# Exploring Structural Changes in Ge-Te Amorphous Films Through Small-Angle Neutron Scattering
## 4 Discussion
### Low-\(Q\) Region: Porod's Region  
In Porod's region [31], the scattering pattern is dominated by the interfaces between different phases or components within a sample, such as particles or pores in a material. The power law in Equation (1) describes the decay of the scattering intensity, which is related to the size and shape of the scattering entities. This region provides vital information about the surface and structural characteristics of the scattering objects. In this region, the main parameter is the exponent \(\beta\), which is critical for interpreting the structural properties of the sample. 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. A value of 3 suggests a situation where the scattering arises from more complex geometries, such as rod-like or cylindrical structures. In contrast, a value of 2 often corresponds to scattering from mass fractals, where the scatterers are distributed in space but not necessarily in a uniform way. The values in Table 1 already indicated two distinct groups of samples, and Figure 3 now clearly highlights this. Thus, in line with the discussion in the Introduction, the composition range is divided into three compositional zones: the first up to \(\approx\)22 at.% Ge (shaded in red), a second transitional region between \(\approx\)22 at.% and \(\approx\)30 at.% (white in the plot), and a third above \(\approx\)30 at.% (shaded in blue). The Ge\({}_{0.28}\)Te\({}_{0.72}\) sample is in the second zone, a transition regime where the fitted parameters may present strong variations. For this sample, the exponent \(\beta\) is in line with the exponents observed for the Ge-rich samples. The analysis of the scattering exponent as a function of increasing Ge content reveals a decrease from 3.25 to 2.75, corresponding to a 15% reduction. This behaviour suggests that the Ge\({}_{x}\)Te\({}_{1-x}\) system exhibits characteristics of both fractal-like structures and complex geometries. Specifically, this range of exponents indicates that the scattering is influenced by structures combining multiple dimensionalities. An exponent approaching 3 reflects a system with a significant surface area, potentially associated with elongated or rod-like \begin{table}
\begin{tabular}{c c c c c c} \hline \(\mathbf{x=0.17}\) & **FSDP** & **PP** & \(\mathbf{x=0.21}\) & **FSDP** & **PP** \\ \hline \(A\) & 0.0576 (28) & 0.2652 (19) & \(A\) & 0.0663 (19) & 0.2627 (19) \\ \hline \(Q\) & 1.0907 (66) & 2.0126 (13) & \(Q\) & 1.1040 (39) & 2.0070 (14) \\ \hline \(\sigma\) & 0.310 (11) & 0.2464 (16) & \(\sigma\) & 0.2555 (57) & 0.2447 (18) \\ \hline \(D\) & 8.62 (30) & 10.83 (7) & \(D\) & 10.44 (23) & 10.90 (8) \\ \hline \(\mathbf{x=0.28}\) & **FSDP** & **PP** & & & \\ \hline \(A\) & 0.0839 (83) & 0.2150 (71) & & & \\ \hline \(Q\) & 0.986 (13) & 2.0156 (54) & & & \\ \hline \(\sigma\) & 0.274 (19) & 0.2685 (74) & & & \\ \hline \(D\) & 9.74 (66) & 9.94 (27) & & & \\ \hline \(\mathbf{x=0.30}\) & **FSDP** & **PP** & \(\mathbf{x=0.45}\) & **FSDP** & **PP** \\ \hline \(A\) & 0.0759 (23) & 0.2805 (30) & \(A\) & 0.0308 (16) & 0.2365 (36) \\ \hline \(Q\) & 1.0188 (33) & 2.0174 (20) & \(Q\) & 0.9340 (44) & 2.0354 (29) \\ \hline \(\sigma\) & 0.2294 (48) & 0.2734 (27) & \(\sigma\) & 0.1269 (57) & 0.2349 (35) \\ \hline \(D\) & 11.53 (24) & 9.76 (10) & \(D\) & 21.03 (94) & 11.36 (17) \\ \hline \end{tabular}
\end{table} 
Table 2: Fitted parameters for the Ge\({}_{x}\)Te\({}_{1-x}\) samples in the high-\(Q\) region, i.e., the Gaussian parameters in Equation (1). The areas \(A\) are in arbitrary units, while peak positions \(Q\) and widths \(\sigma\) are in Å\({}^{-1}\). Correlation distances \(D\) (see text for details) are in Å. The numbers in parentheses represent the uncertainties affecting the last two significant digits of the tabulated values. features, whereas values closer to 2 indicate a degree of fractality.