Anisotropic diffraction of materials with fibre symmetry: application to chitin cuticle.

Understanding the structure-function relationships in anisotropic fibre-symmetric materials is critical for both biological insight and bioinspired design. We present a generalized analytical model for X-ray diffraction intensity from nanofibrillar materials with fibre symmetry, accommodating arbitrary diffraction rings beyond prior axial and equatorial limits. This model integrates 3D orientation, strain heterogeneity and angular misalignment effects, and is validated using wide-angle X-ray diffraction (WAXD) from the Bouligand-structured cuticle of the mantis shrimp (Odontodactylus scyllarus). Using scanning synchrotron WAXD, we extract depth-averaged and sub-lamellar information on 3D fibre orientation and crystalline parameters from 2D scans. Model simulations and experimental fits show accurate reconstruction of the Bouligand texture and reveal spatial gradients in orientation, strain and angular dispersion. By fitting multiple reflections - axial (002), equatorial (110) and intermediate (013) - we improve the robustness in parameter extraction, especially in regions where the Ewald condition is partially satisfied. Our framework enhances the interpretation of WAXD in heterogeneous fibre-based materials and can be embedded into advanced tomographic or machine-learning workflows. This approach is applicable to a broad class of biological and synthetic composites, facilitating high-throughput structural characterization in scenarios where rotation is impractical or impossible.