Decoupling Strain and Crystallite Size Effects in Cerium Oxide Nanoparticles Using Williamson-Hall Analysis

Cerium oxide (CeO 2 ) nanoparticles synthesized through a co-precipitation route were characterized by X-ray powder diffraction (XRD), where peak broadening analysis was employed to estimate crystallite size, microstrain, stress, and deformation energy density. The Williamson-Hall (W-H) and Scherrer methods were employed to quantify crystallite size and lattice strain. To quantify strain and crystallite size effects, three Williamson-Hall models were employed: the isotropic strain model (W-H-ISM), anisotropic strain model (W-H-ASM), and energy density model (W-H-EDM). These models were applied to XRD-derived W-H plots, revealing distinct microstructural characteristics of the nanoparticles. The W-H-ISM provided an overall estimation of lattice strain, while the W-H-ASM accounted for crystallographic-direction-dependent strain variations. The W-H-EDM further correlated strain energy with defect density. This study advances the fundamental understanding of structure-property relationships in CeO 2 nanoparticles, providing critical insights for their tailored design in catalytic, energy storage, and advanced nanomaterial applications.