## 3 Results and Discussion
### Oxidation and Mechanism of Growth of the Oxide Layer  
The cross-sectional thicknesses of the oxide layers grown on these substrates at 650 \({}^{\circ}\)C were examined with the Hitachi S-4800 scanning electron microscope, as shown in Figure 5. The well-defined oxide layers for the samples that were oxidized in N\({}_{2}\) 0.75 wt.% O\({}_{2}\) and N\({}_{2}\) 5 wt.% O\({}_{2}\) showed some cracks of the layers from the substrate surface, in some cases. These cracks were found at the interfaces between the substrates and the oxide layer. At a temperature of 650 \({}^{\circ}\)C, the differences in the thermal expansivities between the oxides forming in the oxide layer and the C84400 copper alloy substrate induce stresses and cracks. In this instance, the coefficient of thermal expansion (CTE) of the ZnO, CuO and PbO are 4.0 \(\times\) 10\({}^{-6}\)/\({}^{\circ}\)C, 4.3 \(\times\) 10\({}^{-6}\)/\({}^{\circ}\)C and 9.4 \(\times\) 10\({}^{-6}\)/\({}^{\circ}\)[PERSON] (1984); [PERSON] (1984), respectively, and are quite lower than the linear expansivity of the C84400 copper alloy, which has a value of 18.8 \(\times\) 10\({}^{-6}\)/\({}^{\circ}\)[PERSON] (1984). The oxide layer experienced compressive stresses, as the C84400 copper alloy expanded faster at the high temperature used in the oxidation, thus causing the cracks observed. Equally, some of the observed cracks may be due to the effect of wear during the polishing of the cross-sections for SEM examination.  
The values of the average oxide layer thickness, measured from the SEM images in Figure 5, are stated in Table 2. The oxidation rate at which these various oxides were formed was evaluated based on the oxide layer thickness as a function of the thermal oxidation time at 650 \({}^{\circ}\)C using the parabolic relation [PERSON] (1984) in Equation (1).  
\[X^{2}=K_{p}t \tag{1}\]  
The rate constant from the curves, \(3.0\times 10^{-4}\)\(\mu\)m\({}^{2}\) s\({}^{-1}\) and \(8.0\times 10^{-4}\)\(\mu\)m\({}^{2}\) s\({}^{-1}\), were calculated for the samples oxidized in the N\({}_{2}\) 0.75 wt.% O\({}_{2}\) and N\({}_{2}\) 5 wt.% O\({}_{2}\) gas mixtures, respectively, through the slopes of the plots. This confirms that by increasing the weight percentage of oxygen in the N\({}_{2}\)-O\({}_{2}\) gas mixture, the rate of the oxidation process, through the growth of the oxide layer, increased remarkably.  
The thermal oxidation and the growth of the CuO, ZnO and PbO granules sufficiently modified the surface morphology and increased the average surface roughness of the surface. The values of the average surface roughness, \(R_{\rm a}\), of these thermally oxidized samples were comparable irrespective of the N\({}_{2}\)-O\({}_{2}\) gas mixture used in the experiments, as stated in Table 2. The maximum \(R_{\rm a}\) values of 2.10 \(\mu\)m and 2.08 \(\mu\)m were obtained after 3 h of the thermal oxidation in the N\({}_{2}\)-0.75 wt.% O\({}_{2}\) and N\({}_{2}\)-5 wt.% O\({}_{2}\) oxidizing gas mixtures, respectively. This increase in the values of the average surface roughness and the resulting rough surfaces of the samples are due to the irregular packing, as well as the morphologies of the various oxides that have been formed during the thermal oxidation.