06-08U
06-08U
Longitudinal dielectric, piezoelectric, elastic, dynamic and thermal properties of KH$_2$PO$_4$ type ferroelectrics
Calculations for KH$_2$PO$_4$ type crystals are performed within the fourparticle cluster approximation for the proton ordering model with taking into account a coupling with the shear strain $\varepsilon _{6}$. Dynamics of the spin subsystem is considered within the Glauber approach, and it is supplemented with the Newtonian dynamics of the shear strain. Expressions for the dynamic dielectric permittivity, elastic stiffness and piezoelectric moduli, as well as sound velocity and attenuation of the crystals are derived. It is shown that the influence of piezoelectric coupling on spontaneous polarization and specific heat of the crystals is minor, but it leads to the piezoelectric resonances.