Calculating Compositional Variation and Common Substitutions for Igneous and Metamorphic Minerals
Department of Earth Sciences, Montana State University
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This problem set uses Excel spreadsheets to calculate mineral formulae from analytical data (typically from the electron microprobe) using a variety of formulations that assume numerous variations of crystal chemical constraints. Ferric iron is recalculated based on charge balance and stoichiometry. End members and mole fractions are also calculated in many instances.
This problem set can be used in introductory mineralogy courses, igneous or metamorphic petrology, or general geochemistry courses for geoscience majors.
Skills and concepts that students must have mastered
Students must have a basic understanding of stoichiometry and charge balance, and a basic understanding of Pauling's Rules of crystal chemistry, mineral structural formulae, and site occupancy is also helpful.
How the activity is situated in the course
This activity can be used as a stand-alone exercise to demonstrate how we derive mineral chemical formulae from compositional data, or it can be used as a first step in more advanced petrology courses to determine mole fraction of components or end members for further applications such as geothermobarometry.
Content/concepts goals for this activity
- To apply the principles of crystal chemistry (e.g. Pauling's Rules) to recalculate mineral formulae, and construct structural formulae based on rules of site occupancy;
- To work directly with mineral compositional data, and to critically evaluate the quality of these data by checking mineral formulae for stoichiometry and charge balance; in particular, treatment of ferric/ferrous iron presents difficulties that must be addressed;
- To demonstrate that mineral formulae recalculations are model dependent, and reported values may vary quite dramatically depending on assumptions chosen in selecting recalculation models;
- To become familiar with the compositional constraints of numerous end-members and varieties of the rock-forming minerals that are used to interpret geologic processes, environments of formation, etc., and
- To establish the basis for applying mineral compositions to more advanced applications such as geothermobarometry.
Higher order thinking skills goals for this activity
Higher order thinking skills include the ability to critically evaluate a) the quality of mineral composition data, and b) the applicability of various recalculation models.
Other skills goals for this activity
Additional skills include using spreadsheets to obtain quantitative results, and use of appropriate graphs to represent compositional variations in families of minerals.
Description of the activity/assignment
This exercise uses a number of Excel spreadsheets to calculate mineral formulae from compositional (microprobe) data. Numerous computational models are presented for most mineral groups (e.g. amphiboles, pyroxenes, micas), and students must critically evaluate which of these models is most applicable. Stoichiometry and charge balance are used to determine ferric/ferrous ratios--which is important for further applications such as geothermobarometry. Students are also asked directed questions about: compositional variation of the rock-forming mineral groups; representative complete, limited, and coupled solid solutions; site occupancy of major elements, as determined by the various computational models used; graphical representation of the calculated mineral formulae; and the composition and significance of certain varieties of these rock-forming minerals are addressed.
Determining whether students have met the goals
The problem consists of a series of short-answer questions on a worksheet, and accompanying X-Y and ternary plots. Short answers and graphical representation of data can readily be evaluated for accuracy, completeness (of descriptions), and thoroughness of responses.
More information about assessment tools and techniques.
Teaching materials and tips
Data Set of Mineral Compositions (Excel 50kB Apr29 08)
-- Representative feldspar, garnet, pyroxene, amphibole, and mica analytical data from Deer, Howie and Zussman, An Introduction to the Rock Forming Minerals (1967)
Mineral Formulae Recalculation Spread Sheets
-- these are the
spreadsheets used to recalculate mineral formulae in this problem set.
Specialized recalculation routines are provided for common rock-forming
minerals such as feldspars, olivine, garnets, pyroxenes, amphiboles,
micas and epidote. Ferric/ferrous iron ratios can be input if known, or
calculated based on stoichiometry and charge balance. Other
recalculation procedures are provided based on models of site occupancy
of the complex silicate minerals.
This exercise is part of the Teaching Phase Equilibria
See the module on Plotting Mineral Compositions and Chemographic Projections
- from Teaching Phase Equilibria.