Quantitative texture analysis and combined analysis

Chateigner, D.; Lutterotti, L.; Morales, M.

doi:10.1107/97809553602060000968

International Tables for Crystallography (2019). Vol. H. ch. 5.3, pp. 555-580
https://doi.org/10.1107/97809553602060000968

Chapter 5.3. Quantitative texture analysis and combined analysis

5.3. Quantitative texture analysis and combined analysis (pp. 555-580) | html | pdf | chapter contents |
D. Chateigner, L. Lutterotti and M. Morales
- 5.3.1. Introduction (p. 555) | html | pdf |
- 5.3.2. Crystallographic quantitative texture analysis (QTA) (pp. 555-567) | html | pdf |
  - 5.3.2.1. Orientation distribution (OD) (pp. 555-558) | html | pdf |
    - 5.3.2.1.1. The orientation space H (pp. 555-556) | html | pdf |
    - 5.3.2.1.2. The orientation distribution (OD) or orientation distribution function (ODF) (p. 556) | html | pdf |
    - 5.3.2.1.3. Pole figures (pp. 556-558) | html | pdf |
      - 5.3.2.1.3.1. Mathematical expression (pp. 556-557) | html | pdf |
      - 5.3.2.1.3.2. Diffraction pole figures and orientation of planes (p. 557) | html | pdf |
      - 5.3.2.1.3.3. From diffraction measurements to pole figures and ODs (p. 557) | html | pdf |
      - 5.3.2.1.3.4. Pole-figure normalization (pp. 557-558) | html | pdf |
  - 5.3.2.2. The fundamental equation of quantitative texture analysis (pp. 558-559) | html | pdf |
  - 5.3.2.3. Resolution of the fundamental equation (pp. 559-562) | html | pdf |
    - 5.3.2.3.1. Generalized spherical-harmonics expansion (pp. 559-560) | html | pdf |
    - 5.3.2.3.2. Vector method (p. 560) | html | pdf |
    - 5.3.2.3.3. WIMV method (p. 560) | html | pdf |
    - 5.3.2.3.4. Arbitrarily defined cells (ADC) method (p. 560) | html | pdf |
    - 5.3.2.3.5. Entropy-maximization method (p. 560) | html | pdf |
    - 5.3.2.3.6. EWIMV method (p. 560) | html | pdf |
    - 5.3.2.3.7. Component method (pp. 560-561) | html | pdf |
    - 5.3.2.3.8. Positivity and exponential harmonics (pp. 561-562) | html | pdf |
    - 5.3.2.3.9. Radon transform and Fourier analysis (p. 562) | html | pdf |
  - 5.3.2.4. Inverse pole figures (pp. 562-563) | html | pdf |
  - 5.3.2.5. OD refinement reliability estimators (p. 563) | html | pdf |
  - 5.3.2.6. Texture-strength factors (pp. 563-564) | html | pdf |
    - 5.3.2.6.1. Texture index (p. 564) | html | pdf |
      - 5.3.2.6.1.1. OD texture index (p. 564) | html | pdf |
      - 5.3.2.6.1.2. Pole-figure texture index (p. 564) | html | pdf |
    - 5.3.2.6.2. Texture entropy (p. 564) | html | pdf |
    - 5.3.2.6.3. Pole-figure and ODF strengths (p. 564) | html | pdf |
    - 5.3.2.6.4. Correlation between F² and S (p. 564) | html | pdf |
  - 5.3.2.7. Texture types (pp. 564-566) | html | pdf |
    - 5.3.2.7.1. Random texture (pp. 564-565) | html | pdf |
    - 5.3.2.7.2. Planar textures (p. 565) | html | pdf |
    - 5.3.2.7.3. Fibre textures (p. 565) | html | pdf |
    - 5.3.2.7.4. Three-dimensional textures (pp. 565-566) | html | pdf |
    - 5.3.2.7.5. Typical OD components (p. 566) | html | pdf |
  - 5.3.2.8. Reciprocal-space mapping (pp. 566-567) | html | pdf |
- 5.3.3. Magnetic quantitative texture analysis (MQTA) (pp. 567-569) | html | pdf |
  - 5.3.3.1. Magnetization curves and magnetic moment distributions (p. 567) | html | pdf |
  - 5.3.3.2. Magnetic pole figures and magnetic ODs (pp. 567-568) | html | pdf |
    - 5.3.3.2.1. Magnetic pole figures and ODs (p. 567) | html | pdf |
    - 5.3.3.2.2. Fundamental equations of MQTA (pp. 567-568) | html | pdf |
  - 5.3.3.3. An example (pp. 568-569) | html | pdf |
- 5.3.4. Modelling of preferred orientation in the Rietveld method (pp. 569-571) | html | pdf |
  - 5.3.4.1. Rietveld and March approaches (p. 569) | html | pdf |
  - 5.3.4.2. March–Dollase approach (pp. 569-570) | html | pdf |
  - 5.3.4.3. Modified March–Dollase models (p. 570) | html | pdf |
  - 5.3.4.4. Donnet–Jouanneaux function (p. 570) | html | pdf |
  - 5.3.4.5. Modelling by spherical harmonics (and exponential) (p. 570) | html | pdf |
  - 5.3.4.6. The use of standard functions (or texture components) (p. 570) | html | pdf |
  - 5.3.4.7. Remarks (pp. 570-571) | html | pdf |
- 5.3.5. Combined analysis: structure, texture, microstructure, stress, phase, layering and reflectivity analyses in a single approach (pp. 571-578) | html | pdf |
  - 5.3.5.1. Problems (pp. 571-572) | html | pdf |
  - 5.3.5.2. Intensity of a pattern and general scheme (p. 572) | html | pdf |
  - 5.3.5.3. Minimum experimental requirements (p. 572) | html | pdf |
