A HARMONIC ANHARMONIC ENERGY PARTITION METHOD FOR LATTICE STATICS COMPUTATIONS

A method of lattice statics analysis is developed. Consideration of an harmonic effects is restricted to finite regions surrounding lattice d efects. All displacements of the crystal are expressed as the effect o f unknown forces applied to a perfect harmonic lattice of infinite ext ent Displacements are related to the unknown applied forces by means o f the Green function of the perfect harmonic lattice, so that equilibr ating forces need only be applied to the anharmonic region. The unknow n forces are determined so as to maximize the complementary energy of the crystal, which yields a lower bound to the potential energy. The m ethod does not require the explicit enforcement of equilibrium or comp atibility conditions across the boundary between the harmonic and anha rmonic regions. The performance of the method is assessed on the basis of selected numerical examples. The rate of convergence of the method with increasing domain size is found to be cubic. This is one or two orders of magnitude faster than rigid boundary methods based on the ha rmonic and continuum solutions, respectively.