## 2 Materials and Methods
### Wear Volume Calculation  
The surface of the samples was scanned with an InfiniteFocus G5 Focus Variation (FV) 3D digital microscope by [PERSON] (Raaba, Austria) with a 20\(\times\) high-resolution lens to measure the amount of wear. The surface enclosed in the square area around the three concentric wear tracks in Figure 5a was acquired at once to have a single reference plane to estimate the wear volume of the three tracks.  
Figure 4: 43 kX FESEM image of the surface of the direct growth sample (on the **(left)**): 10 \(\upmu\)m \(\times\) 10 \(\upmu\)m AFM height map in the centre of the sample coated with direct growth graphene (on the **(right)**). The line profile shows the characteristic dimensions of the globular structure.  
The volume of removed material and deposited or plastically displaced material were calculated with the Volume Parameters Topographic method based on the Abbott-Firestone curve. The method is schematically represented in Figure 6 and relies on Equations (1)-(3). Further details are reported by [PERSON] [57], [PERSON] [58], [PERSON] et al. [59], and [PERSON] et al. [60]. This calculation method of the wear volume was proved by [PERSON] et al. to be the most robust from a statistical point of view. It has higher accuracy and lower uncertainty than the method suggested by the standard ASTM G99-17 and ISO 18535 based on the profilometry of the wear tracks  
\[V_{VP}=V_{m}(m_{r})+V_{v}(m_{r}) \tag{1}\]  
\[V_{m}(h_{0})=K\int_{0}^{h_{0}}S_{mc}(h)dh \tag{2}\]  
\[V_{v}(h_{0})=K\int_{h_{0}}^{1}(1-S_{mc}(h))dh \tag{3}\]  
In Equations (1)-(3), \(V_{m}\) and \(V_{v}\) are the material volume and the void volume, respectively, \(V_{VP}\) is the total damage volume, \(h\) is the surface height, \(S_{mc}\) the cumulative probability distribution of the surface heights (i.e., the Abbott-Firestone curve), and \(K\) is a conversion factor that represents the area of the projected surface topography on a horizontal plane. Given a specific horizontal section plane representing the average position of the unworn surface whose height is \(h_{0}\), \(V_{m}\) represents the volume of material enclosed below the measured surface and above this plane, whilst \(V_{v}\) is the volume of missing material above the surface and below this plane.  
Volume calculations were performed through the open-source software Gwyddion [61]. Rough topographic datasets were imported into Gwyddion, where three annular masks  
Figure 5: (**a**) Region of the samples scanned with the 3D microscope, (**b**) masks applied to the topographic data, (**c**) binary trace of the masked region.  
Figure 6: Void and material volume parameters of the Abbott-Firestone curve.  
identified three regions of interest (ROI), as Figure 5b shows. Setting suitable ROI was necessary to exclude from the volume computations any contributions from roughness and other topographical features of the surrounding surfaces that are not related to the tribological tests. The dataset outside the three annular masks, i.e., the region in black in Figure 5c, was exploited to fit a polynomial function through which the rough topographic acquisition was planarized by shape removal. This practice is imperative to correct the residual error of planarity, and thus, to identify the reference section plane representing the unworn surface accurately. This plane at \(z=h_{0}\) was identified as the median value of the dataset filled in with black filler in Figure 5c. The Abbott-Firestone curve was computed for each wear track individually by elaborating the data inside each annular region of the mask. The integration of the Abbott-Firestone curve schematically represented in Figure 6 provided the quantification of the material removed and displacement during the sliding interactions.