# Phase-Pure Epitaxial b-Axis-Oriented Bronze TiO\({}_{2}\) Films
## 3 Results and Discussion  
### Phase Identification and Epitaxy  
Figure 1 shows wide-angle XRD 20-0 scans of a set of TiO\({}_{2}\) films grown on the three substrates. The film on LAO is phase-pure and exhibits a very intense film peak at 38\({}^{\circ}\). This film's peak can be assigned to the 004 peak of highly crystalline, out-of-plane-oriented anatase, which has been shown to stabilize on LAO substrates in prior work due to the favorable lattice mismatch [16; 17]. On the contrary, the film on MgO is of poor structural quality and shows only a weak peak that can be assigned to the rutile 110 reflection. Thus, this film appears to be epitaxial, with the crystallographic c-axis within the film plane. Previous publications on TiO\({}_{2}\)/MgO films have revealed rutile phases, or rutile/anatase mixtures as well, with the crystallinity strongly dependent on growth conditions [18; 19]. The XRD scan of TiO\({}_{2}\)/MAO shows only one film peak at \(\sim\)48.5\({}^{\circ}\) over the entire scan range from 10 to 90\({}^{\circ}\). We conclude that this film is single-crystalline. It is shown below that the film on MAO is phase-pure and of bronze type. TiO\({}_{2}\) is known for having a plethora of polymorphs in close energetical proximity. Here, we focus on the four main polymorphs that are frequently observed experimentally, i.e., rutile, anatase, brookite and bronze. In order to rule out the stabilization of a more unique TiO\({}_{2}\) phase, we also considered all experimentally observed TiO\({}_{2}\) phases listed in the Crystallography Open Database [20] as well as all theoretically predicted structures listed in the Open Quantum Materials Database [21]. However, none of these phases are in agreement with our XRD data. Figure 2 shows pole figures at the 20 values of prominent reflections for each of the four main polymorphs. It can be seen that no film peaks are observed for the 110 rutile and 111 brookite reflections. These phases are not present in crystalline form. The situation is more complex for the anatase and bronze phases. In both pole figures, film peaks are visible, and it is not immediately clear if the film is phase-pure or if an anatase/bronze mixture is present. Virtually all lattice reflections of the anatase phase are at 20 values that are in the vicinity of lattice reflections of the bronze phase. This fact makes it difficult to discern the two phases solely by the presence of certain film peaks. For example, the peak at 20-48.5\({}^{\circ}\) can be associated with the 020 reflection of the bronze phase that, in bulk bronze-TiO\({}_{2}\), would be located at 20-48.7\({}^{\circ}\). However, the 200 reflection of bulk anatase is located at 20-48.3\({}^{\circ}\). These small differences in the experimentally observed value could  
be easily attributed to stress induced by the lattice, a thermal expansion mismatch to the substrate or slight non-stoichiometry. In order to separate the anatase and bronze phases, their epitaxial relationship to the substrate needs to be considered. Figure 3a shows a scan of the rotational goniometer axis \(\varphi\) at 2\(\theta\) = 25.1\({}^{\circ}\) and the goniometer tilting angle \(\phi\) = 18\({}^{\circ}\). A double peak profile with four-fold symmetry can be seen. The peaks are rotated by \(+/-\) 18\({}^{\circ}\) with respect to the cubic substrate axis. There are two possible scenarios that are in agreement with the XRD data shown in Figures 1, 2 and 3a. They are illustrated in Figure 3b,c. In case one, the film is a b-axis, out-of-plane-oriented bronze film, with the a-axis aligned along the [100] and [010] in-plane axis of the cubic MAO substrates (Figure 3b). This arrangement provides a favorable lattice match along the a-lattice direction, since the lattice parameter of the bronze unite cell a = 12.16 A is only slightly larger (0.2%) than 3/2 of the cubic lattice parameter of MAO\({}_{\text{aMAO}}\) = 8.09 A.