Re: Amphiboles normalization

[John Donovan]

As stated in Computers & Geosciences 62, 1–11:
“How should an algorithm determine which schemes are most appropriate for a given analysis? Hawthorne et al. (2012) showed that the constraints on the amphibole formula arising from the various cation normalization schemes could be treated as criteria. As the criteria are not each satisfied by every amphibole endmember, and as real analyses are imperfect, there will usually be deviations from the criteria. In the spreadsheet, for each of the four normalization schemes, the maximum magnitude of the deviations of the formula proportions from the following criteria is determined: Si < 8 apfu; non-H cations < 16 apfu; sum Si to Ca (+Li) < 15 apfu; sum Si to Mg (+Li) > 13 apfu; sum Si to Na > 15 apfu. The normalization schemes with the smallest maximum deviations are used. To allow for the imperfection of real data, a threshold of 0.005 apfu is used for the deviations, and for the separation of the normalization schemes.”

The spreadsheet therefore automatically determines which normalization scheme or schemes are appropriate, based on the smallest maximum deviations from the criteria listed above.

I'd rather see the results of all normalizations and then choose for myself while applying some petrological guidance.  There is no simple means of extracting an accurate value of Fe2O3 from an electron microprobe analysis of an amphibole.  This has been my point from the beginning.

And what about propagated counting error?  In addition, systematic error in SiO2 (due to choice of standard or matrix corrections) will contribute additional significant uncertainty.

You know what the good news is?  You don't have to use this ferrous/ferric amphibole method, and can instead export the data and use Andrew's spreadsheet externally, or even your own spreadsheet.  It's nice to have choices.   

But since this feature has been requested by a number of our colleagues, and because we're so nice, we developed this method with Andrew's and Aurelien's help, and then implemented it in Probe for EPMA and CalcZAF for everyone, and made all the source code available.   

On counting errors the other good news is that because Probe for EPMA always calculates an average and standard deviation for each sample, along with the analytical sensitivity and t-test errors, these things can readily be estimated. As for accuracy propagation, one can simply select the "Use All Matrix Corrections" option in the Analyze! window in Probe for EPMA and/or the Calculate ZAF or Phi-Rho-Z Corrections window in CalcZAF, and observe the variation in the ferrous/ferric ratios due to matrix correction and/or MACs.

Pretty cool, hey?

[AndrewLocock]

...it is possible to force the ratio of Fe³⁺/ΣFe to 0 (all ferrous iron), or to 1 (all ferric iron), or to any particular value-of-interest
...the user can force the use of any, some, or all of the normalization schemes....

One does not have to rely on the algorithm.

As quoted above, it is possible to make one's own selections.
There are thus at least 7 options: all ferrous iron, all ferric iron, some arbitrary fixed value, or any 1 of the 4 normalization schemes. And of course, one could invoke the use of 2 or more normalization schemes....

Yes, there is no way to extract a highly-accurate estimate of Fe³⁺/ΣFe from an amphibole analysis performed solely by routine EPMA.
That is the essence of the discussion of Schumacher (1997), and the reason behind the normalization schemes discussed therein.

Propagation of error in mineral formulas is dealt with Giaramita & Day (1990) American Mineralogist 75, 170-182.
It is not germane to the calculation of Fe³⁺/ΣFe itself, but rather the utility (accuracy and precision) of the calculation's outcome.

The constituent that most greatly affects the calculation of Fe³⁺/ΣFe is, in fact, OH-content.
Many classical analyses of amphibole will report insufficient amounts (as discussed by Leake 1968 in GSA Special Paper 98) or excess amounts (probably due to inclusions of other minerals), and of course EPMA does not directly determine H at all.

[Brian Joy]

...it is possible to force the ratio of Fe³⁺/ΣFe to 0 (all ferrous iron), or to 1 (all ferric iron), or to any particular value-of-interest
...the user can force the use of any, some, or all of the normalization schemes....

One does not have to rely on the algorithm.

As quoted above, it is possible to make one's own selections.
There are thus at least 7 options: all ferrous iron, all ferric iron, some arbitrary fixed value, or any 1 of the 4 normalization schemes. And of course, one could invoke the use of 2 or more normalization schemes....

Yes, there is no way to extract a highly-accurate estimate of Fe³⁺/ΣFe from an amphibole analysis performed solely by routine EPMA.
That is the essence of the discussion of Schumacher (1997), and the reason behind the normalization schemes discussed therein.

