## 3 Results and Discussion
### Structural Analysis
#### 3.1.1 X-ray Diffraction  
X-ray diffractograms of Al-doped CuO films grown via spray pyrolysis with varying Al concentrations (0.00, 0.50, 0.75 and 1.00%) are displayed Figure 1.  
Two well-defined and sharp peaks are visible, representative of the polycrystalline structure of the deposited films. The most noticeable peaks are observed at 35.59\({}^{\circ}\) and 39.11\({}^{\circ}\) of the Al:CuO films which correspond to the monoclinic crystal structure of CuO phase alongside the (002) and (111) planes, in accordance with standard data reference (JCPDS card N\({}^{\circ}\) 045-0937) and in good agreement with literature [16]. The crystal structure of CuO is monoclinic with four CuO units in the unit cell. The primitive cell contains two CuO units with the long direction parallel to the crystallographic c-axis. It is also noteworthy to mention that, as Al doping increases, the intensity of the peaks increases gradually and considerably, indicating that Al favours grain growth and enhances the crystallinity of the parent-phase CuO. Meanwhile, no additional peaks are detected, thereby demonstrating that doping CuO with a small quantity of Al stabilizes the phase stability and its purity. Direct observation of the film via electronic microscopy revealed no other secondary phases. All lattice constants (\(a\), \(b\) and \(c\)) are determined by using the following equations:  
\[\frac{1}{d_{\mathrm{RJ}}^{2}}=\frac{h^{2}}{a^{2}sin^{2}\beta}+\frac{k^{2}}{b^ {2}}+\frac{l^{2}}{c^{2}sin^{2}\beta}-\frac{2 hlcos\beta}{a\ c\ sin^{2}\beta} \tag{1}\]  
Figure 1: XRD of pure and Al-doped CuO films grown at 350 \({}^{\circ}\)C via spray pyrolysis. \[\lambda=2\ d\sin\theta \tag{2}\]  
Of course, \(h\), \(k\) and \(l\) are the Miller indices, while \(d\) is the lattice spacing as determined by using Bragg's Equation (2) and \(\beta\) = 99.45\({}^{\circ}\). All these parameters (\(a\), \(b\) and \(c\)) of the CuO films are presented in Figure 2, and a gradual decrease with increasing Al concentration is observed. Lattice parameter as a function of temperature and/or composition is an important piece of information in materials science. The variation in lattice parameter is attributed to the lattice strain induced by the introduction of Al\({}^{3+}\) due to the formation of oxygen vacancies. Lattice strain was observed to also decrease with an increase in particle size. However, here it is most remarkable and one should note that the reduction degree of the lattice constant \(c\) is relatively more significant compared to that of \(b\) and \(a\) respectively; i.e., 5.0%, 3.4% and 2.3%. This can be explained by referring to the fact that the Al\({}^{+3}\) ionic radius of 0.53 A is significantly smaller than that of the Cu\({}^{+2}\) ions (0.73 A). Since Al \"dissolves\" into the CuO host lattice, it tends to occupy the Cu sites, thus inducing the development of the lattice and, as a consequence, a monotonic decrease in the lattice parameters. Micro strain (\(\epsilon\)) and crystallite size (D) have been estimated using the main peak (002), by means of the following relationships [19]:  
\[D=\frac{0.9\ \lambda}{\beta cos\theta} \tag{3}\]  
\[\epsilon=\frac{\beta\ cos\theta}{4} \tag{4}\]  
where \(\lambda\) is the X-ray beam wavelength, \(\theta\) is the angle of diffraction, and \(\beta\) is the full width at half maximum of the diffraction peak. From these calculated values, as shown in Figure 3, one observes a significant decrease in crystallite size with increasing Al concentration, i.e., from 88.27 nm for the parent CuO up to 45.1 nm for 1% Al:CuO, representing a reduction of 43%. This demonstrates the polycrystalline nature of the Al:CuO films due to the replacement of Cu\({}^{+2}\) ions by Al\({}^{+3}\) ions during film formation. This is also explained by  
Figure 2: Variation of the lattice parameters (a and c) of pure and Al-doped CuO films grown at 350 \({}^{\circ}\)C via spray pyrolysis as a function of Al concentration. the response from the grain boundary.