CrysAlis^Pro Tip

The Gnomonic Projection and How to Use It

What is the issue?

During long exposures on weakly scattering samples, inelastic scattering may contribute noticeably to the diffractogram, making unit cell indexing challenging. This scattering may come from the sample holder and oils used to mount the sample or air scattering. Electron diffraction may also exhibit inelastic scattering signals from the carbon support of the TEM grids. A human eye might find periodicity in a crowded reciprocal space more efficiently than a computer algorithm—for now.

How to find the unit cell of the crystal?

In the polar zenithal gnomonic projection, all difference vectors between reflections are calculated, normalized, and projected onto a plane tangential to the Ewald sphere. These difference vectors appear as individual pixels in this projection and a line is formed when these vectors appear in a periodic manner; e.g., they are equally spaced and parallel.

Figure 1:Gnomonic projection of the difference vectors in reciprocal space

The task of the user is now to define three of these lines by choosing “Set gnomonic vectors.” These lines cannot intersect each other at a single point and cannot be parallel. Figure 2 shows a histogram of the chosen reciprocal space direction. The abscissa shows the distance from the origin of reciprocal space and the ordinate shows the frequency at which the projected peaks appear.

Figure 2: Three independent gnomic vectors set

In the next step, we are presented with the lattice reduction, and we choose the one with the most meaningful G6-projection distance; see Figure 3. Further information can be obtained here: B. Gruber, Acta Cryst. (1973), A29, 433-440.

Figure 3: Lattice reduction with the most likely Niggli cases

Acknowledgements

We thank Dr. Wolfgang Herrendorf (Institute of Inorganic and Analytical Chemistry, Justus-Liebig-University Gießen) and STOE & Cie GmbH for the inspiration and fruitful discussions in creating this tool.