Analytical Kinetic Theory of Single-Particle and Collective Surface Diffusion
Part of the
NATO Science Series II: Mathematics, Physics and Chemistry
book series (NAII, volume 29)
This paper generalizes the results of a recently developed kinetic theory of surface diffusion conceptually different both from the popular transition state hopping model and from the Fokker-Plank kinetic model (or its equivalent Generalized Langevin approach). Following the first principles of statistical mechanics, the theory is based on the evolution of the particle’s probability density, and takes into account the possibility of a finite change in adparticle energy due to its interaction with the substrate excitations. We show how, in this general way under some simplifying assumptions, one can reach a relatively simple, analytical description of surface diffusion that goes far beyond the abilities of the TST model. Examples are given by the occurrence of long jumps and “anomalous” pre-exponential factors of the diffusion coefficient in the low-density limit. Moreover, the theory allows, for the first time, kinetic treatment of surface diffusion at finite occupancy, resulting in a new sight on mechanisms determining the density dependence of collective diffusivity. Some puzzling aspects of surface cluster diffusion (gliding) can also be elucidated.
KeywordsMigration Anisotropy Hexagonal
Feibelman, P.J. (1989) Theory of adsorbate interactions, Annu. Rev. Phys. Chem.
, 261–290.CrossRefGoogle Scholar
Ratsch, C. and Scheffler, M. (1998) Density-functional theory calculations of hopping rates of surface diffusion, Phys. Rev.
, 13163–13166.Google Scholar
Gomer, R. (1990) Diffusion of adsorbates on metal surfaces, Rep. Prog. Phys
, 917–1002.CrossRefGoogle Scholar
Barth, J.V. (2000) Transport of adsorbates at metal surfaces: Prom thermal migra-tion to hot precursors, Surf. Sci. Rep.
, 75–149.CrossRefGoogle Scholar
Seebauer, E.G. and Allen, C.E. (1995) Estimating surface-diffusion coefficients, Prog. Surf. Sci.
, 265–330.CrossRefGoogle Scholar
Lifshitz, E.M. and Pitaevskii, L.P. (1981) Physical Kinetics
, Pergamon, Oxford.Google Scholar
Ferrando, R., Spadacini, R. and Tommei, G.E. (1993) Diffusion in a periodic potential in the strong collision limit, Chem. Phys. Lett.
, 248–252.CrossRefGoogle Scholar
Ferrando, R., Spadacini, R. and Tommei, G.E. (1993) Kramers problem in periodic potentials—jump rate and jump length, Phys. Rev.
, 2437–2451.Google Scholar
Kreuser, H.J. and Gortel, Z.W. (1986) Physisorption Kinetics
, Springer Ser. Phys. Chem., Springer, Berlin.CrossRefGoogle Scholar
Borman, V.D., Krylov, S.Yu. and Prosyanov, A.V. (1988) Theory of nonequilibrium phenomena at gas-surface interface, Sov. Phys. JETP
, 2110–2121.Google Scholar
Beenakker, J.J.M. and Krylov, S.Yu. (1997) One-dimensional surface diffusion: Density dependence in a smooth potential, J. Chem. Phys.
, 4015–4023.CrossRefGoogle Scholar
Krylov, S.Yu., Prosyanov, A.V. and Beenakker, J.J.M. (1997) One dimensional surface diffusion: Density dependence in a corrugated potential, J. Chem. Phys.
, 6970–6979.CrossRefGoogle Scholar
Beenakker, J.J.M. and Krylov, S.Yu. (1998) Jump length distribution in molecule-on-substrate diffusion, Surf. Sci.
, L816–L821.CrossRefGoogle Scholar
Krylov, S.Yu., Beenakker, J.J.M. and Tringides, M.C. (1999) On the theory of surface diffusion: kinetic versus lattice gas approach, Surf. Sci.
, 233–249.CrossRefGoogle Scholar
Krylov, S.Yu. and Tringides, M.C. (1999) Anomalous preexponential factors in surface diffusion: A kinetic look into the problem, ECOSS-18, Europhys. Conf. Abst.
, abstract Tul440.Google Scholar
Krylov, S.Yu. (1999) Surface gliding of large low-dimensional clusters, Phys. Rev. Lett.
, 4602–4605.CrossRefGoogle Scholar
Krylov, S.Yu. (2000) Failure of ID models for Ir island diffusion on Ir(111)—Krylov replies, Phys. Rev. Lett.
, 1581–1584.CrossRefGoogle Scholar
Wang, S.C., Kurpick, U. and Ehrlich, G. (1998) Surface diffusion of compact and other clusters: Ir-x on Ir(111), Phys. Rev. Lett.
, 4923–4926.CrossRefGoogle Scholar
Maksimov, L.A. and Ilyin, A.V. (1974) Physical Kinetics
, MPhTI, Moscow.Google Scholar
Hänggi, P., Talkner, P. and Borkovec, M. (1990) Reaction-rate theory—50 years after Kramers, Rev. Mod. Phys.
, 251–341.CrossRefGoogle Scholar
Cucchetti, A. and Ying, S.C. (1996) Memory effects in the frictional damping of diffusive and vibrational motion of adatoms, Phys. Rev.
, 3300–3310.Google Scholar
Hofmann, F., Toennies, J.P. and Manson, J.R. (1997) The transition from single phonon to multiphonon energy transfer in atom-surface collisions, J. Chem. Phys.
, 1234–1247.CrossRefGoogle Scholar
Chen, L.Y., Baldan, M.R. and Ying, S.C. (1996) Surface diffusion in the low-friction limit: Occurrence of long jumps, Phys. Rev.
, 8856–8861.Google Scholar
Senft, D.C. and Ehrlich, G. (1995) Long jumps in surface diffusion—one-dimensional migration of isolated adatoms, Phys. Rev. Lett.
, 294–297.CrossRefGoogle Scholar
Linderoth, T.R., et al.
(1997) Surface diffusion of Pt on Pt(llO): Arrhenius behavior of long jumps, Phys. Rev. Lett.
, 4978–4981.CrossRefGoogle Scholar
Kürpick, U., Kara, A. and Rahman, T.S. (1997) Role of lattice vibrations in adatom diffusion, Phys. Rev. Lett.
, 1086–1089.CrossRefGoogle Scholar
Roos, K.R. and Tringides, M.C. (2000) Determination of interlayer diffusion parameters for Ag/Ag(111), Phys. Rev. Lett.
, 1480–1483.CrossRefGoogle Scholar
Jensen, P. (1999) Growth of nanostructures by cluster deposition: Experiments and simple models, Rev. Mod. Phys.
, 1695–1735.CrossRefGoogle Scholar
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