"Investigation of the diffraction of x-rays by liquids was begun soon after the well-known work of Friedrich, Knipping, and Laue proved to be of value in supplying information as to the arrangement of atoms in crystalline matter. Friedrich in 1913 reported x-ray diffraction patterns of Canadian Balsam, paraffin, and amber; three years later Debye and Scherrer, in their work on benzene, (among other liquids investigated) showed that the diffraction phenomenon exhibited was one of interference. Still later, in 1922, Keesom and de Smedt reported similar investigations carried out on argon, nitrogen, and oxygen in the liquid state, the results of which confirmed the physical nature of the effect, as had been postulated by Debye and Scherrer.
Since that time many advances in both the experimental and theoretical aspects of the subject have been made, and a wealth of data has been obtained on at least 23 elements in the liquid state. An excellent summary of this material, together with a discussion of the conventional theoretical treatment has been prepared by Gingrich. As Gingrich indicates, data of this latter type (i.e., for liquid elements) is more conducive to accurate theoretical treatment than polyatomic materials, since fewer assumptions need be applied in deducing the atomic distribution from the diffraction pattern.
A recent paper by Lund treats the theoretical problem from a statistical mechanical viewpoint, in which a configuration subspace with single cell occupancy is envisioned, thus embracing the free-volume concept as recently expounded by Kirkwood. This concept is given considerably more support through a statistical approach than the conventional treatment provides.
It is the purpose of this investigation to determine what differences, if any, arise in the calculation of scattered intensities using the equation derived on a statistical mechanical basis as compared with the results of the conventional scattering equation. This will be done by calculation with both equations the scattered intensities from liquids characterized by certain assumed cell distribution functions. In addition, an attempt will be made to find a means by which the integrations in the original derivations of the scattering equations may be simplified. An inquiry into the effect of varying the ratio of atomic radius to free-volume radius on scattering calculations for a given assumed distribution function will also be carried out, using the results of the simplified derivation"--Introduction, pages 1-2.
Lund, Louis H., 1919-1998
M.S. in Physics
Missouri School of Mines and Metallurgy
v, 45 pages
© 1954 Charles A. Hewett, All rights reserved.
Thesis - Open Access
X-rays -- Scattering -- Mathematical models
X-rays -- Diffraction -- Mathematical models
Crystallography -- Mathematical models
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Link to Catalog Record
Hewett, Charles A., "A model for x-ray scattering from a free-volume liquid" (1954). Masters Theses. 4160.