Ferroelectric Structures

It is now instructive to ask why the achiral calamitic SmC a (or SmC) is not antiferroelectric. Cladis and Brand propose a possible ferroelectric state of such a phase in which the tails on both sides of the core tilt in the same direction, with the cores along the layer normal. Empirically this type of conformational ferroelectric minimum on the free-energy hypersurface does not exist in known calamitic LCs. Another type of ferroelectric structure deriving from the SmCA is indicated in Figure 8.13. Suppose the calamitic molecules in the phase were able to bend in the middle to a collective free-energy minimum structure with C2v symmetry. In this ferroelectric state the polar axis is in the plane of the page. 

By our definition, the tilt plane is normal to the polarization in the ferroelectric state in the illustration in Figure 8.13 this is a vertical plane normal to the plane of the page. Since there is no tilt of the director projected onto this plane, the phase should be considered a type of SmA. We name this structure SmAPp (an untilted polar smectic the subscript F referring to a ferroelectric structure, in this case a ferroelectric state of an antiferroelectric phase). The antiferroelectric phase is therefore also an SmA denoted SmAPA (the subscript A for antiferroelectric). While this idea is certainly intriguing, no such antiferroelectric has yet been discovered. 

Note 7 When the tilt direction alternates from layer to layer, the smectic mesophase is antiferroelectric such mesophases do not possess spontaneous polarization. They can be turned into ferroelectric structures through the application of an electric field. 

Collet E, Lemee-Cailleau MH, Buron-Le Cointe M, Cailleau H, Wulff M, Luty T, Koshihara S, Meyer M, Toupet L, Rabiller P, Techert S (2003) Laser-induced ferroelectric structural order in an organic charge-transfer crystal. Science 300 612-615... 

The diffraction pattern, at room temperature, shows a superposition of a broad peak associated to the ferroelectric phase centered at 20 = 18.97° and a shoulder at 20 = 18.36° corresponding to the non-ferroelectric phase. As the temperature is increased, the intensity of the fainter peak increases and that of the ferroelectric maximum decreases concurrently. At the Curie temperature, the peak characteristic for the ferroelectric structure disappears and only the reflection corresponding to the paraelectric structure is present. On further... 

Figure 1.1 Unit cell of cubic BaTiOs. The arrow schematically indicates one of the possible displacement of the central Ti4+ ion at the transition to the tetragonal ferroelectric structure that leads to a spontaneous polarization, in reality all ions are displaced against each other.

Many ferroelectric materials were found in the past. However, there is a limited number of structures that are adopted by the majority of the commercially important ferroelectric materials. In each of these structures, the ferroelectricity is tied to distortion of the coordination polyhedra of one or more of the cations in the structure. One example is the perovskite structure. Cations that seem to be especially susceptible to forming such distorted polyhedra include Ti, Zr, Nb, Ta, and Hf. All of these ions lie near crossover points between the stability of different electronic orbitals, and so may be likely to form distorted coordination polyhedra [5], Polarizable cations such as Pb and Bi are also common to many ferroelectric materials. In this case, it has been suggested that the lone pair electrons may play an important role in stabilizing ferroelectric structures. Thus the ferroelectric transition temperature and spontaneous distortion of PbTiC>3 is much larger than that of BaTiC>3. 

Ultraviolet Raman spectroscopy has emerged as a powerful technique for characterization of nanoscale materials, in particular, wide-bandgap semiconductors and dielectrics. The advantages of ultraviolet excitation for Raman measurements of ferroelectric thin films and heterostructures, such as reduced penetration depth and enhanced scattering intensity, are discussed. Recent results of application of ultraviolet Raman spectroscopy for studies of the lattice dynamics and phase transitions in nanoscale ferroelectric structures, such as superlattices based on BaTiOs, SrTiOs, and CaTiOs, as well as ultrathin films of BaTiOs and SrTi03 are reviewed. 

