## 3 Results and Discussion
### Thermal Control Property  
Figure 9 shows the reflection spectra of the alumina coatings (NC and CC). The CC has a reflectance coefficient of 70-75% within 417-1418 nm (Figure 9a). Its main absorption boundary is located at 285 nm (Figure 9b). The reflectivity of the NC within 446-1586 nm is more than 75% (Figure 9a). Its maximum absorption peak is located at 227 nm (Figure 9b). The micron-alumina coating has a reflectance coefficient of 70-75% within 417-1418 nm. Over the entire wavelength range, the solar absorptance (\(\alpha_{\rm s}\)) values of the nanostructured and conventional alumina coatings are 0.26 and 0.324. In the NIR band, this difference can be caused by adsorption via gas. However, in the short-wavelength region (in the range of 200-400 nm), the absorption difference is caused by the band gap of the material [9]. According to [PERSON]'s law, i.e., \(\lambda\geq hc/E_{\rm g}\), (\(h\) is [PERSON]'s constant), for intrinsic absorption to occur, the photonic energy must be equal to or greater than the band gap (\(E_{\rm g}\)). Figure 8: Weibull distribution of the hardness test values of (**a**) micron Al\({}_{2}\)O\({}_{3}\) coating (**b**) nano Al\({}_{2}\)O\({}_{3}\) coating. As shown in Figure 10, the band gap corresponding to the maximum absorption peak of the alumina coating was calculated by the Kubelka-Munk method. The band gap of the CC near 285 nm is 3.71 eV (Figure 10A) and the maximum absorption peak of the NC corresponds to a band gap of 5.12 eV (Figure 10B). The blue-shift phenomenon of the main absorption peak in the NC is caused by the increase in the \(\alpha\)-Al\({}_{2}\)O\({}_{3}\) phase. Therefore, the reflectance of the NC is significantly increased compared to the CC within 227-285 nm. This result is consistent with previous reports in the literature [30]. In addition, differences in the microscopic morphology of the coating can also cause differences in spectral reflectance. When solar radiation is incident on the surface of an alumina coating, unlike metal coatings, wherein reflection, absorption, and emission occur only at the thin interface, alumina coatings have low absorption and high transmission at the interface [41,42]. Therefore, the reflectivity of alumina coatings depends on the volume of absorption and the scattering properties of the radiation. As shown in Figure 11, plasma-sprayed nano-alumina coatings typically have a heterogeneous, usually porous, microstructure [29]. When radiation enters the interior of the coating, volume scattering often occurs due to the optical index gaps between the air in the pores and the matrix, which results in the modification of the direction of radiation propagation around the point of heterogeneity and multiple reflections at the interface between heterogeneity and the matrix medium. Some radiation scatters and finally returns to the surface, which can contribute to the reflectivity of the coating. In fact, the intensity and direction of scattered radiation is determined by the inhomogeneity of the medium's  
Figure 10: Determination of the maximum absorption peak of **(A)** CC and **(B)** NC corresponding to band gap determined via Kubelka-Munk method. Figure 9: Reflectivity spectra of Al\({}_{2}\)O\({}_{3}\) coatings in the wavelength range of **(a)** 200–2500 nm and **(b)** 200–400 nm. density and the internal particle scale. The internal scattering of a coating is enhanced with the increase in porosity. In addition, the nanostructured coating has a large number of nanoparticles, as shown in Figure 7d, and backscattering occurs when radiation encounters these particles, which also improves the reflection performance of the coating. Therefore, the NC shows high reflective performance and its degree of volume scattering is enhanced due to the presence of numerous pores and nanoparticles inside. Figure 12 shows the temperature dependence of the emissivity (\(\varepsilon\)) of the CC and NC in 1-22 \(\upmu\)m wavebands.