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International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. B. ch. 1.5, pp. 162-188
https://doi.org/10.1107/97809553602060000553 Chapter 1.5. Crystallographic viewpoints in the classification of space-group representations
a
Faculty of Physics, University of Sofia, bulv. J. Boucher 5, 1164 Sofia, Bulgaria , and bInstitut für Kristallographie, Universität, D-76128 Karlsruhe, Germany |
Footnotes
1
In physics often written as the Seitz symbol ![[({\bi W}|{\bi w})]](/teximages/bach1o5/bach1o5fi86.svg)
.
2 In crystallography vectors are designated by small bold-faced letters. With K we make an exception in order to follow the tradition of physics. A crystallographic alternative would be![[{\bf t}^{*}]](/teximages/bach1o3/bach1o3fi3170.svg)
.
3 The lattice L is often called the direct lattice. These names are historically introduced and cannot be changed, although equations (1.5.3.5)![[link]](/graphics/greenarr.gif)
and (1.5.3.6) show that essentially neither of the lattices is preferred: they form a pair of mutually reciprocal lattices.
4 From definition 3.7.1 on p. 147 of BC, it does not follow that a representation domain contains exactly one k vector from each star. The condition `The intersection of the representation domain with its symmetrically equivalent domains is empty' is missing. Lines 14 to 11 from the bottom of p. 149, however, state that such a property of the representation domain is intended. The representation domains of CDML, Figs. 3.15–3.29 contain at least one k vector of each star (Vol. 1, pp. 31, 57 and 65). On pp. 66, 67 a procedure is described for eliminating those k vectors from the representation domain which occur more than once. In the definition of Altmann (1977), p. 204, the representation domain contains exactly one arm (prong) per star.
5 Corresponding tables and figures for all space groups are available at http://www.cryst.ehu.es/cryst/get_kvec.html .
6 Boyle & Kennedy (1988) propose general rules for the parameter ranges of k-vector coefficients referred to a primitive basis. The ranges listed in Tables 1.5.5.1 to 1.5.5.4 possibly do not follow these rules.
.2 In crystallography vectors are designated by small bold-faced letters. With K we make an exception in order to follow the tradition of physics. A crystallographic alternative would be
.3 The lattice L is often called the direct lattice. These names are historically introduced and cannot be changed, although equations (1.5.3.5)
and (1.5.3.6) show that essentially neither of the lattices is preferred: they form a pair of mutually reciprocal lattices.4 From definition 3.7.1 on p. 147 of BC, it does not follow that a representation domain contains exactly one k vector from each star. The condition `The intersection of the representation domain with its symmetrically equivalent domains is empty' is missing. Lines 14 to 11 from the bottom of p. 149, however, state that such a property of the representation domain is intended. The representation domains of CDML, Figs. 3.15–3.29 contain at least one k vector of each star (Vol. 1, pp. 31, 57 and 65). On pp. 66, 67 a procedure is described for eliminating those k vectors from the representation domain which occur more than once. In the definition of Altmann (1977)
, p. 204, the representation domain contains exactly one arm (prong) per star.5 Corresponding tables and figures for all space groups are available at http://www.cryst.ehu.es/cryst/get_kvec.html .
6 Boyle & Kennedy (1988)
propose general rules for the parameter ranges of k-vector coefficients referred to a primitive basis. The ranges listed in Tables 1.5.5.1 to 1.5.5.4 possibly do not follow these rules.