Equilibration and calculation

In order to reach an equilibrium at various temperatures $T$
(See Fig. 5.6) a sample is equilibrated for $N_{eq}=10,000$ integration time steps (with time step $dt~=~1.02\times10^{-15} sec$). Thereafter the various structural and transport properties of the system were calculated, accumulated and averaged over a long period of $N_{meas}\simeq6,000,000$ MD steps. The trajectories of the atoms of the sample are produced for data analysis by using the canonical ensemble (NVT).

Various physical properties are monitored continuously during the simulation. An equilibrium state is considered to be achieved when there are no significant temporal variations (beyond the statistical fluctuations) in the total energy, layer occupation number, structure order parameters, and diffusion coefficients are seen in any of surface layer. A uniform profile of kinetic temperature across the sample is observed at the equilibrium for each temperature (See Fig. 5.7). The statistical averages have been calculated typically over $3,000$ configurations, separated by $1000$ time steps which is concluded, relying on analysis of behavior of the system properties, to be sufficient to make the collected configurations statistically independent.

Figure: Snapshots of $Va(001)$,$Va(011)$, and $Va(111)$ at $2200$ K.

Figure: Temperature profiles across the $Va(001)$ sample in the equilibrium state (simulations at different temperatures).