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ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2025/paper-2/a9/g/solution

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

Codex  0 2026-10-20

The sum of the three primitive vectors is

(a /2) (1, 1, 1)

, so the surface is a

(111)

plane. Two in-plane translations are

t_{1} = a (1, - 1, 0), t_{2} = a (1, 0, - 1) .

(1)

They have length

L = 2 a

and included angle

6 0^{\circ}

, giving a triangular top-layer lattice. Body-centred sites lie in offset parallel layers, not as additional sites in this same plane. A primitive surface cell is the rhombus spanned by

t_{1}, t_{2}

, of area

A_{s} = ∣ t_{1} \times t_{2} ∣ = 3 a^{2} = 17.3503 \overset{˚}{A}^{2} .

(2)

Figure 1.
Triangular top atomic layer of bcc tungsten (111) and its hexagonal surface Brillouin zone
. **Details**.

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