Lattice Green's function for crystals containing a planar interface

TL;DR

This paper introduces a versatile method to compute lattice Green's functions for planar interfaces in crystals, enabling efficient modeling of defect-interface interactions with flexible boundary conditions.

Contribution

The authors develop a general approach to calculate interfacial Green's functions without assumptions on atomic interactions or orientations, facilitating defect studies in complex interfaces.

Findings

Flexible boundary conditions accurately model screw dislocation interactions with twin boundaries.

The method reduces computational cost by requiring fewer atoms for energy minimization.

Comparison shows improved core structure modeling over fixed boundary conditions.

Abstract

Flexible boundary condition methods couple an isolated defect to a harmonically responding medium through the bulk lattice Green's function; in the case of an interface, interfacial lattice Green's functions. We present a method to compute the lattice Green's function for a planar interface with arbitrary atomic interactions suited for the study of line defect/interface interactions. The interface is coupled to two different semi-infinite bulk regions, and the Green's function for interface-interface, bulk-interface and bulk-bulk interactions are computed individually. The elastic bicrystal Green's function and the bulk lattice Green's function give the interaction between bulk regions. We make use of partial Fourier transforms to treat in-plane periodicity. Direct inversion of the force constant matrix in the partial Fourier space provides the interface terms. The general method makes no assumptions about the atomic interactions or crystal orientations. We simulate a screw dislocation interacting with a $(10\bar{1}2)$ twin boundary in Ti using flexible boundary conditions and compare with traditional fixed boundary conditions results. Flexible boundary conditions give the correct core structure with significantly less atoms required to relax by energy minimization. This highlights the applicability of flexible boundary conditions methods to modeling defect/interface interactions by \textit{ab initio} methods.