The unit cell

The unit cell is the repeating structure found within the crystal. The unit cell may consist of a single molecule of the compound; it could contain two or more molecules in different configurations; it could have multiple molecules which differ by a symmetry operation; or in the case of a molecule posessing symmetry the unit cell might consist of a fraction of the molecule. Along with the main molecule of interest, the unit cell might additionally include other compounds, for example solvents of recrystallisation.

The unit cell does not necessarily contain the entirety of a single molecule within the cell. The unit cell often consists fragments from multiple molecules which together constitute the entire molecule.

Crystal lattices

The unit cell is described as cuboid, a hexahedron with six faces, eight vertices and twelve edges. The cuboid is described using six parameters, three for length (a, b and c) and three for angles (α, β and γ). The angles are α between sides a and b; β between sides b and c; and γ between sides a and c.

The simplest lattice is where a = b = c and α = β = γ = 90°, and this is termed the cubic lattice. There are seven primitive lattices possible with different combinations of shared lengths, angles, or angles being equal to 90°. Where all the lengths (a ≠ b ≠ c) and angles (α ≠ β ≠ γ ≠ 90°) are all different is the triclinic system. The remaining lattices have one or more lengths being equal, or one or more angles being 90°. The lattices are summarised below, and more information on each lattice in turn is provided further down the page.

• Triclinic: a ≠ b ≠ c; α ≠ β ≠ γ ≠ 90°

• Cubic: a = b = c; α = β = γ= 90°

• Monoclinic: a ≠ b ≠ c; β ≠ α = γ = 90°

• Orthorhombic: a ≠ b ≠ c; α = β = γ = 90°

• Rhombohedral: a = b = c; α = β = γ ≠ 90°

• Tetragonal: a = b ≠ c; α = β = γ = 90°

• Hexagonal: a = b ≠ c; α ≠ β ≠ γ = 120°

The Wikipedia article on Unit Cells provides a good overview of the crystal lattices.

Cubic

Cubic is the simplest crystal system, where all the lengths in the lattice are the same, with 90°  angles. There are three main variations of this lattice, those of primitive cubic (cP), body-centered cubic (cI or bcc) and face-centered cubic (cF or fcc).

Triclinic

Triclinic crystals exhibit different lengths for all three dimensions (a, b, c) along with different angles (α, β, γ), with no angle being 90°.