Specifying Unanalyzed Elements For a Proper Matrix Correction

[DavidAdams]

Short answer is you can't for glasses.

The ferric/ferrous excess oxygen calculation is based on charge balance (Droop, 1987) so a formula (number of cations and oxygens) is required for it to work. We even got it to work for most amphibole compositions with a lot of help from Andrew Locock and Aurelien Moy.

But I guess I'm not sure why you want to try this when you already have ferric/ferrous contents from wet chemistry.  Just specify the excess oxygen from ferric iron in PFE and it will perform a matrix correction and should give you nicer totals.

I don't know, I just thought there might be an easy way in the software to input a known ratio for oxidation states for all the various elements out there that have been determined by other techniques such as wet chemistry, XANES, EELS, Raman etc. without having to calculated the excess oxygen external to PfE then input that excess oxygen into the software in order to have it calculated the matrix corrections. I suppose that was a silly assumption on my part. Thanks for the clarification about ferrous/ferric calculation option in the software!

[Probeman]

Short answer is you can't for glasses.

The ferric/ferrous excess oxygen calculation is based on charge balance (Droop, 1987) so a formula (number of cations and oxygens) is required for it to work. We even got it to work for most amphibole compositions with a lot of help from Andrew Locock and Aurelien Moy.

But I guess I'm not sure why you want to try this when you already have ferric/ferrous contents from wet chemistry.  Just specify the excess oxygen from ferric iron in PFE and it will perform a matrix correction and should give you nicer totals.

I don't know, I just thought there might be an easy way in the software to input a known ratio for oxidation states for all the various elements out there that have been determined by other techniques such as wet chemistry, XANES, EELS, Raman etc. without having to calculated the excess oxygen external to PfE then input that excess oxygen into the software in order to have it calculated the matrix corrections. I suppose that was a silly assumption on my part. Thanks for the clarification about ferrous/ferric calculation option in the software!

Oh, sorry. I get what you're after now.

Yes, you can specify the Fe:O ratio using any (1 to 99) integers from the Elements/Cations dialog.

So for example, instead of FeO or Fe2O3 or Fe3O4, you could specify Fe4O5 or Fe4O6 or Fe5O7 or whatever.

[AndrewLocock]

Yes, you can specify the Fe:O ratio using any (1 to 99) integers from the Elements/Cations dialog.

So for example, instead of FeO or Fe2O3 or Fe3O4, you could specify Fe4O5 or Fe4O6 or Fe5O7 or whatever.

There are certain limitations to using the integer Fe_xO_y method for specifying the proportions of ferric- and ferrous iron.
For this method, the ratio of x:y ranges from 2:3 up to 1:1, but both x and y must be integers, e.g., Fe₆₆O₉₉ and Fe₉₉O₉₉.
These correspond to Fe₂O₃ and FeO, respectively.

From inspection of the higher values of y:
The minimum proportion of ferric iron, Fe³⁺/ΣFe (other than zero percent), is 2.041%, given by the moiety Fe₉₈O₉₉.
The maximum proportion of ferric iron, Fe³⁺/ΣFe (other than one hundred percent), is 98.462%, given by the moiety Fe₆₅O₉₇.

One may wish to specify a proportion of ferric iron, Fe³⁺/ΣFe less than 2.041% (or conceivably more than 98.462 w%).
If the concentration of total iron is known (or can be estimated to a reasonable precision), one can calculate and then specify the "excess oxygen".
If the matrix corrections result in a change in the amount of total iron, the "excess oxygen" can be recalculated, and the process iterated manually.

Cheers,
Andrew

[Probeman]

Yes, you are absolutely correct.  If the amount of oxygen you are adding is less than a percent or two (relative), your suggestion of specifying the ferric oxygen as excess oxygen works fine.

Either way, they get included in the matrix (and MAN) corrections.

[Probeman]

I just wanted to note that one can also use the CalcZAF application for making these sorts of excess oxygen calculations.

So for example see this order of clicks and instructions:



1. Note that the default cation ratio for Fe oxide is 1:1 or FeO.  That can be modified of course by clicking on the element row.

