Nanosized CuFe2O4 ferrite was synthesized through the sol-gel self-combustion technique, using iron and copper nitrates with citric acid as fuel. The synthesized ferrite was subsequently analyzed using X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), and Scanning Electron Microscopy (SEM). X-ray diffraction studies validated the crystalline nature of the CuFe2O4, identifying it as having a mixed spinel structure within the Fd3m space group. Particle sizes were quantified using several methods including Debye-Scherrer, Williamson-Hall, Halder-Wagner, modified Debye-Scherrer, and size-strain plot (SSP), with all methods indicating a consistent average particle size of 28 nm. The elastic properties of the nanoparticles were extensively characterized, utilizing both diffraction line broadening (via the Williamson-Hall method) and Fourier-transform infrared spectroscopy (FTIR) to evaluate the materials' structural dynamics. Additionally, microstrain within the crystal lattice and various elastic constants, such as Young's modulus, Shear modulus, Debye temperature, and the velocities of longitudinal and transverse wave propagation were calculated. An electron density distribution was also constructed from the X-ray diffraction data, providing insight into the electronic environment and bonding characteristics of the material.
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