How do you calculate solid-liquid equilibrium for crystallization design?

SLE calculation: at equilibrium, component fugacity is equal in solid and liquid phases. For pure solid: x*gamma*exp(-delta_H_fus/R*(1/T - 1/T_m)) = 1, where delta_H_fus is heat of fusion, T_m is melting point. For solid solutions, include solid phase activity coefficient. Eutectic systems: each component crystallizes independently; eutectic point is where solubility curves intersect. Heat capacity difference affects temperature dependence. Applications: crystallization process design (yield, purity, operating conditions), freeze concentration, and pharmaceutical polymorphism. Complications: solid polymorphism, hydrate/solvate formation, and kinetic effects (supersaturation, metastable zones).