Observation of jump diffusion of isolated sodium atoms on a Cu(001) surface by helium atom scattering

Abstract

The diffusion of sodium adatoms on a Cu(00l) surface has been studied with quasielastic helium atom scattering. A jump mechanism was found with activation energy 51 meV, jump length 2.56 A, and jump attempt frequency vo 0.53 THz. The adatom vibrational frequency parallel to the surface is measured to be 1.23 THz. The data are interpreted with the aid of a realistic molecular-dynamics simulation which reveals that vo is governed by the rate of energy exchange between the adatoms and the substrate, and not, as transition state theory would predict, by the vibrational frequencies of the adatom.PACS numbers: 79.20.Rf The two-dimensional diffusion of atoms on surfaces is an important elementary process in surface chemistry and provides an ideal model system for studying activated processes [1]. In the experiments to be reported here we have used helium atom scattering to identify a singlejump diffusion mechanism, measure the activation energy, and even determine the related vibrational frequencies of adatoms diffusing on a well defined single-crystal surface. The present detailed results make it possible to carry out a direct comparison with a realistic moleculardynamics simulation of the diffusing adatoms' motion which confirms the interpretation of the data and provides information on the role of energy dissipation and multiple jumps.The technique used here relies on the fact that helium atoms have large diffuse scattering cross sections from defects on a crystal surface [2], It has been shown both theoretically [3,4] and experimentally [5] that the diffuse "elastic" scattering from mobile defects has an energy broadening due to the finite residence time of the defect at a particular surface site. From the dependence of this broadening on the scattering wave vector it is possible to determine the microscopic surface diffusion mechanism. The first such experiments were performed on a premelting lead surface [5] just below the melting point where neither the concentration of the diffusing atoms nor the surface structure are well defined [6]. In this new experiment a known small concentration of sodium adatoms (0=0.1) was evaporated onto a clean Cu(001) surface and the angular distributions of elastically scattered helium atoms were used to show that the sodium adatoms are widely separated and interact only weakly with each other by long-range dipole-dipole repulsive forces [7] of the type predicted by Kohn and Lau [8]. The diffusion measurements were made over a range of temperatures far below the bulk copper melting point, where only relatively small substrate vibrations are expected.The theory of the quasielastic scattering phenomena is described elsewhere [3][4][5]9,10]. If diffusion proceeds by single jumps with jump vectors {j} and mean jump frequencies {VJ}, then the quasielastic peak shape is a Lorentzian with an energy FWHM A£(AK)-2ft2>j[l-cos(AK-j)], (1) j where AK is the component of the scattering wave vector parallel to the surface [10]. The periodic behavior of AE with AK arises because if, for a part...

Two-bath model for activated surface diffusion of interacting adsorbates

“…7,8 The thermal effects induced by the surface temperature were accounted for by a Gaussian white noise, this being in agreement with contemporary full 9 where the motion of both the surface atoms and a sample of adatoms scattered over the surface was taken into account. As coverage increases, the Langevin treatment has still been used in the literature, 3 but in combination with molecular dynamics ͑Langevin molecular dynamics, LMD͒, where the interadsorbate forces are commonly described by repulsive dipole-dipole potentials.…”

Microscopic view of epitaxial metal growth: nucleation and aggregation

“…One distinguishes the collective diffusion coef®cient (also known as chemical or Fickian diffusion coef®cient) of an ensemble of mutually interacting particles from the tracer (or intrinsic) diffusion coef®cient describing the mean square displacement of one isolated random walker per unit time. The chemical diffusion is commonly measured by the decay of concentration pro®les or by looking at density¯uctuations of a lattice gas induced by the mobility of the (often repulsively) interacting particles (®eld emission¯uctuation method [30], see also detection of momentum transfer due to particle motion in inelastic He scattering [31]). Recently STM was applied to measure¯icker noise in the tunneling current due to diffusing adatoms passing the tunneling gap [32,33].…”

Hamiltonian theory for vibrational line shapes of atoms adsorbed on surfaces

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“…The parameters are taken so as to model an adsorbed Na particle moving on a cosine potential, a system which has been investigated both theoretically 27,28 and experimentally. 29 In Fig. 3 we show the numerically determined velocity autocorrelation function for this system at two friction values: low, ␥ϭ0.1 0 , and moderate, ␥ϭ0.5 0 , and two different barrier heights V ‡ , compared to the harmonic and anharmonic approximations, Eqs.…”

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