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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Journal ArticleDOI
An Efficient, Energy Stable Scheme for the Cahn-Hilliard-Brinkman System
TL;DR: In this article, an unconditionally energy stable and uniquely solvable finite difference scheme for the Cahn-Hilliard-Brinkman (CHB) system is presented, which is comprised of a CahnHilliard type diffusion equation and a generalized Brinkman equation mod- eling fluid flow.
Journal ArticleDOI
Rigorous Numerics for the Cahn-Hilliard Equation on the Unit Square
TL;DR: In this paper, the authors demonstrate how rigorous computational techniques can be employed to establish computer assisted existence proofs for equilibria of the Cahn-Hilliard equation on the unit square.
Journal ArticleDOI
Multiscale modelling of the morphology and spatial distribution of θ′ precipitates in Al-Cu alloys
TL;DR: In this paper, a multiscale approach based on the phase-field model is developed to simulate homogeneous and heterogeneous formation of θ′ precipitates during high temperature ageing in Al-Cu alloys.
Journal ArticleDOI
Modeling the microstructural evolution of Ni-base superalloys by phase field method combined with CALPHAD and CVM
TL;DR: In this article, a quantitative simulation with phase field method (PFM) in a real alloy system was performed with a new strategy of modeling the microstructure evolution of Ni-base superalloys, in which, the calculation of phase diagrams (CALPHAD) method and cluster variation method (CVM) are combined with the PFM.
Journal ArticleDOI
Dynamics of first-order phase transitions in multicomponent systems: a new theoretical approach.
TL;DR: A new method for determination of the parameters of sub- and supercritical clusters is developed and it turns out that a variety of thermodynamic and kinetic parameters, determining cluster growth, become dependent on cluster size as well.
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.