Many of the ideas in this page are taken from the text by Massa1 and the SHELXTL reference manual2.
Table of Contents
- Diffraction Patterns of Twinned Crystals
- Common Indicators of Twinning
- Handling Twin Structures with Bruker Programs
Some crystalline materials form aggregates made up of individual single crystals joined together by one or more definite macroscopic symmetry relations. These aggregate crystals are known as twins. According to Cahn3 Two empirical facts are central to the crystallography of twins. First, a twinned piece of material is composed of two or more domains in which the orientations of the domains are related by one or more symmetry elements that are not a part of the space group symmetry of a single crystal of the material. Second, the extra symmetry element(s) must be of the kind encountered in crystal morphology, i.e., a center of symmetry, a mirror plane, or a 2-, 3-, 4-, or 6-fold rotation axis. If the extra symmetry element is a mirror plane, called a twin plane, then this plane must be parallel to a lattice plane of the same d-spacing in both domains. If the extra symmetry is a rotation axis, called a twin axis, then this axis must be parallel to a lattice row common to both domains. If the twin contains domains with more than two sets of orientations, then the sets of domains must be related, pairwise, by an extra symmetry element.
It is also possible for two or more crystals to form an aggregate in which the orientations of the crystals are not related by additional symmetry. These pieces are often called twin crystals, even though they do not strictly fit the definition of a twin. If data are collected on these pieces, the data are usually handled as if it was a non-merohedral twin (see below).
If possible, twinned crystals should be avoided in a diffraction experiment. In many cases, a twinned crystal can be optically recognized by its reentrant faces. Some twinned crystals appear to have grooves or depressions in their surfaces. If the crystals of the sample are not opaque and are not uniaxial (cubic), then the crystals may be optically tested for twinning using a microscope with crossed polarizers. Single crystals should extinguish light or become completely dark at certain positions when they are rotated between crossed polarizers. A twin generally will become dark in some parts of the crystal and will transmit light in other parts of the crystal. This test should be performed on at least two surfaces of the crystal to rule out twinning. Such tests are difficult to perform on crystals shaped as very thin plates or very thin needles.
A great deal of information about twinning has been assembled at the Bijvoet Center's web site at the University of Utrecht. Another good description of using the SHELX software to refine a twin was presented by Regine Herbst-Irmer at an ACA workshop. The University of Oxford Crystallography Laboratory has assembled an extensive description of techniques to handle twinned data sets. Numerous diagrams of twinned crystals were prepared by Stephen Nelson at Tulane University.
Diffraction Patterns of Twinned Crystals
Based upon their diffraction patterns, twinned crystals may be grouped into three general categories. Non-merohedral twins have two or more crystalline domains with reciprocal lattices that either do not overlap or only partially overlapped. In contrast, Merohedral twins have domains with diffraction patterns that are completely overlapped. For merohedral twins, the symmetry operations relating the twinned domains are a part of the Laue group of the sample, but are not a part of the space group. Pseudo-merohedral also have domains with completely overlapped diffraction patterns, but the symmetry operation relating the domains is not a part of the Laue group of the sample.
Non-merohedral twins are generally recognized at the time of data collection because of difficulties with indexing or because of obvious multiple sets of reciprocal lattices. Many crystals that are twinned employ this mode of twinning. These twins are sometimes described as having twin lattice quasi-symmetry, TLQS.4 Generally the twin symmetry element is not a symmetry element of the Laue group. If there are completely overlapped spots in the diffraction pattern, the overlapped spots are usually found in zones or lines that are perpendicular to the twin symmetry element. If most of the crystal is from one domain, it is sometimes possible to collect intensity data from this one domain and continue the structure determination as if the crystal were single (realizing that the final R factor may not be as low as it could be if the crystal were truly single). Point detector instruments have difficulty indexing these samples or generate cells with one or more very large cell edges. Thus it is rare for data from these types of twins to be collected with point detector instruments. Since area detectors allow data from all parts of reciprocal space to be collected, analysis of crystals with this type of twinning has become more common. Usually the overlapping of spots from the different domains is significant enough that data from all domains must be considered in the final refinement.
Merohedral twins have a twin symmetry element that is
not a symmetry element of the space group of the sample but is a symmetry
element of the Laue group. Both the direct and reciprocal lattices of the different
domains coincide with one another, making the crystal appear to be single until near
the end of refinement. This type of twinning is sometimes described
as having twin lattice symmetry, TLS, of class I.4 If the volumes of the
different domains are nearly equal, then the additional symmetry element often leads
to the selection of an incorrect higher symmetry space group. It is sometimes
possible to solve and refine the structure in this higher symmetry space group, and
obtain a false average of the two orientations of the actual structure. Frequently,
in such cases, disorder will occur. Conversely, when extensive
is encountered, the structure should be checked to make certain that it is not
One type of twin by merohedry only occurs in non-centrosymmetric space groups -- inversion twinning. These twins are usually easily identified by means of the Flack test5 This type of twinning is also called racemic twinning.
