The calculation of the proportion of ferric iron in an amphibole composition is most thoroughly examined by Schumacher (1997) in the Appendix 2 of the Leake et al. (1997) report on amphibole nomenclature. Table A-2 of Schumacher (1997) uses a particular analysis from Appendix 1 of Deer et al. (1966, p. 515); the subtitle of this latter appendix is “Calculation of a chemical formula from a mineral analysis, hornblende analysis”.
This topic is reprised in Appendix III: Calculation of Fe3+ and (OH) in Amphiboles of the Hawthorne et al. (2012) report on amphibole nomenclature. Appendix Table 1 of Hawthorne et al. (2012) uses the same analysis from Deer et al. (1966, p. 515)
For the Excel spreadsheet to classify chemical analyses of amphiboles following the IMA 2012 recommendations that I authored, the topics of formula normalization and Fe3+ estimation are discussed in the paper published in Computers & Geosciences 62, 1–11.
To clarify: in that spreadsheet 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, by entering the appropriate wt% FeO and/or Fe2O3 values and setting the option “use initial M3+/ΣM? (TRUE or 1/FALSE or 0)” to True or to 1. (Recall the conversion wt% FeO = 0.8998085 Fe2O3).
However, in general, the ratio of Fe3+/ΣFe is not known a priori, and thus some sort of formula normalization must be used, following Schumacher (1997). In the spreadsheet, 4 schemes of cation normalization are possible (modified from Schumacher 1997 to include known Li-content):
1. Sum of all cations from Si to K = 16 apfu.
2. Sum of cations from Si to Na = 15 apfu.
3. Sum of cations (includes Li) from Si to Ca = 15 apfu.
4. Sum of cations (includes Li) from Si to Mg = 13 apfu.
Methods of estimation of Fe3+ contents of amphibole are generally inaccurate in comparison to measured values, but are usually better than no estimate at all.
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.
However, the user can force the use of any, some, or all of the normalization schemes, by setting the following options to True or 1:
Require Si–Ca&Li<=15? (TRUE or 1/FALSE or 0)
Require Si–Mg&Li>=13? (TRUE or 1/FALSE or 0)
Require Si–Na>=15? (TRUE or 1/FALSE or 0)
Require Si–K<=16? (TRUE or 1/FALSE or 0)
If one is deeply interested in the details of this calculation, I recommend to look in the spreadsheet ( version 9.8 ) at the 3.Calculation worksheet, specifically rows 5495 to 5554.
Schumacher (1997) did list additional stoichiometric constraints for certain metamorphic amphiboles.
This is partially captured in Warnings section of the Output of the spreadsheet, specifically if the sum of high-valence C cations (M3+ and M4+) is greater than 2 apfu.
The calculation of the formula proportions of an amphibole does not depend on the subsequently determined name of that amphibole.
References:
Deer, W.A., Howie, R.A., Zussman, J., 1966. An Introduction to the Rock-Forming Minerals. Longman Group Limited, London, U.K.
Hawthorne, F.C., Oberti, R., Harlow, G.E., Maresch, W.V., Martin, R.F., Schumacher, J.C., Welch, M.D., 2012. IMA report, nomenclature of the amphibole supergroup. American Mineralogist 97, 2031–2048.
Leake, B.E., Woolley, A.R., Arps, C.E.S., Birch, W.D., Gilbert, M.C., Grice, J.D., Hawthorne, F.C., Kato, A., Kisch, H.J., Krivovichev, V.G., Linthout, K., Laird, J., Mandarino, J.A., Maresch, W.V., Nickel, E.H., Rock, N.M.S., Schumacher, J.C., Smith, D.C., Stephenson, N.C.N., Ungaretti, L., Whittaker, E.J.W., Guo, Y., 1997.
Nomenclature of amphiboles: report of the subcommittee on amphiboles of the International Mineralogical Association, Commission on New Minerals and Mineral Names. Canadian Mineralogist 35, 219–246.
Schumacher, J.C., 1997. Appendix 2. The estimation of the proportion of ferric iron in the electron-microprobe analysis of amphiboles. In: Leake, B.E., et al. (Eds.), Nomenclature of Amphiboles, vol. 35. Canadian Mineralogist, pp. 238–246.