On an order-parameter model for a binary liquid
T. Lin,Robert C. Rogers +1 more
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About: This article is published in Computational Materials Science. The article was published on 01 Jul 1995. and is currently open access. The article focuses on the topics: Binary number.
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Citations
Solute trapping and solute drag in a phase-field model of rapid solidification
TL;DR: In this article, the authors show that solute trapping occurs when the solute diffusion length DI/V is comparable to the diffuse interface thickness and quantify the relationship between the interface temperature and velocity.
223
On the Gibbs adsorption equation and diffuse interface models
TL;DR: In this article, the authors employ the methodology of J. W. Cahn, which avoids the use of conventional dividing surfaces to define surface excess quantities, and derive a solute surface excess quantity that is independent of a dividing surface convention, and find that the adsorption in this model is influenced by the surface free energies of the pure components of the binary alloy as well as the solute gradient energy coefficient.
26
On the Gibbs adsorption equation and di® use interface models
G. B. McFadden,A. A. Wheeler +1 more
- 01 Jan 2011
TL;DR: It is shown that the Gibbs adsorption equation holds for systems with gradient energy coefficients, provided the appropriate definitions of surface excess quantities are used, and in the context of other diffuse interface models that arise in spinodal decomposition and order–disorder transitions.
22
On a model of nonlocal continuum mechanics part I: existence and regularity
Roger Fosdick,D. E. Mason +1 more
TL;DR: Through analysis of this Euler--Lagrange equation for a special class of influence kernels, the regularity theorem is arrived at which ensures that energy minimizing strain fields must be periodic, piecewise smooth, and possess a finite number of simple discontinuities.
21
•Dissertation
On an Order-Parameter Model of Solid-Solid Phase Transitions
Gail Mackin
- 28 Jul 1997
TL;DR: In this paper, a model of solid-solid phase transitions with an order parameter is presented, which is a special case of the Gurtin-Fried model with a symmetric triple-well free energy.
5
References
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
TL;DR: In this article, it was shown that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc, and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2.
10.4K
•Book
Direct Methods in the Calculus of Variations
Bernard Dacorogna
- 01 Jan 1989
TL;DR: In this paper, the existence theorem for non-quasiconvex Integrands in the Scalar case has been established in the Vectorial case, where the objective function is to find the minimum of the minimum for a non-convex function.
2.3K
An analysis of a phase field model of a free boundary
TL;DR: In this paper, a mathematical analysis of a new approach to solidification problems is presented, where a free boundary arising from a phase transition is assumed to have finite thickness, and the physics leads to a system of nonlinear parabolic differential equations.
855
Translation of J. D. van der Waals' “The thermodynamik theory of capillarity under the hypothesis of a continuous variation of density”
TL;DR: Van der Waals justifies the choice of minimization of the Helmholtz free energy as the criterion of equilibrium in a liquid-gas system (Sections 1−4) as discussed by the authors.
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