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

International Tables for Crystallography (2010). Vol. B, ch. 4.6, p. 603   | 1 | 2 |

Section 4.6.3.2.1. Indexing

W. Steurera* and T. Haibacha

aLaboratory of Crystallography, Department of Materials, ETH Hönggerberg, HCI G 511, Wolfgang-Pauli-Strasse 10, CH-8093 Zurich, Switzerland
Correspondence e-mail:  walter.steurer@mat.ethz.ch

4.6.3.2.1. Indexing

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The indexing of diffraction patterns of composite structures can be performed in the following way:

  • (1) find the minimum number of reciprocal lattices [\Lambda_{\nu}^{*}] necessary to index the diffraction pattern;

  • (2) find a basis for [M^{*}], the union of sublattices [\Lambda_{\nu}^{*}];

  • (3) find the appropriate superspace embedding.

The [(3 + d)] vectors [{\bf a}_{i}^{*}] forming a basis for the 3D Fourier module [M^{*} = \{{\textstyle\sum_{i = 1}^{3 + d}} h_{i}{\bf a}_{i}^{*}\}] can be chosen such that [{\bf a}_{1}^{*}], [{\bf a}_{2}^{*}] and [{\bf a}_{3}^{*}] are linearly independent. Then the remaining d vectors can be described as a linear combination of the first three, defining the [d \times 3] matrix σ: [{\bf a}_{3 + j}^{*} = {\textstyle\sum_{i = 1}^{3 + d}} \sigma_{ji}{\bf a}_{i}^{*},\; j = 1, \ldots, d]. This is formally equivalent to the reciprocal basis obtained for an IMS (see Section 4.6.3.1[link]) and one can proceed in an analogous way to that for IMSs.








































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