Diffusion in Solids. The Diffusion Equations. Atomistic Theory of Diffusion: Fick’s Laws and a Theory for the Diffussion Construct. Random Walk Problem. Random Walk Calculations. Relation of D to Random Walk. Self-Diffusion Vacancy Mechanism in a FCC Crystal. Activation Energy for Diffusion. Other Mass Transport Mechanisms. Permeability versus Diffusion. Convection versus Diffusion. Mathematics of Diffusion. Steady State Diffusion—Fick’s First Law. Non–Steady State Diffusion—Fick’s Second Law
We have undertaken a systematic study of the diffusion barriers encountered by Cu adatoms or very small clusters in various atomic geometries, with the purpose of finding a simple formula able to provide a good estimation of the diffusion barriers as a function of the atomic environment of the diffusing atom. The final aim is to use them as input in a Kinetic Monte Carlo (KMC) code. Indeed, in this type of simulation it is quite risky to consider only a few diffusion mechanisms and, since it is obviously impossible to calculate a priori all of them, a simple expression is highly desired. KMC then allows one to simulate long time scale processes much faster especially when a simple expression is available to estimate barriers.
In another work we have determined the diffusion rates corresponding to most of the elementary diffusion processes that may occur during the growth of a single 2D adisland on Cu(111). We started by studying the diffusion of an adatom along step A and step B using the two methods: The Transition State Theory in the Harmonic Approximation (TST-HA) approach (in the classical limit) and Molecular Dynamics (MD) simulations. We show that the static activation barrier accounts quite well for the results of MD simulations. However, the prefactors obtained in the latter method are different from those given by TST-HA. Furthermore they are quite consistent with the Meyer-Neldel law. We have then determined the static barriers for other diffusion events in the presence of straight steps or in the vicinity of steps with defects, for instance around corners and kinks.