There is a subtle issue regarding elements by difference when the total (without the element by difference) exceeds 100%. For example when calculating water concentration in an alkali glass by the difference of the sum of cations measured (and anions measured or calculated), from 100%. Because when the totals are close to 100%, statistically some points may range over 100% merely by chance. Therefore an appropriate quantification of every data point is critical for a valid average of the H2O by difference. You might want to review the statistical issues in this post before proceeding:

http://probesoftware.com/smf/index.php?topic=922.msg5948#msg5948The point being that we obtain a more accurate average when the element by difference is added in as a *negative* concentration, for those points where the total (without the element by difference), happens to be *greater* than 100%, for whatever reason. The statistical considerations are similar to proper averaging of trace measurements close to zero, as in the post linked here:

http://probesoftware.com/smf/index.php?topic=579.msg3312#msg3312On the other hand, when one is calculating a quantitative map and applying an element (or formula) by difference, because every pixel is not a perfect measurement (due to cracks or pits or heterogeneous interaction volumes at phase boundaries), these negative concentrations could cause a problem for the matrix corrections when applied on a pixel by pixel basis.

For example, one might be measuring oxygen, but if the electron beam falls into a surface crack, there will be very little oxygen Ka emitted due to the much longer absorption path to the spectrometer, while other higher energy emissions lines are less affected. So for example, if one is calculating hydrogen by stoichiometry to excess oxygen (ideal - measured), the resulting *deficit* oxygen will result in a negative result, possibly causing problems due to the non-physical nature of the matrix calculation.

After thinking a bit about it, I've decided to utilize the already existing Force Negative K-Ratios To Zero flag in the Analytical | Analysis Options dialog as seen here:

for the "element by difference", "formula by difference" and the "hydrogen by stoichiometry to excess oxygen" calculations (this flag was already being utilized in the "element by difference" calculation, so this merely makes the other calculations statistically similar). The default will be to allow negative concentrations of these elements to be included in the matrix correction for improved average statistics. But when the Force Negative K-Ratios To Zero checkbox is checked, it will only allow positive concentrations to be included in the matrix correction calculations. This being to deal with non-ideal physical situations when mapping many pixels in a quant map.

This will have benefits when one is calculating quant maps with matrix situations where elements, formulas and hydrogen are being calculated by difference as seen here:

and when pixels in voids, cracks, and phase boundaries are present. Thanks to John Fournelle who brought this issue to my attention.

This change is available in Probe for EPMA v. 12.1.3 and now ready for download.