## 3 Results and Discussion  
### Microstructural Changes in Single-Salt Solutions at Different Temperatures  
In order to address the issue of breaking the similarity between magnesium and lithium structures and enhancing their separation, this study investigates the microstructural changes in the single-salt solutions in the MgSO\({}_{4}\)-LiCl system at different temperatures. Figures 1 and 2 show the Fourier transform infrared spectra and radial distribution functions of 2.5 mol/L MgSO\({}_{4}\), Li\({}_{2}\)SO\({}_{4}\), LiCl, and MgCl\({}_{2}\) solutions at 20 \({}^{\circ}\)C, 40 \({}^{\circ}\)C, and 60 \({}^{\circ}\)C. Table 1 presents the relative peak strengths of various absorption peaks in the infrared spectra of each single-salt solution. In Figure 1, the upper portion represents the experimental infrared spectrum, while the lower portion represents the simulated spectrum. The simulated spectrum exhibits peaks at the same positions as those observed in the experimental spectrum; the matching peak positions between simulated and experimental spectra indicate the accuracy of the solution model, thereby affirming the reliability of the radial distribution functions. From Figure 1, it can be observed that the absorption bands of O-H stretching vibrations at 3340 cm\({}^{-1}\) in the four soluble single-salt solutions exhibit broad spectra with strong intensities, while the peak intensity and width of the O-H bending vibration absorption band at 1640 cm\({}^{-1}\) are significantly pronounced. Both of these trends vary similarly with temperature. Withincreasing temperature, the O-H stretching vibration absorption band shifts to lower wavenumbers, and the peak area of Li2 SO4 increases twofold at 20 \({}^{\circ}\)C, while the other salt solutions undergo minimal changes. In the radial distribution functions, as the temperature rises, the second hydration shell of water molecules around the anions in MgSO4 undergoes changes, while the water molecule distribution around the anions in Li2 SO4, LiCl and MgCl2, and LiCl remains relatively unaffected. Therefore, it can be inferred that the increase in temperature leads to changes in the second hydration shell of MgSO4 ions and alters the number of hydrogen bonds in the Li2 SO4 solution, resulting in changes in water structure. The comparable relative peak strengths of the chloride salt absorption bands are approximately 1, indicating minimal changes in their microstructure. This finding contributes to understanding the potential of altering the temperature of halide solutions to enhance the differentiation in sulfate-water structures. Figure 1: FTIR spectra of magnesium sulfate, lithium sulfate, lithium chloride, and magnesium chloride solutions at different temperatures. Figure 2: Radial distribution functions of magnesium sulfate, lithium sulfate, magnesium chloride, and lithium chloride solutions at different temperatures. In soluble salt solutions, the distinction between sulfate and chloride salts during the temperature variation lies in the presence of complex structures in sulfates, whereas chlorides exist in an ionic form. The complexation structure of sulfate solutions is manifested by two shoulder peaks related to SO4\({}^{2-}\) at 1090 cm\({}^{-1}\) and 980 cm\({}^{-1}\) in the infrared spectra. In the radial distribution functions, two sharp peaks appear at r = 1.49 A and r = 2.41 A in MgSO4 and Li2 SO4 solutions, providing evidence for the presence of complexation structures. The prominent structural changes in chloride salts relate to water structure. In the radial distribution functions, there are no shoulder peaks in the range of 0-8 A, indicating the distribution of water molecules only. The peak at 1090 cm\({}^{-1}\) corresponds to the symmetric stretching vibration of SO4\({}^{2-}\).