CALPHAD-informed phase-field modelling of non-stoichiometric oxide nuclear fuel at very high temperatures, Part II: Thermodynamic closures and numerical application to incipient melting of oxidized fuel

This paper focuses on a two-phase multicomponent phase-field model used for investigating the behaviour of non-stoichiometric oxide nuclear fuels under high temperatures and large temperature gradients. Particular attention is devoted to the thermodynamic closures of the model and to the efficient coupling between phase-field simulations and computational thermodynamics. The liquid–solid interface is described using a non-isothermal linearization of the Kim–Kim–Suzuki model, enabling an efficient treatment of multicomponent systems. The capability and robustness of the proposed model are demonstrated through simulations of incipient melting in a fictitious oxidized fuel, considering both the U-Pu-O ternary system and the U-Pu-O-Gd-Ce quinary system. The computational thermodynamics relies on the OpenCalphad Gibbs Energy Minimizer with the thermodynamic description provided by the Thermodynamics for Advanced Fuels-International Database (TAF-ID). Although the results demonstrate the capability and the robustness of the approach, they also reveal a significant limitation in terms of computational cost associated with the large number of thermodynamic equilibrium calculations. To overcome this limitation, deep feedforward neural networks are developed as computationally efficient surrogates for OpenCalphad. When applied to three-dimensional incipient melting problems, the surrogate reduces the cost of thermodynamic calculations from approximately 50% to approximately 3% of the total solving time while keeping relative L 2 errors below 1% on all major state variables over the full transient and completely eliminating load imbalance caused by CALPHAD calculations. This work provides a foundation for future validation of the proposed CALPHAD-informed phase-field model for studying nuclear fuel behaviour at high temperatures in an industrially relevant system.