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Journal ArticleDOI

Free Energy of a Nonuniform System. I. Interfacial Free Energy

John W. Cahn, +1 more
- 01 Feb 1958 - 
- Vol. 28, Iss: 2, pp 258-267
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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.

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Citations
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Journal ArticleDOI

Modelling of the surface tension of pure components with the gradient theory of fluid interfaces: a simple and accurate expression for the influence parameters

TL;DR: In this article, the gradient theory of fluid interfaces is used to compute the surface tension of substances of industrial interest (hydrocarbons, gases, and refrigerants) once an expression has been derived for their influence parameters.
Journal ArticleDOI

Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions

TL;DR: In this article, the Cahn-Hilliard equation with dynamic boundary conditions is interpreted as a parabolic equation on the boundary and by considering a regularized problem, the existence and uniqueness of solutions are obtained by the Leray-Schauder principle.
Journal ArticleDOI

Modelling thin-film dewetting on structured substrates and templates: Bifurcation analysis and numerical simulations

TL;DR: An extended parameter range of multistability of the pinning and coarsening morphologies is obtained and it is shown that the instability to transversal modes leading to a decay of the ridges into rows of drops may diminish the size of the parameter range where the pining of the thin film to the template is successful.
Journal ArticleDOI

Reflection and transmission of plane waves at surfaces carrying material properties and embedded in second-gradient materials

TL;DR: In this paper, reflection and transmission of compression and shear waves at structured interfaces between second-gradient continua is investigated, and two semi-infinite spaces filled with the same semidefinite spaces are modeled.
Journal ArticleDOI

Some links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continua

TL;DR: In this article, the authors compare two robust models of gradient elasticity and gradient plasticity, and one gradient model of heat transfer, as originally advocated by the second author in the 1980's.
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

R. Becker
- 01 Jan 1938 - 
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

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.
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