In the present study, the synthesis, using the wet co-precipitation method, and characterization of Mg1/3Ni1/3Co1/3Fe2-xGdxO4\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\left({\mathrm{Mg}}_{1/3}{\mathrm{Ni}}_{1/3}{\mathrm{Co}}_{1/3}\right){\mathrm{Fe}}_{2-x}{\mathrm{Gd}}_{x}{O}_{4}$$\end{document}, with x = 0.00, 0.02 and 0.08 wt% nanoparticles were reported. The X-ray powder diffraction (XRD) and transmission electron microscopy (TEM) confirm the formation of nano-spinel ferrite. The crystallite size of Mg1/3Ni1/3Co1/3Fe2-xGdxO4\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\left({\mathrm{Mg}}_{1/3}{\mathrm{Ni}}_{1/3}{\mathrm{Co}}_{1/3}\right){\mathrm{Fe}}_{2-x}{\mathrm{Gd}}_{x}{\mathrm{O}}_{4}$$\end{document} nanoparticles decreased, resulting from the microstrain induced by Gd3+ substitution. However, the lattice parameter “a” increased, in agreement with the difference between the ionic radii of Fe3+ and Gd3+ ions. X-ray photoelectric spectroscopy (XPS) measurements were conducted to verify the elemental composition, valency, and cationic distribution. Furthermore, Fourier-Transform Infrared spectroscopy (FTIR) was used in combination with XPS to estimate the force constants, elasticity parameters, and Debye temperature. Vickers microhardness measurements were carried out to investigate the mechanical behavior of the prepared samples and determine Young’s modulus. The values of Young’s modulus obtained from the microhardness measurements are larger than those obtained from FTIR measurements. However, the results, obtained from both techniques, showed an enhancement with Gd3+ doping.
