The control of geometrical sources of error in X-ray diffraction applied to stress analysis

In order to achieve accurate measurements in X-ray stress analysis it is necessary to control most sources of error involved in this technique. These errors may originate from poor knowledge of the material characteristics such as X-ray elastic constants and preferred orientation, as well as the lack of control of instrumental conditions such as goniometer adjustment, peak location and counting statistics. The present work is a contribution to the implementation of a standard procedure and deals with the main geometrical sources of error which can easily appear in such measurements. This paper presents the basic principles from which these errors have been calculated for both Ω and Ψ goniometers. The results of this calculation are contained in a few equations giving the incident X-ray beam-spot displacement on the sample and the diffraction peak shift as a function of the ψ tilting angle for both missettings of the sample surface and of the incident beam with respect to the ψ rotation axis. The effect on the calculated stress value can be deduced from these data. Experiments which have been carried out to validate the calculated results show very good agreement between theoretical and experimental values. From these results the Ω goniometer appears to be the less sensitive to these geometrical errors, provided that measurements are carried out with only positive ψ tilting values. The Ψ goniometer is a little more sensitive to these errors, but the resulting error on the calculated stress has the same absolute value for both positive and negative ψ values. These equations can be used to obtain very good goniometer adjustments for laboratory apparatus as well as for portable equipment.