Antiferroelectrics

Ferroelectricity is governed by two types of factors (a) chemical bonds, which are short-range forces, and (b) dipolar interactions, which are long-range 

The balance between ferroelectric and antiferro-electric states is delicately poised, and some antiferroelectrics readily transform to ferroelectric states. This transformation is often accompanied by a change in the crystal structure of the solid. For example, orthorhombic lead zirconate, PbZrOa, which is antiferroelectric, can transform to rhombohedral lead zirconate, PbZrOa, which is ferroelectric. In the system PbZrOa-PbTiOa, as the smaller Ti ion replaces the larger Zr + ion, the antiferroelectric phase is replaced by a ferroelectric state. Some ferroelectrics and antiferroelectrics are listed in Table 11.2. 

The fact that an applied field can cause the polarisation to alter its direction implies that the atoms involved make only small movements and that the energy barrier between the different states is low. With increasing temperature the thermal motion of the atoms will increase, and eventually they can overcome the energy barrier separating the various orientations. Thus at high temperatures the distribution of atoms becomes statistical and the crystal behaves as a normal dielectric and no longer as a polar material. This is referred to as the paraelectric state. The temperature at which this occurs is known as the Curie temperature, Tc, or the transition temperature. The relative permittivity often rises to a sharp peak in the neighbourhood of Tb. 

The temperature dependence of the relative permittivity of many ferroelectric crystals in the paraelectric state can be described fairly accurately by a relationship called the Curie-Weiss law  

Hydrogen bonds are formed when a hydrogen atom sits between two electronegative atoms in an off-centre position (Section 3.1.1). At temperatures below the Curie temperature the hydrogen atoms 

In some materials the antiferroelectric state is barely stable or metastable. In such materials, application of an electric field will convert the phase to ferroelectric, as described, but removal of the field leaves the phase in a ferroelectric state. This material then behaves like a typical ferroelectric and displays a conventional hysteresis loop. Heating the material to a high temperature so as to form the paraelectric structure, followed by cooling, can reform the original antiferroelectric state. 

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As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

There is often a wide range of crystalline soHd solubiUty between end-member compositions. Additionally the ferroelectric and antiferroelectric Curie temperatures and consequent properties appear to mutate continuously with fractional cation substitution. Thus the perovskite system has a variety of extremely usehil properties. Other oxygen octahedra stmcture ferroelectrics such as lithium niobate [12031 -63-9] LiNbO, lithium tantalate [12031 -66-2] LiTaO, the tungsten bron2e stmctures, bismuth oxide layer stmctures, pyrochlore stmctures, and order—disorder-type ferroelectrics are well discussed elsewhere (4,12,22,23). 

Landolt-Bitmstein, Ferroelectric and Antiferroelectric Substances, Vol. 9, New Senes Group III, Springer-Vedag, Berlin, Germany, 1977. 

U.N. Venevtzev, E.D. Politova, S.A. Ivanov, Ferroelectrics and antiferroelectrics of barium titanate family, Khimiya, Moscow, 1985 (in Russian). 

Thiophenes of type 31 (X-Y = CH) were generated via Lawesson s reagent-mediated cyclization of 1,4-dicarbonyl compounds 30 under microwave irradiation in the absence of solvent [37]. The reaction was carried by mixing the two solid reagents in a glass tube inserted inside a household microwave apparatus and irradiating until the evolution of H2S ceased. An interesting application of this method is the preparation of liquid crystals and other ferro- and antiferroelectric material such as compound 33 (Scheme 10). 

Fig. 14. A snapshot of a configuration showing the stripe-like structure of the smectic phase formed hy the polar mesogen GB(3.0, 5.0, 1, 3) and the antiferroelectric compensation in adjacent layers. The different orientations of the dipoles are indicated hy the different shading of the ellipsoids...

In this section, we will present the crystal structures of chiral mesogenic compounds exhibiting ferroelectric liquid crystalline phases which are listed in Table 18 [152-166]. Moreover, four compounds of the list show antiferroelectric properties and two compounds form only orthogonal smectic phases. The general chemical structures of the investigated chiral compounds are shown in Fig. 27. 

Zareba et al. [165] described the crystal structure of the chiral 4-(l-methyl-heptyloxycarbonyl)-phenyl 4-heptyloxytolane-4 -carboxylate (C7-tolane) which shows monotropic antiferroelectric and ferroelectric phases. The single-crystal X-ray analysis of this compound shows that the crystal has a smectic-like layer structure composed of largely bent molecules where the chain of the chiral group is almost perpendicular (86°) to the core moiety. Within the layers, the molecules are tilted. The central tolane group of the molecule is roughly planar. 

Table 18) must show a bent structure. This may be one reason for the interlocking and the occurrence of the 21-axis and the antiferroelectricity. But bent structures are possible as well as by gauche conformations like in the described solid state of compound 4-[(S)-2-methylheptyloxy]phenyl 4 -oct-ylbiphenyl-4-carboxylate [153]. 

