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A general normal-beam equatorial diffractometer, with no restrictions on the orientations of the goniometer axes, such as collinearity of the axes \boldphi and \boldtheta, or \boldomega and \boldtheta, is described. The geometries of this type of unrestricted equatorial normal-beam diffractometer can be unequiv­ocally defined by four angular parameters. Analytical solutions of the goniometer equation and intergeo­metrical angle transformations, as well as a routine reflection-scan procedure, unaffected by the goniometer offsets, are presented, along with aplications of the unrestricted normal-beam equatorial diffractometer.
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