 Solution

ID: past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-4/58/a/ii/solution

With an origin at an inversion center, the structure factors are real, so their phases are either

0

π

. Defining

S (h) = sgn F (h)

gives

ρ (x) = F (0) + 2 \sum_{h = 1}^{\infty} S (h) ∣ F (h) ∣ cos (2 πh x) .

Centrosymmetry converts the phase problem into a sign problem; it does not imply that every structure factor is positive.

 New to topics? Read the docs here!