A method is described for determining the magnitude and sense of systematic errors in x-ray diffractometer stress measurements produced by focusing aberrations during diffraction from imperfect specimen contours and wide horizontal beam divergences. Corrections for such systematic errors are presently not made. However, if the highest accuracy and/or absolute values of stress are desired, these must be either taken into account or minimized by control of beam geometry. Equations and computer data are presented to indicate the errors in 2θ and stress (σ) resulting from use of flat, various convex and concave curvatures for primary beam divergences of 1° to 3°, Stress errors are calculated for both the parafocus technique of beam focusing and the stationary or non-focusing method.

The results show that convex and flat specimens always produce negative 2θ deviations from the condition of perfect focus and thus a net positive or tensile stress error. The magnitude of this error increases as the radius of the convex shape decreases and/or the ψangle and beam divergence is increased. Concave specimens with curvatures less than the radius of the concave shape required for perfect focus (see body of report) produce positive 2θ deviations and, therefore, negative or com-pressive stress errors.

The stationary or non-focusing technique produced systematic errors which were 1/3 of those produced by focusing aberrations with the parafocus technique. Fortunately, in both cases the actual errors are not very large (less than ±7.5 ksi), even with divergent beams as large as 3° and convex radii as small as 125”.