Point-group determination by convergent-beam electron diffraction

Abstract

The method of point-group determination from convergent-beam electron diffraction patterns has been established by Buxton, Eades, Steeds & Rackham [Philos. Trans. R. Soc. London (1976), 281, 171-194]. However, Table 2 given by them is inconvenient for practical purposes, since many symmetries of the dark-field and +G dark-field patterns are not given and are left for the reader's consideration. The table is improved and completed with the help of some new symmetry symbols and illustration of symmetries. The new table makes the point-group determination easy and quick. The symmetries of the symmetrical manybeam convergent-beam electron diffraction patterns have been studied by Tinnappel [PhD Thesis (1975), Tech. Univ. Berlin l using group theory. It is shown that the graphical method used by Buxton et al. can reveal the symmetries of these patterns. A method of * Present address: Hitachi Research Laboratory, Hitachi 319-12, Japan. point-group determination which uses three types of symmetrical many-beam patterns, the hexagonal sixbeam, square four-beam and rectangular four-beam patterns, is described. This method requires only one photograph in determining most diffraction groups. This fact means that the method is more convenient and reliable than that of Buxton et al., since their method requires two or three photographs for most cases. Experimental results which verify the theoretical ones are given. The characteristic features of the symmetrical many-beam method are discussed.

Study of the iron-nitrogen phases by electron microdiffraction and convergent beam electron diffraction

“…This is in perfect agreement with the 2mmlR projection diffraction group (Fig. 3b) [2]. Since this diffraction group only corresponds to the m3m point group, the space group for the 03B3 phase is therefore Fm3m.…”

“…It is explained how to overcome the experimental difficulties connected with the small crystal size, the texture of the specimen and the absence of HOLZ reflections on most diffraction patterns. [1] or by a "multibeam" method proposed by Tanaka [2]. The space group can also be inferred from observation of Gjonnes and Moodie lines of dynamical absence present on CBED patterns [3].…”

“…The point group can be identified by using the Tanaka "multibeam" method [2]. From exami- figure 3a only contains 2D information inside the discs and reveals the presence of a 2 fold axis in the 133 reflection and of a mirror in the 220 and 113 reflections.…”

Space-group determination by dynamic extinction in convergent-beam electron diffraction

“…In the symmetrical many-beam CBED patterns (Tanaka, Saito & Sekii, 1983), the GM-line rules are modified. However, the new tables for the symmetrical manybeam cases are not necessary, since the modification is not complicated.…”

Thermal vibrations in convergent-beam electron diffraction

“…The most common application is to identify known structures and their orientations, but CBED has also been used to determine accurate unit-cell dimensions (Jones, Rackham & Steeds, 1977), structure symmetries (Goodman, 1975;Tanaka, Saito & Sekii, 1983) and even atomic positions (Vincent, Bird & Steeds, 1984). Strain fields around defects (Fung, 1985;Carpenter & Spence, 1982), specimen thicknesses (Kelly, Jostsons, Blake & Napier, 1975;Kirkland, Loane, Xu & Silcox, 1989), ionicity (Zuo, Spence & O'Keeffe, 1988) and the phase of complex atomic structure factors (Zuo, Spence & H¢ier, 1989;Bird, James & Preston, 1987) have also been determined.…”