SMALL-ANGLE SCATTERING FROM PRECIPITATES - ANALYSIS BY USE OF A POLYDISPERSE HARD-SPHERE MODEL

A general polydisperse hard-sphere model for analyzing small-angle-scattering data from spherical precipitates in alloys is presented. In the model the size distribution is chosen as a Weibull density distribution and the hard-sphere interaction radius is taken as being proportional to the radius of the precipitates. The Weibull distribution is monomodal, and depending on the parameters describing the distribution, it can skew to either side. Small-angle x-ray- and neutron-scattering data, taken from the literature, from spherical delta' precipitates in Al-Li alloys have been analyzed with the model. It gives very good fits to the experimental data and the results are in agreement with a Li content of 25% in the precipitates. The concentration of Li in the matrix is also in good agreement with the phase diagram of Al-Li found in the literature. Results from the application of a monodisperse hard-sphere model are presented and previous, erroneous, interpretations of the model, found in the literature, are corrected. Finally, the systematic errors from applying a monodisperse model to scattering data from a polydisperse system are investigated, by analyzing simulated data.