I16 6-axis Diffractometer

The I16 diffractometer is a 6-circle kappa geometry diffractometer, capable of aligning a sample in any orientation relative to the incident beam.

The large sample space provides space to fit a wide range of sample environments including cryostats, fields and various detectors.

We use a eulerian geometry to drive the sample and detector positions, however these are not always the true motors, for example Chi is a composite of real motors kappa and kphi.

The Eulerian PDs used to drive the diffractometer angles are:

We typically operate the diffratometer in one of two geometries - Vertical or Horizontal.

Vertical Geometry

In this geometry the scattering plane is vertical in the lab frame. We rotate the detector arm (Delta) vertically as the 2theta angle, eta rotates the sample parallel to the plane (sample theta), chi rotates the sample perpendicular to the scattering plane and phi rotates the sample about the scattering plane.

An example specular reflection scan is:

pos delta c2th([0,0,12]) eta c2th([0,0,12])/2 chi 90 phi 0

Horizontal Geometry

In this geometry the scattering plane is horizontal in the lab frame. We rotate the detector axis (gamma) horizontally as the 2theta angle, mu rotates the sample parallel to the plane (sample theta), chi rotates the sample  perpendicular to the scattering plane and phi (chi=0) or eta (chi=90) rotates the sample about the scattering plane.

An example specular reflection scan is:

pos gamma c2th([0,0,12]) mu c2th([0,0,12])/2

The software Diffcalc is used to move the diffractometer directly in reciprocal space, based on the orientation of the crystal.

Diffcalc

The orientation of the crystal is determined by either setting Orientations manually (based on the visible surfaces of the crystal) or through finding and indexing Bragg reflections.

An example of the alignment commands is provided below:

Here the rotation matrices for the diffractometer are given, based on Euler rotation matrices.

The full sample rotation is an intrinsic rotation about the following axes:

1. mu right-handed rotation about x
2. eta left-handed rotation about z'
3. chi right-handed rotation about y''
4. phi left-handed rotation about z'''

Detectors:

1. gamma right-handed rotation about x
2. delta  left-hended rotation about z'

The following PDF document explains the rotations matrices:

Diffractometer Rotation Matrix

Freely available python code:

https://github.com/DanPorter/i16_diffractometer

If you have any comments, suggestions or corrections, please contact a member of the beamline staff.