Point-group determination by convergent-beam electron diffraction

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 many- beam convergent-beam electron diffraction patterns have been studied by Tinnappel [PhD Thesis (1975), Tech. Univ. Berlin] 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 point-group determination which uses three types of symmetrical many-beam patterns, the hexagonal six- beam, 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.