Ceramics permittivity

In lead zh conate, PbZrOs, the larger lead ions are displaced alternately from the cube corner sites to produce an antifeiToelectric. This can readily be converted to a feiToelectric by dre substitution of Ti" + ions for some of the Zr + ions, the maximum value of permittivity occumirg at about the 50 50 mixture of PbZrOs and PbTiOs. The resulting PZT ceramics are used in a number of capacitance and electro-optic applicahons. The major problem in dre preparation of these solid soluhons is the volatility of PbO. This is overcome by... 

Fig. 107. Temperature dependence of the dielectric permittivity r determined at various frequencies for a ceramic sample ofRbsNb3OF,H.

The ratio of permittivity with the dielectric to the permittivity in vacuum, e/eo, is called the relative permittivity, s, or dielectric constant. The dielectric constant is a material property. Some values of dielectric constants for common ceramic and glass insulators are given in Table 6.3. Since a polarizable material causes an increase in charge per unit area on the plates of a capacitor, the capacitance also increases, and it can be shown that the dielectric constant is related to the capacitance and displacement in vacuum and with the dielectric material as follows ... 

Barium titanate and BaTi03-based materials are most commonly used for ceramic capacitors with high dielectric permittivity. BaTi03 powder of extremely high quality (in respect of its purity, stoichiometry, particles morphology) is required for most of the modem applications. This characteristic may be considerably improved by the application of alkoxide precursors. Thus, it is of no surprise that synthesis of BaTi03 and BaTi03-based materials from metal alkoxides attracted considerable attention for several decades. The first works on... 

Figure 1.15 BaTiOj Temperature dependence of the permittivity for (a) bulk ceramics with different grain sizes and (b) thin films with different grain sizes and (c) microstructure of thin films.

The compositions of most dielectric materials used for ceramic capacitors are based on ferroelectric barium titanate. As discussed in detail in Pragraph 1.3 the permittivity of ferroelectric perovskites shows marked changes with temperature, particularly close to the phase transition. From the device point of view a high dielectric permittivity with stable properties over a wide temperature range is required. There are various specifications which have to be fulfilled (e.g. X7R AC/C(T = 25°C) < 0.15 in a range between -55°C and 125°C). 

For Ba(ZrxTii x)03 all phase boundaries meet at a Zr content x 0.18, see Figure 1.16. Because of the superposition of the particular phase transitions the resulting transition becomes diffuse with a broad maximum of the dielectric permittivity as shown in Figure 1.16. Therefore, this composition has the potential as suitable temperature-stable dielectric for ceramic capacitors. 

Analogous C(V) curves were recorded on pzt bulk ceramics with compositions around the morphotropic phase boundary (mpb). Figure 1.25 displays the relative permittivity as a function of DC-bias for a tetragonal (x = 0.48), a morphotropic (x = 0.52) and a rhombohedral (.x = 0.58) sample. In contrast to thin films additional humps observed in the e E) curves. This could be explained by different coercive fields for 180° and non-180° domains [31]. Their absence in ferroelectric thin films could be taken as evidence for suppressed non-180° domain switching in thin films [30],... 

Figure 1.25 Relative permittivity of 2% Nd-doped PbZrxTii xC>3 bulk ceramics.

Figure 7.7 Temperature dependence of the relative permittivity for PZT ceramics near the mpb. pzt (54/46) undergoes a partial Fr Ft phase transition between 40 and 80°C.

Eqs (2.88) and (2.89) cannot be applied to all solids but they are valid for the many high symmetry ionic structures that are non-polar and non-conductive. Also it has to be borne in mind that in the case of ceramics, grain boundaries can give rise to anomalies in the applied field distribution, and occluded layers of water can contribute to increased permittivities. R.D. Shannon [9] and others have calculated polarizabilities using Eq. (2.89) with the established values of molecular volume (Fm= 1 /N) and permittivity. They find that each constituent ion can be assigned a unique polarizability which is the same whatever other ions they are associated with. Table 2.5 gives the polarizabilities of a wide selection of ions and using these it is possible to calculate the permittivity of any combination... 

Fig. 2.48 The effect of grain size on the permittivity of a BaTiC>3 ceramic. (After K.

Ceramic dielectrics and insulators cover a wide range of properties, from steatite with a relative permittivity of 6 to complex ferroelectric compositions with relative permittivities exceeding 20000. For the purposes of this discussion insulators will be classed with low permittivity dielectrics, although their dielectric loss may be too high for use in capacitors. Reference should be made to Table 5.10 and Fig. 5.40. 

Class I dielectrics usually include low- and medium-permittivity ceramics with dissipation factors less than 0.003. Medium-permittivity covers an sr range of 15-500 with stable temperature coefficients of permittivity that lie between +100 and -2000 MK-1. 

Class II/III dielectrics consist of high-permittivity ceramics based on ferro-electrics. They have er values between 2000 and 20 000 and properties that vary more with temperature, field strength and frequency than Class I dielectrics. Their dissipation factors are generally below 0.03 but may exceed this level in some temperature ranges and in many cases become much higher when high a.c. fields are applied. Their main value lies in their high volumetric efficiency (see Table 5.1). 

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