Theory of Vibrational Excitations in a Solid Solution with the Inclusion of Their Scattering by Multi-Impurity Clusters

Abstract

A theory of vibrational excitations in a solid solution is proposed. This theory allows for scattering of excitations by multi-impurity clusters and offers an adequate description of the complex spectra of the solid solution. The main feature of the theory is that the averaging and the Fourier transformation with respect to the coordinate of the impurity cluster as a whole are performed at the first stage, whereas the averaging over the distances between impurities in the cluster is carried out at the final stage. The calculations are performed in the approximation similar to the average t-matrix approximation and also the coherent-potential approximation. The theory is illustrated by calculating the spectra and dielectric functions of disordered linear chains with one and two atoms per unit cell. The calculated vibrational spectra are in good agreement with the computer calculations performed by Dean.