Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

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



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


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 kE 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.
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
No. 3


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


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], (Accessed June 21, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created August 31, 1998, Updated October 12, 2021