Kinetic Monte Carlo - Examples of Use

Examples of Use

KMC has been used in simulations of the e.g. the following physical systems:

1. Surface diffusion
2. Surface growth (Meng 1996)
3. Vacancy diffusion in alloys (this was the original use in (Young 1966))
4. Coarsening of domain evolution
5. Defect mobility and clustering in ion or neutron irradiated solids including, but not limited to, damage accumulation and amorphization/recrystallization models.
6. Viscoelasticity of physically crosslinked networks (Baeurle 2006)

To give an idea what the "objects" and "events" may be in practice, here is one concrete simple example, corresponding to example 2 above.

Consider a system where individual atoms are deposited on a surface one at a time (typical of physical vapor deposition), but also may migrate on the surface with some known jump rate . In this case the "objects" of the KMC algorithm are simply the individual atoms.

If two atoms come right next to each other, they become immobile. Then the flux of incoming atoms determines a rate r_deposit, and the system can be simulated with KMC considering all deposited mobile atoms which have not (yet) met a counterpart and become immobile. This way there are the following events possible at each KMC step:

• A new atom comes in with rate 'r_deposit
• An already deposited atom jumps one step with rate w.

After an event has been selected and carried out with the KMC algorithm, one then needs to check whether the new or just jumped atom has become immediately adjacent to some other atom. If this has happened, the atom(s) which are now adjacent needs to be moved away from the list of mobile atoms, and correspondingly their jump events removed from the list of possible events.

Naturally in applying KMC to problems in physics and chemistry, one has to first consider whether the real system follows the assumptions underlying KMC well enough. Real processes do not necessarily have well-defined rates, the transition processes may be correlated, in case of atom or particle jumps the jumps may not occur in random directions, and so on. When simulating widely disparate time scales one also needs to consider whether new processes may be present at longer time scales. If any of these issues are valid, the time scale and system evolution predicted by KMC may be skewed or even completely wrong.