  - 5.3.5.4. Theoretical implementation (pp. 572-577) | html | pdf |
    - 5.3.5.4.1. Instrumental broadening calibration (pp. 572-573) | html | pdf |
    - 5.3.5.4.2. Peak-displacement errors (p. 573) | html | pdf |
    - 5.3.5.4.3. Background fitting (pp. 573-574) | html | pdf |
    - 5.3.5.4.4. Reflection intensities (pp. 574-575) | html | pdf |
    - 5.3.5.4.5. Line profiles and sample broadening (p. 575) | html | pdf |
    - 5.3.5.4.6. Texture computation (p. 575) | html | pdf |
    - 5.3.5.4.7. Residual strains/stresses and evaluation of macroscopic tensors (pp. 575-576) | html | pdf |
    - 5.3.5.4.8. Absorption and layers (pp. 576-577) | html | pdf |
  - 5.3.5.5. Implementation (p. 577) | html | pdf |
  - 5.3.5.6. Examination of a solution (pp. 577-578) | html | pdf |
- 5.3.6. Conclusions (p. 578) | html | pdf |
- References | html | pdf |
- Figures
  - Fig. 5.3.1. Crystal and sample reference frames K_B = (x_B, y_B, z_B) and K_A = (x_A, y_A, z_A) (p. 555) | html | pdf |
  - Fig. 5.3.2. Definition of the three Euler angles α_c, β_c and γ_c that define the orientation of one crystallite frame K_B = (a, b, c) of an orthogonal crystal cell in the sample coordinate system K_A (p. 555) | html | pdf |
  - Fig. 5.3.3. (a) P_h(y) diffraction pole figure for one crystallite (p. 556) | html | pdf |
  - Fig. 5.3.4. Relationship between the three-dimensional object f(g) and the pole figures P_h(y) (p. 557) | html | pdf |
  - Fig. 5.3.5. (a) An OD as γ_c sections and (b) as {100} and {001} pole figures (p. 558) | html | pdf |
  - Fig. 5.3.6. The inverse pole-figure sectors as a function of the crystal symmetry (p. 562) | html | pdf |
  - Fig. 5.3.7. Visual examination of the OD refinement reliability using experimental and recalculated normalized {104}, {110}, {113}, {202}, {116}, {211}, {125} and {300} pole figures (in successive order) (p. 563) | html | pdf |
  - Fig. 5.3.8. Entropy variation with texture index for modelled f(g) functions (p. 564) | html | pdf |
  - Fig. 5.3.9. {100}, {001} and {110} pole figures of a planar texture in an orthorhombic crystal system (p. 565) | html | pdf |
  - Fig. 5.3.10. {100}, {001} and {110} pole figures of a cyclic-planar texture in an orthorhombic crystal system (p. 565) | html | pdf |
  - Fig. 5.3.11. {100}, {001} and {110} pole figures of a fibre texture in an orthorhombic crystal system (p. 565) | html | pdf |
  - Fig. 5.3.12. {100}, {001} and {110} pole figures of a cyclic-fibre texture in an orthorhombic crystal system (p. 565) | html | pdf |
  - Fig. 5.3.13. {100}, {001} and {110} pole figures of a three-dimensional texture in an orthorhombic crystal system, with 〈001〉* directions along Z_A and 〈100〉* directions along X_A (p. 565) | html | pdf |
  - Fig. 5.3.14. The difference between a perfect single crystal and a polycrystal with perfect three-dimensional crystallite orientations (p. 566) | html | pdf |
  - Fig. 5.3.15. Isodensity surfaces representing isolated OD components in a Cartesian coordinate system in H space (p. 566) | html | pdf |
  - Fig. 5.3.16. Several isodensity surfaces representing a cyclic-fibre OD (a) and a cyclic-planar OD (b) in H space (p. 566) | html | pdf |
  - Fig. 5.3.17. Illustration of a case for which a magnetization measurement in two perpendicular directions cannot reveal the macroscopic magnetic anisotropy (p. 567) | html | pdf |
  - Fig. 5.3.18. {110} pole figures at zero field (a), under 0.3 T (b) and the difference (c) (p. 568) | html | pdf |
  - Fig. 5.3.19. Illustration of the effects of defocusing and misadjustment on peak shapes and diffractometer resolution function (p. 573) | html | pdf |
  - Fig. 5.3.20. (a) Randomly selected diagrams (at increasing χ values and broadening due to defocusing from bottom to top) illustrating the quality of the fit, together with the textures of AlN and Pt (p. 574) | html | pdf |
  - Fig. 5.3.21. Low-index recalculated pole figures and Z_A inverse pole figures for the three textured phases of the stack (p. 577) | html | pdf |
- Tables
  - Table 5.3.1. Preferred-orientation (PO) modelling methods implemented in some Rietveld packages, and their capability to perform a full texture analysis (QTA) with determination of the OD from several patterns (p. 571) | html | pdf |
  - Table 5.3.2. Results obtained from combined analysis on an AlN/Pt/TiO_x/Al₂O₃/Ni(Co–Cr–Al–Y) stack (p. 577) | html | pdf |

Chapter 5.3. Quantitative texture analysis and combined analysis

Contents