Converting Chemical Analyses to Structural Formulas
Converting a chemical analysis into a mineral’s structural formula is a standard procedure that can be done manually or with a spreadsheet. The goal is to translate weight percent oxide data into a formula that shows how many of each cation occupy each crystallographic site per formula unit. The pyroxene general formula XYZ2O6 serves as the standard worked example, using the full recalculation illustrated in Table 9.4. [1]
Step-by-Step Procedure
Step 1: Obtain Moles of Each Oxide (Column 4)
Divide the weight percent of each oxide species by its molecular weight. For example, if the sample contains 53.8 wt% SiO2 and the molecular weight of SiO2 is 60.08 g/mol, the result is 0.89547 moles of SiO2. This step converts a mass-based measurement into a count of formula units. [1]
Step 2: Calculate Moles of Oxygen and Moles of Cation (Columns 5 and 6)
Multiply the moles of each oxide by the number of oxygen atoms in that oxide to get the moles of oxygen contributed by each species. For SiO2, each mole of oxide contributes two moles of oxygen, so the oxygen contribution is 2 × 0.89547 = 1.79095. Similarly, each mole of Al2O3 provides three moles of oxygen. Sum all oxygen contributions to get the total moles of oxygen in the sample - 2.74030 in the pyroxene example. Separately, calculate the moles of each cation: for SiO2 the moles of Si equal the moles of oxide; for Al2O3 the moles of Al are twice the moles of oxide because each formula unit has two aluminum atoms. [1]
Step 3: Recalculate Cations on a Fixed Oxygen Basis (Column 7)
Different mineral structures contain a fixed number of oxygen anions per formula unit. For pyroxene this number is 6. Divide this target oxygen number by the total moles of oxygen from Column 5 to obtain a recalculation factor - 6 / 2.74030 = 2.18954 in the pyroxene example. Multiply every cation count from Column 6 by this factor to express the formula on the basis of 6 oxygen atoms. This normalization is what makes different analyses of the same mineral directly comparable: once all formulas are written on the same oxygen basis, the number of cations per site can be compared directly. [1]
Step 4: Allocate Cations to Structural Sites (Column 8)
In the final step, cations are assigned to specific crystallographic sites based on knowledge of the mineral structure. For pyroxene, three sites are available: a 4-fold tetrahedral site (Z), a 6-fold octahedral site (Y), and an 8-fold site (X). As a general rule in silicates, silicon and some aluminum are assigned to the tetrahedral Z site first. The remaining aluminum and all other cations are then apportioned to the higher-coordination sites. In the pyroxene example, 1.961 Si and 0.039 Al fill the Z site to a total of 2.000. The 8-fold X site is assigned to the largest cations - Na and Ca - giving 0.948 cations; the remaining 1.053 cations populate the 6-fold Y site. [1]
End-Member Calculation
Once the formula is complete, the data can be used to calculate the relative proportions of end-member compositions for minerals with significant solid solution. For pyroxenes the standard end members are wollastonite (wo, Ca2Si2O6), enstatite (en, Mg2Si2O6), and ferrosilite (fs, Fe2Si2O6). The mole fraction of each end member equals the fraction of Ca, Mg, or Fe among the combined total of Ca + Mg + Fe. For the pyroxene example: % wo = 0.929/1.927 = 48.2%, % en = 0.907/1.927 = 47.1%, % fs = 0.091/1.927 = 4.7%. Minor cations such as Cr, Ti, and Mn are excluded from this particular calculation. [1]
Formula Units per Unit Cell (Z)
Each unit cell contains an integer number of formula units, denoted Z. A formula unit is the collection of atoms shown in the chemical formula as conventionally written. For halite (NaCl), one formula unit consists of one Na and one Cl; because the unit cell contains four Na and four Cl atoms, Z = 4. [1]
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References & Citations
- 1.Introduction to Mineralogy Nesse, W. D.
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