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
Kinetics of fluctuations for systems undergoing phase transitions - interfacial approach
Kyozi Kawasaki,Takao Ohta +1 more
TL;DR: In this article, a dynamical interfacial model for quenched fluid systems is proposed and all the processes known to take place in critical fluid mixtures are identified for this model.
Journal ArticleDOI
An electron microscopy study of precipitation in Cu-Ti sideband alloys
TL;DR: In this paper, it is suggested that these periodic structures arise from spinodal decomposition and the experimental activation energy for the coarsening of the modulated structures is approximately 48 kcal/ mole.
Journal ArticleDOI
Calculation of interfacial properties of demixed fluids using density gradient theory
S. Enders,K. Quitzsch +1 more
TL;DR: In this article, the Cahn−Hilliard gradient theory was combined with the Lipschitz constant to deal with interfacial properties between two coexisting liquid or fluid phases in thermodynamic equilibrium.
Journal ArticleDOI
Phase separation in PM 2000™ Fe-base ODS alloy : Experimental study at the atomic level
TL;DR: In this paper, the coarsening of the three-dimensional microstructure resulting from phase separation during ageing at 748 K of a Fe-based PM 2000™ oxide dispersion strengthened (ODS) steel has been investigated by atom probe tomography and hardness measurements.
Journal ArticleDOI
Interfacial dynamics in demixing systems with ultralow interfacial tension
TL;DR: In this paper, the authors report measurements on fluid-fluid phase separation in a colloid-polymer mixture, which can be followed in great detail due to the ultralow interfacial tension.
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.