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
Dislocation Cell Formation in Metals
TL;DR: In this article, it is shown that an array of dislocations, modelled by parallel screw dislocation, of uniform density, is unstable, and that the instability grows ultimately into a dislocation cell structure and the cell size is given by the dominant wavelength of the density modulation.
Journal ArticleDOI
Clustering on surfaces
TL;DR: In this paper, the authors summarize the current theoretical and experimental understanding of clustering phenomena on surfaces, with an emphasis on dynamical properties, including surface diffusion coefficients and adatom binding energies.
Journal ArticleDOI
Regular Article: Modeling Melt Convection in Phase-Field Simulations of Solidification
TL;DR: In this article, a diffuse interface model is presented for direct numerical simulation of microstructure evolution in solidification processes involving convection in the liquid phase, where the solidification front is treated as a moving interface in the diffuse approximation.
Journal ArticleDOI
Phase Transitions and Generalized Motion by Mean Curvature
TL;DR: In this paper, the authors study the limiting behavior of solutions to appropriately rescaled versions of the Allen-Cahn equation, a simplified model for dynamic phase transitions, and rigorously establish the existence in the limit of a phase-antiphase interface evolving according to mean curvature motion.
Journal ArticleDOI
Nonlinear modelling of cancer: Bridging the gap between cells and tumours
John Lowengrub,Hermann B. Frieboes,Hermann B. Frieboes,Fang Jin,Fang Jin,Yao-Li Chuang,Xiangrong Li,Paul Macklin,Steven M. Wise,Vittorio Cristini +9 more
TL;DR: In this paper, the authors provide an overview of multiscale modelling focusing on the growth phase of tumours and bypassing the initial stage of tumourigenesis, and limit the scope further by considering models of tumor progression that do not distinguish tumour cells by their age and do not consider immune system interactions nor do they describe models of therapy.
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.