A model for out-of-phase boundary induced X-ray diffraction peak profile changes in Aurivillius oxide thin films

Layered crystal structures, such as the Ruddlesden-Popper and Aurivillius families of layered perovskites, have long been studied for their diverse range of functionalities. The Aurivillius family has been extensively studied for its ferroelectric properties and potential applications in various fields, including multiferroic memories. A new analytical model is presented here that explains how out-of-phase boundaries (OPBs) in epitaxial thin films of layered materials affect X-ray diffraction (XRD) peak profiles. This model predicts which diffraction peaks will split and the degree of splitting in terms of simple physical parameters that describe the nanostructure of the OPBs, specifically the structural displacement perpendicular to the layers when moving across the OPB, the angle made by the OPB at the thin-film-substrate interface, and the OPB periodicity and its statistical distribution. The model was applied to epitaxial thin films of two Aurivillius oxides, SrBi₂(Ta,Nb)O₉ (SBTN) and Bi₄Ti₃O₁₂ (BiT), and its predictions were compared with experimental XRD data for these materials. The results showed good agreement between the predicted and observed peak splitting as a function of OPB periodicity for SBTN and for an XRD profile taken from a BiT thin film containing a well characterized distribution of OPBs. These results have proven the model's validity and accuracy. The model provides a new framework for analysing and characterizing this class of defect structures in layered systems containing OPBs.