Ferroelectric medium

Dmitry Matyushov, Arizona State University Using a ferroelectric medium to facilitate charge transfer since the main cause of inefficiency of current artificial photosynthesis... 

The macroscopic optical responses of a medium are given by its linear and nonlinear susceptibilities, which are the expansion coefficients of the material polarization, P, in terms of the Maxwell fields, 1 3]. For a dielectric or ferroelectric medium under the influence of an applied electric field, the defining equation reads... 

Medium-permittivity ceramics are widely used as Class I dielectrics, and in order to be in this category they need to have low dissipation factors. This precludes the use of most ferroelectric compounds in their composition since ferroelectrics have high losses (tan S >0.003), particularly when subjected to high a.c. fields. 

Tinte et al.54 have carried out molecular dynamic simulations of first-principles based effective Hamiltonian for PSN under pressure and of PMN at ambient pressure that clearly exhibit a relaxor state in the paraelectric phase. Analysis of the short-to-medium range polar order allows them to locate Burns temperature Tb. Burns temperature is identified as the temperature below which dynamic nanoscale polar clusters form. Below TB, the relaxor state characterized by enhanced short-to-medium range polar order (PNR) pinned to nanoscale chemically ordered regions. The calculated temperature-pressure phase diagram of PSN demonstrates that the stability of the relaxor state depends on a delicate balance between the energetics that stabilize normal ferroelectricity and the average strength of quenched "random" local fields. 

For further progress it is necessary to specify how E varies with D, or how P depends on Ea. For this purpose, we introduce the constitutive relations D - e(T,V)E or P - ot0(T,V)F0, where e is the dielectric constant and a0 is a modified polarizability. (Conventionally, the polarizability is defined through the relation P - oE, but no confusion is likely to arise through the introduction of this variant.) Note several restrictions inherent in the use of these constitutive relations. First, the material under study is assumed to be isotropic. If this is not the case, e and c 0 become tensors. Second, the material medium must not contain any permanent dipole moments in the preceding constitutive relations P or E vanishes when E0 or D does. Third, we restrict our consideration to so-called linear materials wherein e or a0 do not depend on the electric field phenomena such as ferroelectric or hysteresis effects are thus excluded from further consideration. These three simplifications obviously are not fundamental restrictions but render subsequent manipulations more tractable. Finally, in accord with experimental information available on a wide variety of materials, e and aQ are considered to be functions of temperature and density assuming constant composition, these quantities vary with T and V. 

Replacement of the halite layers in the above series by layers of composition Bi202 leads to a series of Aurivillius phases, with a general formula (Bi202)(A i B 03 +i), where A is a large cation, and B a medium sized cation. The best-known member of this series of phases is the ferroelectric Bi4Ti30i2 in which n = 3 and A is Bi. 

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]. 

I I.J.7 Ferroelectricity due to medium-sized transition-metal cations... 

Ferroelectric properties can be attributed to the presence of medium-sized cations in many oxides with structures related to that of perovskite, for example BaTiOa and KNbOa. These contain ions... 

The vast majority of nematogens are polar compounds but the absence of ferroelectricity in the nematic phase shows that there is equal probability of the dipoles pointing in either direction. Because of this it is generally assumed that the permanent dipolar contribution to the orientational order is negligibly small. However, a simple calculation shows that the interaction between neighbouring dipoles is by no means trivial compared with dispersion forces, particularly in strongly polar materials. We shall now consider a model which takes into account the influence of permanent dipoles and is at the same time consistent with the non-polar character of the medium. ... 

Figure 6,9 Ferroelectric hysteresis loops, schematic (a) typical loop indicating P P and Ej (b) single crystal ABO (c) medium-grained ceramic ABO (d) fine-grained ceramic ABO,...

T, R) is the temperature and size dependent dielectric permittivity of incipient ferroelectric nanoparticles of radius R, (x is the fermion effective mass, is the effective permittivity of the particle environment, 8q is the dielectric permittivity of vacuum (in SI units). Due to the high values of e(r, R) the radius (T, R) > 5 nm is much higher than the lattice constant a = 0.4 nm, proving the validity of the effective mass approximation as well as the self-consistent background for the introduction of dielectric permittivity in the continuous medium approach [60]. 

Pertsev, N.A., Zembilgotov, A.G., and Waser, R. 1998. Aggregate linear properties of ferroelectric ceramics and polycrystalline thin films calculation by the method of effective piezoelectric medium. Journal of Applied Physics 84 [3] 1524-1529. 

Permittivity is a measure of the degree to which an insulating medium can induce an electric charge between conducting planes. It is measured in Farads per meter. The absolute permittivity of free space (Cq) has a value of 8.85 X 10 2 Farad per metre. The relative permittivity (e) of a substance is the ratio of its absolute permittivity to Cq e value of varies from unity (for a vacuum) to over 4000 (for ferroelectrics). The quantity is also called the dielectric constant of specific inductive capacity of the material. 

---