Ferroelectric behaviour

Ferroelectric materials have three main features hysteresis loops formed by the electric displacement D and the electric field E reversal of polarization by application of a step voltage and the phase transition or Curie temperature Tq at which the material loses its ferroelectric properties and becomes paraelectric. 

Most polymers are insulating materials. Thus a polymer film with electrodes on its top and bottom surfaces forms a parallel plate capacitor with a capacitance 

The electric displacement D is a measure of the surface charge density  

In linear dielectrics D is directly proportional to E, increasing and decreasing linearly with E. In ferroelectric polymers, such as PVDF and the VDF TrFE copolymers, the surface charge density increases with the field in a nonlinear manner, and exhibits hysteresis as the field is decreased, with a significant amount of surface charge remaining when the field is completely removed. Subsequent applications and reversals of the electric field produce the characteristic D-E hysteresis loops shown in Fig. 5.4. 

The amount of surface charge density that remains is termed the remnant polarization P, and is caused by a net alignment of dipoles within the crystalline phase of the material. When the direction of the electric field is reversed, the charge rapidly decreases and changes sign. The field at which the polarization passes through zero is termed the 

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It should be noted that, whereas ferroelectrics are necessarily piezoelectrics, the converse need not apply. The necessary condition for a crystal to be piezoelectric is that it must lack a centre of inversion symmetry. Of the 32 point groups, 20 qualify for piezoelectricity on this criterion, but for ferroelectric behaviour a further criterion is required (the possession of a single non-equivalent direction) and only 10 space groups meet this additional requirement. An example of a crystal that is piezoelectric but not ferroelectric is quartz, and ind this is a particularly important example since the use of quartz for oscillator stabilization has permitted the development of extremely accurate clocks (I in 10 ) and has also made possible the whole of modern radio and television broadcasting including mobile radio communications with aircraft and ground vehicles. 

Clathrates are useful for the control of the stereo- and regiospecificity of intra-cavity chemical reactions and can be used to engineer materials properties such as a polarity leading to non-linear optical materials, and ferroelastic or ferroelectric behaviour. 

Ferroelectric behaviour is limited to certain materials and to particular temperature ranges for a given material. As shown for barium titanate in Section 2.7.3, Fig. 2.40(c), they have a Curie point Tc, i.e. a temperature at which the spontaneous polarization falls to zero and above which the properties change to those of a paraelectric (i.e. a normal dielectric). A few ferroelectrics, notably Rochelle Salt (sodium potassium tartrate tetrahydrate (NaKC406.4H20)) which was the material in which ferroelectric behaviour was first recognized by J. Yalasek in 1920, also have lower transitions below which ferroelectric properties disappear. 

Barium titanate, the first ceramic material in which ferroelectric behaviour was observed, is the ideal model for a discussion of the phenomenon from the point of view of crystal structure and microstructure see also [10] and [11]. 

Graduating now to the diamagnetic cation [H2N-NH3]+, one finds much of interest. NMR (of 1H, 2H, 7Li, 14N, 15N) and other measurements of (H2N-NH3) (HSO4) and similar salts, and especially of Li(H2N-NH3)(S04), reveal ferroelectric behaviour and substantial capability of proton conductivity/diffusion through the crystals (e.g. Refs. 70 and 71). 

This is called the ferroelectric effect, by analogy with ferromagnetism Equation (2.48) is analogous to the Curie-Weiss law. A few crystalline materials do indeed display ferroelectric behaviour, but the phenomenon is rare. 

Barium titanate is made from pure BaC03 and Ti02. The compound is first synthesized by heating the powdered mixture at 1100-1300 C. The mix usually contains small amounts of additives altering the ferroelectric behaviour (sec p. 326). 

As already noted, various crystals similar to KDP, where the K-atom or the P-atom of the anion is replaced by homologous atoms, display a similar ferroelectric behaviour. Some of them are antiferroelectrics (41). Recently, some other types of ferroelectrics have been discovered, where the origin of their ferroelectric behaviour is due to the position of the proton itself, which is not the case for KDP-type ferroelectrics where H-bonds are roughly perpendicular to the permanent electric dipole moment fL in the ferroelectric phase and do not directly contribute to the permanent electric moment. Thus such a crystal as... 

Figure 44 Book -shaped palladium complexes showing ferroelectric behaviour.

These polymers have a typical ferroelectric behaviour (Figure 13). These copolymere are soluble and c stallise directly in a non centrosymetric B phase. So one can make thin layers of film (in the wder of some pm) by spin coating. For x = 0.75, the Curie temperature is Tc = 125°C... 

Figure 13. Typical ferroelectric behaviour at the copolymer P(VF2-TrFE)...

The sharpening of the dielectric permittivity peak that occurs between Figure 6.18a and b can be considered to be part of a continuum leading to classical ferroelectric behaviour (Figure 6.18c). This trend is often clear when solid solutions of perovskite phases are examined. For exanple, solid solutions between BaTiOj and the relaxor ferroelectric BiFeOj show an evolution from the classical sharp peak for BaTiOj to a characteristic relaxor peak with a sharp low-temperature margin as the BiFeOj content increases until a broad relaxor peak appears at highest concentrations. 

