Lattice relaxation in high-temperature pure crystalline materials and substitutionally disordered alloys. I. Multiple-scattering formalism for displaced atoms

A unified theory is presented which allows the calculation of the Green function for atoms in solid matter displaced from positions defined by a regular lattice. This theory is based (1) on the construction of Korringa-Kohn-Rostoker (KKR) type structure constants for displaced atoms, and (2) on the quantity termed renormalized interactor, which arises from a reformulation of the well-known KKR theory. It is shown that the concept of the renormalized interactor can be extended to scattering from clusters and also yields the Green function for arbitrarily displaced atoms. The formalism can also be expressed in terms of the T matrix (scattering matrix) of single displaced atoms or of clusters of such atoms. The proposed method can be extended readily to the treatment of displaced atoms in substitutionally disordered alloys or to interstitial impurities in pure metals or alloys.