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Ferrite nanoparticles of Ni${}_{0.35}$Mn${}_{0.35}$Zn${}_{0.3}$Fe${}_{2-x}$Ce_xO₄ ferrite system were produced using sol–gel auto combustion technique. X-ray diffraction analysis confirms the single phase cubic spinel structure of the samples with space group Fd-3m. Replacement of Fe${}^{3+}$ ions by Ce${}^{3+}$ ions increases the lattice parameter 8.4105 Å to 8.4193. Average crystallite size obtained from Scherrer method varies from 21.73nm to 22.71nm with replacement of Fe${}^{3+}$ ions by Ce${}^{3+}$ ions. Williamson–Hall and strain-size plot analysis confirms the nanocrystalline nature of the samples and the micro-strain induced in the cubic crystals is of tensile type. Cation distribution suggests that Zn${}^{2+}$ ions occupy tetrahedral — A-site while Ni${}^{2+}$ ions occupy octahedral — B-site. Majority of the Mn${}^{2+}$ ions prefer A-site and majority of the Ce${}^{3+}$ ions replace Fe${}^{3+}$ ions at octahedral — B-site. High resolution transmission images confirm the homogeneity and nanoparticle nature of the samples. Two main characteristics absorption bands corresponding to spine structure are observed in the Fourier transmission infra-red spectra within the wavenumber range of 350–600cm${}^{-1}$. Stiffness constant, Young’s modulus, rigidity modulus, bulk modulus and Debye temperature were estimated using FTIR data. Debye temperature obtained from the Waldron equation varies from 676K to 692K with the addition of Ce${}^{3+}$ ions. Higher values of elastic moduli are suitable for industrial applications due to increased mechanical strength.

In the present work, Al${}^{3+}$ substituted cobalt ferrites (CoFe${}_{2-x}$Al_xO₄, $x=0.2$, 0.4, 0.6, 0.8) have been synthesized via standard solid-state reaction technique. The incorporation of Al${}^{3+}$ ions in cobalt ferrite has been shown to play an important role in modifying the magnetic properties. The room temperature (300K) ${}^{57}$Fe Mössbauer spectra reveals that the studied samples show two characteristic ferromagnetic zeeman sextets at A and B-sites at lower Al${}^{3+}$ ion concentration (i.e., up to $x=0.4$). However, a paramagnetic relaxation has been noted for higher Al${}^{3+}$ substitution (for $x=0.6$ and 0.8) samples. The dependence of the Mössbauer parameters such as isomer shift, quadrupole splitting, line width and magnetic hyperfine field on Al${}^{3+}$ ion concentration has also been noted. The variations in initial permeability over a wide frequency range (125kHz to 30MHz) at 300K have been recorded. The fairly constant values of initial permeability and the low values of the relative loss factor of the order of 10${}^{-4}$ to 10${}^{-5}$ over the wide frequency range are the important findings of the present work. The observed low values of relative loss factor at high frequencies suggest that the studied ferrites are promising materials to be used in microwave applications.

The influence of iron non-stoichiometry variation on structural, magnetic and dielectric properties in Cobalt ferrite is reported. Cobalt ferrite with compositional formula CoFe${}_{2\pm x}$O₄ ($x=0$, $\pm 0.02$) was prepared through sol-gel synthesis route and sintered at 900^oC/2h. X-ray diffraction confirms the phase evolution of ferrite with additional impurities belonging to $\alpha$-Fe₂O₃ phase and this additional phase disappears for iron deficient sample. The (311) peak shifts towards lower angle for the excess iron sample, whereas it shifts towards higher angle for iron deficient one, confirming the variation in the iron non-stoichiometry. Raman data substantiate the presence of vibrational bands assigned to metal ions in the cobalt ferrites. Change in the peak intensities and peak angle in Raman spectra clearly suggests the movement of cations among octahedral and tetrahedral sites leading to dilution of magnetic character of the samples. Saturation magnetization drastically drops by $\sim 20$% for iron rich and deficient samples but an improvement in coercivity for the iron deficient cobalt ferrite clearly hints the role of anisotropy. A change in dielectric constant value further alludes to the change of iron ions in different valency states.