Debye–Waller factors of zinc-blende-structure materials: dynamic deformation effects

A discussion is given on simple grounds, not explicitly involving the dynamical deformation formalism, of the implications of having the outer part of the electron distribution vibrating significantly differently from the core. The use of a lattice dynamical shell model to represent this effect is examined in some detail, with particular reference to the framework within which such a model gives meaningful results. Predictions are given from the 14-parameter shell models and the 11-parameter valence-shell models for the difference between Debye-Waller B values of the shells and cores and also for the effective Debye-Waller factors for the deforming ions in 14 zinc-blende-structure compounds. It is concluded that the effective X-ray Debye-Waller B at very small sin θ/λ is typically several percent smaller than the core B value, owing to a very substantial reduction in the mean-square displacements of shells compared with cores. Results are also given for the 15-parameter deformation-dipole models for eight materials. These show effects broadly comparable in magnitude to the shell models but more varied in detail. Notably, some models show for the first time a larger rather than smaller Debye-Waller factor for the deforming ion.