X-Ray Diffraction Model for Spiral-Growth-Driven Defects in Layered Thin Films

Out-of-phase boundary (OPB) defects are a hallmark of spiral-driven growth in Aurivillius phase thin films, often arising from screw dislocation-mediated layer propagation. These boundaries are associated with localised strain gradients and modify polarisation and diffraction responses. Existing analytical XRD models that treat OPBs as planar or parallel features have limitations in capturing the vertical gradient in lattice displacement and the angular asymmetry observed in spiral-grown films. In this work, we introduce a generalised model that represents OPBs as stacked pyramidal defects along the film thickness, as observed in transmission electron microscopy (TEM) cross sections. The model incorporates a three dimensional structure factor formalism that accounts for atomic positions, fractional lattice displacements, the inclination of the OPB boundaries and other parameters. Simulated X-ray diffraction patterns based on this model reproduce the asymmetric peak broadening and splitting observed in Bi 4 Ti 3 O 12 thin films with high fidelity and enable a non-destructive estimation of OPB density, and a more realistic description of defect geometry than planar models allow. This work establishes a three-dimensional, predictive framework for spiralmediated OPB defects in layered ferroelectric oxides, offering a basis for defect engineering and materials optimisation in future memory and neuromorphic applications.