## 3 Results and Discussion  
Figure 1 shows the respective XRD spectra of the TiO\({}_{2}\) powders synthesized by the FFCVC method with two acetylene flow rates of 600 and 800 sccm. Figure 1a shows the X-ray diffraction spectra corresponding to an acetylene flow rate of 600 sccm. The main diffraction peak appears at 20 = 25.3\({}^{\circ}\), attributed to anatase (101), and there is a tiny rutile peak at 27.5\({}^{\circ}\) corresponding to rutile (110), found only in the sample at C\({}_{2}\)H\({}_{2}\) 600 sccm, C\({}_{2}\)H\({}_{2}\)/O\({}_{2}\) = 1:3. In Figure 1b, for an acetylene flow rate of 800 sccm, a diffraction peak appearing at 20 = 25.3\({}^{\circ}\) was observed for the samples at C\({}_{2}\)H\({}_{2}\)/O\({}_{2}\) = 1:4, 1:5, and 1:6, and the rutile peak did not appear for C\({}_{2}\)H\({}_{2}\) 800 sccm, C\({}_{2}\)H\({}_{2}\)/O\({}_{2}\) = 1:3. Besides this, the higher the flow rate of oxygen, the stronger the intensity of the rutile peak at 27.5\({}^{\circ}\). The main rutile peaks appearing in spectra for samples from C\({}_{2}\)H\({}_{2}\) 800 sccm, C\({}_{2}\)H\({}_{2}\)/O\({}_{2}\) = 1:4 through C\({}_{2}\)H\({}_{2}\) 800 sccm, C\({}_{2}\)H\({}_{2}\)/O\({}_{2}\) = 1:6 have the same characteristics in terms of narrow rutile peak shape at 27.5\({}^{\circ}\). When comparing Figure 1a,b, the acetylene/oxygen flow ratios are the same. For acetylene flow of 800 sccm, the intensity of the rutile diffraction peak gets stronger as the flow rate of oxygen increases (Figure 1b). However, this trend is reversed for 600 sccm (Figure 1a). Figure 1a has almost the opposite tendency to Figure 1b in terms of rutile formation with acetylene/oxygen flow rate and, accordingly, with the oxygen flow rate. Table 1 shows the grain sizes of anatase and rutile for all the samples prepared under different processing conditions. [PERSON]'s equation (d = 0.9\(\uplambda\)/\(\beta\)cos \(\theta\)) was used to calculate the grain size d by measuring the peak broadening \(\beta\) of the FWHM of the peak. The particle size of rutile is much larger than that of anatase, especially for the set of samples with an acetylene flow rate of 800 sccm. For the set of samples with an acetylene flow rate of 600 sccm, the grain size of rutile is small and is comparable with that of anatase, although it may have a slightly larger value. This suggests that the rutile growth is largely limited. The sub-Lorentzian-like shape of the rutile peak suggests that the population of rutile grains with size less than the average rutile grain size is low. Since the average rutile particle size is still slightly larger than that of anatase, rutile should form through transformation from anatase aggregates composed of only a few anatase grains. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**600 sccm**} & \multicolumn{3}{c}{**800 sccm**} \\ \cline{2-9}  & \multicolumn{2}{c}{Anatase} & \multicolumn{2}{c}{Ratile} & \multicolumn{2}{c}{Anatase} & \multicolumn{2}{c}{Ratile} \\ \cline{2-9}  & \(\beta\) & d (nm) & \(\beta\) & d (nm) & \(\beta\) & d (nm) & \(\beta\) & d (nm) \\ \hline
1:3 & 1.3 & 6.5 & 0.63 & 13.5 & 1.9 & 4.5 & - & - \\
1:4 & 2.1 & 4.1 & - & - & 2.2 & 3.9 & 0.3 & 28.5 \\
1:5 & 2.5 & 3.4 & - & - & 1.9 & 4.5 & 0.3 & 28.5 \\
1:6 & 2.6 & 3.3 & - & - & 1.9 & 4.5 & 0.4 & 21.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The grain sizes of anatase and rutile under various processing conditions. Figure 1: XRD spectra of TiO\({}_{2}\) powders produced by a flat-flame chemical vapor condensation (FFCVC) method using various acetylene/oxygen flow ratios (C\({}_{2}\)H\({}_{2}\)/O\({}_{2}\)). The acetylene flow rates (C\({}_{2}\)H\({}_{2}\)) are (**a**) C\({}_{2}\)H\({}_{2}\) 600 sccm and (**b**) C\({}_{2}\)H\({}_{2}\) 800 sccm. Figure 2 shows the TEM micrograph and diffraction patterns of a sample with C\({}_{2}\)H\({}_{2}\) 800 sccm, C\({}_{2}\)H\({}_{2}\)/O\({}_{2}\) = 1:5. The ring pattern is diffuse and is from the anatase phase, suggesting that the anatase particle size is small.