Generalized temperature-factor formulation with application to cadmium selenide and other wurtzites

The generalized temperature factor is formulated within the framework of the one-particle potential in terms of functions derived from the harmonic functions of Stewart. This formulation is then applied to the wurtzite structure and projection analysis is used to eliminate one component of the potential. Inclusion of the generalized temperature factor in the structure-factor expression for wurtzitc leads to the appearance of harmonically forbidden reflections and the loss of equivalence of non-symmetry-related reflections which occur at the same Bragg angle. The results of a room-temperature X-ray experiment with cadmium selenide are interpreted within the above model to yield cubic anharmonic parameters |β₃₃₂| = |β₃₃₇| = |β₃₁₃| = (0.13 ± 0.01) × 10^-12 erg A^-3. These are used to estimate the anharmonic effect on the position parameter u. Some general conclusions are drawn regarding the possibility of observing similar effects in other wurtzite structures.