Dielectric Constant versus Temperature

Because of very high dielectric constants k > 20, 000), lead-based relaxor ferroelectrics, Pb(B, B2)02, where B is typically a low valence cation and B2 is a high valence cation, have been iavestigated for multilayer capacitor appHcations. Relaxor ferroelectrics are dielectric materials that display frequency dependent dielectric constant versus temperature behavior near the Curie transition. Dielectric properties result from the compositional disorder ia the B and B2 cation distribution and the associated dipolar and ferroelectric polarization mechanisms. Close control of the processiag conditions is requited for property optimization. Capacitor compositions are often based on lead magnesium niobate (PMN), Pb(Mg2 3Nb2 3)02, and lead ziac niobate (PZN), Pb(Zn 3Nb2 3)03. 

Measurement of the temperature dependence of the dielectric constant is an important characterization for a ferroelectric material. As mentioned in the introduction section, when a phase transition occurs in a ferroelectric material, the dielectric constant always behaves anomalously. In general, the real part ofthe dielectric constant, e, shows a maximum at the phase transition temperature, where a change from a ferroelectric phase to the paraelectric one (or vice versa) occurs the value of e being higher than that at room temperature usually by 3 orders of magnitude. Figure 22-6 shows how the dielectric constant of barium titanate changes with temperature. At temperatures above the transition temperature, the variation ofthe dielectric constant (at low frequency) as a function of temperature obeys the Curie-Weiss law (see equation (22-2)). Usually, the peak ofthe dielectric constant versus temperature curve determines the Curie point F, and the Curie-Weiss constant C is determined by the slope ofthe curve of(e ) versus T. 

Fig. 44. The dielectric constant versus temperature for the RA 04 compounds (after Ismail-zade et ai., 1980).

Figure 7. Plots of dielectric constant versus temperature for supercritical water as a function of pressure. The conditions employed in the experimental determination of pH for 0.01 m HCl solution are indicated by the large filled circles. Reprinted from Ref. 5, Copyright (1997) with permission from Elsevier.

Plots of (a) dielectric loss and (b) dielectric constant versus temperature for a mixture of 40 wt% SAN copolymer (75 wt% styrene) plasticized with 60 wt% acetone. Venical axis scaling is varied in (a) and arbitrary vertical axis shifts are made in (b) for clarity. 

Fig. 4.2. Imaginary part e" of the complex dielectric constant versus real part with frequency as a parameter (Cole-Cole plot) at different temperatures. Arrows indicate the frequency of 10 Hz in each case. Insert shows thermal activation energy plot. (See Text)...

Figure 7.3 Dielectric constant ep versus (inverse) temperature for Stockmayer fluids at fixed fluid density p = 0.7. Curves aie labeled according to values of the matrix density.

The dielectric constant curve versus temperature was also investigated for K4[Fe CN)6]-3H20 by Bristoti et al. (80) in the temperature range -80-150°C. Four peaks were observed in the curve from — 80—25°C, due to the presence of the water of hydration. A single peak with a maximum at 105°C was due to a paraelectric order-disorder transition. It is in this temperature region that the dehydration reaction... 

Figure 1 Dielectric constant and dissipation factor versus temperature at different frequencies in a PbO-MgO-NbaOs composition. (From Ref. 13.)...

Figure 8 shows the pyrochlore concentration in the ternary diagram. Compositions with pyrochlore concentration <1% were prepared at 0.24 < jc < 0.27 and 0.15 < y < 0.18. Figure 9 shows the dielectric constant and dissipation factor at 1 kHz versus temperature in five selected compositions with no PT (/ = 0). The dielectric constant have a broad maximum at around -5°C. The magnitude of the maximum depends on the pyrochlore concentration in these compositions. At a temperature slightly (15-20°C) below the Curie temperature, the DF shows a maximum value. At higher temperatures above the Curie temperature, DF is much smaller (<0.005). 

Figure 9 (a) Dielectric constant and (b) dissipation factor versus temperature in five selected compositions in the Pb0-Mg0-Nb20s ternary diagram. The dielectric properties were measured at 1 kHz and 1.0 V. The magnitude of the maxima depend on the pyrochlore concentration. (From Ref. 13.)... 

Figure 9 Dielectric constant of TazOs thin film versus firing temperature.

These books remain the reference works in measuring dielectric and magnetic constants of homogeneous materials. Methods used at that time were limited in frequency band measurements, permitting only the determination of the complex permittivity and permeability at fixed frequencies and sometimes versus temperature variations. 

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