## 3 Results and Discussion
### Mechanism of Lithium Entrapment into Solid Phase  
By referring to the radial distribution function of Li+-SO42- in Figure 4, it can be observed that as the temperature decreases, the distance between hydration layers surrounding Li+-SO42- clusters increases, thereby promoting the formation of lithium sulfate crystals. Based on this hypothesis, a chemical composition analysis was conducted on the solid phase. Table 2 presents the concentration of lithium ions in the solid phase, along with a comparison with the loss of lithium during the isothermal evaporation process, providing clear insights into the mechanism by which Li+ enters the solid phase during temperature variation. Through chemical composition analysis of the solid phase, the lithium content can be determined. A comparison was made between the solid phase obtained after cooling of the brine and the solid phases obtained after the cooling of MgSO4 and Li2 SO4. The morphology and structure of the solid phase were studied, followed by drying treatment of the solid phase. Further clarification of the form of lithium loss was achieved through the utilization of scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), and X-ray diffraction (XRD) analysis. Figure 8a,b represent the solid phase obtained by cooling crystallization of brine. Figure 8c represents the crystals obtained by cooling crystallization of a pure lithium sulfate solution, and Figure 8d represents the crystals obtained by cooling crystallization of a pure magnesium sulfate solution. A comparison reveals that the surface of MgSO4 crystals is rougher than that of Li2 SO4 crystals, and according to the scale in Figure 8c,d, it can be observed that MgSO4 crystals are larger than Li2 SO4 crystals. In Figure 8a, it can be observed that most of the crystals obtained after cooling are MgSO4 crystals. The MgSO4 crystals were observed to exhibit numerous small-particle crystals attached to their surfaces. The EDS analysis revealed the presence of sulfate ions without magnesium in some of these small-particle crystals. Due to the limitations of EDS in detecting lithium content, in cases where the starting materials solely consist of magnesium and lithium, the absence of magnesium and the presence of sulfur and oxygen suggest the possibility of lithium sulfate crystals. Hence, it is speculated that the change in temperature of high-magnesium-lithium-ratio brine leads to a transformation in the complex structure of MgSO4 in solution, resulting in a rearrangement of the hydration layers and promoting MgSO4 crystallization. This alteration in the water structure within the brine facilitates the generation of Li2 SO4 crystals and thus, the entrapment of lithium salts in the solid phase. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Magnesium–** \\ **Lithium Ratio** \\ \end{tabular} } & \begin{tabular}{c} **Lithium Content in** \\ **Non-Equilibrium** \\ **Cooling Solid** \\ **Phase/\%** \\ \end{tabular} & \
\begin{tabular}{c} **Non-Equilibrium** \\ **Cooling Lithium** \\ **Loss Ratio/\%** \\ \end{tabular} &
\begin{tabular}{c} **Isothermal** \\ **Evaporation Lithium** \\ **Loss Ratio/\%** \\ \end{tabular} \\ \hline
5:1 & 0.6800 & 25.06 & \\
10:1 & 0.0925 & 3.36 & \\
20:1 & 0.0600 & 2.21 & \\
40:1 & 0.0300 & 1.11 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of lithium content and loss in solid phase. The composition of the substances was analyzed using the X-ray diffraction (XRD) method. Figure 9 depicts the XRD spectra of crystals obtained from brine with different magnesium-lithium mass ratios after controlled cooling processes. Based on the X-ray diffraction (XRD) results depicted in Figure 9, it can be observed that Li\({}_{2}\)SO\({}_{4}\cdot\)H\({}_{2}\)O exists in the solid phases obtained during the variable-temperature crystallization process of brine with different magnesium-lithium mass ratios.