Multi-cell Monte Carlo as a Gibbs Ensemble approach for solid-state phase prediction

Our recently introduced Multi-Cell Monte-Carlo (MC)^2 algorithm is compared against the Gibbs Ensemble MC approach. (MC)^2 can determine phase boundaries in solid mixtures by imposing the lever-rule, and now additionally, common tangent constraints. The adaption of Gibbs Ensemble MC to crystalline solids has been elusive until now because particle transfer between crystalline cells creates highly energetic point defects. We show that (MC)^2 is in fact the solid-state version of the Gibbs Ensemble, where this restriction is overcome by introducing a lever-rule weighted over multiple cells, representing different phases. We also present the addition of a predictor-corrector scheme that ensures equilibrium by tracking the change in chemical potentials. As a proof of concept the method is applied to solid-solid phases in binaries showing a miscibility gap, and the method is also used to probe the stability of a model quaternary alloy.