18-Geol-A1 Mineralogy and Petrology · December 2019
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Geological Engineering, 18-Geol-A1 Mineralogy and Petrology, 2019-Dec. Closed book; no calculator permitted.
Reference texts: Klein & Dutrow, Manual of Mineral Science, 23rd ed. (silicate structural classification, mineral chemistry and substitution, crystal systems, sulfide/carbonate ore mineralogy); Winter, Principles of Igneous and Metamorphic Petrology, 2nd ed. (magmatic differentiation, Bowen's reaction series, tectonic settings of magmatism, metamorphic/metasomatic processes, volcanic and pyroclastic processes, plate-tectonic cycle).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Whether one element can freely substitute for another at the same crystallographic site is governed chiefly by two properties of the two ions, formalized as Goldschmidt's rules of substitution: ionic radius and ionic charge.
The substituting ion's radius must be close to that of the ion it replaces — conventionally within about 15% — because the crystal lattice's bond lengths and site geometry are fixed by the structure. A radius mismatch beyond this tolerance strains the lattice (bond-length and bond-angle distortion) enough to make substitution energetically unfavourable, restricting solid solution or excluding the substituent to a separate phase.
The substituting ion's charge must match (isovalent substitution, e.g. $\text{Mg}^{2+}\leftrightarrow\text{Fe}^{2+}$ in olivine) or be compensated by a coupled substitution elsewhere in the structure that preserves overall electrical neutrality (heterovalent/coupled substitution, e.g. $\text{Na}^{+}\text{Si}^{4+}\leftrightarrow\text{Ca}^{2+}\text{Al}^{3+}$ in plagioclase). An uncompensated charge mismatch cannot be accommodated because the crystal must remain electrically neutral overall.
Together, ionic radius and charge compatibility explain nearly all of the major solid-solution series in rock-forming minerals (olivine, pyroxene, plagioclase, garnet), control trace-element partitioning between crystallizing minerals and melt (the basis of using trace elements to trace magmatic processes), and govern where economically important trace and minor elements (Ni, Cr, REE) end up during igneous and metamorphic crystallization — a poorly-matched trace element is excluded from the major rock-forming minerals and instead concentrates in the residual melt or a late-forming accessory phase, which is why Goldschmidt's rules underpin ore-deposit geochemistry as much as petrology.
