ρ i is the host electron density at atom i induced by all of the other atoms in the system as follows: (5) where ρ i (r ij ) is the contribution to the electronic density at the site of the atom i, and r ij is the distance between the atoms i and j. Because diamond is much harder than copper, the diamond tool and indenter are both treated as a rigid body in the simulation. Therefore, the atoms in the tool are fixed to each other relatively,

and no potential is needed to describe the interaction between diamond atoms (C-C) [13]. The interaction between copper atoms and diamond atoms (Cu-C) is described by the Morse potential [14]. Although a two-body potential may lead to less accurate solutions selleck compound than a many-body potential does, its parameters can be accurately calibrated by Selleckchem Osimertinib spectrum data. For the Morse potential [14], the two-body potential energy is expressed as follows: (6) where V(r) is the potential energy, D is the cohesion energy,

α is the elastic modulus, and f ii is the second derivative of the potential energy V(r) with respect to the bond length r ij . r ij and r 0 are the instantaneous and equilibrium distances between two atoms, respectively. Table  1 shows magnitudes of these parameters. Table 1 Parameters in the standard Morse potential[14] C-Si Parameter D (eV) 0.087 α (Å−1) 5.14 r 0 (Å) 2.05 MD simulation setup In order to reduce the selleck products boundary effect and size effect, the model scale should be large. As a result, the simulation becomes computationally expensive. To avoid these problems, the periodic boundary condition is set along the Z direction [14]. The specimen surface of the X-Z plan is machined, so it is a free surface. Both Fludarabine the diamond tool and the diamond indenter are set as a rigid body. This was followed by an energy minimization to avoid overlaps in the positions of the atoms. The simulation model was equilibrated to

296 K under the microcanonical (NVE) ensemble, and the initial velocities of the atoms were assigned in accordance with the Maxwell-Boltzmann distribution. Figure  2 shows the simulation procedure of the nanoindentation test on the machining-induced surface. Firstly, the diamond tool cuts the surface along the [ī00] direction for the first time in the X-Z plane (Figure  2a, (1)). After the nanocutting stage, the relaxation starts, in which the tool is fixed in its final position and the fixed boundaries are removed so that the system can be relaxed back to another state of equilibrium (Figure  2b). Then, the diamond indenter moves along the [00ī] direction (as shown in Figure  2a (2) and returns to its initial position (3)). Figure 2 Schematic of nanoindentation tests on machining-induced surface and traces of the diamond indenter and diamond tool.