Past exam of the condensed matter physics course of the University of Oxford / 2019 / 1 / a

A Bravais lattice is the set of pointswhere the primitive lattice translation vectors ${\mathbf{a}}_i$ are linearly independent. Every lattice point has the same translational environment.

An atomic basis is the motif of atoms attached to each point of the Bravais lattice, specified by positions ${\mathbf{r}}_p$ and atomic species. The full crystal consists of atoms at $\mathbf{R}+{\mathbf{r}}_p$, with $\mathbf{R}\in \Lambda$. The Bravais lattice describes translations; the atomic basis describes what is repeated. A primitive cell contains one lattice point but can contain several atoms.