MC-MS: Monte Carlo-Molecular Statics
Definition:A Monte Carlo (→MC) simulation method using molecular dynamics (→MD) potentials and local relaxation to define the energetics used for MC.
Explanation:Unlike standard MC simulations of atomic processes, MC-MS simulations use flexible atomic positions. To define the energy changes between the attempted configuration changes and the corresponding probabilities for these changes, MD potentials are used. This allows necessary atomic details to be included. A configuration change in MC-MS is comprised of two steps. Firstly, a jump of an atom or a group of atoms is performed by assigning a jump with a high probability to the corresponding atom coordinates. This may reflect the jump of an atom into a vacancy site, but also to an interstitial site or a locally extended volume in a grain boundary or dislocation. Secondly, a quasi-static relaxation of atom positions is performed using MD with an additional artificial viscous drag. The corresponding drag coefficient is chosen so that the the system is relaxed rapidly during only few MD time steps. The total energy change is obtained from the final configuration energy and the one before the possible jump. Although the degree of relaxation in the second step is found to influence the final results, its effect is not significantly [Jannot] because global relaxation dominates in comparison with local relaxations. However, it has not been yet tested for kinetic MC simulations (→MD">→kMC) using MD potentials where the amount of relaxation for the unstable transition energy would have a large impact.

MC-MS simulations require much demanding computation than simple MC simulations due to the relaxation steps. However, once applied to the right purpose, they are much more efficient than pure MD simulations because they essentially skip the many unsuccessful attempts for configuration changes.
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A dislocation in Al aligning itself to the orientation of Guinier-Preston-zones (flat Cu precipitates in {100} planes. Left: MC-MS simulation; right: the corresponding transmission electron microscograph.
SFB-Link:In the SFB, MC-MS simulations are to be tested for their applicabillity in deriving grain boundary properties, in particular, the grain boundary energy. However, estimating the first jump for a configuration change is not trivial and must be examined by MD first.
References:E. Jannot: Study of the effect of dislocations on precipitation kinetics by means of atomic simulations. Dissertation, 2008, IMM, RWTH Aachen University, Shaker, ISBN 978-3-8322-8010-9