## 2 Materials and Methods
### Methods
Therefore, it is essential to evaluate the impact of color quenching on the LSC measurements. This effect varies significantly depending on the acid used to dissolve the samples and has direct consequences on both detection efficiency and acquisition time--two critical parameters, particularly when analyzing numerous low-activity samples. The chemical interaction of various acids with Fe and Ni--at concentrations representative of their presence in AISI 316L steel (Fe = 69.06% \(w\)/\(w\), Ni = 9.25% \(w\)/\(w\))--has been evaluated in previous studies [15]. These investigations demonstrated that phosphoric acid (H\({}_{3}\)PO\({}_{4}\)) and phosphorous acid (H\({}_{3}\)PO\({}_{3}\)) were the most effective choices for minimizing color quenching effects associated with both Fe and Ni. The use of these acids enables the attainment of the required Minimum Detectable Concentration (MDC) of 0.3 Bq/g within a reasonable measurement time, thereby making the analytical process more efficient and reliable. LSC samples were prepared in triplicate for each radionuclide using aliquots of 0.5 mL, 1.0 mL, and 2.0 mL of the final solution. Each was brought to a volume of 4 mL with deionized water and mixed with 16 mL of Ultima Gold AB (Figures 4 and 5). \begin{table}
\begin{tabular}{c c} \hline
**Sample** & **Weight (g)** \\ \hline
1 & 0.5070 \(\pm\) 0.0200 \\
2 & 0.5006 \(\pm\) 0.0300 \\
3 & 0.5070 \(\pm\) 0.0180 \\ \hline \end{tabular}
\end{table} 
Table 2: Sample weights for optimization study. Figure 4: LSC vials showing Fe fractions at increasing concentrations. Figure 3: Workflow of the optimization process. For each radionuclide, the overall efficiency was calculated as:  
\[\epsilon=\frac{\text{R}-\text{R}_{\text{b}}}{\text{A}}\]  
where  
* R: sum of double coincidences (light photons detected in coincidence by two photomultipliers) per unit of time in the appropriate range of spectrum channels for the traced sample. * R\({}_{\text{b}}\): sum of double coincidences per unit of time in the appropriate range of spectrum channels for the blank sample. * A: known activity in the vial (Bq). Since activity A is added before performing the chemical procedure, the overall efficiency considers both the chemical yield of the process and the LSC efficiency. Once the efficiency had been calculated, to determine the acquisition time (t) required to reach a target MDC, the following equation was used [16]:  
\[\text{MDC}\left[\frac{Bq}{g}\right]=\ \frac{2.71+4.65\text{-}\sqrt{\text{R}_{ \text{b}}\cdot\text{t}}}{\epsilon\text{-}\text{m}\cdot\text{t}}\]  
where m is the mass of steel in the vial (g) and t is the acquisition time (s). The optimum sample concentration corresponding to the minimum acquisition time was evaluated and chosen for \({}^{55}\)Fe and \({}^{63}\)Ni quantifications (Tables 3 and 4). To achieve the required MDC (0.3 Bq/g), a sample mass of 0.125 g of steel (corresponding to the 1 mL aliquot, vial #2) is the best compromise for \({}^{55}\)Fe quantification. In this case, an acquisition time of about 5 days is needed. The optimal result for \({}^{63}\)Ni is obtained with 0.25 g of steel (corresponding to the 2 mL aliquot, vial #3), requiring only about 6 h of measurement. The trends shown in Tables 3 and 4 reveal the different relationships between sample mass, detection efficiency, and acquisition time for \({}^{55}\)Fe and \({}^{63}\)Ni. For \({}^{55}\)Fe, increasing the sample mass leads to lower efficiency and significantly longer acquisition times. In contrast, for \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Vial** & **Sample Mass (g)** & \(\epsilon\) **(\%)** & **Acq. Time to Reach MDC (Days)** \\ \hline \#1 & 0.063 \(\pm\) 0.002 & 28.3 \(\pm\) 2.0 & 12 \\ \#2 & 0.125 \(\pm\) 0.002 & 21.2 \(\pm\) 1.0 & 5 \\ \#3 & 0.250 \(\pm\) 0.004 & 2.0 \(\pm\) 0.1 & 157 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Efficiency and MDC evaluation for \({}^{63}\)Ni. Figure 5: LSC vials showing Ni fractions at increasing concentrations.