Thermodynamics of Non-equilibrium Diffuse-Interfaces in Mesoscale Phase Transformations

We present a new phase-field formulation for the non-equilibrium interface kinetics. The diffuse interface is considered an integral of numerous representative volume elements (RVEs), in which there is a two-phase mixture with two conserved and two non-conserved concentration fields. This particular way of separating concentration fields leads to two distinct dissipative processes besides the phase boundary migration, i.e., trans-sharp-interface diffusion between different phases within a single RVE and trans-diffuse-interface diffusion between different RVEs within a single phase. A two-part mechanism is proposed to balance the driving forces and energy dissipation for diffusionless and diffusional processes in RVEs. Moreover, the classical interface friction and solute drag can be recovered by integrating the diffuse interface. Compared with the sharp interface theory, the present diffuse interface can reproduce the atomic simulated partial-drag self-consistently in thermodynamics.
Comment: We hope this model can generalize the previous sharp and diffuse interface models (i.e., M.Hillert's dissipation treatment and J.W. Cahn and M. Hillert's solute drag treaments) for mesoscale phase transformations such as solid-state transformation and solidification. Also, the present phase-field model may provide a new tool for far-from-equilibrium microstructural patten formations