Self-consistent theory of anharmonic crystals containing substitutional impurities

A simple model-linear chain- of an anharmonic crystal containing substitutional impurities has been studied on the basis of the nonsymmetrized self-consistent field method. Lattice relaxation near the impurity, mean-square displacement of atoms, as well as third- and fourth-order moments of single-particle probability densities have been calculated. A formula has been obtained for the change of the free energy upon substitution of an intrinsic chain atom by an impurity atom. All the quantities have been expressed via the derivatives of interatomic potentials; this permitted explicit specification of the role of anharmonic effects. © 1987 Plenum Publishing Corporation.