## 3 Results
### Transmission Electron Microscopy Analysis  
The results of the HRTEM analysis are described by several steps beginning with an overview of the tips to evaluate the differences of the nanostructure, subsequently showing the grain size in a magnified image for the center and edge area of the tip, and finally investigating the lattice spacings of the atomic structure by performing the fast Fourier transformation (FFT) of the structure. The lattice constant of face-centered cubic (FCC) Pt (space group Fm-3m) is 3.9231 A at room temperature according to the PDF 4 + card # 00-004-0802 [34]. The interplanar spacings for Pt of the 111, 200, 220, and 311 planes with high intensity can be calculated for the FCC crystal system by  
\[d_{hkl}=\frac{\text{a}}{\sqrt{h^{2}+k^{2}+l^{2}}} \tag{1}\]  
where the Miller indices are h, k, l, the lattice constant is a, and the interplanar spacing is d.  
To show the difference in the nanostructure of the tips, the overview images of the 9 pA, 46 pA, 90 pA, and 260 pA FIB, as well as the 340 pA FEB tips, are shown in Figure 5a-e. From the 9 pA to the 260 pA, a decrease of the grain size from a blurred to a more granular structure becomes apparent regarding the whole tip shown. Concerning this, Figure 5f-j illustrates a magnified view of the end of the tip to perform the FFTs in Figure 5k-o. In the images shown, the differences tend to be distinguishable in terms of grain size. However, the FFT gives a much clearer insight into the differences with respect to the diffraction rings of the nanostructure. An increase in intensity, particularly of the outer rings corresponding to the 220 and 311 planes, can be seen. According to Table 1, the interplanar spacings of these planes are 1.3873 and 1.1826 A and thus just above the resolution limit. The 111 and 200 planes are detectable in all FFTs due to the much larger interplanar spacing. This leads to a decrease in intensity from the center to the outside of the diffraction pattern. Depending on the grain size in the nanostructure, the planes with smaller spacing can be detected or not. Thus, a direct comparison of the different tips shows an increase in the number of smaller grains in which the 220 and 311 planes become visible. Specifically, a slight increase in intensity can be seen from the 9 pA to the 46 pA and 90 pA tips. In contrast, a significant jump in intensity can be seen at the 260 pA tip and the 340 pA FEB tip. As a result, there is a correlation between the ion current or the use of the FEB and the intensity of the diffraction rings. According to the visual inspection of the images, the FFTs confirm the observation of a decreasing grain size when the ion current is increased or the FEB is used. In the following, only the 9 pA and 260 pA, as well as the 340 pA FEB tips, are considered because of the specific differences. A different view of the tips is provided by the binary images of the HRTEM recordings. Figure 6 shows the tips after blurring through a 10 \(\times\) 10 pixel matrix and binarization at a threshold of gray values (0 = black to 255 = white) of 80. Blurring highlights larger grains and reduces the \"noise\" of very small contours in the image. Binarization enhances the contrast between light and dark areas in the image. In addition, the binary image (80%) is merged to the original transparent \begin{table}
\begin{tabular}{c c} \hline \hline
**Plane** & **d [Å]** \\ \hline
111 & 2.2650 \\
200 & 1.9616 \\
220 & 1.3873 \\
311 & 1.1826 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Interplanar spacings of the FCC Pt crystal structure with a lattice constant of 3.9231 Å according to the PDF 4 + card # 00-004-0802 [34]. image (20%) to visualize the actual edge of the tip while the blue markers highlight the particularly large grains in Figure 6b and create a comparison to the grain size in Figure 6a,c. The red markings show the distribution of grains in the direct edge region of the top edge since only these grains contribute to quantum mechanical tunneling through a vacuum gap.