@@ -232,7 +232,7 @@ Does the choice of a lattice need to coincide with the centre of our arbitrary $
> The description of objects with respect to the reference lattice point is known as a **basis**.
The reference lattice point is the chosen lattice point to which we apply the lattice vectors in order to reconstruct the lattice.
In the 'Lattice A' case, the basis is trivial $\star = (0,0)$ since each lattice point corresponds with the $\star$ object. In 'Lattice B', each object is shifted by $0.5a_1$ away from the lattice point. Therefore, its basis is $\star = (1/2,0)$ in fractional coordinates. The basis is especially important when a crystal has many different types of atoms (for example many salts like NaCl)
In the 'Lattice A' case, the basis is trivial $\star = (0,0)$ since each lattice point corresponds with the $\star$ object. In 'Lattice B', each object is shifted by $0.5a_1$ away from the lattice point. Therefore, its basis is $\star = (1/2,0)$. It is expressed in terms of **fractional coordinates** which depends on your definition of lattice vectors. For example, $\star = (1/2,0)$ implies that the position of $\star$ is at $(1/2)\mathbf{a}_{1}+0\mathbf{a}_{2}$. The basis is especially important when a crystal has many different types of atoms (for example many salts like NaCl)
Rather than work with the whole space of the crystal, it is practical to use the smallest possible 'building block' of the crystal - a **unit cell**:
