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 Results for DC.creator="P." AND DC.creator="M." AND DC.creator="de" AND DC.creator="Wolff" in section 9.8.1 of volume C   page 1 of 2 pages.
Introduction
Janssen, T., Janner, A., Looijenga-Vos, A. and Wolff, P. M. de  International Tables for Crystallography (2006). Vol. C, Section 9.8.1, pp. 907-913 [ doi:10.1107/97809553602060000624 ]
... found in insulators as well (Tanisaki, 1961, 1963; Brouns, Visser & de Wolff, 1964). The remarkable morphological properties of calaverite could also ... case. In general, they are elements of a vector module M* and can be written as This leads to the ...

Four-dimensional space groups
Janssen, T., Janner, A., Looijenga-Vos, A. and Wolff, P. M. de  International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4.5, pp. 912-913 [ doi:10.1107/97809553602060000624 ]
Four-dimensional space groups 9.8.1.4.5. Four-dimensional space groups Four-dimensional space groups were obtained in the (3 + 1)-reducible case by Fast & Janssen (1969) and in the general case by Brown, Bülow, Neubüser, Wondratschek & Zassenhaus (1978). The groups were determined on the basis of algorithms developed by ...

Generalized nomenclature
Janssen, T., Janner, A., Looijenga-Vos, A. and Wolff, P. M. de  International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4.4, p. 912 [ doi:10.1107/97809553602060000624 ]
... International Tables for Crystallography (2006). Vol. C, ch. 9.8, p. 912 © International Union of Crystallography 2006 | home | resources | advanced search ...

Four-dimensional crystallography
Janssen, T., Janner, A., Looijenga-Vos, A. and Wolff, P. M. de  International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4.3, pp. 911-912 [ doi:10.1107/97809553602060000624 ]
Four-dimensional crystallography 9.8.1.4.3. Four-dimensional crystallography Let us summarize the results obtained in the previous paragraph. The matrices [Gamma](R) form a faithful integral representation of the three-dimensional point group K with a four-dimensional carrier space . It is a reducible representation having as invariant subspaces the physical ...

Description in four dimensions
Janssen, T., Janner, A., Looijenga-Vos, A. and Wolff, P. M. de  International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4.2, p. 911 [ doi:10.1107/97809553602060000624 ]
... lattice vectors , which can be written as where [cf. (9.8.1.14)] m has now been replaced by and As will be explained ... International Tables for Crystallography (2006). Vol. C, ch. 9.8, p. 911 © International Union of Crystallography 2006 | home | resources | advanced search ...

Bravais classes of vector modules
Janssen, T., Janner, A., Looijenga-Vos, A. and Wolff, P. M. de  International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4.1, pp. 910-911 [ doi:10.1107/97809553602060000624 ]
... by vectors This set of vectors is a vector module M*. The vectors form a basis of the reciprocal lattice ... reciprocal-lattice vector of the basic structure. A vector module M* has point-group symmetry K, which is the subgroup of ... invariant. In the case of an incommensurate one-dimensional modulation, M* is generated by the lattice [Lambda]* of main reflections ...

Basic symmetry considerations
Janssen, T., Janner, A., Looijenga-Vos, A. and Wolff, P. M. de  International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4, pp. 910-913 [ doi:10.1107/97809553602060000624 ]
... by vectors This set of vectors is a vector module M*. The vectors form a basis of the reciprocal lattice ... reciprocal-lattice vector of the basic structure. A vector module M* has point-group symmetry K, which is the subgroup of ... invariant. In the case of an incommensurate one-dimensional modulation, M* is generated by the lattice [Lambda]* of main reflections ...

The symmetry
Janssen, T., Janner, A., Looijenga-Vos, A. and Wolff, P. M. de  International Tables for Crystallography (2006). Vol. C, Section 9.8.1.3.2, pp. 909-910 [ doi:10.1107/97809553602060000624 ]
... taken as independent of j. Under the glide reflection (integer m) present in the basic structure, the transformed positions are Consider the rational approximation of [gamma] given by P/Q, with P and Q relatively prime integers. Then such a glide ...

The diffraction pattern
Janssen, T., Janner, A., Looijenga-Vos, A. and Wolff, P. M. de  International Tables for Crystallography (2006). Vol. C, Section 9.8.1.3.1, p. 909 [ doi:10.1107/97809553602060000624 ]
... that leave the modulated structure invariant are those lattice translations m of the basic structure satisfying the condition = integer . If ... factor vanishes unless there are integers h, k, l, and m such that If q is incommensurate, i.e. if there is ... a modulated phase, one distinguishes between main reflections (for which m = 0) and satellites (for which . The intensities of ...

The simple case of a displacively modulated crystal
Janssen, T., Janner, A., Looijenga-Vos, A. and Wolff, P. M. de  International Tables for Crystallography (2006). Vol. C, Section 9.8.1.3, pp. 909-910 [ doi:10.1107/97809553602060000624 ]
... that leave the modulated structure invariant are those lattice translations m of the basic structure satisfying the condition = integer . If ... factor vanishes unless there are integers h, k, l, and m such that If q is incommensurate, i.e. if there is ... a modulated phase, one distinguishes between main reflections (for which m = 0) and satellites (for which . The intensities of ...

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