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

International Tables for Crystallography (2010). Vol. E, ch. 5.1, p. 394   | 1 | 2 |
doi: 10.1107/97809553602060000787

Chapter 5.1. Symbols used in Parts 5 and 6

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

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

[\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]
[(hkl)] Miller indices of a section plane
[(hkil)] Bravais–Miller indices of a section plane
[(mn0)] 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 [(hkl)]
[\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 [(hkl)] 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 [(hkl)] 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}] Nontrivial symmetry operations of the twin
[{\underline s}_{12}] Side-reversing operations of the twin
[r^{*}_{12}] State-reversing operations of the twin








































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