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Crystallographic symmetry
International Tables for Crystallography (2016). Vol. A, ch. 1.2, pp. 12-21 [ doi:10.1107/97809553602060000920 ]
... element are unique (Flack et al., 2000). References Flack, H. D., Wondratschek, H., Hahn, Th. & Abrahams, S. C. (2000). Symmetry elements ...
Isomorphic subgroups of space groups
International Tables for Crystallography (2016). Vol. A, Section 1.7.1.3, p. 134 [ doi:10.1107/97809553602060000925 ]
Isomorphic subgroups of space groups 1.7.1.3. Isomorphic subgroups of space groups The existence of isomorphic subgroups is of special interest. There can be no proper isomorphic subgroups of finite groups because the difference of the orders does not allow isomorphism. The point group of a space group is finite and its ...
[more results from section 1.7.1 in volume A]
Topics on space groups treated in Volumes A1 and E of International Tables for Crystallography
International Tables for Crystallography (2016). Vol. A, ch. 1.7, pp. 132-139 [ doi:10.1107/97809553602060000925 ]
... walls are discussed. 1.7.1. Subgroups and supergroups of space groups H. Wondratschek a Relations between crystal structures play an important role for ... first attempts to derive sectional layer groups were made by Wondratschek (1971) and by using software written by Guigas (1971) ...
Synoptic table of the space groups
International Tables for Crystallography (2016). Vol. A, Section 1.5.4.3, pp. 95-106 [ doi:10.1107/97809553602060000923 ]
... symbolHermann-Mauguin symbols for standard cell P or RTriple cell H ShortFullExtended 143 P3 H3 144 145 146 R3 147 148 ... space groupSchoenflies symbolHermann-Mauguin symbols for standard cell PTriple cell H ShortFullExtended 168 P6 H6 169 170 171 172 173 174 ... and trigonal space-group symbols is completed by a multiple H cell, which is three times the volume of the ...
[more results from section 1.5.4 in volume A]
Transformation between the two origin-choice settings of I41/amd
International Tables for Crystallography (2016). Vol. A, Section 1.5.3.2.2, p. 90 [ doi:10.1107/97809553602060000923 ]
Transformation between the two origin-choice settings of I41/amd 1.5.3.2.2. Transformation between the two origin-choice settings of I41/amd The zircon example of Section 1.5.1.1 illustrates how the atomic coordinates change under an origin-choice transformation. Here, the case of the two origin-choice descriptions of the same space ...
[more results from section 1.5.3 in volume A]
Example: paraelectric-to-ferroelectric phase transition of GeTe
International Tables for Crystallography (2016). Vol. A, Section 1.5.2.5, pp. 86-87 [ doi:10.1107/97809553602060000923 ]
... one. References Chattopadhyay, T. K., Boucherle, J. X. & von Schnering, H. G. (1987). Neutron diffraction study on the structural phase ... transition in GeTe. J. Phys. C, 20, 1431-1440. Wiedemeier, H. & Siemers, P. A. (1989). The thermal expansion of GeS ...
[more results from section 1.5.2 in volume A]
General change of coordinate system
International Tables for Crystallography (2016). Vol. A, Section 1.5.1.3, p. 83 [ doi:10.1107/97809553602060000923 ]
... . Vol. A1, Symmetry Relations between Space Groups. Edited by H. Wondratschek & U. Müller, 2nd ed. Chichester: John Wiley & Sons. International ...
[more results from section 1.5.1 in volume A]
Transformations of coordinate systems
International Tables for Crystallography (2016). Vol. A, ch. 1.5, pp. 75-106 [ doi:10.1107/97809553602060000923 ]
... coordinate systems. 1.5.1. Origin shift and change of the basis1 H. Wondratschek a andM. I. Aroyo b 1.5.1.1. Origin shift | | Let a ... with a, b, c and the three triple hexagonal cells H with ; ; . The origin for all cells is the ...
Selected order for non-translational generators
International Tables for Crystallography (2016). Vol. A, Section 1.4.3.1, pp. 60-61 [ doi:10.1107/97809553602060000922 ]
Selected order for non-translational generators 1.4.3.1. Selected order for non-translational generators For the non-translational generators, the following sequence has been adopted: (a) In all centrosymmetric space groups, an inversion (if possible at the origin O) has been selected as the last generator. (b) Rotations precede symmetry operations of ...
[more results from section 1.4.3 in volume A]
Sequence of space-group types
International Tables for Crystallography (2016). Vol. A, Section 1.4.1.6, pp. 49-50 [ doi:10.1107/97809553602060000922 ]
Sequence of space-group types 1.4.1.6. Sequence of space-group types The sequence of space-group entries in the space-group tables follows that introduced by Schoenflies (1891) and is thus established historically. Within each geometric crystal class, Schoenflies numbered the space-group types in an obscure way. As early as ...
