Non-Arrhenius Behavior of Surface Diffusion near a Phase Transition Boundary (original) (raw)
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Long jumps in surface diffusion
Journal of Colloid and Interface Science, 2004
Diffusion on metal surfaces is often viewed as the movement of atoms jumping between nearest-neighbor sites. However, statistical predictions suggest that at elevated temperatures longer jumps should become important. Now, with instruments such as the field ion microscope and the scanning tunneling microscope, which reveal individual adsorbed atoms, it has become possible to examine diffusion in some detail. Here we summarize the experimental efforts that have revealed the contributions of long jumps in various diffusion processes.
Role of long jumps in surface diffusion
Physical Review E, 2002
We analyze a probability of atomic jumps for more than one lattice spacing in activated surface diffusion. First, we studied a role of coupling between the x and y degrees of freedom for the diffusion in a twodimensional substrate potential. Simulation results show that in the underdamped limit the average jump length ͗͘ scales with the damping coefficient as ͗͘ϰ Ϫ with 1/2р Շ2/3, so that the diffusion coefficient behaves as Dϰ Ϫ with 0рՇ1/3. Second, we introduced a realistic friction coefficient for the phonon damping mechanism and developed the technique for Langevin equation with a velocity-dependent friction coefficient. The study of diffusion in this model shows that long jumps play an essential role for diffusing atoms of small masses, especially in two limiting cases, in the case of a large Debye frequency of the substrate, when the rate of phonon damping is low, and in the case of a small Debye frequency, when the one-phonon damping mechanism is ineffective.
Jump processes in surface diffusion
Surface Science Reports, 2007
The traditional view of the surface diffusion of metal atoms on metal surfaces was that atoms carry on a random walk between nearest-neighbor surface sites. Through field ion microscopic observations and molecular dynamics simulations this picture has been changed completely. Diffusion by an adatom exchanging with an atom of the substrate has been identified on fcc , and subsequently also on fcc(100) planes. At elevated temperatures, multiple events have been found by simulations in which an atom enters the lattice, and a lattice atom at some distance from the entry point pops out. Much at the same time the contribution of long jumps, spanning more than a nearest-neighbour distance, has been examined; their rates have been measured, and such transitions have been found to contribute significantly, at least on tungsten surfaces. As higher diffusion temperatures become accessible, additional jump processes can be expected to be revealed. (G. Antczak). reactions and catalysis, in sintering as well as in other surface processes. As such there has been considerable interest in how diffusion occurs; during the last few decades much novel and significant material has been discovered. Here we will briefly review what has been learned about how diffusion of single metal atoms takes place on metal surfaces, what sort of atomic jumps occur and how information about these processes has been obtained.
The Journal of Chemical Physics, 1999
It is well known that unlike static equilibrium properties, kinetic quantities in Monte Carlo simulations are very sensitive to the details of the algorithm used for the microscopic transition rates. This is particularly true near the critical region where fluctuations are pronounced. We demonstrate that when diffusion of oxygen adatoms near the order–disorder transition of a lattice-gas model of the O/W(110) model system is studied, the transition rates must be chosen carefully. In particular, we show that the choice by Uebing and Zhdanov [J. Chem. Phys. 109, 3197 (1998)] is inappropriate for the study of critical effects in diffusion.
Collective surface diffusion near a first-order phase transition
Physical Review B, 2011
For a large class of lattice models we study the thermodynamic factor, Φ, of the collective surface diffusion coefficient near a first-order phase transition between two phases at low temperatures. In a two-phase regime its dependence on the coverage, θ, is Φ ≈ θ/[(θ − θ −)(θ + − θ)N ], where N is the number of adsorption sites and θ ± are the single-phase coverages at the transition. In the crossover between the two-phase and single-phase regimes Φ(θ) is shown to have a more complex behavior. The results are applied to a simple 2D lattice model.
