Collective Excitations in Crystals Composed of Disparate Mass Particles

The calculated structure factor of a disordered fcc crystal formed by a disparate-mass mixture shows at low wave vectors ( $k$) a broad high-frequency band in addition to hydrodynamic phonons. The former shows a pronounced $k$ dependence. The average phase velocity of such excitations is lower than that of the longitudinal sound in a crystal of light particles. At larger $k$, the hydrodynamic frequencies decrease with increasing $k$, well below the linear dispersion regime, and finally disappear. The findings are rationalized on the basis of a “two-solid model.”