Solute Trapping and Solute Drag in a Phase-Field Model of Rapid Solidification

Published

September 1, 1998

Author(s)

N A. Ahmad, A A. Wheeler, William J. Boettinger, Geoffrey B. McFadden

Abstract

During rapid solidification, solute may be incorporated into the solid phase at a concentration significantly different than that predicted by equilibrium thermodynamics. This process, known as solute trapping, leads to a progressive reduction in the concentration change across the interface as the solidification rate increases. Theoretical treatments of rapid solidification using traditional sharp-interface descriptions require the introduction of separately-derived non-equilibrium models for the behavior of the interfacial temperature and solute concentrations. In contrast, phase-field models employ a diffuse-interface description, and eliminate the need to specify interfacial conditions separately. While at low solidification rates equilibrium behavior is recovered, at high solidification rates non-equilibrium effects naturally emerge from these models. In particular, in a previous study we proposed a phase-field model of a binary alloy [Wheeler et al. Phys. Rev. E (1993) 1893] in which we demonstrated solute trapping. Here we show that solute trapping is also possible in a simpler diffuse interface model. We show that solute trapping occurs when the solute diffusion length D₁IV is comparable to the diffuse interface thickness. Here V is the interface velocity and D₁ characterizes the solute diffusivity in the interfacial region. We characterize the dependence of the critical speed for solute trapping on the equilibrium partition coeffiient k_E that shows good agreement with experiments by Aziz and co-workers [see M.J. Aziz, Metall. Mater, Trans. A 27, 671 (1996)]. We also show that in the phase-field model, there is a dissipation of energy in the interface region resulting in a solute drag, which we quantify by determining the relationship between the interface temperature and velocity.

Citation

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

Volume

58

Issue

No. 3

Pub Type

Journals

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Keywords

binary alloy, nonequilibrium thermodynamics, phase-field model, rapid solidification, solute trapping

Citation

Ahmad, N. , Wheeler, A. , Boettinger, W. and McFadden, G. (1998), Solute Trapping and Solute Drag in a Phase-Field Model of Rapid Solidification, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150730 (Accessed April 26, 2024)