Calculation of the Spontaneous Polarization and the Dielectric Constant as a Function of Temperature for KH2PO4

The temperature dependence of the spontaneous polarization P is calculated in the ferroelectric phase (T < T-C) of KH2PO4 (KDP) at atmospheric pressure (T-C = 122 K). Also, the dielectric constant e is calculated at various temperatures in the paraelectric phase (T > T-C) of KDP at atmospheric pressure. For this calculation of P and epsilon, 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 T-C. Also, the dielectric constant decreases with increasing temperature and it diverges in the vicinity of the transition temperature (T-C = 122 K) for KDP according to the Curie-Weiss law.