Background Crystalline Antiferroelectrics and Ferrielectrics

Liquid crystal ferri and antiferroelectrics have many features discovered for years of comprehensive studies of corresponding crystalline substances. Thus, it would be convenient and instructive to begin with a short introduction in the structure and properties of antiferroelectric crystals. A difference between ferro-, ferri and antiferroelectrics is schematically shown in Fig. 13.15, where the three very simplified 

In some crystals the location of dipole moments can even be more complicated. For example, in Fig. 13.15c, one layer with the dipoles looking down alternates with two layers where the dipoles are looking up. Therefore we have three-layer periodicity 3/ with two antiparallel layers and one extra polar layer. Such a structure may be considered as a mixture of the ferroelectric and antiferroelectric structures and is called ferrielectric. In case (c), the ferroelectric fraction is one part per period, qp = 1/3 and the spontaneous polarization is finite, Pg = (l/3)Po. For pure antiferroelectric phase qp = 0/2 and for pure ferroelectric one qp = 1/1 = 1. More generally, for different ferrielectric structures qp = nim, where m is the number of layers in the unit cell (period) and m is the ferroelectric layer fracture per unit cell, both being integers. Then, for both n and m oc, nim 1, the difference between n and m become smaller and smaller and the so-called Devil s staircase forms. 

With increasing temperature the order of dipoles in each sublattice decreases and, at a certain temperature, a phase transition into the paraelectric phase occurs. It may be either second or first order transition. In the paraelectric phase local polarization Pq vanishes. The nature of the spontaneous polarization is similar in solid ferro- and antiferroelectrics. In both cases, the dipole-dipole interactions are dominant. For example, if dipoles are situated in the points of the body-centred cubic lattice, they preferably orient parallel to each other and such a structure is ferroelectric. However, the same dipoles placed into the points of a simple cubic 

A difference between ferro- and antiferroelectrics may also be discussed in terms of the soft elastic mode [3], In the infinite ferroelectric crystal, there is no spatial modulation of the spontaneous polarization (only dipole density is periodic). Therefore, at the transition from a paraelecttic to the ferroelectric phase, both the wavevector q for osciUatimis of imis responsible for polarization and the correspondent oscUlatimi frequency co = Kef tend to zero. We may say that the soft elastic mode in ferroelecttics condenses at q 0. In antiferroelectrics, the sign of the local polarization Pq alternates in space with wavevector qo = 2nl2l = n/l and the corresponding imi oscillation frequency is finite, m = Kqf = Kn ll. It means that in antiferroelectrics the soft mode condenses at a finite wavevector n/l and rather high frequency. As a result, in the temperature dependence of the dielectric permittivity at low frequencies, the Curie law at the phase transitimi between a paraelecttic and antiferroelectric phases is not well pronounced. 

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