## 3 Results and Discussion  
### Roughness Analysis  
Table 2 presents the average surface roughness of the as-coated, grinded, and polished bond coats, as well as the corresponding roughness of the 7 YSZ top coats deposited on these bond coats. For better visualisation of the dependence of bond coat surface roughness on top coat roughness, the data are shown in graphical form in Figure 4.  
The 7 YSZ top coat surface deposited on the smoother bond coat is also smoother, indicating that the roughness of the bond coat has a certain effect on the roughness of the 7 YSZ coating prepared by EB-PVD. The lower the roughness of the bond coat, the lower the overall roughness of the top coat prepared by EB-PVD. These observations are consistent with those presented in reference [21].  
However, an exponential dependence was observed between the roughness of the ceramic layer and the roughness of the substrate. This relationship is approximated by the equation:  
\[y=0.5328x^{2}-0.0531x+0.4277 \tag{1}\]  
where \(y\)--Top coat roughness Ra; \(x\)--Bond coat roughness Ra.  
It was found that the grinding of the bond coat significantly affects the surface roughness of the ceramic top coat, whereas polishing does not have such a significant impact. Therefore, further reduction of surface roughness through bond coat polishing does not noticeably influence the roughness of the 7 YSZ coating. This is evidently due to the columnar structure of the ceramic top coat, as best illustrated by the surface profiles shown in  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & **Bond Coat** & **Bond Coat** & **Top Coat Roughness** \\  & **Preparation** & **Roughness Ra [\(\mu\)m]** & **Ra [\(\mu\)m]** \\ \hline I & As-coated & 1.124 & 1.100 \\ V & As-coated & 1.057 & 0.920 \\ IX & As-coated & 0.945 & 0.828 \\ II & Rough grinding & 0.545 & 0.582 \\ VI & Rough grinding & 0.521 & 0.515 \\ X & Rough grinding & 0.529 & 0.541 \\ III & Grinding & 0.236 & 0.562 \\ VII & Grinding & 0.286 & 0.460 \\ XI & Grinding & 0.276 & 0.398 \\ IV & Polishing & 0.018 & 0.405 \\ VIII & Polishing & 0.023 & 0.447 \\ XII & Polishing & 0.020 & 0.390 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Average surface roughness of bond coats and corresponding top coats.  
Figure 3: The coated sample glued to counterpart (**a**) before the tensile adhesion test; and (**b**) after the tensile adhesion test.  
Figure 5: The shape of the ceramic columns, particularly their tips, determines the surface roughness of the ceramic top coat. Although the roughness of the bond coat was reduced by an order of magnitude through polishing, the roughness of the ceramic top coat remains at a level similar to that after the bond coat grinding (compare Figure 5e-h).  
Figure 4: Influence of bond coat surface roughness on top coat roughness approximated by the equation \(y=0.5328x^{2}-0.0531x+0.4277\).  
Figure 5: _Cont._  
Based on the data analysed, it can be concluded that the most significant impact on the roughness of the top coat is seen when the roughness of the bond coat ranges from Ra of 1.1 to 0.5 \(\upmu\)m. Within this range, the bond coat roughness directly influences the top coat roughness because of the larger surface irregularities that are transferred during the deposition process. However, when the roughness of the bond coat is below Ra of 0.2 \(\upmu\)m, its influence on the roughness of the top coat becomes minimal. The lowest achievable surface roughness of the 7 YSZ top coat can oscillate around Ra of 0.4 \(\upmu\)m. Thus, knowing that bond coat polishing does not significantly improve the surface roughness of the ceramic top coat, it is crucial to assess whether it has a significant impact on other properties of the 7 YSZ coating or its morphology.