5.4. ZAF Matrix Corrections
The ZAF correction scheme is based on first principles and provides data reduction for all operating conditions. If there were no inter-element (matrix) effects, the corrected intensity ratio could be converted to concentration using the formula called Castaing's 1st Approximation:
This is equivalent to the case of ideality in Bence-Albee (a = 1). However, as we noted, matrix effects due to absorption and fluorescence of X-rays within the sample and atomic number effects are significant. Matrix corrections can be expressed in the form:
where Funk and Fstd are matrix or ZAF factors for unknown and standard respectively.
The derivation of these factors is described below. Since the factors are dependent on composition, which is initially unknown, ZAF works in an iterative fashion similar to that of Bence-Albee. The intensity data are used with Castaing's 1st Approximation to get initial elemental concentrations that are refined in subsequent iterations until they converge.
ZAF is not very good for elements with X-ray energies less than 1 keV because of a lack of knowledge of the factors discussed below. For these elements it is best to use a standard of similar composition to minimize matrix effects. For example, when analyzing F in apatite, use a fluorapatite standard rather than a fluorphlogopite standard.