A new phase-field model for strongly anisotropic systems

2009 ◽  
Vol 465 (2105) ◽  
pp. 1337-1359 ◽  
Author(s):  
Solmaz Torabi ◽  
John Lowengrub ◽  
Axel Voigt ◽  
Steven Wise
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Interface Model ◽  
Sharp Interface Model ◽  
Anisotropic Surface ◽  
Sharp Corners ◽  
New Phase

We present a new phase-field model for strongly anisotropic crystal and epitaxial growth using regularized, anisotropic Cahn–Hilliard-type equations. Such problems arise during the growth and coarsening of thin films. When the anisotropic surface energy is sufficiently strong, sharp corners form and unregularized anisotropic Cahn–Hilliard equations become ill-posed. Our models contain a high-order Willmore regularization, where the square of the mean curvature is added to the energy, to remove the ill-posedness. The regularized equations are sixth order in space. A key feature of our approach is the development of a new formulation in which the interface thickness is independent of crystallographic orientation. Using the method of matched asymptotic expansions, we show the convergence of our phase-field model to the general sharp-interface model. We present two- and three-dimensional numerical results using an adaptive, nonlinear multigrid finite-difference method. We find excellent agreement between the dynamics of the new phase-field model and the sharp-interface model. The computed equilibrium shapes using the new model also match a recently developed analytical sharp-interface theory that describes the rounding of the sharp corners by the Willmore regularization.

Non-axisymmetric growth of dendrite with arbitrary symmetry in two and three dimensions: sharp interface model vs phase-field model

2020 ◽  
Vol 229 (19-20) ◽  
pp. 2899-2909
Author(s):  
L. V. Toropova ◽  
P. K. Galenko ◽  
D. V. Alexandrov ◽  
M. Rettenmayr ◽  
A. Kao ◽  
...  
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Three Dimensions ◽  
Interface Model ◽  
Sharp Interface Model

scholarly journals Sharp-interface formation during lithium intercalation into silicon

2017 ◽  
Vol 29 (1) ◽  
pp. 118-145 ◽  
Author(s):  
E. MECA ◽  
A. MÜNCH ◽  
B. WAGNER
Keyword(s):  
Free Boundary ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Lithium Ion ◽  
Sharp Interface ◽  
Ion Concentration ◽  
Interface Model ◽  
Sharp Interface Model ◽  
Time Dynamics

In this study, we present a phase-field model that describes the process of intercalation of Li ions into a layer of an amorphous solid such as amorphous silicon (a-Si). The governing equations couple a viscous Cahn–Hilliard-Reaction model with elasticity in the framework of the Cahn–Larché system. We discuss the parameter settings and flux conditions at the free boundary that lead to the formation of phase boundaries having a sharp gradient in lithium ion concentration between the initial state of the solid layer and the intercalated region. We carry out a matched asymptotic analysis to derive the corresponding sharp-interface model that also takes into account the dynamics of triple points where the sharp interface intersects the free boundary of the Si layer. We numerically compare the interface motion predicted by the sharp-interface model with the long-time dynamics of the phase-field model.

scholarly journals Phase-field modeling of grain evolutions in additive manufacturing from nucleation, growth, to coarsening

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Min Yang ◽  
Lu Wang ◽  
Wentao Yan
Keyword(s):  
Additive Manufacturing ◽  
Phase Field ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Nucleation Theory ◽  
Experimental Result ◽  
Classical Nucleation Theory ◽  
Validation Experiment ◽  
Powder Particles

AbstractA three-dimensional phase-field model is developed to simulate grain evolutions during powder-bed-fusion (PBF) additive manufacturing, while the physically-informed temperature profile is implemented from a thermal-fluid flow model. The phase-field model incorporates a nucleation model based on classical nucleation theory, as well as the initial grain structures of powder particles and substrate. The grain evolutions during the three-layer three-track PBF process are comprehensively reproduced, including grain nucleation and growth in molten pools, epitaxial growth from powder particles, substrate and previous tracks, grain re-melting and re-growth in overlapping zones, and grain coarsening in heat-affected zones. A validation experiment has been carried out, showing that the simulation results are consistent with the experimental results in the molten pool and grain morphologies. Furthermore, the grain refinement by adding nanoparticles is preliminarily reproduced and compared against the experimental result in literature.

