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Figure 1
The schematic of a pair of three-beam CBED patterns that involve two Friedel pairs, g and [\overline g], and h and [\overline h], which are used to determine the octant of the three-phase invariant (the uncertainty of the phase measurement is ±22.5°). The pair of three-beam CBED patterns share the same zone axis that is perpendicular to the plane (and we define it as the ZOLZ plane) formed by the reciprocal lattice vectors g, h, −g and −h, but have different Laue circles, where the projections of the incident wavevector onto the ZOLZ plane, Kt (pointing from the centre of Laue circle to a point of interest in the central disc), are in opposite directions. In the magnified view of disc g, two loci, [{\zeta _g} = {\zeta _h}] and [{\zeta _g} = 0] are labelled, and the intersection is the exact three-beam condition ([{\zeta _g} = 0,\; \;{\zeta _h} = 0]). Different parts in the three-beam CBED patterns which are marked with circles and rectangles are compared in order to determine the signs of sin ϕ and cos ϕ. These, together with whether sin ϕ (or cos ϕ) is zero, can be used to constrain the three-phase invariants to within an octant (i.e. [\pm] 22.5°).

IUCrJ
Volume 5| Part 6| November 2018| Pages 753-764
ISSN: 2052-2525
https://doi.org/10.1107/S2052252518012216