In making quantitative X-ray diffraction studies of quantities such as lattice parameters one generally treats the measured quantity as existing at the sample surface. In X-ray residual stress analyses; large lattice parameter gradients as a function of depth below the sample surface are sometimes encountered and the measured stress (as obtained from, these parameter measurements) is affected toy the fact that the X-ray beam penetrates the sample. In order to accurately evaluate residual stress as a function of depth, it is necessary to consider the "depth of penetration" of the X-ray beam.

The authors have treated this problem by considering the measured stress as an average weighted over the depths from which the diffracted information emanates. By using the observed lattice-parameter gradient as a first approximation, it is possible to set up a theoretical expression for the measured stress with the actual stress at the surface as the only unknown. By equating this to the measured value, it is possible to solve for the value at the surface and thus obtain an equation for the variation of lattice parameter as a function of depth. This process may be used reiteratively to improve the accuracy of the approximation. A specific example of the use of this equation will be presented.