Dimensional Phase Field Model Research Articles

Enhanced conservative phase field method for moving contact line problems

AbstractThe traditional Allen–Cahn phase field model doesn't conserve mass and is mostly used in solidification microstructure formation. However, a recently modified Allen–Cahn phase field model has riveted the attention of the academic community. It was obtained by subtracting the curvature‐driven flow term from the advective Allen–Cahn phase field model, and thus improves the boundedness of the phase field. More recently, the model has been further refined with the recovered signed distance function to compute interface normal vectors. This paper develops a three dimensional phase field model, based on the abovementioned Allen–Cahn phase field model. The model was discretized using a finite difference method on a half‐staggered grid. More important, interfacial tension was expressed in a potential form. The model was tested against a number of cases and was applied to impacts in various conditions. Besides, the model was parallelized using the shared memory parallelism, OpenMP, to facilitate computation.

Effect of heterogeneous particle size on nanostructure evolution: A phase-field study

The evolution pathways of nanostrutures at high temperature depends on different thermodynamic (e.g. interfacial energies) and kinetic parameters (e.g. interface diffusivities). In nano-regime, difference in interface curvature provides essential driving force for nanostructure evolution. Phase-field method is a model for interfaces which can correctly capture capillarity-driven phenomena. In this work, we employ a three dimensional phase-field model to study nanostructure evolution for (a) two/three particle (nano-size) systems and (b) nanoparticles arranged in multilayers, for different interface diffusivities and particle sizes. For three particle systems, different unconventional evolution pathways, such as seperation between particles and inverse Ostwald ripening are observed. For multilayer systems, these evolution pathways are found to be interacting in a complex manner. This study provides necessary insights for tailoring nanoporous structures by judiciously choosing initial size distribution of nanoparticles in a multilayer setting.

Precision electric control of magnetic domain wall motions in a multiferroic bilayer based on strain-mediated magnetoelectric coupling

In recent years, multiferroics have drawn much scientific attention in the field of spintronics due to the possibility of ‘zero-current’ manipulation of magnetization. In the present study, a three- dimensional phase field model was developed to investigate strain-mediated magnetoelectric coupling in FeGa/BaTiO3 epitaxial bilayer systems. Due to strong elastic interaction, the spontaneous strain in a BaTiO3 substrate can be efficiently transferred to the FeGa ferromagnetic thin film mounted on it, which resulted in printing of the domain patterns from the former to the latter. The transferred domain structures demonstrated high stability in response to the external magnetic field. Our simulation results showed that the magnetic domain wall motion can be manipulated using ultralow voltage of less than 0.08V. Moreover, our investigation of the lateral size effects of the ferromagnetic layer demonstrated that the magnetic domain wall would not extinct even if the lateral size was reduced to tens of nanometer.

Modelling the Static Recrystallisation Texture of FCC Metals Using a Phase Field Method

A three dimensional phase field model has been developed to simulate the texture formed during the static recrystallisation of FCC metals with medium or high stacking fault energy, such as aluminium, copper and nickel. Before recrystallisation the deformation texture as well as the stored energy was simulated using a three dimensional crystal plasticity finite element model. This output calculated on the distorted finite element mesh was first mapped onto the regular grid of the phase field model using a linear interpolation method and then used as initial condition for the subsequent recrystallisation texture modelling. This model has successfully predicted the typical recrystallisation texture components: cube {001}<100>, R {124}<211> in the aluminium alloy. In addition, the softening fraction and three dimensional microstructure produced during static recrystallisation have also been simulated by this model.

Control of Domain States in Individual PbTiO<sub>3</sub> Nanoparticles by Prescribed Strains

A three dimensional phase field model has been devised to account for the manipulation of domain states in individual ferroelectric (PbTiO3) nanoparticles. Vortex structures and dipole flux domain patterns were obtained by applying tensile and compressive strains, respectively. The direction of the two domain configurations was found to correlate with the plane on which the strains were applied, mainly due to dipole-strain coupling and depression of depolarizing field.

Análise numérica bidimensional da morfologia dendrítica do níquel e do ferro utilizando o método de campo de fase

Nesse trabalho, são apresentados os resultados de simulações bidimensionais da formação de dendritas durante a solidificação do níquel e do ferro puros, utilizando um modelo de campo de fase. A morfologia obtida mostrou-se qualitativamente semelhante à forma dendrítica, com braços primários e secundários bem desenvolvidos. Além disso, as velocidades de crescimento em regime permanente, calculadas no presente trabalho, apresentaram boa conformidade com os dados experimentais em uma grande faixa de super-resfriamentos. Foi observado que a espessura da interface apresenta um forte efeito sobre a morfologia e a velocidade de solidificação. Interfaces espessas reduzem o tempo computacional; entretanto podem gerar resultados inconsistentes. A espessura que apresentou os melhores resultados sem aumento acentuado do tempo de processamento foi 4x10-8m.

