Mineral Formulas

A mineral formula is more than just a list of the elements present - it is a compact structural description that encodes which cations occupy which sites, how many of each are present per formula unit, and whether compositional variation is possible. Writing a formula correctly therefore requires understanding both the chemistry and the crystal structure of the mineral. ^[1]

Rules for Writing Mineral Formulas

Four basic rules govern formula writing for ionic minerals. First, cations are written before anions - the electropositive elements come first, followed by the anionic group or individual anions. Second, charges must balance: the total positive charge of all cations must exactly equal the total negative charge of all anions. Third, cations occupying the same structural site are grouped together. Fourth, when cations occupy different structural sites, they are listed in order of decreasing coordination number - the cation with the highest coordination number (largest site) is written first, and the cation with the lowest coordination number (smallest site) is written last. ^[1] These rules are not always followed for historical reasons, but they provide a useful and consistent framework.

The Diopside Example

Diopside (CaMgSi₂O₆), a common pyroxene, illustrates how these rules are applied in practice. The mineral contains three types of cations - Ca²⁺, Mg²⁺, and Si⁴⁺ - all coordinated with the single anion O^2-. ^[1] From knowledge of cation sizes, we can anticipate their coordination environments: Si⁴⁺, being small, sits in 4-fold (tetrahedral) coordination; Mg²⁺ fits into 6-fold (octahedral) coordination; and Ca²⁺, being larger, occupies 8-fold coordination. The formula CaMgSi₂O₆ places Ca first (highest coordination number of 8), then Mg (coordination 6), then Si (coordination 4), followed by oxygen - exactly the decreasing coordination order that the rules require. ^[1]

Charge balance can be verified by tallying the contribution of each ion: ^[1]

| Ion | Charge | Stoichiometric Coefficient | Total Charge | | --------------- | ---------- | ------------------------------ | ---------------- | ----------------------------------------------------------------------- | | Ca²⁺ | +2 | 1 | +2 | ^[1] | | Mg²⁺ | +2 | 1 | +2 | ^[1] | | Si⁴⁺ | +4 | 2 | +8 | ^[1] | | O^2- | -2 | 6 | -12 | ^[1] | | Total | | | 0 | ^[1] |

The sum is zero, confirming that the formula is electrically balanced. The total charge contributed by each ion is simply its charge multiplied by its stoichiometric coefficient. ^[1]

Expressing Coordination Number

When the coordination number of each cation needs to be explicitly stated - for instance, in crystallographic descriptions or structural comparisons - it is written as a Roman numeral superscript immediately before the cation symbol in the formula. ^[1] For diopside this gives: ^VIIICa ^VIMg ^IVSi₂O₆, which makes the three different site geometries immediately readable from the formula itself.

Expressing Solid Solution in a Formula

When a structural site can be occupied interchangeably by different cations as part of a solid solution series, those cations are enclosed in parentheses within the formula. The pyroxene formula modified to show that its octahedral sites can hold either Mg or Fe becomes ^VIIICa ^VI(Mg,Fe) ^IVSi₂O₆. ^[1]

An alternative notation states the degree of substitution explicitly using a variable coefficient. Olivine written this way becomes (Mg_2-xFe_x)SiO₄, where x can range from 0 (pure forsterite) to 2 (pure fayalite), indicating that complete ionic substitution is possible. ^[1] If, for example, 22% of the octahedral sites in a particular olivine are occupied by Fe²⁺ and 78% by Mg²⁺, then x = 0.44 and the formula becomes Mg_1.56Fe_0.44SiO₄. ^{[1] [1]}

End-Member Notation and Percentage Composition

A third and very convenient way to express mineral composition is in terms of the percentage of each end member. The end-member names are abbreviated to two letters - for olivine, forsterite (Mg₂SiO₄) is abbreviated Fo and fayalite (Fe₂SiO₄) is abbreviated Fa - and the percentage of each is written as a subscript. ^[1] The olivine sample with 78% Mg and 22% Fe would be written Fo₇₈Fa₂₂. Because the two end members must sum to 100%, it is common to report just one - Fo₇₈ carries the same information as Fo₇₈Fa₂₂ because Fa must be 22%. ^[1] This notation is compact, unambiguous, and directly communicates where a sample sits along the solid solution series - making it the most widely used shorthand in descriptive mineralogy.

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