## 3 Results and Discussion
The specific samples and their corresponding compositions, with phosphorus also considered, are given in Table 3.  
The presence of phosphorus at these concentrations would not necessarily be an issue and might have been overlooked in other cases. However, SEM and EDX analyses revealed numerous inclusions within the samples, which were primarily composed of phosphorus and manganese, with some containing more copper and very little aluminum. Figure 9 shows an example of the SEM/EDX analysis, where the inclusions are visible in the electron image (Figure 9a), and the concentrations of manganese and phosphorus are highlighted in the EDX maps (Figure 9c,d). After identifying these inclusions, multiple samples were analyzed to estimate the average composition of the particles, and the results are shown in Figure 10. The main concern is that the high manganese content in these particles means it is not present in the solid solution form of the shape memory alloy, potentially affecting its performance. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Sample Compositions Considering Phosphorus**} \\ \hline
**Sample [\#]** & **Mn [\% at.]** & **Al [\% at.]** & **Cu [\% at.]** & **P [\% at.]** \\ \hline
1 & 8.8 & 17.9 & 73.2 & 0.2 \\
2 & 8.9 & 16.6 & 74.3 & 0.3 \\
3 & 9.5 & 17.8 & 72.6 & 0.1 \\
4 & 9.7 & 17.4 & 72.8 & 0.2 \\
5 & 9.9 & 17.6 & 72.4 & 0.1 \\
6 & 9.9 & 17.2 & 72.6 & 0.2 \\
7 & 10.2 & 17.3 & 72.3 & 0.1 \\
8 & 10.5 & 17.5 & 71.9 & 0.1 \\
9 & 11.0 & 16.4 & 72.4 & 0.1 \\
10 & 11.0 & 15.8 & 73.0 & 0.1 \\
11 & 11.1 & 16.9 & 71.9 & 0.1 \\
12 & 11.2 & 16.7 & 72.0 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average chemical composition of samples in which the presence of phosphorus was detected. Figure 8: Cu-Al-Mn sheet samples used in the study, presented according to their average manganese content and their corresponding thermomechanical history, with each sample’s phase transformation ability highlighted. For the purposes of making the most conservative estimate on the effect that the presence of such inclusions could potentially have on the amount of manganese that is trapped within them rather than being inside the solid solution, a couple of assumptions were made. The  
Figure 10: Average composition of the inclusions observed in the Cu-Al-Mn SMA sheet samples (numbered according to the corresponding sample in Table 3). Figure 9: SEM and EDX analysis performed on sample 4 in the form of maps: (**a**) electron image of the sample, (**b**) EDX map showing Al distribution in the sample, (**c**) EDX map showing P distribution in the sample, (**d**) EDX map showing Mn distribution in the sample. first assumption supposes that the ratio between the atomic percentage of a given element inside the inclusions and the atomic percentage of that same element in the entire sample inclusions is equal across all the elements. This assumption was given as (Equation (1)), where \(\mathrm{P_{inc}}\) and \(\mathrm{P_{bound}}\) stand for the atomic percentage of phosphorus within the inclusion itself and the atomic percentage of phosphorus within the entire samples, which is bound to the inclusion, respectively. The same notation is applied to the remaining elements. The second assumption was that the entirety of the phosphorus measured within the samples was there in the form of the mentioned inclusions. This was based on observations via SEM/EDX, which did not show measurable levels of phosphorus in the areas outside of the mentioned inclusions. This assumption was given as (Equation (2)), where \(\mathrm{P_{tot}}\) refers to the total amount of phosphorus measured in the sample. Combining these two assumptions, it was possible to roughly estimate the atomic percentage of Cu, Al, and Mn bound within the inclusions according to the equations (Equations (3)-(5)) given below.