Why KMC?¶

KMC is a well known method for accelerated dynamics simulations of atomistic systems. The method builds on the separation of timescales between the fast vibrational motion on the one hand and the slow events of interest on the other. Only the slow events are simulated while all other motion in the system is regarded as equilibrated when each slow (and therefore rare) event takes place. Accurate calculations of energies for the elementary processes are typically combined with transition state theory estimates of the corresponding rates to build the input to the KMC simulation: an initial configuration and a list of elementary processes that governs the dynamics of the system. Since no motion that takes place on a short time scale is explicitly treated KMC simulations can often reach long time scales that are difficult to access with other methods.

The lattice KMC method implemented in KMCLib is a particularly efficient form of KMC suitable for simulating systems where the configuration can be expressed on a lattice in space, and where all process in the system take place on this lattice by changing the types associated with the lattice sites. Systems suitable for lattice KMC simulations are typically ordered materials such as the bulk of (defect) crystalline solids and their surfaces. KMCLib implements the lattice KMC method.

Several good description of the KMC method exists in the literature. Arthur F. Voter has written an introductory text to KMC simulations [Ref.1] that I find particularly appealing. There is also a vast bulk of research literature on the subject, from the first publications of the method [Ref.2], [Ref.3], to several more recent reviews (e.g. [Ref.4], [Ref.5], [Ref.6], [Ref.9]), as well as many research papers using the KMC method.

Why KMCLib?¶

Several implementations of the KMC method exist already. So why would you need another one?

Searching the webofknowledge publication database for papers using KMC you find that for the last couple of years several hundred papers using KMC were published each year. But only a small fraction of these publications used any of the publicly available KMC codes. Clearly the available codes do not meet everyone’s needs. A plausible explanation is that the KMC algorithm is simple enough so that anyone with some programming experience can write her own code. Combine this with the need for custom solutions for many systems you end up in a situation where most research groups have their own implementation of the method. This situation is not ideal. Since the majority of these codes never makes it to the public much work is wasted re-inventing the wheel rather than focusing on the models design.

The KMCLib project started from the need of a flexible KMC code that did not require re-compilation to setup or modify a KMC model. We also needed the ability to study diffusion in complex bulk systems that required more flexibility than what could easily be obtained using the common approach of pre-defining all possible processes before the start of the simulation. For complex systems with many possible interactions this list easily grows out of hand. With the introduction of the custom rate calculator interface (KMCRateCalculatorPlugin) we were able to combine well-defined processes on a lattice with rates that depend in a complex way on the surroundings.

KMCLib can be used for studying reactions and diffusion of any surface or bulk system that can be expressed on a lattice in space, but is particularly well equipped for

• Bulk diffusion studies, that are made easy through the built in mean square displacement (MSD) analysis and the ability to track individual atoms during the simulation.

• Extensions to the conventional KMC algorithm, where use of the custom rate calculator can solve the complexity problem where the number of elementary processes grows large for complex systems with long range interactions.

• ab initio KMC schemes with many complex interactions in dense bulk or complex surface systems, where the KMCLib parallelization scheme over process-site pairs to match is most efficient.

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