International
Tables for
Crystallography
Volume E
Subperiodic groups
Edited by V. Kopský and D. B. Litvin

International Tables for Crystallography (2010). Vol. E, ch. 5.2, pp. 404-405   | 1 | 2 |

Section 5.2.3.2.2. Reference tables

V. Kopskýa* and D. B. Litvinb

aFreelance research scientist, Bajkalská 1170/28, 100 00 Prague 10, Czech Republic, and bDepartment of Physics, The Eberly College of Science, Penn State – Berks Campus, The Pennsylvania State University, PO Box 7009, Reading, PA 19610–6009, USA
Correspondence e-mail:  kopsky@fzu.cz

5.2.3.2.2. Reference tables

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Each table of orientation orbits for a certain centring type(s) is followed by reference tables which are organized by arithmetic classes belonging to this centring type(s). The scanned space groups [\cal G] are given in the first row by their sequential number, Schönflies symbol and short Hermann–Mauguin symbol. They are arranged in order of their sequential numbers unless there is a clash with arithmetic classes; a preference is given to collect groups of the same arithmetic class in one table. If space allows it, groups of more than one arithmetic class are described in one table.

The first column is identical with the first column of the table of orientation orbits. On the intersection of a column which specifies the scanned group [\cal G] and of a row which specifies the orientation by its Miller (Bravais–Miller) indices is found the scanning group, given by its Hermann–Mauguin symbol with reference to the auxiliary basis [({\widehat {\bf a}},{\widehat {\bf b}},{\widehat {\bf c}})]. This symbol, which may also contain a shift of origin, instructs us which monoclinic scanning table to consult. The vectors [{\bf a}'], [{\bf b}'], d that determine the lattice of sectional layer groups and the scanning direction are those given in the table of orientation orbits. Depending on the values of parameters m, n, p, q we find the scanning group in its basis [({\bf a}', {\bf b}', {\bf d})] and the respective sectional layer groups.








































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