Comparative estimation of elastic properties of synthesized Dy-doped cobalt ferrites using X-ray diffraction line-profile analysis

Abstract Because the physical properties of nanoparticles are strongly influenced by their crystal structure, crystallite size, and lattice strain, the determination of these parameters is an important aspect of nanomaterial characterization. Consequently, the evaluation and comparison of X-ray diffraction line-broadening methods remain important for obtaining reliable estimates of crystallite size and microstrain. Using the solgel autocombustion method, cobalt ferrites nanoparticles doped with Dy³⁺ ions CoDy x Fe 2− x O 4 (0.00 $$\: \le\:x\le\:$$ 0.08) with a step size of 0.02 were synthesized. X-ray diffraction (XRD) was used to investigate the structural properties. The face-centered cubic crystal structure and purity are validated by XRD patterns. The lattice constant rises from 0.8357 to 0.8367 nm due to doping of Dy³⁺ ions. The crystallite size displayed a composition-dependent, non-monotonic trend with Dy³⁺ substitution, suggesting the combined influence of lattice strain, defect formation, and crystallization kinetics. The size-strain plot (SSP) approach and modified versions of W-H analysis (UDM, USDM, and UDEDM) were used to examine the mechanical characteristics, including stress, strain, and energy density, using X-ray broadening. The outcome verifies that the substitution of Dy³⁺ ions causes an increase in the tensile type strain that was created in the crystal lattice. Compared to other procedures, the Scherrer method yields a lower crystallite size. The lattice distortions were sufficiently minimal for all models to produce consistent results; hence, the model selection for the W-H approach had no discernible impact on the final result. While the crystallite size was roughly 1.5-fold smaller, the value of strain calculated by the SSP approach was 3-fold higher than that found by the W-H method.