6.1 Fundamentals: the Shermann equation for Intermediate thickness samples

In 1955, Sherman proposed a mathematical formula to calculate the radiation intensity arising from the excitation of an analyte in a specimen of known composition. The derivation of this formula is made for an infinite slab sample being irradiated under an angle φ with a collimated excitation beam having a polychromatic emission described by the function I₀(E₀) and the XRF emission being registered by a detector positioned under and angle ψ.

(Inspired from an original lecture by Prof. P. Van Espen, AXES, University of Antwerp)

The Sherman formula is valid for samples of any thickness. Its complexity highlights the laborious character of implementing methods based on theoretical calculations. However, depending on the nature of the excitation radiation and on the value of the product χ_S(E₀,E_i)ρX some simplifications can be made.

Reference: J. Shermann, The theoretical derivation of fluorescent X-ray intensities from mixtures, Spectrochimica Acta 7 (1955) 283