*2.3.3.1 The highest Qf composition with intrinsic compositional density by Kugimiya's research*

Kugimiya [22, 27] presented the highest *Qf* composition with intrinsic compositional density on the Ta and Ba rich side near the BMT-Ba5Ta4O15 tie-line in a BaO-MgO-TaO5/2 partial system (BMT system), as shown in **Figure 21**. He presented three areas divided by the following two lines as shown in **Table 1** and **Figure 21**.

$$\alpha = \mathfrak{F}\mathfrak{y}/\mathfrak{A} \tag{3}$$

$$\mathbf{a} = \mathbf{y}/\mathbf{2} \tag{4}$$

Here, *α* and *γ* are as written in the formula *α*BaO·*γ*TaO5/2. On the *α* = 5*γ*/4 line, Ba1 + *α*(Mg1/3Ta2/3 + 4*<sup>α</sup>*/5*Vα*/5)O3+3*α* solid solutions are formed as the ideal compositions without vacancies in the *A*- and O-sites. In the *B*-site, the vacancy is neutralized and without charge.

In **Figure 21**, the composition with intrinsic compositional high density shows the highest *Q* of 50.0 × 103 on the tie-line between BMT and Ba5Ta4O15 ( = 5/4). The contour lines in **Figure 21** show *Q* values from 2.0 × 103 in the outer area to 25.0 × 103 in the centre. The contour is elongated parallel to the *Q* max line as drawn in **Figure 21,** and it changes steeply on the perpendicular to this line. So, the compositions without oxygen vacancy and with neutralised charge vacancies

**Figure 21.** *BaO-MgO-TaO5/2 partial system (BMT system).*


**Table 1.**

*The chemical formula for three areas divided by two lines: α =* 5*γ/4 and α = γ/2, here, α and γ are in BaαTaγO<sup>α</sup>+5<sup>γ</sup>/2 and vacancies on the A-, B- and O-sites [22].*

are ideal for microwave dielectrics, and the density is high due to the partial substitution of Ta in the site of Mg, which is denoted as intrinsic compositional density [28]. Other regions have some defects degrading the *Qf* values, which were explained on the references [21, 22, 27, 28].

### *2.3.3.2 Phase conditions in the vicinity of BZT by Koga's research*

Koga et al. [24, 25] showed the highest *Qf* composition shifted from the stoichiometric BZT composition. The ordering ratio of the deviated composition was not higher than that of the stoichiometric composition, which was calculated by the Rietveld method. These results were presented by the study of the phase relations in the vicinity of BZT in the BaO-ZnO-Ta2O5 ternary system, as shown in **Figure 22** [24, 25]. These samples were sintered at 1400°C/100 h as reported in Koga's paper. These diffraction patterns fit the Rietveld method well [23, 24]. Ordering ratios obtained are shown in **Figure 23(a)**. Three areas in the vicinity of BZT are presented as shown in **Figure 22**. 1st one (I) is ordering area with BZT single phase, the 2nd one (II) is ordering area with secondary phase and 3rd one (III) is disordering area with BZT single phase.

The first area (I) is characterised as a BZT single phase with an ordered structure and a high *Qf*. The varied compositions E and K have high *Qf* values about 50% higher than that of the stoichiometric BZT composition A. The ordering ratios at E and K are lower than that of stoichiometric BZT at A, but the density at E is the same as that of A [25]. The second (II) is composed by an ordered BZT

**21**

**Figure 24.**

*Dielectric Losses of Microwave Ceramics Based on Crystal Structure*

accompanied by a secondary phase BaTa2O6 with a specific amount of Zn determined by X-ray microanalyser (XMA). The ordering ratio in this area is high at about 70–80% (**Figure 23(a)**). Although the structure is ordered, the *Qf* values decrease in the order of A-N-O-P from stoichiometric BZT (**Figure 23(b)**). The ordered BZT with the secondary phase is located on the Ta2O5 rich side as a eutectic phase diagram system. The third (III) with a disordered single phase shows low *Qf* and low density (**Figure 23(c)**). The low density comes from the numerous pores.

*Ordering ratio (a), Qf (b) and density (c) as a function of composition deviation from stoichiometric BZT.*

tions deviated from the stoichiometric BMT composition which is located in the BMT-Ba5Ta4O15-Ba3Ta2O8 compositional triangle (CT) as shown in **Figure 24**. The positions located in the single-phase BMT, which was indicated by green line. The position is close to the BMT-Ba5Ta4O15 tie-line. A to H eight CTs are formed by BMT and five stable compounds, such as Ba5Ta4O15, MgO, BaO, Ba9MgTa14O45 and Mg4Ta2O9, and three metastable compounds, Ba6Ta2O11, Ba4Ta2O9 and Ba3Ta2O8. In A, B and C-CTs, although the samples demonstrated high density and a high degree

*Part of the BaO-MgO-Ta2O5 phase diagram in the vicinity of BMT divided into eight CTs. Small black dots indicate the target samples. Green line indicates an approximate boundary of the single-phase BMT.*

–340 × 103

GHz posi-

*2.3.3.3 Phase conditions in the vicinity of BZT by Kolodiazhnyi's research*

Kolodiazhnyi [29] also found the highest *Qf* of 330 × 103

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

**Figure 23.**

**Figure 22.** *Phase relations in the vicinity of BZT in the BaO-ZnO-Ta2O5 ternary system.* *Dielectric Losses of Microwave Ceramics Based on Crystal Structure DOI: http://dx.doi.org/10.5772/intechopen.82483*

