Non-Arrhenius Behavior of Surface Diffusion near a Phase Transition Boundary

Abstract

We study the non-Arrhenius behavior of surface diffusion near the second-order phase transition boundary of an adsorbate layer. In contrast to expectations based on macroscopic thermodynamic effects, we show that this behavior can be related to the average microscopic jump rate which in turn is determined by the waiting-time distribution W (t) of single-particle jumps at short times. At long times, W (t) yields a barrier that corresponds to the rate-limiting step in diffusion. The microscopic information in W (t) should be accessible by STM measurements.PACS numbers: 68.35.Fx, 82.20.Pm The migration of atoms and molecules is one of the most important processes taking place on solid surfaces. It appears in many phenomena such as catalytic reactions and surface growth that are important for practical applications [1]. In most experimental and theoretical studies of the surface diffusion constant D, its temperature dependence is analyzed through an assumed Arrhenius form, where D is written as a product of an entropic prefactor D 0 and a term exp(−E D A /k B T ) describing thermally activated jumps over an energy barrier E D A . Although the Arrhenius form can be derived from microscopic considerations in some special cases [2,3], a rigorous justification for its use in interacting systems at finite coverages is not available. Further, even in the cases where D appears to have an Arrhenius temperature dependence over a finite temperature range, its microscopic interpretation may not always be clear. This is because for an interacting system, there may be many microscopic activation barriers. Thus the value of the measured effective diffusion barrier E D A must result from some complex average of all of them, and does not refer to any microscopic process in particular [4].In fact, the values for D 0 and E D A can be strongly temperature-dependent indicating a region of nonArrhenius behavior. This becomes especially pronounced near surface phase transition boundaries, where rapid variations of D have been observed in experiments [4][5][6] and computer simulations [2,7]. Such rapid changes are often accompanied by the well-known "compensation" effect [8], where an apparent increase in E D A is compensated by an increase in the prefactor D 0 [6]. However, in most cases the underlying reasons for non-Arrhenius behavior are not understood. It is the purpose of the present work to study these issues near a second-order phase transition in a surface adsorbate layer. We show that in contrast to the common folklore that an anomalous temperature dependence in D near T c would be predominantly due to non-local thermodynamic effects, it can be explained by the microscopic single-particle jump rate Γ. This quantity is determined by the short-time behavior of the waiting-time distribution W (t) for single-particle jumps. Moreover, we show that for long times, W (t) yields an effective activation barrier that corresponds to the rate-limiting step in diffusion. Thus W (t) provides a connection between microscopic and macroscopic...

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