An observable for vacancy characterization and diffusion in crystals

To locate the position and characterize the dynamics of a vacancy in a crystal, we propose to represent it as the ground state density of a pseudo-quantum probe particle associated to the Hamiltonian which has, for the potential energy, the field generated by the atoms in the sample. In this description, the coefficient of the kinetic energy term is a tunable parameter controlling the density localization in the regions of the relevant minima of the potential energy field. Based on this description, we derive a set of collective variables that we use in rare event simulations to identify some of the vacancy diffusion paths in a 2D crystal. Our simulations reveal that the vacancy migrates according to local and non-local mechanisms, the second involving several lattice sites and producing a long range migration. We also observed a vacancy induced crystal reorientation process. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4796322]