# Twinned Structures

How to deal with twinning

## Twinning

Twinning in crystallography means that the crystal contains more than one domain related by a symmetry operation. Consequently, the diffraction pattern measured is a combination of the diffraction patterns from each of the domains. Twinning makes data analysis more complicated but with advances in computing and software, it is normally possible to resolve twinned crystals. A good introduction to twinning can be found in S. Parsons, (2003), ActaCryst., D59, 1995-2003.

### Common signs

There are a number of warning signs for twinning that have been identified, not all will exist at any one time, but if signs are present it is worth investigating. The following list is derived from a list published in R. Herbst-Irmer & G. M. Sheldrick, (1998), ActaCryst., B54, 443-449, where applicable suggestions of where to check features within Olex2 are highlighted:

• Indexing problems:
• Difficulty obtaining a cell.
• An unusually long axis.
• Split reflections.
• Rint for a higher symmetry group is similar to that of the low symmetry group.
• The metric symmetry is higher than the Laue symmetry of the diffraction pattern e.g. a monoclinic structure with alpha = 90 appears orthorhombic.
• Problems identifying the space group, either the systematic absences are not consistent with a space group or it is uncommon. (To examine this in Olex2 click , the output will be displayed on the screen (and in your text editor after clicking on the notepad icon .)
• The average value of $|E^{2}-1|$ is lower than expected the expected values. Two graphs in Olex2 can assist with assessing this under . There are the options to plot the Cumulative Intensity Distribution and the Wilson Plot which also has an assessment of the average $|E^{2}-1|$ value for the structure below it.
• The structure cannot be solved.
• The refinement is unsatisfactory:
• Fo»Fc for the majority of the most disagreeable reflections. Disagreeable reflections can be omitted under and clicking on Exclude. In addition under, a plot of Fo vs. Fc should have a gradient of ~1 and an intercept ~0, without many reflection deviating from this line. Any reflections that have been omitted will be greyed out, while Fo/Fc versus the resolution should have a value of ~1.
• R1 and wR2 remain unexpectedly high based on the Rint value. Generally the R1 value should be approximately similar to the Rint upon completion, see and .
• Weights: the second value of the weighting scheme remains very high e.g.> 5. To check this see .
• Higher symmetry crystal systems in the lower symmetry Laue classes are often subject to merohedral twinning so this is always worth checking. Possible twin laws can be searched for under .

The first 3 points on the list above should be assessed within the data processing software. The remaining points can be checked within Olex2.

### Treating twinning

Olex2 can automatically search for twin laws and suggest any likely twin laws, or you can input twin laws to test. There are different types of twinning:

#### Merohedral and psedudo-merohedral twinning

Those where the reciprocal lattices (i.e. reflection positions) exactly overlap. It is relatively simple to treat and procedures are described below. In this type of twinning, a twin law and twin scale factor are added to the head of the .ins file below the UNIT instruction in the form

TWIN -1 0 1 0 -1 0 0 0 1 2
BASF 0.1

Where -1 0 1 0 -1 0 0 0 1 2 is a 3 by 3 matrix to define the twin law, 2 is the no. of twin components and BASF is the twin scale factor. An arbitrary value <1 is selected which is subsequently refined

#### Non-merohedral twinning

Non-merohedral twinning, where only some of the reflections overlap, are more complicated and require the preparation of a different type of .hkl file (an HKLF 5 file) prior to refinement within Olex2. A >>BASF number (where number is an arbitrary number <1) line is included in the .ins file, but no TWIN law. Only one twin law can be applied to the data at any time (with the exception of including racemic twinning alongside a twin law). Any twin laws that are being applied to the data are displayed below the refinement statistics at the top of the GUI panel .

### For merohedral and pseudo merohedral twins

Automatic searching for twin laws - this can be done using Olex2 under where the program searches for metrically possible twin laws. If found, the structure is refined against each of them in turn. The $R$-value gives an indication of the quality of the structure - a low $R$-value is better. To select a twin law, click on the relevant twin law.

If a twin law is selected, Olex2 automatically includes the selected twin law and BASF into the .ins file. The matrix (1 0 0 0 1 0 0 0 1) is the untwinned refinement. BASF is the twinned scale factor indicating what percentage of the structure would be the second component i.e. 0.20 (=20%) would suggest 80% is component 1 and 20% is component 2. Currently it is only possible to refine using one twin law (excluding racemic twinning) in Olex2.

#### Manually entering a twin law

Type >>editins or click on to view the top of the .ins file. Somewhere below the UNIT instruction, type >>TWIN followed by the twin law e.g. >>TWIN -1 0 1 0 -1 0 0 0 1 2 and type >>BASF followed by some value <1.

#### Racemic twinning

Type >>editins or click on to view the top of the .ins file. If a twin law is not included, add TWIN on one line and BASF 0.2 on the second line. If a twin law is already included, e.g. TWIN -1 0 1 0 -1 0 0 0 1 2, change 2 to -4 (calculates racemic twinning component for component 1 and component 2 giving 4 components) and add two randomly selected numbers <1 (~0.1 is sensible) to the BASF line which will give the fraction of each component. Racemic twinning is only applicable in non-centrosymmetric space groups. If the BASF refines to some very small number or >1 the twin law is not valid and should be removed. It is possible, return to the original structure () and select the original matrix (1 0 0 0 1 0 0 0 1) or use the function. Non-merohedral twins – using an HKLF 5 file, type >>editins or click on to view the top of the .ins file. Somewhere below the UNIT instruction, type >>BASF number (where `number' is an arbitrary number <1) . Ensure that MERG is set to 0 and that HKLF is set to 5 at the bottom of the .ins file