Jump Rates for Point Defects in Special Positions Held by a Trapping Center of Noncubic Symmetry.

In a previous paper [J. Phys. Chem. Solids , 975 (1966)] the authors have discussed symmetry conditions for equivalence of jump rates operative in point-defect motion between crystallographically equivalent general sites neighboring a trapping center. The treatment is here extended to equivalent special sites to show that the total number of inequivalent jump rates can be expressed as ( )- -1 where and are the orders of the symmetry groups of the trap and defect respectively and where is the number of independently effective pairs of nonself-inverse symmetry operators (paired with their inverses) all in the symmetry group of the trap. The number can be obtained by counting any nonself-inverse operator pair, an element of which, when multiplied by any element of the defect symmetry, equals neither its own inverse nor an element of a pair previously counted. For thermally activated relaxation processes expressions apply for maximum and minimum numbers of jump frequencies involved in complete and partial relaxation processes. For complete relaxation the maximum number is the number of prime factors in the ratio of the order of the symmetry group of the trap to that of the defect group. The minimum number is the minimum number of generators that will raise the defect position symmetry to that of the trap.