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The phase field technique for modeling multiphase materials
KTH, School of Engineering Sciences (SCI), Mechanics.
2008 (English)In: Reports on progress in physics (Print), ISSN 0034-4885, E-ISSN 1361-6633, Vol. 71, no 10, 106501- p.Article, review/survey (Refereed) Published
Abstract [en]

This paper reviews methods and applications of the phase field technique, one of the fastest growing areas in computational materials science. The phase field method is used as a theory and computational tool for predictions of the evolution of arbitrarily shaped morphologies and complex microstructures in materials. In this method, the interface between two phases (e. g. solid and liquid) is treated as a region of finite width having a gradual variation of different physical quantities, i.e. it is a diffuse interface model. An auxiliary variable, the phase field or order parameter phi((x) over right arrow), is introduced, which distinguishes one phase from the other. Interfaces are identified by the variation of the phase field. We begin with presenting the physical background of the phase field method and give a detailed thermodynamical derivation of the phase field equations. We demonstrate how equilibrium and non-equilibrium physical phenomena at the phase interface are incorporated into the phase field methods. Then we address in detail dendritic and directional solidification of pure and multicomponent alloys, effects of natural convection and forced flow, grain growth, nucleation, solid-solid phase transformation and highlight other applications of the phase field methods. In particular, we review the novel phase field crystal model, which combines atomistic length scales with diffusive time scales. We also discuss aspects of quantitative phase field modeling such as thin interface asymptotic analysis and coupling to thermodynamic databases. The phase field methods result in a set of partial differential equations, whose solutions require time-consuming large-scale computations and often limit the applicability of the method. Subsequently, we review numerical approaches to solve the phase field equations and present a finite difference discretization of the anisotropic Laplacian operator.

Place, publisher, year, edition, pages
2008. Vol. 71, no 10, 106501- p.
Keyword [en]
DENDRITIC CRYSTAL-GROWTH, ARBITRARY VISCOSITY CONTRAST, LAMELLAR STRUCTURE FORMATION, UNDERCOOLED METALLIC MELTS, FINITE-ELEMENT SIMULATIONS, HETEROEPITAXIAL THIN-FILMS, ADAPTIVE MESH REFINEMENT, GRAIN-BOUNDARY FORMATION, DIFFUSE INTERFACE MODEL, FOURIER-SPECTRAL METHOD
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-34130DOI: 10.1088/0034-4885/71/10/106501ISI: 000260186800002Scopus ID: 2-s2.0-58149314314OAI: oai:DiVA.org:kth-34130DiVA: diva2:419555
Note
QC 20110527Available from: 2011-05-27 Created: 2011-05-26 Last updated: 2017-12-11Bibliographically approved

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