Development and verification of a phase-field model for the equilibrium thermodynamics of U-Pu-Zr

Abstract

U-Pu-Zr is a promising metallic fuel candidate. However, fuel selection and qualification will require the ability to accurately predict its behavior. Unfortunately, the system’s complex phase behaviors promote formation of heterogeneities that cannot be adequately described using bulk properties. This work presents an equilibrium phase-field model capable of resolving these heterogeneities spatially so that their effects on reactor safety and fuel performance can be understood and predicted. Development of the twelve-phase model is presented beginning with derivation of its CALPHAD free energies. Verification tests show that the model predicts the equilibrium concentrations and overall phase fractions of stable mixtures consistent with analytical methods. Additional assessments show that the model predicts phase transition temperatures with reasonable accuracy. The model is shown to resolve heterogeneities in ternary alloys that could affect composition-dependent properties like neutron cross-sections, thermal conductivities, and melting temperatures. Finally, the model is used to demonstrate that equilibrium thermodynamics has a significant role in constituent redistribution by modeling the formation of radial zones in the presence of a temperature gradient. These zones are qualitatively consistent with those exhibited by EBR-II Fuel Element T179, but results indicate that at least one other significant mechanism must be taken into account to model these behaviors. Overall, the model shows promise and will serve as a thermodynamic foundation onto which more sophisticated models will be built.