Thermodynamics of coherent interfaces under mechanical stresses. II. Application to atomistic simulation of grain boundaries

Abstract

The thermodynamic theory of coherent interfaces developed in Part I of this work is applied to grain boundaries (GBs) subject to nonhydrostatic elastic deformations. We derive expressions for the GB free energy as the reversible work of GB formation under stress. We also present a generalized adsorption equation whose differential coefficients define the GB segregation, GB stress tensor, GB excess volume, and GB excess shear. The generalized adsorption equation generates a set of Maxwell relations describing cross effects between different GB properties. The theory is applied to atomistic simulations of a symmetrical tilt GB in Cu and Cu-Ag alloys. Using a combination of molecular dynamics and Monte Carlo methods, we compute a number of GB excess quantities and their dependencies on the applied stresses, temperature and chemical composition in the grains. We also test several Maxwell relations and obtain excellent agreement between the theory and simulations.