# A High Thermal Conductivity of MgO-H\({}_{2}\)O Nanofluid Prepared by Two-Step Technique
## 3 Results and Discussion  
### The Structural Studies  
Figure 2 shows the XRD spectrum used to analyze the crystalline structure of the obtained MgO nanopowder. The pattern shows an ordered polycrystalline structure with five intense peaks. The low intensity of the diffraction background was clearly indicative of the pure phase of the intended material. Therefore, no distinguishing peaks of any impurities were discovered. The surfactant SDS [CH\({}_{3}\)(CH\({}_{2}\))\({}_{11}\)OSO\({}_{3}\)Na] acts as a catalyst, preventing any fast reactions in the solution. In addition, it acts as a dispersion factor of the formed particles [72]. Hence, the synthesized material is of high purity, free of any secondary products, and nanoscale. The diffraction peaks at 20 values of 36.9271\({}^{\circ}\), 42.8937\({}^{\circ}\), 62.2626\({}^{\circ}\), 74.6169\({}^{\circ}\), and 78.5795\({}^{\circ}\) correspond to the crystalline planes of (111), (200), (220), (311), and (222), respectively. A strong preferential orientation was observed at a diffraction angle of 42.8937\({}^{\circ}\) with Miller indices (200). Similar results have been reported in the literature [73,74]. The specified X-ray peaks matched well with the crystallographic structure according to the JCPDS standard file no. 45-0946 of polycrystalline MgO. The crystallite size (D) was calculated based on the full width at half maximum (FWHM) of the intensive diffraction peak (i.e., the plane 200) by using the Debye-Scherrer's formula [75,76]:  
\[\text{D}=\frac{\text{A}\lambda}{(\text{FWHM})\cos\theta} \tag{4}\]where A is an empirical shape factor equal to 0.94, \(\lambda\) is the wavelength of the X-ray source, and \(\theta\) is the angular position of the diffraction peak. The crystallite size was calculated to be 22.78 nm. The sharp diffraction peaks indicated a high degree of crystallization. The nanostructure of the prepared MgO particles was also revealed by the average particle size of less than 100 nm. All the diffraction peaks of MgO nanopowder revealed an obvious shift towards lower 2\(\theta\) positions, as seen in Table 3. This result may be attributed to the nano scale of the prepared particles, whereas the high density of crystalline boundaries in the nano structure may cause microstrain. The lattice constant and the unit cell volume were estimated by using the Formulas (5) and (6) [75], respectively:  
\[\frac{1}{\text{d}^{2}{}_{\text{(hkl)}}}=\frac{\text{h}^{2}+\text{k}^{2}+\text{ l}^{2}}{\text{a}^{2}} \tag{5}\]  
\[\text{V}=\text{a}^{3} \tag{6}\]  
where d\({}_{\text{hkl}}\) is the interplanetary crystalline distance; h, k, and l are the Miller indices; and \"a\" is the lattice constant. From the results in Table 4, it can be noticed there is relative stretching in the d\({}_{\text{hkl}}\) spacing and lattice constant values as compared with the standard values, since the variation in both is approximately 0.0011 A of the interplanetary distance and 0.0023 A of lattice constant. Consequently, the volume of the unit cell showed relative enlargement, which might be due to the nanoscale of MgO particles. Figure 2: XRD pattern of MgO nanopowder prepared by the co-precipitation method. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Crystalline Planes (hkl)** & **C (111)** & **C (200)** & **C (220)** & **C (311)** & **C (222)** \\ \hline
**Measured (XRD)** & & & & & \\
**20 (deg.)** & & & & & \\
**Standard 20 (deg.) (JCPD S card** & & & & \\
**no. 45-0946)** & & & & & \\ \hline \end{tabular}
\end{table} 
Table 3: Positions of X-ray diffraction peaks (2\(\theta\)) of MgO nanopowder prepared by the co-precipitation. The elemental structure, purity, and surface morphology of the synthesized MgO nanostructure were tested using SEM and EDX techniques. The energy dispersive X-ray spectrum was achieved at the range of 0-10 keV, as shown in Figure 3a. One can clearly observe three evident bands at nearly 0.25 keV, 0.55 keV, and 1.3 keV which correspond to the elements of C, O, and Mg, respectively.