Initially, it appeared that the phase transitions are purely of the order-disorder type [24]. However, it soon became apparent that atomic displacements also contribute to these phase transitions. These displacements are easy to identify, when one compares the molecular arrangements in the ordered -OH 0= bonds in Fig. 1, with the arrangement of these molecules linked by the disordered bond in Fig. 2. The hydrogen-bonded molecules/ions must rotate before the two H-sites become symmetry-equivalent in the paraelectric phase above Tc- These rotations, usually of few degrees, can be termed as angular displacements. In other words, these angular displacements measure the distortions of the ferroelectric structure where the H-atom ordered from the paraelectric structure where the H-atom is dynamically disordered in two equivalent sites. 

Multiferroics with composition BaA/F4 where Af = Mg, Mn, Fe, Co, Ni, Zn have orthorhombic structure with 2 mm point symmetry at high temperatures with extrapolated Curie temperature above the melting point. At T = 25-70 K ferroelastic ferroelectric structure displays purely antiferromagnetic or weak ferromagnetic ordering. 

Fig. 13.17 Field induced switching between the antiferroelectric structure left sketch) and two ferroelectric structures with opposite tilt and spontaneous polarization Pg. The directions of Pg coincides with the field Ex directions [22]...

Fig. 13.25 Geometry for discussion of the electric field-induced ferroelectric-antiferroelectric transition. Antiferroelectric structure (a) in the zero field and ferroelectric structure at the field exceeding the F-AF transition threshold (b)...

If we disregard the elastic, nematic-like term we would see that the distortion has a threshold character with the threshold field ,/, = 2W/Po. It is easy to understand the AF-F threshold is achieved when the field energy is sufficient for the director in even layers to overcome potential barrier W and change its azimuth from % to 0. Above the threshold, > fa, the uniform ferroelectric structure is installed. 

As shown by the X-ray diffraction, polymer-monomer mixture consists of SmC bilayers. A bilayer is the principal unit cell having either non-polar C2h or polar C2v (b) S5mimetry. The former is incompatible with both ferroelectricity or antiferroelectricity, because such a structure has an inversion centre. On the contrary, in sketch (b) each bilayer is polar with Pq vector located in the tilt plane along the y-axis. In a stack of such layers the direction of Pq alternates and the stmcture (b) is antiferroelectiic in its ground state. Only strong electric field Ey causes the transition to the ferroelectric structure shown in sketch (c) as observed in experiment. Note that both the Pq and P = X Pq vectors are always lying in the tilt plane. 

At present, eight different phases are known in banana compounds dependent on particular in-plane packing symmetry and they usually labelled as Bi, B2, -Bg, etc., counted from the isotropic phase [44]. Among them the B2 phase is especially interesting, because it has low viscosity and can easily be switched by an electric field with rather short switching times [45]. In fact, the B2 phase is basically a conglomerate of chiral and achiral antiferroelectric structures SmCAPA and SmCAPA mixed with some percentage of the two ferroelectric structures. 

Pure PZN (as well as PMN) has a trigonal ferroelectric structirre (3/w), pure PT a tetragonal ferroelectric structure (4 i/w) at room temperature. Both components imdergo the phase transition to the paraelectric cubic (m3m) phase at Cirrie temperature. It depends on the chemical composition and varies typically from 150 to 250°C for PZN-PT (for 0-20%PT content) and 0 to 250°C for PMN-PT (0-50% PT content). Both systems PZN-PT and PMN-PT have the morphotropic phase boundary (MPB) between rhombohedral and tetragonal ferroelectric phases - at 8-10%PT in PZN-PT and at 33-35%PT in PMN-PT for the temperature range interesting for technical applications. For the phase diagrams of PZN-PT and PMN-PT see Fig. 7.16. 

Figure 16.4 Illustration of the influence of the polymer chain conformation and the crystalline structure on the dipole moment and ferroelectricity of PVDF (left) polymer chain takes a//-trans conformation, resulting in a net dipole moment for the polymer chain. These polymer chains are packed into a ferroelectric structure /p phase a —8.58 A, b —4.9 A and c = 2.58 A along chain direction) in which the dipole moments line up (right) polymer chain fates trans-gauche conformation, resulting in a zero net dipole moment. These polymer chains are packed into a non-ferroelectric structure (a phase a = 4.96 A, b 9.64 A, and c= 4.62 A along the chain direction) in which the dipole moments cancel each other out.

