Three-dimensional phase-field modeling of spinodal decomposition in constrained films

Seol, Dong Jin; Hu, Sanmei; Li, Yulan; Shen, Jie; Oh, Kyoung-Hee; Chen, Lei

doi:10.1007/bf03027232

Cited by 27 publications

(18 citation statements)

References 17 publications

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“…In linear elasticity, the stress σ ij is related to the elastic strain by Hookes law: (4) where is the total strain measured with respect to the undistorted reference lattice of the parent phase. If we assume conceptually that the total strain is zero at every position, the film does not have any elastic deformation before and after the phase transformation, while the transformed area with non-zero stress-free strain suffers stress field.…”

Section: Phase-field Model Of Cubic-to-tet-ragonal Martensitic Transfmentioning

confidence: 99%

“…They investigated with computer simulation the nucleation process, transformation kinetics and final morphologies of MT in a bulk material. But it is known that the phase transformation kinetics and final morphologies change considerably in thin film material due to the confined geometry compared to bulk material [3,4]. The objective of this work is to study how the kinetics and morphologies of the proper MT are affected by the confined geometry of the thin film attached to the substrate.…”

Section: Introductionmentioning

confidence: 99%

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Cubic to tetragonal martensitic transformation in a thin film elastically constrained by a substrate

Seol

et al. 2003

Met. Mater. Int.

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A 3-dimensional phase-field model is developed to describe the cubic to tetragonal martensitic phase transformation in a thin film attached to a substrate. Elasticity solutions are derived for both elastically anisotropic and isotropic thin films with arbitrary domain structures, subject to the mixed boundary conditions for stressfree and constrained states. The model is applied to an Fe-31%Ni alloy system. The nucleation process as well as the final domain structure strongly depends on the substrate constraint. At a smaller undercooling, the increased strain energy effect results in a lower volume fraction of martensite, a finer domain structure and a longer nucleation period.

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Section: Phase-field Model Of Cubic-to-tet-ragonal Martensitic Transfmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cubic to tetragonal martensitic transformation in a thin film elastically constrained by a substrate

Seol

et al. 2003

Met. Mater. Int.

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“…Phase field models have been used successfully to study a variety of interfacial phenomena like equilibrium shapes of vesicle membranes [12][13][14][15][16]35], blends of polymeric liquids [17,[36][37][38], multiphase fluid flows [19, 23-25, 28, 40-45], dentritic growth in solidification, microstructure evolution [21,22,29], grain growth [8], crack propagation [9], morphological pattern formation in thin films and on surfaces [26,30], self-assembly dynamics of two-phase monolayer on an elastic substrate [27], a wide variety of diffusive and diffusion-less solid-state phase transitions [10,39], dislocation modeling in microstructure, electro-migration and multiscale modeling [34]. Multiple phase-field methods can be devised to study multiphase materials [40].…”

Section: Introductionmentioning

confidence: 99%

Mass-Conserved Phase Field Models for Binary Fluids

Shen¹,

Yang²,

Wang³

2011

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Abstract. The commonly used incompressible phase field models for non-reactive, binary fluids, in which the Cahn-Hilliard equation is used for the transport of phase variables (volume fractions), conserve the total volume of each phase as well as the material volume, but do not conserve the mass of the fluid mixture when densities of two components are different. In this paper, we formulate the phase field theory for mixtures of two incompressible fluids, consistent with the quasi-compressible theory [28], to ensure conservation of mass and momentum for the fluid mixture in addition to conservation of volume for each fluid phase. In this formulation, the mass-average velocity is no longer divergence-free (solenoidal) when densities of two components in the mixture are not equal, making it a compressible model subject to an internal constraint. In one formulation of the compressible models with internal constraints (model 2), energy dissipation can be clearly established. An efficient numerical method is then devised to enforce this compressible internal constraint. Numerical simulations in confined geometries for both compressible and the incompressible models are carried out using spatially high order spectral methods to contrast the model predictions. Numerical comparisons show that (a) predictions by the two models agree qualitatively in the situation where the interfacial mixing layer is thin; and (b) predictions differ significantly in binary fluid mixtures undergoing mixing with a large mixing zone. The numerical study delineates the limitation of the commonly used incompressible phase field model using volume fractions and thereby cautions its predictive value in simulating well-mixed binary fluids.

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“…There have been a number of studies on modeling the elastic effect on morphological evolution in thin films or surfaces This article is based on a presentation made in the 2003 Korea-Japan symposium on the "Current Issues on Phase Transformations", held at Marriott Hotel, Busan, Korea, November 21, 2003, which was organized by the Phase Transformation Committee of the Korean Institute of Metals and Materials. *Corresponding author: sxd42@psu.edu [7][8][9][10][11][12][13][14][15][16][17]. Most of them assumed that the elastic modulus is homogeneous [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

“…*Corresponding author: sxd42@psu.edu [7][8][9][10][11][12][13][14][15][16][17]. Most of them assumed that the elastic modulus is homogeneous [9][10][11][12][13][14][15]. In our previous work [11,12], we analyzed effects of the composition, the film thickness, and the elastic anisotropy on the evolution of spinodally decomposed morphology.…”

Section: Introductionmentioning

confidence: 99%

Effect of substrate constraint on spinodal decomposition in an elastically inhomogeneous thin film

Seol

et al. 2004

Met. Mater. Int.

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Spinodal decomposition in a binary thin film is studied by a three-dimensional (3D) phase field model. A cubic thin film with an (001) orientation is considered. The focus is on the effect of the types of substrate constraint on the morphological evolution during spinodal decomposition as compared to the corresponding bulk. The elastic strain effect is incorporated by solving the elasticity equations for an elastically inhomogeneous thin film with a free surface and constrained by a substrate. Temporal evolution for the composition field, and thus the morphological evolution, is obtained by solving the Cahn-Hilliard equation using a semi-implicit Fourier-spectral method. It is shown that a biaxial substrate constraint has essentially no effect on the spinodally decomposed two-phase morphology which is primarily controlled by the cubically anisotropic elastic interactions. The asymmetry in the strain components along the [100] and [010] directions from the substrate constraint results in the preferential alignment along one of the two directions. In the particular case of a harder phase whose lattice parameter increases with composition, a tensile substrate constraint along the film plane leads to the alignment of two-phase microstructures parallel to the tensile direction.

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Three-dimensional phase-field modeling of spinodal decomposition in constrained films

Cited by 27 publications

References 17 publications

Cubic to tetragonal martensitic transformation in a thin film elastically constrained by a substrate

Cubic to tetragonal martensitic transformation in a thin film elastically constrained by a substrate

Mass-Conserved Phase Field Models for Binary Fluids

Effect of substrate constraint on spinodal decomposition in an elastically inhomogeneous thin film

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