Contribution to the Many Site Theory of the Disordered System

Abstract

The extension of the single site CPA to the many site approximation is investigated in the cellular disordered crystal. The crystal is divided into cells and considered as if it were a ‘molecular crystal’ composed of the cells. The single site CPA is applied to this ‘mixed molecular crystal.’ The three types of the coherent potentials; A) the cell diagonal, B) the k-dependent, C) the site diagonal coherent potential are proposed and their properties are discussed. The approximation by the cell diagonal coherent potential is shown to be equivalent to the cell method reported previously by the author.
The method of the site diagonal coherent potential is very simple and convenient for the numerical calculation. The phonon spectrum of the isotopically disordered chain is calculated by this method and compared with the result by NFC.