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.
The seven crystal systems classify every crystalline mineral by the symmetry and relative lengths/angles of its crystallographic axes; two contrasting examples — one at the high-symmetry end, one at the lowest — are described below.
| System | Axial lengths / angles |
|---|---|
| Hexagonal | 4 axes: 3 equal-length horizontal axes ($a_1=a_2=a_3$) at $120\,{}^{\circ}$ to each other, plus 1 vertical axis $c\ne a$ at $90\,{}^{\circ}$ to the others |
| Triclinic | 3 unequal axes ($a\ne b\ne c$); all three interaxial angles unequal and $\ne 90\,{}^{\circ}$ — the lowest-symmetry system, with no restriction on either axial length or angle |
The hexagonal system has a single 6-fold (or 6/m) principal symmetry axis along $c$, with three equal horizontal axes at $120\,{}^{\circ}$ producing 6-sided prismatic crystal forms. Example: beryl ($\text{Be}_3\text{Al}_2\text{Si}_6\text{O}_{18}$), which forms classic hexagonal prisms terminated by a basal pinacoid, with no cleavage (a cyclosilicate, ring silicate).
The triclinic system has the lowest possible symmetry of any crystal system — only a centre of symmetry (or none at all) — because none of its three axes are equal and none of its three interaxial angles are constrained to $90\,{}^{\circ}$. Example: plagioclase feldspar (e.g. albite, $\text{NaAlSi}_3\text{O}_8$, or anorthite, $\text{CaAl}_2\text{Si}_2\text{O}_8$), which shows two cleavages very close to but not exactly $90\,{}^{\circ}$ (the small deviation is diagnostic against monoclinic K-feldspar) and characteristic polysynthetic albite twinning.
Ranking all seven systems by symmetry — isometric, tetragonal, hexagonal, trigonal, orthorhombic, monoclinic, triclinic, from highest to lowest — hexagonal and triclinic sit at opposite ends of that spectrum, which is a useful pairing for illustrating the full range of what "crystal system" controls: hexagonal's four-axis frame with three equal, symmetric horizontal axes gives its minerals the highest possible rotational symmetry (6-fold) available outside the isometric system, while triclinic's total lack of axial or angular constraint leaves its minerals with essentially none. This same symmetry spectrum is why a mineralogist identifying an unknown crystal in hand specimen or thin section works top-down through the list, first testing for the most restrictive (highest-symmetry) fit before falling back to lower-symmetry systems.
