Lattice relaxation in high-temperature pure crystalline materials and substitutionally disordered alloys. II. Self-consistent treatment of distortion and related problems

Using the formalism of the Korringa-Kohn-Rostoker method in conjunction with the coherent-potential approximation (KKR-CPA) for treating substitutional disorder and the embedded-cluster method, we describe the scattering from single displaced atoms and clusters of displaced atoms embedded in an effective medium. By means of a distribution function this approach leads to a self-consistent treatment of lattice relaxation. Introducing a supermatrix formulation for the KKR-CPA method and using the concept of the renormalized interactor allows us to reformulate the diagonal and off-diagonal elements of the Green function such that (i) impurities or clusters of impurities in an effective medium, displaced or not, can be treated properly and (ii) Bloch spectral functions can be obtained with no further assumptions beyond the level of the KKR CPA. The proposed method, for example, covers the case of lattice relaxation for pure matter at elevated temperatures and treats properly the effects of short-range order in substitutionally disordered materials. In general, it provides a solution to the problem of embedding impurities in pure materials or alloys describable within the muffin-tin approximation for the crystal potential.