Influence of metastable states on collective particle diffusion in the interacting lattice gas model

Abstract

We analyze a system of particles diffusing over an anisotropic crystal surface represented as a lattice gas model. Every second row of adsorption sites has higher energy and the diffusion across rows occurs via metastable states. Double occupancy is forbidden and nearest neighbors along rows interact via repulsive or attractive couplings. A collective diffusion coefficient is derived within the framework of a variational approach. Analytic expressions are investigated as functions of metastable state energies, activation energies, interaction parameters and particle density. It is shown that the interactions of particles that reside at stable or metastable sites change the diffusion over the surface. For some parameters the diffusion coefficients along or across rows are totally changed due to the interactions between particles. Diffusion along rows can be amplified or suppressed by the particle density change for different values of the jump activation energies.

Collective diffusion of dense adsorbate at surfaces of arbitrary geometry

“…On the other hand, diffusion along y-direction exhibits a behavior of switching between the deep and the shallow diffusive channel. Such behavior was earlier observed in the model of hills and valleys 32 , where the number of sites in the deep channel and the shallow one was equal and the transition between them occurred at θ = 1/2 instead of θ = 1/3.…”

“…which is the variational formula used by us to solve various diffusional problems [26][27][28][29][30][31][32][33][34] . M ( k) and N ( k) have been referred to as the expectation value numerator and the normalization denominator, respectively.…”

The collective diffusion coefficient as a shape detector of the surface energy landscape

“…Mech. (2018) 013204 system consisting of rows of alternating depths along which the particles interacted [21].…”

“…The simulations are usually based on Monte Carlo or molecular dynamics, while the analytical approaches can be based on Fokker-Planck, Kramers or master equation. Theory of surface diusion and the dierent approaches for calculating diusion coecients are described in [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. One of the first methods of obtaining coverage-dependent collective diusion coecient was developed by Zwerger [11].…”

“…In [14] dierent methods were described including Kubo-Green formulas in derivation of diusion coecient for more complex systems. A variational approach to the diusion coecient in the form which is used here was first described in [16] and then its applicability was shown in examples of dierent systems of diusing particles [17][18][19][20][21]. In the same time several other methods have been proposed.…”