Modeling vacancy-induced porosity in compositionally-graded complex alloys

A phase-field model of the void evolution is developed to investigate the vacancy-induced Kirkendall porosity within diffusion couples under isothermal annealing conditions. This model encapsulates a comprehensive computational framework for multicomponent diffusion, non-equilibrium vacancy diffusion, voids nucleation, and growth - integrating considerations for surface anisotropy and morphological instability. This novel thermodynamically consistent methodology combines the phase-field model with the vacancy diffusion model and uses thermodynamic and atomic mobility parameters defined by CALPHAD approach. The generalized nature of the method enables us to include both non-equilibrium and equilibrium vacancies, covering all cases of non-ideal/ideal sinks and sources for vacancies, whether at dislocations or void surfaces. Moreover, the model can deal with compositionally complex alloys such as Ni-based superalloys. Along with the full model, a fast variant is also suggested, providing long-time simulations at the experimentally relevant time and space scales valuable for both academic and industrial contexts. The model’s efficacy was demonstrated through precise simulation of voids evolution in a model AlCoCrTa/Ni diffusion couple, mirroring the experimental outcomes observed in the CMSX-10/Ni diffusion couple at 1525 K after 192 h of annealing. This encompassed accurate replication of diffusion profiles and tomographic analysis of voids. A very good agreement with the experimental data was observed, particularly in the distribution of pore volume-fractions and the delineation of void shapes.