Space groups and their description
Wondratschek, H.,
International Tables for Crystallography
(2011).
Vol. A1,
Section 1.2.5.1,
p.
[ doi:10.1107/97809553602060000791 ]
for any finite integer n :
Definition
1.2.5.1.1. A group of isometries in n -dimensional space is called an n -dimensional space group if
(1) contains n linearly independent translations.
(2 ...
Classifications of space groups
Wondratschek, H.,
International Tables for Crystallography
(2011).
Vol. A1,
Section 1.2.5.2,
p.
[ doi:10.1107/97809553602060000791 ]
'. This classification is done in two ways (cf. Sections
1.2.5.4 and
1.2.5.5):
(1) first into geometric crystal classes by the point group of the space group, and then into crystal systems ;
(2) into the arithmetic ...
Point groups and crystal classes
Wondratschek, H.,
International Tables for Crystallography
(2011).
Vol. A1,
Section 1.2.5.4,
p.
[ doi:10.1107/97809553602060000791 ]
is isomorphic to the factor group, i.e. to the group of the cosets.
Definition
1.2.5.4.1. A group of linear parts, represented by a group of matrices, is called a point group . If the linear parts are those of the matrix–column ...
Crystal systems and crystal families
Wondratschek, H.,
International Tables for Crystallography
(2011).
Vol. A1,
Section 1.2.5.5,
p.
[ doi:10.1107/97809553602060000791 ]
Brown, H., Bülow, R., Neubüser, J.,
Wondratschek,
H. & Zassenhaus, H. (1978). Crystallographic Groups of Four-dimensional Space . New York: John Wiley & Sons. Google Scholar
International Tables for Crystallography (2011). Vol. A1 ...
Space groups and space-group types
Wondratschek, H.,
International Tables for Crystallography
(2011).
Vol. A1,
Section 1.2.5.3,
p.
[ doi:10.1107/97809553602060000791 ]
to that space-group type which is described in this set. From those diagrams the Hermann–Mauguin symbol, abbreviated as HM symbol, the Schoenflies symbol and the space-group number are taken.
A rigorous definition is:
Definition
1.2.5.3.1. Two ...
Space groups
Wondratschek, H.,
International Tables for Crystallography
(2011).
Vol. A1,
Section 1.2.5,
p.
[ doi:10.1107/97809553602060000791 ]
groups. Lattices, their Bravais types and lattice systems can also be classified into crystal families of lattices; cf. IT A, Chapter 8.2
.
References
Brown, H., Bülow, R., Neubüser, J.,
Wondratschek,
H. & Zassenhaus, H ...
