A Theory of the Mobility of (H₃O)⁺ Defects in Ice Crystal

Abstract

The mobility of an ionic defect, H₃O⁺ defect, in ice is studied on a new model which introduces both coherence in successive transfer-steps of a H₃O⁺ defect and randomness in transfer direction. States containing a H₃O⁺ defect are assumed to be coupled with each other by tunneling of proton to form wave-like states as in the case of spin waves in ferromagnetic crystals. The density of states of the coupled system, approximated by a Bethe lattice, is calculated. The mobility of H₃O⁺ defect is calculated using the Kubo formula. The mobility converges because of the randomness in transfer direction though no other scattering mechanisms are assumed. The value of mobility is obtained as 1.8×10⁻⁵ cm²/V·sec at −10°C. Because of coherence the mobility of H₃O⁺ defect is estimated at about 15 times the mobility calculated for incoherent transfer.