Graphical Fourier-coefficient analysis as a paper-based method for teaching structure factors

Weirich, T.E.

doi:10.1107/S2056989026000745

Acta Crystallographica Section E
Acta Crystallographica
Section E CRYSTALLOGRAPHIC COMMUNICATIONS

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Figure 13
Representation of the structure-factor components A and B of different signs within the complex plane (Argand plot). For numerical calculations using equation 4

, it is important to note that there exists an ambiguity regarding the true value of the phase angle $[\alpha]$ of the structure factor. This is because the slope determined from equation 4

is identical if the signs of A and B are both the same (as shown in the above example) or if they are different, which yields a negative slope. As the true value for the phase angle $[\alpha]$ is dependent on the signs of A and B, it may require a correction. So, for example, if A is positive and B is negative, the permitted phase angle must be within 270° ( $[3\pi /2]$ ) and 360° ( $[2\pi]$ ). The necessary corrections are summarized in the lookup table in Table 1

, together with an example for each.

CRYSTALLOGRAPHIC
COMMUNICATIONS

ISSN: 2056-9890

Volume 82| Part 2| February 2026| Pages 235-243

https://doi.org/10.1107/S2056989026000745

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