Choosing a unit cell

In the 2D lattice below is is possible to pick any parallelogram to be the unit cell. In practice it is best to choose the smallest unit cell or the unit cell which provides the most symmetry.

All the parallelograms represent valid unit cells

For some lattice patterns, the smallest unit cell doesn't describe the present symmetry. It is then desirable to pick a larger unit cell which does describe the symmetry. If the unit cell contains another lattice point it is called non-primitive, otherwise it is primitive.

The smallest unit cell doesn't reflect the symmetry within the structure

In the special case where there is an angle of 120° between the lattice directions, it is best to use a hexagonal unit cell. This unit cell is primitive and, when repeated, leads to 6-fold symmetry.

This idea holds for 3D lattices though it is more complicated to demonstrate. Below is a simple example that shows two different units cells for a cubic close packed lattice. (Crystal packing will be discussed later in this TLP)

Shown is a rotating cubic close packed structure

This idea holds for 3D lattices though it is more complicated to demonstrate. Below is a simple example that shows two different units cells for a cubic close packed lattice. (Crystal packing will be discussed later in this TLP)

The parallepiped shows one possible unit cell

This idea holds for 3D lattices though it is more complicated to demonstrate. Below is a simple example that shows two different units cells for a cubic close packed lattice. (Crystal packing will be discussed later in this TLP)

The cube shows another possible unit cell. This is the preferred unit cell for cubic close packed structures because it contains the most symmetry