# Fluctuating XRD Sapphire Intensity

A few months back my colleagues and I are facing a problem where the intensity of our sapphire peak fluctuates every time an XRD phase analysis was done, even when the scan was done on the same sample.

By accident, I found that the orientation of the sapphire substrate with respect to phi axis somehow plays a part in the situation.

So, I decided to do a scan following the procedure below:
1. Moved the 2-theta to the diffraction angle of (30-30) plane of my sapphire substrate, which is ~68.3 degrees
2. As this is a symmetric scan, omega has been rotated to ~34.2 degrees
3. Shutter was opened, and the phi axis has been rotated 360 degrees

Below is the result:

It can be seen that although 2-theta has been placed at the diffraction angle of the sapphire substrate, diffraction only occurs at two main regions in phi, which are approximately:
1. -63 to -12 degrees
2. 85 to 140 degrees

For now, only samples with sapphire substrates have this kind of problem. It is not known if other samples involving silicon or GaAs substrates have the same issue.

Can anyone help explain the theory behind this observation?

Thank you

Sapphire peaks are very sharp, so even a slight misalignment will kill your intensity. It looks as if you tried to perform an azimuth scan, i.e. rotate the crystal about the Bragg planes while keeping the Bragg peak aligned. This will work only if the reciprocal lattice vector is aligned *exactly* along the phi axis of rotation. In practice that is a bit difficult to achieve. If there is some misalignment, then phi couples to the Bragg angle and you combine a rocking curve scan and an azimuth scan. If you carefully examine your UB matrix you can probably determine the angle of misalignment.

You might try to step phi in, say, steps of 5 degrees and perform a rocking curve scan at each value of phi. The integrated intensity of the rocking curve scans should not very - at least not strongly.

Sapphire peaks are very sharp, so even a slight misalignment will kill your intensity. It looks as if you tried to perform an azimuth scan, i.e. rotate the crystal about the Bragg planes while keeping the Bragg peak aligned. This will work only if the reciprocal lattice vector is aligned *exactly* along the phi axis of rotation. In practice that is a bit difficult to achieve. If there is some misalignment, then phi couples to the Bragg angle and you combine a rocking curve scan and an azimuth scan. If you carefully examine your UB matrix you can probably determine the angle of misalignment.

You might try to step phi in, say, steps of 5 degrees and perform a rocking curve scan at each value of phi. The integrated intensity of the rocking curve scans should not very - at least not strongly.
Million thanks for the reply and explanation.
1. I did not realise that this is an azimuth scan.
2. Since this result, we have always align the phi axis to the angle with the best intensity before performing phase analysis scans.
3. I am sorry, M Quack, but can you explain the term UB matrix? Thank you.

The UB matrix is actually the product of two matrices, U and B.

B performs the transformation from HKL coordinates to an orthonormal coordinate system of reciprocal space with the c-axis along z. For cubic crystals B is just (2pi/a, 0,0; 0, 2pi/a, 0; 0,0,2pi/a). For hexagonal it is not diagonal because the angle between the a* and b* axes is not 90 deg, and so on. It depends only on the lattice parameters a,b,c and lattice angles alpha, beta, gamma.

U is a rotation matrix that describes how the crystal is oriented relative to the innermost rotation axis of your diffractometer. If your sample is mounted on a goniometer head on the phi axis, then tweaking the goniometer head tilts will modify the matrix U.

This is described in most books about x-ray diffraction, but I highly recommend reading the original article by Busing and Levy:

Acta Cryst. (1967). 22, 457-464 [ doi:10.1107/S0365110X67000970 ]
Angle calculations for 3- and 4-circle X-ray and neutron diffractometers
W. R. Busing and H. A. Levy

http://scripts.iucr.org/cgi-bin/paper?a05492

The UB matrix is actually the product of two matrices, U and B.

B performs the transformation from HKL coordinates to an orthonormal coordinate system of reciprocal space with the c-axis along z. For cubic crystals B is just (2pi/a, 0,0; 0, 2pi/a, 0; 0,0,2pi/a). For hexagonal it is not diagonal because the angle between the a* and b* axes is not 90 deg, and so on. It depends only on the lattice parameters a,b,c and lattice angles alpha, beta, gamma.

U is a rotation matrix that describes how the crystal is oriented relative to the innermost rotation axis of your diffractometer. If your sample is mounted on a goniometer head on the phi axis, then tweaking the goniometer head tilts will modify the matrix U.

This is described in most books about x-ray diffraction, but I highly recommend reading the original article by Busing and Levy:

Acta Cryst. (1967). 22, 457-464 [ doi:10.1107/S0365110X67000970 ]
Angle calculations for 3- and 4-circle X-ray and neutron diffractometers
W. R. Busing and H. A. Levy

http://scripts.iucr.org/cgi-bin/paper?a05492
Thank you for introducing the UB matrix. Somehow I am not aware of this.

The literature is very interesting, although I may have to digest the contents slowly.