18-Geol-A1 Mineralogy and Petrology · December 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Geological Engineering, 18-Geol-A1 Mineralogy and Petrology, 2018-Dec. Closed book; no calculator permitted.
Reference texts: Klein & Dutrow, Manual of Mineral Science, 23rd ed. (silicate/oxide structural classification, mineral chemistry and formulas, crystal systems); Winter, Principles of Igneous and Metamorphic Petrology, 2nd ed. (magmatic differentiation, Bowen's reaction series, metamorphic agents/facies, volcanic and pyroclastic processes, partial melting); Boggs, Petrology of Sedimentary Rocks, 2nd ed. (carbonate mineral diagnostics).
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 three (or four, for hexagonal) crystallographic axes: isometric (cubic), tetragonal, orthorhombic, hexagonal, trigonal (rhombohedral), monoclinic and triclinic, ranked from highest to lowest symmetry.
| System | Axial lengths / angles |
|---|---|
| Isometric (cubic) | $a=b=c$; all angles $90\,{}^{\circ}$ |
| Tetragonal | $a=b\ne c$; all angles $90\,{}^{\circ}$ |
| Orthorhombic | $a\ne b\ne c$; all angles $90\,{}^{\circ}$ |
| Hexagonal | 4 axes: 3 equal horizontal at $120\,{}^{\circ}$, 1 vertical $c\ne a$ at $90\,{}^{\circ}$ to the others |
| Trigonal (rhombohedral) | $a=b=c$; all angles equal, $\ne 90\,{}^{\circ}$ (often referenced to the hexagonal axial set) |
| Monoclinic | $a\ne b\ne c$; two angles $90\,{}^{\circ}$, one ($\beta$) $\ne 90\,{}^{\circ}$ |
| Triclinic | $a\ne b\ne c$; all three angles $\ne 90\,{}^{\circ}$ |
The highest-symmetry system: three mutually perpendicular axes of equal length ($a=b=c$, all angles $90\,{}^{\circ}$), giving the greatest number of symmetry elements of any system (four 3-fold axes along the cube diagonals, plus 3-fold and 2-fold axes). Common forms are the cube, octahedron and dodecahedron. Examples: garnet ($X_3Y_2(\text{SiO}_4)_3$, no cleavage, dodecahedral habit), galena ($\text{PbS}$, perfect cubic cleavage), and pyrite ($\text{FeS}_2$, cubic/pyritohedral crystal faces).
Three unequal axes ($a\ne b\ne c$), two of the three interaxial angles are $90\,{}^{\circ}$ and the third ($\beta$) is oblique ($\ne 90\,{}^{\circ}$), giving a single 2-fold axis of symmetry (or a single mirror plane). It is the most common crystal system among rock-forming minerals. Examples: orthoclase feldspar ($\text{KAlSi}_3\text{O}_8$, two cleavages at $90\,{}^{\circ}$ to each other because the oblique axis is perpendicular to both cleavage planes), gypsum ($\text{CaSO}_4\cdot 2\text{H}_2\text{O}$), and augite (monoclinic pyroxene).
