Ferroelectric frequency effect

Crystals with one of the ten polar point-group symmetries (Ci, C2, Cs, C2V, C4, C4V, C3, C3v, C(, Cgv) are called polar crystals. They display spontaneous polarization and form a family of ferroelectric materials. The main properties of ferroelectric materials include relatively high dielectric permittivity, ferroelectric-paraelectric phase transition that occurs at a certain temperature called the Curie temperature, piezoelectric effect, pyroelectric effect, nonlinear optic property - the ability to multiply frequencies, ferroelectric hysteresis loop, and electrostrictive, electro-optic and other properties [16, 388],... 

Here we focus on the effect of dipolar dispersion laws for high-frequency collective vibrations on the shift and width of their spectral line, with surface molecules inclined at an arbitrary angle 6 to the surface-normal direction. For definiteness, we consider the case of a triangular lattice and the ferroelectric ordering of dipole moments inherent in this lattice type.56,109 Lateral interactions of dynamic dipole moments p = pe (e = (sin os, sin6fcin , cos )) corresponding to collective vibrations on a simple two-dimensional lattice of adsorbed molecules cause these vibrations to collectivize in accordance with the dispersion law 121... 

Static dielectric measurements [8] show that all crystals in the family exhibit a very large quantum effect of isotope replacement H D on the critical temperature. This effect can be exemphfied by the fact that Tc = 122 K in KDP and Tc = 229 K in KD2PO4 or DKDP. KDP exhibits a weak first-order phase transition, whereas the first-order character of phase transition in DKDP is more pronounced. The effect of isotope replacement is also observed for the saturated (near T = 0 K) spontaneous polarization, Pg, which has the value Ps = 5.0 xC cm in KDP and Ps = 6.2 xC cm in DKDP. As can be expected for a ferroelectric phase transition, a decrease in the temperature toward Tc in the PE phase causes a critical increase in longitudinal dielectric constant (along the c-axis) in KDP and DKDP. This increase follows the Curie-Weiss law. Sc = C/(T - Ti), and an isotope effect is observed not only for the Curie-Weiss temperature, Ti Tc, but also for the Curie constant C (C = 3000 K in KDP and C = 4000 K in DKDP). Isotope effects on the quantities Tc, P, and C were successfully explained within the proton-tunneling model as a consequence of different tunneling frequencies of H and D atoms. However, this model can hardly reproduce the Curie-Weiss law for Sc-... 

By analogy to the SDPC model, the parameters A, Aj, K, K , M, and M of the MSDPC model have the same value for KDP and DKDP. For the KDP and DKDP system of classical PO4 dipoles in ferroelectric ordered state at T = 0 K, all PO4 dipoles have components fit = (0> F-)- The potential energy per dipole and the ferroelectric-mode frequency in this state are given by the same relations from the SDPC model (Eq. 8 and fe = ( ( (/Usl/Af) / ), where B = 0. To reproduce the same saturated dipole value Fs = and the same saturated force value Fs = 2Kfs = 0.6 evA for KDP, the constants A and K have the same values as do the constants A + B and K in the SDPC model, respectively. Therefore, the isotope effect on Fs and Fs has the same... 

Dispersions of nanoparticles in ferroelectric liquid crystals (FLCs) predominantly focused on induced or altered electro-optic effects, but also on the alignment of FLCs. Raina and co-workers reported on a gradual decrease of the dielectric permittivity, e, by doping with SiC>2 nanoparticles at frequencies up to 1 kHz and a rather minor increase of as well as an increase in optical transmission at frequencies above 2 kHz [279]. Liang et al. used BaTiC>3 nanoparticles (31 nm in diameter after grinding commercially available 90 nm nanoparticles Aldrich) and showed, perhaps expectably, a twofold increase in the spontaneous polarization... 

The class of ferroelectric materials have a lot of useful properties. High dielectric coefficients over a wide temperature and frequency range are used as dielectrics in integrated or in smd (surface mounted device) capacitors. The large piezoelectric effect is applied in a variety of electromechanical sensors, actuators and transducers. Infrared sensors need a high pyroelectric coefficient which is available with this class of materials. Tunable thermistor properties in semiconducting ferroelectrics are used in ptcr (positive temperature coefficient... 

In contrast, the nonlinearities in bulk materials are due to the response of electrons not associated with individual sites, as it occurs in metals or semiconductors. In these materials, the nonlinear response is caused by effects of band structure or other mechanisms that are determined by the electronic response of the bulk medium. The first nonlinear materials that were applied successfully in the fabrication of passive and active photonic devices were in fact ferroelectric inorganic crystals, such as the potassium dihydrogen phosphate (KDP) crystal or the lithium niobate (LiNbO,) [20-22]. In the present, potassium dihydrogen phosphate crystal is broadly used as a laser frequency doubler, while the lithium niobate is the main material for optical electrooptic modulators that operate in the near-infrared spectral range. Another ferroelectric inorganic crystal, barium titanate (BaTiOj), is currently used in phase-conjugation applications [23]. 

Ferroelectric lithium niobate (LiNbOs) has been of considerable interest because of its nonlinear optical properties. Conversion of infrared into visible radiation in LiNb03 crystals has been observed (Midwinter and Warner, 1967 Arutyunyan and Mkrtchyan, 1975). Electro-optic coefficients of LiNbOs have been determined for a wide range of frequencies ranging from the visible (Smakula and Claspy, 1967) to the millimeter-wave portion of the spectrum (Vinogradov et al., 1970). Other nonlinear optical properties such as photovoltaic effects (Kratzig and Kurz, 1977) and optically induced refractive index changes (Ashkin et al., 1966 Chen, 1969) have also been observed. 

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