Chiral determination: direct interpretation of convergent-beam electron diffraction patterns using the series expansion of Cowley and Moodie.

Given a small number of structure factors of a known chiral structure of unknown hand, it is shown that the hand can be determined from the sign of the contrast difference of two reflections in a suitably oriented convergent-beam electron diffraction (CBED) pattern. A simple formula for this difference, which takes into account all the significant second-order scattering, is derived using the series expansion of Cowley and Moodie for n-beam diffraction. The reason for the success of a three-beam interpretation is investigated. The method is applied to patterns from thin crystals in which a mirror projection symmetry can be found and its validity is demonstrated by agreement with experiment using samples of known hand. The advantages of recording patterns near major zone axes are discussed as well as some other experimental aspects of chiral determination using CBED.