International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 2.5, pp. 310311
Section 2.5.3.2.4. Diffractiongroup determination
M. Tanaka^{f}

All the symmetry elements of the diffraction groups can be identified from the symmetries of a WP and DPs. But it is practical and convenient to use just the four patterns WP, BP, DP and ±DP to determine the diffraction group. The symmetries appearing in these four patterns are given for the 31 diffraction groups in Table 2.5.3.3 (Tanaka, Saito & Sekii, 1983), which is a detailed version of Table 2 of Buxton et al. (1976). All the possible symmetries of the DP and ±DP appearing at different crystal orientations are given in the present table. When a BP has a higher symmetry than the corresponding WP, the symmetry elements that produce the BP are given in parentheses in column II except only for the case of 4_{R}. When two types of vertical mirror planes exist, these are distinguished by symbols m_{v} and m_{v′}. Each of the two or three symmetries given in columns IV and V for many diffraction groups appears in a DP or ±DP in different directions.

It is emphasized again that no two diffraction groups exhibit the same combination of BP, WP, DP and ±DP, which implies that the diffraction groups are uniquely determined from an inspection of these pattern symmetries. Fig. 2.5.3.3 illustrates the symmetries of the DP and ±DP appearing in Table 2.5.3.3, which greatly eases the cumbersome task of determining the symmetries. The first four patterns illustrate the symmetries appearing in a single DP and the others treat those in ±DPs. The pattern symmetries are written beneath the figures. The other symbols are the symmetries of a specimen. The crosses outside the diffraction discs designate the zone axis. The crosses inside the diffraction discs indicate the exact Bragg position.

Illustration of symmetries appearing in darkfield patterns (DPs) and a pair of darkfield patterns (±DP) for the combinations of symmetry elements. 
When the four patterns appearing in three photographs are taken and examined using Table 2.5.3.3 with the aid of Fig. 2.5.3.3, one diffraction group can be selected unambiguously. It is, however, noted that many diffraction groups are determined from a WP and BP pair without using a DP or ±DP (or from one photograph) or from a set of a WP, a BP and a DP without using a ±DP (or from two photographs).
References
Buxton, B., Eades, J. A., Steeds, J. W. & Rackham, G. M. (1976). The symmetry of electron diffraction zone axis patterns. Philos. Trans. R. Soc. London Ser. A, 181, 171–193.Tanaka, M., Saito, R. & Sekii, H. (1983). Pointgroup determination by convergentbeam electron diffraction. Acta Cryst. A39, 357–368.