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
Citations
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Phase-field simulation of sintering and related phenomena : A vacancy diffusion approach
Klara Asp,John Ågren +1 more
TL;DR: In this article, a phase-field model of sintering and related phenomena in a two-phase system and in a multiphase system is presented, which considers diffusion of vacancies as the atomic mechanism for redistribution of material and uses the familiar model of thermal vacancies in a crystal as energy formulation.
Journal ArticleDOI
The stability of nanobubbles
TL;DR: The experimental evidence for the existence of nanobubbles is summarized in detail in this paper, and the paradox represented by their stability and the apparent contradiction with the Laplace-Young equation is discussed in detail.
Journal ArticleDOI
The shape of the van der Waals loop and universal critical amplitude ratios
Michael E. Fisher,Shun-yong Zinn +1 more
TL;DR: In this paper, the shape of a van der Waals loop for a fluid, ferromagnet, etc, is analyzed on the basis of universal critical amplitude ratios for three-dimensional Ising-type systems.
Journal ArticleDOI
Mush microphysics and the reactivation of crystal-rich magma reservoirs
TL;DR: In this article, a pore-scale multiphase heat and fluid transport model was developed to understand the effect of a percolating fluid phase on the partial melting and reactivation of crystal mushes.
Journal ArticleDOI
Conservative nonlinear difference scheme for the Cahn-Hilliard equation—II
S.M. Choo,S.K. Chung,K. I. Kim +2 more
TL;DR: In this article, the authors considered numerical solutions for the Cahn-Hilliard equation using the Crank-Nicolson type finite difference method and proved the existence of the solution for the difference scheme.
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.