Introduction to the tables
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.3,
p.
[ doi:10.1107/97809553602060000624 ]
In terms of external and internal shift components, the reflection condition can be written as With and, (
9.8.3.14) gives For and, (
9.8.3.15) takes the form (
9.8.3.13) : When the modulation wavevector has a rational ...
Examples
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.3.5,
p.
[ doi:10.1107/97809553602060000624 ]
is C -centred monoclinic. For the satellites, the same general condition holds (hklm, h + k = even). From Table
9.8.3.6, one sees after a change of axes that the Bravais class of the modulated structure is Table
9.8.3.2 ...
Symmetry elements
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.3.3.1,
p.
[ doi:10.1107/97809553602060000624 ]
So the superspace group is determined by the arithmetic crystal class of its point group and the corresponding translational components. The symbol for the arithmetic crystal class has been discussed in Subsection
9.8.3.2 . Given a point-group ...
Guide to the use of the tables
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.3.4,
p.
[ doi:10.1107/97809553602060000624 ]
crystals (e.g. surfaces) with one- and two-dimensional modulation (Janssen,
Janner & de Wolff, 1980). In the following, we discuss briefly the information given. Examples of their use can be found in Subsection
9.8.3.5 .
To determine ...
Reflection conditions
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.3.3.2,
p.
[ doi:10.1107/97809553602060000624 ]
becomes
In terms of external and internal shift components, the reflection condition can be written as With and, (
9.8.3.14) gives For and, (
9.8.3.15) takes the form (
9.8.3.13) : When the modulation ...
Tables of Bravais lattices
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.3.1,
p.
[ doi:10.1107/97809553602060000624 ]
of this class (see Chapter 1.4) plus an indication for the row matrix σ (having entries). In this way, one obtains the so-called one-line symbols used in Tables
9.8.3.1 and
9.8.3.2 .
Table
9.8.3.1 | top | pdf ...
Tables of superspace groups
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.3.3,
p.
[ doi:10.1107/97809553602060000624 ]
as With and, (
9.8.3.14) gives For and, (
9.8.3.15) takes the form (
9.8.3.13) : When the modulation wavevector has a rational part, one can choose another basis (Subsection 9.8.2.1) such that K ′ = K + m q r has integer ...
Table for geometric and arithmetic crystal classes
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.3.2,
p.
[ doi:10.1107/97809553602060000624 ]
Incommensurate and commensurate modulated structures
In Table
9.8.3.3, the geometric and the arithmetic crystal classes of (3 + 1)-dimensional superspace are given.
Table
9.8.3.3 | top | pdf |
(3 + 1 ...
Ambiguities in the notation
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.3.6,
p.
[ doi:10.1107/97809553602060000624 ]
Incommensurate and commensurate modulated structures
The invariant part of the translation part of a (3 + 1)-dimensional superspace-group element is uniquely determined by (
9.8.3.5) . This does not imply that for each element ...
