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Orientations and Rotations 
Computations in Crystallographic Textures


Springer Verlag
2004, X, 200 p. 32 illus., Hardcover
ISBN: 3-540-40734-0


 
The book is about mathematical and computational foundations of texture analysis. Numerical techniques are indispensable in texture analysis, so the book is primarily addressed to researchers and students using these techniques in practice. Orientations and Rotations is very different from other books on textures in its content and focal point. Major part of the book is devoted to orientations and rotations in general. Opening chapters contain an extensive and thorough introduction to rotations in three dimensions (including parameterizations and geometry of the rotation space). Further chapters are also general but they will be of interest for readers dealing with orientations of symmetric objects. This subject is essential for crystallographic textures since most crystal structures are symmetric. The final chapters concern more practical aspects of textures (such as the determination of orientations from diffraction patterns and the calculation of effective elastic properties of polycrystals). The book may be of interest for scientists working on plasticity, grain boundaries, recrystallisation, grain growth, and numerous other issues in which textures must be taken into account. Because of the extensive parts on rotations in general, the book can be valuable for a very broad audience.

Table of contents:

Preliminaries 
    Rotations as Displacements
    Composition of Rotations
    Improper Rotations
    Matrix Representation
    Formal Approach to Orthogonal Transformations 

Parameterizations
    Half–turns
    Cayley Transformation and Rodrigues Parameters
    Axis and Angle Parameters
    Euler Angles
    Cayley–Klein Parameters
    Quaternions
    Rotation Vector
    Rotation Matrix in Non–Cartesian Coordinate Systems
    Miller Indices
    Computational Properties of Parameterizations

Geometry of the Rotation Space
    SO(3) as a Riemannian Manifold
    Exponential Mapping
    SO(3) as a Lie Group
    Integration on SO(3)

More on Small Orientation Changes
    Vector of Infinitesimal Rotation
    Rotation Rate Field and Continuity Equation
    Short Excursion into Mechanics

Some Statistical Issues
    Mean Orientation
    Distributions on the Rotation Manifold
    Generation of Orientations
    Comparing Smooth Orientation Functions

Symmetry
    Finite Point Groups
    Crystallographic Point Groups
    Asymmetric Domains
    Asymmetric Domains in Rodrigues Space

Misorientation Angle and Axis Distributions
    Misorientation Angle Distributions
    Distributions of Rotation Axes

Crystalline Interfaces and Symmetry
    Symmetrically Equivalent Boundaries
    Boundary Distributions

Crystallographic Textures
    Texture Components in Cubic–Orthorhombic Case
    Rational Orientation Relationships
    Coincident Sublattices

Diffraction Geometry
    Elementary Relations
    Orientations of Individual Crystallites
    Orientation Distributions from Pole Figures

Effective Elastic Properties of Polycrystals
    Definitions and Simplest Principles
    Perturbation Methods
    Related Issues

Reviews:

1. S. Matthies, Journal of Applied Crystallography 38, 1042-1043 (2005).
2. H. Klein, Crystal Research and Technology 40, 283-284 (2005).
3. J. Wheeler, Geological Magazine 143, 556-557 (2006).
4. T. Böhlke, Technische Mechanik 26, 66-67 (2006).



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