Local modes inRb1−cKcalloys: A neutron scattering study

The lattice dynamics of ${\mathrm{Rb}}_{1-c}{\mathrm{K}}_c$ alloys with $c=0.06, 0.18, \mathrm{and} 0.29$ have been investigated by neutron scattering, using crystals grown for the experiment by a modified Bridgman method. Local modes associated with the K atoms are observed which, as $c$ is increased, rise in frequency, increase in intensity and begin to exhibit noticeable dispersion. The local-mode intensity exhibits a strong wave-vector dependence whose form does not change much with $c$. At the zone-boundary point $N$, $\left(\frac{2\pi }{a}\right)(2.5, 2.5, 0)$ in ${\mathrm{Rb}}_{0.71}$ ${\mathrm{K}}_{0.29}$, the local mode is about three times as intense as the band mode. It is apparent that, as $c\to 1$, the local mode must evolve into the band mode of pure K. A substantial broadening of the local mode is also apparent at this wave vector and concentration, probably indicating the presence of local environment effects. We compare our results with coherent-potential-approximation calculations, both with and without inclusion of force-constant disorder. The calculations, carried out by Mostoller and Kaplan, and independently by Grünewald and Scharnberg, indicate a softening in the nearest-neighbor Rb-K force constants of about 15% relative to the Rb-Rb force constants. We also compare our results with molecular-dynamics calculations by Jacucci, Klein, and Taylor.