## 3 Results and Discussion
### The Microstructure and Phase of the Coatings
The root-mean-square heights (Rq) of the surfaces of the CC and NC are 9.984 \(\upmu\)m and 18.347 \(\upmu\)m. According to the literature, the surface roughness of a coating is inversely proportional to the melting degree of the powder [37]. As a result, the nanostructured coating exhibits a higher degree of surface roughness due to the lower melting degree of the nanopowder. The cross-sectional morphologies of the coatings are shown in Figure 7. The interfaces among the substrate, the NiCrCoAlY bonding layer, and the ceramic coating can be observed. The thickness of the bonding layer in both coatings is 70-120 \(\upmu\)m, the thickness of the ceramic coating of the CC ranges from 287-342 \(\upmu\)m (Figure 7a), and the thickness of the ceramic coating of the NC ranges from 285-317 \(\upmu\)m (Figure 7c). The porosity of the coating was measured by MicroEYE 3000 software. The average porosity observed in the CC was 3.48% compared to 5.21% for the NC. Figure 6: Surface morphology of (**a**) micro Al\({}_{2}\)O\({}_{3}\) coating; (**b**) nano Al\({}_{2}\)O\({}_{3}\) coating. Figure 7: Cross-sectional morphology of (**a**,**b**) micro Al\({}_{2}\)O\({}_{3}\) coating and (**c**,**d**) nano Al\({}_{2}\)O\({}_{3}\) coating. Figure 7b,d show high-magnification FESEM images of the pores of the plasma-sprayed CC and NC, respectively. It can be observed that the pores of the CC show the typical lamellar structure of a plasma-sprayed coating (Figure 7b), whereas partially/unfused nanoparticles can be seen in the pores of the NC with the fully melted lamellae bonded together in a mesh (Figure 7d). The microhardness of the coatings was measured using a Vicker's micro hardness tester, with a load of 0.9807 N applied to the polished cross-sections of the coatings for 15 s. The average microhardness values for the CC and NC were 1079.7 HV and 1168.8 HV, respectively. The average micro hardness of the NC is higher than the CC due to the following reasons: (1) At low loads, the microhardness of the coatings depends largely on their phase composition rather than coarse pores, cracks, etc. [38]. (2) According to the Hall-Petch theory, the increase in the hardness of an NC is also related to its nanograin size [39]. Weibull statistical analysis was used to further analyze the hardness parameter, as shown Figure 8[40]. Figure 8a shows a single linear distribution of the fitted Weibull curve for the CC, which is due to the essentially uniform coating organization and the small variation in the hardness values. However, as shown Figure 8b, the Weibull curve fitted for the NC consists of two lines with different slopes: section A--low hardness due to poor interparticle bonding (cohesion); section B--high hardness due to the presence of unfused particles with an \(\alpha\)-Al\({}_{2}\)O\({}_{3}\) phase. The difference in the hardness distribution of the coatings is also verified by the microstructure; the hardness distribution of the conventional coating reflects its micromorphology, which is basically composed of completely melted laminates, while the hardness distribution of the nano-coating is related to the two-state distribution of the microstructure.