Journal ArticleDOI
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
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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
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Journal ArticleDOI
A density functional theory of polymer phase transitions and interfaces
TL;DR: In this paper, the authors employ density functional methods to derive the free energy and grand potential functionals appropriate to homopolymers and blends and demonstrate the formal equivalence of the theory of polymers to that of nonuniform atomic systems.
Journal ArticleDOI
Vanishing viscosities and error estimate for a Cahn–Hilliard type phase field system related to tumor growth
TL;DR: In this article, the authors perform an asymptotic analysis for two different vanishing viscosity coefficients occurring in a phase field system of Cahn-Hilliard type that was recently introduced in order to approximate a tumor growth model.
Journal ArticleDOI
Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities
TL;DR: In this article, the authors prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions.
Journal ArticleDOI
Microstructure evolution during the isostructural decomposition of TiAlN—A combined in-situ small angle x-ray scattering and phase field study
Axel Knutsson,Jennifer Ullbrand,Lina Rogström,Niklas Norrby,Lars Johnson,Lars Hultman,Jonathan Almer,M.P. Johansson Jõesaar,B. Jansson,Magnus Odén +9 more
TL;DR: In this paper, the spinodal decomposition and coarsening of metastable cubic Ti0.33Al0.67N and Ti 0.50Al0.50N was studied by in-situ small angle x-ray scattering, in combination with phase field simulations.
Journal ArticleDOI
Strong solutions for two-dimensional nonlocal Cahn–Hilliard–Navier–Stokes systems
TL;DR: In this article, it was shown that the global attractor is the union of all the bounded complete trajectories which are strong solutions in two dimensions, provided that the potential is real analytic and the external forces vanish.
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.