For (b), two models are plausible One may assume either an antiferro-electric pattern of tilted columns for which small fields cause a deviation of the tilt directions and for which a larger threshold field changes the pattern of tilt directions into a ferroelectric structure. Alternatively, a helical tilt may be distorted at lower fields and unwound at higher fields. As the helix pitch in columnar phases is usually much shorter than the wavelength of visible light, no selective reflection of light is expected and one may best distinguish between the two cases by X-ray or circular dichroism measurements. Only... 

Nonlinear optical measurements on elastomers were performed by J. Benne et al. with mechanically aligned samples. Due to the alignment procedure, the helicoidal superstructure is untwisted and the two-step cross-linking process locks in the ferroelectric structure. Without applying external fields, these networks spontaneously produce frequency doubling and, from the SHG signal in a Marker-fringe experiment, the C2 symmetry of the elastomer is confirmed [35], [36]. 

As an example, the joint analysis of IR and Raman spectra provided evidence of the partial ordering of cations in a Fe-Cr corundum-type mixed sesquioxides, which are used industrially as high temperature water-gas shift catalysts, but are also active in olefin oxidative dehydrogenation. X-ray diffraction (XRD) patterns of these solids indicate the conmdum-type structure without any superstructure. This implies that iron and chromium ions are randomly distributed. IR and Raman spectra instead definitely show that cations are at least partially ordered in layers such as in the ilmenite-type superstructure. Similarly, XRD analysis shows a cubic (non-ferroelectric) structure of nanometric BaTi03, while vibrational spectroscopies reveal microscopic asymmetry of this structure. Similarly, IR spectroscopy allowed the determination of the state of vanadium in solid solution in Ti02 anatase catalysts, and the presence of Ti" + in the silicalite framework of TSl catalysts, " used for the selective oxidation of phenol and the ammoximation of cyclohexanone with hydrogen peroxide. 

The positions of atomic columns can be determined with picometer precision by considering the phase of the restored exit wave and this has been used to map local ferroelectric structural distortions in a GeTe and BaTiOs nanoparticles.Combined with holographic polarization imaging these studies indicate that a linearly ordered and monodomain polarization state exists even at nanometre dimensions (Fig. 1). 

Ferroelectric order in single ferroelectric domain BaTiOs nanoparticles has been examined recently by Polking et al These particles were also prepared through solvothermal methods, using a two-phase approach. The reaction conditions were altered to prepare nanocubes and quasi-spherical nanoparticles. Abberation corrected transmission electron microscopy has probed the ferroelectric structural distortions in these nanoparticles. In conjuction with off-axis electron holography, which maps the electric fields created by atomic displacement, this has resulted in direet imaging of the ferroeleetrie polarisation. 

Actually, it turned out that the material where the first ferroelectric switching was observed has a ferroelectric structure, where the neighbor polarization directors make a 60° angle with each other. The columns have elliptical cross sections, and they form quasi-hexagonal lattices (each column has six neighbors). Under the electric field the polarization directions have to rotate... 

Depending on the composition and crystal symmetry the hydrogen-bond dipoles may be oriented to form a ferroelectric structure. Such an arrangement b more probable Cor odd polyamides than for even ones. For an illustratioo. see Ref. 6 (p. 403). 

Historically, nearly all the early investigations into the ferroelectric properties of PVDF were carried out on thin ( 25 jam) films. This was necessary for very good reasons. Most importantly, the material must be oriented to develop an incipient ferroelectric structure. This is most conveniently done by using conventional thin film making equipment, which stretches a preformed polymer strip in either one or two in-plane directions. In addition to this requirement, very high fields (typically 100 kV mm ) must be applied to the oriented polymer during the poling... 

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