Deformation dipole model and lattice dynamics of zinc-blende-structure compounds

The deformation-dipole-model (DDM) formalism is derived for a crystal of arbitrary symmetry and applied to the zinc-blende structure. In its present form, the model is more general than the one proposed by Karo and Hardy, the principal difference consisting in introducing interactions called nonlocal electric polarizabilities, analogous to the shell-shell interactions of the shell model. Both approaches are compared and it is shown that in ionic crystals the present version of the DDM provides the same description of core motion as the shell model. Parameters of one model are then expressed in terms of the other model, for ionic structures; the case of covalent crystals is also briefly discussed. A simplified form of the DDM was used in numerical calculations for 15 crystals with $T_d^4$ symmetry. Model parameters fitted to elastic, piezolectric, optical and, for eight compounds, also to neutron-diffraction measurements gave a good description of phonon frequencies. Some of the parameters appeared to be smoothly varying functions of the interatomic distance or ionicity.