"Thus, the determination of the structure of the material, and obtaining a distribution function which will enable the theoretical scattering to be predicted is the major problem.
In this work the diffraction material shall be considered to contain scattering regions of identical geometrical forms at such a distance from one another that they will essentially scatter the incident beam independently of their closest neighbor. An effort will be made to determine a correlation function characteristic of these forms, which may be interpreted as a distribution function, that might allow the low angle scattering pattern to be predicted. This correlation function will be independent of atomic structure. Then, if there were N geometrical forms in the sample, the total scattered intensity from the N forms would be N times that expected from one. The scattering at very small angles will be dominant, provided the wavelength or the radiation is small compared to the spatial extent of the scatterer. It will be this part of the pattern with which the work here is concerned.
The geometrical forms for which the correlation functions will be derived are, the linear case, circle, square, and the cube, each or constant electronic density. Physically, the circle might be taken as an approximation for a region in the form or a cylinder, whose length was very much less than the wavelength or incident x-ray beam. In a like manner the linear case and the square could be approximations to three dimensional shapes.
The calculated diffraction pattern found by use of the correlation function, which may contain a dimension of the geometrical form, may be used to find the dimension of the form by a fit of the theoretical curve to the experimental intensity curve.
The theoretical scattering may further be extended to cover the case in which the entire substance which is irradiated is considered to be the scatterer and is of the geometrical form under consideration. In this case the physical dimensions of the substance are large compared to the radiation wavelength and the scattering will be at very small angles.
It should be understood that the division of the experimental scattering intensity curve into its components, one of which is the small angle component, is arbitrary. Where the experimental curve shows excessive scattering at small angles, the small angle component has been taken to be that from zero angle (extrapolated) to the first minimum of the curve. The inhomogeneities, which are taken to be the geometrical forms already mentioned, are responsible for the small angle scattering"--Introduction, pages 3-5.
Lund, Louis H., 1919-1998
M.S. in Physics
Missouri School of Mines and Metallurgy
iv, 36 pages
© 1955 James Edwin Thomas, Jr., All rights reserved.
Thesis - Open Access
Small-angle x-ray scattering
Scattering (Physics) -- Mathematical models
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Link to Catalog Record
Thomas, James Edwin Jr., "Correlation functions for use in small angle x-ray scattering" (1955). Masters Theses. 2587.