Kinetic lattice gas model of collective diffusion in a one-dimensional system with long-range repulsive interactions

Abstract

Collective diffusion is investigated within the kinetic lattice gas model for systems of particles in one dimension with repulsive long-range interactions which are known to result in a staircaselike phase diagram with an infinite sequence of incompressible crystalline phases separated one from another by unstable compressible liquidlike phases. Using a recently proposed ͓Gortel and Załuska-Kotur, Phys. Rev. B 70, 125431 ͑2004͔͒ variational method, an analytic expression for the particle density dependence of the diffusion coefficient is derived in which commonly postulated static and kinetic factors are unambiguously identified. It is shown that while the static factor exhibits singular coverage dependence due to a sharp drop of compressibility when the system enters a crystalline phase, the kinetic factor may substantially modify this behavior. Depending on details of the activated state interactions controlling the migration kinetics the diffusion coefficient may also be singular or, at another extreme, it may be a continuously smooth function of density. In view of these observations recent results on efficient low temperature self-reorganization through devil's staircase phases in the dense Pb/ Si͑111͒-ͱ 3 ϫ ͱ 3 are discussed.

Collective diffusion in a non-homogeneous interacting lattice gas

“…in a series of follow-up works [23]- [28]. Most of these works deal with homogeneous onedimensional systems with short range interactions but some progress has also been made in two dimensions [23,28], non-homogeneous substrates [27,28] and systems with long range particle-particle interactions [26,29]. In this approach the collective diffusion coefficient is related to the lowest eigenvalue of a rate matrix which describes the kinetics of microscopic states of the system.…”

Low-Temperature Ultrafast Mobility in Systems with Long-Range Repulsive Interactions:Pb/Si(111)

“…Recently, an analytic method was proposed for lattice gas models with arbitrary interactions between the atoms. The method is described in [16,17], with [17] dealing specifically with its application to systems with LR interactions in 1D.…”

Collective diffusion in the presence of substrate inhomogeneities and particle–particle interactions

“…[23] has been subsequently refined and applied to a variety of problems [24][25][26][27][28]. In essence, the problem of finding the density/coverage dependent collective diffusion coefficient in a system of interacting particles adsorbed on a crystalline substrate is reduced to that of finding the smallest eigenvalue of a rate matrix using the variational approach akin to that used in quantum mechanics to find the ground state energy of a physical system.…”

“…[23] and then progressively refined in a series of follow-up works [24][25][26][27][28]. Most of these works deal with homogeneous one-dimensional systems with short range interactions but some progress has been also made in two dimensions [24], non-homogeneous substrates [28] and systems with long range particle-particle interactions [27,29]. In most of the applications so far, the designation 'variational' has not fully justified because variational parameters minimizing the eigenvalue have not been used -they could be easily guessed for these relatively simple applications.…”