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Results for DC.creator="P." AND DC.creator="M." AND DC.creator="de" AND DC.creator="Wolff" in section 9.8.4 of volume C page 1 of 2 pages. |
Theoretical foundation
International Tables for Crystallography (2006). Vol. C, Section 9.8.4, pp. 937-945 [ doi:10.1107/97809553602060000624 ]
... a basic structure with lattice periodicity. Let us denote by M* the set of all integral linear combinations of the vectors ... a set of free Abelian generators, therefore the rank of M* is n. The dimension of M* is the dimension of the Euclidean space spanned by ...
Equivalent positions and modulation relations
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.4.2, pp. 940-941 [ doi:10.1107/97809553602060000624 ]
Equivalent positions and modulation relations 9.8.4.4.2. Equivalent positions and modulation relations A (3 + d)-dimensional space group that leaves a function invariant maps points in (3 + d)-space to points where the function has the same value. The atomic positions of a modulated crystal represent such a pattern, and the superspace ...
Symmetry elements
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.4.1, p. 940 [ doi:10.1107/97809553602060000624 ]
... International Tables for Crystallography (2006). Vol. C, ch. 9.8, p. 940 © International Union of Crystallography 2006 | home | resources | advanced search ...
Superspace groups
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.4, pp. 940-941 [ doi:10.1107/97809553602060000624 ]
... The diffraction from incommensurate crystal structures has been treated by de Wolff (1974), Yamamoto (1982a,b), Paciorek & Kucharczyk (1985), Petricek, Coppens & Becker ... crystal structure. Acta Cryst. A41, 462-466. Perez-Mato, J. M., Madariaga, G. & Tello, M. J. (1986). Diffraction symmetry ...
Bravais classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3.3, p. 940 [ doi:10.1107/97809553602060000624 ]
... International Tables for Crystallography (2006). Vol. C, ch. 9.8, p. 940 © International Union of Crystallography 2006 | home | resources | advanced search ...
Crystallographic systems
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3.2, p. 940 [ doi:10.1107/97809553602060000624 ]
... International Tables for Crystallography (2006). Vol. C, ch. 9.8, p. 940 © International Union of Crystallography 2006 | home | resources | advanced search ...
Holohedry
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3.1, pp. 939-940 [ doi:10.1107/97809553602060000624 ]
... diffraction spots as a set invariant, thus the vector module M* also. As discussed in Subsection 9.8.4.2, each of the elements ... dimensions leaves the lattice * invariant for which the vector module M* is the projection. Conversely, if one has a point group ... the case of an incommensurate crystal, the projection of * on M* is one-to-one as one can see as ...
Systems and Bravais classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3, pp. 939-940 [ doi:10.1107/97809553602060000624 ]
... diffraction spots as a set invariant, thus the vector module M* also. As discussed in Subsection 9.8.4.2, each of the elements ... dimensions leaves the lattice * invariant for which the vector module M* is the projection. Conversely, if one has a point group ... the case of an incommensurate crystal, the projection of * on M* is one-to-one as one can see as ...
Geometric and arithmetic crystal classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.2.2, p. 939 [ doi:10.1107/97809553602060000624 ]
... of modulated structures a standard basis can be chosen (for M* and correspondingly for ). According to equation (9.8.4.15), for each ... is so because in the incommensurate case the correspondence between M* and is uniquely fixed by the embedding rule (9.8.4.10) (see ... point group and a standard basis for the vector module M* because of relation (9.8.4.15). In three dimensions, there ...
Laue class
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.2.1, pp. 938-939 [ doi:10.1107/97809553602060000624 ]
Laue class 9.8.4.2.1. Laue class Definition 1.The Laue point group of the diffraction pattern is the point group in three dimensions that transforms every diffraction peak into a peak of the same intensity.2 Because all diffraction vectors are of the form (9.8.4.5), the action of an element R of the Laue ...
International Tables for Crystallography (2006). Vol. C, Section 9.8.4, pp. 937-945 [ doi:10.1107/97809553602060000624 ]
... a basic structure with lattice periodicity. Let us denote by M* the set of all integral linear combinations of the vectors ... a set of free Abelian generators, therefore the rank of M* is n. The dimension of M* is the dimension of the Euclidean space spanned by ...
Equivalent positions and modulation relations
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.4.2, pp. 940-941 [ doi:10.1107/97809553602060000624 ]
Equivalent positions and modulation relations 9.8.4.4.2. Equivalent positions and modulation relations A (3 + d)-dimensional space group that leaves a function invariant maps points in (3 + d)-space to points where the function has the same value. The atomic positions of a modulated crystal represent such a pattern, and the superspace ...
Symmetry elements
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.4.1, p. 940 [ doi:10.1107/97809553602060000624 ]
... International Tables for Crystallography (2006). Vol. C, ch. 9.8, p. 940 © International Union of Crystallography 2006 | home | resources | advanced search ...
Superspace groups
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.4, pp. 940-941 [ doi:10.1107/97809553602060000624 ]
... The diffraction from incommensurate crystal structures has been treated by de Wolff (1974), Yamamoto (1982a,b), Paciorek & Kucharczyk (1985), Petricek, Coppens & Becker ... crystal structure. Acta Cryst. A41, 462-466. Perez-Mato, J. M., Madariaga, G. & Tello, M. J. (1986). Diffraction symmetry ...
Bravais classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3.3, p. 940 [ doi:10.1107/97809553602060000624 ]
... International Tables for Crystallography (2006). Vol. C, ch. 9.8, p. 940 © International Union of Crystallography 2006 | home | resources | advanced search ...
Crystallographic systems
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3.2, p. 940 [ doi:10.1107/97809553602060000624 ]
... International Tables for Crystallography (2006). Vol. C, ch. 9.8, p. 940 © International Union of Crystallography 2006 | home | resources | advanced search ...
Holohedry
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3.1, pp. 939-940 [ doi:10.1107/97809553602060000624 ]
... diffraction spots as a set invariant, thus the vector module M* also. As discussed in Subsection 9.8.4.2, each of the elements ... dimensions leaves the lattice * invariant for which the vector module M* is the projection. Conversely, if one has a point group ... the case of an incommensurate crystal, the projection of * on M* is one-to-one as one can see as ...
Systems and Bravais classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3, pp. 939-940 [ doi:10.1107/97809553602060000624 ]
... diffraction spots as a set invariant, thus the vector module M* also. As discussed in Subsection 9.8.4.2, each of the elements ... dimensions leaves the lattice * invariant for which the vector module M* is the projection. Conversely, if one has a point group ... the case of an incommensurate crystal, the projection of * on M* is one-to-one as one can see as ...
Geometric and arithmetic crystal classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.2.2, p. 939 [ doi:10.1107/97809553602060000624 ]
... of modulated structures a standard basis can be chosen (for M* and correspondingly for ). According to equation (9.8.4.15), for each ... is so because in the incommensurate case the correspondence between M* and is uniquely fixed by the embedding rule (9.8.4.10) (see ... point group and a standard basis for the vector module M* because of relation (9.8.4.15). In three dimensions, there ...
Laue class
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.2.1, pp. 938-939 [ doi:10.1107/97809553602060000624 ]
Laue class 9.8.4.2.1. Laue class Definition 1.The Laue point group of the diffraction pattern is the point group in three dimensions that transforms every diffraction peak into a peak of the same intensity.2 Because all diffraction vectors are of the form (9.8.4.5), the action of an element R of the Laue ...
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