X-Ray Scattering at Small Angles by Finely-Divided Solids. I. General Approximate Theory and Applications

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Abstract
The general approximate theory of x-ray scattering at small angles by finely divided solids is reviewed. It is assumed that the x-ray scattering data can be interpreted in terms of a particle size distribution, with particle-to-particle scattering negligible. Scattered intensity curves for Maxwellian, Gaussian, and rectangular size distributions are calculated, and several procedures for obtaining a size distribution from the experimental scattering data are described. Details of the experimental technique are given, and evidence is presented to show that appreciable error can result if crystal-monochromated radiation is not used. General procedures are given for applying corrections to the experimental data for the slit geometry used. Scattering data, mass distribution curves, and average particle sizes are presented for amorphous silica gels and for crystalline oxides of alumina, nickel and iron. These data are shown to correlate well with the results of crystal size measurements by x-ray diffraction line broadening and with specific surface measurements. The average particle size values determined from the experimental data are shown to have considerable significance, at least for the type of materials considered here.

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