GIBBS-THOMSON AND OTHER QUANTITATIVE RELATIONS IN DENDRITIC CRYSTAL GROWTH

Fractals ◽  
1996 ◽  
Vol 04 (02) ◽  
pp. 169-174
Author(s):  
A. TANAKA ◽  
T. YOKOYAMA
Keyword(s):  
Crystal Growth ◽  
Surface Energy ◽  
Numerical Simulations ◽  
Melting Temperature ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Quantitative Relation ◽  
Dendritic Crystal

The Gibbs-Thomson relation is well-known in crystal growth. That implies that the temperature of interface is not equal to the melting temperature due to its surface energy. It is, however, a qualitative relation near equilibrium, not clear not only qualitatively but also quantitatively far equilibrium. One of the authors has measured quantitative relation in experimental dendritic, i.e., far equilibrium, crystal growth. We also carried out numerical simulations using Phase Field Model, and obtained new relation. We will discuss this in detail here.

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.

Study on Microstructural Evolution of Binary Alloy Crystal Growth in Directional Solidification Process

2013 ◽  
Vol 470 ◽  
pp. 100-103
Author(s):  
Dong Sheng Chen ◽  
Ming Chen ◽  
Rui Chang Wang
Keyword(s):  
Crystal Growth ◽  
Directional Solidification ◽  
Binary Alloy ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Pure Substance ◽  
Columnar Dendrite

PFM (phase field method) was employed to study microstructure evolution, and considering the effect of solute concentration to the undercooling, we developed a phase field model for binary alloy on the basis of pure substance model. In the paper, the temperature field and solute field were coupled together in the phase field model to calculate the crystal growth of magnesium alloy in directional solidification. The simulation results showed a non-planar crystal growth of planar to cellular to columnar dendrite, the comparison of different dendrite patterns were carried out in the numerical simulation, and with the increasing of the anisotropy, the second dendrite arms became more developed.

Phase Field Method Simulation of Dendrite Crystal Growth of Metal Nickel Based on Fractal Theory

2012 ◽  
Vol 190-191 ◽  
pp. 522-527
Author(s):  
Zhi Yi Ruan ◽  
Sheng Da Zeng ◽  
Li Xin Lin ◽  
Lu Rong Wu
Keyword(s):  
Crystal Growth ◽  
Growth Model ◽  
Phase Field ◽  
Field Model ◽  
Fractal Theory ◽  
Phase Field Model ◽  
Crystal Nucleation ◽  
Pure Substance ◽  
Simulation Results ◽  
Matlab Programming

Using fractal theory simulation of dendrite crystal DLA growth model of pure substance, the undercooling during solidification process of crystal nucleation is simulated; and then in the crystal nuclei are formed on the basis of a pure substance, the phase field model and combined with the finite difference method further differentiation simulation of dendrite crystal growth. According to MATLAB programming, the simulation results obtained by field and temperature field can be seen in the DLA growth, growth model with random premise, for the same kind of material simulated dendrite crystal have both similarities and differences exist. Then, we can get the conclusion, through fractal growth of DLA model with phase field model of dendrite nucleation, growth process is carried out the simulation results, a simple by phase field model is more accord with the dendrite crystal in the experiment.

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