A microscopic model for the description of the proton subsystem dynamics in superionic crystals with hydrogen bonds is developed. Besides the inclusion of the proton-transport mechanism, the effect of the displacement of the nearest oxygens during hydrogen-bond formation is taken into account. The latter effect is the cause of the strong proton-phonon coupling that leads to the polaronic effect. Using the occupation number formalism, the virtual (in superionic phases) or ordered (in low-temperature phases) character of the hydrogen-bonded system is taken into account on the basis of the proton-ordering model. Protonic conductivity studies are carried out in the framework of the Kubo theory for the cases of superionic phases as well as low-temperature phases with different types of proton ordering (as an example the M3H(XO4)2 class of crystals is considered). The temperature dependencies of the conductivity are analysed. The activation energies for the static conductivity are determined; for this case the influence of the internal field which appears as a result of the proton ordering is investigated.

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The proton conductivity in the hydrogen-bonded systems with strong correlations between protons is investigated theoretically in the context of the two-stage transport modeling approach. The distortions of the nearest ionic groups at the formation of the hydrogen bond are shown to be the reason for the strong proton–phonon coupling and polaronic effect. We evaluate as an example the conductivity for M3H(XO4)2-class of crystals with high proton mobility in (001) conducting planes. We analyze the temperature dependencies of the conductivity and its interbond and intrabond contributions in the vicinity of the transition from the disordered superionic to the ordered state. We investigate also the main peculiarities in the frequency dependencies of the conductivity appearing due to the proton interactions and compare our results with the previous conclusions obtained for the chains of noninteracting protons.