A hierarchical additive framework is developed for the quantitative interpretation of X-ray scattering (SAXS) from lamellar crystalline materials. The formulation extends the classical decomposition I(q) = P(q)S(q), with I(q) the scattering intensity, P(q) the form factor, and S(q) the structure factor, by explicitly coupling the contributions of three structural regimes: low-q power-law (fractal-like) aggregation, intermediate-q Guinier curvature arising from finite nanocrystal dimensions, and high-q Bragg reflections associated with lamellar periodicity. Each regime is expressed analytically and linked through shared structural parameters, ensuring physical consistency across length scales. The scattering intensity is interpreted as the Fourier transform of the electron-density correlation function, following Debye’s original formulation (Debye, 1915), which naturally accommodates cross-correlations between internal morphology and interparticle organization. Simulated scattering profiles illustrate how parameter variations influence the overall signature, and the model is applied to synchrotron SAXS data from cocoa-butter triacylglycerols to demonstrate practical fitting performance. The resulting approach provides a compact and physically rigorous description of hierarchical lamellar systems and offers a generalizable framework for complex materials in which form and structure factors cannot be treated independently.
Marangoni et al. (Mon,) studied this question.