13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- In order to study the chirality and size effects on the elastic properties of silicene nanoribbons, MD simulations are performed using LAMMPS [18]. Several inter-atomic potentials have been used in the MD simulations, including EDIP [19,20], Stillinger-Weber (SW) [21], Erhart-Albe [22], MEAM [23]. Isothermal-Isobaric (NPT) simulations are performed at a given temperature for 100 ps with a time step of 0.1 fs to let the system reach its equilibrium configuration. The strain is then applied along the uniaxial direction to perform uniaxial tensile tests. The applied strain rate is 0.005/ps. The pressure component vertical to the loading direction is controlled to maintain the uniaxial tensile condition. The strain increment is applied to the structure after every 10000 time steps with the step size of 0.1 fs. All the MD simulations are carried out at 300K and the temperature is controlled by employing the Nosé-Hoover thermostat [24]. The Velocity-Verlet algorithm is employed to integrate the equations of motion. Figure 1 A silicene nanoribbon, along with the definitions of zigzag and armchair directions, bond types, and bond angles. 3. Results and discussion As shown in Figure 1, we investigate the mechanical properties of rectangular bulk silicene in both the zigzag direction and armchair direction. The silicene thickness is assumed to 0.42 nm which is twice size of van der waals radius of silicon [25]. In ab initio calculations, the Young’s modulus in both zigzag and armchair directions of bulk silicene with 60 atoms (1.94 nm × 2.01 nm) is calculated from 2 2 0 1 E Y V ε ∂ = ∂ with a low strain (≤2%), where 2 2 E ε ∂ ∂ is the second derivative of the total energy with respect to the strain of the silicene and 0V is the minimum total energy volume. The calculated results are 148.5 and 140.7 GPa along zigzag direction and armchair direction, respectively. In MD simulations, in order to investigate the effect of chirality on the mechanical properties of bulk silicene, we perform displacement-control uniaxial tensile tests in both zigzag and armchair directions of bulk silicene with 7168 atoms (around 21 nm × 21 nm) with periodic boundary conditions in the in-plane two directions. Figure 2 shows the strain-stress relations for uniaxial tensile tests in both zigzag and armchair directions from MD simulations. The Young’s modulus is evaluated using the expression, / Y σ ε = in the elastic region, where σand εare the stress and strain, respectively. Table I displays the Young’s modulus of bulk silicene for different potentials, and a comparison with ab initio calculations is also shown. As we can see from Table I, the calculated Young’s modulus of bulk silicene using EDIP model is a little bigger than the ab initio calculations because the EDIP model is a short ranged potential, which will lead to an increased stiffness [26]. The results from Erhart-Albe are a little smaller than the ab initio calculations. However, the stress increases dramatically when the strain reaches certain value (see
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