Discrete lattice models of point defects

The calculation of point defect properties using discrete lattice models is reviewed. Particular attention is given to the distortion field around a point defect and the interaction between point defect pairs. Both real space and reciprocal space methods are considered. There are two direct space approaches commonly used: one involves the direct minimization, with respect to the lattice displacements, of the total energy of N atoms interacting via a pairwise potential phi(r); alternatively the crystal symmetry may be exploited by group theory procedures if the Defect Green's function method is used. This method is based on the Born-von-Karman model of a lattice and uses the zero frequency limit of the phonon Green's function which gives the static response of the defect lattice to an applied force. The reciprocal space approach (the Kanzaki method) is based on the Fourier transformation of the real space equilibrium equations; this results in a set of decoupled equations which can be explicitly solved for the Fourier amplitudes of the displacement field which may then be found by Fourier inversion. The equivalence of the Defect Green's function and Kanzaki methods is demonstrated and it is shown that they reduce to the equivalent elasticity result in the asymptotic, small wave vector, limit. Specific numerical results for the displacement fields and relaxation volumes of vacancies and interstitials and the interaction of point defect pairs in copper, aluminium, iron and molybdenum are discussed. (author)