A phase-field model with two-component order parameter for spontaneous crystallization in a melt of pure metal

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’.

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Coexistence of magnetic and charge order in a two-component order parameter description of the layered superconductors

Superconductor Science and Technology ◽

10.1088/0953-2048/27/12/124008 ◽

2014 ◽

Vol 27 (12) ◽

pp. 124008 ◽

Cited By ~ 5

Author(s):

Mauro M Doria ◽

Alfredo A Vargas-Paredes ◽

Marco Cariglia

Keyword(s):

Order Parameter ◽

Charge Order ◽

Layered Superconductors ◽

Two Component ◽

Component Order ◽

Component Order Parameter

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Phase Field Simulation of Parameters Affecting Dendrite Growth in a Forced Flow

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.228-229.44 ◽

2011 ◽

Vol 228-229 ◽

pp. 44-49

Author(s):

Xun Feng Yuan ◽

Yu Tian Ding

Keyword(s):

Flow Velocity ◽

Phase Field ◽

Dendritic Growth ◽

Field Model ◽

Phase Field Model ◽

Pure Metal ◽

Dendrite Growth ◽

Forced Flow ◽

Low Flow ◽

Tip Radius

The phase-field model coupled with a flow field was used to simulate the dendrite growth in the undercooled pure metal melt. The effects of flow velocity, supercooling and anisotropy on the dendritic growth were studied. Results indicate that melt flow can enhance the emergence of side-branches, the morphology of the dendrite was composed of the principal branches and side-branches. With an increase in flow velocity and supercooling, the velocity of upstream dendritic tip increases, but the tip radius decreases first and then increases. With an increase in anisotropy values, the velocity of upstream dendritic tip increases and the tip radius decreases. The results of calculation agreed with LMK theory in the case of low flow velocity and anisotropy.

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