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
Interfacial properties of water + alcohol mixtures
Sabine Enders,Heike Kahl +1 more
TL;DR: In this paper, the Cahn-Hilliard theory was combined with the original statistical associated fluid theory equation of states (SAFT EOS) in order to describe both the phase behaviour and interfacial properties with respect of association.
Journal ArticleDOI
Time-Fractional Allen–Cahn Equations: Analysis and Numerical Methods
Qiang Du,Jiang Yang,Zhi Zhou +2 more
TL;DR: In this paper, the authors considered a time-fractional Allen-Cahn equation, where the conventional first order time derivative is replaced by a Caputo fractional derivative with order ��\alpha \in (0,1)
Journal ArticleDOI
Diffuse-interface modelling of droplet impact
TL;DR: In this article, the impact of micron-size drops on a smooth, flat, chemically homogeneous solid surface is studied using a diffuse-interface model (DIM) based on the Cahn-Hilliard theory that couples thermodynamics with hydrodynamics, and is extended to include non-90° contact angles.
Journal ArticleDOI
Superelasticity of slim hysteresis over a wide temperature range by nanodomains of martensite
Dong Wang,Sen Hou,Yu Wang,Xiangdong Ding,Shuai Ren,Xiaobing Ren,Xiaobing Ren,Yunzhi Wang,Yunzhi Wang +8 more
TL;DR: By nanostrain-domain engineering of shape memory alloys via impurity doping, the authors showed a new mechanism that leads to superelasticity with slim hysteresis across a wide temperature range.
Journal ArticleDOI
Modeling dendritic solidification of Al–3%Cu using cellular automaton and phase-field methods
TL;DR: In this paper, the authors compared a cellular automaton (CA) and a phase-field (PF) model to simulate equiaxed dendritic growth during the solidification of cubic crystals.
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.