Inclusion of force constant and mass disorder in a self-consistent theory of phonons in high concentration alloys

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Abstract
Various correlation functions appearing in the theory of vibrating substitutional alloys with an arbitrary concentration of defects, including mass disorder as well as force-constant changes are calculated. The force-constant matrix is chosen such that the formalism of the locator-CPA can be applied to calculate the configuration averages. In order to make sure that the infinitesimal translational invariance is not violated by the averaging procedure, it is necessary to incorporate this requirement into the self-consistent equations. In the limiting case of mass defects only known results are thus rederived from another point of view. Numerical results are shown which demonstrate the effect of force-constant changes on the frequency spectrum and on the shifts and widths of phonon frequencies.