Twin refinement

In SHELXL the twin refinement method of Pratt et al. (1971) and Jameson (1982) has been implemented. values are calculated by  

For completely overlapping lattices, a normal intensity data file (standard HKLF4 format) can be used together with the following two instruction lines  

The matrix rij is the twin law and n the number of twin domains. The batch scale factor BAS F is followed by n — 1 starting values for the fractional contributions. The default value for n is 2, which corresponds to a twin with two domains. 

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 

The HKLF 5 is given at the end of the. ins file, replacing the line that reads HKLF 4. BASF is used as in the case before. As merging is no longer allowed the default value for MERG assumed by SHELXL is now 0. 

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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 twin refinement clearly resulted in an improvement. Table 7.3 compares the two refinements with and without the TWIN command. 

Refinement as an obverse/reverse twin leads to a significant improvement (see Table 7.4 and the files retl-03.res andretl-03.1st) Figure 7.11 shows the final model. The structure was previously determined from an untwinned crystal (Clegg, 1982) and the quality of the twin refinement is comparable to that of the original untwiimed refinement. 

The hexagonal structure which has been recently refined more accurately [67] is built of two distinct parts a ZnGe hexagonal flat layer in which the Zn-Ge bond length is 2.470 A and a Zn2Ge2 corrugated twinned layer (Zn-Ge =... 

Checking the data quality is strongly recommended inspection of the Wilson plot and data reduction statistics is very useful in judging the extent of the resolution to which the data can realistically be used. Pathologically bad data, for example those from a split crystal, twinned data, systematically incomplete data, low resolution overloads will always make model building and refinement hard if not impossible. 

Zeolite structures pose unconventional problems for crystal structure refinement. These problems arise from positional disorder pseudo-symmetry, twinning, high mobility of some atoms, and (sometimes) the inaccessibility of single-crystal data. Methods are discussed for investigating split atoms, Si-Al distribution, pseudo-symmetry, and for dealing with parameter correlation and limited data sets. Some additional techniques which have not been applied to zeolite structures are mentioned. 

Canepa [9] suggested that one of the two molecular forms of acetylcholine bromide reported by Sorum [6, 7] was incorrect. Dunitz [10], on the other hand, observed some unusual systematic absences and suggested that the crystal used was a twinned P2i/c rather than a single P2i specimen. In response to these observations, Svinning and Sorum [11] refined the structure of acetylcholine bromide based on previous photographic intensities corrected for twinning by Canepa, Pauling and... 

AP9 Further refinement of 1AP9,C taking twinning into account 2.35 X-ray, CLP... 

ADP are non-positive definite , that is, they do not define an ellipsoid at all but an open surface, this usually indicates grossly erroneous data (e.g. due to twinning) or a wrong space group (e g. a cenfrosymmetric structure is refined as noncentrosymmetric). 

Penn RL, Banfield JF (1998b) Oriented attachment and growth, twinning, polytypism, and formation of metastable phases Insights from nanociystalline Ti02. Am Mineral 83 1077-1082 Post JE, Bish DL (1989) Rietveld refinement of crystal stmctnres nsing powder X-ray diffraction data. Rev Mineral 20 277-308... 

Herbst-lrmer R, Sheldrick GM (1998) Refinement of twinned structures with SHELXL97. Acta Crystallogr Sect B-Struct Sci 54 443-449... 

All in all, the WPPM approach can provide a simultaneous structure and microstructure refinement, based on physical models of the phases under study, without using any arbitrary profile function. Considering the terms of Equation (26), refinement parameters to be optimized in a least-squares analysis are relatively few, namely, mean (p) and variance (cr) of a suitable distribution of coherent domain sizes, dislocation density (p), effective outer cut-off radius (R ) and character (/e, effective fraction of edge dislocations), twin fault (P), deformation fault (a) and APB (y) probabilities. 

Resolution of the Difficulty Data were recollected and refinement was effected through the use of all of the data. For those reflections to which both individuals of the twin contribute, the composite reflection hkl was taken to be... 

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