## 4 Discussion
### Distribution of REEs
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Element** & **Total Sample** & \begin{tabular}{c} **Goethite-Rich** \\ **Fraction** \\ \end{tabular} & \begin{tabular}{c} **Cancrintic-Rich** \\ **Fraction** \\ \end{tabular} & \
\begin{tabular}{c} **Coarse-Grained** \\ **Magnetic Fraction** \\ \end{tabular} &
\begin{tabular}{c} **Coarse-Grained** \\ **Non-Magnetic Fraction** \\ \end{tabular} \\ \hline La & 237.90 & 226.20 & 239.40 & 46.60 & 47.30 \\ Sc & 82.90 & 79.20 & 84.40 & 47.50 & 61.80 \\ Ce & 438.90 & 414.00 & 437.90 & 115.70 & 117.80 \\ Pr & 49.26 & 48.41 & 51.04 & 11.98 & 13.25 \\ Nd & 193.63 & 189.56 & 197.13 & 49.00 & 55.93 \\ Sm & 37.29 & 37.07 & 37.83 & 10.84 & 13.58 \\ Eu & 8.49 & 8.35 & 8.61 & 2.45 & 3.43 \\ Gd & 33.48 & 30.34 & 34.33 & 10.92 & 14.59 \\ Tb & 4.64 & 4.50 & 4.79 & 1.72 & 2.31 \\ Dy & 27.01 & 25.49 & 27.30 & 10.90 & 14.68 \\ Ho & 5.18 & 5.05 & 5.17 & 2.31 & 3.18 \\ Er & 15.36 & 14.58 & 15.52 & 6.44 & 9.13 \\ Tm & 2.24 & 2.08 & 2.17 & 1.04 & 1.46 \\ Yb & 14.84 & 13.49 & 14.98 & 6.88 & 10.81 \\ Lu & 22.10 & 2.02 & 2.25 & 1.11 & 1.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: REE concentrations (all in ppm) in the studied grain fractions. Figure 8: Examples for the result of the trial-and-error method at different (a\({}_{1}\), a\({}_{2}\), a\({}_{\text{tot}}\)) values (**a–c**). (**d**) The best solution found. The best fit coincides with a\({}_{1}\) = 35%, a\({}_{2}\) = 62%, and a\({}_{\text{tot}}\) = 60%, that is the goethite-rich separate contains \(\sim\)35%, the cancinrite-rich one contains \(\sim\)62%, while the original sample contains \(\sim\)60% of cancinrite. These numbers nevertheless refer exclusively to a two-phase (cancinrite, goethite) system and the unknown amounts of all other minerals decrease the above proportions in the case of the whole mud. The low REE concentration of these diluent phases causes that most concentrations measured in the original mud sample and there in the cancinrite-rich separate are rather close to each other. The main result of the modelling is nevertheless the list of REE concentrations characteristic for the pure end members, cancinrite and goethite (Table 6) as well as their ratios, the enrichment factors for each REE. The data give a numerical proof for a previous statement that cancinrite accumulates significantly more of each REE than goethite does. These concentrations are also much higher than those typical are in the original red mud (Table 6). The enrichment factors can be calculated in an identical way between cancinrite and the coarse grain separate as well. In this calculation, magnetic and non-magnetic fractions were handled together (Table 6). The values suggest that these mineral phases are of a minor role in REE accumulation. Evaluating the mode in which cancinrite and goethite accumulate REEs is out of the scope of the present paper. However, it has been known from experimental mineralogical results that the crystal structure of both phases is appropriate to physically adsorb the REEs. The adsorption capacity of goethite is usually very good, but it depends on numerous parameters, like Al-content, crystallinity, temperature, and pH [23]. Some experiments confirm that goethite adsorbs La very well at a pH \(>\) 5 [24], while [25] found Sc to adsorb on goethite surfaces, by analyzing its behaviour during leaching experiments. Cancrinite has channels defined by a 12-membered silicate ring in its structure [26; 27] and