Sample-curvature error in stress measurement made with an X-ray diffractometer

The effect of an arbitrary sample curvature on the centroid-shift and the broadening (variance) of a diffraction-line profile is discussed for the Seemann–Bohlin geometry of a diffractometer. The errors in stress measurement arising from the curvature of the sample surface are estimated. The shift of the centroid and, hence, the error in stress increase with increasing equatorial divergence and curvature of the sample. For example, for a cylinder of radius 10 mm, Δσ/K increases from 0.075° at 1° divergence to 0.32° at 2° divergence for ψ = 0°, 60° and Bragg angle 70°. The analysis helps one to choose the experimental parameters to keep the errors small; in case this is not possible, the expressions derived in this paper can be used to compute the correction factors. The position on the detector arm of the receiving slit corresponding to the minimum variance is different from that given by the Seemann–Bohlin para-focusing condition. However, the line-widths for the two positions do not differ appreciably.