Phase-field simulation of diffusion couples with an augmented multi-phase-field approach
Diffusion couple experiments are effective tools in investigation of alloy thermodynamics and kinetics, but their advantages can be counter balanced by the overlap of different mechanisms. Thus, computer simulations are appropriate underlying tools to investigate them. Among various computer simulations, the so-called multi-phase-field (MPF) is the most appropriate choice, which can be applicable to an arbitrary number of different phases or grains. However, the condition of equal diffusion potential or a so-called quasi-equilibrium condition (shown in Fig. 1(a)) assumed in the current MPF model is contradict to the fact that the initial states are usually off-equilibrium (see Fig. 1(b)) in real diffusion couples. Moreover, the couple of phase-field model to real CALPHAD (CALculation of PHAse Diagram) thermodynamic and kinetic databases is a prerequisite for quantitative simulations of diffusion couples. But the currently available ways linking to CALPHAD databases are unsatisfactory. Furthermore, the contribution of grain boundary diffusion and vacancy diffusion is also important for the diffusion couples with numbers of grains at low temperatures.
Aiming to achieve the above goals, an augmented general MPF model is to be developed in the present work, and it will include (i) a new approach to replace the quasi-equilibrium constraint; (ii) a new method linking to the CALPHAD database; and (iii) incorporation of the grain boundary and vacancy diffusion. The new approach to replace the quasi-equilibrium constraint in the present augmented MPF model is to assume a finite relaxation kinetic for the compositions at the interface. For the new method linking to the CALPHAD database, the concept of sublattice element concentration is introduced to substitute the element concentration. As for the order/disorder transition, a strategy to define a hypothetical disorder phase is utilized. The way to combine the grain boundary diffusion and vacancy diffusion when studying the grain growth in nanocrystalline material by Steinbach is employed here. The presently developed MPF model was applied in the technologically important ternary Al-Fe-Ni system, and the simulated results are also comprehensively compared with the experimental ones and the 1D DICTRA simulated ones.