Bulk mediated surface diffusion: non Markovian desorption with�finite first moment
The European Physical Journal B, 2005
Here we address a fundamental issue in surface physics: the dynamics of adsorbed molecules. We study this problem when the particle's desorption is characterized by a non Markovian process, while the particle's adsorption and its motion in the bulk are governed by a Markovian dynamics. We study the diffusion of particles in a semi-infinite cubic lattice, and focus on the effective diffusion process at the interface z = 1. We calculate analytically the conditional probability to find the particle on the z = 1 plane as well as the surface dispersion as functions of time. The comparison of these results with Monte Carlo simulations show an excellent agreement.
Atomic jumps during surface diffusion
Physical Review B, 2009
The characteristics of atomic displacements during surface diffusion of Cu on Cu͑111͒ are studied by means of molecular dynamics simulations. It is found that even at very low substrate temperatures, the majority of the jumps are correlated, i.e., the displacement directions are not randomly chosen but rather keep some sort of memory from the previous moves and are influenced by them. Long jumps, spanning several surface unit cells, are observed at all temperatures. From an analysis of their length probability distribution information can be obtained about the mechanisms of friction and energy transfer between the diffusing adatom and the substrate. Both long jumps and recrossings ͑displacements in which the adatom moves back and forth between two adjacent adsorption sites͒ appear with a higher activation energy than normal diffusion. Finally, the influence of the instantaneous atomic configuration of the substrate on the adatom's trajectory is also highlighted.
Journal of Physical Chemistry B, 2004
The dynamics of Brownian particles diffusing across a one-dimensional, incoherent stochastic potential of mean force in the Smoluchowski regime has been intensely investigated by several groups. In recent work, we have developed a phenomenological equation of motion that extends this representation throughout the friction regime and, in particular, extends it to the low-friction regime relevant to surface diffusion. Resonant activation is observed throughout; it is manifested by a peak in the transport as a function of the correlation time in the potential fluctuations. The phenomenological equation of motion has now been utilized to probe the dynamics on a variety of one-and two-dimensional surfaces in order to provide a qualitative description of the fundamental factors that govern the surface hopping events of an adsorbate weakly bound to a metal surface. The primary focus is placed on differences that may arise when the substrate is modeled using a oneor two-dimensional potential of mean force, thereafter the effects of spatially coherent or incoherent barrier heights are also addressed. The two-dimensional behavior can be adequately described by the direct product of two separable one-dimensional analogues, as might naïvely be expected, provided the lattice spacing is sufficient to decouple the two degrees of freedom. Coherency between the barriers affects the rates to a smaller degree and is significant only when the barriers are strongly correlated in time.
Surface diffusion in the low-friction limit: Occurrence of long jumps
Physical Review B, 1996
We present a molecular dynamics ͑MD͒ study of a Brownian particle in a two-dimensional periodic potential. For a separable potential, the study of the diffusion constant along the symmetry directions reduces to two one-dimensional problems. In this case, our MD study agrees with the existing analytical results on the temperature and the friction () dependence of the diffusion constant (D). For a nonseparable and anisotropic potential such as the adsorption potential on a bcc͑110͒ surface, the present study predicts an alternative Dϳ1/ 0.5 dependence in the low friction regime as opposed to the Dϳ1/ dependence found in previous studies of one-dimensional or separable potentials. We find that the dependence of D on in the low friction regime is directly related to the occurrence of long jumps. The probability for the long jumps depends not only sensitively on the value of the friction but also on the geometry of the surface. On the bcc͑110͒ surface, the path connecting adjoining adsorption sites does not coincide with the direction of easy crossing at the saddle point. Consequently, the probability of deactivation is enhanced, leading to the reduction of long jumps and the different dependence of D on .
A note on a statistical-mechanical treatment of activation-limited surface diffusion
Reaction Kinetics and Catalysis Letters, 1974
A brief review is given of a class of simple statistical-mechanical models for s~rface diffusion, applicable to the limiting case where diffusioual "hopping" is controlled by the thermal activation rate of the adsorbed particle. A theoretical result of Reyes, for the pre-exponential or "frequency" factor, is discussed and compared briefly to experiment.