International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2010). Vol. B, ch. 1.4, p. 119   | 1 | 2 |

Section 1.4.4.1. Introduction

U. Shmuelia

1.4.4.1. Introduction

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The purpose of this section, and the accompanying table, is to provide a representation of the 230 three-dimensional crystallographic space groups in terms of two fundamental quantities that characterize a weighted reciprocal lattice: (i) coordinates of point-symmetry-related points in the reciprocal lattice, and (ii) phase shifts of the weight functions that are associated with the translation parts of the various space-group operations. Table A1.4.4.1[link] in Appendix A1.4.4[link] collects the above information for all the space-group settings which are listed in IT A (1983)[link] for the same choice of the space-group origins and following the same numbering scheme used in that volume. Table A1.4.4.1[link] was generated by computer using the space-group algorithm described by Shmueli (1984)[link] and the space-group symbols given in Table A1.4.2.1[link] in Appendix A1.4.2[link]. It is shown in a later part of this section that Table A1.4.4.1[link] can also be regarded as a table of symmetry groups in Fourier space, in the Bienenstock–Ewald (1962) sense which was mentioned in Section 1.4.1[link]. The section is concluded with a brief description of the correspondence between Bravais-lattice types in direct and reciprocal spaces.

References

International Tables for Crystallography (1983). Vol. A, Space-Group Symmetry, edited by Th. Hahn. Dordrecht: Reidel.
Shmueli, U. (1984). Space-group algorithms. I. The space group and its symmetry elements. Acta Cryst. A40, 559–567.








































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