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Within the modified model of proton ordering of one-dimensional ferroelectrichaving hydrogen bonds of PbHPO$_4$-type, their thermodynamic and dynamiccharacteristics are studied and calculated taking into account the linear (bycrystal deformations $\varepsilon_i$ ($i=1,3$) and $\varepsilon_4$)contributions into the energy of a proton system but without taking intoaccount the tunneling in the two-particle cluster approximation. There has beenobtained a good quantitative description of the temperature dependence ofpolarization, static dielectric permittivity, heat capacity and frequencydependence of dynamic dielectric permittivity at different temperatures forPbHPO$_4$ and PbHDO$_4$ crystals.

Thermodynamic and dynamic dielectric properties of one-dimensional hydrogen bonded ferroelectric of PbHPO$_4$-type