Thermodynamics and complex dielectric permittivity of mixed crystals of the Rb1-x(NH4)xH2PO4 type

We propose a pseudospin model for proton glasses of the Rb1-x (NH4)(x)H2PO4(Rb1-x(ND4)(x)D2PO4) type, which takes into account the energy levels of hydrogens (deuterons) around the PO4 group, long-range interactions between the hydrogen bonds, and an internal random deformational field. Within the framework of a cluster approximation and a mean field approximation over the long-range interactions, we derive a system of equations for the state parameters for the regions which are in the ferroelectric and antiferroelectric states, as well as in the proton glass state. Within the Glauber dynamics approach, we obtain a system of equations for the frequency-dependent linear responses of polarization and the proton glass order parameter. We obtain a qualitative description of the temperature behavior of dielectric permittivities of the K1-x (ND4)(x)D2PO4 and Rb1-x(NH4)(x)H2AsO4 compounds at different frequencies. The origin of low-temperature peak in the imaginary part of dielectric permittivity in proton glasses is discussed.