Adaptive Phase Field Model Research Articles

Adaptive phase field modeling of morphological instability and facet formation during directional solidification of SiGe alloys

An adaptive phase field model is used to study the morphological instability and the facet formation during a directional solidification of SiGe alloys. Using highly anisotropic surface free energy and cusp kinetic functions, as well as a proper temperature gradient, the simulated critical growth velocity for various alloy concentrations is in good agreement with classical theories and experimental observations. The simulated facet formation and kinetics are also consistent with the experiments as well.

Phase field modeling of facet formation during directional solidification of silicon film

Adaptive phase field modeling is conducted to study the facet formation during directional solidification of silicon film. The necessary condition for morphological instability is examined first based on the classic theory for the reported experiments. With a proper thermal gradient, the simulated onset velocity is found consistent with the experimental observations and the classic theory. The effects of anisotropy of kinetic coefficients and interfacial energy are also considered, and the simulated morphologies are significantly affected. The range of the kinetic cusp function affects the facet tips, while the anisotropy of interfacial free energy changes the wavelength of facets. Nevertheless, the simulation of kinetic undercooling on the facets is not successful, and the computational difficulty is discussed.

Adaptive three-dimensional phase-field modeling of dendritic crystal growth with high anisotropy

The modeling of dendritic crystal growth of highly anisotropic materials is important in understanding the physics of nature phenomena, such as snow growth, and industrial processes, such as polycrystalline silicon growth. Phase-field modeling has emerged as a powerful tool in such a simulation, but the description of the anisotropic function for three-dimensional (3D) interfacial energy without miss-orientation remains quite difficult. In this paper, a simple method is proposed in our 3D adaptive phase field model. The simulated equilibrium shapes with different anisotropic strengths are first compared with the exact solutions, and they are in good agreement. The dendritic growth of a pure material with different anisotropic strengths for various supercoolings is further simulated, and the morphologies are discussed.

Adaptive phase field modeling of grain boundary diffusion

The phase field modeling (PFM) has emerged as a powerful tool for the simulation of the solidification of polycrystalline alloys. The use of the diffusive interface in PFM allows the treatment of the complicated morphology. However, in dealing with the grain boundary diffusion, it is difficult to simulate the diffusion process that is independent of the interface thickness. To amend this, we propose a model that imbeds a grain boundary diffusion term in the existing adaptive phase field model. In this new model, the simulated solute transport is independent of the interface thickness, and the simulated grain boundary diffusion is in good agreement with the classic solution.

Three-dimensional adaptive phase field modeling of directional solidification of a binary alloy: 2D–3D transitions

Morphological instability is an important subject in alloy directional solidification, and the development of cell allay is important to alloy properties. In nature, as a result of cell arrangement, this problem is often three-dimensional (3D), even for thin-film, and its simulation is rather difficult. We have developed a 3D adaptive phase field model to simulate efficiently the directional solidification of a binary alloy. The morphological transition from 2D to 3D approximations are illustrated, and compared with available analytical and simulated results. The effect of anisotropy on the cell arrangement is discussed as well.

Adaptive finite elements with high aspect ratio for dendritic growth of a binary alloy including fluid flow induced by shrinkage

An adaptive phase field model for the solidification of binary alloys in two space dimensions is presented. The fluid flow in the liquid due to different liquid/solid densities is taken into account. The unknowns are the phase field, the alloy concentration and the velocity/pressure in the liquid. Continuous, piecewise linear finite elements are used for the space discretization, a semi-implicit scheme is used for the time discretization. An adaptive method allows the number of degrees of freedom to be reduced, the mesh triangles having high aspect ratio whenever needed. Numerical results are presented, showing that the fluid flow due to different liquid/solid densities must be taken into account. Moreover, numerical experiments pertaining to micro-porosity and hot tearing are reported.