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Model for non-equilibrium vacancy diffusion applied to study the Kirkendall effect in high-entropy alloys
The effect of the non-equilibrium vacancy on the Kirkendall porosity formation was studied by means of a developed model of the multi-component diffusion with vacancies (MDV) which includes the intrinsic fluxes with vacancy gradient and non-ideal sources and sinks for vacancies. For this study, the diffusion couple experiments in multi-component alloys were chosen. To handle the case of concentration-dependent equilibrium vacancy concentration, we introduced the interaction parameters between the components and vacancies, which can have strong effects on the equilibrium vacancy concentration in alloys and on thermodynamic factors. The diffusion profiles of components and vacancies were simulated by using thermodynamic and kinetic data. The different intensity of the vacancy annihilation/generation and different initial vacancy distributions were considered. Furthermore, we show that the conventional model of diffusion in multi-component systems is a particular case of the MDV with a specific sink/source term. The conventional model was extended by the vacancy diffusion term, similar to the MDV, which significantly reduces the vacancy gradient and the pore formation near the Matano plane. The numerical results demonstrate that the diffusion profiles of substitutional components slightly depend on the sink/source intensity if the none-zero net flux of substitutional components is not significant and the sources and sinks of vacancies are not sparse, whereas the porosity depends very strongly and correlates with the vacancy distribution. For the simulation of variable equilibrium vacancy concentrations using the MDV, the corresponding interaction parameters related to vacancies are necessary to be included in the thermodynamic assessment.