If the physical volumes of the different domains are far from equal, then the intensities of the reciprocal lattice will show the true Laue symmetry and usually lead to the correct space group. Since the data set is, however, distorted by the presence of the minor component, the structure will usually not refine well. Merohedral twin laws for all Laue groups are given in the table below which is derived from the International Tables for Crystallography6.
As with merohedral twins, Pseudo-merohedral twins have reciprocal lattices that can be indexed on a single lattice and hence appear to be single crystals. Also as with merohedral twins, data sets of these compounds show difficulty with structure solution and especially structure refinement. Often lowering the crystal system symmetry will help with the structure solution. At this point
|Holohedry||Bravais Lattice||Point Group||Possible twin|
|mmm||oP, oS, oI, oF||222
|1, .m., .2.|
1, .m., .2.
|1, .m, .2|
|1, .m., .2., m..,|
..m, 2.., ..2
.m., m.., ..m
1, m.., ..2 / .2.
1, m.., ..m / .m.
1, .m., .2.
1, .m., ..m
|m3m||cP, cI, cF||23
|1, ..m, ..2|
Pseudo-merohedral twins have lattice parameters that suggest higher Laue symmetry than the symmetry appropriate for the point group of the sample and have a twin element that emulates the additional symmetry of a higher symmetry Laue group. For example consider a monoclinic sample with β = 90° that has a twin plane on (100). The twin domain will have peaks that are too close to be distinguished from the first domain. If the volumes of the two domains are nearly equal, the intensities will appear to have mmm symmetry instead of 2/m, and the structure will not be solvable. Once the nature of the twinning is recognized and included in the model, the structure solution and refinement usually proceed without further problems.
The measured intensities often have observable data from one domain that is superimposed on the systematically absent locations of another domain. In such cases, if twinning is not suspected, a space group may be chosen with few translational symmetry elements, such as C2221 or Pmmm. When such relatively rare space groups are encountered, and the structure is difficult to solve, it is worth considering the possibility of twinning.
Once the different domains are indexed and the twin law(s) identified, these types of data sets can usually be refined to quite reasonable results. The appropriate indexing of the different domains is usually recognized either visually by such computer programs as RLATT7, or computationally by DIRAX8, GEMINI9, or CELL_NOW13. The intensity data for each domain is then integrated, reduced, and finally all data sets are combined for refinement.
A related type of pseudo-merohedral twinning occurs when the reciprocal cell parameters are such that in every second, third, or nth layer the reciprocal lattices of the two components overlap. Data sets from crystals with these types of twins can easily be collected with either point or area detectors. It is possible to interpret the overlapping reciprocal lattices in terms of a smaller single reciprocal cell, i.e. a larger real cell. The structure produced from this smaller cell is obviously wrong, but the nature of the problem may not be apparent. Often the first hint that something is wrong comes from the presence of implausible systematic absences.10 These twins are sometimes classified as having twin lattice symmetry, TLS, of class II.4
If the overlapped data are required for structure determination,
the relative contributions of the different domains are first estimated and these
contributions are applied to
detwin the overlapped data. If volume
fractions of the crystal are known then the relative contributions are calculated
from x = V1/(V1 + V2). Initial refinements
using the nonoverlapped data can also produce estimates for x. The
intensities of the overlapped data may then be estimated using the
Fhkl2 = F12 [x/(2x - 1)] - F22 [(1 - x)/(2x - 1)]
where F12 and F22 are the true intensities for the overlapped hkl peak.
Common Indicators of Twinning2
Experience has shown that there are a number of characteristic warning signs for twinning. Of course, not all of these indicators can be present in every twinned sample. However, if several are noted, then the possibility of twinning in the sample should be explored.
The mean value for |E2-1| is much lower than the 0.736 expected for a noncentrosymmetric crystal. The intensities from peaks overlapped by more than one twin domain tend to have few very strong or very weak peaks leading to low values for this statistic.
The data exhibit implausible or unusual systematic absences. (a possible partial-merohedral twin)
The data exhibit no systematic absences for glide planes or screw axes, and the structure is not solvable or solves with difficulty. (a possible partial-merohedral twin)
For the most poorly fit data, the Fo2 values are consistently larger than the Fc2 values.
The space group appears to be either tetragonal or trigonal.
The model is in a centrosymmetric space group and is highly disordered.
The metric symmetry of the cell parameters is higher than the Laue symmetry.
The R(int) for a higher symmetry Laue group is only slightly higher than the R(int) for a lower symmetry Laue group.
Nonmerohedral twins may be indicated by the following.
The cell has one or more unusually long axes, and many of the data are weak or absent.
The cell is indexed or refined only with great difficulty.
