Crystallographic Data
Crystallography
Crystals consist of periodic repetitions of identical cells, each containing one or more atoms or molecules. The smallest repeating cell that can be used to construct the crystal is the unit cell. The unit cell is a purely mathematical concept and the choice of absolute position of the atom within the cell is unimportant. If the unit cell contains a single atom, the cell is called primitive and the lattice is a Bravais lattice.
The analysis of crystallographic data to determine whether a unit cell possesses a Bravais lattice is somewhat complicated. If we start with a primitive cell and then build the lattice, the lattice is a Bravais lattice. However, if we start with the lattice and determine that it may have been built from a non-primitive cell, we cannot conclude that the lattice is not a Bravais lattice. We either have to reexamine the data to find a primitive cell which can be used to build the lattice or prove that such a cell does not exist.
A cell, which may be used to build the lattice, but which is not a unit cell, is called a super-cell. In some contexts a clever choice of a super-cell may be more convenient to work with than the primitive cell.