 Solution

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

Ordering reflections by

d_{hk l}^{- 2} = (h^{2} + k^{2}) / a^{2} + l^{2} / c^{2}

with

c ≃ 0.9 a

, the first three nonzero families are $001$ , $110$ and $111$ . The

100

F_{001} = 2 (f_{Au} - f_{Cu}), F_{110} = 2 (f_{Au} - f_{Cu}), F_{111} = 2 (f_{Au} + f_{Cu}) .

The atomic scattering factors in each expression are evaluated at that reflection's scattering vector, so equal symbolic forms need not mean equal numerical amplitudes at different angles. In particular, the low-angle superlattice peaks need not be the strongest peaks.

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