1. Introduction
The Qinghai magnesium-sulfate-subtype salt lake in China contains abundant mineral resources such as potassium, magnesium, and lithium [
1]. However, lithium in the lake brine is usually present in trace amounts. Due to the high magnesium–lithium ratio (generally more than 40:1) in the brine [
2] and their similar physicochemical properties, efficient separation is difficult to achieve [
3]. Current separation methods result in significant lithium losses when applied to high-magnesium–lithium-ratio brines, posing a challenge for achieving enhanced separation and a reduction in lithium losses.
The traditional natural evaporation process directly utilizes MgCl
2 as the raw material for magnesium–lithium separation [
4]. However, the high concentration of MgCl
2 solution leads to high viscosity, resulting in a lithium loss of 36~70% in the liquid phase [
5]. Despite this, there exists a type of magnesium-sulfate-type brine in salt lake production that can achieve effective magnesium removal and enhance magnesium–lithium separation [
6] due to its properties of being supersaturated and having a low viscosity under high-temperature conditions [
7]. In fact, the temperature is higher, so the separation of salt components is easier; if the system is supersaturated, the separation effect will be significantly enhanced, and the separation performance will even be increased by 30% [
7]. The properties of low viscosity and supersaturation at high temperatures are possessed by sulfate-type salt lake brines [
8], which can provide convenient conditions for magnesium–lithium separation. However, the lithium loss mechanism and the process-enhanced separation mechanism of this process are still unclear, requiring clarification of the microstructure, hydrogen bonding, and complexation. Therefore, it is necessary to elucidate the effects of enhanced magnesium–lithium separation and the causes of lithium losses from changes in solution structure and molecular levels.
Methods for studying the solution structure include Raman spectroscopy, infrared spectroscopy [
9], and X-ray diffraction. Generally, inorganic salts do not produce infrared characteristic peaks. However, in salt solutions, the water structure near ions can be altered. Water preferentially solvates cations with oxygen and hydroxyl groups solvate anions, increasing the complexity of the water structure and leading to spectral changes. Therefore, infrared spectroscopy can be used to characterize the microstructure of water in inorganic salt solutions by analyzing the shifts [
10] and intensities of the O-H stretching band [
11]. Cheng et al. [
12] studied the O-D stretching band in K
2SO
4 and MgSO
4 solutions using FTIR and analyzed the water structure changes induced by these salts. Deepak Ojha et al. [
13] used two-dimensional infrared spectroscopy to investigate the effects of halide salts as solutes on the diffusion dynamics of the OD stretching vibrational spectra in the water medium at different temperatures. Guo et al. [
14] used FTIR to demonstrate the strength of interactions between water and solvent molecules in the hydration layer by observing the frequency shift of the O-H bond. Moilanen et al. [
15] observed the water structure surrounding ions in aqueous salt solutions using the FTIR technique. Borkowski et al. [
16] observed changes in the water vibrational spectra in halide salt solutions using FTIR. Therefore, infrared spectroscopy can be used to analyze the changes in water structure caused by soluble salts with varying temperatures, providing support for magnesium–lithium separation during cooling processes.
Experimental infrared spectroscopy involves the absorption or scattering of specific wavelengths of infrared radiation to reveal the molecular composition and structural characteristics of a sample. On the other hand, simulated infrared spectroscopy can predict the infrared spectral features of a sample through theoretical calculations and various computational methods. It helps uncover the effects of different molecular configurations and environments on the infrared spectrum, aiding in the interpretation of experimental observations. The combination of both approaches allows for mutual validation and supplementation. In their study, Grabska et al. [
17] employed a combination of two infrared spectroscopy techniques to provide a better explanation of water structure. Ben-Amotz [
18] utilized complementary information from two infrared spectroscopy methods to elucidate ion polarization. Roget et al. [
19], using infrared techniques in conjunction with kinetic analysis, investigated the interaction and structural evolution of water and chloride ions in a LiCl solution. Therefore, employing the mutual confirmation of two infrared spectroscopy methods can offer a more comprehensive understanding of the microscopic structural changes in brine during the temperature-enhanced magnesium–lithium separation process.
This study utilizes infrared spectroscopy and molecular dynamics simulations to investigate the microstructural changes in soluble magnesium–lithium salt solutions during temperature variations. It examines the effects of changes in magnesium and lithium salt solutions on the efficiency of magnesium–lithium separation and lithium losses in order to elucidate the mechanisms behind lithium loss and process enhancement.
2. Experimental Section
A simulated brine solution was prepared with a magnesium–lithium ratio of approximately 40:1, based on the composition of brine samples obtained after potassium extraction from the Qinghai salt lake, China. This solution was then subjected to room-temperature evaporation, after the addition of Na2SO4·10H2O, with a composition of Mg2+ 48 g/L, Na+ 50.23 g/L, Cl− 138.2 g/L, Li+ 1.236 g/L, K+ 13.86 g/L, and SO42− 77.25 g/L.
