Self-Consistent-Field Approximations in Disordered Alloys

The connection between Taylor's recent self-consistent calculations of phonon frequency spectra in disordered alloys and those of Davies and Langer in the usual self-consistent-field approximation is established. It is found that Taylor's results are equivalent to summing the same diagrams summed by Davies and Langer, but with proper compensation against multiple occupancy of sites by defects. The recently developed technique of Elliot, Aiyer, and Leath, which self-consistently adjusts the diagram rules to obtain proper compensation, is used. This method is quite general and clearly can be used for other self-consistent calculations is disordered alloys.