Crystallographic texture and group representations

The crystallographic groups are precisely the discrete groups of isometries in E d whose fundamental region is compact

Two discrete groups are said to be geometrically isomorphic if they are conjugate subgroups in the group of all nonsingular affine transformations of E d

: rotations or reflections), that leave a point fixed while moving each atom of the crystal to the position of an atom of the same kind Chapter 3 14 Bravais Lattices 5 Chapter 3

The geometric aspects and relations amongst the component particles or crystals are referred to as the crystallographic texture or preferred orientation

Textures can be quantified in many ways

The most common [citation needed] parameter is the crystal size distribution