Journal ArticleDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
Reads0
Chats0
TLDR
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
More filters
Journal ArticleDOI
Fractional Cahn–Hilliard, Allen–Cahn and porous medium equations
TL;DR: In this article, a fractional variant of the Cahn-Hilliard equation is introduced and the existence and uniqueness of weak solutions to the related initial-boundary value problem is proved.
Journal ArticleDOI
Phase field modeling of void nucleation and growth in irradiated metals
TL;DR: In this paper, a phase field model for void formation in metals with vacancy concentrations exceeding the thermal equilibrium values is presented, which allows for a unified treatment of void nucleation and growth under the condition of random generation of vacancies, which is similar to vacancy generation by collision cascade in irradiated materials.
Journal ArticleDOI
Decoupled Energy Stable Schemes for Phase-Field Models of Two-Phase Complex Fluids
Jie Shen,Xiaofeng Yang +1 more
TL;DR: Numerical approximations of phase-field models for two-phase complex fluids derived from an energetic variational formulation into a form which is suitable for numerical approximation and establish their energy laws are considered.
Journal ArticleDOI
Quantitative evaluation of spinodal decomposition in Fe-Cr by atom probe tomography and radial distribution function analysis.
TL;DR: The RDF is capable of representing very subtle decomposition, which is not possible using frequency diagrams, and thus a proposed theoretical treatment of the experimental RDF creates the possibility to determine amplitude at very early stages of spinodal decomposition.
Journal ArticleDOI
Mean field kinetic theory description of evaporation of a fluid into vacuum
TL;DR: In this article, numerical solutions of the Enskog-Vlasov equation for a fluid of spherical molecules interacting by Sutherland potential have been studied for the evaporation of a liquid slab into vacuum.
References
More filters
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.