Entropy and Kinetics of Point-Defects in Two-Dimensional Dipolar Crystals

Abstract

We study in experiment and with computer simulation the free energy and the kinetics of vacancy and interstitial defects in two-dimensional dipolar crystals. The defects appear in different local topologies which we characterize by their point group symmetry; $C_n$ is the n-fold cyclic group and $D_n$ is the dihedral group, including reflections. The frequency of different local topologies is not determined by their almost degenerate energies but dominated by entropy for symmetric configurations. The kinetics of the defects is fully reproduced by a master equation in a multi-state Markov model. In this model, the system is described by the state of the defect and the time evolution is given by transitions occurring with particular rates. These transition rate constants are extracted from experiments and simulations using an optimisation procedure. The good agreement between experiment, simulation and master equation thus provides evidence for the accuracy of the model.