*3.2.1 Structural and valence-state properties of Ba*2*Tb(Bi,Sb)O*<sup>6</sup> *samples*

X-ray diffraction patterns of Ba2TbBiO6 are shown in **Figure 8**. For the parent Ba2TbBiO6 with a monoclinic structure (the space group *I*2*=m*), the lattice parameters were estimated from the x-ray diffraction data to be *a* ¼ 6*:*1099 Å, *b* ¼ 6*:*0822 Å, *<sup>c</sup>* <sup>¼</sup> <sup>8</sup>*:*5939 Å and *<sup>β</sup>* <sup>¼</sup> <sup>89</sup>*:*888<sup>∘</sup> , which fairly agree with previous data [20]. The peak intensity of (101) reflection (the inset of **Figure 8**) is responsible for the degree of B-site ordering in the double-perovskite crystal structures. When the B site ordering is assumed to be �70 %, the tiny profiles around the (101) peak are well fitted by the least squared method using the RIETAN-FP program [37].

For the Ba2Pr(Bi,Sb)O6 system, the polycrystalline samples for *x*<0*:*5 are formed in almost single phases of the monoclinic structure, while the *x*≥0*:*5 samples crystallize in a cubic structure with the space group *Fm*3*m* [24]. Substitution of the smaller Sb<sup>5</sup><sup>þ</sup> (0.60 Å) ion at the Bi5<sup>þ</sup> (0.76 Å) site causes a monotonic decrease in the lattice parameters. For Ba2TbBi0*:*5Sb0*:*5O6, we obtain the lattice parameters *<sup>a</sup>* <sup>¼</sup> <sup>8</sup>*:*4511 Å and *<sup>α</sup>* <sup>¼</sup> <sup>90</sup><sup>∘</sup> . **Figure 8b** shows tolerance factor vs. Sb content (x) for Ba2<sup>þ</sup> <sup>2</sup> Tb<sup>3</sup>þBi<sup>5</sup><sup>þ</sup> <sup>1</sup>�*<sup>x</sup>*Sb<sup>5</sup><sup>þ</sup> *<sup>x</sup>* O6 and Ba2<sup>þ</sup> <sup>2</sup> Tb<sup>4</sup>þM1<sup>4</sup><sup>þ</sup> <sup>1</sup>�*<sup>x</sup>*M24<sup>þ</sup> *<sup>x</sup>* O6 with M1<sup>4</sup>þ= Bi<sup>3</sup><sup>þ</sup> 0*:*5Bi<sup>5</sup><sup>þ</sup> <sup>0</sup>*:*<sup>5</sup> and

### **Figure 8.**

*(a)X-ray diffraction patterns of Ba*2*TbBiO*6*. Inset shows the enlarged diffraction data. The emergence of (101) reflection indicates B-cation ordering which is characteristic of the ordered double-perovskite structure. (b) Tolerance factor vs Sb content for Ba*2*TbBi*<sup>1</sup>�*xSbxO*6*. The solid and dotted lines denote Ba*<sup>2</sup><sup>þ</sup> <sup>2</sup> *Tb*<sup>3</sup>þ*Bi*<sup>5</sup><sup>þ</sup> <sup>1</sup>�*xSb*<sup>5</sup><sup>þ</sup> *<sup>x</sup> O*<sup>6</sup> *and Ba*<sup>2</sup><sup>þ</sup> <sup>2</sup> *Tb*<sup>4</sup>þ*M1*<sup>4</sup><sup>þ</sup> <sup>1</sup>�*xM2*<sup>4</sup><sup>þ</sup> *<sup>x</sup> O*<sup>6</sup> *with M1*<sup>4</sup>þ*= Bi*<sup>3</sup><sup>þ</sup> 0*:*5*Bi*<sup>5</sup><sup>þ</sup> <sup>0</sup>*:*<sup>5</sup> *and M2*<sup>4</sup>þ*=Sb*<sup>3</sup><sup>þ</sup> 0*:*5*Sb*<sup>5</sup><sup>þ</sup> <sup>0</sup>*:*5*. The crystallographic phase diagram consisting of the monoclinic, rhombohedral and cubic phases is given as a function of tolerance factor in ref. [36].*

