On the sign ambiguity of triplet phases in nonsystematic many-beam effects in CBED patterns

The possibility to determine not only the magnitude but also the sign of three-phase structure invariants from nonsystematic many-beam effects in convergent-beam electron diffraction (CBED) patterns is discussed. From the full dynamical many-beam intensity expression it is clear that it is a principal difference between equivalent three-beam cases of opposite sign of the triplet phases. However, the difference and thus the ability to distinguish between the two cases depends strongly both on the relative magnitude of the structure factors involved and the specimen thickness for which the actual CBED discs are obtained. The largest differences are obtained for a weakly coupled three-beam case where the intensity in the line of the primary reflection, which in this case coincides with the kinematical two-beam position, has a distinct maximum or minimum at the three-beam condition depending on the sign of the triplet phase. In a strong coupling case where the intensity in the primary-reflection line near the three-beam condition is split into two individual segments, the differences are generally less and are not so obvious and quantitative measurements are necessary to distinguish the two cases of opposite sign of the triplet phases. Calculated examples with respect to a nonsystematic three-beam example in the noncentrosymmetric InP are given.