Twinning by reticular merohedry

A typical example is obverse/reverse twinning of a rhombohedral structure (Herbst-Irmer and Sheldrick, 2002). 

Then it estimates the fractional contributions of the second domain. 

With obverse/reverse twinning there are four types of reflections reflections with —h + k + l = 3n and h — k + I 3n are only observed for the main domain, reflections with —h + k + l 3n and h — k + l = 3n have non-zero intensity only for the second domain, reflections with —h + k + l 3n and h - k + I 3natie absent for both domains, and reflections with —h + k + l = 3n and h - k +1 = 3n have contributions from both domains. Because only one third of the reflections (those with I = 3n) are affected by the twinning, stmcture solution is normally not a severe problem, because two thirds of the reflections have contributions from only one domain and are often sufficient for stmcture solution.  

For the refinement of an obverse/reverse twin SHELXL needs a special reflection file in HKLF 5 format and the refinement is not possible with a single TWIN command (see the two examples in 7.8.3 and 7.8.4). This restriction is unnecessary and will be removed if and when there is a new release of the program. After producing the HKLF5 format file further merging of equivalent reflections is not possible. Therefore the data should be merged before producing this file. Otherwise all data would be treated as independent, which leads to mathematically incorrect standard uncertainties. 

Reflections that are absent for both domains are omitted, and in practice it may well be expedient to omit also those reflections that have only a contribution from the second domain. Reflections that have a contribution only from the main domain are unchanged and are assigned the batch number 1. Reflections with contributions from both domains are split into their two components —h — kl and hkl (if the twin axis is parallel to c) or — — ft — / and hkl (if the twin axis is perpendicular to c)  

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If only part of the reflections have a contribution from the second domain (twinning by reticular merohedry and non-merohedral twins), a special reflection file is necessary, which is read in by the command... 

In the following sections we present examples of how to refine twinned structures with SHELXL. All files you may need in order to perform the refinements yourself are given on the CD-ROM that accompanies this book. The first example is a case of merohedral twinning that will acquaint you with the basics of practical twin refinement. The second example describes a typical pseudo-merohedral twin such as every crystallographer will encounter sooner or later. Two different examples for twinning by reticular merohedry are given next and the chapter ends with two cases of non-merohedral twinning. 

The first two [Eqn. (7)] or four [Eqn. (8)] cosets give the twin laws by metric merohedry, the others give the twin laws by reticular merohedry. Twin operators in each coset are equivalent by the action of the symmetry elements of the syngony. 

By expressing the twin laws through the Shubnikov s two-color group notation (in which the twin elements are dashed Curien and Le Corre 1958), the three twin laws are 6 2 2 6 m l, 3T2//w. The complete twin [i.e. twin by merohedry or reticular... 

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