spec - Local Sector 7 web page

¢¢¢¢Sector sSectors correspond to different symmetry transformations of (2θ , ω , χ , φ )and may beof help in avoiding blind spots. Sectors can also be useful for samples in cryostats orovens. All modes can have the positions chosen for the motors further influenced bythe choice of sector. However, the modes azimuth-fixed, alpha-fixed and betafixedonly allow sectors numbered zero through three, below.For a given pair of incident and scattered X-ray beams, k iand k f,there are eight orientationsof the crystal in the spectrometer that give the same scattering since theypresent equivalent projections to the incident and scattered beams. The eight orientationsare labeled as sectors 0 through 7.Four of the orientations come from the symmetries of a pair of vectors. They correspondto the identity operation (i.e., the current diffraction angles), a rotation of 180°about k i,arotation of 180° about the bisector of k iand k f,and a rotation about z by£180° θ. The last two symmetries are based on interchanging the role of theentrance angle and the exit angle of the X-rays on the sample. These four ¢ symmetriesgive sectors 0, 2, 4 and 6 in fourc. For each of these four positions another positioncan be obtained by increasing θ by 180°, ©¢£¢ ¥decreasing φ ° and changing thesign of χ. S¡¤£ ¥ §¥¨ ¡¤£ ¢§ ¢ ¥increased by 180. These orientations give sectors 1, 3, 5 and 7. Studying these operationsshows that sectors 2, 3, 6 and 7 have opposite signs of 2θ from the current position.Sectors 2, 3, 4 and 6 have flipped the up direction of the sample (normal to thescattering plane) to the down direction.¥£ ¥ ¢§ ¢£¢ ¥¥§ ¥¤£ ¥¡ ¤ θ and φ can beThe value of g_sect determines in which sector of reciprocal space the diffractometeroperates.The actual transformations of the angles are:0 1 2 3 4 5 6 7¢ ¢ 2θ → 2θ 2θω → ω ω 80°χ → χ¢ £¢ ¢ £¢ ££θθ 2θ 2θθθω 180° ω ω 180° ω ω ω 80°χ χχ χ 80° 180° χ 180° χ χ 80°φ → φ φ ¢ 80° φ ¢ φ 80° φ 80° ¢ φ ¢ φ 80° φ¢ ¢ ¢ ¢¢ ¢ ¢ ¢¢ ¢In addition, a sector 8 is defined that can be used when the χ and φ circles of thediffractometer are arc segments in contrast to the complete circle. Sector 8 minimizes⎪χ 0°⎪and ⎪φ ⎪.¤ ¢INTERIM WORK-IN-PROGRESS (8/16/01) NOT FOR GENERAL DISTRIBUTION FOUR-CIRCLE REFERENCE 173