Reduction of Crystallographic Point Groups to Subgroups by Homogeneous Stress

It is assumed that the symmetry operations possessed by a homogeneously stressed crystal will be those common to the crystal and to the stress. Application of stress either leaves a point group unaltered or lowers it to a subgroup. Any stress-induced minimum step of symmetry lowering can be caused by unaxial stress but three of the possible stress-induced compound steps of symmetry lowering require biaxial stress. The uniaxial or biaxial stress required for any stress-induced symmetry lowering is tabulated and stereograms are given for each of the minimum steps showing the relation of the remaining symmetry operations to the initial symmetry and showing the splitting of a set of initially equivalent general directions into inequivalent subsets. These stereograms provide a direct representation of the splitting of a general position in a crystal into inequivalent subsets for the symmorphic space groups and the latter are listed; the effect of glide planes and screw axes must be considered in the remaining space groups yet the stereograms still provide the correct pattern of splitting. Uses of the stereograms, for instance, to obtain the splitting of a special position, are described.