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4.4. - Four-Circle Modes



As noted above, because there are three Euler angles (,,) 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 (2,,,). 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 is defined as = - (2)/2, and is referred to as OMEGA.

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

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


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