Thermal drag of the antiphase domain boundary motion

Karma and Rappel [1] recently developed a new sharp interface asymptotic analysis of the phase-field equations that is especially appropriate for modeling dendritic growth at low undercoolings. Their approach relieves a stringent restriction on the interface thickness that applies in the conventional asymptotic analysis, and has the added advantage that interfacial kinetic effects can also be eliminated. However, their analysis focussed on the case of equal thermal conductivities in the solid and liquid phases; when applied to a standard phase-field model with unequal conductivities, anomalous terms arise in the limiting forms of the boundary conditions for the interfacial temperature that are not present in conventional sharp-interface solidification models, as discussed further by Almgren [2]. In this paper we apply their asymptotic methodology to a generalized phase-field model which is derived using a thermodynamically consistent approach that is based on independent entropy and internal energy gradient functionals that include double wells in both the entropy and internal energy densities. The 1 additional degrees of freedom associated with the generalized phase-field equations can be chosen to eliminate the anomalous terms that arise for unequal conductivities.

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“…The leading order temperature equation is (29) Integrating and matching with the outer solution twice in succession gives that u(O)…”

mentioning

confidence: 99%

Thin interface asymptotics for an energy/entropy approach to phase-field models with unequal conductivities

McFadden

Wheeler

Anderson

2000

Physica D: Nonlinear Phenomena

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“…Krzanowski and Allen, 43 and Cahn and Novick-Cohen 39 considered solute-drag effects at a migrating HOI. Umantsev 13 considered the influence of the internal energy excess on the dynamics of HOI in the framework of the Onsager theory of linear response and showed that such excess causes drag effect on the motion of HOI. The drag alters the effective interfacial mobility as follows:…”

Section: Homophase Interfacesmentioning

confidence: 99%

“…A number of questions, however, remained unaddressed by the simplified Onsager-type formulation in Ref. 13. For instance, what is the temperature distribution around the interface?…”

Section: Homophase Interfacesmentioning

confidence: 99%

“…27,42 The second term represents the thermal correction given by Onsagertype macroscopic theory. 13 The third term is the continuum correction due to dissipative processes inside the interface considered in the present treatment.…”

Section: ͑68͒mentioning

confidence: 99%

“…Recently we analyzed the influence of the internal energy excess on the dynamics of the antiphase domain boundary in the framework of the Onsager theory of linear response. 13 We derived an evolution equation that takes into account the finite rate of energy transfer in the transition region and showed that the internal energy transport causes a drag effect and temperature hump in the transition region. Although the principal result that the necessity to move energy together with the interface results in slowing down of its motion was obtained in the paper on the grounds of simple symmetry arguments, some questions remained unanswered.…”

Section: Introductionmentioning

confidence: 99%

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Thermal effects in dynamics of interfaces

Umantsev

2002

The Journal of Chemical Physics

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Dynamical Ginzburg-Landau theory is applied to the study of thermal effects of motion of interfaces that appear after different phase transitions. These effects stem from the existence of the surface thermodynamic properties and temperature gradients in the interfacial transition region. Thermal effects may be explained by the introduction of a new thermodynamic force exerted on the interface, called here Gibbs-Duhem force, and the internal energy density flux through the interface. The evolution equations for the interfacial motion are derived. For the experimental verification of the thermal effects during continuous ordering the expression is derived for the amplitude of temperature waves.

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