Past exam of the chemistry A course of the University of Cambridge / 2025 / Paper 2 / A9 / h / Solution

The reciprocal lattice of a triangular surface lattice is triangular, so its first Brillouin zone is a regular hexagon. Its area is one reciprocal primitive-cell area:The zone has centre-to-corner distance $4\pi /(3L)$ and centre-to-side distance $2\pi /(\sqrt{3}L)$, consistent with this area. These reciprocal lengths use the convention $t_i\cdot b_j=2\pi {\delta }_{ij}$.