Computing grain boundary “phase” diagrams

Grain boundaries (GBs) can be treated as two-dimensional (2-D) interfacial phases (also called “complexions”) that can undergo interfacial phase-like transitions. As bulk phase diagrams and calculation of phase diagram (CALPHAD) methods serve as a foundation for modern materials science, we propose to extend them to GBs to have equally significant impacts. This perspective article reviews a series of studies to compute the GB counterparts to bulk phase diagrams. First, a phenomenological interfacial thermodynamic model was developed to construct GB lambda diagrams to forecast high-temperature GB disordering and related trends in sintering and other properties for both metallic and ceramic materials. In parallel, an Ising-type lattice statistical thermodynamic model was utilized to construct GB adsorption (segregation) diagrams, which predicted first-order GB adsorption transitions and critical phenomena. These two simplified thermodynamic models emphasize the GB structural (disordering) and chemical (adsorption) aspects, respectively. Subsequently, hybrid Monte Carlo and molecular dynamics atomistic simulations were used to compute more rigorous and accurate GB “phase” diagrams. Computed GB diagrams of thermodynamic and structural properties were further extended to include mechanical properties. Moreover, machine learning algorithms were combined with atomistic simulations to predict GB properties as functions of four independent compositional variables and temperature in a 5-D space for a given GB in high-entropy alloys or as functions of five GB macroscopic (crystallographic) degrees of freedom plus temperature and composition for a binary alloy in a 7-D space. Other relevant studies are also examined. Future perspective and outlook, including two emerging fields of high-entropy grain boundaries (HEGBs) and electrically (or electrochemically) induced GB transitions, are discussed.