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 I_{hkl} from a single crystal, the experiment
yields
k_{m} I_{hkl}(crystal_{1}) +
(1-k_{m}) I_{h'k'l'}(crystal_{2})
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 k_{m}.
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.
The metric symmetry is higher than the Laue symmetry.
The R_{merge}-value for the higher symmetry Laue group is only slightly higher
than for the lower symmetry Laue group.
The mean value for |E^{2}-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.
The space group appears to be trigonal or hexagonal.
There are impossible or unusual systematic absences.
Although the data appear to be in order, the structure cannot be solved.
The Patterson function is physically impossible.
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:
There appear to be one or more unusually long axes, but also many absent
reflections.
There are problems with the cell refinement.
Some reflections are sharp, others split.
K=mean(F_{o}^{2})/mean(F_{c}^{2})
is systematically high for the reflections with low intensity.
For all of the 'most disagreeable' reflections, F_{o} is much greated
than F_{c}.
3 Frequently encountered twin laws
The following cases are relatively common:
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)
Orthorhombic with a and b approximately equal in
length may emulate tetragonal
Monoclinic with beta approximately 90° may emulate orthorhombic:
Monoclinic with a and c approximately equal and
beta approximately 120° may emulate hexagonal [P2_{1}/c would give
absences and possibly also intensity statistics corresponding to P6_{3}].
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."
PICTURES
Full size versions of the example pictures can be viewed by clicking on the iconised
ones.