Small-angle scattering curves of densely packed particulate solids obtained by nucleation and growth kinetics

The computation of small-angle scattering (SAS) curves is still an open problem in densely packed systems. This fact reduces the applicability of SAS largely, in particular to solid-state densely packed systems. Solid-state transformations often follow nucleation and growth kinetics. In this case, even for isotropic growth the spherical symmetry of the precipitates is broken due to impingement, and their actual shape becomes unknown. However, in these systems the developed microstructure is given by the transformation kinetics. Because the SAS curve is given by the microstructure, the SAS curve should also be determined by the nucleation and growth protocol. In this work this link is revealed and the kinetics of the system is connected with the average radial density function. Statistical considerations allow us to determine the adequate inter-particle correlation function, enabling the computation of the SAS curve along the transformation. The formalism is applied to a system where grains appear randomly at initial time and grow with a constant growth rate (p-cell system). The resulting SAS curve at different times are computed and compared to Monte Carlo simulations, showing quantitative agreement for transformed fractions up to 95%.