Related papers: Phase Field Models versus Parametric Front Trackin…
We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the…
We present the second set of benchmark problems for phase field models that are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input…
A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. By rigorous asymptotic analysis we show that the sharp-interface limit of this model recovers the continuum model equations for the…
Dendrites are one of the most widely observed patterns in nature and occur across a wide spectrum of physical phenomena. In solidification and growth patterns in metals and crystals, the multi-level branching structures of dendrites pose a…
The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and…
This paper surveys recent numerical advances in the phase field method for geometric surface evolution and related geometric nonlinear partial differential equations (PDEs). Instead of describing technical details of various numerical…
The solidification of polycrystalline materials can be modelled by orientation-field models, which are formulated in terms of two continuous fields: a phase field that describes the thermodynamic state and an orientation field that…
Phase-Field Crystal (PFC) models are able to resolve atomic length scale features of materials during temporal evolution over diffusive time scales. Traditional PFC models contain solid and liquid phases, however many important materials…
In this paper the development of a physically consistent phase-field theory of solidification shrinkage is presented. The coarse-grained hydrodynamic equations are derived directly from the N-body Hamiltonian equations in the framework of…
We investigate a phase-field-crystal model for homogeneous nucleation. Instead of solving the time evolution of a density field towards equilibrium we use a String Method to identify saddle points in phase space. The saddle points allow to…
Based on static and dynamical density functional theory, a phase-field-crystal model is derived which involves both the translational density and the orientational degree of ordering as well as a local director field. The model exhibits…
Many metal manufacturing processes involve phase change phenomena, which include melting, boiling, and vaporization. These phenomena often occur concurrently. A prototypical 1D model for understanding the phase change phenomena is the…
The solidification and macro-segregation problem involving unsteady multi-physics and multi-phase fields is typically a complex process with mass, momentum, heat, and species transfers among solid, mushy, and liquid phase regions. The…
In this paper we describe a new model for solidification with heat flux using the phase field crystal (PFC) framework. The equations are thermodynamically consistent, in the sense that the time rate of change of the entropy density is…
Advanced phase-field techniques have been applied to address various aspects of polycrystalline solidification including different modes of crystal nucleation. The height of the nucleation barrier has been determined by solving the…
In this contribution tracking control designs using output feedback are presented for a two-phase Stefan problem arising in the modeling of the Vertical Gradient Freeze process. The two-phase Stefan problem, consisting of two coupled free…
We characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. During late-stage solidification, crystal-melt interfaces may attract or…
In the literature, two quite different phase-field formulations for the problem of alloy solidification can be found. In the first, the material in the diffuse interfaces is assumed to be in an intermediate state between solid and liquid,…
The computer simulation of quasistationary Stefan problem has been realized. Different representations of the Laplacian growth model are considered. The main attention has been paid for the interface dynamics represented by integro…
The effect of nonequilibrium solute trapping by a growing solid under rapid solidification conditions is studied using a phase-field model. Considering a continuous steady-state concentration profile across the diffuse solid-liquid…