A simple numerical approach for reconstructing the atomic stresses at grain boundaries from quantum-mechanical calculations.

The atomistic stress state at a metal grain boundary is an intrinsic attribute which affects many physical and mechanical properties of the metal. While the virial stress is an accepted measure of the atomistic stress in molecular dynamics simulations, an equivalent definition is not well-established for quantum-mechanical density functional theory (DFT) calculations. Here, we introduce a numerical technique, termed the sequential atom removal (SAR) approach, to reconstruct the atomic stresses near a symmetrical-tilt Σ5(310)[001] Cu grain boundary. In the SAR approach, individual atoms near the boundary are sequentially removed to compute the pair (reaction) force between atoms, while correcting for changes to the local electron density caused by atom removal. We show that this SAR approach accurately reproduces the spatially-varying virial stresses at a grain boundary governed by an embedded atom method potential. The SAR approach is subsequently used to extract the atomistic stresses of the grain boundary from DFT calculations, from which we reconstruct a continuum-equivalent grain boundary traction distribution as a quantitative descriptor of the grain boundary atomic structure.