 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
statetostate
transitions are
treated directly
using MC
method [1].
The rate of the
individuals jumps is
typically given
by the euqation
below, where Γ_{0}
is the attempt
frequency as
determined by
transition state
theory, ΔE
is the energy
barrier of the
individual
transition process,
k_{B}
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 bondcutting
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. 
Picture / Figure / Diagram: 



Result of a kMC simulation of Fe2at%Cu2at%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. 123, 2007 

