Calculation of the Spontaneous Polarization and the Dielectric Constant as a Function of Temperature for

The temperature dependence of the spontaneous polarization P is calculated in the ferroelectric phase of KH2PO4 (KDP) at atmospheric pressure (TC = 122 K). Also, the dielectric constant ε is calculated at various temperatures in the paraelectric phase of KDP at atmospheric pressure. For this calculation of P and ε, by fitting the observed Raman frequencies of the soft mode, the microscopic parameters of the pure tunnelling model are obtained. In this model, the proton-lattice interaction is not considered and the collective proton mode is identified with the soft-mode response of the system. Our calculations show that the spontaneous polarization decreases continuously in the ferroelectric phase as approaching the transition temperature TC. Also, the dielectric constant decreases with increasing temperature and it diverges in the vicinity of the transition temperature (TC = 122 K) for KDP according to the Curie-Weiss law