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Results for DC.creator="T." AND DC.creator="Janssen" in section 9.8.1 of volume C page 1 of 2 pages. |
Introduction
International Tables for Crystallography (2006). Vol. C, Section 9.8.1, pp. 907-913 [ doi:10.1107/97809553602060000624 ]
... as five-, eight- or twelvefold axes. For a review, see Janssen & Janner (1987). We denote a basis for the lattice ... previous section. Conceptually, it corresponds (de Wolff, 1974, 1977; Janner & Janssen, 1977) to enlarging the class of symmetry transformations admitted, from ... be obtained directly by considering as additional coordinate the phase t of the modulation. The positions in three dimensions are ...
Four-dimensional space groups
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4.5, pp. 912-913 [ doi:10.1107/97809553602060000624 ]
... were obtained in the (3 + 1)-reducible case by Fast & Janssen (1969) and in the general case by Brown, Bülow ... determined on the basis of algorithms developed by Zassenhaus (1948), Janssen, Janner & Ascher (1969a,b), Brown (1969), and Fast & Janssen (1971). In the book by Brown, Bülow, ...
Generalized nomenclature
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4.4, p. 912 [ doi:10.1107/97809553602060000624 ]
Generalized nomenclature 9.8.1.4.4. Generalized nomenclature In Section 9.8.4, the theory is extended to structures containing d modulations, with . In this case, each point-group transformation in internal space is given by and the associated internal translation by the (d-dimensional) vector . Thus, The transformations R and are represented by ...
Four-dimensional crystallography
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
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4.2, p. 911 [ doi:10.1107/97809553602060000624 ]
... having as three-dimensional intersection (say defined by the hyperplane t = 0) the modulated crystal structure (a specific example has been ...
Bravais classes of vector modules
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4.1, pp. 910-911 [ doi:10.1107/97809553602060000624 ]
Bravais classes of vector modules 9.8.1.4.1. Bravais classes of vector modules For a modulated crystal structure with a one-dimensional modulation, the positions of the diffraction spots are given by vectors This set of vectors is a vector module M*. The vectors form a basis of the reciprocal lattice [Lambda ...
Basic symmetry considerations
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4, pp. 910-913 [ doi:10.1107/97809553602060000624 ]
... having as three-dimensional intersection (say defined by the hyperplane t = 0) the modulated crystal structure (a specific example has been ... were obtained in the (3 + 1)-reducible case by Fast & Janssen (1969) and in the general case by Brown, Bülow ... determined on the basis of algorithms developed by Zassenhaus (1948), Janssen, Janner & Ascher (1969a,b), Brown (1969), and Fast & Janssen ( ...
The symmetry
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.3.2, pp. 909-910 [ doi:10.1107/97809553602060000624 ]
... previous section. Conceptually, it corresponds (de Wolff, 1974, 1977; Janner & Janssen, 1977) to enlarging the class of symmetry transformations admitted, from ... be obtained directly by considering as additional coordinate the phase t of the modulation. The positions in three dimensions are then ... intersection of the lines of the atomic positions (parametrized by t) with the hyperplane t = 0. For the modulated structure ...
The diffraction pattern
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.3.1, p. 909 [ doi:10.1107/97809553602060000624 ]
The diffraction pattern 9.8.1.3.1. The diffraction pattern To introduce what follows, the simple case of a displacively modulated crystal structure is considered. The point-atom approximation is adopted and the modulation is supposed to be a sinusoidal plane wave. This means that the structure can be described in terms of atomic ...
The simple case of a displacively modulated crystal
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.3, pp. 909-910 [ doi:10.1107/97809553602060000624 ]
... previous section. Conceptually, it corresponds (de Wolff, 1974, 1977; Janner & Janssen, 1977) to enlarging the class of symmetry transformations admitted, from ... be obtained directly by considering as additional coordinate the phase t of the modulation. The positions in three dimensions are then ... intersection of the lines of the atomic positions (parametrized by t) with the hyperplane t = 0. For the modulated structure ...
