Crystal Structure: Lattices & the 7 Crystal Systems

In an ordinary glass the atoms are parked at random, like cars in a jammed lot. In a crystal the atoms occupy fixed positions that repeat perfectly in all three directions, like seats in a vast, regular stadium. That repeating scaffold is the crystal lattice.

You can tile the whole lattice by repeating one tiny box — the unit cell — over and over, like stacking identical bricks. The atoms that actually sit inside each brick (which atom goes where) is the motif. Lattice + motif = the entire crystal. Change either one and you have a different mineral.

You might think there are countless possible lattices, but the mathematics of symmetry are strict: when you account for every combination of equal-or-unequal edges and right-or-not-right angles, only seven basic shapes can fill three-dimensional space by repetition. These are the seven crystal systems:

• Cubic (isometric) — a cube: all edges equal, all angles 90°. (halite, pyrite, diamond, gold)
• Tetragonal — like a square post: two equal edges, a third different, all angles 90°. (zircon)
• Orthorhombic — a rectangular box: three unequal edges, all angles 90°. (olivine, sulfur)
• Hexagonal — a hexagonal prism. (beryl, apatite)
• Trigonal (rhombohedral) — a cube sheared so all edges are equal but angles are not 90°. (calcite, dolomite, quartz; note: trigonal species are also commonly described on hexagonal axes, a = b ≠ c, γ = 120°)
• Monoclinic — three unequal edges; two angles 90°, one not. (gypsum, micas)
• Triclinic — the least symmetric: no equal edges, no right angles. (plagioclase feldspar, kyanite)

A mineral's system is a fingerprint of its symmetry, and symmetry controls everything from crystal shape to how it bends light.

In diamond, every carbon bonds strongly to four neighbours arranged at the corners of a tetrahedron, building a rigid three-dimensional cage that runs through the whole crystal. There is no weak layer anywhere, so diamond resists scratching from everything else (Mohs 10).

In graphite, the carbons bond into flat hexagonal sheets; within a sheet the bonds are strong, but the bonds between sheets are weak. Press graphite against paper and the sheets slide off onto the page — which is exactly how a pencil works. Same atoms, different architecture: one cages them, the other layers them. That single difference makes the two hardest and softest minerals out of the same element.