An Improved Average Atomic Number Calculation for Estimating Backscatter and Continuum Production in Compounds

It is often assumed that electron backscatter and continuum (bremsstrahlung) productions emitted from electron-solid interactions during X-ray microanalysis in compounds can be extrapolated from pure element observations by means of the assumption of average atomic number, or Z-bar (Z¯). For pure elements the average Z is equal to the atomic number, but this direct approach fails for compounds. The use of simple atomic fractions yields completely spurious results, and while the commonly used mass fraction Z averaging produces fairly reasonable results, we know from physical considerations that the mass of the neutron plays only a negligible role in such interactions below ∼1 MeV. Therefore, including the mass or atomic weight in such calculations can only introduce further errors in these models. We present an expression utilizing atomic fractions of the atomic numbers of the elements in the compound (Z fraction), with an exponent to account for the variation in nuclear screening as a function of the element Z value.