Collective diffusion in a non-homogeneous interacting lattice gas

Abstract

Collective diffusion in an interacting adsorbate on a nonhomogeneous one-dimensional substrate is investigated within the framework of a variational approximation. The substrate inhomogeneity, appropriate to a periodically stepped adsorbate, is represented by a Schwoebel barrier at the step edge and a modified binding at the step site. An elementary cell of a periodic substrate consists of n identical terrace sites and one step site, i.e. it contains n + 1 sites. The adsorbed particles are allowed to interact with each other, both in equilibrium as well as during the transit of a hopping particle over the potential energy barrier separating the initial and the target adsorption site. The interactions modify the rates of particle jumps between the adsorption sites. Cases n = 1, 3 and 4 are investigated in considerable detail and, where appropriate, a comparison with the available computer simulation results in the literature for an analogous two-dimensional system is made. It is shown that preferential geometrical arrangements at several adsorbate densities (coverages) induced by repulsive intra-adsorbate interactions lead to features on the diffusion coefficient versus the coverage curves which can be consistently interpreted. The origin of these features and their relation to intra-adsorbate correlations are examined and discussed. Where possible, the variational theoretical results are confronted with the results of our own computer simulation studies of diffusion.

Many-particle surface diffusion coefficients near first-order phase transitions at low temperatures

“…with τ ± = θ(µ t ± d) = θ ± ± (χ ± /β)d + O(N −5/4 ). Intervals (20) are very narrow and concentrated around θ ± .…”

“…One of the intriguing problems that has attracted particular attention is the presence of phase transitions and their effects on surface diffusion. Since lattice gases can be used to model such transitions, they have provided a convenient framework also in this regard [7,8,[11][12][13][14][15][16][17][18][19][20]. However, below critical temperatures ordered phases may arise due to lateral interactions, and sophisticated arguments should be applied to analyze surface diffusion [7].…”

Diffusion of Ga adatoms at the surface of GaAs(001) c(4x4) $α$ and $β$ reconstructions

“…The analytic formulas have this advantage over other methods that they give results as a function of temperature and of all other model parameters. We propose new, variational approach, that was first shown to work for many-particle diffusion process [32][33][34][35][36] . Below we show how the variational approach can be used in calculation of tracer diffusion coefficient, which describes also diffusion in the system of low density.…”

Collective surface diffusion near a first-order phase transition

“…One of the relevant transport coefficients for surface diffusion is the collective (or chemical) surface diffusion coefficient, D c . It is associated with the decay of fluctuations in the adparticle density at large time and space intervals and is defined via the Fick's first law, J = −D c ∇θ, where J is the surface diffusion flux and θ is the surface coverage.Considering suitable 2D lattice gas models, computer simulation methods have been frequently applied in theoretical studies of D c (and of surface diffusion in general) with a particular interest in the presence of phase transitions and their effects on surface diffusion [3,4,5,6,7,8,9,10,11,12]. Usually, the observation that D c = Φ D CM [1] was used, where D CM is the center of mass diffusion coefficient and represents kinetic properties of D c , while Φ = N oc /( N 2 oc − N oc 2 ) is associated with thermodynamic properties of D c and is called the thermodynamic factor (N oc is the number of adsorption sites in a system occupied by adparticles and · denotes the statistical mean value).…”

“…Considering suitable 2D lattice gas models, computer simulation methods have been frequently applied in theoretical studies of D c (and of surface diffusion in general) with a particular interest in the presence of phase transitions and their effects on surface diffusion [3,4,5,6,7,8,9,10,11,12]. Usually, the observation that D c = Φ D CM [1] was used, where D CM is the center of mass diffusion coefficient and represents kinetic properties of D c , while Φ = N oc /( N 2 oc − N oc 2 ) is associated with thermodynamic properties of D c and is called the thermodynamic factor (N oc is the number of adsorption sites in a system occupied by adparticles and • denotes the statistical mean value).…”