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Figure 2
Verification that signatures can distinguish different crystal structures and encode different orientations. Compared are the low-frequency parts of the one-sided FFT amplitude spectra for the aluminium, Al3Sc and tungsten synthetic data sets after projecting along specific crystallographic directions ([110], [110] and [111]). The two rows in the middle display the results for the L12 crystal structure (with the aluminium substructure in the upper and the scandium substructure in the lower middle row). The x axis shows amplitude spectrum bin IDs. The vertical orange lines mark the theoretical lattice plane spacing for lattice planes which are stacked perpendicular to the respective crystallographic (projection) directions. Exemplified for the b.c.c. tungsten structure, we expect to find an alternating sequence of 〈100〉 and 〈200〉 planes with 0.5aW spacing and an equal planar density of the tungsten atoms for the two inspected crystallographic plane sets. We assume the signal length is [{\cal L} = 2^m] with m = 8. The sampling frequency is [f_{\rm s} = {{{\cal L}} / {2(R + \Delta R)}}] with ΔR = R/2m−1 − 1. For R = 2.0 nm and a reciprocal spacing f = 1/0.5aW, we can verify that the amplitude peaks in the 19th bin ([b = \lfloor {f {\cal L} / f_{\rm s}} \rfloor]).

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