A theory of vibrations of solid solutions with inclusion of the cluster effects: Non-self-consistent and self-consistent approximations

A theory of vibrational spectra of solid solutions proposed by the author has been developed, in which a cluster of n cells statistically filled with impurity atoms is used as a phonon scattering unit. The calculation of vibrational 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 = 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 (in real crystals, it is damping due to anharmonicity). The spectrum has also been calculated in the generalized self-consistent approximation. This calculation gives a smeared structureless curve, which absolutely does not agree either with the theoretical calculation in the non-self-consistent approximation or with the results obtained by Dean. This means that the generalized self-consistent approximation overestimates the weight of the incoherent scattering processes, which leads to averaging of the phases. The spectrum of a three-dimensional solid solution is calculated using a simple model of the crystal.