International Tables for Crystallography (2006). Vol. C, Section 9.8.1, pp. 907-913 [ doi:10.1107/97809553602060000624 ]
... as five-, eight- or twelvefold axes. For a review, see Janssen & Janner (1987). We denote a basis for the lattice ... previous section. Conceptually, it corresponds (de Wolff, 1974, 1977; Janner & Janssen, 1977) to enlarging the class of symmetry transformations admitted, from ... be obtained directly by considering as additional coordinate the phase t of the modulation. The positions in three dimensions are ...
Four-dimensional space groups
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4.5, pp. 912-913 [ doi:10.1107/97809553602060000624 ]
... were obtained in the (3 + 1)-reducible case by Fast & Janssen (1969) and in the general case by Brown, Bülow ... determined on the basis of algorithms developed by Zassenhaus (1948), Janssen, Janner & Ascher (1969a,b), Brown (1969), and Fast & Janssen (1971). In the book by Brown, Bülow, ...
Generalized nomenclature
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4.4, p. 912 [ doi:10.1107/97809553602060000624 ]
Generalized nomenclature 9.8.1.4.4. Generalized nomenclature In Section 9.8.4, the theory is extended to structures containing d modulations, with . In this case, each point-group transformation in internal space is given by and the associated internal translation by the (d-dimensional) vector . Thus, The transformations R and are represented by ...
Four-dimensional crystallography
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
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4.2, p. 911 [ doi:10.1107/97809553602060000624 ]
... having as three-dimensional intersection (say defined by the hyperplane t = 0) the modulated crystal structure (a specific example has been ...
Bravais classes of vector modules
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4.1, pp. 910-911 [ doi:10.1107/97809553602060000624 ]
Bravais classes of vector modules 9.8.1.4.1. Bravais classes of vector modules For a modulated crystal structure with a one-dimensional modulation, the positions of the diffraction spots are given by vectors This set of vectors is a vector module M*. The vectors form a basis of the reciprocal lattice [Lambda ...
Basic symmetry considerations
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.4, pp. 910-913 [ doi:10.1107/97809553602060000624 ]
... having as three-dimensional intersection (say defined by the hyperplane t = 0) the modulated crystal structure (a specific example has been ... were obtained in the (3 + 1)-reducible case by Fast & Janssen (1969) and in the general case by Brown, Bülow ... determined on the basis of algorithms developed by Zassenhaus (1948), Janssen, Janner & Ascher (1969a,b), Brown (1969), and Fast & Janssen ( ...
The symmetry
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.3.2, pp. 909-910 [ doi:10.1107/97809553602060000624 ]
... previous section. Conceptually, it corresponds (de Wolff, 1974, 1977; Janner & Janssen, 1977) to enlarging the class of symmetry transformations admitted, from ... be obtained directly by considering as additional coordinate the phase t of the modulation. The positions in three dimensions are then ... intersection of the lines of the atomic positions (parametrized by t) with the hyperplane t = 0. For the modulated structure ...
The diffraction pattern
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.3.1, p. 909 [ doi:10.1107/97809553602060000624 ]
The diffraction pattern 9.8.1.3.1. The diffraction pattern To introduce what follows, the simple case of a displacively modulated crystal structure is considered. The point-atom approximation is adopted and the modulation is supposed to be a sinusoidal plane wave. This means that the structure can be described in terms of atomic ...
The simple case of a displacively modulated crystal
International Tables for Crystallography (2006). Vol. C, Section 9.8.1.3, pp. 909-910 [ doi:10.1107/97809553602060000624 ]
... previous section. Conceptually, it corresponds (de Wolff, 1974, 1977; Janner & Janssen, 1977) to enlarging the class of symmetry transformations admitted, from ... be obtained directly by considering as additional coordinate the phase t of the modulation. The positions in three dimensions are then ... intersection of the lines of the atomic positions (parametrized by t) with the hyperplane t = 0. For the modulated structure ...
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