2.2 Crystal structures and systems

Crystal Structures and Symmetry

Crystal structure and mineral properties

A mineral's crystal structure is the orderly, repeating arrangement of its atoms, ions, or molecules. This internal architecture is determined by the mineral's chemical composition and the types of bonds holding it together.

Crystal structure directly controls physical and chemical properties like hardness, cleavage, and optical behavior (transparency, color). Two minerals can have the same chemical formula but completely different properties if their atoms are arranged differently. Diamond and graphite are both pure carbon, but diamond's tightly bonded 3D framework makes it the hardest natural mineral, while graphite's loosely stacked sheets make it soft enough to use in pencils.

Symmetry arises from the repetition of atomic arrangements within the structure. The key symmetry elements are:

• Planes of symmetry: imaginary flat surfaces that divide a crystal into mirror-image halves
• Axes of symmetry: imaginary lines around which a crystal can be rotated and look the same (a two-fold axis repeats every 180°, a four-fold axis every 90°, etc.)
• Center of symmetry: a central point where every feature on one side has an identical feature at an equal distance on the opposite side

The specific combination of symmetry elements a mineral possesses determines which crystal system it belongs to.

Seven crystal systems and symmetry

Every mineral falls into one of seven crystal systems, defined by the lengths of their axes and the angles between them. They range from the highly symmetrical cubic system down to the triclinic system with almost no symmetry.

• Cubic (Isometric): The most symmetrical system. Four three-fold axes of symmetry, three equal axes ($a = b = c$), all perpendicular to each other. Examples: halite, garnet.
• Hexagonal: One six-fold axis of symmetry. Four axes total, with three equal axes in one plane perpendicular to a fourth axis of different length. Examples: beryl, apatite.
• Trigonal: One three-fold axis of symmetry. Three equal axes equally inclined to each other but not perpendicular. Examples: calcite, quartz. (Note: some classification schemes group trigonal within the hexagonal system.)
• Tetragonal: One four-fold axis of symmetry. Two equal axes perpendicular to a third axis that is longer or shorter ($a = b \neq c$). Examples: zircon, rutile.
• Orthorhombic: Three mutually perpendicular two-fold axes or planes of symmetry. Three unequal axes ($a \neq b \neq c$), all perpendicular. Examples: olivine, topaz.
• Monoclinic: One two-fold axis or one plane of symmetry. Three unequal axes, with only one pair perpendicular. Examples: gypsum, orthoclase.
• Triclinic: The least symmetrical system, with only a center of symmetry (or none at all). Three unequal axes, none perpendicular. Examples: plagioclase feldspar, kyanite.

A helpful way to remember the progression: as you move from cubic to triclinic, the axes become more unequal and the angles less regular, so symmetry decreases at each step.

Crystal Forms and Unit Cells

Common crystal forms and systems

A crystal form is the set of faces on a crystal that are related by symmetry. Different crystal systems produce different characteristic shapes. Here are some of the most common:

Cubic system

• Cube: six square faces, each perpendicular to one axis. Pyrite and halite commonly grow as cubes.
• Octahedron: eight equilateral triangular faces. Diamond and fluorite often display this form.

Tetragonal system

• Tetragonal prism: four rectangular faces parallel to the vertical axis with two square faces on top and bottom. Zircon crystals show this shape.
• Tetragonal pyramid: four triangular faces meeting at a point above a square base. Wulfenite is a classic example.

Hexagonal system

• Hexagonal prism: six rectangular faces parallel to the vertical axis with hexagonal faces on top and bottom. Beryl (including emerald) and apatite grow this way.
• Hexagonal pyramid: six triangular faces meeting at a point above a hexagonal base. Quartz crystals often show pyramidal terminations.

Trigonal system

• Rhombohedron: six rhombus-shaped faces with equal edges. Calcite and dolomite commonly form rhombohedra, and calcite's rhombohedral cleavage is one of its most recognizable features.

The orthorhombic, monoclinic, and triclinic systems produce various prisms and pyramids as well, but with lower symmetry their forms tend to be less regular and harder to recognize at a glance.

Unit cells in crystal structures

The unit cell is the smallest repeating unit that, when stacked in three dimensions, builds up the entire crystal structure. Think of it like a single tile in a mosaic: one tile defines the pattern, and repeating it fills the whole surface.

Each unit cell is defined by six parameters:

1. Three edge lengths: $a$, $b$, and $c$
2. Three angles between those edges: $\alpha$ (angle between $b$ and $c$), $\beta$ (angle between $a$ and $c$), and $\gamma$ (angle between $a$ and $b$)

The specific values of these parameters determine which crystal system the mineral belongs to. For example, a cubic unit cell has $a = b = c$ and $\alpha = \beta = \gamma = 90°$.

The arrangement of atoms within the unit cell controls the mineral's chemical and physical properties. There are three main types of unit cells:

• Primitive (P): Atoms sit only at the corners of the cell. Cesium chloride has this arrangement.
• Body-centered (I): Atoms at the corners plus one atom at the center of the cell. Sodium and tungsten are body-centered.
• Face-centered (F): Atoms at the corners plus one atom at the center of each face. Copper, gold, and silver all have face-centered unit cells, which is part of why they're so ductile.