Group-theoretical principles of texture analysis of polycrystalline materials

A unified group-theoretical approach to the problem of reduction of the orientation space of a crystallographic texture has been developed. The concept of a function of invariant internal distance in a group space is introduced. Left and right group translations, internal automorphisms, motions of t...

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Bibliographic Details
Published in:Bulletin of the Russian Academy of Sciences. Physics 2007-12, Vol.71 (12), p.1737-1747
Main Author: Yashnikov, V. P.
Format: Article
Language:English
Subjects:
Automorphisms
Crystallography
Dirichlet problem
Invariants
Orientation
Parameterization
Texture
Translations
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Summary:A unified group-theoretical approach to the problem of reduction of the orientation space of a crystallographic texture has been developed. The concept of a function of invariant internal distance in a group space is introduced. Left and right group translations, internal automorphisms, motions of the general form, and inversion transformations of the space SO(3) have been studied. It is shown that the Dirichlet-Voronoi partition, being dual to the intrinsic point group of the crystallographic lattice of grain with the initial orientation, is regular with respect to the group of motions (right translations) generated by the elements of the intrinsic point group. Invariant derivation of reduced (true) orientation spaces of crystallographic textures, which does not require a particular specific parameterization of the group space SO(3), is reported.
ISSN:1062-8738
1934-9432
DOI:10.3103/S1062873807120143