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ID: past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2019/paper-1/3/c/iii/solution

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Past exam of the materials science course of the University of Cambridge / 2019 / Paper 1 / 3 / c / iii / Solution by

Codex  0 2026-10-20

The first peak is

001

, with

d_{001} = c

; the second is

110

, with

d_{110} = a / 2

. Applying Bragg's law with

λ = 0.193604 nm

gives

c = \frac{λ}{2 sin 15.3 0 ^{\circ}} = 0.3669 nm, a = b = \frac{λ}{2 sin 20.2 4 ^{\circ}} = 0.3957 nm .

Thus

c / a = 0.927

, consistent with the approximate ratio used to order the reflections. These are the lengths of the supplied larger basal cell; the primitive basal lattice parameter is

a / 2 = 0.2798 nm

.

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