scholarly journals Correspondence between a phase-field theory and a sharp-interface theory for crystal growth

1997 ◽  
Vol 9 (1) ◽  
pp. 33-60 ◽  
Author(s):  
Eliot Fried
Keyword(s):  
Field Theory ◽  
Crystal Growth ◽  
Phase Field ◽  
Sharp Interface ◽  
Interface Theory

scholarly journals A regularized phase-field model for faceting in a kinetically controlled crystal growth

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200227
Author(s):  
T. Philippe ◽  
H. Henry ◽  
M. Plapp
Keyword(s):  
Crystal Growth ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Interface Problem ◽  
Kinetically Controlled ◽  
Interface Theory ◽  
Coarsening Dynamics

At equilibrium, the shape of a strongly anisotropic crystal exhibits corners when for some orientations the surface stiffness is negative. In the sharp-interface problem, the surface free energy is traditionally augmented with a curvature-dependent term in order to round the corners and regularize the dynamic equations that describe the motion of such interfaces. In this paper, we adopt a diffuse interface description and present a phase-field model for strongly anisotropic crystals that is regularized using an approximation of the Willmore energy. The Allen–Cahn equation is employed to model kinetically controlled crystal growth. Using the method of matched asymptotic expansions, it is shown that the model converges to the sharp-interface theory proposed by Herring. Then, the stress tensor is used to derive the force acting on the diffuse interface and to examine the properties of a corner at equilibrium. Finally, the coarsening dynamics of the faceting instability during growth is investigated. Phase-field simulations reveal the existence of a parabolic regime, with the mean facet length evolving in t , with t the time, as predicted by the sharp-interface theory. A specific coarsening mechanism is observed: a hill disappears as the two neighbouring valleys merge.

Phase field model derivation for rapid crystal growth in polycrystalline alloys

2020 ◽  
Vol 229 (2-3) ◽  
pp. 453-458
Author(s):  
Irina G. Nizovtseva ◽  
Nele Moelans ◽  
Alexander A. Ivanov
Keyword(s):  
Crystal Growth ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Polycrystalline Alloys ◽  
Model Derivation

Nucleation and Bulk Crystallization in Binary Phase Field Theory

2002 ◽  
Vol 88 (20) ◽  
Author(s):  
László Gránásy ◽  
Tamás Börzsönyi ◽  
Tamás Pusztai
Keyword(s):  
Field Theory ◽  
Phase Field ◽  
Bulk Crystallization ◽  
Binary Phase

Phase-field-crystal simulation of nonequilibrium crystal growth

2014 ◽  
Vol 89 (1) ◽  
Author(s):  
Sai Tang ◽  
Yan-Mei Yu ◽  
Jincheng Wang ◽  
Junjie Li ◽  
Zhijun Wang ◽  
...  
Keyword(s):  
Crystal Growth ◽  
Phase Field ◽  
Phase Field Crystal
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