10-18U
10-18U
Dielectric, piezoelectric and elastic properties of KH$_2$PO$_4$ and RbH$_2$PO$_4$ ferroelectrics. Bloch equations method
Within modified proton ordering model with taking into account tunneling of protons on hydrogen bonds and linear on strains $\varepsilon _6 $, $\varepsilon _4 $ and $\varepsilon _5 $ contributions into energy of proton system, within mean field approximation we calculated dielectric, piezoelectric, elastic, and within Bloch method also dynamic characteristics of KH$_2$PO$_4$ type ferroelectrics. It is shown, that proposed theory let us to obtain good agreement of theoretical results with experimental data for KH$_2$PO$_4$ and RbH$_2$PO$_4$ only in paraelectric phase. Thorough analysis of excitation spectrum of KH$_2$PO$_4$ type ferroelectrics within the model is carried out.