**4. Discussion**

#### *4.1. On Al2O3(001)*

Our previous report on the growth of NTO [22] showed that films deposited on Si(100) were (00*l*) oriented, with the orientation assumed to be from an inherent preferred growth direction. Annealing of those samples improved the crystallinity, but did not alter the symmetry, as seen by the absence of the (003) and (009) reflections. On Al2O3, the same *R*−3*<sup>c</sup>* symmetry is observed for as deposited films, but annealing induces ordering of the structure, resulting in the *R*−3 symmetry. For NTO, the disordered phase is only thermodynamically stable at temperatures above 1292 ◦C [7,8,25], and has not previously been obtained at room temperature by any other technique. The present case is thus ye<sup>t</sup> another example of the ability of ALD to produce films with metastable phases, given careful selection of substrates and temperature treatment [26].

The mismatch factor, *f*, is usually given as *f* = 100% · (*as* − *af*)/*as*, where *as* and *af* denote the lattice parameters of the substrate and the film, respectively. The relevant way of looking at film-substrate mismatch in this system would be to compare the oxygen lattices at the interface. This gives a mismatch of −3.0%, when comparing the average O–O distances for the (001) surface of Al2O3 and NTO. The negative value of the mismatch indicates that there is a compressive strain from the substrate. Indeed, the as-deposited film has a shorter *a* axis, compared to the literature value. At the same time, the *c* axis is longer, due to the Poisson e ffect. Annealing relaxes the film, both in the basal plane and in the (00*l*) direction, with only 0.1% strain left.

The broadening of the symmetrical NTO (006) reflection along *q* and the asymmetrical NTO (1 0 10) reflection along the Ewald sphere indicates that the film consists of numerous crystallites with somewhat random texture. This could stem from abundant nucleation early in the deposition, and that the numerous crystals grow as narrow pillars throughout the film. The resulting film would have many grain boundaries and a surface with many smaller crystallites, which consequentially results in a low roughness, as indeed observed by AFM.

With an epitaxial relationship between substrate and film, one might expect the same multiplicity of reflections in the ϕ scan. However, as presented above, the NTO film has twice the number of reflections compared to Al2O3. We hypothesize that this comes from atomic steps on the substrate surface revealing trigonal surface terminations rotated at 60◦ from each other (Figure 22), as also seen for growth of CaCO3 on Al2O3(001) [27]. The apparent six-fold rotational symmetry of the NTO film stems from two sets of crystallites, each with three-fold rotational symmetry, superimposed on each other. This feature also increases the likelihood of high nucleation density. The heteroepitaxial film is both out-of- and in-plane oriented, even though the number of reflections in the ϕ scan is di fferent for the film and the substrate, resulting in the film||substrate epitaxial relationship: NTO(001)[100]||Al2O3(001)[100].

**Figure 22.** Oxygen lattices of the (001) plane in Al2O3, viewed along the *c* axis, showing the 60◦ rotation between the top (**a**) and bottom (**b**) faces of octahedrons around Al3+. The four grey diamonds in each cartoon indicate the edges of four unit cells.

#### *4.2. On LaAlO3(100)*

While the epitaxial relationship for NTO||Al2O3 is easy to envision, the same is not true for NTO||LAO. There are no obvious lattice matches between either of the two preferred orientations of the deposited film and the (100) surface of the LAO substrate. In addition, it is hard to untangle the nature of the (*h*0*h*) orientation, as it was impossible to map any related asymmetrical reflections.

With two preferred orientations the film can grow in one of three ways: either (a) the film consists of a layer with (00*l*) orientation close to the substrate and a (*h*0*h*) oriented layer on top, (b) the layers in (a) are inverted, or (c) there is a mix of crystallites with both orientations and no layered structure (Figure 23).

**Figure 23.** Cartoon of possible constellations for the two orientations observed in NTO on LAO.

We are unfortunately unable to conclude which constellation is the most probable, even with basis in the observed variations in texture and surface roughness of the films obtained in this work (see Supplementary Material Section S2 for a more thorough discussion).

