# Exploring Structural Changes in Ge-Te Amorphous Films Through Small-Angle Neutron Scattering
## 3 Results  
Figure 1 shows the SANS diffractograms recorded at room temperature for all Ge\({}_{x}\)Te\({}_{1-x}\) samples. All the curves display similar behaviour, showing a linear regime (in the log-log plot) in the low-\(Q\) region (below 0.1 A\({}^{-1}\)) and exhibiting two diffraction peaks in the high-\(Q\) region (above 0.3 A\({}^{-1}\)): at about 1 A\({}^{-1}\) for the FSDP and at about 2 A\({}^{-1}\) for the Principal Peak (PP). Despite these similarities, some differences are evident at a glance. The two samples with lower germanium content display nearly the same behaviour in the low-\(Q\) region, while the others exhibit much higher intensity and different slopes.  
To quantitatively analyse the diffractograms shown in Figure 1, fitting is performed in the range 0.03 to 2.3 A\({}^{-1}\) using the following fitting function:  
\[f(Q)=\gamma+\alpha\;Q^{-\beta}+\sum_{\text{label}=\text{FSDP, PP}}\frac{A_{\text{label}}}{\sqrt{2\pi}\;\sigma_{\text{label}}}\exp \left(-\frac{(Q-Q_{\text{label}})^{2}}{2\sigma_{\text{label}}^{2}}\right), \tag{1}\]  
where \(\gamma\) is the background. This function has two main contributions: a power-law function to describe the low-\(Q\) region (below 0.1 A\({}^{-1}\)), also known as [PERSON]'s region, and a couple of Gaussian peaks describing the high-\(Q\) (or diffraction) region. The \(\alpha\) parameter takes into account the intensity of the SANS signal (proportional to the neutron counts per detection channel), and \(\beta\) is the exponent of the power function. For the Gaussian peaks, the parameters are the usual ones: \(A_{\text{label}}\), \(Q_{\text{label}}\), and \(\sigma_{\text{label}}\) (label: FSDP or PP) are the area, the centre, and the standard deviation, respectively. Figure 2 shows the fit corresponding to the Ge\({}_{0.17}\)Te\({}_{0.83}\) sample, representing the typical fit for all samples. The resulting parameters from this fitting process are shown  
The strong variation in the \(\alpha\) and \(\beta\) parameters shown in Table 1 allows for a clear separation of the five samples into two distinct groups: up to 22 at.% and above 30 at.% Ge, with the sample with 28 at.% Ge being in a transition zone. The most relevant parameter in [PERSON]'s region is the exponent \(\beta\), which is shown in Figure 3.  
When the exponent is 4, this power law is known as Porod's law [33] and typically describes a surface-dominated scattering from a well-defined structure, such as a large aggregate or particle with smooth interfaces.  
Figure 3: The power-law exponent \(\beta\), as obtained from the fit of the low-\(Q\) region, is plotted as a function of Ge content \(x\). The dashed line is a smoothed spline that only serves as a guide for the eye. The red-, white-, and blue-shaded areas correspond to the different zones observed as a function of the Ge content. Labels and arrows indicate the expected values of \(\beta\) for typical structures or behaviours.  
Figure 2: The fit of the model given by Equation (1) to the Ge\({}_{0.17}\)Te\({}_{0.83}\) sample data. The fitted parameters and their optimised values are shown in Tables 1 and 2.