Diagonalization of the action matrix and determination of the invariant tensor
Ephra[iuml ]m, M.,
Janssen, T.,
Janner, A. and
Thiers, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.2.7.4.3,
p.
[ doi:10.1107/97809553602060000901 ]
...
Overview
Ephra[iuml ]m, M.,
Janssen, T.,
Janner, A. and
Thiers, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.2.7.1,
p.
[ doi:10.1107/97809553602060000901 ]
...
Tensors
Ephra[iuml ]m, M.,
Janssen, T.,
Janner, A. and
Thiers, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.2.7.2,
p.
[ doi:10.1107/97809553602060000901 ]
...
Invariant tensors
Ephra[iuml ]m, M.,
Janssen, T.,
Janner, A. and
Thiers, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.2.7.4.6,
p.
[ doi:10.1107/97809553602060000901 ]
indices are equal (permutation tensor, see Section 1.1.3.7.2).
Example (8). Calculation with characters. See Table
1.2.7.2 .
Table
1.2.7.2 | top | pdf |
Calculation with characters ...
Construction of a basis
Ephra[iuml ]m, M.,
Janssen, T.,
Janner, A. and
Thiers, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.2.7.4.1,
p.
[ doi:10.1107/97809553602060000901 ]
...
Characters
Ephra[iuml ]m, M.,
Janssen, T.,
Janner, A. and
Thiers, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.2.7.3,
p.
[ doi:10.1107/97809553602060000901 ]
As an example, the generalized character table for the three-dimensional point group is given in Table
1.2.7.1 .
Table
1.2.7.1 | top | pdf |
Data connected with the character table for point group ...
Action of the generators of the point group G on the basis
Ephra[iuml ]m, M.,
Janssen, T.,
Janner, A. and
Thiers, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.2.7.4.2,
p.
[ doi:10.1107/97809553602060000901 ]
...
Determination of tensor products and their decomposition
Ephra[iuml ]m, M.,
Janssen, T.,
Janner, A. and
Thiers, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.2.7.4.5,
p.
[ doi:10.1107/97809553602060000901 ]
...
Determination of the vector representation
Ephra[iuml ]m, M.,
Janssen, T.,
Janner, A. and
Thiers, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.2.7.4.4,
p.
[ doi:10.1107/97809553602060000901 ]
...
Introduction to the accompanying software TenĪar
Ephra[iuml ]m, M.,
Janssen, T.,
Janner, A. and
Thiers, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.2.7,
p.
[ doi:10.1107/97809553602060000901 ]
Representations of crystallographic groups
1.2.7.1. Overview
| top | pdf |
The determination of tensors with specified properties often requires long calculations. In principle the algorithms are simple, but in complicated ...