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
Multimaterial structural topology optimization with a generalized Cahn–Hilliard model of multiphase transition
Shiwei Zhou,Michael Yu Wang +1 more
TL;DR: In this paper, a phase field method for the optimization of multimaterial structural topology with a generalized Cahn-Hilliard model is described, where the mass concentration of each material phase is considered as design variable.
Journal ArticleDOI
Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations
TL;DR: In this article, a numerical simulation of the Navier-Stokes-Korteweg equations, a phase-eld model for water/water vapor two-phase flow, is presented.
Journal ArticleDOI
Diffuse interface model for structural transitions of grain boundaries
TL;DR: In this paper, the conditions for structural transitions at the core of a grain boundary separating two crystals were investigated with a diffuse interface model that incorporates disorder and crystal orientation, and the model predicts that limited structural disorder near the grain boundary core can be favorable below the melting point.
Journal ArticleDOI
Asymptotic behavior of a Cahn-Hilliard-Navier-Stokes system in 2D
TL;DR: In this article, a model for the flow of a mixture of two homogeneous and incompressible fluids in a two-dimensional bounded domain is considered, where the model consists of a Navier-Stokes equation governing the fluid velocity coupled with a convective Cahn-Hilliard equation for the relative density of atoms of one of the fluids.
Journal ArticleDOI
Solution-processed organic transistors based on semiconducting blends
Jeremy Smith,R. W. Hamilton,Iain McCulloch,Natalie Stingelin-Stutzmann,Martin Heeney,Donal D. C. Bradley,Thomas D. Anthopoulos +6 more
TL;DR: The latest advances in the use of solution processable organic semiconductor blends for organic field effect transistor (OFET) applications are reviewed in this article, where multi-component, thin film microstructure formation from solution with particular focus on phase separation and crystallisation of components.
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.