The analysis of X-ray diffraction profiles from imperfect solids by an application of convolution relations

In this investigation an attempt has been made to correlate the experimentally observed X-ray diffraction profile from imperfect solids with the one obtained theoretically from an approach of simultaneous convolution of the true diffraction profile resulting from the imperfection content of the materials and the instrumental profile, considering realistic distribution functions. The expressions for the intensity distributions are derived from the simultaneous convolution of Schoening's true profile (originating from the Gaussian strain profile and the Cauchy crystallite-size profile) and the instrumental profile having either Gaussian or Cauchy functional forms, and the theoretical forms are compared to those observed from some silver- and copper-base cold-worked alloys and vapour-deposited thin silver films. The agreement is fairly good for both first- and second-order reflections with small deviations in the tail region, which may arise from uncertainty in the background-level estimation, consideration of functions purely symmetrical in form and neglect of absorption and TDS effects. A further agreement of Schoening's true profile with Stokes's corrected deconvoluted true profile implies the validity of Schoening's approximation.