2. Click the Enter Composition As Formula String button and enter whatever ratio you want from 1 to 99 for the cation and 0 to 99 for oxygen.  For example Fe98O99 or very slightly more oxidized than FeO (in CalcZAF you can actually enter any short integer (1 to 32K) for the formula units, unlike PFE). Click OK.

3. Next click the Calculation Options button and check the Display Results as Oxide Formula checkbox. Click OK.

4. Click the Calculate button and you will obtain the following output:

fe98o99, sample 1

Current Mass Absorption Coefficients From:
LINEMU   Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV

  Z-LINE   X-RAY Z-ABSOR     MAC
      Fe      ka      Fe  6.8270e+01
      Fe      ka      O   2.2548e+01
      O       ka      Fe  4.0015e+03
      O       ka      O   1.1999e+03

 ELEMENT  ABSFAC  ZEDFAC  FINFAC STP-POW BKS-COR   F(x)e
   Fe ka  1.0157  4.3900  4.4588   .2087   .9161   .9846
   O  ka  1.4270  3.9154  5.5873   .2438   .9546   .7008

SAMPLE: 32767, TOA: 40, ITERATIONS: 0, Z-BAR: 21.95976

 ELEMENT  ABSCOR  FLUCOR  ZEDCOR  ZAFCOR STP-POW BKS-COR   F(x)u      Ec   Eo/Ec    MACs
   Fe ka   .9974  1.0000  1.0534  1.0507  1.0759   .9791   .9871  7.1120  2.1091 58.0072
   O  ka  1.7001   .9927   .8553  1.4435   .7847  1.0900   .4122   .5317 28.2114 3372.68

 ELEMENT   K-RAW K-VALUE ELEMWT% OXIDWT% ATOMIC% FORMULA KILOVOL                                       
   Fe ka  .00000  .73813  77.554  99.773  49.746   1.000   15.00                                       
   O                      22.446    .227  50.254   1.010                                       
   TOTAL:                100.000 100.000 100.000   2.010

The Fe is displayed as FeO (99.73%), since that is the currently defined stoichiometry for Fe, but the oxygen (0.227%) is displayed as the *excess" oxygen based on the formula Fe98O99!

Note you have to re-check the Display Results as Oxide Formulas for each new formula entered.  Try it out.

[Joe Boesenberg]

Are there any proper correction procedures for situations where the sample mineral is porous? I am thinking of two cases: some serpentine minerals and chert. Obviously, you get low totals. You have the added problem that both phases can have significant water. I get asked very often can you just scale up the analysis to 100 and I constantly tell the users "no". But is there a correction procedure that can be applied? Thanks.

[Anette von der Handt]

You may want to look into particle analyses by EPMA, specifically the peak-to-background ratio method. This is the usual recommendation to approaching quantitative analysis of porous samples. Otherwise, there are also recommendation to utilize standardless Monte Carlo simulations.

As per the Reed (2005) book: Another possibility is to measure peak-to-background ratios and make use of the fact that the effect of particle geometry on the continuum is similar to that on characteristic X-rays of the same energy (Statham and Pawley, 1977; Small, Newbury and Myklebust, 1979). Concentrations can be derived from peak-to-background ratios measured on the sample compared with ratios measured on standards. In ED spectra it is often necessary to remove the peaks by ‘stripping’ in order to determine the background, owing to the lack of suitable peak-free regions in the spectrum. The precision of measured peak to-background ratios is governed by the statistical error in the relatively low background intensity: this necessitates longer acquisition times than are customarily used for measuring peaks.

Some more references that may be relevant:
Goldstein, J.I., Newbury, D.E., Michael, J.R., Ritchie, N.W.M., Scott, J.H.J., Joy, D.C. (2018). Analysis of Specimens with Special Geometry: Irregular Bulk Objects and Particles. In: Scanning Electron Microscopy and X-Ray Microanalysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6676-9_23
Newbury, D. E. (2004). Quantitative electron probe microanalysis of rough targets: Testing the peak‐to‐local background method. Scanning: The Journal of Scanning Microscopies, 26(3), 103-114.
Sorbier, L., Rosenberg, E., & Merlet, C. (2004). Microanalysis of porous materials. Microscopy and Microanalysis, 10(6), 745-752.
Sorbier, L., Rosenberg, E., Merlet, C., & Llovet, X. (2000). EPMA of porous media: A Monte Carlo approach. Microchimica Acta, 132, 189-199.

