## 4 Discussion  
In this investigation, the egg white mediated green synthesis brought about the formation of Cu\({}_{1.5}\)Mn\({}_{1.5}\)O\({}_{4}\) NPs as a single phase, and the mean average crystallite was approximately 75 nm. However, it can be seen from Table 1 that there is micro-strain and dislocation in the crystal lattice of Cu\({}_{1.5}\)Mn\({}_{1.5}\)O\({}_{4}\) NPs. A dislocation inside a crystal structure is a crystallographic defect (slight misalignment), which greatly affects the properties of materials. The standard atomic array of the perfect crystals is skewed by this defect [22; 23; 24; 25; 32; 33; 34]. Within the crystal lattices, the strain confirms the existence of defects. In addition, the XRD and FTIR studies confirm that Cu\({}_{1.5}\)Mn\({}_{1.5}\)O\({}_{4}\) NPs have a single-spinel structure. Furthermore, Cu\({}_{1.5}\)Mn\({}_{1.5}\)O\({}_{4}\) NPs can be prepared via a solid state reaction between Cu and Mn oxides via a ceramic path [15; 17; 18]. At the beginning of the solid state relation between unreacted Cu and Mn oxides, a thin layer of the copper manganite is formed to cover the unreacted oxides and prevent these oxides from interacting together. This thin layer acts as an energy barrier that must be overcome by the diffusion process to achieve the complete conversion of the unreacted oxides into Cu\({}_{1.5}\)Mn\({}_{1.5}\)O\({}_{4}\) NPs. In other words, the counter-diffusion of copper and manganese ions through a relatively rigid manganite film about the surface of Cu and Mn oxides led to the formation of particles of Cu\({}_{1.5}\)Mn\({}_{1.5}\)O\({}_{4}\). Furthermore, by reacting with manganese ions, oxygen passes through the reacted region to be added to the CuO interface and form spinel. Indeed, techniques such as the route of preparation can be used to facilitate this diffusion [15; 17]. Copper manganite (Cu\({}_{1.5}\)Mn\({}_{1.5}\)O\({}_{4}\)) formation occurs according to the following stoichiometric reaction:  
\[6\text{CuO}+3\text{Mn}_{2}\text{O}_{3}+0.5\text{O}_{2}\to 4\text{Cu}_{1.5} \text{Mn}_{1.5}\text{O}_{4} \tag{4}\]presence of a stabilizing agent [18; 36; 37; 38]. These researchers confirmed abundant Cu\({}^{+}\) and Mn\({}^{4+}\) cations according to the following reaction:  
\[\text{Cu}^{2+}+\text{Mn}^{3+}\rightarrow\text{Cu}^{+}+\text{Mn}^{4+} \tag{5}\]  
It was recently confirmed that it was not possible to prepare a pure cubic spinel Cu\({}_{1.5}\)Mn\({}_{1.5}\)O\({}_{4}\) phase [39; 40; 41; 42; 43]. Many other authors mentioned that during the sintering phase of Cu-containing spinel materials, Cu\({}^{+}\) can be produced. Any oxidation of Cu\({}^{+}\) to Cu\({}^{2+}\) on cooling in air does not allow the residual CuO to be incorporated into the spinel material [15; 42]. This action led to the coexistence of Cu\({}_{1.5}\)Mn\({}_{1.5}\)O\({}_{4}\) and CuO as a second phase. Similar results were observed in our previous works, which indicate the formation of Cu\({}_{1.5}\)Mn\({}_{1.5}\)O\({}_{4}\) with both CuO or Mn\({}_{2}\)O\({}_{3}\) by using the ceramic method with and without glycine via the thermal treatment of calculated amounts of copper nitrate and different manganese precursors [14; 15]. The glycine assisted combustion route followed by heating treatment at 900 \({}^{\circ}\)C for a mixture of copper and manganese nitrates resulted in the formation of Cu\({}_{1.5}\)Mn\({}_{1.5}\)O\({}_{4}\) with Mn\({}_{2}\)O\({}_{3}\) as a second phase [14]. Additionally, the heat treatment at 800 \({}^{\circ}\)C for a mixture of copper nitrate and manganese carbonate brought about the production of Cu\({}_{1.5}\)Mn\({}_{1.5}\)O\({}_{4}\) and Mn\({}_{2}\)O\({}_{3}\) crystallites [15]. However, in this study, the presence of 5 mL egg white inhibited the oxidation of Cu\({}^{+}\) to Cu\({}^{2+}\), yielding Cu\({}_{1.5}\)Mn\({}_{1.5}\)O\({}_{4}\) without the appearance of any secondary phase. This does not negate the presence of Cu\({}^{2+}\) ions, especially at octahedral sites.