 Solution

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

Summing phase-weighted atomic scattering factors over the four positions gives

F_{hk l} = f_{Au} [1 + (- 1)^{h + k}] + f_{Cu} [(- 1)^{h + l} + (- 1)^{k + l}] .

h, k

have different parity, the reflection vanishes. If they have equal parity, this becomes

2 [f_{Au} + (- 1)^{h + l} f_{Cu}]

. The difference reflections reveal chemical order; they disappear when all sites instead have the same average scattering factor.

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