Synthesis, investigation, structural and elastic properties of Mg$_{x}$Zn$_{1-x}$Fe$_{2}$O$_{4}$ nanoparticles

Magnesium-Zinc ferrite nanoparticles of different compositions are synthesized by using the sol-gel auto-combustion method with citric acid as a fuel. Structural characteristics were studied using X-ray diffraction technique and it confirms the formation of cubic spinel structure. The ferrite nanoparticle size of synthesized powder ranges from 22 – 24 nm. The effect of change in Mg$^{2+}$ content results in a change of the lattice parameter of ferrite nanoparticles. In the present paper, the structural parameters such as cation-cation and cation-anion distances, tetrahedral, octahedral bond lengths and bond angles, hopping lengths, shared, unshared tetrahedral, and octahedral edge are reported. FTIR spectra show two prominent peaks around 524 – 532 cm$^{-1}$ (tetrahedral site) and 409 – 432 cm$^{-1}$ (octahedral site) and the force constants of the octahedral and tetrahedral site of Mg–Zn ferrite were calculated. The elastic moduli and other factors such as longitudinal, transverse and mean velocity, Poisson ratio, and Debye temperature were determined.