An improved small-angle X-ray scattering analysis of δ′ precipitation in an Al–Li alloy for growth kinetic studies

An improved method for small-angle X-ray scattering (SAXS) data analysis is developed to reconstruct the free-form particle size distribution of δ′ precipitation in an Al–Li alloy. This improved method consists of four iterative steps; the interparticle interference is also included. The indirect transform method (ITM) plus a hard-sphere (HS) model which considers the depleted zones are used in the analysis of δ′ precipitation in an Al–Li alloy. Two parameters, namely the hard-sphere volume fraction, η_HS, and the ratio of hard-sphere radius to the particle radius, R_HS/R, which determine the structure factor of the interparticle effect, are iteratively calculated using the monodisperse assumption and Gaussian size distribution. These two parameters are finally used in reconstructing the particle size distribution by the ITM + HS method. This method is tested by analysing simulated SAXS data and shows a better agreement than found in similar studies. This improved method is applied to analyse a set of experimental SAXS intensities from δ′ (Al₃Li particles) precipitation in an Al–9.7 at.% Li alloy. The monodisperse results are compared with the polydisperse ITM + HS results. The current ITM + HS method fits the SAXS data better than the other methods. The variations of average radii with aging time were found to follow the kinetic power law. The SAXS results are used to investigate the theoretical kinetic model of the volume-fraction effect on late-stage coarsening (Ostwald ripening). By comparing both experimentally obtained asymptotic size distributions of δ′ particles as well as coarsening rate constants with those predicted by the various kinetic models, the modified Lifshitz–Slyozov–Wagner (MLSW) theory is found to be in better agreement with the experimental results than the other theories.