A multiple-component order parameter phase field model for anisotropic grain growth

1997 ◽  
Vol 238 (1) ◽  
pp. 94-100 ◽  
Author(s):  
M.K. Venkitachalam ◽  
L.-Q. Chen ◽  
A.G. Khachaturyan ◽  
G.L. Messing
Keyword(s):  
Grain Growth ◽  
Phase Field ◽  
Order Parameter ◽  
Field Model ◽  
Phase Field Model ◽  
Multiple Component ◽  
Component Order ◽  
Component Order Parameter

scholarly journals Order parameter re-mapping algorithm for 3D phase field model of grain growth using FEM

2016 ◽  
Vol 115 ◽  
pp. 18-25 ◽  
Author(s):  
Cody J. Permann ◽  
Michael R. Tonks ◽  
Bradley Fromm ◽  
Derek R. Gaston
Keyword(s):  
Grain Growth ◽  
Phase Field ◽  
Order Parameter ◽  
Field Model ◽  
Phase Field Model ◽  
Mapping Algorithm

scholarly journals Coarse-graining for fast dynamics of order parameters in the phase-field model

2018 ◽  
Vol 376 (2113) ◽  
pp. 20170203 ◽  
Author(s):  
D. Jou ◽  
P. K. Galenko
Keyword(s):  
Master Equation ◽  
Thermodynamic Equilibrium ◽  
Phase Field ◽  
Order Parameter ◽  
Field Model ◽  
Local Thermodynamic Equilibrium ◽  
Phase Field Model ◽  
Coarse Graining ◽  
Order Parameters ◽  
Coarse Grained

In standard descriptions, the master equation can be obtained by coarse-graining with the application of the hypothesis of full local thermalization that is equivalent to the local thermodynamic equilibrium. By contrast, fast transformations proceed in the absence of local equilibrium and the master equation must be obtained with the absence of thermalization. In the present work, a non-Markovian master equation leading, in specific cases of relaxation to local thermodynamic equilibrium, to hyperbolic evolution equations for a binary alloy, is derived for a system with two order parameters. One of them is a conserved order parameter related to the atomistic composition, and the other one is a non-conserved order parameter, which is related to phase field. A microscopic basis for phenomenological phase-field models of fast phase transitions, when the transition is so fast that there is not sufficient time to achieve local thermalization between two successive elementary processes in the system, is provided. In a particular case, when the relaxation to local thermalization proceeds by the exponential law, the obtained coarse-grained equations are related to the hyperbolic phase-field model. The solution of the model equations is obtained to demonstrate non-equilibrium phenomenon of solute trapping which appears in rapid growth of dendritic crystals. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

Simulation of Ideal Grain Growth Using the Multi-Phase-Field Model

2007 ◽  
Vol 558-559 ◽  
pp. 1177-1181 ◽  
Author(s):  
Philippe Schaffnit ◽  
Markus Apel ◽  
Ingo Steinbach
Keyword(s):  
Grain Size ◽  
Grain Growth ◽  
Phase Field ◽  
Large Scale ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Two Dimensions ◽  
Von Neumann ◽  
Average Grain Size

The kinetics and topology of ideal grain growth were simulated using the phase-field model. Large scale phase-field simulations were carried out where ten thousands grains evolved into a few hundreds without allowing coalescence of grains. The implementation was first validated in two-dimensions by checking the conformance with square-root evolution of the average grain size and the von Neumann-Mullins law. Afterwards three-dimensional simulations were performed which also showed fair agreement with the law describing the evolution of the mean grain size against time and with the results of S. Hilgenfeld et al. in 'An Accurate von Neumann's Law for Three-Dimensional Foams', Phys. Rev. Letters, 86(12)/2685, March 2001. Finally the steady state grain size distribution was investigated and compared to the Hillert theory.

Computer Simulation of Grain Growth in Three Dimensions by the Phase Field Model with Anisotropic Grain-Boundary Mobilities

2007 ◽  
Vol 539-543 ◽  
pp. 2437-2442
Author(s):  
Yoshihiro Suwa ◽  
Yoshiyuki Saito ◽  
Hidehiro Onodera
Keyword(s):  
Grain Boundary ◽  
Grain Growth ◽  
Phase Field ◽  
Large Scale ◽  
Field Model ◽  
Phase Field Model ◽  
High Mobility ◽  
Minor Component ◽  
Three Dimensions ◽  
A Minor

The kinetics and topology of grain growth in three dimensions were simulated using a phase-field model with anisotropic grain-boundary mobilities. In order to perform large scale calculations we applied both modifications of algorithms and parallel coding techniques to the Fan and Chen's phase-field algorithm. Kinetics of abnormal grain growth is presented. It is observed that the grains of a minor component which are at the beginning surrounded preferentially by boundaries of high mobility grow faster than the grains of a major component until the texture reverses completely. Additionally, topological results of grain structures, such as grain size distributions and grain face distributions, are discussed

Phase–field model of isothermal solidification with multiple grain growth

2009 ◽  
Vol 18 (5) ◽  
pp. 1985-1990 ◽  
Author(s):  
Feng Li ◽  
Wang Zhi-Ping ◽  
Zhu Chang-Sheng ◽  
Lu Yang
Keyword(s):  
Grain Growth ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Isothermal Solidification

Dual Scale Simulation of Grain Growth Using a Multi Phase Field Model

2001 ◽  
Vol 677 ◽  
Author(s):  
Ingo Steinbach ◽  
Markus Apel
Keyword(s):  
Grain Boundary ◽  
Grain Growth ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Individual Characteristics ◽  
Interfacial Stress ◽  
Pinning Force ◽  
Pinning Effect ◽  
Multi Phase

ABSTRACTThe kinetics of grain growth in multicrystalline materials is determined by the interplay of curvature driven grain boundary motion and interfacial stress balance at the vertices of the grain boundaries. A comprehensive way to treat both effects in one model is given by the time dependent Ginzburg Landau model or phase field model. The paper presents the application of a multi phase field model, recently developed for solidification processes to grain growth of a multicrystalline structure. The specific feature of this multi phase field model is its ability to treat each grain boundary with its individual characteristics dependent on the type of the grain boundary, its orientation or the local pinning at precipitates. The pinning effect is simulated on the nanometer scale resolving the interaction of an individual precipitate with a curved grain boundary. From these simulations an effective pinning force is deduced and a model of driving force dependent grain boundary mobility is formulated accounting for the pinning effect on the mesoscopic scale of the grain growth simulation. 2-D grain growth simulations are presented.

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