Propagation of error in mineral formulas is dealt with Giaramita & Day (1990) American Mineralogist 75, 170-182.
It is not germane to the calculation of Fe³⁺/ΣFe itself, but rather the utility (accuracy and precision) of the calculation's outcome.

The constituent that most greatly affects the calculation of Fe³⁺/ΣFe is, in fact, OH-content.
Many classical analyses of amphibole will report insufficient amounts (as discussed by Leake 1968 in GSA Special Paper 98) or excess amounts (probably due to inclusions of other minerals), and of course EPMA does not directly determine H at all.

I've attached a paper by DeAngelis and (Owen) Neill (2012, Computers and Geosciences 48:134-142), who wrote a program that implements the error treatment of Giaramita and Day (1990).  Anyone who recalculates analyses for Fe2O3 should explore the propagated counting error.

Determination of H2O was difficult even in classical analytical work.  My only point in emphasizing systematic error in SiO2 is that I'm not sure that people necessarily consider this issue when recalculating for Fe2O3.

[Brian Joy]

Of course for most amphiboles, it's a relatively small effect, but for Fe-Ti oxides and magnetites the effect is surprisingly large. For hematites/magnetites it's a >1% change in the Fe concentrations:

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

Remember that I was the one who tried to point this out to you several years ago after I'd built this capability into my own program (i.e., automated recalculation of Fe2O3/FeO for simple oxides and silicates), but you hadn't yet in PFE.

[John Donovan]

Of course for most amphiboles, it's a relatively small effect, but for Fe-Ti oxides and magnetites the effect is surprisingly large. For hematites/magnetites it's a >1% change in the Fe concentrations:

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

Remember that I was the one who tried to point this out to you several years ago after I'd built this capability into my own program (i.e., automated recalculation of Fe2O3/FeO for simple oxides and silicates), but you hadn't yet in PFE.

Yes, I remember that very well.  In fact, it was one of the reasons we implemented this feature in CalcZAF for off-line calculations and in Probe for EPMA for on-line data acquisition.  I only mentioned the small matrix effect of ferric oxygen in amphiboles because you said you hadn't implemented it yet in your code. But I agree, it's a surprisingly large effect in Fe-Ti oxides. 

In fact, it's similar in magnitude to the effect on Si of including water by difference into the matrix correction for hydrous glasses (versus just applying the water by difference calculation in Excel without a subsequent matrix re-correction):

https://probesoftware.com/smf/index.php?topic=11.msg235#msg235

[sem-geologist]

Amphibole is really wonderful mineral in igneous systems as it records P T and other stuff all by-self (no paragenesis needed compared to in example Pl-Hbl thermometer).

Its classification... is really a "wonderful" example how things "goes south" when some committee (we love these, don't we?) starts to invent/ change / reorganize an already over-complicated classification. It got to the point of being completely impractical (painful) to use in petrology.

Luckily the practical amphibole application can work leaving that nomenclature mess completely aside and still works wonderfully (I have in mind the Ridolfi & Renzulli's Ca-amphibole geothermobarometers (starting from 2012 version; the 2010 version - was not so accurate)). The R&R thermobarometer also doesn't care about iron valence. I guess the Fe+3/Fe+2 (leading to more correct Oxygen estimate) would give better matrix correction for Na.

But the real problem is that unless experimental amphiboles would had the same treatment (matrix correction including the oxygen from Fe2+ and Fe3+) such more precise and accurate recalculation on our fresh unknown amphibole, and feeding such more accurate amphibole data to such thermobarometer calculations could lead actually to less accurate PT estimations.

This is much more broader problem (with no clear way out), it is not only this thermobarometer -  lots of thermobarometers (other minerals) bases on modeling on chemical composition obtained with older more simple EPMA protocoles. I.e. Peaksight only recently (from 6.5) started to include calculated water to matrix correction. Often methodology sections of these works are not verbose if/how the quality of composition analyses were crosschecked with blind standards or there is too little detail to rule out/in some analytical biases (like dead time). And we can then find ourselves in situation that we need very lax measurement protocols for analysis for thermobarometry (not using all features to make it similarly biased), but we want all accuracy-improving bells and whistles switched "on" for data being published, and referee would complain why reported element composition data (fully corrected) differs from data fed into thermobarometer (not corrected).

So to conclude, such built-in (amphibole) recalculation option could also have some unintentional drawbacks if models would expect biased composition. Going for more accurate data acquisition makes sense only if everyone would move there at once and if application methods (thermobarometric models) would adapt to that too. Also when publishing such more accurately acquired data we need to insist that such information would not be cut out from the methodology section (I had seen numerous times methodology sections being butchered, so that it would be not too long).