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Or ientation Matr ixAngle calculations for the four-circle diffractometer are described in detail in Busingand Levy. 2 Youmay also refer to that paper to learn how to calculate the orientationmatrix. The orientation matrix, UB, describes the sample orientation with respect tothe diffractometer angles. Given UB, itispossible to calculate the diffractometerangles (2θ , θ , χ , φ )necessary to rotate a particular scattering vector Q, indexed by(H, K, L ), into the diffraction position. The matrix B transforms the given (H, K, L )into an orthonormal coordinate system fixed in the crystal. The matrix U is the rotationmatrix that rotates the crystal’sreference frame into the spectrometer’s.The first step in constructing an appropriate orientation matrix is to enter the samplecrystal lattice parameters a, b, c, α, β and γ. 3 These are real-space parameters, asmight be found in Wychoff 4 or Pearson. 5 Use the macro setlat to assign values:1.FOURC> setlat 3.61 3.61 3.61 90 90 902.FOURC>Next, you must specify the sets of values of (2θ , θ , χ , φ )atwhich two Bragg reflectionsare in the diffracting position. One of these is called the primary reflection. Fourcensures that the values of (H, K, L )reported for the primary reflection agree (towithin a scale factor) with the values entered. However, because of experimentalerrors and/or uncertainties in the unit cell parameters, the values of (H, K, L )reported for the other Bragg reflection, called the secondary reflection, may not agreeperfectly with the entered values (although they should be close).Youcan use the or0 and or1 macros to enter the parameters for the primary and secondaryreflections, respectively. However, the or0 and or1 macros require that thediffractometer be moved to the associated reflections, as these macros use the currentangles and the entered (H, K, L )inthe calculation of the orientation matrix. Alternatively,you can use the setor0 and setor1 macros, which prompt for both (H, K, L )and the angles that define the orientation matrix, without moving the spectrometerto the given settings.2 W. R.Busing and H .A. Levy, Acta Cryst. 22, 457 (1967). Note however, that this paper uses right-handedcoordinates systems and left-handed rotations for all rotations except for χ, which is right-handed.3 The conventional symbols for the crystal lattice angles include α and β. These angles are unrelated to theorientation angles α and β defined in the introduction. The different meanings should be clear from context.4 R. W.G.Wychoff, Crystal Structures (Wiley, New York, 1964).5 P. Villars and L.D. Calvert, Pearson’s Handbook of Crystallographic Data for Intermetallic Phases (AmericanSociety for Metals, Metals Park, Ohio, 1985).168 FOUR-CIRCLE REFERENCE INTERIM WORK-IN-PROGRESS (8/16/01) NOT FOR GENERAL DISTRIBUTION