## 3 Results and Discussion
### Rutile Formation Mechanisms  
As reported, the formation of rutile has two kinds of mechanisms. One is that rutile can even form readily after its nucleation in an oxygen-deficient environment [24]. This mechanism is related to the packing of the octahedral structure of the TiO\({}_{6}\) unit [25]. It is known that more octahedra connect to each other by corner-sharing in rutile than in anatase, while more octahedra connect by edge-sharing in anatase than in rutile, where edge- and corner-sharing are illustrated in Figure 3. If one oxygen atom is missing in two edge-shared octahedra, the shared edge may be unlocked and form a corner-shared structure (Figure 3b). The corner-shared octahedra allow a greater degree of freedom in the tilt and rotation of octahedron concerning each other, thus providing a better chance of packing themselves from a more loosely packed anatase structure to a more densely packed, yet stable, rutile structure. The alignment of octahedra by corner-sharing is promoted in an oxygen-deficient environment; hence, rutile nucleation is enhanced in an oxygen-deficient environment. Thus, the formation of rutile by nucleation is developed in an oxygen-deficient climate, and the rutile grain size can be tiny in an oxygen-deficient environment. Another mechanism for rutile formation is through the aggregation of anatase grains to form a specific critical size (\(>\)15 nm) for triggering phase transformation from anatase to rutile at high temperatures (usually greater than 600 \({}^{\circ}\)C). Under this condition, the grain size of rutile is larger than 15 nm [26; 27; 28; 29], bigger than the grain size of rutile formed via the previous mechanism. According to [PERSON]'s equation (d = 0.93/\(\beta\)cos \(\theta\)) [30], it is known that the crystallite size can be determined from the full width at half-maximum (FWHM) of XRD peaks. The diffraction peaks become broader; the grain size of the particle becomes smaller. In Figure 1b, it can be seen clearly that the rutile peak at 27.5\({}^{\circ}\) is sharp and narrow compared with the anatase peak at 25.3\({}^{\circ}\), indicating  
Figure 2: A typical TEM micrograph and corresponding diffraction pattern of a sample with C\({}_{2}\)H\({}_{2}\) 800 sccm, C\({}_{2}\)H\({}_{2}\)/O\({}_{2}\) = 1:5. (a) Micrograph; (b)diffraction pattern. that the rutile grains are much larger than the anatase grains. As a result, it can be concluded that the rutile phase in the mixed powder is formed through the latter mechanism for an acetylene flow rate of 800 sccm. On the contrary, if the rutile were to form through nucleation in an oxygen-deficient environment, the rutile grains would be small, comparable with the grain size of anatase. As discussed earlier, the formation of rutile is related to the acetylene flow rate of 800 sccm; in this experiment, acetylene acts as the fuel for the combustion. When more acetylene flows into the chamber, more heat is created to induce the combustion reaction to form TiO\({}_{2}\) nanoparticles with mixed-phase anatase and rutile. Thus, the rutile formation was more pronounced in the samples with an acetylene flow rate of 800 sccm than in those with 600 sccm. The increasing trend of rutile formation with oxygen flow rate for the set of samples with an acetylene flow rate of 800 sccm should not be due to increased temperature of the flame because the stoichiometric ratio of oxygen to acetylene for the full combustion of acetylene is 2.5, and excess oxygen flow higher than this stoichiometric ratio reduces the flame temperature. Thus, the enhancement of rutile with the oxygen flow rate should be attributed to the increased aggregation or growth of anatase grains due to the increased oxygen partial pressure. There were different trends of rutile formation with acetylene flow rates of 600 sccm and 800 sccm.