Splitting of a Set of Equivalent Sites in Centrosymmetric Space Groups Into Subsets Under 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 macroscopic state of stress. Application of stress either leaves a space group unaltered or lowers it to a subgroup. Such lowering can always be considered to take place in successive steps each of which leaves no group intermediate between the starting group and the subgroup. Each such step can be accomplished by a uniaxial stress; for the centrosymmetric space groups, all but one of the symmetry reductions consisting of two or more successive steps can also be accomplished by a uniaxial stress. A set of sites all of which are equivalent in the unstrained crystal may split into two or more subsets under stress. For each space group all possibilities are taken into account by considering the behavior of the general position (most general set of symmetry related sites) because the behavior of each special position can easily be derived by specializing the description of the general position. The splitting of the general position under homogeneous stress is tabulated for all possibilities for each centrosymmetric space group.