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Crystal Twinning

Many of the ideas in this page are taken from the text by Massa1 and the SHELXTL reference manual2.

Table of Contents

Twinning

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 disorder is encountered, the structure should be checked to make certain that it is not twinned.

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

Merohedral Twinning Relationships
Holohedry Bravais Lattice Point Group Possible twin
operations
1 aP 1 1
2/m mP, mS 2
m
1
1
mmm oP, oS, oI, oF 222
mm2
1
1
4/mmm tP, tI 4
4
4/m
422
4mm
42m, 4m2
1, .m., .2.
1, .m., .2.
.m.
1
1
1
3m hR 3
3
32
3m
1, .m, .2
.m
1
1
6/mmm hP 3
3
321, 312
3m1, 31m
3m1, 31m
6
6
6/m
622
6mm
62m, 6m2
1, .m., .2., m..,
..m, 2.., ..2
.m., m.., ..m
1, m.., ..2 / .2.
1, m.., ..m / .m.
m..
1, .m., .2.
1, .m., ..m
.m.
1
1
1
m3m cP, cI, cF 23
m3
432
43m
1, ..m, ..2
..m
1
1

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 following formula:11,12

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.

Nonmerohedral twins may be indicated by the following.

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 to 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.

References

  1. W. Massa, Crystal Structure Determination, Springer-Verlag:New York, 2004, 150.

  2. G. M. Sheldrick, SHELXTL Reference Manual, 1997, Bruker-AXS, Inc., Madison, WI

  3. R. W. Cahn, Advances in Physics, 1954, 363-445.

  4. C. Giacovazzo, Fundamentals of Crystallography, 1992, Oxford Univ. Press:New York, 83-87.

  5. H. D. Flack, Acta Cryst., 1983, A39 876-881.

  6. International Tables for Crystallography, Vol. C, Kynoch:New York, 1998, 13.

  7. RLATT, 1998, Bruker-AXS, Inc., Madison, WI

  8. A. J. M. Duisenberg. DIRAX: A program for indexing twinned crystals, Lab. voor Kristalen Structuurchemie, U. Utrecht, Padualaan 8, 3584 CH Utrecht, Netherlands; A. J. M. Duisenberg, J. Appl. Cryst., 1992, 25, 92-96.

  9. R. A. Sparks, GEMINI, 1999, Bruker-AXS, Inc., Madison, WI

  10. M. J. Buerger, Crystal Structure Analysis, Wiley:New York, 1960, 53-68; M. J. Buerger, Anais acad. Brasil. cienc., 1954, 26, 111-121.

  11. W. Massa, S. Wocadlo, S. Lotz, and K. Dehnicke, Z. anorg. allg. Chem., 1990, 587, 79-88.

  12. P. Van der Sluis, Thesis. U. of Utrecht, 1989.

  13. G. Sheldrick, Cell_Now, 2004, Bruker-AXS, Inc., Madison, WI