## 3 Results and Discussion
\[\frac{\mathrm{P_{inc}}}{\mathrm{P_{bound}}}=\frac{\mathrm{Mn_{inc}}}{\mathrm{ Mn_{bound}}}=\frac{\mathrm{Al_{inc}}}{\mathrm{Al_{bound}}}=\frac{\mathrm{Cu_{inc}}}{ \mathrm{Cu_{bound}}} \tag{1}\]  
\[\mathrm{P_{bound}}=\mathrm{P_{tot}} \tag{2}\]  
\[\mathrm{Mn_{bound}}=\frac{\mathrm{Mn_{inc}}\cdot\mathrm{P_{tot}}}{\mathrm{P_{ part}}} \tag{3}\]  
\[\mathrm{Al_{bound}}=\frac{\mathrm{Al_{inc}}\cdot\mathrm{P_{tot}}}{\mathrm{P_{ inc}}} \tag{4}\]  
\[\mathrm{Cu_{bound}}=\frac{\mathrm{Cu_{inc}}\cdot\mathrm{P_{tot}}}{\mathrm{P_{ inc}}} \tag{5}\]  
Based on the EDX measurements of the overall sample compositions and the estimated average compositions of the inclusions, given in Figure 10, applying the approach laid out above, an estimate of the concentrations of Al, Mn, and Cu bound inside the inclusions was made as well as the difference with respect to the measurements in which the presence of phosphorus was simply neglected. The resulting estimates can be found in Table 4. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multirow{2}{*}{**Average Percentage Bound to P**} & \multicolumn{4}{c}{**Average Al, Mn, Cu in Solid**} & \multicolumn{4}{c}{**Average Composition Change**} \\  & & & & **Solution** & & & **Al** & **Mn** & **Cu** \\ \hline
1 & 0.011 & 0.4 & 0.04 & 18.0 & 8.4 & 74 & 0.1 & \(-\)0.4 & 1 \\
2 & 0.031 & 0.59 & 0.165 & 16.735 & 8.39 & 74.88 & 0.135 & \(-\)0.51 & 0.38 \\
3 & 0.0050 & 0.184 & 0.022 & 17.8505 & 9.345 & 72.804 & 0.0505 & \(-\)0.155 & 0.104 \\
4 & 0.021 & 0.41 & 0.09 & 17.487 & 10.84 & 73.16 & 0.087 & 1.14 & 0.26 \\
5 & 0.18 & 0.4 & 1.4 & 16.6 & 10.8 & 72.6 & 0.2 & \(-\)0.2 & 0.0 \\
6 & 0.01250 & 0.221 & 0.079 & 16.757 & 11.025 & 72.220 & 0.057 & \(-\)0.175 & 0.120 \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multirow{2}{*}{**St. dev. of Percentage Bound to P**} & \multicolumn{4}{c}{**St. dev. of Al, Mn, Cu in Solid**} & \multicolumn{4}{c}{**St. dev. of the Composition Change**} \\  & & & & **Solution** & & & **Al** & **Mn** & **Cu** \\ \hline
1 & 0.006 & 0.1 & 0.03 & 0.5 & 0.4 & 1 & 0.9 & 0.7 & 2 \\
2 & 0.001 & 0.01 & 0.008 & 0.004 & 0.01 & 0.02 & 0.004 & 0.01 & 0.02 \\
3 & 0.0003 & 0.002 & 0.001 & 0.0008 & 0.002 & 0.003 & 0.0008 & 0.002 & 0.003 \\
4 & 0.002 & 0.01 & 0.01 & 0.006 & 0.01 & 0.02 & 0.006 & 0.01 & 0.02 \\
5 & 0.04 & 0.1 & 0.3 & 0.1 & 0.1 & 0.6 & 0.1 & 0.1 & 0.6 \\
6 & 0.0005 & 0.004 & 0.003 & 0.002 & 0.005 & 0.009 & 0.002 & 0.005 & 0.009 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Estimates of aluminum, manganese, and copper bound inside the inclusions, as well as in solid solution, and the difference in composition with respect to measurements that do not consider phosphorus. Looking specifically at the difference in aluminum and manganese concentrations between the two cases, which vary from 0.05 to 0.2% at., and from 0.155 up to as much as 1.14% at., respectively, indicates that the presence of phosphorus inside the Cu-Al-Mn SMA sheets, even in such low quantities as 0.1% at., might have a significant impact on their phase transformation temperatures and/or transformation capacity due to the alloy's high sensitivity to small compositional variations.