Temperature-dependent interatomic forces

Abstract

A method of optimizing the thermally averaged structure of a defect in a crystal at a finite temperature is presented. The basic idea is to augment the interatomic forces that apply at OK with temperature-dependent contributions that arise from the minimization of the free energy at a finite temperature. The structure and thermodynamic properties of the defect can then be obtained with a molecular statics program. The free energy is expressed within the harmonic approximation, but since the interatomic potential at O K is anharmonic, there is an additional temperature-dependent force arising from the vibrational free energy. The same term gives rise to the thermal expansion of the perfect crystal. A second-moment approximation is applied to the phonon local density of states. Projections of thermodynamic functions onto individual atomic sites are then expressed analytically. When the vibrational free energy is differentiated, the resulting force is N-body in nature even for a pairwise interatomic potential. The second-moment approximation is tested by comparing Grüneisen constants for Finnis-Sinclair transition-metal potentials computed according to this scheme with those recently computed using full quasi-harmonic theory. Finally the structure and thermodynamic excess properties of a [Sgrave]= 13, (001) twist boundary are computed and compared with recent experimental data for Au.