Debye-Waller Factor for Zinc-Blende-Type Crystals

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Abstract
The Debye-Waller factors have been calculated for a number of zinc-blende-type crystals from the eigenfrequencies and eigenvectors of the phonon states as obtained from the modified-rigidion model of lattice dynamics. On the average the contribution from the acoustic-phonon states to the mean-square displacements of the constituent atoms was found to be more significant than that from the optical-phonon states. However, the relative optical-phonon-state contribution was found to be more significant in the lighter atom, and in fact in some cases at low temperatures, it was found to exceed the acoustic-phonon-state contribution. In all the cases studied, the mean-square displacements of the lighter atom were found to be larger. Lindeman's criterion for melting was tested by evaluating the ratio of the sum of the root-mean-square displacements of the constituent atoms to the nearest-neighbor distance. This ratio is approximately constant for the zinc-blende compounds. However, the average ratio for the II-VI compounds was found to be slightly larger than that for the III-V compounds. The calculated results are discussed in relation to available experimental data.