The Theta Scan

The common XRD method for surface orientation determination is based on the Bragg equation:

2⋅d⋅sin ϑ = n⋅λ,

which describes the relation between X-ray wavelength λ, lattice plane distance d, and the reflection glance angle ϑ. n indicates the diffraction order of the reflection, usually 1.

The angle between X-ray beam and detector is set to the reflection condition for a certain lattice plane that is given by the Bragg equation. To find the reflection, both X-ray and detector are moved coupled and simultaneously the sample is rotated. The direction of the lattice plane perpendicular is then calculated from the position of the reflection peak. There is no specific name for this method, thus we call it the "Theta Scan".

Theta Scan of the (0 0 12) reflection of a c-sapphire wafer; the barycenter of the peak is at 0.065° tilt.

Successful Theta Scans on at least two different lattice planes are needed to determine the complete crystal orientation. The reflections should be accessible to the diffractometer without moving the sample.

Advantages of this method are the relatively simple diffractometer alignment and its flexibility. The alignment can be calculated for each case using the Bragg equation, which is no problem as long as the material is known. There is virtually no limit to the measurable orientations. The possible resolution is only limited by the spectral width of the beam and the mechanical precision of the instrument. The disadvantages are the rather long measurement time (some minutes) and the problem of finding enough reflections.