X-ray diffraction analysis for the determination of elastic properties of zinc-doped manganese spinel ferrite nanocrystals (Mn0.75Zn0.25Fe2O4), along with the determination of ionic radii, bond lengths, and hopping lengths

Zinc-doped manganese spinel ferrite nanocrystals with chemical formula Mn0.75Zn0.25Fe2O4 were synthesized by the chemical co-precipitation method. The structural properties of the synthesized nanoparticles were studied by X-ray diffraction analysis (XRD), whereas morphological analysis was performed by high-resolution transmission electron microscopy (HR-TEM) and scanning electron microscopy. The XRD study confirmed the formation of single-phase spinel face-centered cubic nanocrystals with an average size of approximately 19 nm. HR-TEM analysis gave an average particle size of approximately 15 nm, with the nanocrystals being almost spherical. The selected-area electron diffraction pattern obtained in the HR-TEM study clearly indicated the polycrystalline nature of the nanocrystals. The Fourier transform infrared spectrum confirmed the formation of a pure spinel ferrite structure. Williamson-Hall plot analysis, using the XRD data, was used to obtain information on the different elastic properties, such as residual strain, stress, and energy density, considering the uniform deformation model, the uniform stress deformation model, and the uniform deformation energy density model. The results were compared with the results obtained by the size-strain plot method. The XRD data were used to determine the lattice parameter, which was found to be 0.81 nm. With use of the calculated lattice parameter, the ionic radii, bond lengths of the tetrahedral and octahedral sites, and hopping lengths of the spinel ferrite nanocrystals were calculated. Finally, a magnetic study using a vibrating-sample magnetometer showed that the nanocrystal sample is superparamagnetic.