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By parametrizing the conic surfaces spanned by the reciprocal-lattice vector under the action of the rotation axes, a new procedure for angle calculations for a diffractometer is presented. It is applied to obtain angle settings in various modes for a newly developed sixcircle diffractometer.

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By transforming the Takagi equations into a representation using angular coordinates, it is in principle possible to obtain analytical expressions for the coefficients in a series expansion for the primary extinction factor in perfect crystals with a circular diffraction plane. In practice, it has been possible to obtain the first five terms in the expansion. This involves establishing recurrence relations for the families of Bragg and Laue boundaryvalue Green functions combined with integrations over the entrance and exit surfaces. The calculations, which cover the whole range of values for the scattering angle, Ooh, are performed using the mathematical software systems Mathematica and Maple.

Expressions for the x-ray attenuation factor in homogeneous samples with circular cross sections (cylinders and spheres) have been derived. Depending on sample radius, detection geometry and absorption properties, the values of the attenuation factor may significantly differ from those obtained from the commonly assigned model for sample geometry: the semi-infinite slab. As shown, the obtained expressions may serve as a base for more elaborate correction procedures relating to self-absorption in EXAFS fluorescence measurements.