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
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Journal ArticleDOI
Eddy viscosity of parity-invariant flow.
Bérengère Dubrulle,Uriel Frisch +1 more
TL;DR: In this article, a general formalism is developed to determine eddy viscosities for incompressible flow of arbitrary dimensionality subject to forcing periodic in space and time, and the dynamics of weak large-scale perturbations is obtained by a multiscale analysis.
Journal ArticleDOI
TIMBIR: A Method for Time-Space Reconstruction From Interlaced Views
K. Aditya Mohan,Singanallur Venkatakrishnan,John W. Gibbs,Emine Begum Gulsoy,Xianghui Xiao,Marc De Graef,Peter W. Voorhees,Charles A. Bouman +7 more
TL;DR: Recon reconstructions of both simulated and real X-ray synchrotron data are presented, which indicate that TIMBIR can improve temporal resolution by an order of magnitude relative to existing approaches.
Journal ArticleDOI
Coarsening dynamics of the convective Cahn-Hilliard equation
TL;DR: In this article, a sharp-interface theory is proposed to characterize the coarsening dynamics associated with a convective Cahn-Hilliard equation (cCH) in one space dimension, where two types of phase boundaries (kink and anti-kink) arise, due to the presence of convection, and their motions are governed to leading order by a nearest-neighbors interaction co-arsening dynamical system.
Journal ArticleDOI
Phase nucleation through confined spinodal fluctuations at crystal defects evidenced in Fe-Mn alloys
A. Kwiatkowski da Silva,Dirk Ponge,Zirong Peng,Gerhard Inden,Yifeng Lu,Andrew J. Breen,Baptiste Gault,Dierk Raabe +7 more
TL;DR: Spinodal fluctuations at dislocations and grain boundaries in an iron alloy are observed, which may be precursors in a multistep nucleation process.
Journal ArticleDOI
Finite element approximation of a Cahn−Hilliard−Navier−Stokes system
TL;DR: A semi-discrete and a practical fully discrete finite element approximation of a Cahn-Hilliard-Navier-Stokes system arises in the modelling of multiphase fluid systems and the convergence of the fully discrete approximation is shown.
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.