## 3 Results and Discussion  
This in situ experiment recorded the film evolution continuously in reciprocal space, without interrupting the sputtering process. Exemplary patterns for the GISAXS detector can be seen in Figure 1. To analyze these patterns in more detail, horizontal cuts were taken at the level of the Yoneda peak [12]. The Yoneda peak occurs when the exit angle of the scattered beam is close to the critical angle due to signal enhancement from the Vineyard effect [13]. This results in a bright band of intensity at the critical angle (\(\alpha_{c}\)). Below the critical angle the scattering intensity decreases quadratically to zero. With the refraction index \(n=1-\delta+i\beta\) including the real part \(\delta\) and the imaginary part \(i\beta\), it depends strongly on the wavelength \(\lambda\) and the electron density. Therefore, it is a material dependent effect when the wavelength is constant. These patterns (seen in Figures 1 and 2a) show a clear evolution perpendicular to the Yoneda peak over the deposition time. This relates to density correlations and arise from a the structure factor with characteristic modulations parallel to the surface. The peaks were fitted with a pseudo-Voigt function (see Figure 2) \(pV(x)=\eta G(x)+(1-\eta)L(x)\), with G(x) the sum of a Gaussian peak and \(L(x)\) the Lorentzian peak, as well as the mixing parameter \(\eta\) which describes the fraction of each function. It shows that the particle distance initially appears at higher \(q_{y}\) and shifts towards smaller \(q\) over deposition time. This shift indicates a coalescence, i.e., mainly a fusion phenomenon of adjacent nuclei or clusters, which leads to an increase of the average center-to-center distance. From the fit, we can take the FWHM, amplitude and position. The latter depicts the center-to-center distance, as mentioned before. The amplitude indicates the amount of scattering sources. The peak width is related to the distribution and displays the disorder of cluster and particle arrangement. Therefore, the FWHM is also a strong indicator which indicates a transition from fast increasing ordering to a slower growth of a two-dimensional (2D) cluster arrangement. This means a conversion from a diffusion-mediated coalescence regime to an adsorption-driven cluster growth regime. This expansion persists until one cluster grows radially into another one by the movement of grain boundaries and not by coalescence anymore (shown in Figure 3a-c). This means the surface is covered and the newly arriving particles contribute only in the vertical growth. This describes the early formation (nucleation, diffusion, adsorption and grain growth) for thin films as known from literature [5; 6; 10]. The relation \(D\approx 2\pi/q\) enables us to track the mean cluster distance during the growth as a quantitative parameter. The peak broadening in Figure 3a at around 120 s corresponds to the growing additional scattering source of crystalline BaTiO\({}_{3}\) particles until the crystalline particles with \(\delta=5.8\) g/cm\({}^{2}\) have taken over the whole layer. From the development of the Yoneda peak itself, we were able to get further information about the growth dynamics. Therefore, we have taken cuts in the \(q_{y}\)-direction at the position of the Yoneda peak (see Figure 3c). The temporal evolution of the intensity at the Yoneda peak corresponds to the surface coverage or particle density at the surface, which leads to a change in the scattering distribution. At the beginning of the deposition, a clear Yoneda peak of \(SiO_{2}\) can be seen. At a deposition time of 20 s, the Yoneda peak of amorphous BaTiO\({}_{3}\), with a \(\delta=2.9\) g/cm\({}^{2}\), appears and after a deposition time of 60 s, another Yoneda peak appears. This is a relatively broad peak that shows up at \(\delta=5.8\) g/cm\({}^{2}\) which correspond to polycrystalline BaTiO\({}_{3}\). As mentioned above, the Yoneda peak depends on the material--on the electron density, to be precise, which changes when the crystallization launches.