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Results for DC.creator="A." AND DC.creator="Janner" in section 9.8.3 of volume C |
Introduction to the tables
International Tables for Crystallography (2006). Vol. C, Section 9.8.3, pp. 915-937 [ doi:10.1107/97809553602060000624 ]
... 1)-dimensional lattice is determined by the three-dimensional vectors a*, b*, c* and the modulation vector q. The former three vectors give by duality a, b, and c, the external components of lattice basis vectors ... 3 = [gamma]) of the modulation vector q with respect to a conventional basis a*, b*, c*. The arithmetic crystal ...
Examples
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.5, p. 936 [ doi:10.1107/97809553602060000624 ]
Examples 9.8.3.5. Examples (A) Na2CO3 Na2CO3 has a phase transition at about 753K from the hexagonal to the ... unstable and below the transition temperature Ti = 633K there is a modulated [gamma]-phase (de Wolff & Tuinstra, 1986). At ...
Guide to the use of the tables
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.4, pp. 935-936 [ doi:10.1107/97809553602060000624 ]
... groups are given for three-dimensional incommensurate modulated crystals with a modulation of dimension one and for two-dimensional crystals (e.g. surfaces) with one- and two-dimensional modulation (Janssen, Janner & de Wolff, 1980). In the following, we discuss briefly ... lower than that implied by the main reflections. One chooses a conventional basis (qr = 0) for the vector module, and ...
Reflection conditions
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.3.2, pp. 921-935 [ doi:10.1107/97809553602060000624 ]
... conditions 9.8.3.3.2. Reflection conditions The indexing of diffraction vectors is a matter of choice of basis. When the basis chosen is not a primitive one, the indices have to satisfy certain conditions known ... factor vanishes unless is an integer. The form of such a reflection condition in terms of allowed or forbidden sets ...
Symmetry elements
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.3.1, pp. 916-921 [ doi:10.1107/97809553602060000624 ]
Symmetry elements 9.8.3.3.1. Symmetry elements The transformations belonging to a (3 + 1)-dimensional superspace group consist of a point-group transformation given by the integral matrix [Gamma](R ... arithmetic crystal class has been discussed in Subsection 9.8.3.2. Given a point-group transformation , the associated translation is determined up ...
Tables of superspace groups
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.3, pp. 916-935 [ doi:10.1107/97809553602060000624 ]
... of superspace groups 9.8.3.3.1. Symmetry elements | | The transformations belonging to a (3 + 1)-dimensional superspace group consist of a point-group transformation given by the integral matrix [Gamma](R ... arithmetic crystal class has been discussed in Subsection 9.8.3.2. Given a point-group transformation , the associated translation is determined up ...
Table for geometric and arithmetic crystal classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.2, p. 916 [ doi:10.1107/97809553602060000624 ]
... point group Ks has external part KE, which belongs to a three-dimensional system. Depending on the Bravais class of the ... of the modulation wavevector. The three arithmetic crystal classes implying a lattice belonging to the Bravais class are , , and . The ...
Tables of Bravais lattices
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.1, pp. 915-916 [ doi:10.1107/97809553602060000624 ]
... 1)-dimensional lattice is determined by the three-dimensional vectors a*, b*, c* and the modulation vector q. The former three vectors give by duality a, b, and c, the external components of lattice basis vectors ... 3 = [gamma]) of the modulation vector q with respect to a conventional basis a*, b*, c*. The arithmetic crystal ...
Ambiguities in the notation
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.6, pp. 936-937 [ doi:10.1107/97809553602060000624 ]
... the notation The invariant part of the translation part of a (3 + 1)-dimensional superspace-group element is uniquely determined by ... that for each element of the point group there is a translation for which the invariant part is unique up to lattice vectors. The reason is that, for a given element R of the point group and given ...
International Tables for Crystallography (2006). Vol. C, Section 9.8.3, pp. 915-937 [ doi:10.1107/97809553602060000624 ]
... 1)-dimensional lattice is determined by the three-dimensional vectors a*, b*, c* and the modulation vector q. The former three vectors give by duality a, b, and c, the external components of lattice basis vectors ... 3 = [gamma]) of the modulation vector q with respect to a conventional basis a*, b*, c*. The arithmetic crystal ...
Examples
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.5, p. 936 [ doi:10.1107/97809553602060000624 ]
Examples 9.8.3.5. Examples (A) Na2CO3 Na2CO3 has a phase transition at about 753K from the hexagonal to the ... unstable and below the transition temperature Ti = 633K there is a modulated [gamma]-phase (de Wolff & Tuinstra, 1986). At ...
Guide to the use of the tables
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.4, pp. 935-936 [ doi:10.1107/97809553602060000624 ]
... groups are given for three-dimensional incommensurate modulated crystals with a modulation of dimension one and for two-dimensional crystals (e.g. surfaces) with one- and two-dimensional modulation (Janssen, Janner & de Wolff, 1980). In the following, we discuss briefly ... lower than that implied by the main reflections. One chooses a conventional basis (qr = 0) for the vector module, and ...
Reflection conditions
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.3.2, pp. 921-935 [ doi:10.1107/97809553602060000624 ]
... conditions 9.8.3.3.2. Reflection conditions The indexing of diffraction vectors is a matter of choice of basis. When the basis chosen is not a primitive one, the indices have to satisfy certain conditions known ... factor vanishes unless is an integer. The form of such a reflection condition in terms of allowed or forbidden sets ...
Symmetry elements
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.3.1, pp. 916-921 [ doi:10.1107/97809553602060000624 ]
Symmetry elements 9.8.3.3.1. Symmetry elements The transformations belonging to a (3 + 1)-dimensional superspace group consist of a point-group transformation given by the integral matrix [Gamma](R ... arithmetic crystal class has been discussed in Subsection 9.8.3.2. Given a point-group transformation , the associated translation is determined up ...
Tables of superspace groups
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.3, pp. 916-935 [ doi:10.1107/97809553602060000624 ]
... of superspace groups 9.8.3.3.1. Symmetry elements | | The transformations belonging to a (3 + 1)-dimensional superspace group consist of a point-group transformation given by the integral matrix [Gamma](R ... arithmetic crystal class has been discussed in Subsection 9.8.3.2. Given a point-group transformation , the associated translation is determined up ...
Table for geometric and arithmetic crystal classes
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.2, p. 916 [ doi:10.1107/97809553602060000624 ]
... point group Ks has external part KE, which belongs to a three-dimensional system. Depending on the Bravais class of the ... of the modulation wavevector. The three arithmetic crystal classes implying a lattice belonging to the Bravais class are , , and . The ...
Tables of Bravais lattices
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.1, pp. 915-916 [ doi:10.1107/97809553602060000624 ]
... 1)-dimensional lattice is determined by the three-dimensional vectors a*, b*, c* and the modulation vector q. The former three vectors give by duality a, b, and c, the external components of lattice basis vectors ... 3 = [gamma]) of the modulation vector q with respect to a conventional basis a*, b*, c*. The arithmetic crystal ...
Ambiguities in the notation
International Tables for Crystallography (2006). Vol. C, Section 9.8.3.6, pp. 936-937 [ doi:10.1107/97809553602060000624 ]
... the notation The invariant part of the translation part of a (3 + 1)-dimensional superspace-group element is uniquely determined by ... that for each element of the point group there is a translation for which the invariant part is unique up to lattice vectors. The reason is that, for a given element R of the point group and given ...
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