The 12 NTO (1 0 10) reflections observed in the ϕ scan can be explained similarly to NTO on Al2O3. That is, the film does not actually have a 12-fold rotational symmetry, but four sets of crystallites—each set in-plane oriented, with a three-fold rotational symmetry. The orientation of the sets of crystallites are shifted by 90◦ with respect to each other, resulting in 12 reflections in the ϕ scan. Both the substrate and a NTO(*h*0*h*) layer could facilitate this. In any case, it is clear that the nucleation density is high, as the di fferent sets of NTO(00*l*) crystallites must have nucleated separately. If the NTO(00*l*) crystallites nucleated on the LAO(100) surface, as in constellation (a) or (c), the epitaxial relationship with the substrate would be: NTO(001)[100]||LAO(100)010, with 010 representing the four identical [010] directions on the LAO(100) surface.

#### *4.3. On SrTiO3(100)*

As with NTO on LAO, there are no obvious lattice matches between the film and the substrate. Still, the deposited film shows an in-plane (*h*0*h*) orientation. The four asymmetrical reflections from the film are perfectly out of phase with the four reflections from the substrate. This means that the direction of the NTO(220) scattering vector, projected down to the substrate surface, is 45◦ off from the same projection of the STO(330) scattering vector. Figure 24 shows the STO(100) and NTO(101) oxygen lattices, with the film lattice rotated according to the projections of the asymmetrical scattering vectors (see Supplementary Material Section S3 for details). The average O–O distance of the film lattice perpendicular to the projection of the NTO(220) direction is close to the oxygen spacing of STO(100). The mismatch along one row of NTO oxygen atoms is only −0.6%. However, when considering the direction along the NTO(220) scattering vector the mismatch between every second layer of oxygen atoms in STO(100) compared to every layer in NTO(101) is 18.4%.

**Figure 24.** Schematic showing the direction of the STO(330) scattering vector projected down on the oxygen lattice of the STO(100) plane, represented by the corners of the blue matrix. Superimposed is the direction of the NTO(220) scattering vector projected down on the substrate plane, and the oxygen lattice of the NTO(101) plane, represented by red circles.

The number of reflections in the ϕ scan can be explained in the same way as for NTO on Al2O3 and LAO. A single crystalline, (*h*0*h*) oriented, NTO film would have only one (*hh*0) reflection in a ϕ scan. The STO(100) surface has four identical (010) directions: (010), (010). (001) and (001), resulting in the four-fold rotational symmetry seen in the ϕ scan. As the NTO film does not nucleate as a continuous layer, the initial islands of (*h*0*h*) oriented crystallites do not differentiate between the STO010 directions. Some of the crystallites will be in-plane oriented with the STO(010) direction, and some with the other directions. An epitaxial relationship between film and substrate can thus be described as: NTO(101)[220]||STO(100)010.

#### *4.4. On MgO(100)*

Unlike the previous cases, AFM of NTO on MgO show clear signs of bigger crystals. This resonates well with the smaller FWHM of the symmetrical NTO(202) reflection, indicating the presence of larger and/or less tilted crystallites. However, again, there are no obvious lattice matches between the MgO(100) surface and NTO, neither in general, nor when comparing the NTO(101) oxygen lattice with the oxygen lattice of the MgO(100) surface. Nevertheless, the film is indeed in-plane orientated with the substrate, but in the same manner as for NTO on STO. The ϕ scan reflections from the substrate and film are overlapping. This means that the direction of the asymmetrical scattering vectors, when projected down on the MgO(100) surface plane, are pointing in the same direction (Figure 25). Regarding a row of NTO oxygen atoms perpendicular to the projection of the MgO(311) scattering direction, there is a seemingly good lattice match for every second layer of oxygen atoms. The calculated mismatch is only 2.4%, but as can be seen from Figure 25, this is only true for selected rows of NTO oxygen atoms. When considering the whole oxygen lattice of NTO it does not correspond very well with the MgO(100) oxygen lattice. Still, the film is in-plane oriented with all the identical MgO011 directions, and the epitaxial relationship is determined to be: NTO(101)[220]||MgO(100)011.

**Figure 25.** Schematic showing the direction of the MgO(311) scattering vector projected down on the oxygen lattice of the MgO(100) plane, represented by the corners of the green matrix, which also corresponds to the unit cell of MgO. Superimposed is the direction of the NTO(220) scattering vector projected down on the substrate plane, and the oxygen lattice of the NTO(202) plane, represented by red circles.
