A rigorous observable for vacancy characterization and diffusion in crystals

Details A rigorous observable for vacancy characterization and diffusion in crystals A rigorous observable for vacancy characterization and diffusion in crystals

2012-04-01

arxiv.org/abs/1204.0192v1

Physics

Condensed Matter

Materials Science

Scientific paper

We introduce an observable field to describe the dynamics of a single vacancy in a crystal. This field is the density of a pseudo quantum wavefunction representing the vacancy, which, in turn, is the ground state eigenfunction of an Hamiltonian associated to the potential energy field generated by the atoms in the sample. In our description, the $\hbar^2/2 m$ coefficient of the kinetic energy term is a tunable parameter that makes the density localized in the regions of 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, in addition to the simple and expected nearest neighbor hopping path, collective migration mechanisms of the vacancy. These mechanisms involve several lattice sites and produce a long range migration. Finally, we also observed a vacancy induced crystal reorientation process.

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