[more results from section 1.4.1 in volume A]
International Tables for Crystallography (2016). Vol. A, ch. 1.2, pp. 12-21 [ doi:10.1107/97809553602060000920 ]
... element are unique (Flack et al., 2000). References Flack, H. D., Wondratschek, H., Hahn, Th. & Abrahams, S. C. (2000). Symmetry elements ...
Isomorphic subgroups of space groups
International Tables for Crystallography (2016). Vol. A, Section 1.7.1.3, p. 134 [ doi:10.1107/97809553602060000925 ]
Isomorphic subgroups of space groups 1.7.1.3. Isomorphic subgroups of space groups The existence of isomorphic subgroups is of special interest. There can be no proper isomorphic subgroups of finite groups because the difference of the orders does not allow isomorphism. The point group of a space group is finite and its ...
[more results from section 1.7.1 in volume A]
Topics on space groups treated in Volumes A1 and E of International Tables for Crystallography
International Tables for Crystallography (2016). Vol. A, ch. 1.7, pp. 132-139 [ doi:10.1107/97809553602060000925 ]
... walls are discussed. 1.7.1. Subgroups and supergroups of space groups H. Wondratschek a Relations between crystal structures play an important role for ... first attempts to derive sectional layer groups were made by Wondratschek (1971) and by using software written by Guigas (1971) ...
Synoptic table of the space groups
International Tables for Crystallography (2016). Vol. A, Section 1.5.4.3, pp. 95-106 [ doi:10.1107/97809553602060000923 ]
... symbolHermann-Mauguin symbols for standard cell P or RTriple cell H ShortFullExtended 143 P3 H3 144 145 146 R3 147 148 ... space groupSchoenflies symbolHermann-Mauguin symbols for standard cell PTriple cell H ShortFullExtended 168 P6 H6 169 170 171 172 173 174 ... and trigonal space-group symbols is completed by a multiple H cell, which is three times the volume of the ...
[more results from section 1.5.4 in volume A]
Transformation between the two origin-choice settings of I41/amd
International Tables for Crystallography (2016). Vol. A, Section 1.5.3.2.2, p. 90 [ doi:10.1107/97809553602060000923 ]
Transformation between the two origin-choice settings of I41/amd 1.5.3.2.2. Transformation between the two origin-choice settings of I41/amd The zircon example of Section 1.5.1.1 illustrates how the atomic coordinates change under an origin-choice transformation. Here, the case of the two origin-choice descriptions of the same space ...
[more results from section 1.5.3 in volume A]
Example: paraelectric-to-ferroelectric phase transition of GeTe
International Tables for Crystallography (2016). Vol. A, Section 1.5.2.5, pp. 86-87 [ doi:10.1107/97809553602060000923 ]
... one. References Chattopadhyay, T. K., Boucherle, J. X. & von Schnering, H. G. (1987). Neutron diffraction study on the structural phase ... transition in GeTe. J. Phys. C, 20, 1431-1440. Wiedemeier, H. & Siemers, P. A. (1989). The thermal expansion of GeS ...
[more results from section 1.5.2 in volume A]
General change of coordinate system
International Tables for Crystallography (2016). Vol. A, Section 1.5.1.3, p. 83 [ doi:10.1107/97809553602060000923 ]
... . Vol. A1, Symmetry Relations between Space Groups. Edited by H. Wondratschek & U. Müller, 2nd ed. Chichester: John Wiley & Sons. International ...
[more results from section 1.5.1 in volume A]
Transformations of coordinate systems
International Tables for Crystallography (2016). Vol. A, ch. 1.5, pp. 75-106 [ doi:10.1107/97809553602060000923 ]
... coordinate systems. 1.5.1. Origin shift and change of the basis1 H. Wondratschek a andM. I. Aroyo b 1.5.1.1. Origin shift | | Let a ... with a, b, c and the three triple hexagonal cells H with ; ; . The origin for all cells is the ...
Selected order for non-translational generators
International Tables for Crystallography (2016). Vol. A, Section 1.4.3.1, pp. 60-61 [ doi:10.1107/97809553602060000922 ]
Selected order for non-translational generators 1.4.3.1. Selected order for non-translational generators For the non-translational generators, the following sequence has been adopted: (a) In all centrosymmetric space groups, an inversion (if possible at the origin O) has been selected as the last generator. (b) Rotations precede symmetry operations of ...
[more results from section 1.4.3 in volume A]
Sequence of space-group types
International Tables for Crystallography (2016). Vol. A, Section 1.4.1.6, pp. 49-50 [ doi:10.1107/97809553602060000922 ]
Sequence of space-group types 1.4.1.6. Sequence of space-group types The sequence of space-group entries in the space-group tables follows that introduced by Schoenflies (1891) and is thus established historically. Within each geometric crystal class, Schoenflies numbered the space-group types in an obscure way. As early as ...
[more results from section 1.4.1 in volume A]
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