Bridging the small-angle X-ray scattering–X-ray diffraction gap in disordered layered materials: the CLADIFFMOD unified framework

A unified multi-scale model is presented for the simultaneous description of small-angle X-ray scattering (SAXS) and X-ray diffraction (XRD) in disordered 2:1 clay minerals, providing a computationally tractable approximation that bridges the two analytical traditions under the tested experimental conditions. The total scattered intensity is expressed as a continuous physically consistent function of the scattering vector magnitude, decomposed into three physically distinct contributions: a polydisperse disc form factor governing the SAXS regime, a Monte Carlo implementation of the Drits–Tchoubar Markov-chain stacking model for basal 00 l reflections and a Debye equation turbostratic scattering term for in-plane hkl correlations. The three contributions are coupled through a sigmoid crossover approximation designed to provide a continuous transition between morphology-dominated and stacking-dominated scattering regimes. The crossover amplitude is measured directly from the experimental data and constitutes the primary coupling observable between morphological and crystallographic length scales. A critical innovation over existing approaches is the treatment of intra-stack heterogeneity: stacking sequences are generated layer by layer via a first-order Markov chain with transition matrix T . The model is validated against five experimental datasets acquired on an Na-montmorillonite reference under controlled relative humidity conditions. The framework is implemented in the open Python code CLADIFFMOD and is directly transferable to any 2:1 disordered clay mineral by substitution of the hydration-state dictionary and the Markov transition matrix.