Some data are sharp and others appear to be split.
Handling Twin Structures with Bruker Programs
Both merohedral and pseudo merohedral twins are modeled in the Shelx refinement program using both the TWIN and BASF instructions. The twin law(s) are typically entered using the TWIN instruction. Complete instructions are given in chapter 7 of the Shelx-97 users manual. Chapter 6 of this manual describes many common twin laws. The Rotax program is particularly useful at identifying the twin law(s).
Non-merohedral twins are treated in different ways depending on the relative volumes of the twin domains in the sample. For samples with one very strong domain and one or more very weak twin domain(s), it is common to simply integrate the data on the predominant domain and ignore the weak domain(s) during structure solution and refinement. For samples with more than one strong domain, the data must be integrated assuming the multiple domains.
Non-merohedral twins require that the separate orientation matrices for each domain be identified as described above. Once the different orientation matrices are identified, the second and subsequent orientation matricies are entered into a *.p4p file containing the first orientation matrix. The lines labelled CELL, CELLSD, ORT1, ORT2, ORT3, ZEROS, and ADCOR from the other twin domains must be copied into the file with the first orientation matrix. Note that the domains are identified separately by adding an integer after the commands above, eg., CELL2, CELLSD2, ORT12, ORT22, ORT32, ZEROS2, and ADCOR2. A third domain would use the integer 3, and a fourth domain would use the integer 4, etc. The first domain should not be indicated by an integer. An example is shown below.
CELL 12.0536 12.0536 6.4294 90.0000
90.0000 90.0000 934.131
CELLSD 0.0004 0.0004 0.0002 0.0012 0.0012 0.0015 0.087
ORT1 4.9101941e-002 -4.1741710e-002 9.7944692e-002
ORT2 -3.0716989e-002 4.3493658e-002 1.1927310e-001
ORT3 -5.9399031e-002 -5.6997448e-002 1.9285880e-002
ZEROS 0.0000000 0.1656704 0.4175613 -0.1481 -0.1586 -0.1426
ADCOR 0.5199 -1.4360 -0.0085 -0.1184 0.0174 0.0449
CELL2 12.0357 12.0391 6.4145 89.9775 90.0463 90.0436 929.455
CELLSD2 0.0064 0.0065 0.0039 0.0089 0.0108 0.0212 1.536
ORT12 0.3148598E-01 -0.1939359E-01 0.1396472
ORT22 -0.4873452E-01 0.5718325E-01 0.6659055E-01
ORT32 -0.5947151E-01 -0.5703856E-01 0.1918907E-01
ZEROS2 0.0000000 0.0356271 0.7619487 0.0000 0.0000 0.0000
ADCOR2 0.0517 -3.1139 -0.0124 -0.3948 -0.3265 -0.0343
Data integration in the currently distributed version of Saint requires
two separate steps. First start Saint+ using the *.p4p files that were
created during data collection. Delete the *.p4p files for runs 2,3, etc. For
the first run, select the *.p4p file modified to contain the different
orientation matrices. In the Integrate menu set the crystal system for integration
Unconstrained and check the Crystal translations box under this
category. Disable continuous crystal and detector orientation updating. Set the
X, Y, and Z dimensions of the spots to reasonable sizes for the sample and the
instrument. In the Advanced Intgrate menu set the number of frames stored to
monitor reflection overlap to 25. Exit from Saint+.
In a command prompt window, set the directory to the directory containing
the saint.ini file for this structure. At OU, this directory is usually
f:\frames\project\work. Start the Saint program, and move to the
Integrate and then Advanced options menu. In the A option, change the
Twin box size ratio to 1.5. In the 2 option, change the
Minimum common volume to 0.2. Exit the Advanced options menu,
and start the integration with the
! command. The program will
now output the raw data into *.mul files rather than *.raw files.
The absorption correction must be performed by the Twinabs program. It
is recommended that generate both an hklf 4 format file and an hklf 5 format
file. The data in both of these files can be merged. The hklf 4 file is
typically used to solve and initially refine the structure. The hklf 5 file
is needed for the final refinement. When using the hklf 5 file, be sure to
add a BASF command in the XL program with n-1 numbers, where n is the number
of twin domains. These n-1 numbers should all be between 0 and 1. The XL
input instruction file should also include a
LIST 7 command and
the number on the HKLF command should be changed from 4 to 5. Finally, the
hklf 4 file should be renamed from *.hkl to *.hkl4 and the hklf 5 file should
be renamed to *.hkl.
Note that changing from hklf 4 to hklf 5 refinement may cause the R factors to increase dramatically for the first cycle or two. The R factors should refine to reasonable values after 4-6 cycles. The large change in R factors is primarily due to the different scaling of the two data sets.
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H. D. Flack, Acta Cryst., 1983, A39 876-881.
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RLATT, 1998, Bruker-AXS, Inc., Madison, WI
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