International Tables for Crystallography (2019). Vol. H, ch. 5.5, pp. 601-616
https://doi.org/10.1107/97809553602060000970

Chapter 5.5. Multigrain crystallography and three-dimensional grain mapping

Contents

  • 5.5. Multigrain crystallography and three-dimensional grain mapping  (pp. 601-616) | html | pdf | chapter contents |
    • 5.5.1. List of symbols  (p. 601) | html | pdf |
    • 5.5.2. Introduction  (pp. 601-602) | html | pdf |
    • 5.5.3. Experimental setup  (pp. 602-603) | html | pdf |
    • 5.5.4. Diffraction geometry  (pp. 603-605) | html | pdf |
      • 5.5.4.1. The laboratory and rotated coordinate systems  (p. 603) | html | pdf |
      • 5.5.4.2. Detector coordinate systems  (pp. 603-604) | html | pdf |
      • 5.5.4.3. Diffraction  (p. 604) | html | pdf |
      • 5.5.4.4. Forward projection, no detector tilt  (pp. 604-605) | html | pdf |
      • 5.5.4.5. Forward projection with detector tilt and non-centred sample  (p. 605) | html | pdf |
        • 5.5.4.5.2. Detector tilt specification II  (p. 605) | html | pdf |
    • 5.5.5. Indexing  (pp. 605-606) | html | pdf |
      • 5.5.5.1. Detector tilt specification I  (p. 605) | html | pdf |
    • 5.5.6. Multigrain crystallography  (pp. 606-607) | html | pdf |
      • 5.5.6.1. Monophase materials  (pp. 606-607) | html | pdf |
      • 5.5.6.2. Multiphase materials containing unknown phases  (p. 607) | html | pdf |
    • 5.5.7. Centre-of-mass and stress mapping  (pp. 607-608) | html | pdf |
    • 5.5.8. 3D grain and orientation mapping  (pp. 608-609) | html | pdf |
      • 5.5.8.1. Approach 1: Grain-by-grain volumetric mapping  (p. 608) | html | pdf |
      • 5.5.8.2. Approach 2: Orientation mapping by Monte Carlo optimization  (pp. 608-609) | html | pdf |
    • 5.5.9. Representation of crystallographic orientation  (pp. 609-613) | html | pdf |
      • 5.5.9.1. Euler angles (Bunge definition)  (pp. 609-610) | html | pdf |
      • 5.5.9.2. Rodrigues vectors  (pp. 610-611) | html | pdf |
      • 5.5.9.3. Unit quaternions  (pp. 611-612) | html | pdf |
        • 5.5.9.3.1. Quaternion basics  (p. 611) | html | pdf |
        • 5.5.9.3.2. Relation between unit quaternions and orientations  (pp. 611-612) | html | pdf |
        • 5.5.9.3.3. Distance  (p. 612) | html | pdf |
      • 5.5.9.4. Bounding cubes  (pp. 612-613) | html | pdf |
    • 5.5.10. Representation of elastic strain  (p. 613) | html | pdf |
      • 5.5.10.1. Definition of strain  (p. 613) | html | pdf |
      • 5.5.10.2. Strain-to-stress conversion  (p. 613) | html | pdf |
    • 5.5.11. Crystal symmetry in relation to multigrain samples  (pp. 613-614) | html | pdf |
      • 5.5.11.1. Fundamental zone  (p. 614) | html | pdf |
      • 5.5.11.2. Determining the orientation in the fundamental zone  (p. 614) | html | pdf |
      • 5.5.11.3. Use of symmetry-equivalent orientations for strain and stress characterization  (p. 614) | html | pdf |
    • 5.5.12. Discussion  (p. 614) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 5.5.1. Sketch of the 3DXRD principle  (p. 602) | html | pdf |
      • Fig. 5.5.2. Typical 3DXRD data from a coarse-grained undeformed polycrystal  (p. 602) | html | pdf |
      • Fig. 5.5.3. Definition of the detector pixel coordinate system (see text)  (p. 604) | html | pdf |
      • Fig. 5.5.4. Grain areas reconstructed by Voronoi tessellation based on experimentally measured centres of mass (the points)  (p. 607) | html | pdf |
      • Fig. 5.5.5. Stress map of 1750 grains around a notch in an Mg AZ321 sample during tensile deformation  (p. 608) | html | pdf |
      • Fig. 5.5.6. Rendition of the 3D grain structure in a cylindrical β-Ti specimen containing 1008 grains, as obtained by the DCT algorithm  (p. 608) | html | pdf |
      • Fig. 5.5.7. Map of one layer from a cylinder of high-purity nickel  (p. 609) | html | pdf |
      • Fig. 5.5.8. Monte Carlo based reconstruction of a test case representing 20% deformed aluminium  (p. 609) | html | pdf |
      • Fig. 5.5.9. Definition of the Euler angles (ϕ1, φ, ϕ2) according to Bunge (1969)  (p. 610) | html | pdf |
      • Fig. 5.5.10. Definition of the Rodrigues vector r  (p. 610) | html | pdf |
      • Fig. 5.5.11. Symmetry of projection lines through point r0 in Rodrigues space  (p. 611) | html | pdf |
      • Fig. 5.5.12. Three-dimensional illustration of the concepts of bounding squares  (p. 612) | html | pdf |
      • Fig. 5.5.13. The TEM equivalent of 3DXRD orientation mapping  (p. 614) | html | pdf |
    • Tables
      • Table 5.5.1. Irreducible part of Euler space for the seven Bravais classes  (p. 614) | html | pdf |