Quantitative phase-field model of alloy solidification

Blas Echebarria, Roger Folch, Alain Karma, and Mathis Plapp
Phys. Rev. E 70, 061604 – Published 17 December 2004

Abstract

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 [A. Karma, 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 [R. F. Almgren, 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 [A. Karma and W.-J. Rappel, 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.

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  • Received 7 April 2004

DOI:https://doi.org/10.1103/PhysRevE.70.061604

©2004 American Physical Society

Authors & Affiliations

Blas Echebarria*

  • Physics Department and Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, Massachusetts 02115, USA and Laboratoire de Physique Statistique, Ecole Normale Supérieure, Paris, France

Roger Folch

  • Instituut-Lorentz, Universiteit Leiden, Postbus 9506, 2300 RA Leiden, The Netherlands

Alain Karma

  • Physics Department and Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, Massachusetts 02115, USA

Mathis Plapp

  • Laboratoire de Physique de la Matière Condensée, CNRS/Ecole Polytechnique, 91128 Palaiseau, France

  • *Permanent address: Departament de Física Aplicada, Universitat Politècnica de Catalunya, Barcelona, Spain.

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Vol. 70, Iss. 6 — December 2004

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