bandwidth and peak intensity in comparison with experimental values. Line identification and Phase identification From the Bragg law presented in Eq. (2.1), the d-spacing for a peak is calculated using its respective angular position. As shown in Appendix 1, the four peaks located at angle positions and 104.26° correspond to (001), (002), 2θ=22.82°, 46.53°, 72.61° (003) and (004) STO peaks. The first thin film peak at is undoubtedly assigned 2θ=36.7ᵒ to anatase (004). The unknown peak displayed in Fig. 12 at in samples 2θ=79.76ᵒ PTS0318 and PSS0218, although it might be confused with rutile (212), is assigned to anatase (008). The reason is, as shown in Fig. 12, from the adjustment of model to anatase (004), a high order Bragg peak appears in the same position as the unknown 2θ peak. Hence, it is anatase (008). This example highlights the capabilities of the model: whereas with the traditional line identification the unknown peak could have been assigned to rutile (212), with the utilization of present model, once anatase (004) has been modelled, a higher Bragg order appears and matches the peak at 79.76ᵒ. Fig. 12 shows only anatase (004) and (008). According to the simulation, the reason why the other anatase peaks are missing is that peaks such as (002) and (003) are very weak, and hence covered up by noise; anatase (001) is of medium intensity, however it locates at which is out of the experimental range. With the around 2θ=4.64° absence of any peaks of other allotropes such as rutile, the TiO2 in the three samples shows only anatase phase. The presence of anatase (004) and (008) confirms the assumption made when the model was built: due to the particular STO and anatase lattice parameters, the TiO2 film grows with a preferential orientation that minimizes the lattice mismatch with the
bandwidth and peak intensity in comparison with experimental values. Line identification and Phase identification From the Bragg law presented in Eq. (2.1), the d-spacing for a peak is calculated using its respective angular position. As shown in Appendix 1, the four peaks located at angle positions 2θ=22.82°, 46.53°, 72.61° and 104.26° correspond to (001), (002), (003) and (004) STO peaks. The first thin film peak at 2θ=36.7ᵒ is undoubtedly assigned to anatase (004). The unknown peak displayed in Fig. 12 at 2θ=79.76ᵒ in samples PTS0318 and PSS0218, although it might be confused with rutile (212), is assigned to anatase (008). The reason is, as shown in Fig. 12, from the adjustment of model to anatase (004), a high order Bragg peak appears in the same 2θ position as the unknown peak. Hence, it is anatase (008). This example highlights the capabilities of the model: whereas with the traditional line identification the unknown peak could have been assigned to rutile (212), with the utilization of present model, once anatase (004) has been modelled, a higher Bragg order appears and matches the peak at 79.76ᵒ. Fig. 12 shows only anatase (004) and (008). According to the simulation, the reason why the other anatase peaks are missing is that peaks such as (002) and (003) are very weak, and hence covered up by noise; anatase (001) is of medium intensity, however it locates at around 2θ=4.64° which is out of the experimental range. With the absence of any peaks of other allotropes such as rutile, the TiO2 in the three samples shows only anatase phase. The presence of anatase (004) and (008) confirms the assumption made when the model was built: due to the particular STO and anatase lattice parameters, the TiO2 film grows with a preferential orientation that minimizes the lattice mismatch with the
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