The diffusion of an atom on a solid surface

Abstract

A microscopic model for the diffusional motion of an atom chemisorbed on a solid surface is presented. The atom located at a given site is described by a set of states which can be divided into two classes. One class is composed of states whose energy is located below the intersite barrier. A particle described by one of these states can go to a neighboring site only through tunneling. The second class of states have higher energy than the intersite barrier. They are delocalized and an atom occupying such a state can change its site with relative ease. The vibrational motion of the lattice can transfer energy to or take it from the particle and it can also change the intersite transfer probability. As a result the particle may undergo three types of processes: 1) change state but not site (vertical transitions); 2) change site and state (oblique transitions); or 3) change site but not energy (horizontal transitions). The theory derives a kinetic equation for the probability that at a given time the particle is located at a given site and has a specified energy. This is then used to compute the mean square displacement of the particle and its diffusion coefficient. All these quantitities are expresed in terms of rate coefficients for horizontal, oblique, and vertical transitions. Microscopic expressions are provided for these quantities as a function of the particle phonon coupling, intersite transfer probability, particle energies, and lattice properties. The temperature dependence of the rate coefficients is analyzed numerically. If tunneling is minimal and a change of site can occur only after the phonon transfer promotes the particle in a state located above the intersite barrier, an Arrhenius temperature dependence of the diffusion coefficient is observed. The form of the functional dependence of the pre-exponential factor on temperature changes with anharmonicity, Einstein frequency, and phonon particle coupling. If the lattice is harmonic the activation energy is equal to the intersite barrier plus the energy of the distortion of the lattice upon chemisorption. If anharmonicity is important the activation energy is close or equal to the intersite barrier. If tunneling is important non-Arrhenius temperature dependence may be observed.