*2.2.2.1 Structure*

The crystal structure of the pseudo tungsten-bronze Ba6−3xR8+2xTi18O54 (*R* = rare earth) solid solutions [48–51] includes the perovskite blocks of 2 × 2 unit cells with rhombic (*A*1) sites and pentagonal (*A*2) sites, as shown in **Figure 9**, which are named after the tetragonal tungsten-bronze structure with 1 × 1 perovskite blocks and pentagonal sites [20, 48, 50]. On this compound, two large sites including Baand *R*-ions are placed such as *A*1 and *A*2. The Ba-ions engaged on the pentagonal *A*2-sites and *R*-ions *A*1-sites on the perovskite blocks. Two more sites, *B* and *C* are positioned on the tungsten-bronze crystal structure. The *B*-site is the same as the TiO6 octahedral place in the perovskite, and the *C*-site is a triangular site which is usually empty. This crystal structure of this compound has a special relationship with the perovskite structure. If the two ions are the same size, the structure will change to perovskite with only an *A*1-site owing to the combination of the

#### **Figure 9.**

*Crystal structure of the pseudo tungsten-bronze solid solutions. Rhombic (A1) sites located in 2 × 2 unit cells of perovskite blocks, and pentagonal (A2) and trigonal sites (C).*

**11**

**Figure 10.**

*of Ba6−3xR8+2xTi18O54.*

*Dielectric Losses of Microwave Ceramics Based on Crystal Structure*

pentagonal *A*2-site and the trigonal *C*-sites [20, 52]. The crystal data are as follows: orthorhombic crystal system of space group *Pbnm* (No. 62), point group *mmm* and

.

. The super

lattice parameters *a* = 12.13, *b* = 22.27, *c* = 7.64 Å, *Z* = 2 and *D*x = 5.91 g/cm3

The structure has a super lattice along the *c*-axis with a double lattice of perovskite as shown in **Figure 7(b)** of an oscillation photograph with super diffraction lines [53, 54]. The crystal data of the fundamental lattice are as follows: orthorhombic crystal system of space group *Pbam* (No. 55), point group *mmm* and lattice

lattice is depending on the tilting of TiO6 octahedra as shown in **Figure 7(d)**. The tilting was endowed in the density map (**Figure 7(c)**) which is of the fundamental lattice superimposed on a superstructure framework. The top oxygen ions (O(1), O(4), O(6), O(8) and O(14)) of octahedra are separated into two along the *c*-axis. The left figure of **Figure 7(d)** shows the reason for splitting of the top oxygen [20]. However, this super lattice is not depending on the order-disorder phase transition as complex perovskite as explained at 2.3 section. The tilting of octahedra might be

The chemical formula of the solid solutions is Ba6−3*xR*8+2*x*Ti18O54, and the structural formula is [Ba4]*A*2[Ba2−<sup>3</sup>*xR*8+2*x*]*A*1Ti18O54. Here, the amount of Ba in the *A*1-sites becomes zero (2 − 3*x* = 0), that is, *x* = 2/3. This composition is special as the following sentence: the structural formula is [Ba4]*A*2[*R*8+4/3]*A*1Ti18O54 which is occupied separately by Ba in *A*2 and by *R* in *A*1 as shown in **Figure 10(b)**. This special

**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

*Structure of disordering (a), compositional ordering (b) and defects in A2-sites (c), depending on the x values* 

parameters *a* = 12.13, *b* = 22.27, *c* = 3.82 Å, *Z* = 1 and *D*x = 5.91 g/cm3

depending on the size of *A*-ion in the perovskite block.

composition is called "compositional ordering" [20, 21, 42].

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

*2.2.2.3 Compositional ordering*

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

*2.2.2.2 Tilting*

pentagonal *A*2-site and the trigonal *C*-sites [20, 52]. The crystal data are as follows: orthorhombic crystal system of space group *Pbnm* (No. 62), point group *mmm* and lattice parameters *a* = 12.13, *b* = 22.27, *c* = 7.64 Å, *Z* = 2 and *D*x = 5.91 g/cm3 .
