A novel SAXS model for multi-texture systems: application to CaCO3 calcination using in-situ USAXS-SAXS-WAXS

SAXS models, used to calculate the micro-textural properties (porosity, specific surface, correlation length, correlation function) of porous materials, are especially relevant for in-situ material characterization. Certain classes of porous materials, including those generated during solid decompositions, are characterized by distinct regions with different micro-textures. Classical SAXS models cannot be applied directly to such multi-texture systems, thus a novel SAXS model for multi-texture systems is proposed in this work and validated by using measurements of micro-textural properties of a calcined CaCO3 powder, obtained using time-resolved in-situ synchrotron radiation USAXS, SAXS and WAXS data. The proposed model, in contrast to the direct application of classical SAXS models, is capable of correctly predicting the expected linear trend of the particle internal porosity with respect to the CaCO3 conversion and provides a complete description of the micro-textural properties, in very close agreement with experimental data available in the literature. In the reaction product region the correlation function, as well as the other micro-textural properties, is essentially constant during the solid decomposition, and is accurately represented by a two-parameter model. Based on the proposed SAXS model, a simplified expression of the differential scattering cross section, as a product of the CaO mass fraction times a time-independent function of the correlation function, is obtained; such expression can reliably predict the experimental scattering intensity profiles over time.