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Results for DC.creator="T." AND DC.creator="Janssen" 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 ]
... j being of species A when the internal position is t. In particular, for a given atomic species, without occupational modulation ...
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 ]
Symmetry elements 9.8.4.4.1. Symmetry elements The elements of a (3 + d)-dimensional superspace group are pairs of Euclidean transformations in 3 and d dimensions, respectively: i.e. are elements of the direct product of the corresponding Euclidean groups. The elements form a three-dimensional space group, but the same does not hold ...
Superspace groups
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.4, pp. 940-941 [ doi:10.1107/97809553602060000624 ]
... j being of species A when the internal position is t. In particular, for a given atomic species, without occupational modulation ...
Bravais classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3.3, p. 940 [ doi:10.1107/97809553602060000624 ]
Bravais classes 9.8.4.3.3. Bravais classes Definition 6.Two lattices belong to the same Bravais class if their holohedral point groups are arithmetically equivalent. This means that each of them admits a lattice basis of standard form such that their holohedral point group is represented by the same set of integral matrices. References ...
Crystallographic systems
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3.2, p. 940 [ doi:10.1107/97809553602060000624 ]
Crystallographic systems 9.8.4.3.2. Crystallographic systems Definition 5.A crystallographic system is a set of lattices having geometrically equivalent holohedral point groups. In this way, a given holohedral point group (and even each crystallographic point group) belongs to exactly one system. Two lattices belong to the same system if there are orthonormal bases ...
Holohedry
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3.1, pp. 939-940 [ doi:10.1107/97809553602060000624 ]
Holohedry 9.8.4.3.1. Holohedry The Laue group of the diffraction pattern is a three-dimensional point group that leaves the positions (and the intensities)3 of the diffraction spots as a set invariant, thus the vector module M* also. As discussed in Subsection 9.8.4.2, each of the elements of the Laue group ...
Systems and Bravais classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3, pp. 939-940 [ doi:10.1107/97809553602060000624 ]
Systems and Bravais classes 9.8.4.3. Systems and Bravais classes 9.8.4.3.1. Holohedry | | The Laue group of the diffraction pattern is a three-dimensional point group that leaves the positions (and the intensities)3 of the diffraction spots as a set invariant, thus the vector module M* also. As discussed in Subsection 9.8.4.2 ...
Geometric and arithmetic crystal classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.2.2, p. 939 [ doi:10.1107/97809553602060000624 ]
Geometric and arithmetic crystal classes 9.8.4.2.2. Geometric and arithmetic crystal classes According to the previous section, in the case of modulated structures a standard basis can be chosen (for M* and correspondingly for ). According to equation (9.8.4.15), for each three-dimensional point-group operation R that leaves the diffraction pattern ...
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 ]
... j being of species A when the internal position is t. In particular, for a given atomic species, without occupational modulation ...
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 ]
Symmetry elements 9.8.4.4.1. Symmetry elements The elements of a (3 + d)-dimensional superspace group are pairs of Euclidean transformations in 3 and d dimensions, respectively: i.e. are elements of the direct product of the corresponding Euclidean groups. The elements form a three-dimensional space group, but the same does not hold ...
Superspace groups
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.4, pp. 940-941 [ doi:10.1107/97809553602060000624 ]
... j being of species A when the internal position is t. In particular, for a given atomic species, without occupational modulation ...
Bravais classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3.3, p. 940 [ doi:10.1107/97809553602060000624 ]
Bravais classes 9.8.4.3.3. Bravais classes Definition 6.Two lattices belong to the same Bravais class if their holohedral point groups are arithmetically equivalent. This means that each of them admits a lattice basis of standard form such that their holohedral point group is represented by the same set of integral matrices. References ...
Crystallographic systems
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3.2, p. 940 [ doi:10.1107/97809553602060000624 ]
Crystallographic systems 9.8.4.3.2. Crystallographic systems Definition 5.A crystallographic system is a set of lattices having geometrically equivalent holohedral point groups. In this way, a given holohedral point group (and even each crystallographic point group) belongs to exactly one system. Two lattices belong to the same system if there are orthonormal bases ...
Holohedry
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3.1, pp. 939-940 [ doi:10.1107/97809553602060000624 ]
Holohedry 9.8.4.3.1. Holohedry The Laue group of the diffraction pattern is a three-dimensional point group that leaves the positions (and the intensities)3 of the diffraction spots as a set invariant, thus the vector module M* also. As discussed in Subsection 9.8.4.2, each of the elements of the Laue group ...
Systems and Bravais classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.3, pp. 939-940 [ doi:10.1107/97809553602060000624 ]
Systems and Bravais classes 9.8.4.3. Systems and Bravais classes 9.8.4.3.1. Holohedry | | The Laue group of the diffraction pattern is a three-dimensional point group that leaves the positions (and the intensities)3 of the diffraction spots as a set invariant, thus the vector module M* also. As discussed in Subsection 9.8.4.2 ...
Geometric and arithmetic crystal classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.4.2.2, p. 939 [ doi:10.1107/97809553602060000624 ]
Geometric and arithmetic crystal classes 9.8.4.2.2. Geometric and arithmetic crystal classes According to the previous section, in the case of modulated structures a standard basis can be chosen (for M* and correspondingly for ). According to equation (9.8.4.15), for each three-dimensional point-group operation R that leaves the diffraction pattern ...
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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