## 3 Results and Discussion
### Correlation of Surface Profile Parameters and Dross Formation
For channels with \(D_{nom}\geq 6\) mm, _Psk_ is negative when the roughness is high and positive when the roughness is low. This indicates that in areas with high roughness the profile is skewed above the mean plane. For the smaller channel sizes, this trend is not as clear. The practical use of _Psk_ is not straightforward, whereas \(Pku\), which reacts much stronger to extremes, can be used very similar to \(Pmp\) to identify the spikiness of a profile, i.e., to what degree the profile consists of deep valleys and high peaks (\(Pku>3\)) or shallow valleys and soft hills (\(Pku<3\)). Flat sections (as found at \(\beta\) = 0\({}^{\circ}\)) tend to yield unreliable results for \(Pku\) as can be seen in Figure 14. While \(Pku\) is similar to \(Pmp\), extremes are affecting \(Pmp\) more strongly. This means that \(Pku\) is better for general spikiness of a profile and \(Pmp\) is good for evaluating irregular height distributions such as flat surfaces suddenly having an agglomeration resulting in a high profile peak. The final profile parameter investigated in this work was the fractal dimension (_FracDim_). It was found that the roughness trend yielded by the fractal dimension, calculated using the _RMS_ method, was opposite to that of the parameters found to adequately characterize the roughness magnitude. In other words, a high fractal dimension was typically calculated for a profile with low \(Pa\)-values. The heights of a typical profile extracted through a section with cross formation will not be self-similar at different scales, which will not translate into a \"complex\" profile according to the self-affinity principle of fractal dimensions. On the other hand, when a section is free of random particles and agglomerations, the extracted profile will be highly self-similar resulting in a high fractal dimension. This can be confirmed by for example inspecting Figure 14 where a large \(\beta\)-range is almost free of sintered particles (280\({}^{\circ}<\beta<\) 330\({}^{\circ}\)), which results in calculated fractal dimensions of around 1.7. Similarly, a small section at around \(\beta\) = 170\({}^{\circ}\) is almost free of random extremes, resulting in a fractal dimension of up to 1.7. This trend could mean that the fractal dimension can be used to characterize the degree of random particle sintering at a given \(\beta\) for LPBF channels and, therefore, identify key orientations with the tendency to have large and randomly distributed sintered particle agglomerations. Table 4 shows the calculated average profile parameter values for each of the investigated channels. The investigated channels can generally be divided into two groups: group 1 consists of smaller channels with \(D_{nom}\leq 3\) mm and group 2 consists of larger  
channels with \(D_{nom}\geq 6\) mm. Within the two groups, each group has approximately the same quantitative average profile parameter values calculated for \(Pa\), \(PI0z\), \(Pz\), \(Pq\), and \(Pp\). _Psk_ is positive for \(D_{nom}\leq 3\) mm and close to zero for \(D_{nom}\geq 6\) mm, indicating a generally more even distribution of peaks and valleys in larger channels. _Pku_ is generally above 3 for all channels, except for \(D_{nom}=2\) mm, indicating a general spikiness of the surface roughness in aluminum LPBF channels. The average fractal dimension is increasing with decreasing channel diameter. This is likely related to dress formations and particle agglomerations taking up more of the overall space in the channel. The profile versions of the material volume parameters, _Pmc_, _Pvc_, _Pmp_, and _Pvv_ are \"area\" dependent and, therefore, the parameters can only be used to compare values within the same channel size. For \(D_{nom}=6\) mm, it can be seen how the parameters are varying slightly between the five investigated channels (A, B, C, D and E) with the most variation being observed in _Pmp_, indicating that the extremes of the height distributions are mostly affected by variation in the manufacturing process, which is also to be expected.