Vacancy Hopping & Ionic Conductivity

This simulator renders a 6×6×6 cubic sublattice of a mobile ion species riddled with Schottky vacancies — empty lattice sites left behind when ions are removed from the crystal. Each ion adjacent to a vacancy has a probability per second of hopping into it, set by the Arrhenius activation law with the migration barrier you choose. Raise the temperature and hops fire faster everywhere; raise the applied field and hops along the field direction become more likely than hops against it, turning the random walk into a net ionic drift current — exactly the mechanism behind solid electrolyte conductivity in real batteries and fuel cells. Live readouts track the instantaneous lattice hop rate, cumulative hop count, the Nernst–Einstein ionic conductivity σ, and the net drift current density.