We note that the bilayer smectic phase which may be formed in main-chain polymers with two odd numbered spacers of different length (Fig. 7), should also be polar even in an achiral system [68]. This bilayer structure belongs to the same polar symmetry group mm2 as the chevron structure depicted in Fig. 17b, and macroscopic polarization might exist in the tilt direction of molecules in the layer. From this point of view, the formation of two-dimensional structure of the type shown in Fig. 7, where the polarization directions in neighbouring areas have opposite signs, is a unique example of a two dimensional antiferroelectric structure. 

Fig. 17a-c. Sketches of the molecular arrangements for the smectic structure with alternating layer-to-layer tilt a conventional and chevron smectic C layering in low molecular mass mesogens b ferroelectric hilayer chevron structures for achiral side-chain polymers c antiferroelectric hilayer chevron structures for achiral side-chain polymers. Arrows indicate the macroscopic polarization in the direction of the molecular tilt... 

In bilayer phase the dipole arrangement is antiferroelectric-like. However there are... 

Dalai NS, Gunaydin-Sen O, Bussmann-Holder A (2007) Experimental Evidence for the Coexistence of Order/Disorder and Displacive Behavior of Hydrogen-Bonded Ferroelectrics and Antiferroelectrics. 124 23-50 Dalai NS, see Bussmann-Holder A (2007) 124 1-21 Daul CA, see Atanasov M (2003) 106 97-125... 

The v2 bending vibration is a quartet or, in a simplified picture, two Davydov doublets as a consequence of a site-symmetry-induced doublet (see Fig. 2.6).40 A system of particular interest is CO/NaCl(100) it is characterized by inclined molecular orientations with =25° and antiferroelectric ordering of chains at low temperatures (see Fig. 2.7) which is removed on the phase transition at T 25 K. This structural information is deduced from the observed Davydov splitting of the spectral line for the CO stretching vibrations at 2155 cm 1 and T<24 K (see Fig. 

Two-dimensional Bravais lattices with no higher than second-order axes of symmetry are characterized by a non-degenerate dipole ground state. On a rectangular lattice, the dipoles are oriented along the chains with the least intersite distances ax and antiferroelectric ordering in neighboring chains. As an example, for... 

In the general case of arbitrary two-dimensional Bravais lattices (not rectangular and rhombic), the ground state, depending on the lattice parameters (x0 and y0 in Fig. 2.13), is characterized by ferroelectric (0.25 < x0 <0.5) or stratified bisublattice antiferroelectric ordering (0 < x0 < 0.25). 

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.

In lead zirconate, PbZr03, the larger lead ions are displaced alternately from the cube comer sites to produce an antiferroelectric. This can readily be converted to a ferroelectric by the substitution of Ti4+ ions for some of the Zr4+ ions, the maximum value of permittivity occurring at about the 50 50 mixture of PbZrC>3 and PbTiC>3. The resulting PZT ceramics are used in a number of capacitance and electro-optic applications. The major problem in the preparation of these solid solutions is the volatility of PbO. This is overcome by... 

This situation changed dramatically in 1996 with the discovery of strong electro-optic (EO) activity in smectics composed of bent-core, bowshaped, or banana-shaped achiral molecules.4 Since then, the banana-phases exhibited by such compounds have been shown to possess a rich supermolecular stereochemistry, with examples of both macroscopic racemates and conglomerates represented. Indeed, the chiral banana phases formed from achiral or racemic compounds represent the first known bulk fluid conglomerates, identified 150 years after the discovery of their organic crystalline counterparts by Pasteur. A brief introduction to LCs as supermolecular self-assemblies, and in particular SmC ferroelectric and SmCA antiferroelectric LCs, followed by a snapshot of the rapidly evolving banana-phase stereochemistry story, is presented here. 

Since P must remain normal to z and n, the polarization vector forms a helix, where P is everywhere normal to the helix axis. While locally a macroscopic dipole is present, globally this polarization averages to zero due to the presence of the SmC helix. Such a structure is sometimes termed a helical antiferroelectric. But, even with a helix of infinite pitch (i.e., no helix), which can happen in the SmC phase, bulk samples of SmC material still are not ferroelectric. A ferroelectric material must possess at least two degenerate states, or orientations of the polarization, which exist in distinct free-energy wells, and which can be interconverted by application of an electric field. In the case of a bulk SmC material with infinite pitch, all orientations of the director on the tilt cone are degenerate. In this case the polarization would simply line up parallel to an applied field oriented along any axis in the smectic layer plane, with no wells or barriers (and no hysteresis) associated with the reorientation of the polarization. While interesting, such behavior is not that of a true ferroelectric. 

Along with the prediction and discovery of a macroscopic dipole in the SmC phase and the invention of ferroelectric liquid crystals in the SSFLC system, the discovery of antiferroelectric liquid crystals stands as a key milestone in chiral smectic LC science. Antiferroelectric switching (see below) was first reported for unichiral 4-[(l-methylheptyloxy)carbonyl]phenyl-4/-octyloxy-4-biphenyl carboxylate [MHPOBC, (3)],16 with structure and phase sequence... 

Figure 8.8 Structure and phase sequence of (R)-MHPOBC is shown. One of most famous smectic LCs, antiferroelectric switching in SSFLC cells was first discovered with this material.

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