Artificial boundary conditions for atomic simulations of face-centered-cubic lattice

摘要

We design a class of matching boundary conditions for atomic simulations of the face-centered-cubic lattice. Such a condition takes the form of a linear constraint for atoms near the boundary. A normal matching boundary condition is obtained by matching the dispersion relation in the long wave limit. A two-angle matching boundary condition is constructed through operator multiplication with the help of apparent wave propagation. The edge atoms and the corner atoms are treated in a consistent manner. Reflection coefficient analysis and wave-packet tests verify the effectiveness of the proposed boundary conditions for general incidence, not limited to long waves. The treatment is local in both space and time, yielding negligible additional numerical cost. Vector wave formulation is also presented, and applied to nanoindentation simulations.