking and twin faults
      1. 5.5.1. From Line shifts and Fourier analysis
        1. 5.5.1.1. Face-centered cubic materials
        2. 5.5.1.2. Hexagonal compact materials
      2. 5.5.2. Popa approach
    6. 5.6. Dislocations
      1. 5.6.1. Dislocation density
      2. 5.6.2. Wilkens’ model and Fourier analysis
    7. 5.7. Crystallite size distributions
      1. 5.7.1. Normal size distribution function
      2. 5.7.2. Lognormal distribution function
      3. 5.7.3. Gamma distribution function
      4. 5.7.4. Anisotropic distribution functions
    8. 5.8. Rietveld approach
      1. 5.8.1. Constant wavelength data
      2. 5.8.2. Time of flight (TOF) neutrons
  11. Chapter 6: Quantitative Phase Analysis
    1. 6.1. Standardized experiments
    2. 6.2. Polycrystalline samples
    3. 6.3. Amorphous-crystalline aggregates
      1. 6.3.1. Crystallinity fraction [RUL 61]
      2. 6.3.2. Amorphous modeling [LEB 95]
    4. 6.4. Detection Limit
  12. Chapter 7: Residual Strain-Stress Analysis
    1. 7.1. Strain definitions
    2. 7.2. ε33 strain determination
      1. 7.2.1. Isotropic polycrystalline sample
      2. 7.2.2. Single crystal
    3. 7.3. Complete strain tensor determination
      1. 7.3.1. Isotropic polycrystalline samples
        1. 7.3.1.1 Triaxial stress state
        2. 7.3.1.2. Biaxial stress state
        3. 7.3.1.3. Uniaxial stress state
      2. 7.3.2. Single crystal samples
        1. 7.3.2.1. Cubic and orthorhombic crystal systems
        2. 7.3.2.2. Stress tensor
    4. 7.4. Textured samples
      1. 7.4.1. Introduction
      2. 7.4.2. Non-linear least-squares fit
      3. 7.4.3. Strain and stress distribution functions
  13. Chapter 8: X-Ray Reflectivity
    1. 8.1. Introduction
      1. 8.1.1. Definition of the reflectivity
      2. 8.1.2. Specular and off-specular reflectivity
      3. 8.1.3. Combined specular and off-specular scans
    2. 8.2. X-rays and neutrons refractive index
      1. 8.2.1. X-rays
      2. 8.2.2. Neutrons
    3. 8.3. The critical angle of reflection
      1. 8.3.1. X-rays
      2. 8.3.2. Neutrons
    4. 8.4. Fresnel formalism (specular reflectivity)
      1. 8.4.1. Reflection coefficient and reflectivity
        1. 8.4.1.1. Reflection coefficient
        2. 8.4.1.2. Flat sample reflectivity
        3. 8.4.1.3. Single layer on substrate
        4. 8.4.1.4. More complex structures
      2. 8.4.2. Transmission coefficient
      3. 8.4.3. Yoneda wings
    5. 8.5. Surface roughness
      1. 8.5.1. Roughness representation
      2. 8.5.2. Single layer on a substrate
    6. 8.6. Matrix formalism (specular reflectivity)
    7. 8.7. Born approximation
    8. 8.8. Electron density profile
    9. 8.9. Multilayer reflectivity curves
    10. 8.10. Instrumental corrections
      1. 8.10.1. Correction for an irradiated area
      2. 8.10.2. Imperfectly parallel beam
  14. Chapter 9: Combined Structure-Texture-Microstructure-Stress-Phase Reflectivity Analysis
    1. 9.1. Initial queries
    2. 9.2. Implementation
    3. 9.3. Experimental set-up
    4. 9.4. Instrument calibration
      1. 9.4.1. Peak broadenings
        1. 9.4.1.1. χ broadening
        2. 9.4.1.2. 2 θ broadening
        3. 9.4.1.3. ω broadening
        4. 9.4.1.4. General broadening
      2. 9.4.2. Peak shifts
      3. 9.4.3. Background variations
