Potential Functions and the Simulation of Defects in Lattice Dynamical Defect Problems

Abstract

The use of interatomic potential functions in the study of lattice dynamical defect problems has some differences from their use in other types of defect problems. In general, only the second derivatives of the potential function evaluated at the equilibrium separation between atoms in a crystal (the atomic force constants) are required. The latter can certainly be determined once an interatomic potential function is known, but can sometimes be determined indirectly without recourse to an assumed analytic expression for the potential function. For many substitutional impurities the potential of interaction between the atom or ion and the atoms of the host crystal is not known ab initio, and the atomic force constants have to be determined from experiment. In such cases the restrictions imposed on the force constants by the invariance and transformation properties of the force on an atom under infinitesimal, rigid-body translations and rotations of the crystal, as well as by the point symmetry of the defect site, can reduce considerably the number of independent, nonzero force constants that have to be determined. These conditions are described and their importance for a correct description of the dynamical properties of lattice defects is illustrated by applications drawn from the study of isolated point defects and of extended defects such as crystal surfaces. Finally, the results of attempts at first-principles calculations of the interactions between substitutional defects and the host crystal, in ionic crystals and in metals, are summarized and commented upon.