A Phase-Field - Finite Element Model for Instabilities in Multilayer Thin Films
Cahn-Hilliard type of phase-field (PF) model coupled with elasticity equations is used to study the instabilities in multilayer thin films. The governing equations of the solid state phase transformation include a 4th order partial differential equation representing the evolution of the conserved PF variable (concentration) coupled to 2nd order partial differential equations representing the mechanical equilibrium. A mixed order Galerkin finite element (FE) model is used including C0 interpolation functions for the displacement, and C1 interpolation functions for the concentration. It is shown that quadratic convergence, expected for conforming elements, is achieved from this coupled mixed-order FE model. Using the PF - FE model, first, we studied the effect of compositional strain on the PF interface thickness and the results of simulations are compared with the analytical solutions of an infinite thin film diffusion couple with a flat interface. Morphological instabilities in binary multilayer thin films are investigated. The alloys with and without intermediate phase are considered, as well as the cases with stable and metastable intermediate phase. Maps of transformations in multilayer systems are carried out considering the effects of initial thickness of layers, compositional strain, and growth of a stable/unstable intermediate phase on the instability of the multilayer thin films. It is shown that at some cases phase transformation, intermediate phase nucleation and growth, or deformation of layers due to high compositional strain can lead to the coarsening of the layers which can result in different mechanical and materials behaviors of the original designed multilayer.
M. Asle Zaeem et al., "A Phase-Field - Finite Element Model for Instabilities in Multilayer Thin Films," Materials Research Society Symposium Proceedings, vol. 1297, pp. 35-46, Materials Research Society, Nov 2011.
The definitive version is available at https://doi.org/10.1557/opl.2011.461
2010 Materials Research Society Fall Meeting (2010: Nov. 29-Dec. 3, Boston, MA)
Materials Science and Engineering
Keywords and Phrases
Analytical solutions; Conforming elements; Elasticity equations; FE model; Finite element models; Flat interface; Galerkin finite elements; Governing equations; Initial thickness; Interface thickness; Intermediate phase; Interpolation function; Materials behavior; Mechanical equilibrium; Metastable intermediate; Mixed order; Morphological instability; Multi-layer system; Multi-layer thin film; Phase fields; Phase transformation; Phase-field models; Quadratic convergence; Solid state phase transformation; Thin-film diffusion; Computer simulation; Coupled circuits; Deformation; Elasticity; Film preparation; Film thickness; Finite element method; Growth (materials); Interfaces (materials); Interpolation; Iron alloys; Materials properties; Multilayer films; Partial differential equations; Phase transitions; Multilayers
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01 Nov 2011