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X-Cell - a novel and robust indexing program for medium- to high-quality powder diffraction data

X-Cell is a patent-pending, novel, robust, efficient, integrated, and easy-to-use indexing algorithm which uses an extinction-specific dichotomy procedure to perform an exhaustive search of parameter space to establish a complete list of all possible unit cell solutions.

X-Cell provides the essential algorithmic support for researchers investigating both organic and inorganic crystal structures from medium-quality conventional laboratory powder diffraction data to high-quality synchrotron powder diffraction data obtained from X-ray, neutron, and electron radiation sources.

Issues that can be overcome with X-Cell include:

  • Impurities
  • Zero-point shift
  • Strong overlapping peaks
  • Peak position errors (e.g. preferred orientation)
  • Extreme cell geometries (e.g. long and flat unit cells)
  • Unit-cell doubling.

What is reported here are the results of three X-Cell validation studies reported in J. Appl. Cryst., 2003, 36 , 356-365.

Validation Study 1 - Comparison of CPU Times and Success Rates

Two series of calculations were carried out to realistically evaluate X-Cell against three commonly in use indexing programs - ITO, 2 TREOR, 3 and DICVOL 4 :

  1. To compare the CPU time requirements of X-Cell and DICVOL, and
  2. To compare the success rates of X-Cell with ITO, TREOR, and DICVOL under realistic working conditions.

To compare the CPU time requirements of X-Cell and DICVOL 12 powder diffraction patterns were indexed on a Dell Latitude laptop with a single Pentium III processor running at 1.2 GHz. For each compound, the calculation times, the number of observed and calculated peaks, the crystal system, and the space group were recorded.

The results showed that, despite the fact that X-Cell searchers all 99 powder extinction classes separately and determines the zero-point shift in addition to the unit-cell parameters, the time taken to find the correct unit cell is roughly the same for the two programs. This suggests that the implementation of the successive dichotomy approach is significantly more efficient in X-Cell than in DICVOL.

To compare the success rates of X-Cell with ITO, TREOR, and DICVOL under realistic working conditions, 24 compounds were studied. Diffraction peak positions were determined using MS Modeling's Reflex by locating the peak maxima. These diffraction peaks were then indexed by the 4 indexing programs.

The results showed that X-Cell always found the correct unit cell among the 5000 indexing solutions, demonstrating the ability of X-Cell to perform an exhaustive unit cell search in the presence of impurity peaks, strong peak overlap or preferred orientation.

Validation Study 2 - Indexing the Powder Diffraction Pattern of Bicyclo-3,7-dione Despite Impurity Peaks

An experimentally obtained powder diffraction pattern of bicyclo-3,7-dione measured using synchrontron radiation was indexed using X-Cell with impurity tolerance levels set at 0-7 in all but the triclinic crystal system. The best solution was obtained in a tretragonal powder extinction class that contains only the space groups of P 4 1 2 1 2 and P 4 3 2 1 2, with lattice parameters a = b =6.85 Å and c =16.85 Å. The result of the corresponding Pawley refinement showed that 11 impurity peaks were found among the 31 selected peaks (35%) with 6 impurity peaks among the first 10 selected peaks (60%). From the difference plot, it can be seen that all impurity have rather low intensity, in agreement with a contamination of the main crystalline phase with a small amount of an impurity phase.


Figure 1 Pawley Refinement of bicyclo-3,7-dione. Short and long vertical lines indicate calculated peak positions and peaks selected for indexing, respectively. Impurity peaks are marked by arrows.

The crystal structure of bicyclo-3,7-dione was subsequently solved using MS Modeling's Reflex Plus, confirming the indexing solution beyond doubt. These results show the high tolerance of X-Cell to impurity peaks.

Validation Study 3 - Indexing the Powder Diffraction Pattern of Nonane, Long Cell, and Strong Peak Overlap

Long and flat unit cells are often particularly difficult to index, because all low-angle reflections belong to a single row or zone in reciprocal space, while the remaining parameters of the reciprocal lattice are defined by strongly overlapping and low scattering intensity reflections at higher 2θ values.

To facilitate the indexing of long and flat unit cells, X-Cell allows for a multi-step procedure. In a first step, using only a small number of reflections at very low 2θ values, the user can first search for zones. If a zone is found that fits the experimental data, accurate 2D cell parameters and the zero point shift of the diffraction pattern can be determined by Pawley refinement in MS Modeling.

Comparing the reflections belonging to the zone to the experimental powder diffraction pattern, it is possible to identify the reflections that characterize the remaining cell parameters. In a second step, the completed list of peak positions, the lattice constants of the zone, and the zero-point shift are used as the input and the 3D unit cell is determined with X-Cell.

The powder diffraction pattern of nonane was recorded by neutron scattering at a wavelength of 1.59432 Å. 25 peaks were selected and indexed by X-Cell overnight on a HP Alpha server. The search was carried out in all crystal systems at impurity levels 0-4.


Figure 2 Pawley Refinement of nonane. Short and long vertical lines indicate calculated peak positions and peaks selected for indexing.

Nonane has triclinic unit cell with a long axis, the cell parameters being a =4.088, b =4.630, and c =28.810 Å, α =97.228°, β=91.004°, and γ=74.980°. The best solution was verified by Pawley refinement. From Figure 2, it is easy to understand why it is difficult to index long unit cells. All the diffraction peaks up to about 20° belong to a single row in reciprocal space and defined only one of the six lattice parameters of a triclinic cell. The remaining 5 lattice parameters are defined by the strongly overlapping peaks in the angular region beyond 20°.

This result showed that X-Cell is capable of handling long cell and strong peak overlap where other indexing programs fail.

References

1. M. A. Neumann, J. Appl. Cryst ., 2003, 36 , 356-365.
2. J. W. Visser, J. Appl. Cryst. , 1969, 2 , 89-95.
3. P. E. Werner, L. Ericksson, and M. Westdahl, J. Appl. Cryst. , 1968, 1 , 108-113.
4. A. Boultif and D. Louer, J. Appl. Cryst. , 1991, 24 , 987-993.

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