International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by Th. Hahn

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. A. ch. 4.3, p. 62

Section 4.3.2.2. Transformation of space-group symbols

E. F. Bertauta‡

a Laboratoire de Cristallographie, CNRS, Grenoble, France

4.3.2.2. Transformation of space-group symbols

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How does a monoclinic space-group symbol transform for the various settings of the same unit cell? This can be easily recognized with the help of the headline of Table 4.3.2.1,[link] completed to the following scheme: [\matrix{{\bf a}{\underline{\bf b}}{\bf c} &{\bf c}\bar{\underline{\bf b}}{\bf a} &{\bf cab} &{\bf ac}\bar{\bf b} &{\bf bca} &{\bar{\bf b}\bf{ac}} &\hbox{Unique axis}\ b\cr {\bf bca} &{\bf a}{\bar{\bf c}}{\bf b} &{\bf ab}{\underline{\bf c}} &{\bf ba}\bar{\underline{\bf c}} &{\bf cab} &{\bar{{\bf c}}\bf ba} &\hbox{Unique axis}\ c\cr {\bf cab} &{\bf b}{\bar{\bf a}}{\bf c} &{\bf bca} &{\bf cb}\bar{\bf a} &{\underline{\bf a}}{\bf bc} &\bar{\underline{\bf a}}{\bf cb} &\hbox{ Unique axis}\ a.\cr}] The use of this three-line scheme is illustrated by the following examples.

Examples

  • (1) [C2/c] (15, unique axis b, cell choice 1)

    Extended symbol: [\matrix{\noalign{\vskip 12pt}C1\ 2/c\ 1.\hfill\cr 2_{1}/n\ \hfill\cr}]

    Consider the setting cab, first line, third column. Compared to the initial setting abc, it contains the `unique axis b' in the third place and, consequently, must be identified with the setting abc, unique axis c, in the third column, for which in Table 4.3.2.1[link] the new symbol for cell choice 1 is listed as [\matrix{\noalign{\vskip 12pt}A11\ 2/a\hfill\cr 2_{1}/n.\hfill\cr}]

  • (2) [C2/c] (15, unique axis b, cell choice 3)

    Extended symbol: [\matrix{\noalign{\vskip 12pt}I1\ 2/a\ \ 1.\hfill\cr 2_{1}/c \hfill\cr}]

    Consider the setting [{\bar{\bf b}}{\bf ac}] in the first line, sixth column. It contains the `unique axis b' in the first place and thus must be identified with the setting [\bar{\underline{\bf a}}{\bf cb}], unique axis a, in the sixth column. From Table 4.3.2.1,[link] the appropriate space-group symbol for cell choice 3 is found as [\matrix{\noalign{\vskip 12pt}I\ 2/b\ 11.\hfill\cr 2_{1}/ c\ \hfill\cr}]








































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