Research
Temperature Dependence of Dielectric Loss Tangent in KDP (KH2PO4) Type Crystals
Considering third- and fourth-order phonon anharmonic interactions terms in the four particle cluster model Hamiltonian proposed by Blinc et al [1982 J Phys, C15 4661] for the stochastic motion of − 4 H2PO groups for KDP (KH2PO4) type ferroelectrics, expressions for soft mode frequency and loss tangent are evaluated. For the calculations, method of double time temperature dependent Green’s function has been used. By fitting model values of physical quantities, the dielectric loss in paraelectric phase of KDP (KH2PO4) crystal at 9.2 GHz for field along the a-axis (tanδ a ) , and c-axis (tanδ c ) have been calculated which compare well with experimental results of Kaminow et al [1963Phy Rev,129 1562]. A good agreement has been found. In the microwave frequency rage, an increase in frequency is followed by an increase in transverse and longitudinal dielectric loss tangent. The loss decreases with increase in temperature for KDP (KH2PO4) crystal, in their paraelectric phase. This shows Curie-Weiss type behavior of the dielectric loss tangent.
Temperature Dependence of Inverse Dielectric Susceptibility in KDP-Type Crystals
By using four particle cluster model Hamiltonian along with third and fourth order phonon anharmonic interaction terms for KDP-type crystals, expressions for renormalized soft mode frequency and inverse dielectric susceptibility have been obtained. The method of double time temperature dependent Green’s function has been used for calculation. Fitting the values of model parameters, the temperature dependence of soft mode frequency and inverse dielectric susceptibility has been evaluated. The inverse dielectric susceptibility was observed increases linearly with temperature, for KDP crystal, in its paraelectric phase. Theoretical results are compared with experimental results of Kim et al [Physics Review B73, 134114 (2006) and Current Applied Physics 9(2009) 1307]. A good agreement has been found between the reported and present results.
Dielectric properties of order-disorder type crystals
The soft mode dynamical model has been used to study the dielectric properties of order-disorder-type crystals. Using the model Hamiltonian proposed by Blinc [Advances in Phys, 29 (1972) 701] and has been modified by Bist et al [GJSFR,10,18(2010)], the expressions for the dielectric constant and tangent loss have been derived and discussed for order-disorder, KH2PO4 type-crystals with the help of double time temperature dependent Green’s function techniques and Dyson’s equation treatment. Using appropriate parameters given by Ganguli et al [Phys Rev. B21, 2937 (1980)] the transverse dielectric constant and observed dielectric constant have been calculated and compared with experimental results of Raman Intensity[Ferroelectrics 52, 91 (1983)], Busch [Helv. Phys. Acta. 11, 265 (1938)], Kaminow et al [Phys. Rev. 138A, 1539 (1963)], and Deguchi et al [J. Phys. Soc. Jpn. 49, 1887 (1980)]. The observed dielectric constant explains the Curie-Weiss behaviour of dielectric constant along the c-axis of KH2PO4 crystal in the paraelectric phase. Also the temperature dependence of tangent loss in paraelectric phase for KH2PO4 at 9.2 GHz for field along the a-axis, and the c-axis have been calculated and compared with experimental results of Kaminow et al [Phys. Rev. 138A, 1539 (1963)]. It is observed that these results are in good agreement with each other and with the results obtained by other methods. At higher temperature the loss deviates from the Curie-Weiss type behaviour and increases linearly with temperature. This behaviour suggests that at higher temperatures the phonon anharmonicity contributes significantly in the observed loss.
Temperature Dependence of Relaxation Rate in KH2PO4 above Tc
With the help of the modified four-particle cluster model Hamiltonian [GJSFR, 10, 18(2010)], the theoretical expressions for the relaxation rate of polarization fluctuation have been evaluated and discussed for the KH2PO4 (KDP)- type crystals by using the double-time thermal dependent retarded Green’s functions techniques and Dyson’s equation treatment. The correlations appearing in the dynamic equation have been evaluated using double-time thermal dependent retarded Green’s functions techniques and Dyson’s equation treatment. Without any decoupling the higher order correlations have been evaluated using the renormalized Hamiltonian. By fitting model values in the theoretical expressions, temperature dependence of relaxation rate is calculated for the KH2PO4 (KDP)-type crystals. Theoretical results are compared with experimental result of Garland and Novotny [1969 Phys Rev. 177 971]. A good agreement has been found.
Relaxation processes and ultrasonic attenuation in KDP type ferroelectrics
The anharmonic four - particle cluster model Hamiltonian for stochastic motion H2PO4 - of groups has been used to study the physical properties of KDP type ferroelectrics. Using Green’s function method and Dyson’s equation the renormalized frequency of the coupled system and collective wave half width have been evaluated with the help of model Hamiltonian by considering the anharmonicity upto fourth order. The higher order correlations have been decoupled using symmetric decoupling scheme at the later stage after applying the Dyson’s treatment and have been evaluated using the renormalized Hamiltonian. The relaxational behaviour and ultrasonic attenuation have been related to the width of collective mode. The temperature dependence of ultrasonic attenuation coefficient, dielectric constant and loss tangent has been discussed in terms of a relaxational soft mode.
