The accuracy of stress measurement using the X-ray diffraction method

The accuracy of stress measurement using the X-ray diffraction method relies on both the accuracy of peak location and the goodness-of-fit of the assumed linear model that relates the peak shift to the specimen orientation. In the absence of systematic effects it is the uncertainty in peak location due to random counting statistics that provides the major source of error. This note derives an analytical expression to describe the effect of these counting statistics on the ultimate precision of diffraction peak location and hence derived stress value. The results are discussed with reference to the available instrumentation and used as a basis for optimizing the performance of a system that incorporates a linear position-sensitive proportional counter for stress measurement.