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Figure 2
The image at the bottom shows the Fourier map of a two-dimensional unit cell of a one-atom structure, with atom positions at xy = (0, 0) and (1/2, 1/2). The corresponding diffraction pattern is shown in Fig. 1[link]. For this structure, a triplet with all strong structure factors is (0, 2) (1, 1) (1, 3). As shown in (a) and (b), the two Fourier waves (0, 2) and (1, 1) have both a 0° phase angle and begin with a maximum at the top left corner of the unit cell, producing bright maxima at the positions of the atoms. According to Table 1[link] and Equation 8[link], the Fourier waves (1, 3) and its Friedel counterpart (−1, −3) must have the same zero phase angle to agree with Sayre's proposal. The sum of the corresponding Fourier waves (a) to (c) is shown in map (d), which exhibits pronounced maxima at the positions of the atoms.

Journal logoCRYSTALLOGRAPHIC
COMMUNICATIONS
ISSN: 2056-9890
Volume 82| Part 5| May 2026| Pages 534-543
https://doi.org/10.1107/S2056989026003300
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