Journal ArticleDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
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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.Abstract:
It is shown that the free energy of a volume V of an isotropic system of nonuniform composition or density is given by : NV∫V [f 0(c)+κ(▿c)2]dV, where NV is the number of molecules per unit volume, ▿c the composition or density gradient, f 0 the free energy per molecule of a homogeneous system, and κ a parameter which, in general, may be dependent on c and temperature, but for a regular solution is a constant which can be evaluated. This expression is used to determine the properties of a flat interface between two coexisting phases. In particular, we find 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 . The predicted interfacial free energy and its temperature dependence are found to be in agreement with existing experimental data. The possibility of using optical measurements of the interface thickness to provide an additional check of our treatment is briefly discussed.read more
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Journal ArticleDOI
Dynamics at the solid-liquid transition: Experiments at the freezing point
TL;DR: In this article, a review of the properties of the solid state, the liquid state, and interfaces at the freezing point is given, which can be described by laws of corresponding states, so-called melting rules.
Journal ArticleDOI
Thermodynamic modeling of ionic liquid systems: development and detailed overview of novel methodology based on the PC-SAFT.
TL;DR: In this paper, a perturbed-chain statistical associating fluid theory (PC-SAFT) was used to calculate the thermodynamic properties of different homologous series of ionic liquids based on the bis(trifluormethylsulfonyl)imide anion ([NTf2]).
Journal ArticleDOI
Amplitude expansion of the binary phase-field-crystal model.
TL;DR: Amplitude representations of a binary phase-field-crystal model are developed for a two-dimensional triangular lattice and three-dimensional bcc and fcc crystal structures, providing an explicit connection between phase-fields-crystals and phase- field models.
Journal ArticleDOI
An adaptive multigrid algorithm for simulating solid tumor growth using mixture models
TL;DR: A fully adaptive, nonlinear multigrid/finite difference method for efficiently solving the equations of a three-dimensional multispecies diffuse interface model of tumor growth is described and the convergence of the algorithm is demonstrated.
Journal ArticleDOI
Computer simulation of phase transformation and plastic deformation in IN718 superalloy: Microstructural evolution during precipitation
Ning Zhou,Duchao Lv,Hualei Zhang,Donald McAllister,F. Zhang,Michael J. Mills,Yunzhi Wang,Yunzhi Wang +7 more
TL;DR: In this paper, the phase-field method is used to simulate statistically representative multiphase microstructures observed in the alloy, the Kim-Kim-Suzuki treatment of interfaces is employed.
References
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Journal ArticleDOI
The Principle of Corresponding States
TL;DR: The principle of corresponding states in modern form has been applied to the following properties: the critical state, the virial coefficient, the Boyle point, the densities of coexistent phases, the vapor pressure of the liquid, the entropies of evaporation and of fusion, the coefficient of thermal expansion of liquid and the triple point temperature and pressure, the heat capacity of liquid, and the surface tension of liquid as mentioned in this paper.
Book ChapterDOI
Zur Theorie des Austauschproblems und der Remanenzerscheinung der Ferromagnetika
TL;DR: The Slatersche Methode as mentioned in this paper is an analog zur Jordan-Kleinschen Theorie in eine nichtlineare Wellengleichung im dreidimensionalen Raum, wobei das Absolutquadrat der Wellenfunktion anschaulich als Spindichte gedeutet werden kann.
Journal ArticleDOI
Die Keimbildung bei der Ausscheidung in metallischen Mischkristallen
TL;DR: In this article, ausscheidung in einem ubersattigten binaren Mischkristall is considered, das die Energie eines Misch-kristalls durch einfache Addition of Nachbarbindungen berechnet werden darf.
Journal ArticleDOI
Domain Structure of Rochelle Salt and K H 2 P O 4
Toshito Mitsui,Jiro Furuichi +1 more
TL;DR: In this paper, it has been shown that rochelle salt in the ferroelectric state consists of many domains and that the domain structure in an annealed crystal is caused by the electrostatic self energy.