Effect of particle-hole symmetry on the behavior of tracer and jump diffusion coefficients

This paper analyzes the effect of particle-hole symmetry on the behavior of the tracer diffusion coefficient as well as the jump diffusion coefficient. The coefficients are obtained by performing a random walk of individual atoms in a two-dimensional square lattice at monolayer, using the $n$-fold way Monte Carlo simulation. Different hopping mechanisms have been introduced to study the effect of particle-hole symmetry. For hopping kinetics where the initial-state interactions are involved, the diffusion coefficient at high coverage falls several orders of magnitude due to the effect of particle-hole symmetry. For hopping kinetics where the final-state interactions are present, the effect is the opposite. For those involving both initial- and final-state interactions, like the so-called interaction kinetics, the effect of particle-hole symmetry is also discussed. This effect seems to be critical for repulsive lateral interactions, for which the behavior of the diffusion coefficients is modified by introducing the particle-hole symmetry condition.

Figure 1

An example of the hopping process and the transition rate. Dashed lines denote the pair contribution, and solid lines denote the trio contribution.

Figure 2

(a) Normalized tracer diffusion coefficient and (b) normalized jump diffusion coefficient vs $\theta$ and $\tau$ for the hopping kinetics with initial-state interactions. The lower temperature corresponds to $\tau =0.3$ and the temperature step is $\Delta \tau =0.1$.

Figure 3

(a) Normalized tracer diffusion coefficient and (b) normalized jump diffusion coefficient vs $\theta$ and $\tau$ for the hopping kinetics with final-state interactions. The lower temperature corresponds to $\tau =0.3$ and the temperature step is $\Delta \tau =0.1$.

Figure 4

Comparison between the normalized jump diffusion coefficients calculated by using $C_{ij}=0$ (open symbols) and with $C_{ij}\ne 0$ (filled symbols) for $\tau =0.3$. The circles correspond to the initial-state kinetics, while the squares correspond to the final-state kinetics.

Figure 5

(a) Normalized tracer diffusion coefficient and (b) normalized jump diffusion coefficient vs $\theta$ and $\tau$ for the interaction kinetics with $\gamma =1$ and $C_{ij}\ne 0$. The lower temperature corresponds to $\tau =0.3$ and the temperature step is $\Delta \tau =0.1$.

Figure 6

Comparison between normalized jump diffusion coefficient calculated by using the interaction kinetics (open squares) with $\gamma =1$ and $C_{ij}\ne 0$ and that obtained by using a simple metropolis scheme (filled circles).

Figure 7

Comparison between the normalized tracer diffusion for the interaction kinetics with $\gamma =1$, $\tau =0.3$, and different PHS conditions ($C_{ij}\ne 0$, solid symbols; $C_{ij}=0$, open symbols).

Figure 8

Comparison between the normalized tracer diffusion coefficient calculated using the initial-state kinetics: $C_{11}=0$, open squares; $C_{22}=0$, solid circles.

Figure 9

(a) Normalized tracer diffusion coefficient and (b) normalized jump diffusion coefficient vs $\theta$ and $\tau$ for the interaction kinetics, with $\gamma =-1$ and $C_{ij}\ne 0$. The lower temperature corresponds to $\tau =0.3$ and the temperature step is $\Delta \tau =0.1$.

Figure 10

(a) Normalized tracer diffusion coefficient and (b) normalized jump diffusion coefficient vs $\theta$ and $\tau$ for the interaction kinetics, with $\gamma =1$ and $C_{ij}=0$. The lower temperature corresponds to $\tau =0.3$ and the temperature step is $\Delta \tau =0.1$.

Figure 11

Influence of the initial configuration in the tracer diffusion coefficient for $C_{ij}\ne 0$ and $\tau =0.3$. Solid squares correspond to $\gamma =1$ and equilibrium initial condition; open squares correspond to $\gamma =1$ and nonequilibrium initial condition. Solid circles correspond to $\gamma =-1$ and equilibrium initial condition; open circles corresponds to $\gamma =-1$ and nonequilibrium initial condition.

Figure 12

Schematic representation of the configurations to obtain the PHS conditions. Parts (a)–(e) correspond to Eqs. (23, 24, 25, 26, 27), respectively.