<b>Structural and Microstructural Characterization of Cu-Doped NiFe<sub>2</sub>O<sub>4</sub> Nanoparticles Using Williamson-Hall Method</b>

In this study report, Cu-doped ferrite nanoparticles (CuxNi1-xFe2O4), which are normally the size of less than 100 nanometers were achieved using the sol-gel method. This method consists of using citric acid as fuel, which leads to auto combustion. In this report, the samples mentioned above will be analyzed using the following techniques (XRD, FESEM, EDX), where X-ray diffraction indicated that the specimens consist of spinel phase with face-centered cubic (FCC) structure. The results showed the lattice constant of the material increased from (8.320) Å to (8.323) Å, which indicated fact that the ionic radius of copper (72) Å has a bigger size than the ionic radius of nickel (69) Å which led to an increase in the lattice constant, the crystal size was measured using Scherrer method with the three Williamson Hall models. First, the Williamson Hall Uniform Deformation Model (UDM), second Williamson Hall Uniform Stress Model (USDM), and third Williamson Hall Uniform Deformation Energy Density Model (UDEDM). All these models adapted to define the characteristics related to stress (σ), internal tendance (ε), and deformation energy density (U). The calculated size was compared by the two methods where the crystal size ranged from (19 - 55) nm, and the phenomenon of crystal expansion due to positive stress was observed through the positive slop that appeared in the Williamson Hall models The sample taken was examined further with it morphology character using the method known field emission scanning electron microscopy This has confirmed that the particle shape to be of spherical or sub-spherical, and the size of particle to be within the nano range. The energy-dispersive X-ray spectroscopy indicated that no other new elements resulted from this compound