Linearization-based method for solving a multicomponent diffusion phase-field model with arbitrary solution thermodynamics

This article describes a phase-field model for an isothermal multicomponent, multiphase system which avoids implicit interfacial energy contributions by starting from a grand potential formulation. A method is developed for incorporating arbitrary forms of the equilibrium thermodynamic potentials in all phases to determine an explicit relationship between chemical potentials and species concentrations. The model incorporates variable densities between adjacent phases, defect migration, and dependence of internal pressure on object dimensions ranging from the macro- to nanoscale. A demonstrative simulation of an overpressurized nanoscopic intragranular bubble in nuclear fuel migrating to a grain boundary under kinetically limited vacancy diffusion is shown.

Figure 1

Validation of model by comparison between simulation results and the Young-Laplace theory assuming $P^{gas,0}=0$.

Figure 2

Concentration of species 1 and 2 in the system for different equilibrium bubble sizes normalized to the density of 1 in the liquid. The bubble is on the left of the step variation in concentrations. The concentration of 2 in the bubble rises as the pressure and density increase.

Figure 3

Concentration of species 2 normalized to the density of 1 in the liquid in the system for different equilibrium bubble sizes. The one-parameter Margules equation is used in order to restrict the amount of 2 that can exist in the liquid phase, as comparable to Fig. 2. The bubble is on the left of the step variations in concentration.

Figure 4

The partition coefficients of species 2 with and without the Margules equation. The partition coefficient is able to vary as a function of bubble size.

Figure 5

Snapshots of the time evolution of the intragranular bubble migrating and merging with the grain boundary, colored according to pressure. The simulation is azimuthally symmetric about the bottom boundary.

Figure 6

Pressure along the central axis in Fig. 5. The upwards variation indicates the pressure in the bubble, which begins approximately at the intragranular bubble pressure and then evolves to the intergranular pressure as it meets the grain boundary.