Ludwig–Soret effect formulated from the grain-boundary-phase model

The Ludwig–Soret effect is a phenomenon wherein thermal diffusion is induced by a temperature gradient. The governing differential equation to explain this phenomenon has been derived phenomenologically based on the Onsager theorem in non-equilibrium thermodynamics. In this study, we applied the grain-boundary-phase (GBP) model to the Ludwig–Soret effect. This model has been originally proposed for calculating the amount of grain boundary segregation in alloys. The flux equation for the thermal diffusion of vacancies was reasonably derived through parallel-tangent construction of the Gibbs energy curves utilized in the GBP model. Moreover, the thermal vacancy diffusion in a pure metal was simulated. The results illustrated that the excess vacancies in the pure metal preferentially moved to the high-temperature region. The direct application of the thermodynamic Gibbs energy parameters in the CALPHAD method is essential to analyze the thermal diffusion phenomenon. Furthermore, the oxygen vacancy diffusion in Zr(O,Va)2 under a considerably large temperature gradient was calculated, and a similar result was obtained, wherein the excess oxygen vacancies moved to the high-temperature region. This finding may explain the rapid atom diffusion observed during the flash sintering process.