PHASE-FIELD MODELING OF ELASTIC EFFECTS IN EUTECTIC GROWTH WITH MISFIT STRESSES

2012 ◽  
Vol 04 (01) ◽  
pp. 1250024
Author(s):  
ZOHREH EBRAHIMI ◽  
JOAO REZENDEH
Keyword(s):  
Phase Field ◽  
Elastic Energy ◽  
Field Model ◽  
Phase Field Model ◽  
Solidification Process ◽  
Eutectic Growth ◽  
Point Of View ◽  
Eutectic Solidification ◽  
Elastic Model ◽  
Sharp Interface Model

Elastic interactions, arising from a difference of lattice spacing between two coherent phases in eutectic alloys with misfit stresses, can have an influence on microstructural pattern formation of eutectic colonies during solidification process. From a thermodynamic point of view the elastic energy contributes to the free energy of the phases and modifies their mutual stability. Therefore, the elastic stresses will have an effect on stability of lamellae, lamellae spacing and growth modes. In this paper, a phase-field model is employed to investigate the influence of elastic misfits in eutectic growth. The model reduces to the traditional sharp-interface model in a thin-interface limit, where the microscopic interface width is small but finite. An elastic model is designed, based on linear microelasticity theory, to incorporate the elastic energy in the phase-field model. Theoretical and numerical approaches, required to model elastic effects, are formulated and the stress distributions in eutectic solidification structures are evaluated. The two-dimensional simulations are performed for directed eutectic growth and the simulation results for different values of the misfit stresses are illustrated.

Phase-Field Simulation of Three-Dimensional Dendritic Growth

2010 ◽  
Vol 97-101 ◽  
pp. 3769-3772 ◽  
Author(s):  
Chang Sheng Zhu ◽  
Jun Wei Wang
Keyword(s):  
Computational Methods ◽  
Phase Field ◽  
Interfacial Energy ◽  
Dendritic Growth ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Computational Time ◽  
Field Simulation ◽  
Undercooled Melt

Based on a thin interface limit 3D phase-field model by coupled the anisotropy of interfacial energy and self-designed AADCR to improve on the computational methods for solving phase-field, 3D dendritic growth in pure undercooled melt is implemented successfully. The simulation authentically recreated the 3D dendritic morphological fromation, and receives the dendritic growth rule being consistent with crystallization mechanism. An example indicates that AADCR can decreased 70% computational time compared with not using algorithms for a 3D domain of size 300×300×300 grids, at the same time, the accelerated algorithms’ computed precision is higher and the redundancy is small, therefore, the accelerated method is really an effective method.

scholarly journals A ternary Cahn–Hilliard–Navier–Stokes model for two-phase flow with precipitation and dissolution

2020 ◽  
pp. 1-35
Author(s):  
Christian Rohde ◽  
Lars von Wolff
Keyword(s):  
Phase Field ◽  
Stokes Equations ◽  
Solid Phase ◽  
Immiscible Fluids ◽  
Sharp Interface ◽  
Ion Concentration ◽  
Navier Stokes ◽  
Interface Model ◽  
Sharp Interface Model ◽  
Two Phase

We consider the incompressible flow of two immiscible fluids in the presence of a solid phase that undergoes changes in time due to precipitation and dissolution effects. Based on a seminal sharp interface model a phase-field approach is suggested that couples the Navier–Stokes equations and the solid’s ion concentration transport equation with the Cahn–Hilliard evolution for the phase fields. The model is shown to preserve the fundamental conservation constraints and to obey the second law of thermodynamics for a novel free energy formulation. An extended analysis for vanishing interfacial width reveals that in this limit the sharp interface model is recovered, including all relevant transmission conditions. Notably, the new phase-field model is able to realize Navier-slip conditions for solid–fluid interfaces in the limit.

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