Evaporation of single atoms from an adsorbate island or a step to a terrace: Evaporation rate and the underlying atomic-level mechanism

We examine the kinetics of atom ''evaporation'' from an adsorbate island onto the surrounding single-crystal surface. In our model the atoms forming the island move on a square lattice with rate constants qualitatively consistent with the values found for metal-on-metal systems. At the temperatures of interest here the rates are such that only atoms having no neighbors along the island's edge can evaporate. The rate constant of this elementary evaporation step is denoted by k(e). Our simulations show that an atom leaves an N-particle island at a time t with a probability proportional to exp [-k(N)t] The rate constant k(N) is determined by simulations and has several very interesting properties. (1) It depends on temperature according to the Arrhenius formula, but with an activation energy that is substantially higher than that of k(e). (2) The rate constants k(N) and k(e) are connected through k(N)/k(e) = [n(s)], where [n(s)] is the mean number of single edge atoms per island. (3) In most cases one can use for [n(s)] in this relationship a value calculated from an equilibrium ensemble; this leads to a very efficient method for calculating k(N). (4) The size dependence of k(N) is unexpected: we find that k(N) is proportional to N-0.36 for all temperatures, and for several values of k(e). These findings provide insights into the statistical properties of evaporation and also lead to a substantial simplification of simulations of particle transport between islands; rather than simulate all atomic events in detail, one can perform preliminary calculations to obtain the evaporation rates k(N), for all the island sizes N of interest, and then use these rates to simulate the atom exchange kinetics.