General Method for Determining Lattice Point Defect Configurations Including their Dependence on Electron Redistribution

Abstract

A general method is proposed for determining the equilibrium configurations of single lattice point defects and complexes thereof. The equilibrium configuration of the lattice containing impurities, interstitials, and vacancies is determined by using a variational approach minimizing the energy of the crystal. The energy of the crystal is explicitly expressed in terms of the displacements of the ions. It is assumed that the energy of the system of ions, including the point defects, arises from two-body interactions. The energy of the system of valence or conduction electrons is derived in the general form from a Hamiltonian including the coupling between the distorted lattice and the electrons. The wave functions of the valence or conduction electrons are given by an integral equation derived from the Hartree-Fock equation. The explicit dependence of the wave functions on the displacements of the ions is obtained from the integral equation by using the Born approximation. Using these wave functions the energy of the considered system of electrons is explicitly expressed in terms of the displacements. To apply the method in practice the wave functions and the crystal energy need to be evaluated explicitly.