Thermodynamic properties of phase-field models for grain boundary segregation

GB energy changes with the matrix composition in various phase-field models and the classical two-phase model for grain boundary segregation. The black, blue and red solid curves are the GB energies for α = 2, 3 and 4, respectively. Solid lines, dashed lines and dotted lines represent the GB energy changes from model II, model I and classical two-phase model, respectively.154