In this paper, Mn0.3−xMgxCu0.2Zn0.5Fe3O4 (x = 0.00, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30) nanoparticles were prepared by the nitrate-citrate technique at low temperature. The structural, microstructural, magnetic and elastic properties of the samples were characterized by X-ray diffraction (XRD), Fourier-transform infrared spectroscopy, Transmission electron microscopy, field emission-scanning electron microscopy and vibrating-sample magnetometer at room temperature. Rietveld refinement of the XRD patterns indicated the formation of the single phase cubic spinel structure (space group Fd-3m) without any detectable impurity phase in all the samples that also was confirmed by FTIR studies. The lattice parameter is found to increase non-monotonically with an increase in Mg ion concentration. Also, the bond lengths and bond angles (A and B sites) of the studied ferrites were calculated by the refining of the XRD data. The values of the crystallite size decrease with increasing micro-strain (and conversely) and both of them reach extremum at x = 0.15. The low remanence and coercivity values confirmed the formation of the superparamagnetic ferrites nanoparticles. The saturation magnetization of the samples gradually grows with Mg substitution and reach extremum at x = 0.15. Variation of saturation magnetization with Mg content can be mainly attributed to change of cation distribution, and Yafet-Kittel angle occurred between magnetic moments on B-site in the samples. The values of Young's modulus, Debye temperature, bulk modulus, rigidity modulus of the samples were determined by the values of elastic constant and wave velocities obtained from the force constants. The improvement of the elastic properties of sample x = 0.05 could be explained regarding the smaller values of the lattice parameter (a), the bond length and angle and the smaller crystallite size.
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