Determine Twin Matrix from Fo/Fc Data

This function carries out an after-the-fact analysis for missed or unaccounted for twinning. It is based on an analysis of reflections with large differences between observed and calculated structure factors (i.e. I(obs) >> I(calc)). Those differences may be due to overlap by a strong reflection from a rotated lattice.

TwinRotMat addresses the same issue as the Windows program ROTAX by Simon Parsons and Bob Gould but is not identical, both in terms of underlying algorithms and approach. It might be useful to compare the results of both approaches.

Ideally, twinning is already discovered in the early stages of data collection and taken care of. This applies in particular for data collected on CCD detector systems when not all reflection spots are covered by the assumed lattice. Exceptions are cases of (pseudo)merohedral twinning where signs of twinning turn up in the data processing stages. Examples are: problems with the structure determination, poor refinement and (high) unexplained density peaks.

This routine addresses cases of (reticular)(pseudo) merohedral twinning. Cases where data are based on an artificially higher volume twin lattice are not covered. (i.e. monoclinic structure in orthorhombic supercell twin lattice - generally accompanied by strange systematic extinctions).

A tentative rotation twin axis and associated matrix is suggested.

The analysis is based on the well known fact that unaccounted for twinning shows up in a significant number of reflections with I(obs) much greater than I(calc). In that case, it can be assumed that those (relatively weak) reflection are overlapped by strong reflections with approximately the same theta value. Each such an occurrence leads to a tentative rotation axis. Rotation axis that are observed most frequently are tested for there capability to explain all the observed intensity differences. Both an approximate twinning factor (BASF) and approximate effect on the R-value are listed. Suitable matrices are listed in green.

The algorithm searches for reciprocal lattice two-fold twinning axis, indicated in (). However, also the nearest direct axis direction within the -5 to +5 index range is reported in []. Subsequently, those axis are also tested for there ability to lower the R-value. The matrix with the largest R-drop is reported. Positive Freq numbers (i.e. the number of supporting indications for the twin opereration) indicate a best rotation about the direction in (). Negative Freq num,bers indicate a best rotation about the vector in [].

The program needs an '.fcf' file (e.g. shelxl.fcf) [or a .cif + .fcf] for the analysis.

Cases of merohedral twinning are normally handled in a subsequent BASF/TWIN refinement.

Alternatively, an HKLF 5 type of file for the best solution is written to a file with extension '.hkp' to be used for subsequent SHELXL refinement.

Options are provided to display the twinning effect in reciprocal space.

Iobs-Icalc/sigma Crit: PAR(413) = 10.0
Theta Criterium: PAR(414) = 0.05
Indexfit criterium: PAR(415) = 0.1

The analysis can be invoked in various ways, given an CIF + FCF

1 - Via the PLATON main menu option TwinRotMat. Default parameters can be manipulated in the side menu.

2 - The -T option that bypasses the alternative invocation from the PLATON menu. In this case, the calculated structure factors will be calculated from the data in the CIF, prior to the analysis for twinning.

platon -T compound.cif

Example:s103b.fcf. Monoclinic, twinned about (1 0 0). Overlap in 0, 6 & 12 th l-layer.

PLATON Analysis Result:

2-Rotation about ( 1 0 0 )

Rotation Matrix:

1 0 0.8347
0 -1 0
0 0 -1

An HKLF 5 type SHELXL file is written.

Two files are created, b_tw.ins and _tw.hkl are created suitable for subsequent refinement with SHELXL.


12-Feb-2020 A.L.Spek