# Comparing wt% to at% which is normalized to 100%

I have measured the element composition of a sample using ICP-OES, and reported my results in wt%. A study which has analyzed the same sample types, but with an electron microprobe, has reported their element concentrations in at%, which in addition are normalized to 100 %. I would like to compare my results to those in the article, but I am not sure how.

I am able to convert the atomic percentages to weight percentages, but I am not sure how to tackle the normalization of the data. When I add the wt% of my sample, I only get to about 50%. This loss is attributed to that I have not analyzed oxygen and carbon, which I suspect would make up a significant portion of the sample weight.

However, the study I want to cite has indeed analyzed both oxygen and carbon, and all the other elements I have measured. I do not suspect that they have a very large portion of at% unaccounted for. Therefore I believe their un-normalized data is quite similar to their normalized data.

So, how should I proceed with comparing my data to theirs? Should I just argue, like I have done here, that I think their data is "comparable enough"?

I would appreciate any insight on the subject!

• I think this question will be difficult to answer without knowing more about the data. First can you elaborate on what you mean by "normalization"? Do you mean that in the at% study, all measurements added together were only 96% or 90% or 80% or something, and so to get all measurements to add to 100%, the simply divided each measurement by 0.96 (or 0.9 or 0.8)? Commented Apr 21, 2015 at 19:31
• Second, how to the raw at% measurements work? Atom percent has units of atoms of X per total atom (times 100). Are they measuring the raw number of total atoms in their OES experiment? Or are they just comparing their results to some calibration standard for each element measured? If the former, it should be straightforward to convert to wt%. If the latter, you should convert their calibration standards from at% to wt% and then recalculate their results. Commented Apr 21, 2015 at 19:34
• If you're missing at% or wt% data on more than one element, then I think you have an underdetermined system of linear equations with infinite solutions. If you don't measure every single element directly, which would be ideal, you can either only have one element missing (and assume it is entirely responsible for all the missing at% and wt%, which can be dangerous), or you need some sort of a priori knowledge of the chemical composition of the sample (e.g., if you know for sure that all nitrogen and oxygen atoms are in the form of $\ce{-NO2}$ groups, then clearly %at O = 2 * %at N) Commented Apr 21, 2015 at 19:57
• Curt: the article (Gunst et al. 2000, J. Environ. Monit., vol. 2, pp. 65-71) does not clarify the method of normalization; they simply state that they normalize the data to 100%. The technique with which they have measured the concentrations is wavelength-dispersive X-ray analysis, using an electron microprobe. The authors say that, "The X-ray count rates for each individual particle and for standard samples were obtained from elemental distribution maps.". I remember from laboratory exercises that the software asked it we wanted the percentages to add to 100, so I think it's a common thing.
– Yoda
Commented Apr 21, 2015 at 20:27
• Nicolau: The chemical composition is complex, and a variety of elements are present in several different chemical forms. Manganese, for instance, would be present as different oxides, or as SiMn complexes. I cannot attribute the lacking wt% to any one element, or any one molecule, but I assume that carbon and oxygen make up a significant part of the lacking sample weight.
– Yoda
Commented Apr 21, 2015 at 20:31