Anharmonic analysis of defective crystals with many-body interactions using symmetry reduction

In this paper we first classify and formulate various types of defects with respect to their symmetries and then show that with this general formulation, one can study the structures and energetics of defects in different crystalline materials effectively. We present all the calculations for the embedded-atom-type potentials but the formulation can, in principle, be applied for any many-body interatomic potential. As examples of defects in crystals with many-body interactions, we study point defects, free surfaces and grain boundaries in fcc Cu and grain boundaries in NiAl. We discuss free surface modelling by relaxing both a semi-infinite lattice and a slab with increasing finite thickness. We demonstrate through several numerical examples that our general framework of anharmonic lattice statics can be used for comparing different interatomic potentials in terms of the structure and energy they predict for a given defect. In the case of fcc Cu, we show how both the structures and energetics of different defects can strongly depend on the choice of potentials.