A comparative approach for estimating microstructural characteristics of BaTi1−xZrxO3 (0.0 ≤ x ≤ 0.3) nanoparticles via X-ray diffraction patterns

Abstract

Barium titanate materials are currently a special topic for scientific research due to their effective technological applications. The tetragonal BaTi_1-xZr_xO₃ (0.0 ≤ x ≤ 0.3) nanoparticles (NPs) were synthesized using a modified citrate technique. The current work provides a comparative approach for the calculation of crystallite size, stress, strain, and elastic characteristics based on X-ray diffraction (XRD) patterns. Various models have been developed to analyze XRD data; these models differ in their assumptions, mathematical approaches, and the type of information they provide. The Scherrer model ignores lattice micro-structures that develop in nanostructures, such as intrinsic strain. To overcome such drawbacks, three Williamson-Hall models, (the uniform deformation model (UDM)), the uniform stress deformation model (USDM), and the uniform deformation energy density model (UDEDM) have been discussed. According to the USDM model, with increasing Zr ion concentrations, interplanar space increases, causing a drop in Young’s modulus. All the previous approaches take into account the diffraction angle (2θ)-dependent peak broadening, which is thought to represent a combination of size and strain-driven induced broadening.

Graphical Abstract