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Nonconventional settings of orthorhombic space groups
Müller, U.  International Tables for Crystallography (2011). Vol. A1, Section 3.1.4, pp. 469-470 [ doi:10.1107/97809553602060000802 ]
Nonconventional settings of orthorhombic space groups 3.1.4. Nonconventional settings of orthorhombic space groups Orthorhombic space groups can have as many as six different settings, as listed in Chapter 4.3 of Volume A. They result from the interchange of the axes in the following ways: Cyclic exchange: or . Exchange of two ...

Origin shifts
Müller, U.  International Tables for Crystallography (2011). Vol. A1, Section 3.1.3, pp. 468-469 [ doi:10.1107/97809553602060000802 ]
Origin shifts 3.1.3. Origin shifts In a group-subgroup relation, an origin shift may be necessary to conform to the conventional origin setting of the subgroup. This causes coordinate changes for corresponding atomic positions and is therefore undesirable for the purpose of comparing related crystal structures. However, in some cases an ...

Cell transformations
Müller, U.  International Tables for Crystallography (2011). Vol. A1, Section 3.1.2, p. 468 [ doi:10.1107/97809553602060000802 ]
Cell transformations 3.1.2. Cell transformations When comparing related crystal structures, unit-cell transformations are troublesome. They result in differing sets of atomic coordinates for corresponding atoms; this can make comparisons more complicated and structural relations may be obscured. Frequently, it is more convenient not to interchange axes and to avoid transformations ...

Wyckoff positions
Müller, U.  International Tables for Crystallography (2011). Vol. A1, Section 3.1.1.6.5, p. 468 [ doi:10.1107/97809553602060000802 ]
Wyckoff positions 3.1.1.6.5. Wyckoff positions The columns under the heading `Wyckoff positions' contain the Wyckoff symbols of all sites of the subgroups that result therefrom. They are given in the same sequence as in the top line(s). If the symbols at the top run over more than one line ...
     [more results from section 3.1.1 in volume A1]

Guide to the tables
Müller, U.  International Tables for Crystallography (2011). Vol. A1, ch. 3.1, pp. 466-472 [ doi:10.1107/97809553602060000802 ]
... between space groups. Acta Cryst. A40, 593-600. Müller, U. (1992). Berechnung der Anzahl möglicher Strukturtypen für ... I. Das Rechenverfahren. Acta Cryst. B48, 172-178. Müller, U. & Brelle, A. (1995). Über isomorphe Untergruppen von Raumgruppen der ...

Exercising care in the use of group-subgroup relations
Müller, U.  International Tables for Crystallography (2011). Vol. A1, Section 1.6.7, pp. 54-55 [ doi:10.1107/97809553602060000795 ]
... carbonate. Acta Cryst. B32, 3344-3346. Bock, O. & Müller, U. (2002b). Symmetrieverwandtschaften bei Varianten des ReO-Typs. Z. Anorg. ...

Comments concerning phase transitions and twin domains
Müller, U.  International Tables for Crystallography (2011). Vol. A1, Section 1.6.6, p. 54 [ doi:10.1107/97809553602060000795 ]
Comments concerning phase transitions and twin domains 1.6.6. Comments concerning phase transitions and twin domains When a compound forms several polymorphic forms, a Bärnighausen tree can serve to show whether second-order phase transitions are feasible between them and what kinds of twin domains may be formed during such a ...

Handling cell transformations
Müller, U.  International Tables for Crystallography (2011). Vol. A1, Section 1.6.5, pp. 52-54 [ doi:10.1107/97809553602060000795 ]
Handling cell transformations 1.6.5. Handling cell transformations It is important to keep track of the coordinate transformations in a sequence of group-subgroup relations. A Bärnighausen tree can only be correct if every atomic position of every hettotype can be derived from the corresponding positions of the aristotype. The mathematical ...

Large families of structures. Prediction of crystal-structure types
Müller, U.  International Tables for Crystallography (2011). Vol. A1, Section 1.6.4.7, pp. 51-52 [ doi:10.1107/97809553602060000795 ]
... Solid State Chem. 42, 300-321. Bock, O. & Müller, U. (2002a). Symmetrieverwandtschaften bei Varianten des Perowskit-Typs. Acta Cryst. B58, 594-606. Bock, O. & Müller, U. (2002b). Symmetrieverwandtschaften bei Varianten des ReO-Typs. Z. Anorg. ... deren Ordnungs- und Leerstellenvarianten. Dissertation, Universität Karlsruhe. Müller, U. (1978). Strukturmöglichkeiten für Pentahalogenide mit Doppeloktaeder- ...
     [more results from section 1.6.4 in volume A1]

Bärnighausen trees
Müller, U.  International Tables for Crystallography (2011). Vol. A1, Section 1.6.3, pp. 44-46 [ doi:10.1107/97809553602060000795 ]
Bärnighausen trees 1.6.3. Bärnighausen trees To represent symmetry relations between different crystal structures in a concise manner, we construct a tree of group-subgroup relations in a modular design, beginning with the space group of the aristotype at its top. Each module represents one step of symmetry reduction to ...

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