 Solution

ID: past-exam-of-the-condensed-matter-physics-course-of-the-university-of-oxford/2022/1/d/ii/solution

Use the same atomic basis phases as in the ordered structure factor, replacing each atomic scattering factor by its site average. For the reflection with equal integer parity,

S_{111} = ⟨ f_{c} ⟩ + 3 ⟨ f_{f} ⟩ = f_{Au} + 3 f_{Cu} .

Conservation of the total composition removes the alloy sublattice order parameter from this amplitude. For the reflection with mixed integer parity,

S_{110} = ⟨ f_{c} ⟩ - ⟨ f_{f} ⟩ = ρ (f_{Au} - f_{Cu}) .

The coherent powder diffraction wave intensities consequently satisfy

I_{111} (ρ) = I_{111} (1), I_{110} (ρ) = ρ^{2} I_{110} (1) .

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