CrysAlis^Pro Tip

The Euler-kappa Calculator

What is it?

A calculator to convert Kappa-goniometer angles to Eulerian (and back).

Why should I use it?

It’s a convenient way to move to positions in an orthogonal coordinate system.

How can I use it?

Old-school crystallographers may remember the “Eulerian cradle” design for crystal orienting on a diffractometer, which often included a full 360° chi circle, as on the Rigaku AFC-5, AFC-6, or AFC-7, where the chi axis is always perpendicular to the omega axis. It’s slightly easier to calculate how to position a particular reflection onto a particular point in space (important with point detectors where every reflection was measured in the horizontal plane of the beam). And some of us still think in terms of the chi angle; i.e., putting the sample at χ=90° when, for example, aligning a high-pressure cell on the diffractometer.

Many of us use the command line in CrysAlis^Pro to drive the angles to a specific location; i.e., the command ‘gt a -10 0 50 12’ moves to omega=-10°, detector_theta=0°, kappa=50° and phi=12°. Less common but useful is to move to Eulerian angles: ‘gt e 0 0 90 0’ to move to chi=0° (with others at Eulerian zero). This is approximately the same as ‘gt a -57 0 134 -57’ but a lot easier to visualize!

You can access a (currently undocumented) menu in CrysAlis^Pro by typing ‘gt e’ with no other parameters. The following appears:

This allows the transformation from one coordinate system to the other. A press of the blue Euler→Kappa button switches the calculation to the other direction. If performed in online mode, the GT a button populates the command-line with the resulting ‘gt a …’ command.

Enjoy another way to test your 3-dimensional visualization!