Microstructural investigation of plastically deformed Pb(1−x)Snxalloys: an X-ray profile-fitting approach

Abstract

A detailed X-ray line-profile analysis is presented on five compositions of Pb–Sn alloys in the face-centred cubic (f.c.c.) α phase. Analysis has been performed within the framework of the Warren–Averbach method and the Williamson–Hall method through a profile-fitting algorithm assuming a pseudo-Voigt (pV) profile shape function convoluted with an asymmetric function. The effect of cold-working on the alloys is analysed in terms of defect-related parameters and defect distribution. The alloys decompose beyond the composition Pb–13.2 at.% Sn. Cold-working produces very weak structural broadening in Pb–Sn alloys, along with negligible incidence of deformation-fault probability. However, the presence of the Sn-rich β phase enhances the fault probability. The plot of \ln \langle \varepsilon^2\rangle^{1/2}versus\ln L is a straight line and the slope is around −0.26 to −0.43, indicating that the strain-broadened profile is intermediate between a Gaussian and a Lorentzian profile. The origin of the `hook' effect in the size Fourier plot is attributed to non-Gaussian strain distribution or strain gradients in the diffracting columns. The effect of recovery is noticeable and is probably due to polygonization. Furthermore, the rate of recovery is greater in Pb–Sn alloys compared to Pb–Sb alloys for identical solute concentrations.