Nonlinear lattice parameter–concentration relationship and its role in microstructural evolution of alloys

Elastic interactions are a key driving force in microstructural evolution. While conventional phase-field models typically employ Vegard’s law — assuming a linear dependence of lattice parameters on solute concentration — this approximation breaks down in concentrated alloys, where the relationship becomes inherently nonlinear. In this work, we develop an advanced phase-field model that explicitly incorporates nonlinear elastic interactions by capturing the nonlinear dependence of lattice parameters on concentration. This enhanced formulation reveals that such nonlinearities can substantially alter the equilibrium concentration profiles, leading to more accurate predictions of microstructural behavior.