## 3 Results and Discussions  
### Structural Analysis  
XRD patterns of single TiO\({}_{2}\) as well as Ba/TiO\({}_{2}\) nanomaterials are displayed in Figure 1. The diffraction peaks of TiO\({}_{2}\) and Ba/TiO\({}_{2}\) nanomaterials at 20 values were 25.09\({}^{\circ}\), 37.65\({}^{\circ}\), 47.89\({}^{\circ}\), 53.89\({}^{\circ}\), 55.07\({}^{\circ}\), 62.40\({}^{\circ}\), 70.04\({}^{\circ}\) and 75.00\({}^{\circ}\), matching well with JCPDS data (21-1272) having (101), (004), (200), (105), (211), (204) crystal planes, respectively [26]. No other characteristic peaks were reflected in the XRD pattern. Hence, both samples exhibited tetragonal structure, and corresponding lattice constant values are shown in Table 1. In the case of Ba/TiO\({}_{2}\) nanomaterials, an increase in intensity was evidenced due to the incorporation of Ba\({}^{2+}\) (1.42 nm) into the TiO\({}_{2}\) host lattice because the ionic radius of Ba\({}^{2+}\) is greater than that of Ti\({}^{4+}\) (0.74 nm), which resulted in an increase in crystallinity. This substitution caused lattice distortion, inflation of the TiO\({}_{2}\) nanocrystal, and internal stress due to Ba doping [40], which reduced nucleation growth (particle size controller) [41]. Another study showed that doping of substrates with Ba caused shrinkage of the crystallite size of modified nanomaterials [42].  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Photacactive** & **FWHM (20)** & **d-Spacing (Å)** & **Crystallite** & **Lattice Constant (Å)** & **Unit Cell** & **Density (\(\rho\))** & **Specific Surface** \\ \cline{3-8}
**Material** & **FWHM (20)** & **d-Spacing (Å)** & **Size(D) (nm)** & **a = b** & **C** & **(Å)\({}^{3}\)** & **(g/cm\({}^{3}\))** & **Area (m\({}^{2}\)/g)** \\ \hline TiO\({}_{2}\) & 0.568 \(\pm\) 0.026 & 3.494 & 25 & 3.778 \(\pm\) 0.005 & 9.480 \(\pm\) 0.012 & 135.31 & 3.9 & 61 \\ \hline Ba/TiO\({}_{2}\) & 0.876 \(\pm\) 0.038 & 3.504 & 16 & 3.781 \(\pm\) 0.002 & 9.470 \(\pm\) 0.004 & 135.38 & 3.9 & 95 \\ \hline \end{tabular}
\end{table}
Table 1: Structural parameters derived from XRD patterns of the synthesized TiO\({}_{2}\) and Ba/TiO\({}_{2}\) photonanode.  
The structural constraints of synthesized TiO\({}_{2}\) and Ba/TiO\({}_{2}\) nanomaterials were calculated using the following formulas [43]:  
\[\frac{1}{d^{2}}=\frac{h^{2}+k^{2}}{a^{2}}+\frac{l^{2}}{c^{2}} \tag{1}\]  
\[t=\frac{0.9\lambda}{\beta\cos\theta} \tag{2}\]  
where \(d\) is the \(d\)-spacing between two consecutive lattices observed from XRD, (_h,k,l_) indicate the miller indices, \(t\) is the crystallite size, \(\beta\) is the full with half maximum, \(a\), \(b\), and \(c\) display as lattice constant for \(a=b\) in tetragonal structure, \(\lambda\) indicates the wavelength of the X-ray radiation used, and \(\theta\) refers to the diffraction angle;  
\[\rho=\frac{nM}{NV} \tag{3}\]  
\[S_{a}=\frac{6}{D.\rho} \tag{4}\]  
where, \(\rho\) is the density of the prepared sample, \(n\) is 4 for anatase phase TiO\({}_{2}\) and 2 for rutile phase TiO\({}_{2}\), \(M\) is the molecular weight of the prepared nanomaterials, \(N\) corresponds to Avogadro's constant value, \(V\) is the volume of the prepared nanomaterials, and \(Sa\) states the specific surface of the prepared sample. Table 1 shows the calculated structural values derived from the XRD patterns of TiO\({}_{2}\) and Ba/TiO\({}_{2}\) nanomaterials. The average crystallite sizes estimated were 25 nm for single TiO\({}_{2}\) and 16 nm for Ba/TiO\({}_{2}\) nanomaterials, respectively. When Ba ions were doped into the TiO\({}_{2}\) lattice, a decrease in nucleation (and subsequent growth rate) was observed for TiO\({}_{2}\) nanomaterials, leading to a reduction in particle size of Ba/TiO\({}_{2}\). The reduction in particle size increases the surface area of TiO\({}_{2}\). The specific surface area of TiO\({}_{2}\) (61 m\({}^{2}\)/g) was smaller than that of Ba/TiO\({}_{2}\) (95 m\({}^{2}\)/g). This favored dye adsorption in the photo electrode, thereby improving photovoltaic performance in the DSSC.