If the Structure Factor equation,

is expressed in terms of cosine and sine functions: This can be simplified further in the case of centrosymmetric unit cells; in such cells, for every atom at location (x, y, z) there is an identical atom at (-x, -y, -z). Because sin(-x) = -sin(x), the sin terms cancel and the structure factor expression simplifies to: In addition, if an atom at (x, y, z) produces a scattering with a phase angle of α, an identical atom at (-x, -y, -z) will produce a scattering with a phase angle of -α, leading to a resultant phase angle of 0° (if the individual α's are less than 90°) or 180° (if the individual α's are greater than 90°):



Thus, in the centrosymmetric case, each structure factor is limited to phases of 0° or 180°. And, because cos0° = +1 and cos180° = -1, determining the phase of a structure factor in a centrosymmetric unit cell is just a matter of determining the sign of the structure factor: