Equivalent positions and modulation relations
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.4.4.2,
p.
[ doi:10.1107/97809553602060000624 ]
...
Point groups
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.4.2,
p.
[ doi:10.1107/97809553602060000624 ]
be expressed as This follows directly from (
9.8.4.19) and the definition of the reciprocal standard basis (
9.8.4.13) . From (
9.8.4.16) and (
9.8.4.17), a simple relation can be deduced between σ and the three constituents ...
Structure factor
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.4.4.3,
p.
[ doi:10.1107/97809553602060000624 ]
A, is the probability of atom j being of species A when the internal position is t .
In particular, for a given atomic species, without occupational modulation and a sinusoidal one-dimensional displacive modulation According to (
9.8.4.45 ...
Theoretical foundation
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.4,
p.
[ doi:10.1107/97809553602060000624 ]
with respect to a lattice basis of standard form (
9.8.4.13) . It is then faithfully represented by integral matrices that are of the form indicated in (
9.8.4.17) and (
9.8.4.18) .
9.8.4.3.2. Crystallographic systems
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Laue class
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.4.2.1,
p.
[ doi:10.1107/97809553602060000624 ]
and the definition of the reciprocal standard basis (
9.8.4.13) . From (
9.8.4.16) and (
9.8.4.17), a simple relation can be deduced between σ and the three constituents,, and of the matrix Γ(R): Notice that the elements of are integers ...
Systems and Bravais classes
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.4.3,
p.
[ doi:10.1107/97809553602060000624 ]
. It is then faithfully represented by integral matrices that are of the form indicated in (
9.8.4.17) and (
9.8.4.18) .
9.8.4.3.2. Crystallographic systems
| top | pdf |
Definition 5. A crystallographic system is a set ...
Crystallographic systems
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.4.3.2,
p.
[ doi:10.1107/97809553602060000624 ]
...
Symmetry elements
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.4.4.1,
p.
[ doi:10.1107/97809553602060000624 ]
with the corresponding translation v in V [see (
9.8.4.32) ]. In other words, a basis of the lattice does not simply split into one basis for V and one for .
As for elements of a three-dimensional space group, the translational component ...
Holohedry
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.4.3.1,
p.
[ doi:10.1107/97809553602060000624 ]
occur.
For modulated crystal structures, the holohedral point group can be expressed with respect to a lattice basis of standard form (
9.8.4.13) . It is then faithfully represented by integral matrices that are of the form indicated in (
9.8.4.17 ...
Bravais classes
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.4.3.3,
p.
[ doi:10.1107/97809553602060000624 ]
...
