 Solution

ID: 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:

A_{BZ} = \frac{( 2 π ) ^{2}}{A _{s}} = 2.27537 \overset{˚}{A}^{- 2} .

The zone has centre-to-corner distance

4 π / (3 L)

and centre-to-side distance

2 π / (3 L)

, consistent with this area. These reciprocal lengths use the convention

t_{i} \cdot b_{j} = 2 π δ_{ij}

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