Lattice Dynamics of Alkali Halides

The deformable-shell model developed by Basu and Sengupta and later substantiated by a potential form by Sarkar and Sengupta has found wide application in describing the different static properties of ionic crystals of both NaCl and CsCl structures. But so far a complete calculation of dynamical properties of ionic crystals has been reported for only one crystal. Further, from a critical comparison of the different lattice-dynamical models which effectively introduce many-body interactions between the ions, we have found that there are certain differences between them, some of which are quite fundamental in nature. Moreover, of the current phenomenological models, the deformable-shell model alone is capable of reasonably treating both the static and the dynamic properties of the crystals. Hence it is important to know the results of the calculation according to different models. In this work we present the lattice-dynamic calculation on the following five crystals, NaCl, NaBr, KI, KCl, and KBr according to the deformable-shell model. In order to obtain the parameters, the well-known macroscopic quantities have been used and no least-square-fitting procedure has been adoped. The parameters obtained from the theory have been used to calculate the phonon dispersion relation in both the symmetry and the off-symmetry directions (where experimental results are available) and the variation of the Debye temperature from the frequency spectra for these crystals. We have consistently used the polarizable negative-ion model for all of them. The results thus obtained agree well with experiment. Other theoretical-model results are also discussed in detail.