A Finite Element-Phase Field Study of Solid State Phase Transformation: Coarsening of Coherent Precipitates and Instability of Multilayer Thin Films


Governing equations for solid state phase transformation are derived by coupling Cahn-Hilliard type of phase field model to elasticity equations. The governing equations include 2nd order partial differential equations for elasticity coupled with a 4th order evolution partial differential equation for the conserved phase field variable. A mixed order finite element model is developed for the computations with C0 interpolation functions for displacement and C1 interpolation functions for the phase field variable. Developed finite element-phase field model is used to study coarsening of systems of coherent particles and also investigate morphological instabilities of multilayer thin films in solid state binary systems. It was shown that compositional mismatch elastic stresses in precipitates-matrix systems and multilayer thin films significantly affect the instability of these systems and alter the kinetics of transformations.

Meeting Name

TMS 2011 - 140th Annual Meeting and Exhibition (2011: Feb. 27-Mar. 3, San Diego, CA)


Materials Science and Engineering

Keywords and Phrases

Binary systems; Coherent precipitates; Elastic stress; Elasticity equations; Field model; Field studies; Finite Element; Finite element models; Governing equations; Interpolation function; Mixed order; Morphological instability; Multi-layer thin film; Order evolution; Phase field models; Phase fields; Phase transformation; Solid state phase transformation; Elasticity; Equations of state; Film preparation; Finite element method; Interpolation; Linear transformations; Multilayer films; Partial differential equations; Phase interfaces; Phase transitions; Multilayers

International Standard Book Number (ISBN)


Document Type

Article - Conference proceedings

Document Version


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Publication Date

01 May 2011