  Stress measurement methods using X-ray diffraction (XRD methods) are based on
so-called fundamental equations. The fundamental equation is described in the
coordinate system that best suites the measurement situation, and, thus, making
a comparison between different XRD methods is not straightforward. However, by
using the diffraction vector representation, the fundamental equations of
different methods become identical. Furthermore, the differences between the
various XRD methods are in the choice of diffraction vectors and the way of
calculating the stress from the measured data. The stress calculation methods
can also be unified using the general least-squares method, which is a common
least-squares method of multivariate analysis. Thus, the only difference
between these methods turns out to be in the choice of the set of diffraction
vectors. In light of these ideas, we compare three commonly used XRD methods:
the sin^2 psi method, the XRD^2 method, and the cos alpha method using the
estimation of the measurement errors.

Materials Science