Theory of Random Alloy Vibrations with Account for Cluster Effects

V. S. Vinogradov

《Chinese Journal of Physics》 49卷1期 (2011/02) Pp. 420-428

並列摘要

A theory of vibration spectra of solid solutions has been developed. In this theory, a cluster of n cells statistically filled with impurity atoms is used as a phonon scattering unit. The calculation of vibration spectra of a disordered linear chain in the generalized non-self-consistent approximation has demonstrated a strong dependence of the spectrum on the number n for n≤4. For n=6, the calculated spectrum is in an excellent agreement with the result of the computer experiment performed by Dean for a chain of 8000 atoms. The maximum number of impurities in the cluster to be considered depends on the magnitude of the initial damping (due to anharmonicity). The spectrum of the linear chain has also been calculated in the usual and generalized self-consistent approximation. These calculations give smeared structureless curves, which absolutely does not agree either with the theoretical calculation in the non-self-consistent approximation or with the results obtained by Dean. This failure is related to the mean-field properties of self-consistent theories. The spectrum of a three-dimensional solid solution is calculated using a simple model of the crystal.