A general procedure for analysing stacking faults and antiphase boundaries in crystals by using diffraction contrast imaging and/or defocus convergent-beam electron diffraction

Abstract

Abstract A general and systematic procedure is proposed for identifying an arbitrary stacking fault or antiphase boundary in crystals. This procedure is aimed at determining the displacement vector R at the fault plane without knowledge or assumptions about it beforehand and is suitable for both diffraction contrast imaging and defocus convergent-beam electron diffraction techniques. It contains three main points: (i) the extinctive reflection which corresponds to a phase shift of multiples of 2° in a systematic row (g, 2g, 3g,…) is used to determine the fractional part of the dot product g R; (ii) the displacement vector R is determined uniquely from the fractional parts of g R for three reflections g (i = 1, 2, 3), which just form a primitive cell of the reciprocal lattice; (iii) the intrinsic/extrinsic nature of a stacking fault in a face centred cubic crystal is obtained directly from the relationship between R and the foil normal. In addition, based on the second point, all stacking faults and antiph...