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

114 Dielectric Material

equations:

temperature [1]:

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√

> 2 2

(1)

(2)

2

2 2

(3)

0

<sup>2</sup> . <sup>3</sup> *Opt*

 

3 3 *<sup>L</sup> c nq m m*

*C T Q*

2

2 2 0

*T nq m*

 

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

where c is the elastic coupling parameter of phonons; m is reduced mass; q, n are ion charge

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

*MW L Opt i T*

T – Q; this leads in accordance with the Liddein–Sax–Teller (LST) relation:

to the Curie – Weiss law for permittivity:

2

and concentration; ε0 is an electric constant [1].

*MW L*

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

2

and

*IR MW Opt*

loss, as well as their variation in the MW range as a function of temperature.

 

0

3 3 *<sup>T</sup> c nq m m*

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