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PLEASE NOTE: Most of this has been taken directly from chapter 6 of the SHELX-97 Manual.

1 Introduction

A typical definition of a twinned crystal is the following: "Twins are regular aggregates consisting of crystals of the same species joined together in some definite mutual orientation" (Giacovazzo, 1992). For this to happen two lattice repeats in the crystal must be of equal length to allow the array of unit cells to pack compactly. The result is that the reciprocal lattice diffracted from each component will overlap, and instead of measuring only Ihkl from a single crystal, the experiment yields
km Ihkl(crystal1) + (1-km) Ih'k'l'(crystal2)

For a description of a twin it is necessary to know the matrix that transforms the hkl indices of one crystal into the h'k'l' of the other, and the value of the fractional component km. Those space groups where it is possible to index the cell along different axes are also very prone to twinning.

2 The warning signs for twinning

Experience shows that there are a number of characteristic warning signs for twinning. Of course not all of them can be present in any particular example, but if one finds several of them, the possibility of twinning should be given serious consideration.

  1. The metric symmetry is higher than the Laue symmetry.
  2. The Rmerge-value for the higher symmetry Laue group is only slightly higher than for the lower symmetry Laue group.
  3. The mean value for |E2-1| is much lower than the expected value of 0.736 for the non-centrosymmetric case. 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 intensities will be distributed so that there are fewer extreme values. This can be seen by plotting the output of TRUNCATE or ECALC.
  4. The space group appears to be trigonal or hexagonal.
  5. There are impossible or unusual systematic absences.
  6. Although the data appear to be in order, the structure cannot be solved.
  7. The Patterson function is physically impossible.
  8. The following points are typical for non-merohedral twins, where the reciprocal lattices do not overlap exactly and only some of the reflections are affected by the twinning:

  9. There appear to be one or more unusually long axes, but also many absent reflections.
  10. There are problems with the cell refinement.
  11. Some reflections are sharp, others split.
  12. K=mean(Fo2)/mean(Fc2) is systematically high for the reflections with low intensity.
  13. For all of the 'most disagreeable' reflections, Fo is much greated than Fc.

3 Frequently encountered twin laws

The following cases are relatively common:

  1. Twinning by merohedry. The lower symmetry trigonal, rhombohedral, tetragonal, hexagonal or cubic Laue groups may be twinned so that they look (more) like the corresponding higher symmetry Laue groups (assuming the c-axis unique except for cubic)
  2. Orthorhombic with a and b approximately equal in length may emulate tetragonal
  3. Monoclinic with beta approximately 90° may emulate orthorhombic:
  4. Monoclinic with a and c approximately equal and beta approximately 120° may emulate hexagonal [P21/c would give absences and possibly also intensity statistics corresponding to P63].
  5. Monoclinic with na + nc ~ a or na + nc ~ c can be twinned. See HIPIP examples.

Acknowledgement in SHELX manual

"I should like to thank Regine Herbst-Irmer
            who wrote most of this chapter."


Full size versions of the example pictures can be viewed by clicking on the iconised ones.

Cumulative intensity distribution for twin Cumulative intensity distribution for twin

More information

More information on twinning can be found at: Fam and Yeates' Introduction to Hemihedral Twinning, which includes a Twinning test.

And a concise but in-depth description of twinning has been written by E. Koch for the International Tables Volume C (1992), pages 10-14.

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