Inversion centers, ferroelectrics

It is known that the crystal symmetry defines point symmetry group of any macroscopic physical property, and this symmetry cannot be lower than corresponding point symmetry of a whole crystal. The simplest example is the spontaneous electric polarization that cannot exist in centrosymmetric lattice as the symmetry elements of polarization vector have no operation of inversion. We remind that inversion operation means that a system remains intact when coordinates x, y, z are substituted by —x, —y, —z. If the inversion center is lost under the phase transition in a ferroic at T < 7), Tc is the temperature of ferroelectric phase transition or, equivalently, the Curie temperature), the appearance of spontaneous electrical polarization is allowed. Spontaneous polarization P named order parameter appears smoothly... 

It has been shown above, that mismatch of the film and substrate parameters and the absence of inversion center near the surface together, lead to appearance of built-in electric field, see Eq. (3.17). Here we shall show that this field essentially influences almost all the properties of ferroelectric thin films. (Qualitatively this influence is similar to that of external electric field. However, the external field can be turned off, while built-in field is absent only for the free-standing film, i.e. that without... 

Fig. 3.31 The calculated EPR absorption spectrum of paramagnetic impurity with inversion center for ferroelectric nanopowders with first order phase transition. The size distribution function parameters Rq/Rc = 5 (1), 3 (2), 2.1(3), 1.2 (4) a/Rc = 0.1 (a), 1.4 (b) [101]...

The unit cells in the lattice of the lower-symmetry phases that are stable below the Curie temperature have ea permanent electrical dipole moment. In analogy with the magnetic phases, these are called ferroelectric if the moments are coupled in parallel and antiferroelectric if they are antiparallel. When the temperature is decreased to below the Curie temperature the symmetry becomes lower than cubic, the inversion center disappears, and the compound becomes piezoelectric. Figure 4.24 shows the change in properties at the phase transition of BaTi03. Further down... 

A piezoelectric solid (e.g., quartz) acquires an electrical dipole moment upon mechanical deformation and, conversely, if it is subjected to an electric field E it becomes distorted by an amount proportional to the field strength E. The dipole moment disappears without the mechanical force. Piezoelectricity is only possible in lattices that do not have an inversion center. Electrostriction is also mechanical distortion in an electric field (strain proportional to E ) but ionic lattices that have a center of symmetry also show this effect. Figure 4.25 is a schematic representation of the source of these effects using the interatomic potential curve. A ferroelectric material is not only piezoelectric but its lattice has a permanent electric dipole moment (below its Curie temperature), which most other piezoelectric materials (such as quartz) do not have. 

The first successful observations of SHG from cholesteryl carbonate were explained in terms of a lack of the inversion center in small liquid crystalline swarms ". Later, - without any success, there has been carried out extensive search for the SHG in nematic, cholesteric and smectic (non-ferroelectric) liquid crystals, and the previous result was accounted for by the presence of solid crystals in the cholesteric phase. 

During the development of liquid crystals, there was an ongoing discussion if ferroelectricity could exist in LC materials. Until then, ferroelectricity only existed in solids with a specific crystal structure having no inversion symmetry center. Ferroelectricity was considered to be impossible in gases or liquids, but since liquid crystals have a regularity to some extent, the expression of a ferroelectric liquid in... 

Ferroelectrics are also members of the 20 point groups that have no inversion center. Noncentrosymetric crystals may not have a dipole moment in their relaxed state, but when distorted, the center of negative charge is separated from the center of positive charge and a dipole moment results. Such crystals are piezoelectrics. All ferroelectrics and pyroelectrics are also piezoelectrics, but not all piezoelectrics are ferroelectrics. Piezoelectrics are used in strain and pressure gages, accelerometers, microphones and speakers, and linear actuators. 

Among different applications of the CJTE structural phase transitions are the most important one. However as they already were briefly discussed above now we will focus the attention on ferroelectricity. The first general ideas in the field belong to Bersuker [4]. The development of these ideas went in two directions a) systems with local pseudo-JT effect characterized by wide energy gaps and local center of inversion b) systems with small energy gap between the ground and excited states (JT or pseudo-JT effect) in crystals without local center of inversion. 

Fig. 8. Simple model of order-disorder or displacive ferroelectric phase transition. Left, ferroelectricity by relative displacement of the anion and cation sublattices (a) displacive model, where r — 0 in the HTP and the atoms are translated by r/0 in the LTP. The order parameter is r. (b) Order-disorder model in the high-temperature phase, the ions are symmetrically disordered with equal probabilities p+ — p — 1/2 over two positions r — +rQ. In the low-temperature phase, the occupancies of the sites become unequal with probabilities p p +. The order parameter is the difference Ap — p+—p. The spontaneous polarization Psocr and PsccAp for the displacive model and order-disorder model, respectively. Right, ferroelectricity by alignment of molecular dipoles (c) displacive model in the HTP, all the molecules are aligned with a = 0 in the LTP, the molecules are rotated around the center of inversion with angles +a/0, the order parameter is a. (d) Order-disorder model. The spontaneous polarization Ppx ct and PsccAp for the displacive model and order-disorder model, respectively.

The nonlinear properties of FLCs attracted considerable attention both from the fundamental and technical points of view [132-134]. Since, in ferroelectric phases the center of inversion is absent (Fig. 7.1), the amplitude of the optical second harmonic generation (SHG) ought to be fairly strong, especially in commercially available FLC mixtures with high spontaneous polarization [133]. Reference [134] shows the ways of designing new FLC substances with the increased molecular second-order hyperpolarizability comparable to that of solid electrooptical crystals such as LINbOs. 

As the primitive cell of the arsenic structure contains two atoms the simplest superstructure is realized in the GeTe type. Replacement of As As by GeTe removes the center of symmetry and therefore these phases can be piezoelectric and even ferroelectric. Removal of the inversion symmetry makes the three... 

Can liquids in which the constituents are dipoles be ferroelectric For instance, if we could make a colloidal solution of small particles of the ferroelectric BaTi03, would this liquid be ferroelectric The answer is no, it would not. It is true that such a liquid would have a very high value of dielectric susceptibility and we might call it superparaelec-tric in analogy with the designation often used for a colloidal solution of ferromagnetic particles, which likewise does not show any collective behavior. An isotropic liquid cannot have polarization in any direction, because every possible rotation is a symmetry operation and this of course is independent of whether the liquid lacks a center of inversion, is chiral, or not. Hence we have at least to diminish the symmetry and go to anisotropic liquids, that is, to liquid crystals, in order to examine an eventual appearance of pyroelectricity or ferroelectricity. To... 

In addition to the 10 point groups mentioned above there are 10 more point groups that lack a center of inversion but are not polar. These are Csh, d2,3,4,6,2d 3h/ S4, t and ta- or 6, 222, 32,422,622,42m, 62m, 4,23, and 43m. Crystals in this class, when distorted, may produce a dipole and are called piezoelectrics. Therefore, all ferroelectrics and pyroelectrics are also piezoelectrics, but not all piezoelectrics are pyroelectrics or ferroelectrics. 

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