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kMC

kMC: kinetic Monte Carlo
Definition:A Monte Carlo (→MC) method to simulate the time evolution of atomic distributions in a material
Explanation:In molecular dynamics (→MD) modeling, the accurate integration of the equations of atomic motion requires a small time step (∼10−15 s) to resolve the atomic vibrations; therefore it can only simulate the process during a short duration. kMC is used to overcome this limitation and to study atomic processes that take place on longer time scales such as diffusion. The main idea behind the kMC is the fact that the dynamics of the long atomic precess consists of diffusive jumps from state to state in a configuration space. Rather than following the trajectory through every vibrational position, these stochastic state-to-state transitions are treated directly using MC method [1].

The rate of the individuals jumps is typically given by the euqation below, where Γ0 is the attempt frequency as determined by transition state theory, ΔE is the energy barrier of the individual transition process, kB is the Boltzmann constant and T is the temperature. The energy values are most reliably obtained from ab initio calculations by using either nudged elastic band calculations or a linear bond-cutting model. Applications of kMC include the determination of an atomic diffusion coefficient in complex structures as well as the formation of precipitate phases in a matrix.
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Diagram:


Result of a kMC simulation of Fe-2at%Cu-2at%Si. The golden balls indicate the position of the Cu atoms and the onset of precipitate formation. The purple balls are Si atoms. The red ball shows the position of the single vacancy used in the present simulation.
References:[1] A. Voter, Introduction to the kinetic Monte Carlo method. In Radiation Effects of Solids, NATO Science Series, Volume 235, pp. 1-23, 2007