Symbols used in Parts 5 and 6

Kopskyacute, V.; Litvin, D. B.

doi:10.1107/97809553602060000651

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

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International Tables for Crystallography (2006). Vol. E. ch. 5.1, p. 392 | 1 | 2 |
https://doi.org/10.1107/97809553602060000651

Chapter 5.1. Symbols used in Parts 5 and 6

V. Kopský^a ^* and D. B. Litvin^b

^a Department of Physics, University of the South Pacific, Suva, Fiji, and Institute of Physics, The Academy of Sciences of the Czech Republic, Na Slovance 2, PO Box 24, 180 40 Prague 8, Czech Republic, and ^bDepartment of Physics, Penn State Berks Campus, The Pennsylvania State University, PO Box 7009, Reading, PA 19610–6009, USA
Correspondence e-mail: kopsky@fzu.cz

In this chapter, the symbols used in Parts 5 and 6 of this volume are defined.

Keywords: crystallography; subperiodic groups; rod groups; layer groups; frieze groups; nomenclature.

$[\cal G]$	Scanned space group
P	Origin of the coordinate system of the scanned space group $[\cal G]$
$[{\bf a}]$ , $[{\bf b}]$ , $[{\bf c}]$	Conventional basis vectors of the scanned space group $[\cal G]$
$[(P;{\bf a},{\bf b},{\bf c})]$	Conventional coordinate system of the scanned space group $[\cal G]$
	Miller indices of a section plane
	Bravais–Miller indices of a section plane
	Miller indices for special orientations with variable parameter
$[V({\bf a}',{\bf b}')]$	Orientation of planes defined by Miller or Miller–Bravais indices
$[{\cal H}({\cal G},(hkl)) = {\cal H}({\cal G},V({\bf a}',{\bf b}'))]$	Scanning group for the scanned group $[{\cal G}]$ and orientation $[V({\bf a}',{\bf b}')]$ defined by Miller indices
$[\cal H]$	Shorthand notation for the scanning group
$[{\bf a}']$ , $[{\bf b}']$ , $[{\bf d}]$	Conventional basis vectors of the scanning group
$[{\bf a}']$ , $[{\bf b}']$	Conventional basis vectors of the sectional layer groups for a given orientation of the section plane
$[{\bf d}]$	Basis vector of the scanning group in the scanning direction
$[{\widehat {\bf a}}]$ , $[{\widehat {\bf b}}]$ , $[{\widehat {\bf c}}]$	Auxiliary basis of a monoclinic scanning group
s	Distance of a section plane from the origin P in units of d
$[P + s{\bf d}]$	Location of the section plane along the scanning line
$[{\cal L}(P + s{\bf d}; (hkl))]$	Sectional layer group of a plane with orientation passing through the point $[P+s{\bf d}]$
$[{\cal L}(s{\bf d})]$	Shorthand notation for this sectional layer group
$[(P + s{\bf d}; {\bf a}', {\bf b}',{\bf d})]$	Reference coordinate system for the sectional layer group
$[s_{o} = {{1}/{f}}]$	Length of the fundamental region along d in units of d
$[f = {{1}/{s_{o}}}]$	Number of planes of a general translation orbit in the interval $[0 \leq s \,\lt\, 1]$
$[{\sf S}_{\sf 1}]$ , $[{\sf S}_{\sf 2}]$	Single domain states
$[({\sf S}_{\sf 1},{\sf S}_{\sf 2})]$	Ordered domain pair
$[\{{\sf S}_{\sf 1},{\sf S}_{\sf 2}\}]$	Unordered domain pair
$[{\cal F}_{12}]$	Symmetry group of an ordered domain pair
$[{\cal J}_{12}]$	Symmetry group of an unordered domain pair
$[({\sf S}_{\sf 1}\|(hkl),s{\bf d}\|{\sf S}_{\sf 2}) =]$ $[({\sf S}_{\sf 1}\|{\bf n},s{\bf d}\|{\sf S}_{\sf 2})]$	Domain twin with a central plane of orientation and sidedness defined by Miller indices or by a normal $[{\bf n}]$ , and location $[s{\bf d}]$
$[{\overline {\sf F}}_{12}]$ , $[{\widehat {\sf F}}_{12}]$	Sectional layer group of the central plane under the action of the group $[{\cal F}_{12}]$ and its floating subgroup
$[{\overline {\sf J}}_{12}]$ , $[{\widehat {\sf J}}_{12}]$	Sectional layer group of the central plane under the action of the group $[{\cal J}_{12}]$ and its floating subgroup
$[{\sf T}_{12}]$	Symmetry group of the domain twin
$[f_{12}]$	Trivial symmetry operations of the twin
$[{\underline t}^{*}_{12}]$	Non-trivial symmetry operations of the twin
$[{\underline s}_{12}]$	Side-reversing operations of the twin
$[r^{*}_{12}]$	State-reversing operations of the twin

International Tables for Crystallography (2006). Vol. E. ch. 5.1, p. 392
https://doi.org/10.1107/97809553602060000651