Tables for
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.6, p. 857

Section Lattice diagram

D. B. Litvina*

aDepartment 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: Lattice diagram

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For each three-dimensional magnetic space group, a three-dimensional lattice diagram is given in the upper left-hand corner of the first page of the tables of properties of that group. (For all other magnetic groups, the corresponding lattice diagram is given within the symmetry diagram, see Section[link] below.) This lattice diagram depicts the coordinate system used, the conventional unit cell of the space group [{\cal F}], the magnetic space group's magnetic superfamily type and the generators of the translational subgroup of the magnetic space group. In Fig. we show lattice diagrams for two orthorhombic magnetic space groups: (a) Pmc21 and (b) P2bmc′21. The generating lattice vectors are colour coded. Those coloured black are not coupled with time inversion, while those coloured red are coupled with time inversion. In the group Pmc21, a magnetic group of the type [{\cal F}], the lattice is an orthorhombic P lattice, see Fig.[link](a), and no generating translation is coupled with time inversion. In the second group, P2bmc′21, a magnetic group of type [{\cal M}_R], the lattice is an orthorhombic P2b lattice, see Fig.[link](b), and the generating lattice vector in the y direction is coupled with time inversion.


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Lattice diagrams of (a) the three-dimensional magnetic space group 26.1.168 [{\cal F} = Pmc2_1] and (b) the three-dimensional magnetic space group 26.10.177 [{\cal M}_R = P_{2b} m'c'2_1= {\cal F}({\cal D}) = Pmc2_1(Pca2_1)].

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