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Four-CircleModesAs noted above, because there are three Euler angles (θ , χ , φ )while the direction ofthe scattering vector Q is specified by only two angles, there is a degeneracy associatedwith the transformation from (H, K, L ) to (2θ,θ,χ,φ). The degeneracy isresolved in fourc by providing a constraint. In fourc, the different constraints arecalled modes. The value of the g_mode geometry parameter determines the prevailingmode.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 counter-clockwise rotation about thediffraction vector. The zero of ψ is determined by a reference vector, different fromthe diffraction vector. The azimuthal angle ψ is defined to be zero when this vector isin the diffraction plane.The angles α (ALPHA )and β (BETA )are defined such that the angles between theazimuthal reference vector and the incident and scattered X-rays are 90° ¢ α and90° ¢ β,respectively. One commonly used azimuthal reference vector is the sample’ssurface normal, which then makes α and β correspond to the incident and exit anglesof the X-rays on the surface.Omega Equals Zero (g_mode =0)The simplest constraint is ω =0.reached in this mode.Any (H, K, L ) with a small enough 2θ can beOmega Fixed (g_mode =1)In this mode ω is fixed to a finite value. Suppose you want to go the the (0, 0, 2) Braggreflection but with ω =10. You would then type2.FOURC> setmode 1Now using Omega-Fixed mode.3.FOURC> OMEGA=104.FOURC> br 0 0 25.FOURC>INTERIM WORK-IN-PROGRESS (8/16/01) NOT FOR GENERAL DISTRIBUTION FOUR-CIRCLE REFERENCE 169