[Joe Boesenberg]

Thanks Anette,

I will take a look at the references you supplied.


Would the analysis still be valid, if the standard were the same mineral and porous, just as the unknown (chert standard and chert unknown), or am I degrading now the analysis, by compromising the standard? The porosity may not be the same in both, but would be closer.

Thanks.
Joe

[Probeman]

Are there any proper correction procedures for situations where the sample mineral is porous? I am thinking of two cases: some serpentine minerals and chert. Obviously, you get low totals. You have the added problem that both phases can have significant water. I get asked very often can you just scale up the analysis to 100 and I constantly tell the users "no". But is there a correction procedure that can be applied? Thanks.

Great question. Anette's response is exactly on-point, so I can just mention a few random thoughts about porosity...

Porosity is a complicated subject. In the extreme porosity does not matter in (non-thin film) analysis EPMA as the distance between the atoms does not make a difference for the matrix corrections as long as the incident electrons come to rest inside the sample (interaction volume).  And technically, for fully conductive samples where the porosity/voids are "filled" with vacuum, the porosity should also not make any difference.

However, problems with porosity begin to be a problem when the sample is not conductive and/or the voids are able to retain surface charging, and/or the voids are filled with some gas or liquid, and/or the voids are coated with adsorbed water, etc.  Then Anette's suggestions are worth applying.

To answer your last question, yes, if we had a standard serpentinite that had the same exact porosity characteristics as our unknown, that could normalize out these effects, but of course that is not usually an option!   

And regarding water, yes absolutely it should be included in the matrix correction!  First to obtain an accurate matrix correction for the other elements which will be affected quite strongly by this "missing" water:

https://probesoftware.com/smf/index.php?topic=92.msg8485;topicseen#msg8485

In fact even a few wt% missing water can affect the matrix correction surprisingly enough as this hydrous glass analysis shows:

https://probesoftware.com/smf/index.php?topic=92.msg8439;topicseen#msg8439

See also:

Roman, D. C., Cashman, K. V., Gardner, C. A., Wallace, P. J., & Donovan, J. J. (2006). Storage and interaction of compositionally heterogeneous magmas from the 1986 eruption of Augustine Volcano, Alaska. Bulletin of Volcanology, 68, 240-254.

[John Donovan]

I'm adding a description of this specify unanalyzed element concentrations by input text file here so I can refer to it in another post.

A long, long time ago... Heather Lowers at the USGS in Denver asked for a way to input lots of concentrations analyzed from another technique into Probe for EPMA by using a text file which listed the sample names and element concentrations using this button:



I've never used it, but apparently they do. Here is the section from  the User Reference Manual on this feature:

[Probeman]

I just wanted to mention the paper published last year by Dungan, Donovan, Locock and Bullock which demonstrates improved accuracy for major elements (especially Fe), when excess oxygen from ferric iron is included in the matrix correction. See attached pdf below which was published last year in American Mineralogist.

See also this post by John Donovan pointing out how to perform these calculations in Probe for EPMA (and CalcZAF) based on a suggestion from Andrew Locock and Anette von der Handt to utilize the method of Droop (1989) for calculating excess oxygen from ferric iron back in 2019:

https://probesoftware.com/smf/index.php?topic=92.msg8593#msg8593

This implementation of this was assisted by Anette von der Handt and Andrew Locock which was extended to amphibole calculations. The idea for including  excess oxygen from ferric iron is an old idea, but based on ideas contributed by many other people including John Donovan, Brian Joy, Aurelien Moy and John Fournelle on the need to include all unanalyzed elements into the matrix correction for the most accurate EPMA analyses.

In the case on excess oxygen from ferric iron in Hematite, without incorporating this excess oxygen, the Fe concentrations will be low by around 1 wt% absolute, resulting in not only a low total, but also inaccurate Fe (and Ti in Fe-Ti oxides).

