Tracer diffusion in ordered lattice-gas systems with defect-controlled transport mechanisms
Tracer diffusion in an ordered two-dimensional lattice-gas system with square lattice symmetry is studied theoretically and by means of computer simulations. It is well known that the ordering with c 2 2 symmetry formed in the vicinity of half-filling of lattice sites is due to strong nearest neighbor repulsive interaction. In this case, the tracer migration occurs mainly by elementary displacements of structural defects. This paper focuses on the dimer transport mechanism which was accounted for with insufficient accuracy in previous publications. The long-time asymptotics of the dimer-tracer correlation function i.e., a three-particle correlation function , which describes concerted tracer-dimer motion, is obtained analytically. We analyze a specific exchange mechanism, relevant to tracer diffusion only. Also, the contribution of generation-recombination jumps to tracer diffusion is taken into account. The theoretical data agree well with the results of intensive Monte Carlo simulations.
One-dimensional diffusion: validity of various expressions for jump rates.
The coverage dependence of the one-dimensional collective diffusion coefficient is analyzed by using the gradient expansion of the local density. The transition probabilities are written as an expansion of the probabilities of the occupation configurations. Since the detail balance principle determines only a part of the diffusion terms in the expansion, different functional relations are proposed for these terms. The diffusion coefficient is obtained for various choices of these relations. However, some of them seem to be not physically sound and the diffusion coefficient does not behave properly. The range of validity of various expressions for the jump rates is determined and phase diagrams are shown. Besides that, it is shown that the transition state theory guarantees physically suitable behavior of the coefficient of one-dimensional diffusion.
Surface diffusion in the low-friction limit: Occurrence of long jumps.
We present a molecular dynamics ~MD! study of a Brownian particle in a two-dimensional periodic potential. For a separable potential, the study of the diffusion constant along the symmetry directions reduces to two one-dimensional problems. In this case, our MD study agrees with the existing analytical results on the temperature and the friction (h) dependence of the diffusion constant (D). For a nonseparable and anisotropic potential such as the adsorption potential on a bcc~110! surface, the present study predicts an alternative D;1/h dependence in the low friction regime as opposed to the D;1/h dependence found in previous studies of one-dimensional or separable potentials. We find that the dependence of D on h in the low friction regime is directly related to the occurrence of long jumps. The probability for the long jumps depends not only sensitively on the value of the friction but also on the geometry of the surface. On the bcc~110! surface, the path connecting adjoining adsorption sites does not coincide with the direction of easy crossing at the saddle point. Consequently, the probability of deactivation is enhanced, leading to the reduction of long jumps and the different dependence of D on h . @S0163-1829~96!09035-2#