X ray characteristic intensity Ii , emerging from element i in a bulk sample irradiated with an electron beam may be obtained throughwhere the function ϕi(ρz) is the distribution of ionizations for element i with the mass depth ρz, ψ is the take-off angle and μi the mass absorption coefficient to the radiation of element i.A number of models has been proposed for ϕ(ρz), involving several features concerning the interaction of electrons with matter, e.g. ionization cross section, stopping power, mean ionization potential, electron backscattering, mass absorption coefficients (MAC’s). Several expressions have been developed for these parameters, on which the accuracy of the correction procedures depends.A great number of experimental data and Monte Carlo simulations show that the general shape of ϕ(ρz) curves remains substantially the same when changing the incident electron energy or the sample material. These variables appear in the parameters involved in the expressions for ϕ(ρz). A good description of this function will produce an adequate combined atomic number and absorption correction.
Minkowski’s inequality and sums of squares