Superspace Groups for One-dimensionally Modulated Structures

by Akiji Yamamoto, NIRIM, Japan

All superspace groups for one-dimensionally modulated structures (756 superspace groups, excluding enantiomorphic pairs) are given. These are classified into 6 systems. For publications using this table, the following paper should be cited. Akiji Yamamoto, Acta Crystallographica A52, 509-560, (1996).

Click one of 6 items. The table of each superspace group lists the wave vector, superspace groups, equivalent superspace groups if any, centering translations for the non-primitive lattice, symmetry operations for the (first) superspace group and reflection conditions if any. The symbol is similar to the two-line symbol but instead of the prefix, the wave vector is used.

Reference

A. Yamamoto, T. Janssen, A. Janner and P. M. de Wolff, Acta Cryst. A41 (1985) 528.

Superspace Groups for Two-dimensionally Modulated Structures

by Akiji Yamamoto, NIRIM, Japan

A provisional list of all (3355) superspace groups for two-dimensionally modulated structures (superspace groups, excluding enantiomorphic pairs) are given. These are classified into 6 systems. For publications using this table, the following paper should be cited. Akiji Yamamoto, Acta Crystallographica A52, 509-560, (1996).

Click one of 6 items. The table of each superspace group lists the wave vector, superspace groups, equivalent superspace groups if any, centering translations for the non-primitive lattice, symmetry operations for the (first) superspace group and reflection conditions if any. The symbol is similar to the one-line symbol in 4D superspace groups but has the pair of wave vectors are used. The symbols .ss., .st. etc. stand for the translation along 4-th and 5-th direction when the rotational part is 2x2 identity matrix. The symbol g represents the glide plane in the 2D internal space.

Superspace Groups for Three-dimensionally Modulated Structures

by Akiji Yamamoto, NIRIM, Japan (added Jun. 20, 2000)

A provisional list of all (11764) superspace groups for three-dimensionally modulated structures (superspace groups, excluding enantiomorphic pairs) are given. These are classified into 7 systems. For publications using this table, the following paper should be cited. Akiji Yamamoto, Proc. Aperiodic 2000.

Click one of 7 items. The table of each superspace group lists the wave vector, superspace groups, equivalent superspace groups if any, centering translations for the non-primitive lattice, symmetry operations for the (first) superspace group and reflection conditions if any. The symbol is similar to the one-line symbol in 4D superspace groups but has the triplet of wave vectors are used. The symbols .sss., .0st. etc. stand for the translation along 4-th, 5-th and 6-th direction when the rotational part is 3x3 identity matrix. The symbol g represents the glide plane in the 2D internal space.

Reference

A. Yamamoto, "Crystallography of Quasiperiodic Structures", Acta Cryst. A52 (1996) 509-560.

A. Yamamoto, "Tward Automatic Analysis of Modulated and Composite Crystals", Proc. Aperiodic 2000 to be published.