A phase-field model with irradiation-enhanced diffusion for constituent redistribution in U-10wt%Zr metallic fuels

Abstract

Constituent redistribution is a unique phenomenon to metal fuels that threatens the safety of such fuel forms. Therefore, it is imperative to establish models to understand the intrinsic mechanisms and predict the redistribution kinetics. In this work, we derived the conservative field equations of the phase-field model from near-equilibrium thermodynamic theory. A macroscopic constituent redistribution phase-field model was developed by introducing the effect of irradiation on the atom mobility and the effect of temperature on the interface mobility. An expression of phase boundary width, applicable to both microscopic and macroscopic scenarios was proposed. The interfacial parameters of the model and the Zr concentration distribution near the fuel surface were discussed at last. These works may help understand constituent redistribution characteristics and promote the application of the phase-field method in studying constituent redistribution in macroscopic scenarios.

Modeling of Zirconium Atom Redistribution and Phase Transformation Coupling Behaviors in U-10Zr-Based Helical Cruciform Fuel Rods under Irradiation

“…( ) g γ γ = − ; f αβ denotes the bulk free energy density function for the phases of α and β [32]; f γ is the bulk free energy density for the γ phase [32]. Similar as that in Ref.…”

“…In Ref. [32], some other material parameters were also adjusted to reflect the influences of irradiation swelling and microstructure variation. In this study, different adjustment factors are also employed to the thermal conductivities of integration points, as pointed out in Section 3.…”

“…Essentially, the non-homogeneous temperature field is the dominant driving force in initiating the subsequent coupling behaviors. Consequently, the transient temperature field is simultaneously modeled in this study, which is different from the treatment in some references that use an unvaried radial temperature distribution [32].…”

“…The DP-81 pin geometry, power, and surface temperature data are taken from Hofman et al [12], with an initial radius of 2.17 mm and a linear power of 24 kW/m. The possible outer surface temperatures range from 890 K to 916 K [43], and an outer surface temperature of 900 K is considered in this study, similar to those in some other references [30,32]. Due to the fact of Zr atom redistribution during irradiation, the thermal conductivity model related to temperature and Zr atom concentration is used [18].…”

“…Nevertheless, the Zr atom interdiffusion coefficients were generally scaled up by a certain number of times to match the experimental data. Wen et al [32] perceived that the strong irradiation effects caused by the fission fragments should be responsible for this enhancement. So far, a quantitative relationship of the Zr atom diffusion coefficient with the fuel fission rate is absent.…”