**1. Introduction**

The development of modern telecommunication systems calls for the creation of novel materials with a high level of electrophysical parameters in the MW range. These materials must have in the MW range a high permittivity (ε ≥ 20), a low dielectric loss ( tg δ ≤ 10-3 – 10-4) and a high thermostability of electrophysical properties (temperature coefficient of permittivity (TCε) or resonant frequency (f) 10-6K-1). Such materials can be used in the development of resonant elements of radio-frequency filters, solid state oscillators, substrates for hybrid MW circuits, allow the size of communication systems to be greatly reduced and improve their parameters. Moreover, the use of them reduces the manufacturing and operating costs for modern communication systems.

The choice of the permittivity value of MW materials is largely determined by the frequency range of the operation of communication systems, the type of exciting wave and the requirement of the optimal size of dielectric element. The value of ε determines the size of radio components. The influence of microminiaturization is based on the fact that the electromagnetic wavelength in dielectric decreases in inverse proportion to √ ε. Therefore, in the decimeter wave band, high-Q thermostable materials with high permittivity value (ε ≥ 80-600) are required, whereas in the centimeter and millimeter wave bands, thermostable materials with ε ~ 15-30 but with extremely high Q (Q× f ≥80000, where Q = 1/ tg δ and f is frequency in GHz) are needed.

It should be noted that low dielectric loss in the MW range 109 – 1011 Hz is characteristic only of optical and infrared polarization mechanisms. Other polarization mechanisms give rise, as a rule, to considerable dielectric loss [1].

In the case of optical polarization, dielectrics are characterized by a low negative temperature coefficient of permittivity (TCε ~ 10-5K-1). However, the dielectric contribution of optical

© 2012 Belous, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

polarization is usually small. Therefore, large permittivity values together with high temperature stability of dielectric parameters and low dielectric loss can be observed only in the dielectrics where the main contribution to polarization is made by infrared polarization mechanism [1, 2]. This mechanism is bound up with cation and anion sublattice displacement in electric field, which is only possible in ionic crystals. The contribution of infrared polarization mechanism to permittivity may be ∆ εir = 1 – 104 in the MW range. The temperature instability of ε increases, as a rule, with increasing ε. The large magnitude of infrared polarization is usually due to the presence of a soft mode in crystal, whose frequency varies by the critical law ωT = A√ T – Q; this leads in accordance with the Liddein–Sax–Teller (LST) relation:

$$\frac{\mathcal{E}\_{\rm MW}}{\mathcal{E}\_{\rm OPT}} = \prod\_{i} \frac{o\_{\rm L}^{2}}{o\_{\rm T}^{2}} \tag{1}$$

Microwave Dielectrics Based on Complex Oxide Systems 115

The present paper considers the structure peculiarities, electrophysical properties and possible applications of inorganic microwave (MW) dielectrics based on oxide systems.

MW dielectrics are often synthesized on the basis of solid solutions, e.g. Ba(Zn, Mg)1/3(Nb, Ta)2/3O3 [3, , 5], (La, Ca)(Ti, Al)O3 [6, 7], etc. The substance of this approach is that solid solutions are formed by the interaction of phases belonging to the same crystal structure, which have in the MW range a different trend of the plot of permittivity against temperature and a low dielectric loss. Paraelectric is characterized by a low dielectric loss; for example, CaTiO3, which crystallizes in perovskite structure, can be used in the CaTiO3 – LaAlO3 system as a phase with negative temperature coefficient of permittivity (TCε < 0) [6]. At the same time, LaAlO3 can be used as a phase with perovskite structure having TCε > 0 [7]. By varying the ratio CaTiO3 /LaAlO3, one can control the value of TCε. Positive TCε in dielectrics in the MW range usually indicates the presence of a high-temperature phase transition, which is connected with the existence of spontaneously polarized state (ferroelectrics, antiferroelectrics). However, the materials in which spontaneous polarization exists have, as a rule, a considerable dielectric loss in the MW range, which is inadmissible for the creation of high–Q dielectrics. In LaAlO3, there is no spontaneous polarization. It should be noted that there are very few materials having TCε > 0 in the MW range and a low dielectric loss. Therefore, the development of high-Q MW dielectrics with high ε and positive temperature

**2. MW dielectrics based on (La, Ca)(Ti, Al)O3 solid solutions** 

coefficient of permittivity (TCε > 0) is of independent scientific and practical interest.

**3. Control of the TCε value by influencing the phonon spectrum** 

which crystallize in defect-perovskite structure in a wide x range (Fig 1).

**Figure 1.** Crystal structure of La2/3-x(Na, K)3xTiO3 perovskite

As follows from the analysis of expressions (3), the trend of the plot of ε against temperature in the MW range can be controlled by influencing the phonon spectrum. One of the ways of influencing the phonon spectrum in some types of structures can be iso- and heterovalent substitutions in cation sublattices. As an example, we chose La2/3-x (Na, K)3x TiO3 materials,

to the Curie – Weiss law for permittivity:

$$
\varepsilon\_{\rm MW} = \varepsilon\_L + \frac{\mathcal{C}}{T - Q} \tag{2}
$$

where ωL and ωT are the frequencies of longitudinal and transverse optical phonons in the center of Brillouin zone (one of the transverse phonons is soft), C is a constant, Q is Curie – Weiss temperature, εL is dielectric contribution, which depends only slightly on temperature [1].

The frequency of transverse and longitudinal optical phonons can be calculated from the equations:

$$
\rho \alpha\_{\Gamma}^{2} = \frac{c}{m} - \frac{nq^{2}}{3\varepsilon\_{0}m} \cdot \frac{\varepsilon\_{\alpha} + 2}{3} \text{ and } \; \alpha\_{\perp}^{2} = \frac{c}{m} + \frac{2nq^{2}}{3\varepsilon\_{0}m} \cdot \frac{\varepsilon\_{\alpha} + 2}{3} \tag{3}
$$

where c is the elastic coupling parameter of phonons; m is reduced mass; q, n are ion charge and concentration; ε0 is an electric constant [1].

The parameters c, n, εopt are temperature-dependent; they decrease with rising temperature due to thermal expansion (lattice anharmonicity). It is evident from system (3) that ωL is a weak function of temperature because it is determined by the sum of two terms, whereas the dependence ωT (T) may be strong since ωT depends on the difference of two terms (see Eqs (3)). The variation of this difference as a function of temperature depends on which effect predominates: the variation of c/m (minuend) or the variation of the subtrahend, which depends on n, εopt. Depending on ωT, the dielectric contribution ∆ εir also varies with temperature [1]:

$$
\Delta \varepsilon\_{IR} = \varepsilon\_{MW} - \varepsilon\_{Opt} = \frac{nq^2}{m o\_T^2 \varepsilon\_0} \cdot \left(\frac{\varepsilon\_{Opt} + 2}{3}\right).
$$

The above analysis shows that the chemical composition can influence, in principle, the contribution of different polarization mechanisms and hence the value of permittivity and loss, as well as their variation in the MW range as a function of temperature.

The present paper considers the structure peculiarities, electrophysical properties and possible applications of inorganic microwave (MW) dielectrics based on oxide systems.