    5. 9.5. Refinement strategy
      1. 9.5.1. Global scheme
      2. 9.5.2. Solution examination
    6. 9.6. Examples
      1. 9.6.1. QTA of single-phased materials
        1. 9.6.1.1. Single-phased bulks
          1. 9.6.1.1.1. PZT ceramics elaborated by molten flux
          2. 9.6.1.1.2. Thickness: grain size ratio effect in thin-rolled nickel
          3. 9.6.1.1.3. Mullite ceramics from muscovite-kaolinite alternate layers
        2. 9.6.1.2. QTA of single layers
          1. 9.6.1.2.1. Nacre-like electrodeposited CaCO3
      2. 9.6.2. QTA and isotropic QMA
        1. 9.6.2.1. Magnetically aligned slip-casted Al2O3 ceramics
      3. 9.6.3. Anisotropic crystallite shape, texture, cell parameters, and thickness
        1. 9.6.3.1. Diffraction pattern from single sample orientation
        2. 9.6.3.2. Nanocrystalline silicon films on Si-(001) and amorphous SiO2
        3. 9.6.3.3. Gold thin films on Si-(001) single crystal substrates
      4. 9.6.4. Layering, isotropic shape, microstrains, texture, and structure
      5. 9.6.5. Phase and texture
        1. 9.6.5.1. Texture removal
        2. 9.6.5.2. Crystalline multiphase textured compounds
          1. 9.6.5.2.1. Top-seeded MTG grown YBa2Cu3O7-δ /Y2BaCuO5 ensembles
          2. 9.6.5.2.2. Sinter-Forged Bi2223/Bi2212 samples
        3. 9.6.5.3. Amorphous-crystalline multiphase textured compounds
          1. 9.6.5.3.1. Irradiated fluorapatite ceramics
          2. 9.6.5.3.2. GaN-doped SiO2 matrices
      6. 9.6.6. Texture of modulated structures
        1. 9.6.6.1. Ca3Co4O9 ceramics
          1. 9.6.6.1.1. Hot-forged magnetically aligned slip-casted Co349 ceramics
          2. 9.6.6.1.2. Reactive templated grain-growth Co349 ceramics
        2. 9.6.6.2. Hot-forged [Bi0.81CaO2]2[CoO2]1.69 misfit ceramics
      7. 9.6.7. Texture, residual stresses and layering
        1. 9.6.7.1. AlN/Pt/TiOx/Al2O3/Ni-Co-Cr-Al-Y stacks
      8. 9.6.8. Texture and structure
        1. 9.6.8.1. Biogenic crystals of the shells of C. lampas lampas
        2. 9.6.8.2. Other mollusc shell layers
        3. 9.6.8.3. Mimicking nacre in coatings on Ti-4Al-6V substrates
  15. Chapter 10: Macroscopic Anisotropic Properties
    1. 10.1. Aniso- and isotropic samples and properties
    2. 10.2. Macroscopic/microscopic properties
      1. 10.2.1. TM and T tensors
      2. 10.2.2. Microscopic properties
        1. 10.2.2.1. Classifications of properties
        2. 10.2.2.2. Extensive and intensive variables
        3. 10.2.2.3. Work element of conjugated variables
        4. 10.2.2.4. Generalized thermodynamics
          1. 10.2.2.4.1. Generalized energy and free enthalpy
          2. 10.2.2.4.2. Linear generalized total derivatives
          3. 10.2.2.4.3. Property tensor reduction by symmetry operators
        5. 10.2.2.5. Thermal properties
          1. 10.2.2.5.1. Heat capacity
          2. 10.2.2.5.2. Thermal conductivity
          3. 10.2.2.5.3. Thermal diffusivity
        6. 10.2.2.6. Electric and optical properties
          1. 10.2.2.6.1. Dielectric properties
          2. 10.2.2.6.2. Optical linear properties
          3. 10.2.2.6.3. Optical rotation properties
          4. 10.2.2.6.4. Electrical conductivity-resistivity
          5. 10.2.2.6.5. ElectroOptic effects
          6. 10.2.2.6.6. Four-wave mixing
