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Lattice-gas theory of collective diffusion in adsorbed layers
journal contribution
posted on 2023-06-08, 18:28 authored by A Danani, R Ferrando, Enrico Scalas, M TorriA general theory for collective diffusion in interacting lattice-gas models is presented. The theory is based on the description of the kinetics in the lattice gas by a master equation. A formal solution of the master equation is obtained using the projection-operator technique, which gives an expression for the relevant correlation functions in terms of continued fractions. In particular, an expression for the collective dynamic structure factor Sc is derived. The collective diffusion coefficient Dc is obtained from Sc by the Kubo hydrodynamic limit. If memory effects are neglected (Darken approximation), it turns out that Dc can be expressed as the ratio of the average jump rate and of the zero-wavevector static structure factor S(0). The latter is directly proportional to the isothermal compressibility of the system, whereas is expressed in terms of the multisite static correlation functions gn. The theory is applied to two-dimensional lattice systems as models of adsorbates on crystal surfaces. Three examples are considered. First, the case of nearest-neighbour interactions on a square lattice (both repulsive and attractive). Here, the theoretical results for Dc are compared to those of Monte Carlo simulations. Second, a model with repulsive interactions on the triangular lattice. This model is applied to NH3 adsorbed on Re(0001) and the calculations are compared to experimental data. Third, a model for oxygen on W(110). In this case, the complete dynamic structure factor is calculated and the width of the quasi-elastic peak is studied. In the third example the gn are calculated by means of the discretized version of a classical equation for the structure of liquids (the Crossover Integral Equation), whereas in the other examples they are computed using the Cluster Variation Method.
History
Publication status
- Published
Journal
International Journal of Modern Physics BISSN
0217-9792Publisher
World Scientific PublishingExternal DOI
Issue
19Volume
11Page range
2217-2279Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2014-10-02Usage metrics
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