 MC: Monte Carlo simulation 
Definition:  A simulation method
for discrete atom
movement based on
jump probabilities
derived from
thermodynamics 
Explanation:  In general
MC
simulations,
configurations of
complex interacting
entities are rated
by a criterion
defining their
deviation from an
ideal or final
state. In discrete
steps (a.k.a.
MCsteps), the
configuration is
randomly altered
(usually by a small
amount) and
reevaluated. During
the evalutioan, the
proabability of the
configuration is
calculated and the
configuration change
is determined
accordingly. Then,
the next
MCstep with a new
random change is
tested repetitively
in a
virtual infinite
loop, so that the
system approaches
its ideal
state.
As an example of MC
simulations in
materials
science, atomic
configurations are
tested in order to
find an
ideal spatial
distribution for a
mixture of chemical
elements. The tested
alterations are atom
exchanges
or
vacancy/interstitial
jumps.
The optimisation
criterion is the
minimization of the
free energy or
enthalpy. In
thermodynamic MC
simulations, the
probability for the
configuration change
is calculated as a
Boltzmann term
considering the
energy change
involved. In kinetic
MC (→kMC)
simulations ,
the configuration
change is considered
to be thermally
activated, and
accordingly the
activation energy
for the change
is used to define
the transition
probability.
In order to get
physically sound
results,
it is important to
describe the energy
change between
the configurations
accurately. In
simple simulations,
only nearest (or
second nearest)
neighbour
interactions between
atoms are taken into
account, and
discrete atom
positions in a fixed
crystal lattice are
prescribed. However,
such simple
approaches do not
account for
longrange
interactions like
elasticity (see e.g.
[Jannot et
al.]) or
ferromagnetism. For
an elaborate
simulation,
such effects must be
considered in
addition to the
local changes. An
alternative are
MonteCarloMolicular Statics
(→MCMS)
simulations, which
use a fully
consistent energetic
description from
molecular dynamics
(→MD)
potentials or,
ideally, from ab
initio
calculations. 
Picture / Figure / Diagram: 

MCsimulated distribution of the pipe diffusion coefficient of Cu around a dissociated edge dislocation in Al at 300 K (left) and 900 K (right).


SFBLink:  In more specialized MCMS approach, Monte Carlo simulations are tested for applicability in deriving grain boundary properties from MD potentials, with the perspective of using ab initio calculated data. As indicated by the example of pipe diffusion above, any kind of atomistic process can be considered. 
References:  A. D. Rollett, P. Manohar: The MonteCarloMethod. In: Continuum Scale Simulation of Engineering Materials (Eds.: D. Raabe, L.Q. Chen, F. Barlat, F. Roters), WileyVCH 2004, 77114. E. Jannot, V. Mohles, B. Thijsse: Calculation of the elastic energy of a solid solution. Phil. Mag. 90 (2010), 963–975 

