Green's function boundary conditions in two-dimensional and three-dimensional atomistic simulations of dislocations

A method for dynamically updating the boundary conditions of atomistic simulations is presented. The lattice Green's function boundary relaxation method, originally introduced by Sinclair et al. in 1978, is extended to treat three-dimensional (3D) simulations. The boundary conditions for two-dimensional (2D) and 3D defect cells are evaluated using line and point force distributions respectively. The method is general and has been incorporated into several potential interaction schemes. Examples of the method using embedded-atom method potentials are presented for the following: simulation of a straight (a/2)[110] screw dislocation in Ni; an isolated a(001) kink on an (a/2)[111] screw dislocation in bcc Fe; simulation of a periodic array of a(001) kinks on an (a/2)[111] screw dislocation in bcc Fe. The first simulation is 2D in nature and the last two defects are 3D.