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Long time scale simulations of solids undergoing atomic and spin transitions
FA 31 ()
Atomic rearrangements in solids, for example migration of defects, diffusion of atoms
or chemical reactions, typically involve overcoming an energy barrier and the time
interval between such events is many orders of magnitude longer than the time scale
of atomic vibrations. Computer simulations based on direct solution of the classical
equation of motion often cannot cover long enough time intervals. A different
simulation approach is needed to simulate long time scale evolution in solids. For
complex systems where the atomic structure and mechanism of transitions is unknown,
such long time scale simulations are particularly relevant. The adaptive kinetic
Monte Carlo (AKMC) approach will be described in this presentation. It is based on
the two step WKE procedure, which involves the identification of an optimal transition
state and subsequent dynamical trajectories started at the transition state. For each
state of the system, possible transition mechanisms are explored and transition rates
determining, followed by a kinetic Monte Carlo algorithm to pick a transition and
advance the clock. The key problem is the identification of a good transition state
for each state of the system without bias towards a particular mechanism or final state.
Within the harmonic approximation to transition state theory this requires finding all
relevant saddle points on the potential energy rim surrounding the energy well
corresponding to the current state. More generally, a dividing surface corresponding to
maximum free energy needs to be identified. We have developed methods for finding such
transition state surfaces and implemented them in software for distributed computing.
Application to defects and diffusion in and on the surface of solids as well as spin
transitions in nano-clusters will be presented.