Vacancy Hopping & Ionic Conductivity (2D)

This simulator renders an 18×18 square 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. A second panel draws the field-tilted hopping energy landscape live, and a third tracks the lattice hop rate over time, alongside readouts for cumulative hop count, the Nernst–Einstein ionic conductivity σ, and the net drift current density.