Titlebook: Crystallographic Texture and Group Representations; Chi-Sing Man Book 2023 Springer Nature B.V. 2023 Quantitative texture analysis.Orienta

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Ideal Crystals and the Crystallographic Groups,In this chapter we cover, for later use, some basics on crystallography and crystallographicgroups.

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Orientation Distribution Function,Readers who have no prior exposure to quantitative texture analysis or have no strong urge to study at once various formulations and conventions (including those of Bunge and Roe) may skip Sects. 4.1.1, 4.4, and 4.5 on a first reading.

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SO(3) and O(3) as Riemannian Manifolds,Let . be the translation space of the three-dimensional physical Euclidean space, and let Lin be the space of linear transformations on ..

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Texture Analysis Based on the Orthogonal Group,With ODFs defined on SO(3), classical texture analysis suffers from the limitation that the groups of texture and crystallite symmetry . and . are restricted to be rotational.

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Group Representations,Let . be a finite-dimensional vector space over the field ? of complex numbers, which we shall simply call complex vector space.

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