"The study of liquids and the knowledge of an adequate description of liquid structure have not advanced as rapidly as it has in the case of solids and gases. In a perfect crystal, the atoms or molecules are held in equilibrium positions by strong intermolecular forces. There are vibrations about these positions, but the translational energy is negligible. The molecules of an ideal gas move independently of each other and the intermolecular potential energy may be neglected. For each of these cases it is possible to derive a partition function from which the properties of the state can be readily derived.
The liquid state presents quite a different problem. The intermolecular forces are sufficiently great to keep the molecules in the condensed phase, but considerable translational motion is allowed. However, the structure of the liquid may be treated as quasi-crystalline, where each atom is trapped, at least temporarily, in a small spherical cell. Within this cell the atom can move independently of its neighbors. On this basis the probability of a neighbor atom being found between the distances r and r + dr can be calculated. In this manner the radial density function can be derived, and the volume of the cell in which the center of a given atom is free to move can be determined.
Studies of the x-ray diffraction patterns obtained from liquid elements have revealed much information concerning the structure of the liquid state. They have led to a direct determination of the distribution of atoms around any given atom. This description of the structure of the liquid state may be correlated with and used to determine the characteristic properties of the liquid.
It is the purpose of this paper to apply an analytical radial density, or atomic distribution function as proposed by Wall to experimentally determined distribution curves. The validity of the function is tested for the first time over a wide range of temperature for liquid mercury. The calculated curves are shown for comparison with those obtained by Fourier analysis of x-ray diffraction photographs. From this information the latent heats of fusion and vaporization are calculated and compared with observed values.
An attempt is made to correlate the free volume, within which the atom center is free to move, with the free surface energy of the liquid. The liquid is treated as a continuous medium permeated with microscopic cavities or holes of variable size. These holes, having a radius equal to that of the free volume, are not considered as a separate phase. Therefore the energy associated with the creation of such a hole should not be the total surface tension. An appropriately modified surface tension, operative at the surface of the hole, does lead to a formula adequately representing the surface tension over a wide range of temperature"--Introduction, pages 1-2.
Lund, Louis H., 1919-1998
M.S. in Physics
Missouri School of Mines and Metallurgy
v, 22 pages
© 1951 Robert Lee Choate, All rights reserved.
Thesis - Open Access
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Choate, Robert Lee, "An application of the atomic distribution function of liquid mercury" (1951). Masters Theses. 2997.