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 $0$ or $\pi$. Defining $S(h)=\mathrm{sgn}F(h)$ givesCentrosymmetry converts the phase problem into a sign problem; it does not imply that every structure factor is positive.