Quantitative phase-field model of alloy solidification.

By B. Echebarria, R. Folch, Alain Karma, Mathis Plapp. Physical review. E, Statistical, nonlinear, and soft matter physics, 2004

668 citations recorded by the source corpus.

We present a detailed derivation and thin interface analysis of a phase-field model that can accurately simulate microstructural pattern formation for low-speed directional solidification of a dilute binary alloy. This advance with respect to previous phase-field models is achieved by the addition of a phenomenological "antitrapping" solute current in the mass conservation relation [Phys. Rev. Lett. 87, 115701 (2001)]]. This antitrapping current counterbalances the physical, albeit artificially large, solute trapping effect generated when a mesoscopic interface thickness is used to simulate the interface evolution on experimental length and time scales. Furthermore, it provides additional freedom in the model to suppress other spurious effects that scale with this thickness when the diffusivity is unequal in solid and liquid [SIAM J. Appl. Math. 59, 2086 (1999)]], which include surface diffusion and a curvature correction to the Stefan condition. This freedom can also be exploited to make the kinetic undercooling of the interface arbitrarily small even for mesoscopic values of both the interface thickness and the phase-field relaxation time, as for the solidification of pure melts [Phys. Rev. E 53, R3017 (1996)]]. The performance of the model is demonstrated by calculating accurately within a phase-field approach the Mullins-Sekerka stability spectrum of a planar interface and nonlinear cellular shapes for realistic alloy parameters and growth conditions.

Subfields: Aerospace Engineering, Atmospheric Science, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/12cf732d41d488cd54072655c56365d44941c740

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Citations in the corpus

Finite interface dissipation phase field modeling of Ni–Nb under additive manufacturing conditions (2019, methodology): “This approach has been widely adopted in the literature to model directional solidification [27, 62].”
Phase-field models in materials science (2009, methodology): “The derivation is only sketched here and the reader is referred to the original literature [1, 42, 43, 44].”
The phase field technique for modeling multiphase materials (2008, methodology): “A rigorous derivation of the model and a thin interface analysis was presented by Echebarria et al [119].”
Sharp interface tracking using the phase-field equation (2007, methodology): “For the Laplacian of the phase field, a 9-point finite-difference stencil commonly used in phase-field simulations [37,53] is adopted, i.”
An introduction to phase-field modeling of microstructure evolution (2008, methodology): “To overcome the artificial effects caused by a difference in diffusion coefficient on both sides of the interface, the thin-interface matching was combined with a non-variational9 anti-trapping current in the equation for mass conservation that counterbalances for the solute trapped at the artificia”