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
A phase field model for the simulation of grain growth in materials containing finely dispersed incoherent second-phase particles
TL;DR: In this paper, a phase field model is presented for simulating grain growth in materials containing small incoherent second-phase particles that are constant in time, and the model of [L.-Q. Chen, W. Yang, Phys. Rev.
Journal ArticleDOI
A phase-field model for chemo-mechanical induced fracture in lithium-ion battery electrode particles
TL;DR: In this paper, a finite strain theory for chemo-elasticity coupled with phase-field modeling of fracture is proposed to regularize a sharp crack topology, which leads to battery capacity fade.
Journal ArticleDOI
Efficient energy stable numerical schemes for a phase field moving contact line model
Jie Shen,Xiaofeng Yang,Haijun Yu +2 more
TL;DR: The efficiency and fast convergence of the proposed schemes with spectral spatial approximations are numerically verified andrete energy laws that are consistent to the continuous ones are proved.
Journal ArticleDOI
A study of the coarsening in tin/lead solders
W. Dreyer,Wolfgang H. Müller +1 more
TL;DR: In this article, the authors present a model based on continuum theory to simulate the coarsening process observed during thermo-mechanical treatment of binary tin-lead solders, where Fourier transforms and spectral theory are used for the numerical treatment of the thermoelastic as well as of the diffusion problem encountered during phase separation in these alloys.
Journal ArticleDOI
Thermodynamics of grain boundary premelting in alloys. I. Phase-field modeling
TL;DR: In this article, the authors analyzed the rich nature of the premelting transition of grain boundaries in solid solutions using a multi-phase field model, whereas Part II employs atomistic Monte Carlo simulations.
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.