*Electromagnetic Materials and Devices*

**Table 1.**

are ideal for microwave dielectrics, and the density is high due to the partial substitution of Ta in the site of Mg, which is denoted as intrinsic compositional density [28]. Other regions have some defects degrading the *Qf* values, which

*The chemical formula for three areas divided by two lines: α =* 5*γ/4 and α = γ/2, here, α and γ are in* 

α **Chemical formula Vacancy**

*α* > 5*γ*/4 Ba1+*α*(Mg1/3Ta2/3+*γ*V*<sup>α</sup>* <sup>−</sup>*<sup>γ</sup>*)O3+*<sup>α</sup>*+5*<sup>γ</sup>*/2 V2*<sup>α</sup>* <sup>−</sup>5*γ*/2 *A*: fill, *B*, O: vacancy *α* = 5*γ*/4 Ba1+*α*(Mg1/3Ta2/3+4*α*/5V*α*/5)O3+3*<sup>α</sup> A,* O: fill, *B*: vacancy 5*γ*/4 > *α* > *γ*/2 Ba1+*α*V5*<sup>γ</sup>*/6 −2*<sup>α</sup>*/3(Mg1/3Ta2/3+*γ* V*<sup>α</sup>*/3−*<sup>γ</sup>*/6) O3+*<sup>α</sup>*+5*γ*/2 *A*, *B*: vacancy, O: fill *α* = *γ*/2 Ba1+*α*Vα(Mg1/3Ta2/3+*γ*)O3+6*<sup>α</sup> A*: vacancy, *B*, O: fill *α* < *γ*/2 Ba1+*α*V*<sup>γ</sup>−<sup>α</sup>*(Mg1/3Ta2/3+*γ*)O3+*<sup>α</sup>*+5*<sup>γ</sup>*/2 V*<sup>γ</sup>*/2−*<sup>α</sup> A*, O: vacancy, *B*: fill

Koga et al. [24, 25] showed the highest *Qf* composition shifted from the stoichiometric BZT composition. The ordering ratio of the deviated composition was not higher than that of the stoichiometric composition, which was calculated by the Rietveld method. These results were presented by the study of the phase relations in the vicinity of BZT in the BaO-ZnO-Ta2O5 ternary system, as shown in **Figure 22** [24, 25]. These samples were sintered at 1400°C/100 h as reported in Koga's paper. These diffraction patterns fit the Rietveld method well [23, 24]. Ordering ratios obtained are shown in **Figure 23(a)**. Three areas in the vicinity of BZT are presented as shown in **Figure 22**. 1st one (I) is ordering area with BZT single phase, the 2nd one (II) is ordering area with

secondary phase and 3rd one (III) is disordering area with BZT single phase.

*Phase relations in the vicinity of BZT in the BaO-ZnO-Ta2O5 ternary system.*

The first area (I) is characterised as a BZT single phase with an ordered structure and a high *Qf*. The varied compositions E and K have high *Qf* values about 50% higher than that of the stoichiometric BZT composition A. The ordering ratios at E and K are lower than that of stoichiometric BZT at A, but the density at E is the same as that of A [25]. The second (II) is composed by an ordered BZT

were explained on the references [21, 22, 27, 28].

*BaαTaγO<sup>α</sup>+5<sup>γ</sup>/2 and vacancies on the A-, B- and O-sites [22].*

*2.3.3.2 Phase conditions in the vicinity of BZT by Koga's research*

**20**

**Figure 22.**

**Figure 23.** *Ordering ratio (a), Qf (b) and density (c) as a function of composition deviation from stoichiometric BZT.*

accompanied by a secondary phase BaTa2O6 with a specific amount of Zn determined by X-ray microanalyser (XMA). The ordering ratio in this area is high at about 70–80% (**Figure 23(a)**). Although the structure is ordered, the *Qf* values decrease in the order of A-N-O-P from stoichiometric BZT (**Figure 23(b)**). The ordered BZT with the secondary phase is located on the Ta2O5 rich side as a eutectic phase diagram system. The third (III) with a disordered single phase shows low *Qf* and low density (**Figure 23(c)**). The low density comes from the numerous pores.

#### *2.3.3.3 Phase conditions in the vicinity of BZT by Kolodiazhnyi's research*

Kolodiazhnyi [29] also found the highest *Qf* of 330 × 103 –340 × 103 GHz positions deviated from the stoichiometric BMT composition which is located in the BMT-Ba5Ta4O15-Ba3Ta2O8 compositional triangle (CT) as shown in **Figure 24**. The positions located in the single-phase BMT, which was indicated by green line. The position is close to the BMT-Ba5Ta4O15 tie-line. A to H eight CTs are formed by BMT and five stable compounds, such as Ba5Ta4O15, MgO, BaO, Ba9MgTa14O45 and Mg4Ta2O9, and three metastable compounds, Ba6Ta2O11, Ba4Ta2O9 and Ba3Ta2O8. In A, B and C-CTs, although the samples demonstrated high density and a high degree

#### **Figure 24.**

*Part of the BaO-MgO-Ta2O5 phase diagram in the vicinity of BMT divided into eight CTs. Small black dots indicate the target samples. Green line indicates an approximate boundary of the single-phase BMT.*

of order, they showed low *Qf* values, attributed to the possible presence of the Ba9MgTa14O45 second phase. Moreover, in D, E and F-CTs, as the samples were very low density, no electromagnetic resonance peaks were detected.
