Recovering thermodynamic consistency of the antitrapping model: a variational phase-field formulation for alloy solidification.

The phenomenological antitrapping phase-field model has attained much success in describing alloy solidification. The heuristically introduced antitrapping current enables removing artificial effects due to the use of large interfacial width. Nevertheless, such a model is not thermodynamically consistent and has not been fitted into a variational framework. Here we present two approaches to develop a variational phase-field model to describe patten formation in alloys. Following the principles of linear irreversible thermodynamics we build in the cross-coupling between the phase transition rate and solute diffusion current. Our formulation not only naturally incorporates the antitrapping current but also predicts the conjugated mesoscopic solute drag effect. A more general form of the antitrapping current is obtained by thin-interface analysis. Benchmark simulations on isothermal dendrite growth are carried out to show the capability of our model to quantitatively characterize the interface evolution and solute profile even with a large interface width used. Importantly, our theory also provides general insights on how to obtain the genuine dynamic coupling between nonconserved and conserved order parameters. This leads to a thermodynamically consistent generalization of the celebrated model C proposed by Hohenberg and Halperin [Rev. Mod. Phys. 49, 435 (1977)].