Within the framework of proton model with taking into account the piezoelectric interaction with the shear strain ε 6 , a dynamic dielectric response of KD 2 PO 4 type ferroelectrics is considered. Experimentally observed phenomena of crystal clamping by high frequency electric field, piezoelectric resonance and microwave dispersion are described. Ultrasound velocity and attenuation are calculated, peculiarities of their temperature dependence at the Curie points are described. Existence of a cut-off frequency in the frequency dependence of attenuation is predicted.

We propose a pseudospin model for proton glasses of the Rb 1−x (NH 4 )xH 2 PO 4 (Rb 1−x (ND 4 )xD 2 PO 4 ) type, which takes into account the energy levels of hydrogens (deuterons) around the PO 4 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 K 1−x (ND 4 )xD 2 PO 4 and Rb 1−x (NH 4 )xH 2 AsO 4 compounds at different frequencies. The origin of low-temperature peak in the imaginary part of dielectric permittivity in proton glasses is discussed.

Within the framework of the proposed unified proton ordering model for the ferroelectric compounds of the KH 2 PO 4 family, in the four-particle cluster approximation for the short-range interactions and mean field approximation for the long-range interactions, we calculate thermodynamic and longitudinal dynamic characteristics of the KD 2 PO 4 type ferroelectrics and ND 4 D 2 PO 4 type antiferroelectrics. Calculations for partially deuterated K(H 1−x Dx) 2 PO 4 type ferroelectrics and N(H 1−x Dx) 4 (H 1−x Dx) 2 PO 4 type antiferroelectrics are performed within the mean crystal approximation. It is shown that at the proper choice of the theory parameters, a good quantitative description of experimental data for the KH 2 PO 4 family crystals is obtained.

We propose a two-sublattice proton ordering model for the quasione-dimensional CsH 2 PO 4 ferroelectric with hydrogen bonds, which takes into account linear on lattice strains u 1 , u 2 , u 3 and u 5 contribution to the energy of proton subsystem. The model also takes into account the dependence of effective dipole moments of pseudospins on the order parameters, which enables one to agree the effective dipole moments in paraelectric and ferroelectric phases. Within this model in two-particle cluster approximation on short-range interactions and in the mean field approximation on long-range interactions, there is investigated the behaviour of spontaneous polarization, longitudinal dielectric permittivity and molar heat capacity under the action of hydrostatic pressure and longitudinal electric field. The phase transition into antiferroelectric phase under high pressures is explained. The character of smearing of the paraelectric-ferroelectric phase transition as well as suppression of the antiferroelectric phase at the presence of electric field is studied.

Within the framework of the modified proton model with taking into account the interaction with the shear strain ε 6 , a dynamic dielectric response of ND 4 D 2 PO 4 type antiferroelectrics is considered. Dynamics of the piezoelectric strain is taken into account. Experimentally observed phenomena of crystal clamping by high frequency electric field, piezoelectric resonance and microwave dispersion are described. Ultrasound velocity and attenuation are calculated. Character of behaviour of attenuation in the paraelectric phase and the existence of a cut-off frequency in the frequency dependence of attenuation are predicted. At the proper choice of the parameters, a good quantitative description of experimental data for longitudinal static dielectric, piezoelectric and elastic characteristics and sound velocity for ND 4 D 2 PO 4 and NH 4 H 2 PO 4 is obtained in the paraelectric phase.