## 3 Results and Discussion
### Mechanism of Lithium Ion Separated from Brine Solution  
The differentiation of magnesium and lithium structures by changing the temperature in multi-ion systems has been observed to enhance the separation of magnesium and lithium. During the temperature change process, the supersaturation state of brine is the key to the separation of magnesium and lithium with minimal lithium loss. However, further investigation is still required to understand the loss of lithium in the liquid phase during the cooling process. Therefore, the loss of lithium in the liquid phase is further explored by comparing isothermal evaporation and controlled cooling processes. During the isothermal evaporation process of brine with a magnesium-lithium mass ratio of 40:1, variations in the concentrations of various ions were observed through ICP  
Figure 4: Radial distribution function of SO\({}_{4}\)\({}^{2-}\) and Cl\({}^{-}\) in simulated brine with a magnesium–lithium mass ratio of 40:1 at different temperatures. OES (Thermo Fisher Scientific ICAP6300, Waltham, MA, USA) analysis as water evaporated. Figure 5 depicts the changes in the magnesium-lithium ratio and lithium loss in the liquid phase during isothermal evaporation. As brine evaporates, the magnesium-lithium ratio in the solution decreases, and the amount of lithium loss gradually increases. This could be due to the synchronous dissociation of Mg\({}^{2+}\)-Cl\({}^{-}\) complexes surrounding Mg\({}^{2+}\) ions and the interaction of Li\({}^{+}\)-Cl\({}^{-}\) complexes, leading to partial lithium doping in magnesium crystals and resulting in lithium loss. As is shown in Figure 5, when the evaporation ratio exceeds 16%, the change in the magnesium-lithium mass ratio decreases. This is because as evaporation proceeds, the concentration of MgCl\({}_{2}\) in brine gradually increases. The evaporation ratio of water molecules in the liquid phase is higher than that of magnesium chloride ions. MgCl\({}_{2}\) is a structurally dispersed salt with strong water-retention capacity in the solution, resulting in increased viscosity of the brine and hindrance of water molecule evaporation [4]. This inhibition of evaporation weakens the separation of magnesium and lithium. When the evaporation ratio exceeds 50% and evaporation is stopped, the final brine magnesium-lithium ratio decreases to 23.43 with a lithium loss of 36.65%. Based on the analysis of the isothermal evaporation of brine, it has been found that lithium is carried away in the form of a magnesium-lithium-complex salt (MgCl\({}_{2}\)-LiCl\(\cdot\)6H\({}_{2}\)O) during the crystal precipitation process. As is summarized in Sections 3.1 and 3.2, the similarity of the magnesium-lithium structure can be altered by controlling the temperature, thus allowing for improvements in the evaporation crystallization method. By analyzing the radial distribution functions between ions depicted in Figure 2, the microstructural changes between ions in the brine can be inferred. The structure of MgSO\({}_{4}\) undergoes modifications under temperature influence, with the embedding of SO\({}_{4}\)\({}^{2-}\) in the first hydration layer and increased activity of contact ions. Additionally, rearrangement occurs in the second hydration layer, promoting crystallization [20]. Similarly, the structure of Li\({}_{2}\)SO\({}_{4}\) is affected by temperature, leading to the breaking of hydrogen bonds between water molecules and SO\({}_{4}\)\({}^{2-}\) ions, resulting in changes in the surrounding water molecule structure, as illustrated in Figure 6. Consequently, through temperature control, it is possible to distinguish between the structures of MgSO\({}_{4}\) and lithium salts in brine, thereby enhancing the separation of magnesium and lithium. Figure 5: Magnesium–lithium ratio and concentration changes in the liquid phase during isothermal evaporation process. (When the evaporation ratio is less than 16%, it is in Stage I, during which the lithium-magnesium mass ratio changes significantly, and the ratio of lithium loss increases.