## 2 Principle of Measuring Cutting Edge Radius  
There are three steps in the process of measuring the diamond tool cutting edge radius using the proposed edge reversal method, as shown in Figure 1.  
The first step is related to the cutting-edge replication shown in Figure 1. The single point diamond tool, a piece of copper workpiece, and a nanoindentation system are employed. An indentation mark, referred to as the reverse cutting edge artifact, is fabricated by indenting the diamond tool into the workpiece with the bisector of the included angle between its rake face and clearance face perpendicular to the workpiece surface using the nanoindentation system. The configuration and the principle of the nanoindentation system is introduced later. The reverse cutting edge artifact is, thus, directly transcribed from the geometry of the diamond tool. The second step is related to the AFM measurement of the actual cutting edge of the diamond tool. The diamond tool, with the cutting edge radius, \(R_{\text{tool}}\), is positioned under the AFM cantilever with the bisector of the included angle between its rake face and clearance face along the vertical axis. An AFM cantilever is moved by an \(XY\)-stage and a \(Z\)-scanner of the AFM along the \(X\)-, \(Y\)- and \(Z\)-directions to align the AFM cantilever tip with the apex of the diamond tool cutting edge. After an accurate alignment, the AFM cantilever is brought to scan across the diamond tool cutting edge. Since the tip radius \(R_{\text{tip}}\) of the AFM cantilever is comparable to the cutting edge radius, \(R_{\text{tool}}\), of the diamond tool, the scan trace of the AFM with an apex radius of \(R_{\text{tool\_m}}\) is a convolution of the AFM tip and the diamond tool cutting edge, as shown in Figure 1. Therefore, the following equation can be obtained:  
\[R_{\text{tool\_m}}=R_{\text{tool}}+R_{\text{tip}} \tag{1}\]  
Figure 1: Principle of the proposed edge reversal method. The third step is related to the AFM measurement of the reverse cutting edge artifact. Then, the reverse cutting edge artifact is measured by the AFM. The apex radius of the reverse cutting edge is defined as \(R_{\text{mark}}\), which is also comparable to the AFM tip radius \(R_{\text{tip}}\). After the alignment between the AFM cantilever tip and the apex of reverse cutting edge, the AFM tip scans across the reverse cutting edge artifact to map out its topography. The scanned image is also a convolution of the AFM tip and the reverse cutting edge artifact. Therefore, the following equation can be obtained:  
\[R_{\text{mark\_m}}=R_{\text{mark}}-R_{\text{tip}} \tag{2}\]  
The copper workpiece surface displays a certain degree of elastic recovery after the diamond tool is withdrawn from the surface in the nanoindentation process [23; 24]. The relationship between the actual cutting edge radius and reverse cutting edge radius can be expressed as:  
\[R_{\text{tool}}=(1-\xi)R_{\text{mark}} \tag{3}\]  
where \(\xi\) represents the elastic recovery coefficient of the reverse cutting edge artifact. According to Equations (1)-(3), cutting edge radius of the diamond tool can be evaluated to be:  
\[R_{\text{tool}}=\frac{1}{2-\xi}(R_{\text{tool\_m}}+R_{\text{mark\_m}}) \tag{4}\]  
Therefore, cutting edge radius of the diamond tool can be obtained without being influenced by the AFM tip radius. As can be seen from Equation (4), the achievable accuracy of this method depends on the elastic recovery coefficient \(\xi\). It has been verified that the elastic recovery coefficient, \(\xi\), of the reverse cutting edge would be reduced to 0.012 from 0.068 when the indentation depth was increased to 20 nm from 2.5 nm based on molecular dynamics (MD) simulations [22]. The detail of the MD simulation can be found in [22] and is not repeated in this paper for the sake of clarity. The difference between \(R_{\text{mark}}\) and \(R_{\text{tool}}\) was evaluated to be 0.24 nm when the indentation depth was set to be 200 nm.