Phonon dispersion inK0.5Rb0.5Cl and KCl0.5Br0.5mixed crystals

Phonon dispersion relations in ${\mathrm{K}}_{0.5}$ ${\mathrm{Rb}}_{0.5}$Cl and K${\mathrm{Cl}}_{0.5}$ ${\mathrm{Br}}_{0.5}$ have been measured by coherent inelastic neutron scattering at 300 K. Some of the acoustic phonons and most of the optical phonons are split and show two peaks of nearly equal weight around the mean position. Both the observed maxima show a similar dispersion against the wave vector. The observed phonon frequencies are generally less than the mean of the respective frequencies in the pure crystals. The phonon data have been analyzed in terms of a generalized shell model. The first-neighbor radial force constants and the effective ionic charge are found to be smaller than the mean value for the pure crystals. The elastic constants evaluated by the shell-model fit to the neutron scattering data for ${\mathrm{K}}_{0.5}$ ${\mathrm{Rb}}_{0.5}$Cl are (${10}^{11}$ dyn/${\mathrm{cm}}^2$)$C_{11}=4.0\mathrm{}\pm 0.1$, $C_{44}=0.54\mathrm{}\pm 0.03$, and $C_{12}=0.8\mathrm{}\pm 0.15$, and for K${\mathrm{Cl}}_{0.5}$ ${\mathrm{Br}}_{0.5}$ are $C_{11}=4.0\mathrm{}\pm 0.1$, $C_{44}=0.59\mathrm{}\pm 0.05$, and $C_{12}=0.8\mathrm{}\pm 0.15$. The values are in agreement with those measured by the sound-echo technique.