An explicit integration approach for predicting the microstructures of multicomponent alloys

Predicting the complex microstructures of practical materials has been a longstanding goal since Gibbs’s pioneering work on predictions for equilibrium of heterogeneous systems. The most promising approach for achieving this goal is integrating Calculation of Phase Diagrams (CALPHAD) with phase-field models. This CALPHAD-coupled phase-field model requires two Gibbs free energy minimisation conditions: equal diffusion potential and internal equilibrium, both grounded in the second law of thermodynamics. However, as implicit functions, these minimisation conditions suffer from the curse of dimensionality when applied to multicomponent systems, which imposes significant constraints on simulation capabilities. Here we propose an approach that incorporates the equal diffusion potential and internal equilibrium conditions into a single explicit function in phase-field equations. In simulations across various practical materials, our model achieved equal diffusion and internal equilibrium conditions. Furthermore, it overcame dimensionality limitations, enabling computations for systems with up to 20 components. Thus, the proposed approach proves highly versatile and efficient, supporting a wide range of practical applications.