The Anharmonic Temperature Factor for Crystals with the Hexagonal Wurtzite Structure and Its Inclusion in Models for Least-squares Refinement of Intensity Data

Abstract

The anharmonic temperature factor for binary compounds of the ANB8-N type possessing the wurtzite structure is derived as a perturbation expansion about the harmonic case. The terms in this expansion are obtained from combinations of spherical harmonics. The derivation utilizes group theory and follows the treatment of Von der Lage and Bethe (1947) and Nizzoli (1976). A set of constraints between the cubic anharmonic coefficients in the one-particle potential (OPP), which appear in the temperature factor, is then derived, enabling least-squares refinements to be carried out successfully. The use of the anharmonic temperature factor, with these constraints, is shown to result in a significant reduction in Hamilton's R factor for two extensive data sets.