spec

Software for Diffraction

4.4. - Four-Circle Modes



As noted above, because there are three Euler angles (θ,χ,φ) while the direction of the scattering vector Q is specified by only two angles, there is a degeneracy associated with the transformation from (H,K,L) to (2θ,θ,χ,φ). The degeneracy is resolved in fourc by providing a constraint. In fourc, the different constraints are called modes. The value of the g_mode geometry parameter determines the prevailing mode.

Fourc defines several angles in order to specify certain of the modes.

The angle ω is defined as ω = θ - (2θ)/2, and is referred to as OMEGA.

The angle ψ (referred to as AZIMUTH) specifies a clockwise rotation about the diffraction vector. The zero of ψ is determined by a reference vector, different from the diffraction vector. The azimuthal angle ψ is defined to be zero when this vector is in the diffraction plane.

The angles α (ALPHA) and β (BETA) are defined such that the angles between the azimuthal reference vector and the incident and scattered X-rays are 90°-α and 90°-β, respectively. One commonly used azimuthal reference vector is the sample's surface normal, which then makes α and β correspond to the incident and exit angles of the X-rays on the surface.