M24<sup>þ</sup> = Sb3<sup>þ</sup> 0*:*5Sb5<sup>þ</sup> <sup>0</sup>*:*5. The tolerance factor of double perovskite compounds Ba2(Pr,Tb) (Bi,Sb)O6 is given by the following equation,

$$t = \frac{r\_{\rm Ba} + r\_{\rm O}}{\sqrt{2} \left(\frac{r\_{\rm Tb} + r\_{\rm M}}{2} + r\_{\rm O}\right)},\tag{1}$$

where *r*Ba, *r*O, *r*Tb, and *r*M¼ð Þ Bi,Sb are the ionic radii of the respective ions (in details, refer to [24]). The crystallographic phase diagram consisting of the monoclinic, rhombohedral and cubic phases is given as a function of tolerance factor in ref. [36]. The crystal structures obtained for the x = 0 and x = 0.5 samples are almost consistent with the phase diagram reported. Assuming the tetravalent state of Tb4þ, we obtain the value of t = 0.97914, indicating the stability of a cubic structure for the x = 0.5 sample. The microstructures and pelletized precursors for the Ba2TbBiO6 parent sample prepared by the citrate pyrolysis method are shown in **Figure 2b** and **c**. The crystalline grains of the citrate sample have an average size ranging from about 0.2 to 0.5 micron. On the other hand, the grain diameters of the solid-sate sample are distributed on a micron order scale and about one-order grater than those of the former. The citrate pyrolysis process fabricates uniformly dispersed grains with sub micron size compared with the solid-state preparation technique (see [24]).

The magnetic susceptibility data for the Ba2Tb(Bi1�*<sup>x</sup>*,Sb*x*) O6 compounds (*x*=0 and 0.5) were measured as a function of temperature under a magnetic field of 0.1 T. (not shown here) The effective magnetic moments (*μ*eff) are estimated from the magnetization data using the Curie–Weiss law. For the parent and x = 0.5 citrate samples, we obtain *μ*eff= 8.91 *μ*<sup>B</sup> and 8.86 *μ*B, as listed in **Table 2**. Moreover, we try to evaluate the ratio of the Tb3<sup>þ</sup> and Tb4<sup>þ</sup> ions using the equation,

$$
\mu\_{\rm eff}^2 = \mathcal{y}\mu\_{\rm eff}^2 \left(\text{Tb}^{3+}\right) + (\mathbf{1} - \mathbf{y})\mu\_{\rm eff}^2 \left(\text{Tb}^{4+}\right) \tag{2}
$$

where *μ*eff (Tb3þ) = 9.72 *μ<sup>B</sup>* and *μ*eff (Tb4þ) = 7.94 *μB*. For the parent and x = 0.5 citrate samples, we obtain that the ratio of Tb3<sup>þ</sup> and Tb4<sup>þ</sup> ions is 0.52 : 0.48 and 0.49 : 0.51, respectively. The mixed valence state expected from the magnetic data qualitatively consists with the above discussion on the stability of cubic structure for the x = 0.5 sample. The magnetic data suggest that about half of Re ions (Re = Pr and Tb)


*The effective magnetic moments μ*eff *were estimated from the magnetization data using the Curie–Weiss law. IPA, MB and Opt. denote gaseous 2-propanol decomposition, methylene blue degradation, and optical measurements, respectively.*

*a Ref. [24]. b Ref. [38].*

**Table 2.** *Sample details of Ba*2*(Pr,Tb)(Bi,Sb)O*<sup>6</sup> *used in the experiments.* are oxidized to the tetravalent state over the whole range of Sb substitution [24]. In a previous analysis of X-ray photoemission spectroscopy [39], it has been shown that a predominant peak of Pr3<sup>þ</sup> coexists with a smaller shoulder structure of Pr4þ, giving further evidence for the mixed valence state of the Pr ion.
