Recovering thermodynamic consistency of the antitrapping model: A variational phase-field formulation for alloy solidification
Abstract
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.0034-686110.1103/RevModPhys.49.435 49, 435 (1977)].
- Publication:
-
Physical Review E
- Pub Date:
- January 2013
- DOI:
- 10.1103/PhysRevE.87.012402
- Bibcode:
- 2013PhRvE..87a2402F
- Keywords:
-
- 81.10.Aj;
- 64.70.dg;
- 89.75.Kd;
- Theory and models of crystal growth;
- physics of crystal growth crystal morphology and orientation;
- Crystallization of specific substances;
- Patterns