Teaching Phase Equilibria
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Mineral Formulae Recalculation

John Brady, Smith College and Dexter Perkins, University of North Dakota

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:

  1. Divide the weight percentage of each oxide by the formula weight of that oxide.
  2. Multiply the resulting "mole number" of each oxide by the number of oxygens in the oxide formula.
  3. 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").
  4. 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.

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