## 3 Results and Discussion
### Assessment of the Tailings' Heterogeneity at the Micro Scale
Bi and Ge serve as examples of CRMs whose concentrations fluctuate below and above their LOQ values. To better illustrate the data analysis, Y, Ce, Ge, and Bi were selected. Their measured concentration values in the 40 specimens, along with their associated standard deviation, are presented in Table 2. \begin{table}
\begin{tabular}{l c c c c c} \hline  & & & & & \\ \hline \multicolumn{6}{c}{**Description Method: TurboQuant Pellets**} \\ \hline  & & **Aliquot No. 1** & & & **Aliquot No. 22** \\ \hline \multirow{2}{*}{**Z**} & \multirow{2}{*}{**Symbol**} & **Concentration** & *** SD** & **Concentration** & **SD** \\  & & **[**\%wt.]** & **[**\%wt.]** & **[**\%wt.]** & **[**\%wt.]** \\ \hline
29 & CuO & 0.025287 & 0.000150 & 0.026669 & 0.000158 \\
30 & ZnO & 0.125794 & 0.000300 & 0.120923 & 0.000281 \\
31 & **Ga** & 0.001243 & 0.000040 & 0.001316 & 3.63 \(\times 10^{-5}\) \\
32 & **Ge** & 0.000461 & 0.000040 & 0.000172 & 0.000040 \\
33 & As\({}_{2}\)O\({}_{3}\) & 0.000866 & 0.000090 & 0.000789 & 9.10 \(\times 10^{-5}\) \\
34 & Se & 5.06 \(\times\)\(10^{-5}\) & 0.00002 & 0.00005 & 2.05 \(\times 10^{-5}\) \\
35 & Br & 0.001244 & 0.000020 & 0.00134 & 2.03 \(\times 10^{-5}\) \\
37 & Rb\({}_{2}\)O & 0.00869 & 0.00003 & 0.007784 & 3.21 \(\times 10^{-5}\) \\
38 & SrO & 0.016866 & 0.000040 & 0.018128 & 3.56 \(\times 10^{-5}\) \\
39 & Y & 0.002172 & 0.000030 & 0.001990 & 3.20 \(\times 10^{-5}\) \\
40 & ZrO\({}_{2}\) & 0.029554 & 0.000240 & 0.028678 & 0.000240 \\
41 & **Nb\({}_{2}\)O\({}_{5}\)** & 0.001186 & 0.000070 & 0.00122 & 6.65 \(\times 10^{-5}\) \\
42 & Mo & 0.000831 & 0.000060 & 0.00081 & 6.38 \(\times 10^{-5}\) \\
47 & Ag & 0.000535 & 0.000160 & 0.000530 & 0.000152 \\
48 & Cd & 0.000398 & 0.000060 & 0.000410 & 5.50 \(\times 10^{-5}\) \\
50 & **SnO\({}_{2}\)** & 0.002718 & 0.000130 & 0.002817 & 0.000137 \\
51 & Sb\({}_{2}\)O\({}_{5}\) & 0.000882 & 0.000110 & 0.000900 & 0.000118 \\
52 & Te & \textless 0.00030 & - & \textless 0.00030 & - \\
53 & I & \textless 0.00030 & - & \textless 0.00030 & - \\
55 & Cs & 0.000953 & 0.000590 & 0.000950 & 0.000532 \\
56 & Ba & 0.069997 & 0.001000 & 0.062817 & 0.000879 \\
57 & **La** & \textless 0.00020 & - & \textless 0.00020 & - \\
58 & **Ce** & 0.003449 & 0.000760 & 0.003740 & 0.000840 \\
72 & **Hf** & 0.00055 & 0.00007 & 0.000531 & 6.85 \(\times 10^{-5}\) \\
73 & **Ta\({}_{2}\)O\({}_{5}\)** & \textless 0.00063 & - & \textless 0.00063 & - \\
74 & **WO\({}_{3}\)** & 0.001896 & 0.000140 & 0.001834 & 0.000129 \\
79 & Au & 0.000131 & 0.000060 & - & - \\
80 & **Hg** & \textless 0.00010 & - & \textless 0.00010 & - \\
81 & Tl & 0.000117 & 0.000020 & 0.00012 & 2.16 \(\times 10^{-5}\) \\
82 & PbO & 0.021109 & 0.000100 & 0.0233090 & 0.000108 \\
83 & **Bi** & 0.000172 & 0.000060 & \textless 0.00010 & - \\
90 & Th & 0.000883 & 0.000040 & 0.000888 & 3.81 \(\times 10^{-5}\) \\
92 & **U** & 6.94 \(\times\)\(10^{-5}\) & 0.00001 & 6.51 \(\times\)\(10^{-5}\) & 8.92 \(\times\)\(10^{-6}\) \\  & **Total** & **99.21829** & \multicolumn{2}{c}{**98.7713**} \\ \hline \end{tabular}  
* SD: standard deviation of the XRFS laboratory procedure; ** elements in CRM list are typewritten in bold.  
\end{table} 
Table 1: Cont. A robust statistical analysis conducted in accordance with ISO 13508 [29] and ISO 5725-5 [39] provided more accurate values for Y (median 21.4, with a standard deviation of 1.3), while for Ce, the median was 34.5 ppm with a standard deviation of 1.8 ppm. The proposed model is not applicable to Y and Ce elemental concentrations, as their concentration values are all above the LOQs and exhibit a clustering tendency. However, for Ge and Bi, the use of the proposed model is mandatory as some of their concentration values fall below their LOQs, and the histograms of the data suggest a uniform distribution of the analytical outcomes (Figure 7). The histogram of the concentration values for Ge and Bi do not exhibit a clustering tendency, suggesting that the concentration values are uniformly distributed (Figure 7a,b).