Incommensurate composite crystal structures
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.5.1,
p.
[ doi:10.1107/97809553602060000624 ]
to . In particular, for, one has, because of (
9.8.5.2) and (
9.8.5.4), and
Note that one has, for any t from as is a linear operator. Because of the linearity, this holds for every k from as well. Since belongs ...
Generalizations
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.5,
p.
[ doi:10.1107/97809553602060000624 ]
crystal as a whole.
The proof is as follows. If k belongs to, the vector belongs to . In particular, for, one has, because of (
9.8.5.2) and (
9.8.5.4), and
Note that one has, for any t from ...
The incommensurate versus the commensurate case
Janssen, T.,
Janner, A.,
Looijenga-Vos, A. and
Wolff, P. M. de,
International Tables for Crystallography
(2006).
Vol. C,
Section 9.8.5.2,
p.
[ doi:10.1107/97809553602060000624 ]
Because for an incommensurate structure these vectors form a dense set in, the phase of the modulation function with respect to the basic structure is not determined. For a commensurate modulation, however, the points (
9.8.5.12) form a discrete set ...
