Theory of electronic spectra in linear quaternary alloys

The Coherent Potential Approximation (CPA) is generalized to treat the electronic spectra of quaternary alloys of the types k^CyB-^_^ D and A^B-^.j^ CyD-j^ . As a first application of this theory, the electronic spectra for model one dimensional, one-state-per-atom, nearest-neighbor tight binding quaternary alloys of both types have been calculated. Results are presented for such spectra and are compared with exact numerical spectra, obtained for 10,000 atom random chains. The CPA results do not reproduce all of the detailed features of the exact spectra, but do correctly -predict the trends in the spectra with varying compositions x and y.