A rigorous, general characteristic fluorescence correction for the electron microprobe analysis of samples of given geometry is developed, and specific versions of this equation are presented for the calculation of the fluorescence produced (a) within a homogeneous thin film, (b) in a thin film by x‐ray emission from substrate layers of arbitrary thickness and (c) in a spherical particle. Results of the use of these equations are compared with those obtained using empirical expressions for thin films and show that the empirical expressions are accurate only for films less than 1 μm in thickness. A simplified empirical correction is proposed for particles that is in good agreement with the rigorous correction. The results of calculations using these expressions show that a 2000 Å thick film or a 1 μm diameter particle typically has about 10% of the relative contribution from characteristic fluorescence as occurs in an infinitely thick polished specimen (TPS), a 1 μm thick film has about 30–40% of the contribution in a TPS and a 10 μm diameter particle has more than 50% of the contribution in a TPS. Thus, in particular matrices, certain elements in a 2000 Å thin film or a 1 μm particle can have characteristic fluorescence corrections as high as 5%.
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