A study of the breakdown of Friedel's law in electron backscatter Kikuchi diffraction patterns: application to zincblende-type structures

Abstract

The breakdown of Friedel's law has been observed in backscatter Kikuchi diffraction patterns (BKDP) obtained in the scanning electron microscope (SEM) from a series of zincblende structures including GaAs, InP, GaSb, CdHgTe and the minerals sphalerite (ZnS), chalcopyrite (CuFeS2) and tetrahedrite (Cu12Sb4S13). Differences in intensities were observed between the reflections 51{\bar 1} and 5{\bar 1}{\bar 1} in InP, GaSb, CdHgTe and sphalerite, thus allowing the non-centrosymmetric point group {\bar 4}3m to be determined. In GaAs, differences in intensities were noted between {\bar 5}11 and {\bar 4}{\bar 1}. In chalcopyrite and tetrahedrite, non-equivalent intensities were observed between {\bar 2}15 and 2{\bar 1}{\bar 5} and between 3{\bar 1}{\bar 2} and 31{\bar 2}, respectively. In addition, BKDPs obtained from chalcopyrite revealed a small displacement at the point where the pair of equivalent reflections {\bar 4}06 and 460 intersect within the Kikuchi band 02{\bar 2}. The presence of this displacement together with observation of the breakdown of Friedel's law confirmed the tetragonal point group {\bar 4}2m for chalcopyrite. Although the point groups of GaAs, chalcopyrite and tetrahedrite were derived successfully using BKDPs, determination of their space groups proved unsuccessful. The superstructure reflections were invisible because the structure factors are very small. The behaviour of the invisible 200 reflection in GaAs is investigated using many-beam dynamical intensity profiles calculated across the h00 systematic row of reflections. Dynamical intensity profiles calculated across the h00 systematic rows of reflections for Ge, InP and sphalerite are also discussed.