Proton conduction mechanism in M3H(XO4)2 crystals: the trigonal asymmetric hydrogen bond model

Localized diffusive proton motions in the solid-state protonic conductor Rb3H(SeO4)2 were studied at 500 K with quasielastic incoherent neutron scattering on the 10−11–10−10 s time scale. The experimentally determined model-independent ‘apparent’ EISF is used as a guidance to deduce an approximate proton density distribution for this time interval, as the starting point for developing the trigonal-asymmetric hydrogen bond (TAHB) model. The incoherent scattering function of this model is derived and the resulting theoretical EISF compared to the experiment. The obtained values of the model parameters, the order parameter η and the jump distance R21, indicate that—in spite of its very fast relaxational motions in the neighbourhood of the oxygen—the proton essentially remains bonded to a selenate top oxygen for a period of the order of at least 10−10 s. Nevertheless, but with rather low probability, it is also making—in the 10−11–10−10 s time interval—brief steps into the hydrogen bridge. We interpret these observations as the consequence of dynamic disorder in the form of an intracrystalline chemical equilibrium reaction: alternation between the association of the monomers [HSeO4]1− and [SeO4]2−, resulting in the dimer [H(SeO4)2]3− (H-bond formation) and the dissociation of the latter into the two monomers (H-bond breaking). At 500 K, this reaction has a rather asymmetric character: The average life-time of the dimer is about 20 times shorter than that of the monomers.