Aurelien Moy will be publishing a technical paper describing the physics of these various matrix effects for various unanalyzed elements situations, including excess oxygen, but also for other elements, e.g., carbon in carbonates, water in hydrous glasses, boron in boro-silicates, etc.

See also these other publications:

Tingle, Tracy N., et al. "The effect of “missing”(unanalyzed) oxygen on quantitative electron probe microanalysis of hydrous silicate and oxide minerals." Geological Society of America Abstracts with Programs. Vol. 28. No. 6. 1996.

Moy, Aurélien, et al. "On the Importance of Including All Elements in the EPMA Matrix Correction." (2023): 855-856.

[John Donovan]

One of the interesting aspects to Probe for EPMA is that one can calculate the same data in multiple ways, for example, one can acquire data using off-peak backgrounds and calculate the quant results using the off-peak background method. 

But one can also take that same data (usually one should first copy the MDB file to another folder just to keep things straight), and then proceed to apply MAN backgrounds to those same measurements by simply ignoring the off-peak intensities as described here:

https://probesoftware.com/smf/index.php?topic=4.msg2255#msg2255
https://probesoftware.com/smf/index.php?topic=987.msg6455#msg6455

One will find that one can attain about 40% better precision than off-peak backgrounds (in 1/2 the acquisition time!) as explained in our 2016 paper (Donovan et al., 2016, Amer. Min.) and also improve accuracy by utilizing a blank correction.

However, one can also calculate the same data using different ways of specifying unanalyzed elements as well. For example one could specify a fixed concentration of an element, or one could specify to calculate an unanalyzed element (or formula) by difference.

Recently Anette von der Handt measured oxygen for some materials using quantitative x-ray mapping and wanted to compare the measured (and calculated excess oxygen) using measured oxygen, with the Droop et al. method for calculating excess oxygen from ferric iron based on charge balance and a mineral formula.  I'll post on using the ferric/ferrous method in CalcImage in the CalcImage board in a moment, but let's start with the Droop method for calculating excess oxygen in Probe for EPMA first, because I had to remember how this needs to be done, when oxygen is measured.

So, we've measured oxygen and now we have a result in say a magnetite material:



And we're within ~1.3% relative so not too bad (of course using empirical MACs from Pouchou and Bastin!). But now we want to see how this direct measurement result compares to simply calculating our excess oxygen from ferric iron, because, well you know, we had to give up a spectrometer just to measure oxygen!  And maybe using the Droop charge balance method we can do just as well, at least maybe for excess oxygen in magnetites...

So we go (after making a copy of our MDB file!) into the Calculation Options dialog in Probe for EPMA and select the Ferrous/Ferric method for our magnetite material and specify oxygen by stoichiometry, and then we get this error:



Doh!  If we try and quantify with both measured oxygen *and* oxygen calculated by stoichiometry, we will be adding oxygen *twice* into the matrix correction, and that's no good, right?

OK, so what do we do?  Well, we need to disable the measured oxygen for quantification from the Elements/Cations dialog as seen here:



And now we can go back into Calculation Options and specify our ferric/ferrous formula and oxygen by stoicihiometry. Now when we quantify our magnetite material we obtain this result:



Wait, what the heck?  We've got our excess oxygen from ferric iron calculated properly (6.88 wt%) but our totals are low by exactly that amount!  And that's because although the excess oxygen from ferric iron was calculated and included into the matrix correction, it was not output to the user!  And that's because there's no place to print it out since the only oxygen column present is the measured oxygen column which is reserved for the measurement results and we disabled the measured oxygen for quantification.

So what we need to do is, add oxygen as an *unanalyzed* element to our element list as seen here:



Remember, an unanalyzed element is simply an element *without* an x-ray line specified.  Now let's calculate the concentrations again:



Well now, that's pretty neat, isn't it?       But it took me a minute to remember all this when looking at Anette's x-ray maps in CalcImage, where she basically wanted to do the same thing but for maps!  I'll post more about that in a bit in the CalcImage topic...