Tests of the Polymorphous Coherent Potential Approximation

Abstract

The coherent potential approximation (CPA) is a powerful mathematical technique for approximating the electronic structure of substitutional solid solution alloys. Most applications of the CPA to date have assumed an isomorphous model of the alloy in which all of the A atoms are assumed to be the same, as are all of the B atoms. The derivation of self-consistent potentials for the alloys within the framework of the CPA and the isomorphous model leads inevitably to the conclusion that the Madelung potential at each site must be zero. The approximate theory resulting from this derivation is called the KKR-CPA. The polymorphous CPA (PCPA) makes use of supercells that contain many atoms, and the Madelung potentials at all of the sites are calculated exactly. PCPA calculations produce a polymorphous alloy model in which every atom in the supercell is different. Tests will be shown that demonstrate the advantages of the PCPA over the KKR-CPA in explaining experiments that depend critically on the charge transfer in an alloy.