# Mineral Formulae Recalculation

## What is it?

Chemical analyses for silicate minerals are commonly reported in weight percentages of the oxides of the elements determined. Although little weighing is involved in most modern chemical analyses (electron microprobe or energy dispersive x-ray spectrometer) weight percentages are reported for historic reasons (chemists performed their analyses using gravimetric techniques). Oxygen is normally not determined. It is assumed that each mineral is electrically neutral and that the positive charges on the cations are balanced by an appropriate quantity of oxygen anions. Weight percentages are not the most convenient format for many uses of mineral analyses. They obscure relationships that may be obvious when the compositions of minerals are expressed in terms of formulas (atomic proportions). This page provides information and tools for the calculation of minerals formulas from chemical analyses.

## Principles of Formula Calculation

Retrieval of standard chemical formulas for minerals from chemical analyses is an exercise in (a) conversion of units of quantity and (b) normalization of sums to match the commonly used formula conventions. The basic steps for formula calculation are:

- Divide the weight percentage of each oxide by the formula weight of that oxide.
- Multiply the resulting "mole number" of each oxide by the number of oxygens in the oxide formula.
- Multiply the resulting "oxygen number" of each oxide by a normalization constant (equal to the number of oxygens in the desired formula divided by the sum of the "oxygen numbers").
- Multiply the "normalized oxygen numbers" of each oxide by the number of cations per oxygen in the oxide formula.

In some cases, the resulting mineral formula is modified by assigning the cations to their probable crystallographic sites based on their probable coordination numbers.

Because electron beam analyses do not differentiate among the valence states of iron (iron is normally reported as FeO), the formula calculation procedure may be different for different iron-bearing minerals. For some minerals (pyroxenes, olivine), by making the assumption that all the cation-sites are full and the mineral has perfect charge balance, the proportion of the Fe that is Fe^{+3} can be calculated to satisfy that assumption. For other minerals (amphiboles, micas), upper and lower limits to the proportion of Fe that is Fe^{+3} can be calculated based on stoichiometric constrains.

## Spreadsheets for Mineral Formula Calculation

Excel spreadsheets for calculating mineral formulas for specific minerals are collected here.

- Generic Formula Spreadsheet (Excel PRIVATE FILE 25kB Mar21 08)--Use this version if Fe
^{+3}analyses are available, or if FeO = FeO_{total}(ignoring the possibility of presence of Fe^{+3}); normalize to oxygen per formula unit for the mineral of interest. Another mineral formula recalculation (Excel 180kB Jan27 10) spreadsheet submitted by Alicia López-Carmona and Emilio Segovia-Díaz. - Andy Tindle's Mineral Recalculation Software
- Olivine, Pyroxene, Garnet, Spinel and Feldspar Spreadsheets (Excel PRIVATE FILE 86kB Feb1 17)--Use this version for microprobe data, where FeO = FeO
_{total}; recalculates Fe^{+3}based on stoichiometry and charge balance.*Fe*_{2}O_{3}data may also be entered directly if independent analyses are available. [Note: Rhian Jones pointed out an error in this spreadsheet that was corrected on March 20, 2015. My apologies if it causes problems for anyone -- DP]

- Amphibole Formula Spreadsheet (Excel PRIVATE FILE 47kB Mar30 07)--use microprobe data; this version calculates Fe
^{+3}by charge balance, as well as numerous mineral formulae based on different assumptions of site occupancy. - Mica Formula Spreadsheet (Excel PRIVATE FILE 48kB Mar30 07)-use microprobe data; this version calculates Fe
^{+3}by charge balance as well as numerous mineral formulae based on different assumptions of site occupancy. - Clinopyroxene Formula Spreadsheet (Excel PRIVATE FILE 29kB Mar26 08)-use microprobe data; this version calculates Fe
^{+3}based on stoichiometry and charge balance. - Epidote Formula Spreadsheet (Excel PRIVATE FILE 13kB Mar30 07)-use microprobe data; this version calculates epidote formulae by calculating FeO
_{total}as Fe^{+3}.

## Teaching Activity

- Mineral Formulae Recalculation Exercise--This problem set uses the above spreadsheets to recalculate mineral formulae, assign cation site occupancy, determine relative proportions of end members, introduces important varieties of the rock forming minerals, and requires students to look critically at the data and assumptions that are built into numerous recalculation models. An accompanying dataset uses selected feldspar, garnet, pyroxene, amphibole, and mica analytical data from Deer, Howie and Zussman,
*An Introduction to the Rock Forming Minerals (1967)*.

## Related Links

- Description of electron microprobe (EPMA) instrumentation and applications - John Goodge, University of Minnesota at Duluth
- Extending Mineralogy by Electron Microprobe Analysis - John Goodge, University of Minnesota at Duluth
- Simple Formula Calculation Instructions (Acrobat (PDF) PRIVATE FILE 19kB Mar30 07) - John Brady, Smith College

## Readings

- Bernard E. Leake, Alan R. Woolley, Charles E.S. Arps, William D. Birch, M. Charles Gilbert, Joel D. Grice, Frank C. Hawthorne, Akira Kato, Hanan J. Kisch, Vladimir G. Krivovichev, Kees Linthout, Jo Laird, Joseph A Mandarino, Walter V. Maresch, Ernest H. Nickel, Nicholas M.S. Rock, John C. Schumacher, David C. Smith, Nick C.N. Stephenson, Luciano Ungaretti, Eric J.W. Whittaker, and Guo Youzhi (1997) Nomenclature of amphiboles: Report of the Subcommittee on Amphiboles of the International Mineralogical Association, Commission on New Minerals and Mineral Names. American Mineralogist, v. 82, 1019-1037.
- Micas, (1984) Reviews in Mineralogy, Volume 13, S. W. Bailey (ed); see chapter 1: Classification and Structures of the Micas.
- Amphiboles: Crystal Chemistry, Occurrence, and Health Issues, (2007) Reviews in Mineralogy and Geochemistry Volume 67 F. C. Hawthorne, Roberta Oberti, Giancarlo Della Ventura, and Annibale Mottane (Eds); see chapter 2, Classification of the Amphiboles.