Journal ArticleDOI
Statistical Mechanics of Fusion
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TLDR
A statistical mechanical theory of fusion based upon the use of local free energies is presented in this paper. But this theory is restricted to the case of a set of parameters and is not suitable for all parameters.Abstract:
A statistical mechanical theory of fusion based upon the use of local free energies is presented. An integral equation is formulated for the distribution function of average density in a region occupied by a system of molecules. Periodic solutions characteristic of a crystalline phase are found for certain ranges of values of a set of parameters depending upon temperature and volume. When the parameters decrease below certain critical values, all terms of the Fourier series representing the distribution function vanish with the exception of the constant term. A uniform density distribution characteristic of a fluid phase is then obtained. The melting parameters of argon at several pressures are calculated with the aid of the theory and compared with experiment.read more
Citations
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On the liquid phase instability criterion
V. N. Ryzhov,E. E. Tareyeva +1 more
TL;DR: The criterion of instability of liquid towards solid formation (different from the Kirkwood's one) is derived on the base of investigation of the exact closed integral equation for the singlet distribution function as mentioned in this paper.
Journal ArticleDOI
An approximate equation for the radial distribution function in the hard sphere model
N.S. Gonchar,A.B. Rudyk +1 more
TL;DR: In this paper, the authors investigated the spatially homogeneous solution of a new approximate equation for the radial distribution function of classical hard core systems and showed that its bifurcation may be connected with a phase transition.
Journal ArticleDOI
Spontaneous symmetry breaking in nonlinear problems
TL;DR: Group representation theory is an important tool in analyzing the splitting of the energy levels of a Hamiltonian under symmetry-destroying perturbations (e.g., the Stark effect); but these methods also apply in a natural and elegant way to the nonlinear problems of bifurcation theory.
Journal ArticleDOI
Nematic-smectic phase transitions in liquid crystals
TL;DR: In this article, a new lattice theory of nematic-smectic phase transitions is presented by introducing both translational and orientational order parameters, and a lattice model for phase transition is presented.
Journal ArticleDOI
Solid-fluid transition of two- or three-dimensional systems with infinite-range interaction
TL;DR: In this article, the authors introduce particle systems whose potentials do not decay with distance and calculate their partition function exactly using a method similar to that for lattice systems with infinite-range interaction.
References
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Journal ArticleDOI
Statistical Mechanics of Fluid Mixtures
TL;DR: In this paper, the chemical potentials of the components of gas mixtures and liquid solutions are obtained in terms of relatively simple integrals in the configuration spaces of molecular pairs, and the molecular pair distribution functions appearing in these integrals are investigated in some detail, in their dependence upon the composition and density of the fluid.
Journal ArticleDOI
Thermodynamics of Crystals and Melting
TL;DR: In this article, the free energy of a rigid body is calculated as a function of temperature, and of the six homogeneous strain components, for a regular (cubic) lattice.
Journal ArticleDOI
Critical phenomena in gases - I
TL;DR: In this paper, it was shown that the van der Waals equation is not valid for gases at high densities such as obtain in the neighbourhood of the critical point, and that the usual method of representing isotherms as simple functions of density or pressure ceases to be useful.