Quantitative electron microprobe analysis of homogeneous bulk samples

where Q*i is the cross section per atom for ionization of the selected subshell of the i element, taking into account both direct ionization by the electrons of energy E and the effect of indirect ionizations at that subshell caused by the Coster-Kronig transitions. N, ρ, t and N are Avogadro's number, the density and thickness of a very thin tracer layer made of the i element and the number of primary electrons, respectively. The mass fraction, atomic weight, fluorescence yield and weight of line for the i element is designated by ci, Ai, ω and a, respectively, while Ω and ε are the solid angle and the detection efficiency of the detector. The integral in curly bracket in the center describes the depth distribution of ionization in the bulk sample with respect to the tracer layer and the self-absorption of the X-rays. We shall deal with these quantities in more details later.