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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Comparison between potentiostatic and galvanostatic intermittent titration techniques for determination of chemical diffusion coefficients in ion-insertion electrodes
TL;DR: In this paper, the authors analyzed the limitations of potentiostatic and galvanostatic intermittent titration techniques (PITT and GITT, respectively) for determination of the differential (incremental) intercalation capacitance, Cdif, and the chemical diffusion coefficient, D, of Li ions in these ion-insertion electrodes (IIEs).
Journal ArticleDOI
Systematic prediction of kinetically limited crystal growth morphologies.
TL;DR: A new, combined experimental and theoretical approach is developed to make reliable predictions for the limiting case of surface reaction kinetics controlled growth, able to predict the growth for both convex and concave surfaces, with faceted and curved features.
Journal ArticleDOI
Pattern formation in plasticity
TL;DR: The approach of gradient-dependent constitutive equations as advocated by the author and his co-workers to address pattern-forming instabilities in plastic deformation is reviewed and new results are presented for both micro- and macro-plasticity phenomena.
Journal ArticleDOI
Numerical Study of the Cahn-Hilliard Equation in One, Two and Three Dimensions
TL;DR: In this paper, a stable and fast conservative finite difference scheme was proposed to solve the Cahn-Hilliard (CH) equation with two improvements: a splitting potential into an implicit and explicit in time part and the use of free boundary conditions.
Journal ArticleDOI
A Second-Order, Weakly Energy-Stable Pseudo-spectral Scheme for the Cahn---Hilliard Equation and Its Solution by the Homogeneous Linear Iteration Method
TL;DR: The numerical efficiency can be greatly improved, since the highly nonlinear system can be decomposed as an iteration of purely linear solvers, which can be implemented with the help of the FFT in a pseudo-spectral setting.
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.