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Hot Topics in Contemporary Crystallography
by Croatian Association of Crystallographers
****** Šibenik, Croatia, May, 10th to 15th, 2014 |
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Croatian Association of Crystallographers ***** Bijenièka c. 54 HR-10000 Zagreb Croatia
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Introduction to Twinning and Examples of (Pseudo-)Merohedral Twins (Lecture) Nowadays most of the crystal structures of small molecules are solved and refined by powerful programs with only little human intervention. But there are still some problems that need the knowledge of the crystallographer. One of these problems is twinned crystals. General aspects of twinning like definition, different types of twinning, detecting twinning and some typical warning signs will be discussed. Some examples of twinned structures will be presented. It will be shown how we detect the twinning and how the structures were solved and refined. Twinning
Regine
Herbst-Irmer,
Institute of Inorganic Chemistry, University of Göttingen, Germany, "Twins are regular aggregates consisting of individual crystals of the same species joined together in some definite mutual orientation".1 Two features are necessary for the description of a twin: the twin law describing the symmetry operator that transforms one orientation into the other and the fractional contribution of each twin component. Depending on the twin law four kinds of twins may be distinguished2: Twinning by merohedry, by pseudo-merohedry, by reticular merohedry and non-merohedral twins. For merohedral twins the different twin domains superimpose exactly and the twinning is not directly detectable from the reflection pattern. This can be similar for twinning by pseudo-merohedry, where the twinning mimics a higher symmetry crystal class or reticular merohedry, where there is an exact overlap of part of the reflections while all others are unaffected by the twinning. For non-merohedral twins the different reciprocal lattices do not overlap exactly leading to exactly, partially and non-overlapped reflections. The diffraction pattern should normally reveal this type of twinning. Therefore the main problems for the first three types are detection of the twinning, determination of the space group and solving the structure, while for non-merohedral twins the main problem is the data processing including the cell determination. (Pseudo-)merohedral twinning is not detectable from the reflection pattern, but the intensity distribution of twins is different from that of untwinned crystals. So the mean value of |E2-1| is often lower for twins than normal. If the space group is correct, twins can be solved using the same programs as usual. But the solution is sometimes not as straight forward. The program SHELXD3 is even able to utilise the twin law and the fractional contribution. In SHELXL3 the twin fraction will be refined.4,5 This is much more precise than refining against untwinned data. There are a number of characteristic warning signs of twinning, as given in the following list.6 Of course not all of them can be present in any particular example and for all of them other causes are possible: a) The metric symmetry is higher than the Laue symmetry. b) The Rint-value for the higher symmetry Laue group is only slightly higher than for the lower symmetry Laue group. c) If different crystals of the same compound show significantly different Rint values for the higher symmetry Laue group, this clearly shows that the lower symmetry Laue group is correct and indicates different extents of twinning. d) The mean value for |E2-1| is much lower than the expected values e) The space group appears to be trigonal or hexagonal. f) The apparent systematic absences are not consistent with any known space group. g) Although the data appear to be in order, the structure cannot be solved. h) The Patterson function is physically impossible. i) There appear to be one or more unusually long axes. j) There are problems with the unit cell refinement. k) Some reflections are sharp, others split. l) K = mean(Fo2) / mean(Fc2) is systematically high for reflections with low intensity. m) For all of the “most disagreeable reflections” in the .lst file, Fo is much greater than Fc. n) Strange residual electron density, which cannot be resolved as solvent or disorder. o) High R-values although the data seem to be of good quality. 1. Giacovazzo, C. ed. (2002). Fundamentals in Crystallography, I.U.Cr. & O.U.P.: Oxford, UK. 2. Friedel, G. (1928). Leçons de Cristallographie. Paris: Berger-Levrault. 3. Sheldrick, G. M. (2008) Acta Cryst., A64, 112-122. 4. Pratt, C. S., Coyle, B. A. & Ibers J. A. (1971). J. Chem. Soc. 2146 - 2151. 5. Jameson, G. B. (1982). Acta Cryst. A38, 817 - 820. 6. Herbst-Irmer, R. & Sheldrick, G. M. (1998). Acta Cryst. B54, 443 - 449. 7. Müller, P., Herbst-Irmer, R., Spek, A. L.,Schneider, T. R., Sawaya, M. R. (2006) Crystal Structure Refinement – A Crystallographer‘s Guide to SHELXL, Oxford University Press.
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The workshop is generously supported by:
Ministry of Science, Education and Sports of the Republic of Croatia
International Union of Crystallography
European Crystallographic Association
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