Cooling permittivity

In comparison to ordinary dielectrics, the permittivities of the so-called ferroelectric materials are about 103 times larger. The ferroelectric material can be transformed into a new type of material called piezoelectric material by heating the ferroelectric above its Curie temperature and then cooling it in a powerful electric field. A piezoelectric crystal changes its polarization once subjected to a mechanical strain. As a result, it can deform mechanically under an electric field or produce electric impulses as a result of mechanical impulses. Currently, piezoelectric materials are widely used as force or pressure transducers with fast response times and very sensitive output. Permittivities of common dielectric and ferroelectric materials are given in Table 1.9. 

A ferroelectric model material is barium titanate BaTi03. On cooling from high temperatures, the permittivity increases up to values well above 10,000 at the phase transition temperature Tc. The inverse susceptibility as well as the dielectric permittivity follows a Curie-Weiss law x1 f 1 oc (T — O). The appearance of the spontaneous polarization is accompanied with a spontaneous (tetragonal) lattice distortion. 

The grain size of a ferroelectric ceramic has a marked effect on the permittivity for the size range 1-50 /mi (see Fig. 2.48). Below about 1 /mi the permittivity falls with decreasing grain size. An important factor leading to this behaviour is the variation in the stress to which a grain is subjected as it cools through the Curie point. 

Finally, in Figure 3, after two hours (240 minutes total curing) of heating at 120"C, the sample was cooled back to room temperature. The permittivities went back to approximately 2.7 due to the removal of the thermal randomization of dipoles in RTV. However, the loss factors were so low that only the 0.1 Hz was observed, indicating it was definitely cured further than before heating (compare Figures 1,2,3). The continuous decrease of loss factor at low frequency (such as 0.1 Hz) after 360 minutes of cure time is a good indication of the continuous further cure of the RTV silicone but at a much slower rate. 

This anisotropy, illustrated by refractive index, extends to other properties, and common properties of interest would be the anisotropy in linear polarizability (Aa), dielectric permittivity (Ae), and diamagnetism (Ax). In the nematic phase, these properties are quite strongly temperature dependent the order parameter, S, increases as samples cool away from the N-I transition. This is illustrated in Figure 19 where it is also seen that the parallel component has the stronger temperature dependence as it is the orientational correlations that increase on cooling. 

A Solartron 1260 Impedance Analyzer was used to make measurements of C, capacitance, and G, conductance, over a range of frequencies form 5 Hz to 100 kHz both during cooling and heating. From the known geometry of the cell, values of the complex permittivity e = e - fe"were calculated where e = C/Q and s " = G/wejC riiere co = 2n fi equency, C is the measured air-filled capacitance of the cell with a 1.59mm gap, and = 8.854 X 10 C J W . 

The relative permittivity and other dielectric behaviour of a relaxor ferroelectric as a function of temperature is often different depending upon whether the sample is cooled from higher temperatures in an electric field (FC) or in no electric field (ZFC). For example, the non-ferroelectric low-tenperature state of a canonical relaxor can be transformed irreversibly into a ferroelectric state by the application of a sufficiently high electric field or if the material is cooled in the presence of an electric field. As with non-canonical relaxors, this state transforms to the ergodic state above... 

Fig. 21.2. (a)Evolution with temperature of the neutron diffraction patterns of isopropanol. Both in the hquid and in the super cooled liquid state(SCL) the diffraction patterns are characteristic of an amorphous material. The crystalline state presents characteristic narrow Bragg peaks of a crystalline phase, (b) Evolution with temperature of the main relaxation of isopropanol. Molecular mobility at T > Tg is revealed by the main relaxation of isopropanol as reflected by the maximum in frequency of the imaginary part, t", of the complex dielectric permittivity. The main relaxation appears in both the super-cooled and the liquid state. However, in the crystalline state, where no signiflcant molecular mobility is expected, the relaxation vanishes [6,7]. Isopropanol was quenched from the liquid to the glassy state... 

Figure 2 Dielectric permittivity and loss of two, CaCOj-filled PP samples measured at 100 kHz and 120 Hz during heating and cooling. Sample A contains 30 wt.% nontreated filler, while Sample B contains 30 wt.% stearate treated filler. (In part after [4] and unpublished data).

Antiferroelectric. A dielectric of high permittivity which undergoes a change in crystal structure on cooling through a CURIE TEMPERATURE (q.V.) bUt which possesses no spontaneous polarisation. The state is visualised as polarisation of adjacent lines of atoms in opposite directions. 

In order to decrease temperature gradients inside the vacuum chamber during the measurements, the temperature was slowly varied so that the temperature dependence of the permittivity of one sample was recorded for about 8 h. Beginning from the initial temperature of 25 °C, the system was slowly (for about 2.5 h) cooled by the thermostat to 0 °C, then slowly (for about 4h) heated to 40 °C, and finally cooled to 25 °C for 1.5 h. During the entire cycle, the capacitance was determined (and the corresponding value of permittivity was calculated) in 5 °C steps. Therefore, the permittivity at 25 °C was measured three times per cycle, which allowed us to judge the existence of the temperature hysteresis in the system under consideration. 

It is usually admitted that polar domains of nanometric size exist at temperamres much higher than Tm, a state termed super-paraelectric. During cooling, they will increase in size and number. Dispersion of sizes and variations in composition are at the origin of the frequency dispersion and are responsible for the widemng of the relative permittivity peak. Below T, the polar phase occupies a large volume fraction of the sample, even attains the percolation threshold, without however invading the whole sample, like is the case for any ordinary ferroelectric material. However, an apphed electric field is susceptible to provoke the transition towards a ferroelectric state. 

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