Interfacial strain in the superlattice series formed by m unit cells of ferroelectric PbTiOj and n unit cells of dielectric SrTiOj also produces curious behaviour. Normal ferroelectric behaviour is found when the layers are relatively thick. This diminishes as layer thicknesses fall but surprisingly, at the lowest values, ferroelectricity recovers. In bulk PbTiOj octahedral tilt is suppressed and in SrTiOj octahedral rotation is suppressed. However, in superlattices these distortions become possible, creating a strain between the two perovskite slices. As the slabs become thin, the strain component of the interfaces becomes relatively greater and ultimately, in the thinnest layers, is able to induce polarisation and an increased ferroelectric response. 

The January issue of Journal of Materials Science is devoted to Frontiers of Ferroelectricity (J. Mater. Sci., 41 [1] (2006), including a review of relaxor ferroelectric behaviour ... 

H2O and ion jumps. In MHXO4 (MDXOJ compounds, the substitution of selenium by sulphur decreases strongly the HXO. " reorientation while substitution of hydrogen by deuterium reduces the proton jump relaxation to half its initial value due to the mass effect (Fig. 25.3) When cesium ions are substituted by ammonium ions, a new very slow relaxation in the 3-10 MHz region is introduced. A regular NH4 tetrahedron has no permanent dipole but a distorted ion has a dipole and the dipole intensity is strongly correlated to ferroelectric behaviour. 

Tan, B.Q., Li, J.-F., and Viehland, D. (1997) Ferroelectric behaviours dominated by mobile and randomly quenched impurities in modified lead zirconate titanate ceramics. Philos. Mag. B, 76 (1), 59-74. 

Compound 20 is an example of a phenanthrene discotic material that incorporates peripheral chiral units based on lactic acid. Compound 20 only exhibits ferroelectric behaviour when mixed with other chiral phenanthrene compounds. 

Zhang, Q. M., Bharti, V., Zhao, X. (1998) Giant electrostriction and relaxor ferroelectric behaviour in electron-irradiated poly(vinylidene fluoride-trifluoroethylene) copolymer, Sci., 280, 2101-3. 

According to the dielectric results in the previous section, decreasing the temperature at which these measurements were taken should increase the hysteresis gap (ferroelectric behaviour), and increasing the temperature should further decrease the hysteresis. This was observed by Carl et al. (Carl and Geisen 1973) for PLZT (9.0/65/35). The slim ferroelectric behaviour of these PLZT compositions makes them ideal for use as ptrecision sensors and actuators, since they have almost no remnant polarization when the field is removed. Hence, the risk of depoling is eliminated in this case. 

If all the coefficients of equation (2) are known, one can accurately predict the longitudinal strain under a varying electric field for a given piezoelectric or electrostrictive material, and even for a material exhibiting both piezoelectric and electrostrictive effects, such as irreversible electrostrictive materials. For ideal reversible electrostrictive materials, which possess no remnant polarization at zero electric field, the odd power term of the electric field in equation (2) vanishes. However, we will consider the relaxor PLZT ceramics studied in this chapter as irreversible electrostrictives, to account for any ferroelectric behaviour under dc bias fields, and we will therefore include both terms of the electric field in equation (2). 

These materials have the ilMnOs R = Sc or small, rare earth cation) stoichiometry,and have been erroneously referred to as hexagonal perovskites. The compounds do not exhibit the perovskite structure. The Mn cations are not octahedrally coordinated, rather the cation is surrounded by five oxide anions in a trigonal prismatic coordination environment. Also the R cations are not 12-coordinate, as would be the case in a perovskite, but are in seven-fold coordination. The materials are multi-ferroic, with anti-ferromagnetic and ferroelectric properties.The nature of the polarity and therefore the ferroelectric behaviour was only recently described. Careful structural studies indicated that although the dipole moments are attributable to the R-O bonds and not the Mn-O bonds, the R-cations are not directly responsible for the ferroelectric behaviour. The noncentrosymmetry is attributable to the tilting of the MnOs polyhedra, which in conjunction with the dipole moments in the R-O bonds results in ferroelectric behaviour. Thus the ferroelectric behaviour in these materials is termed improper " and occurs by a much different mechanism than BaTiOs or even BiFeOs. 

It is suggested that the reason ferroelectric behaviour occurs in the Co and Ni phases and not the Mn and Fe analogues is attributable to geometric constraints and size effects. ° Boracite-type compounds have the stoichiometry M3B7O13X (M = Cr, Mn, Fe, Co, Ni, or Cu X = Cl, Br, or I) and exhibit three-dimensional crystal structures. The structures consist of... 

On shrinking particle sizes down to nanometer dimensions, the ferroelectric behaviour in BaTiOs has been found to be supressed. In an elfort to probe this phenomenon of size-dependent ferroelectricity. Page et al. have performed real space investigations of 5 nm BaTiOs nanoparticles prepared by the solvothermal treatment of barium metal in titanium isopropoxide. ... 

Investigations in the 1970s were extended to include copolymers of vinylidene fluoride (VDF) with related fluorinated vinyl monomers vinyl fluoride (VF), trifluoroethylene (TrFE) and tetrafluoroethylene (TeFE) [7, 8]. The latter two copolymers were found to crystallize into polar form without the stretching stage required by PVDF. This facilitates processing, and thus offers a wider range of potential device structures. Research in the 1980s has therefore focused on the ferroelectric behaviour and piezoelectric activity of vinylidene fluoride-trifluoroethylene copolymers. 

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