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Symmetry in the Space of Euler Angles

✍ Scribed by Dr. J. Pospiech; A. Gnatek; Dr. K. Fichtner

Publisher
John Wiley and Sons
Year
1974
Tongue
English
Weight
636 KB
Volume
9
Category
Article
ISSN
0232-1300

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

For the analysis and description of textures the orientation distribution function f(g) is used. Orientations g as points in β€œorientation space” are usually characterized by the Euler angles Ο†~1~, Θ, Ο†~2~. The symmetries of the function f(g) result from the symmetries of the crystal and those of the specimen.

The symmetries in orientation space induced by both the point group symmetry of the crystal and of the specimen are analysed. Any combination of crystal and specimen symmetries yield a group of linear transformations in orientation space; this group corresponds to one of the 230 space groups.

If the point group of the crystal or the point group of the specimen belong to the cubic system the resulting group of linear transformations does not contain all induced symmetries.

Tables with the induced space groups are given for all combinations of crystal and specimen symmetries.

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