Journal ArticleDOI
Statistical Mechanics of Fusion
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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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Radial Distribution Functions and the Equation of State of a Fluid Composed of Rigid Spherical Molecules
TL;DR: In this paper, the integral equation for the radial distribution function of a fluid of rigid spherical molecules has been integrated numerically in the Kirkwood approximation and in the Born-Green approximation over a wide range of densities.
Journal ArticleDOI
Theory of Translational and Orientational Melting with Application of Liquid Crystals. I
TL;DR: A theory of translational and orientational melting with application to liquid crystals is presented in this article in a manner analogous to that of Kirkwood and Monroe by introducing both translational or orientational order parameters.
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A molecular theory of the solid–liquid interface. II. Study of bcc crystal–melt interfaces
David W. Oxtoby,A. D. J. Haymet +1 more
TL;DR: In this paper, the authors extended and applied their previously developed order parameter theory for the solid-liquid interface and showed how the differential equations for interfacial structure from their earlier work may be reformulated in terms of a variational principle and demonstrate that the quantity minimized gives the surface free energy.
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On the van der Waals Theory of the Vapor‐Liquid Equilibrium. II. Discussion of the Distribution Functions
TL;DR: In this paper, the authors derived general expressions for the two-and three-particle distribution functions for the same one-dimensional fluid model discussed in Part I, and showed that these distribution functions depend on all the eigenvalues and eigenfunctions of the basic Kac integral equation.
Journal ArticleDOI
Theory of Translational and Orientational Melting with Application to Liquid Crystals
TL;DR: A theory of melting with application to liquid crystals in which both translational and orientational order parameters are taken into account is developed in a manner similar to that of Kirkwood and Monroe as discussed by the authors.
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.
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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.
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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.