Lattice Dynamics and Ionic Deformation in Some Alkali Halides

Equations of motion are derived for a shell model in which the shells are allowed to deform. Dispersion curves are then calculated for NaF, NaCl, NaBr, and NaI from measured dielectric, infrared, and elastic constants. A comparison with published phonon frequencies shows that a simple model with radial deformation gives some improvement over a rigid-shell model. A rather more general treatment with increased radial deformation produces even better curves. However, the LO (0,0,1) zone-boundary phonons are not well represented by either model. The eigenvectors from the rigid-shell model and from the best deformable-shell models are then used to work out the ionic form-factor changes in NaCl when (0,0,η) phonon states are excited, and the corresponding changes in the x-ray one-phonon cross sections along the (0,0,1) axis are obtained. It is found that the rigid-shell model gives small variations in the cross sections resulting from the displacements of the shells, and that the radial deformations give additional changes. The models predict the occurrence of asymmetries in x-ray scattering, but the intensity differences are an order of magnitude less than the effects which have been observed. Further calculations with the inclusion of deformation of the inner electrons are required.