Setting the UB Matrix

The UB matrix describes how reciprocal lattice coordinates are oriented on the diffractometer. The B matrix is determined by the lattice constants and converts (h, k, l) from reciprocal lattice units to Cartesian reciprocal-space coordinates. The U matrix describes how the crystal is mounted relative to the diffractometer sample circles.

Reference-Reflection Method

The usual workflow is to determine U from one or more observed reference reflections:

  1. Open a scan and display an image that contains a known reflection.

  2. Double-click the reflection position in the image. This creates a reference marker in the Reciprocal space navigation window.

  3. Move the marker if needed. The marker position defines the detector coordinates, and the selected image number defines the sample rotation angle for that observation.

  4. Enter or correct the reflection h, k, and l values in the reference-reflection table.

  5. Repeat for a second linearly independent reflection when possible.

  6. Click Calculate U.

Two linearly independent reflections fully determine the orientation matrix. For the common surface-diffraction case, orGUI can also estimate an orientation from a single reference reflection by assuming that the L direction points toward the z/azimuth reference direction. This is useful for quick setup when a clear reflection near L = 0 is visible, but a two-reflection orientation is the more general procedure.

Expert Matrix Editing

The menu entry Reciprocal Space -> Edit orientation matrix opens the expert path for editing the matrix directly. This is intended for cases where the orientation can be inferred from known symmetry or from an already established experiment geometry. It is less forgiving than the reference-reflection method, especially in grazing-incidence geometries.

Validation

After calculating the matrix, enable View -> CTR reflections and step through the active scan. The calculated CTR or Bragg positions should follow the features in the detector images. If they do not, check the assigned hkl values, the selected image number of each reference reflection, the detector calibration, and the beamline scan-axis convention.

The underlying calculation follows the Busing and Levy orientation-matrix method adapted to the orGUI diffractometer geometry. The observed detector coordinates and scan angles define momentum-transfer vectors in the inner sample-circle frame; U is then obtained by matching those vectors to the corresponding reciprocal lattice vectors.