X-Ray Scattering at Small Angles by Finely-Divided Solids. II. Exact Theory for Random Distributions of Spheroidal Particles

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Abstract
The theory of the scattering of x-rays at small angles is given for a continuous distribution in size of randomly spaced and oriented spheroidal particles having arbitrary, but fixed, shape. Families of scattering curves are presented for spheres, and for spheroids ranging in shape from flat disks to long rods. Both Maxwellian and rectangular types of particle mass distribution are used. A fit between the experimental and a calculated scattering curve enables one, under favorable circumstances, to determine the mass distribution in the test sample. However, an unambiguous interpretation of the experimental scattering curve on the basis of the small angle scattering theory is not possible without additional evidence from independent investigations of such quantities as particle shape and sample specific surface.