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=== Twinning by Merohedry === | === Twinning by Merohedry === | ||
In a merohedral twin, the twin law is a symmetry operator of the crystal system, but not of the point group of the crystal. This means that the reciprocal lattices of the different twin domains superimpose exactly and the twinning is not directly detectable from the reflection pattern. This type is possible in the trigonal, tetragonal, hexagonal and cubic crystal systems, which have more than one Laue group. The twin law corresponds to the two-fold operation that is present in the apparent Laue group, but not in the true space group. Only for trigonal crystals is there more than one possible twin law. | In a merohedral twin, the twin law is a symmetry operator of the crystal system, but not of the point group of the crystal. This means that the reciprocal lattices of the different twin domains superimpose exactly and the twinning is not directly detectable from the reflection pattern. This type is possible in the trigonal, tetragonal, hexagonal and cubic crystal systems, which have more than one Laue group. The twin law corresponds to the two-fold operation that is present in the apparent Laue group, but not in the true space group. | ||
Twinning in P3, P4, P6 and cubic crystals often involves only two domains (hemihedry). Only for trigonal crystals is there more than one possible twin law. Higher forms of merohedral twinning then exist: tetartohedry (4 twin domains) and ogdohedry (8 twin domains). | |||
=== Twinning by Pseudo-Merohedry === | === Twinning by Pseudo-Merohedry === | ||
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=== Twinning by Reticular Merohedry === | === Twinning by Reticular Merohedry === | ||
Some of the reflections overlaps exactly, while others are non-overlapped. A typical example is an obverse/reverse twin in case of a rhombohedral crystal. Thus, this kind of twinning lets R3 look like P3<sub>1,2</sub>, and R32 like P3<sub>1,2</sub>21. However, 1/3 of all reflections are still zero. | |||
=== Non-Merohedral Twins === | === Non-Merohedral Twins === | ||
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== Solution == | == Solution == | ||
[http://dx.doi.org/10.1107/S0108767387099951 Yates & Rees, Acta Cryst. (1987). A43, 30-36] give a method for solving a twinned structure using MIR. This requires four independent derivatives. | |||
== Refinement == | |||
Refinement of merohedrally and pseudo-merohedrally twinned data data is possible using [[CNS]] (for input files, see CNS homepage - main menu - input files - x ray - twinning), [[ccp4dev:Refinement_with_Refmac5|Refmac]] or [[Phenix|phenix.refine]] ([http://www.phenix-online.org/documentation/refinement.htm#anch38 Refinement using twinned data]) and has "always" been possible with [[SHELXL]] ([http://shelx.uni-ac.gwdg.de/~rherbst/twin.html Twin-Refinement with SHELXL]). | |||
Be aware that R-factors may not be directly comparable: [http://www.ysbl.york.ac.uk/refmac/papers/Rfactor.pdf G. Murshudov, Appl. Comput. Math., V.10, N.2, 2011, pp.250-261] and [http://journals.iucr.org/d/issues/2013/07/00/ba5190/index.html Evans P.R., Murshudov G.N. (2013) How good are my data and what is the resolution? Acta Cryst D69, 1204-1214] | |||
== '''Warning Signs for Twinning''' == | == '''Warning Signs for Twinning''' == | ||
Experience shows that there are a number of characteristic warning signs of twinning, as given in the following list. Of course not all of them can be present in any particular example, but if one or several apply, the possibility of twinning should be given serious consideration. | Experience shows that there are a number of characteristic warning signs of twinning, as given in the following list. Of course not all of them can be present in any particular example, but if one or several apply, the possibility of twinning should be given serious consideration. | ||
# The metric symmetry is higher than the Laue symmetry. | |||
# The Rint-value for the higher symmetry Laue group is only slightly higher than for the lower symmetry Laue group. | |||
# 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. | |||
# The mean value for |E^2-1| is much lower than the expected value of 0.736 for the non-centrosymmetric case (see also [[Intensity statistics]]). If we have two twin domains and every reflection has contributions from both, it is unlikely that both contributions will have very high or that both will have very low intensities, so the combined intensities are distributed to give fewer extreme values. | |||
# The space group appears to be trigonal or hexagonal. | |||
# The apparent systematic absences are not consistent with any known space group. | |||
# Although the data appear to be in order, the structure cannot be solved. This may of course also happen if the cell is wrong, for example with an halved axis | |||
# The cell volume is too small for the size of the molecule, or the Patterson function is physically impossible. | |||
The following features are typical of non-merohedral twins, where the reciprocal lattices do not overlap exactly and only some of the reflections are affected by the twinning: | |||
# There appear to be one or more unusually long axes. | |||
# There are problems with the unit cell refinement. | |||
# Some reflections are sharp, others split. | |||
# K = mean(Fo^2)/mean(Fc^2) is systematically high for reflections with low intensity. This may also indicate a wrong choice of space group in the absence of twinning. | |||
== See also == | |||
[[ccp4dev:Twinning|Twinning]] in the CCP4 developers' wiki | |||
== References == | |||
Giacovazzo, C. ed. (2002). Fundamentals in Crystallography, I.U.Cr. & O.U.P.: Oxford, UK. | |||
=== Other Helpful Papers on Twinning === | |||
Parsons, S. Introduction to twinning. Acta Cryst (2003) D59, 1995-2003. | |||
Dauter, Z. Twinned crystals and anomalous phasing. Acta Cryst (2003) D59, 2004-2016 | |||
[http://journals.iucr.org/d/issues/1999/10/00/ba0026/ba0026.pdf Chandra, N., Ravi Acharya, K., and Moody, P.C.E. (1999) Analysis and characterization of data from twinned crystals. Acta Cryst. D55, 1750-1758] | |||
=== Examples, with background references === | |||
Detecting and overcoming hemihedral twinning during the MIR structure determination of Rna1p. Hillig RC, Renault L. Acta Crystallogr D Biol Crystallogr. 2006 Jul;62(Pt7):750-65. | |||
== | === Other Crystal Pathologies === | ||
Zwart, PH et al. Surprises and pitfalls arising from (pseudo)symmetry. Acta Cryst (2008) D64, 99-107. | |||