Proton strings and rings in atypical nucleation of ferroelectricity in ice*

Ordinary ice has a proton-disordered phase which is kinetically metastable. Upon doping with KOH at low temperature the transition to ferroelectric (FE) ice takes place, with a mechanism that needs clarification. We introduce a lattice model based on dipolar interactions plus a frustrating term that enforces the ice rule (IR). In the absence of IR-breaking defects, standard Monte Carlo (MC) simulations leave the defect-free ice model in a state of disordered proton ring configurations with the correct Pauling entropy. A replica-exchange accelerated MC sampling enables full equilibration, reaching low-temperature FE order through a well defined first order phase transition. When proton vacancies mimicking the KOH impurities are planted into this IR-conserving lattice, they enable standard MC to work, revealing the kinetics of evolution of ice from proton disorder to partial FE order below the transition temperature. Replacing ordinary nucleation, each impurity opens up a proton ring generating a linear string, an actual ferroelectric hydrogen-bond wire that expands with time. The predicted dependence of FE order fraction upon dopant concentration and quenching temperature agree well with that of real KOH doped ice.