Finite Element Approximation of a Three Dimensional Phase Field Model for Void Electromigration

We consider a finite element approximation of a phase field model for the evolution of voids by surface diffusion in an electrically conducting solid. The phase field equations are given by the nonlinear degenerate parabolic system $$\gamma\frac{\partial u}{\partial t}-\nabla.(b(u)\nabla[w+\alpha\phi])=0,\qquad w=-\gamma\Delta u+\gamma^{-1}\Psi'(u),\qquad\nabla.(c(u)\nabla\phi)=0$$ subject to an initial condition u 0(?)?[?1,1] on u and flux boundary conditions on all three equations. Here ???>0, ????0, ? is a non-smooth double well potential, and c(u):=1+u, b(u):=1?u 2 are degenerate coefficients. On extending existing results for the simplified two dimensional phase field model, we show stability bounds for our approximation and prove convergence, and hence existence of a solution to this nonlinear degenerate parabolic system in three space dimensions. Furthermore, a new iterative scheme for solving the resulting nonlinear discrete system is introduced and some numerical experiments are presented.

Pattern Formation in Solidification of Chondrules using A Three Dimensional Phase Field Model

Pattern Formation in Solidification of Chondrules using A Three Dimensional Phase Field Model

Front Fluctuations in One Dimensional Stochastic Phase Field Equations

We consider a conservative system of stochastic PDE's, namely a weakly coupled, one dimensional phase field model with additive noise. We study the fluctuations of the front proving that, in a suitable scaling limit, the front evolves according to a non-Markov process, solution of a linear stochastic equation with long memory drift.

Stochastic Phase Field Equations: Existence and Uniqueness

We consider a conservative system of stochastic PDE's, namely a one dimensional phase field model perturbed by an additive space-time white noise. We prove a global existence and uniqueness result in a space of continuous functions on + × . This result is obtained by extending previous results of Doering (3) on the stochastic Allen-Cahn equation.

Ba-Cu-O溶媒中におけるY<SUB>2</SUB>BaCuO<SUB>5</SUB>粒子の粗大化のフェーズフィールドモデル解析

It had been experimentally found that the rate constant (K) of the coarsening cubic-law for Y2BaCuO5 (Y211) particles in Ba-Cu-O melts has been classified into two groups for the volume fraction (Vf), under 15% and over 20%, of Y211 particles, in which the drastic reduction of K existed from the low Vf to the high Vf groups. In the present study, coarsening kinetics for the Y211 particles was simulated using a two dimensional phase field model (PFM) that was proposed for the interface movement of Y211 particles to be tracked. The coarsening simulation of Y211 particles as a stoichiometric compound was performed by solving the diffusion equation, in which the deviation of the solute concentration in the solid phase was restricted to be a negligibly small value. The present PFM calculation indicated that this significant reduction of K appeared between 15% and 20% of the area fraction (Af) of Y211. It was implied that the rate constant reduction was caused by the transition of the coarsening mechanism from the mean field model to the communicating neighbor one, which was quantitatively confirmed by the observation of the different shapes of solute concentration contour lines around disappearing particles and the radical shape transformation of the particles size distribution from Af15% to Af20%.

A three-dimensional phase-field model for computer simulation of lamellar structure formation in γTiAl intermetallic alloys

A three dimensional phase-field model of α ′ 2→ α 2+ γ transformation is developed to simulate the formation of coherent multi-domain lamellar structures in γTiAl intermetallic alloys. The model takes into account the effect of coherency strain associated with the lattice rearrangement accompanying the phase transformation, and the anisotropy in interfacial energy. Simulation studies based on the model successfully predicted the essential features associated with the multi-domain lamellar structures observed experimentally. It is shown that the coherency strain accommodation is the dominating factor responsible for the formation of the lamellar structure. The neighboring lamellae of γ phase are found to have either a twin or a pseudo-twin relationship, with the former being dominant. It is found that strain-induced correlated nucleation plays an important role in the formation of the twined lamellae. The lamellar thickness is determined by the interplay among the elastic strain energy, interfacial energy and bulk chemical free energy. Domains within individual lamellae are isotropic and domain boundaries are smoothly curved. No special self-accommodating morphological patterns are observed on the (0001) α2 plane, which is very different from the pattern formation predicted for the coherent hexagonal → O-phase transformations.