Ferroelectric/piezoelectric temperature dependence

PVDF is mainly obtained by radical polymerisation of 1,1-difluoroethylene head to tail is the preferred mode of linking between the monomer units, but according to the polymerisation conditions, head to head or tail to tail links may appear. The inversion percentage, which depends upon the polymerisation temperature (3.5% at 20°C, around 6% at 140°C), can be quantified by F or C NMR spectroscopy [30] or FTIR spectroscopy [31], and affects the crystallinity of the polymer and its physical properties. The latter have been extensively summarised by Lovinger [30]. Upon recrystallisation from the melted state, PVDF features a spherulitic structure with a crystalline phase representing 50% of the whole material [32]. Four different crystalline phases (a, jS, y, S) may be identified, but the a phase is the most common as it is the most stable from a thermodynamic point of view. Its helical structure is composed of two antiparallel chains. The other phases may be obtained, as shown by the conversion diagram (Fig. 7), by applying a mechanical or thermal stress or an electrical polarisation. The / phase owns ferroelectric, piezoelectric and pyroelectric properties. 

Piezoelectric coefficients are also temperature dependent quantities. This is true for both the intrinsic and the extrinsic contributions. Typically, the piezoelectric response of a ferroelectric material increases as the transition temperature is approached from below (See Figure 2.3) [3], Where appropriate thermodynamic data are available, the increase in intrinsic dijk coefficients can be calculated on the basis of phenomenology, and reflects the higher polarizability of the lattice near the transition temperature. The extrinsic contributions are also temperature dependent because domain wall motion is a thermally activated process. Thus, extrinsic contributions are lost as the temperature approaches OK [4], As a note, while the temperature dependence of the intrinsic piezoelectric response can be calculated on the basis of phenomenology, there is currently no complete model describing the temperature dependence of the extrinsic contribution to the piezoelectric coefficients. 

It should be noted that in practice, the piezoelectric response will typically not continue to rise all the way to the transition temperature, as elevated temperatures induce depoling of the ferroelectric, unless appropriate care is taken to insure that the material remains polarized (e. g. by application of a bias electric field). Depoling of this type is often important at temperatures of 1/2 of the Curie temperature, making high transition temperature materials interesting both for the decreased temperature dependence in the response, and the wider use range that can be achieved. 

Vinylidene fluoride-trifluoroethylene (VF2-F3E) copolymers exhibit a ferroelectric-paraelectric phase transition, the first such case found for a synthetic polymer. In this transition, the electric polarization and piezoelectric constant of the film disappear above the Curie point (Tcurie)- The temperature dependence of the dielectric constant, , obeys the so called Curie-Weiss law ... 

Titanates are double oxides of the form MeTiOa or Me2Ti04. Barium titanate BaTiOa and its solid solution crystals with other titanates are especially well-known. BaTiOs crystallizes in the perovskite structure. Its technical importance results from its ferroelectric and associated piezoelectric properties, its high dielectric constant at room temperature, and the interesting semiconducting properties which it exhibits when doped [13]. The remarkable temperature dependence of the electrical resistance of such doped material (the temperature coefficient can be metal-like) is used to advantage in control and circuit devices. 

Another possibly applicable crystal is Lithium sulfate (Li2S04.H20). It could be used below 90° C for its relatively high piezoelectric coefficients (especially for hydrostatic coefficient dh = 16.4 x 10 CN ) as a hydrostatic pressure sensor. Especially high hydrostatic piezoelectric coefficient (1000-2000 x 10 CN ) exhibits also the semiconductive ferroelectric crystal SbSI (see Fig. 7.18). Its hydrostatic piezoelectric coefficient is extremely high, but strongly temperature dependent especially at room temperature 22° C. 

Figure B.4 shows the theoretical temperature dependence of the spontaneous polarization P and the dielectric permittivity e. Considering that, for the ferroelectric state, e = C/2(Tc - T) and = >/((Tc -T)/eoCP), the temperature dependence of the piezoelectric strain constant d is obtained as...

Nalwa H, Fukada E (eds) (1995) Ferroelectric polymers. Marcel dekker. New York Newman B et al (1980) The piezoelectricity of poly(vinyhdene fluoride). J Appl Phys 51 5161 Omote et al (1997) Temperature dependence of elastic, dielectric, and piezoelectric properties of single crystalline films of vinylidene fluoride trifluoroethylene copolymer. J Appl Phys 81 2760... 

The development of active ceramic-polymer composites was undertaken for underwater hydrophones having hydrostatic piezoelectric coefficients larger than those of the commonly used lead zirconate titanate (PZT) ceramics (60—70). It has been demonstrated that certain composite hydrophone materials are two to three orders of magnitude more sensitive than PZT ceramics while satisfying such other requirements as pressure dependency of sensitivity. The idea of composite ferroelectrics has been extended to other appHcations such as ultrasonic transducers for acoustic imaging, thermistors having both negative and positive temperature coefficients of resistance, and active sound absorbers. 

Piezoelectricity and ferroelectricity are the result of electric dipole effects that are due to ions shifting from their initial positions in the lattice. This effect, which is strongly structure-dependent, was discussed above. Pyroelectric materials have permanent electric dipole moments, their magnitude varying with temperature. In infrared detectors, use is made of the ferroelectric phase transitions in perovskites. 

To summarize the ferroelectric and piezoelectric properties of the discussed polymers, some important ferroelectric and piezoelectric parameters are tabulated in Table 4. As discussed in the previous sections, the ferroelectric and piezoelectric properties of polymeric and polymeric composite systems depend on various factors, such as crystallinity, pohng conditions, glass transition temperature, and before and after electrical poling treatments (electrical, mechanical, and thermal treatments). In addition to the factors mentioned above, for composite systems, laminates or blends, fraction of constituents, and interfacial polarization are also important. Therefore, the... 

Quartz, since it is a piezoelectric and not a ferroelectric, has no hysteresis loss when it oscillates, thus quartz crystal oscillators are widely used as frequency control devices in radios, computers, and watches. Since the frequency is a function of the mass of the crystal, they can serve as deposition monitors (quartz crystal microbalances) with sensitivities of less than 1 ng. By functionalizing the surface to absorb specific gases, they can also act as chemical sensors. The temperature sensitivity of a quartz crystal oscillator can be minimized by choosing the cut of the crystal relative to the optical axis, which is necessary for its use as a frequency standard. On the other hand, a cut can be chosen to maximize the frequency dependence on temperature and quartz crystal thermometers with millikelvin resolution are available. 

Timability of perovskites is defined according to the dielectric nonlinearity of as functions of electric field above the Ciuie temperature. Ferroelectries for applications in electrically tunable devices are generally in the paraelectric phase [3,4,7-10,13]. The reason is that most of the ferroelectries in polar phase are also piezoelectric. Piezoelectric transformations cause large losses at relatively low microwave frequencies, and additional losses in polar phase are associated with the domain wall movements. Another reason hindering the applications of a ferroelectric in a polar phase is the hysteresis in field-dependent dielectric characteristics [7]. 

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