Chapters / Chapter 1 · Solid state / Topic 2 of 14

Lattice and unit cells

A crystal consists of a basic structural unit, or motif, repeated in three dimensions. The basic unit may be a single atom, molecule or ion, or a group of atoms or molecules, which has an identical environment throughout the crystal. It is also called the basis of the crystal. A basis has the same stoichiometric composition as the crystal itself.

The lattice, or space lattice, is the geometrical idealisation of the structure. It is obtained by placing a point at the same location of each basis in the crystal; the resulting three-dimensional distribution of points in space forms the lattice. A crystal structure is generated by associating each lattice point with a basis.

A unit cell is the smallest part of the crystal which can generate the whole crystal structure through repetition in three dimensions by simple translational displacement, stacking unit cells together along their faces without leaving any space.

Lattice parameters

A unit cell is described by six numbers: a, b, c, the lengths of the three edges, and α, β, γ, the angles between the edges (α between b and c, β between a and c, γ between a and b).