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.
- 4.4.1. - Omega Equals Zero (
g_mode = 0)