Two-mode behavior of mixed crystals

Abstract

A simple model has been developed to study the phonons in mixed crystals showing either one-mode or two-mode behavior. A nonrandomness parameter $\ensuremath{\beta}$ is introduced to represent the phenomenon of two-mode behavior in mixed systems of the type ${A}_{1\ensuremath{-}x}{B}_{x}C$. When $\ensuremath{\beta}$ is reduced to zero, the model gives one-mode behavior. Though the method developed is general in its application to any structure and any concentration $x$, the calculations have been done for ${\mathrm{K}}_{0.5}$${\mathrm{Rb}}_{0.5}$I, a mixed alkali-halide system, the one which shows two-mode behavior in its class for all concentrations $x$ in the range $0lxl1$. The theoretical results are in good agreement with the experimental ones.