## 3 Results and Discussion
This is were it shows an alteration around 30 s after the start of the deposition. It starts with a broadening of the Yoneda wing in \(q_{z}\), leads to a second line at the density of polycrystalline BaTiO\({}_{3}\), and ends with a disappearing line at the density of the amorphous clusters. These density findings accord with the literature values for BaTiO\({}_{3}\)[14; 15]. Figure 2: Exemplary region of the GISAXS detector of the two dimensional GISAXS patterns taken at the surface diffraction beam line P03 at PETRA III (**a**). The bottom line starts at the sample horizon and denoted are the beamstop, the Yoneda level, the inter-modular detector gaps (IDG, black stripe). The intensity evolution of the horizontal cuts at the level of the Yoneda peak (**b**). And the Pseudo-Voigt fits of the Yoneda-cuts during the deposition at 600 \({}^{\circ}\)C (**c**). The data points displaying the background subtracted data and the lines the corresponding fit. During this experiment, we collected the wide angle scattering (WAX) with a second detector simultaneously. An exemplary pattern taken after 500 s of deposition is shown in Figure 4, it shows a detector tilt and rotation corrected pattern which was azimuthal resorted using the Python package pyFAI [16]. The software was calibrated by performing a measuring with a NIST standard. Figure 4: Exemplary two-dimensional GIXRPD false color plot showing a tilt, rotation and azimuthal resorted single patterns of GIXRPD of BaTiO\({}_{3}\) after 1000 s of deposition at 600 \({}^{\circ}\)C. White markers show diffraction lines for bulk cubic BaTiO\({}_{3}\)[17]. The offset is an effect of temperature and finite-size effects. The powder diffraction rings show a clear indication for preferred orientation and also double peak structures and peak broadening where the lattice parameter a = b \(\
eq\) c, are indicating tetragonal BaTiO\({}_{3}\) structure. The high-intensity small peaks are background coming from the AlO\({}_{2}\) sample holder and the black part on the bottom is the sample surface. Also shown in the top right corner is the original shape of the 2D detector. Figure 3: (**a**) is showing the intensity evolution of at the Yoneda level and (**b**) the results from the Pseudo-Voigt Fits, given the peak width sigma (S) and the center position (C) as well as the cluster size (CS) for the first 90 s. (**c**) shows the \(q_{z}\)-cuts at the \(q=0\) position. (**d**) shows the cluster grow model for the for the first 60 s. Showing 3 nm sized hemispherical shaped particles arranged in a 2D hexagonal lattice. The peak positions for cubic BaTiO3 are marked and show a good agreement. Small offsets at the higher angle peaks are shown and can be explained as finite-size effect and temperature introduced stress on the wafer and the thin film. The peak broadening of the [200]-peak and the double peak structure at the [211]-peak can be explained with the occurrence of tetragonal BaTiO3. The preferred orientation arises from particles being oriented on the surface and enhancing the intensities of more defined Bragg reflections, while reducing the intensities of others. [18] The preferred orientation is diminishing with increasing film thickness as shown in Figure 5. This can be explained with the fast increasing film thickness, a layer-plus-island growth and the therefore decreasing influence of the surface and relaxation process due to misfit dislocations [5; 6], but still can be seen until the end of deposition. Figure 6 shows the peak evolution by plotting the azimuthal resorted patterns versus time during the deposition at 600 \({}^{\circ}\)C and selected GIXRPD pattern after 100, 500 and 1000 s. Figure 7 shows exemplary pseudo-Voigt fits of the peaks. The increasing amplitude corresponds to the quantity of diffraction sources, i.e., crystallites, and the peak width correspond to the nano-crystalline size. The azimuthal integrated patterns versus time can be fitted with a pseudo-Voigt function to extract the peak width and amplitude.