G-vectors are the scattering vector associated with the diffraction. The are nodes of the reciprocal space or, in direct space, normal to the diffracting plane.

For a given reflection in the crystal, G_hkl is perpendicular to the diffracting place (hkl) and its norm is 2π/d_hkl. The real space coordinate of G_hkl can be calculated from the experimental measurements, namely the x-ray wavelength λ, the diffraction angle 2θ, the azimuth angle η, and the rotation angle ω (see section on experiment geometry) and the detailed calculation in fable_geometry_version_1.0.8.pdf.

The x-ray wavelength λ is known, so is the rotation angle ω. There are issues, however, to evaluate the diffraction angle 2θ and the azimuth angle η. What is measured is the location of a diffraction spot on a detector. Calculating 2θ and η from the location of a diffraction spot on a detector requires calibration.

This step is typically performed with ImageD11.

At this point, you should know the O-Matrix of your experiment. If not, go back to the section on understanding the concept of the O-Matrix.

ImageD11 can be started by typing the following command in a terminal

 ImageD11_gui.py

Peaks found during peak search can be loaded by clicking on Transformation –> Load filtered peaks and choose the corresponding .flt file. You can display the peaks by calling the corresponding menu item in Transformation. You can either plot peaks in the 2D diffraction geometry (y/z plot), or after transforming detector peak positions into diffraction 2θ and the azimuth η angles (2θ/η plot).

If things look weird after you switch from (y/z) to 2θ/η plots of vice-versa, trying calling the Clear plot button at the bottom of the interface. Clear does only erase the plot, the data is still there.

Go in to Transformation –> Edit parameters and enter all parameters you know. These include

• the sample symmetry and unit cell parameters,
• the O-Matrix,
• the x-ray wavelength,
• the sample to dectector,
• information on beam center.

Because of different conventions used by different softwares, the beam center might change from your calibration (in Fit2D, Dioptas, or anything you use). For instance, if have a 2048×2048 pixels image and found a beam center at 1000 and 900 during calibration, the correct value in ImageD11 should be one of 1000, 900, 1048, or 1148. Use the 2θ/η plot in order to see which one works.

Most of the peaks should appear to be on imaginary vertical lines. Zoom in and check, if these lines are actually vertical. If not, you might

• have strain in your sample,
• have a wrong beam center,
• need to refine the detector tilts.

. If the line looks like a sinus curve of exactly one period this is due to a wrong beam center. To fix this, go back to Edit parameters and activate the check marks for the y-position and z-position of the detector. Press Ok and click on Fit for several times until the spots don't move anymore. The imaginary lines should now be completely straight (if you don't have strain). If they are not, you can try to fit other parameters.

At some point you can click on Transformation –> Add unit cell peaks. Red tick marks will appear which indicate the expected positions of the vertical lines. With this you can check whether your input parameters (cell parameters, detector distance, …) were correct.

For the calculation, the software ImageD11 can be used. First, you have to load the peaks you found (e.g. .flt file from PeakSearch and enter the parameters. You can compute the G-vectors by following three steps:

1. Click Transformation –> Assign peaks to powder rings (nothing will happen)
2. Click Transformation –> Compute g-vectors (nothing will happen)
3. Click Transformation –> Save g-vectors. Make sure they get the ending .gve.