The relaxed atomic structure from Section 1.09.6.2.1 at zero stress can be used to construct initial conditions for MD simulations for computing dislo­cation mobility at finite temperature. The dislocation in Section 1.09.6.2.1 is periodic along its length (z-axis) with a relatively short repeat distance (2 [Г12]). In a real crystal, the fluctuation of the dislocation line can be important for its mobility. Therefore, we extend the simulation box length by five times along z-axis by replicating the atomic structure before starting the MD simulation. Thus, the MD simulation cell has dimensions 30[111], 40[T10], 10 [T 12] along the x, y z axes, respectively, and contains 10 7070 atoms.

In the following section, we compute the disloca­tion velocity at several shear stresses at T = 300 K. For simplicity, the simulation in which the shear stress is applied is performed under the NVT ensem­ble. However, the volume of the simulation cell needs to be adjusted from the zero-temperature value to accommodate the thermal expansion effect. The cell dimensions are adjusted by a series of NVT simulations using an approach similar to that used in Section 1.09.6.1.2, except that exx, £yy, ezz are allowed to adjust independently. As we have found in Section

1.09.6.1.2 that for a perfect crystal, the thermal strain at 300 K is e = 0.00191, exx, £yy, ezz are initialized to this value at the beginning of the equilibration.

After the equilibration for 10 ps, we perform MD simulation under different shear stresses axy up to 100 MPa. The simulations are performed under the NVT chain method using the Velocity Verlet algorithm with At = 1 fs. The shear stress is applied by adding external forces on surface atoms, in the same way as in Section 1.09.6.2.1 . The atomic configurations are saved periodically every 1 ps. For each saved configuration, the CSD parameter45 of each atom is computed. Due to thermal fluctuation, certain atoms in the bulk can also have CSD values exceeding 0.6 A2. Therefore, only the atoms whose CSD value is between 4.5 and 10.0 A2 are classified as dislocation core atoms.

Figure 9(a) plots the average position (x) of dis­location core atoms as a function of time at different applied stresses. Due to PBC in x-direction, it is possible to have certain core atoms at the left edge of the cell with other core atoms at the right edge of the cell, when the dislocation core moves to the cell border. In this case, we need to ensure that all atoms are within the nearest image of one another, when computing their average position in x-direction. When the configurations are saved frequently enough, it is impossible for the dislocation to move by more than the box length in the x-direction since the last time the configuration was saved. Therefore, the average dislocation position (x) at a given snap­shot is taken to be the nearest image of the average dislocation position at the previous snapshot so that the (x)(t) plots in Figure 9(a) appear as smooth curves.

Figure 9(a) shows that all the (x)(t) curves at t= 0 have zero slope and nonzero curvature,

indicating that the dislocation is accelerating. Even­tually, (x) becomes a linear function of t, indicating that the dislocation has settled down into steady-state motion. The dislocation velocity is computed from the slope of the (x){t) in the second half of the time period. Figure 9(b) plots the dislocation velocity obtained in this way as a function of the applied shear stress. The dislocation velocity appears to be a linear function of stress in the low stress limit, with mobility M = v/(exy • b) = 2.6 x 104Pa-1 s_1. Dislocation mobility is one of the important material input parameters to dislocation dynamics (DD) simulations.46-48

For accurate predictions of the dislocation veloc­ity and mobility, MD simulations must be performed for a long enough time to ensure that steady-state dislocation motion is observed. The simulation cell size also needs to be varied to ensure that the results have converged to the large cell limit. For large simulation cells, parallel computing is usually necessary to speed up the simulation. The LAMMPS program49 (http://lammps. sandia. gov) developed at Sandia National Labs is a parallel simulation program that has been widely used for MD simulations of solids.