Dipole ferroelectrics

A related phenomenon with electric dipoles is ferroelectricity where there is long-range ordermg (nonzero values of the polarization P even at zero electric field E) below a second-order transition at a kind of critical temperature. 

Chiral Smectic. In much the same way as a chiral compound forms the chiral nematic phase instead of the nematic phase, a compound with a chiral center forms a chiral smectic C phase rather than a smectic C phase. In a chiral smectic CHquid crystal, the angle the director is tilted away from the normal to the layers is constant, but the direction of the tilt rotates around the layer normal in going from one layer to the next. This is shown in Figure 10. The distance over which the director rotates completely around the layer normal is called the pitch, and can be as small as 250 nm and as large as desired. If the molecule contains a permanent dipole moment transverse to the long molecular axis, then the chiral smectic phase is ferroelectric. Therefore a device utilizing this phase can be intrinsically bistable, paving the way for important appHcations. 

Barium titanate [12047-27-7] has five crystaUine modifications. Of these, the tetragonal form is the most important. The stmcture is based on corner-linked oxygen octahedra, within which are located the Ti" " ions. These can be moved from their central positions either spontaneously or in an apphed electric field. Each TiO octahedron may then be regarded as an electric dipole. If dipoles within a local region, ie, a domain, are oriented parallel to one another and the orientation of all the dipoles within a domain can be changed by the appHcation of an electric field, the material is said to be ferroelectric. At ca 130°C, the Curie temperature, the barium titanate stmcture changes to cubic. The dipoles now behave independentiy, and the material is paraelectric (see Ferroelectrics). 

The structure formation in an ER fluid was simulated [99]. The characteristic parameter is the ratio of the Brownian force to the dipolar force. Over a wide range of this ratio there is rapid chain formation followed by aggregation of chains into thick columns with a body-centered tetragonal structure observed. Above a threshold of the intensity of an external ahgn-ing field, condensation of the particles happens [100]. This effect has also been studied for MR fluids [101]. The rheological behavior of ER fluids [102] depends on the structure formed chainlike, shear-string, or liquid. Coexistence in dipolar fluids in a field [103], for a Stockmayer fluid in an applied field [104], and the structure of soft-sphere dipolar fluids were investigated [105], and ferroelectric phases were found [106]. An island of vapor-liquid coexistence was found for dipolar hard spherocylinders [107]. It exists between a phase where the particles form chains of dipoles in a nose-to-tail... 

A ferroelectric crystal is one that has an electric dipole moment even in the absence of an external electric held. This arises because the centre of positive charge in the crystal does not coincide with the centre of negative charge. The phenomenon was discovered in 1920 by J. Valasek in Rochelle salt, which is the H-bonded hydrated d-tartrate NaKC4H406.4H 0. In such compounds the dielectric constant can rise to enormous values of lO or more due to presence of a stable permanent electric polarization. Before considering the effect further, it will be helpful to recall various dehnitions and SI units ... 

In the operation of ferroelectric liquid crystal devices, the applied electric field couples directly to the spontaneous polarisation Ps and response times depend on the magnitude E Ps. Depending on the electronic structure (magnitude and direction of the dipole moment as well as position and polarity of the chiral species) and ordering of the molecules P can vary over several orders of magnitude (3 to 1.2 x 10 ), giving response times in the range 1-100 ps. 

Stimulated by these observations, Odelius et al. [73] performed molecular dynamic (MD) simulations of water adsorption at the surface of muscovite mica. They found that at monolayer coverage, water forms a fully connected two-dimensional hydrogen-bonded network in epitaxy with the mica lattice, which is stable at room temperature. A model of the calculated structure is shown in Figure 26. The icelike monolayer (actually a warped molecular bilayer) corresponds to what we have called phase-I. The model is in line with the observed hexagonal shape of the boundaries between phase-I and phase-II. Another result of the MD simulations is that no free OH bonds stick out of the surface and that on average the dipole moment of the water molecules points downward toward the surface, giving a ferroelectric character to the water bilayer. 

Mclnnes EJL (2006) Spectroscopy of Single-Molecule Magnets. 122 69-102 Merunka D, Rakvin B (2007) Anharmonic and Quantum Effects in KDP-Type Ferroelectrics Modified Strong Dipole-Proton Coupling Model. 124 149-198 Meshri DT, see Singh RP (2007) 125 35-83... 

Above a specific temperature, the Curie temperature, a ferroelectric substance becomes paraelectric since the thermal vibrations counteract the orientation of the dipoles. The coordinated orientation of the dipoles taking place during the ferroelectric polarization is a cooperative phenomenon. This behavior is similar to that of ferromagnetic substances, which is the reason for its name the effect has to do nothing with iron (it is also called seignette or rochelle electricity). 

No ferroelectricity is possible when the dipoles in the crystal compensate each other due to the crystal symmetry. All centrosymmetric, all cubic and a few other crystal classes are... 

The ferroelectric ground state of dipoles on a triangular lattice, with the degenerate inclination angles relative to the lattice axes, was revealed in Ref. 56. The characteristics of this state are given by the following equations (see also Ref. 59) ... 

Fig. 2.13. Two-dimensional Bravais lattice with the basis vectors a)s a2, and the reciprocal lattice vectors bi, b2. The solid and dashed arrows at angles A and 0A give the ferroelectric (k = 0) and antiferroelectric (k = bi/2) configurations of dipoles in the ground state.

Ferroelectric ordering in certain infinite two-dimensional lattices is due to the long-range contribution of dipole forces. Thus, it is not surprising that in limited two-dimensional lattices numerical calculations of dipole interactions lead to the replacement of ferroelectric states with macrovortex states64 which approximate to ferroelectric states far from the center of the limited lattice (coinciding with the center of the macrovortex). 

If a ferroelectric ground state is realized on a two-dimensional lattice with a symmetry axis of order higher than two (as with a triangular dipole lattice), the... 

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