        7. 10.2.2.7. Magnetic properties
          1. 10.2.2.7.1. Magnetic induction, field and magnetization
          2. 10.2.2.7.2. Diamagnetics
          3. 10.2.2.7.3. Paramagnetics
          4. 10.2.2.7.4. Ferro- and ferrimagnetics
        8. 10.2.2.8. Mechanical properties
          1. 10.2.2.8.1. Static mechanical properties
          2. 10.2.2.8.2. Bulk acoustic waves (BAW)
        9. 10.2.2.9. ThermoElectric (TE) properties
          1. 10.2.2.9.1. Pyroelectricity
          2. 10.2.2.9.2. Seebeck and Peltier effects
          3. 10.2.2.9.3. Power factor
          4. 10.2.2.9.4. Figure of merit
        10. 10.2.2.10. ThermoMechanic (TMe) properties
        11. 10.2.2.11. ElectroMechanic (EMe) properties
          1. 10.2.2.11.1. Piezoelectric effect
          2. 10.2.2.11.2. Acoustic waves propagation in piezoelectrics
          3. 10.2.2.11.3. 2nd order piezoelectric effect
          4. 10.2.2.11.4. Electrostriction
        12. 10.2.2.12. MagnetoMechanic (MMe) properties
          1. 10.2.2.12.1. Piezomagnetic effect
          2. 10.2.2.12.2. Acoustic waves propagation in piezomagnetics
          3. 10.2.2.12.3. 2nd order piezomagnetic effect
          4. 10.2.2.12.4. Magnetostriction
        13. 10.2.2.13. MagnetoElectric (ME) properties
          1. 10.2.2.13.1. Linear magnetoelectric effect
          2. 10.2.2.13.2. Non-linear magnetoelectric effect
          3. 10.2.2.13.3. Hall effect and magnetoresistance
        14. 10.2.2.14. MagnetoOptic (MO) effects and magnetic birefringence
          1. 10.2.2.14.1. Generalized MagnetoOptic formulation
          2. 10.2.2.14.2. Faraday rotation
          3. 10.2.2.14.3. Cotton-Mouton effect
          4. 10.2.2.14.4. Magnetic birefringence
          5. 10.2.2.14.5. Induced gyrotropic birefringence (IGB)
        15. 10.2.2.15. Mechano-Optic (MeO) properties
          1. 10.2.2.15.1. Linear photoelastic effect
          2. 10.2.2.15.2. AcoustoOptic effect
        16. 10.2.2.16. Atomic diffusion
        17. 10.2.2.17. PiezoMagnetoElectric (PME) properties
        18. 10.2.2.18. Multiferroics
      3. 10.2.3. Macroscopic properties anisotropy and modeling
        1. 10.2.3.1. Averaging of tensors
          1. 10.2.3.1.1. Volume average
          2. 10.2.3.1.2. Arithmetic average over orientations
          3. 10.2.3.1.3. Geometric average over orientations
        2. 10.2.3.2. Heat capacity
        3. 10.2.3.3. Thermal expansion
        4. 10.2.3.4. Electric polarization
        5. 10.2.3.5. Mechanical properties
          1. 10.2.3.5.1. The Voigt model
          2. 10.2.3.5.2. The Reuss model
          3. 10.2.3.5.3. The Hill model
          4. 10.2.3.5.4. The geometric mean model
          5. 10.2.3.5.5. Some examples
        6. 10.2.3.6. Bulk acoustic waves from OD and Ciℓmn
          1. 10.2.3.6.1. Photoexcited acoustic waves in fiber textured Au films
          2. 10.2.3.6.2. Hetero-epitaxial and fibre textured LiNbO3 films
        7. 10.2.3.7. Thermoelectric properties
          1. 10.2.3.7.1. RTGG Co349 ceramics
          2. 10.2.3.7.2. Hot-forged [Bi0.81CaO2]2[CoO2]1.69 misfit ceramics
        8. 10.2.3.8. Magnetization in oriented easy-plane ErMn4Fe8C
        9. 10.2.3.9. Dielectric constant
  16. Bibliography
  17. Glossary
  18. Abbreviations
  19. Mathematical Operators
  20. Index