*2.2.3 Microwave dielectric properties of pseudo tungsten-bronze solid solutions*

**Figure 8** shows the microwave dielectric properties of the solid solutions as a function of composition *x* of Ba6−<sup>3</sup>*xR*8+2*x*Ti18O54 [20, 21, 42]. The quality factor (*Qf*) changes nonlinearly and has the highest value at particular point *x* = 2/3 with compositional ordering specified above [55]. The highest *Qf* value might be depending on the internal strain. **Figure 11(a)** confers internal strain *η* obtained from the slope of equation *β*cos*θ* = *r*/*t* + 2*η*sin*θ*. The internal strain *η* of the special point *x* = 2/3 is the lowest with the compositional ordering as a function of composition *x* as shown

**Figure 10.**

*Structure of disordering (a), compositional ordering (b) and defects in A2-sites (c), depending on the x values of Ba6−3xR8+2xTi18O54.*

#### **Figure 11.**

*Internal strain η values obtained from the slope of equation βcosθ = r/t + 2ηsinθ as a function of sinθ for x = 0.3, 0.5, 2/3 and 0.7 (a) and strain η (d-spacing) as a function of composition x (b).*

**Figure 12.** *Microwave dielectric properties as a function of ionic radius of R ion.*

in **Figure 11(b)**. The internal strain comes from the fluctuation of *d*-spacing of the lattice broadening the full width at half maximum (FWHM) [20, 21, 56].

The *Qf* value at the special point *x* = 2/3 shows the highest of 10.5 × 103 GHz in the Sm system, 10.0 × 103 GHz in the Nd system and 2.0 × 103 GHz in the La system as depicted in **Figure 8(a)** [20, 21, 56]. The *Qf* values reducing in the order of Sm, Nd, Pr and La are depending on the ionic radius relating size difference between Ba and *R* [57], and that of La is deviating from the *Qf* line through the Sm, Nd and Pr as shown in **Figure 12**. If the sizes are similar, the crystal structure should become perovskite structure. In the case of Sm, the difference is maximum which introduces the stability of the crystal structure. The size of La ion is similar to Ba, so the structure might be unstable to be low *Qf*.

#### *2.2.4 Symmetry and ordering for Q*

On the microwave dielectrics, high *Q* has been brought by a high potential material, which has an over-well-proportional rigid crystal structure with symmetry

**13**

**Figure 13.**

*Dielectric Losses of Microwave Ceramics Based on Crystal Structure*

for miniaturisation based on their high *Qf* and high *ε*r.

• The special point of *x* = 2/3 on the structural formula of

high temperatures is a high symmetry cubic structure of *Pm*¯

formula which shows the highest *Qf* value.

1/3*B*5+

[11–13]. That is, the structure should be without electric defects, nondistortion and strain. Complex perovskites were described later, it is believed that ordering by long time sintering brings high *Q*, but we are pointing out symmetry is the predominant factor [14, 15]. In the case of indialite/cordierite, indialite with high symmetry shows higher *Q* than cordierite with ordering [17, 18, 39]. This case has an orderdisorder phase transition. On the other hand, in the case of pseudo tungsten-bronze solid solutions which has no phase transition, one of ordering that is the compositional ordering brings high *Q* [20, 21]. In the case of no symmetry change, ordering

• The pseudo tungsten-bronze solid solutions have been used for mobile phones

• The compound has a unique point of *x* = 2/3 on the Ba6−<sup>3</sup>*xR*8+2*x*Ti18O54 chemical

[Ba4]*A*2[Ba2−<sup>3</sup>*xR*8+2*x*]*A*1Ti18O54 is the composition at which Ba-ions disappear on the *A*1-sites because 2 − 3*x* = 0. That is the point of compositional ordering.

• The compositional ordering brings high *Q* by maintaining the stability of the

There are many kinds of complex perovskites such as 1:1, 1:2 and 1:3 type in *B*-site and 1:1 type in *A*-sites [21]. In this chapter, 1:2 type complex perovskite

Ba(Mg1/3Ta2/3)O3 (BMT) and Ba(Zn1/3Nb2/3)O3 (BZN). These complex perovskite compounds have order-disorder phase transitions (**Figure 13(a)** and **(b)**) [58]. The ordered phase that appears at low temperatures is a trigonal (rhombohedral)

*Complex perovskite crystal structure composed by Mg/TaO6 octahedra located between BaO3 closed packing layer, showing relationship between cubic and trigonal crystal lattice. Perspective figure (a) and (110) plane (b).*

2/3)O3 are presented such as Ba(Zn1/3Ta2/3)O3 (BZT),

<sup>3</sup>*m*1 (No. 164), and the disordered phase appearing at

<sup>3</sup>*m* (No. 221), as shown

*DOI: http://dx.doi.org/10.5772/intechopen.82483*

*2.2.5 Conclusions for pseudo tungsten-bronze*

is predominant.

crystal structure.

**2.3 Complex perovskites**

structure of space group *P*¯

compounds *A*2+(*B*2+

*Dielectric Losses of Microwave Ceramics Based on Crystal Structure DOI: http://dx.doi.org/10.5772/intechopen.82483*

[11–13]. That is, the structure should be without electric defects, nondistortion and strain. Complex perovskites were described later, it is believed that ordering by long time sintering brings high *Q*, but we are pointing out symmetry is the predominant factor [14, 15]. In the case of indialite/cordierite, indialite with high symmetry shows higher *Q* than cordierite with ordering [17, 18, 39]. This case has an orderdisorder phase transition. On the other hand, in the case of pseudo tungsten-bronze solid solutions which has no phase transition, one of ordering that is the compositional ordering brings high *Q* [20, 21]. In the case of no symmetry change, ordering is predominant.
