Heterogeneity Effects in X-Ray Analysis*

Abstract

A fundamental quantitative treatment of the heterogeneity effects in X-ray fluorescence has been made. The theory predicts that the grain-size effect appears only in a limited region of grain sizes which depends on the wavelength of the primary radiation and the nature of the compounds in the mixture. With monochromatic radiation, the fluorescence intensity showed increase or decrease by a factor of a few units as grain size is decreased, A factor as large as 12, the theoretical value, has been observed in one particular experiment. Usually the grain-size effect can be eliminated by intensive grinding. For the light elements fine grinding is disastrous if long wavelengths are used. By an appropriate choice of the wavelength it is possible to eliminate the effect even without grinding. The mathematical treatment also predicts, but less rigorously, a grain-size effect in X-ray diffraction.The effect on the fluorescence intensities by changes in the chemical composition of the grains that contain the fluorescent element is predicted by the theory.These findings are discussed in relation to the analysis of elements when polychromatic beams are used.