Error in 2π from single-crystal diffractometers due to sample absorption in a divergent primary beam

The primary-beam divergence of an X-ray four-circle diffractometer is the source of an error in the measured scattering angles from absorbing single crystals. A correction for this error is included in a least-squares program for lattice-constant determination. It is shown with α-LiIO₃ as an example that both accuracy and precision are enhanced. The 2θ corrections are typically as large as 0.03° for a spherical crystal with μR = 1.5 and R = 0.15 mm. The results indicate an obtainable accuracy of about 0.02% in lattice constants even if μR≳1.