5.4.1. Atomic Number Correction (Z)
The atomic number effect controls the amount of incident energy from the electron beam that is actually put into the sample. This effect consists of two components: backscattering and electron-stopping power (or retardation). Both are a function of average Z and, to a lesser degree, the accelerating voltage.
Backscattered electrons leave the sample carrying energy without producing X-rays. The fraction of electrons backscattered from the sample, nb, ranges from about 0.12 for Al to 0.55 for U. At lower Z, more electrons stay within the sample to produce X-rays. The backscatter correction factor (Fb) reflects the X-ray intensity lost due to backscattering and is expressed as a fraction (r) relative to the intensity that would be produced with no backscattering:
This fraction in part depends on the overvoltage, but not to a significant degree. The factor rarely exceeds 1.2 for Z less than 30.
The stopping-power correction (S) relates the amount of incident energy to the amount absorbed by atoms of specific Z. The electron-capture cross-section decreases with increasing Z. Thus, light atoms have a higher ratio of atomic number to atomic weight (Z/A) and interact with disproportionately larger numbers of incident electrons. The characteristic intensity per unit concentration of a heavy element is less when combined with a light element than in a sample of the pure element. Fs for a given element is:
S may be calculated using:
The mean ionization potential may be approximated by 11.5 Z.
Values for S must be calculated for each element separately because each has a different Ec. The average value of S for the unknown is calculated in a manner analogous to the mass absorption coefficient, using the mass concentrations fractions of the elements:
The net Z correction factor for both effects is: Fb x Fs.
The effects of backscattering and stopping power are opposing and can be canceling. For example, in the analysis of Fe2O3 with pure iron as a standard, the stopping power of oxygen reduces the intensity of Fe-Ka from the oxide relative to that from the pure standard. However, the lower mean atomic number of Fe2O3 (15.2) compared with pure iron (Z = 26) results in a smaller backscattering loss for the oxide when compared with the metal. The net effect is that the intensity of Fe-Ka is 7.2% lower (at 15 keV) than calculated on a basis of the relative concentrations in the two materials.