"A liquid or a dense gas may be regarded either as a very imperfect gas in which multiple collisions are frequent or as a distorted crystal in which the long range order has been lost. The crystal-like approach has not led to formal solutions, but it has led to several approximate treatments which can be used to give numerical results.
The two main types of approaches which have been used are: the cell theories, in which the liquid is regarded as a distorted crystal with one molecule located at or near each lattice point; and the hole theories, in which it is realized that liquids differ from crystals in that some of the lattice sites are vacant….
There have been two major developments of the cell theories: that of Eyring and his colleagues and that due to Leonard-Jones and Devonshire. Both these groups of investigators established their theories of the liquid state by means of well-founded physical intuition. The basic expressions which were the starting point for their researches have been justified by Kirkwood, who has shown rigorously what assumptions are inherent in both theories. Kirkwood, starting from the general principles of statistical mechanics and using certain well defined approximations, expresses the Gibbs configuration integral as a sum of integrals corresponding to single and multiple occupancy of the cells of a reference lattice. The integral corresponding to single occupancy is then evaluated with the approximate probability density, expressed as a product of functions of the coordinates of individual molecules, which leads to minimum free energy under the restraints of constant temperature and volume. The minimization of the free energy gives an integral equation for the probability density within each cell or the lattice. A first approximation of the solution of this equation yields a partition function identical with that of the Lennard-Jones Devonshire free volume theory. If convergent, an iteration of Kirkwood's integral equation might provide an improvement on the Lennard-Jones Devonshire theory.
The purpose of this research is to determine whether or not the iteration of Kirkwood's integral equation is convergent for liquid Argon"--Introduction, pages 1-3.
Lund, Louis H., 1919-1998
M.S. in Physics
Missouri School of Mines and Metallurgy
iv, 33 pages
© 1958 Eugene D. Fabricius, All rights reserved.
Thesis - Open Access
Long range order (Solid state physics)
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Fabricius, Eugene D., "Iterative solutions of Kirkwood's integral for liquid argon" (1958). Masters Theses. 2555.