## 5 Discussion
### Geochemical Characteristics of Garnets in Skarn  
#### 5.2.1 Mechanism of Rare Earth Element into Garnet  
The chemical formula of garnet is \(\mathrm{X_{3}Y_{2}Z_{3}O_{12}}\), where \(\mathrm{X}\) is the divalent cation of the dodecahedron, usually \(\mathrm{Ca^{2+}}\), \(\mathrm{Mg^{2+}}\), \(\mathrm{Mn^{2+}}\), \(\mathrm{Fe^{2+}}\) in octa-coordination; \(\mathrm{Y}\) is the trivalent cation of the octahedron, usually \(\mathrm{Fe^{3+}}\), \(\mathrm{Al^{3+}}\), \(\mathrm{Cr^{3+}}\) in hexa-coordination; \(\mathrm{Z}\) is the divalent cation of the tetrahedron, generally occupied by \(\mathrm{Si^{4+}}\) in tetra-coordination [21]. Previous studies have  
Figure 12: Isocon diagrams of the TS-10 profile from outer skarn to marble. (**a**) Migration trend of major elements, (**b**) Migration trend of REEs, (**c**) Migration trend of ILEs, (**d**) Migration trend of HFSEs. Plotting methods refer to [PERSON] et al. (2009) [38]. Marble-outer skarn plots are not normalized and are drawn assuming a constant total system mass. Should be noted that this can only reflect the trend information, not an absolute quantitative analysis. The original data of the diagrams can be found in Supplementary Table S3b. shown that trace elements enter garnets mainly through the following four mechanisms: (1) Surface adsorption, (2) Occlusion, (3) Substitution, and (4) Solid solution [22]. The first two mechanisms are mainly controlled by mineral growth kinetics, while the latter two are mainly controlled by crystal chemistry [14]. There is still debate on how REEs and trace elements enter into garnets. U, REE\({}^{3+}\) and Y\({}^{3+}\) can only enter the octahedral position by replacing divalent cations such as Ca\({}^{2+}\)[24,45]. The substitution of Eu\({}^{2+}\) is equivalent and will not cause charge imbalance (Formula (1)). However, U, REE\({}^{3+}\) and Y\({}^{3+}\) substitutions are inequivalent and can only be replaced by coupled substitution or creating vacancies to avoid charge imbalance (Formula (2)) [14]. \[\text{Ca}_{3}(\text{Al},\text{Fe})_{2}\text{Si}_{3}\text{O}_{12}+3\text{Eu}^{2 +}\left(\text{aq}\right)=\text{E}\text{u}_{3}(\text{Al},\text{Fe})_{2}\text{Si} _{3}\text{O}_{12}+3\text{Ca}^{2+}(\text{aq}) \tag{1}\]  
\[\text{Ca}_{3}(\text{Al},\text{Fe})_{2}\text{Si}_{3}\text{O}_{12}+3\text{ REE}^{2+}(\text{aq})+3(\text{Al}^{3+},\text{Fe}^{3+})\left(\text{aq} \right)=\text{REE}_{3}(\text{Al},\text{Fe})_{2}(\text{Al},\text{Fe})_{3} \text{O}_{12}+3\text{Ca}^{2+}(\text{aq})+3\text{Si}^{4+}(\text{aq}) \tag{2}\]  
From the perspective of crystal chemistry, there may be four possible mechanisms that influence the variation characteristics of REEs in the garnet from the Tongshan deposit. (1) REE\({}^{3+}\) can couple with monovalent cations, such as Na\({}^{+}\), to enter the X site, which is represented as \(2[\text{X}^{2+}]^{\text{VIII}}\)\(\rightarrow\)\([\text{X}^{+}]^{\text{VIII}}\)\(+\)\([\text{REE}^{3+}]^{\text{VIII}}\). This mechanism typically forms garnet containing Na [46]. However, the content of Na in spessarting garnets from the Tongshan deposit is extremely low, even lower than the detection limit of the instrument. This suggests that the Na-REE\({}^{3+}\) coupled substitution mechanism is unlikely to exist in garnets from the Tongshan deposit. (2) REE\({}^{3+}\) can couple with divalent cations, such as Fe\({}^{2+}\) and Mg\({}^{2+}\), to enter both X and Y sites, which is represented as \([\text{X}^{2+}]^{\text{VIII}}\)\(+\)\([\text{Y}^{3+}]^{\text{VI}}\)\(\rightarrow\)\([\text{REE}^{3+}]^{\text{VIII}}\)\(+\)\([\text{Y}^{2+}]^{\text{VI}}\) (Menzerite-type substitution) [47,48]. Menzerite-type substitution requires garnet to be enriched in Y and heavy REEs, with Y content being higher than that of REE. In samples TS-10-6/7/8, REE\({}^{3+}\) has a positive correlation with Mg\({}^{2+}\), but there is no negative correlation trend between Fe\({}^{2+}\) and REE\({}^{3+}\) (Figure 13d,e).