Phase-field model of solidification of a binary alloy

Bi, Zhiqiang; Sekerka, Robert F.

doi:10.1016/s0378-4371(98)00364-1

Cited by 94 publications

(63 citation statements)

References 37 publications

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“…As in reference [38], standard non-classical diffuse interface expressions for ρ 1 , ρ 2 and φ are used, which results in a functional of the form,…”

Section: Acknowledgementsmentioning

confidence: 99%

Modeling the early stages of reactive wetting

2010

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Recent experimental studies of molten metal droplets wetting high temperature reactive substrates have established that the majority of triple-line motion occurs when inertial effects are dominant. In light of these studies, this paper investigates wetting and spreading on reactive substrates when inertial effects are dominant using a thermodynamically derived, diffuse interface model of a binary, three-phase material. The liquid-vapor transition is modeled using a van der Waals diffuse interface approach, while the solid-fluid transition is modeled using a phase field approach. The results from the simulations demonstrate an O t − 1 /2 spreading rate during the inertial regime and oscillations in the triple-line position when the metal droplet transitions from inertial to diffusive spreading. It is found that the spreading extent is reduced by enhancing dissolution by manipulating the initial liquid composition. The results from the model exhibit good qualitative and quantitative agreement with a number of recent experimental studies of hightemperature droplet spreading, particularly experiments of copper droplets spreading on silicon substrates. Analysis of the numerical data from the model suggests that the extent and rate of spreading is regulated by the spreading coefficient calculated from a force balance based on a plausible definition of the instantaneous interface energies. A number of contemporary publications have discussed the likely dissipation mechanism in spreading droplets. Thus, we examine the dissipation mechanism using the entropy-production field and determine that dissipation primarily occurs in the locality of the triple-line region during the inertial stage, but extends along the solid-liquid interface region during the diffusive stage. * Electronic address: daniel.wheeler@nist.gov 1 arXiv:1006.4881v1 [cond-mat.mtrl-sci]

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“…As in reference [38], standard non-classical diffuse interface expressions for ρ 1 , ρ 2 and φ are used, which results in a functional of the form,…”

Section: Acknowledgementsmentioning

confidence: 99%

Modeling the early stages of reactive wetting

2010

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“…In the context of solidification it has been applied on models for pure substances [10,26], alloys [30,5], multi-phase systems [16], and systems with both multiple phases and components [17] in order to derive sharp interface limits (first order asymptotics). We remark that, in some cases, this ansatz has been verified by rigorously showing that, in the limit as ε → 0, the sharp interface model is obtained from the diffuse interface model (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Second order phase field asymptotics for multi-component systems

Garcke¹,

Stinner²

2006

Interfaces Free Bound.

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Abstract. We derive a phase field model which approximates a sharp interface model for solidification of a multicomponent alloy to second order in the interfacial thickness ε. Since in numerical computations for phase field models the spatial grid size has to be smaller than ε the new approach allows for considerably more accurate phase field computations than have been possible so far.In the classical approach of matched asymptotic expansions the equations to lowest order in ε lead to the sharp interface problem. Considering the equations to the next order, a correction problem is derived. It turns out that, when taking a possibly nonconstant correction term to a kinetic coefficient in the phase field model into account, the correction problem becomes trivial and the approximation of the sharp interface problem is of second order in ε. By numerical experiments, the better approximation property is well supported. The computational effort to obtain an error smaller than a given value is investigated revealing an enormous efficiency gain.

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“…The thermodynamically agreed MPF were considered in a number of papers [9][10][11][12][13]. The derivation of evolutionary equations in these works is based on the main principles of irreversible thermodynamics.…”

Section: Phase Field Modelmentioning

confidence: 99%

On model of microstructure formation during selective laser melting of metal powder bed

Mirzade¹,

Dubrov²

2017

Collection of Selected Papers of the III International Conference on Information Technology and Nanotechnology

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A model of phase field has been developed to investigate the microstructure evolution during selective laser melting (SLM) of metal powder bed. A two-component (degree of order, orientation field) ordering parameter has been used, for which the permissive relationships have been derived reasoning from the principle of entropy production positivity. The application of this principle has made possible obtaining the thermodynamically agreed evolutionary equations for the components of the ordering parameter, conjugate with the fields of temperature, admixture concentration and elastic deformations for the non-isothermal conditions of crystallization of pure metal melts and multicomponent alloys. The model of the microstructure is adjoint with the macroscopic thermodynamic model of SLM that accounts for the processes of heat transfer, thermo-capillary convection and evolution of the melt free surface.

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Phase-field model of solidification of a binary alloy

Cited by 94 publications

References 37 publications

Modeling the early stages of reactive wetting

Modeling the early stages of reactive wetting

Second order phase field asymptotics for multi-component systems

On model of microstructure formation during selective laser melting of metal powder bed

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