Single-salt solutions of MgSO4, Li2SO4, LiCl, and MgCl2, with a concentration of 2.5 mol/L, as well as simulated brine solutions with magnesium–lithium ratios of 160:1, 80:1, 40:1, 20:1, 10:1, and 5:1, were prepared and heated under reflux at 80 °C. The resulting MgSO4-LiCl saturated solution was then slowly cooled to around 60 °C, at which point the solution became supersaturated (i.e., the concentration of MgSO4 is empirically approximately 1.3 times its standard solubility). The temperature was then further lowered to room temperature (around 20 °C). During this cooling stage, approximately one-third of the dissolved MgSO4 crystallized and precipitated, significantly reducing the magnesium–lithium ratio of the brine. This is the most distinctive feature of this separation method.
Furthermore, because the brine was cooled from a relatively high temperature (60 °C), the viscosity of the brine was low during the cooling process, which prevented a large amount of Li+ from being trapped in MgSO4 crystals and then avoided serious lithium process losses.
The changes in the temperature and state of the brine solution were recorded. After the solid–liquid separation, the crystals were collected, and the magnesium–lithium separation was completed. FTIR spectroscopy was used to observe changes in the structure of the single-salt and brine solutions before and after cooling, over a range of wave numbers from 3800 cm−1 to 650 cm−1. The morphology and composition of the crystals were analyzed using SEM, EDS, and XRD, and the magnesium–lithium separation was confirmed via chemical analysis. The laboratory instruments used in this study included a Fourier transform infrared spectrometer (Thermo Fisher Scientific Nicolet iS50, Waltham, MA, USA), an X-ray diffractometer (Rigaku Corporation Smartlab, Tokyo, Japan), an inductively coupled plasma atomic emission spectrometer (Thermo Fisher Scientific ICAP6300, Waltham, MA, USA), a scanning electron microscope, and an energy dispersive X-ray spectroscopy system (JSM-IT500HR, JEOL, Tokyo, Japan), among others.
Different temperature conditions (20–60 °C) were established for the MgSO
4-H
2O, Li
2SO
4-H
2O, LiCl-H
2O, and MgCl
2-H
2O systems. The B3LYP functional was utilized, and all simulated systems were maintained at a constant pressure and temperature using the Nose–Hoover barostat and Nose–Hoover thermostat, with parameter settings of 1 atm and 298 K, 313 K, and 333 K. The vibrational frequencies and reaction kinetics were calculated with a convergence criterion of 10
−6 eV. The following thresholds were used for geometry optimization: 1 × 10
5 Hartree for maximum energy change, 2 × 10
−3 Hartree/A for maximum force, and 5 × 10
−3 A for maximum displacement. The radial distribution function of anions (SO
42−, Cl
−) in the solute was analyzed, and the distribution of water molecules around the ions before and after temperature changes was compared to provide a molecular-level explanation for the control of magnesium–lithium separation during cooling. Similar methods have been used in many inorganic salt solution systems [
20,
21,
22].
3. Results and Discussion
3.1. 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.
Figure 1 and
Figure 2 show the Fourier transform infrared spectra and radial distribution functions of 2.5 mol/L MgSO
4, Li
2SO
4, LiCl, and MgCl
2 solutions at 20 °C, 40 °C, and 60 °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. With increasing temperature, the O-H stretching vibration absorption band shifts to lower wavenumbers, and the peak area of Li
2SO
4 increases twofold at 20 °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 MgSO
4 undergoes changes, while the water molecule distribution around the anions in Li
2SO
4, LiCl and MgCl
2, and LiCl remains relatively unaffected. Therefore, it can be inferred that the increase in temperature leads to changes in the second hydration shell of MgSO
4 ions and alters the number of hydrogen bonds in the Li
2SO
4 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.
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 SO
42− 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 Å and r = 2.41 Å in MgSO
4 and Li
2SO
4 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 Å, indicating the distribution of water molecules only. The peak at 1090 cm
−1 corresponds to the symmetric stretching vibration of SO
42−. Based on
Figure 1 and
Table 1, it can be observed that with increasing temperature, the relative strength of MgSO
4 is approximately 1, while the peak area of Li
2SO
4 increases by 1.79 times at 20 °C, indicating minimal changes in the number of free SO
42− ions in the MgSO
4 solution and an increase in free SO
42− ions in the Li
2SO
4 solution. The shoulder peak at 980 cm
−1, attributed to the contact ion pair of SO
42−, shows that the relative strengths of the absorption peaks in MgSO
4 and Li
2SO
4 are approximately 1 with increasing temperature. However, in the radial distribution functions, the distribution of water molecules in the second hydration shell of SO
42− in the MgSO
4 solution undergoes changes, while the distribution of water molecules surrounding SO
42− in the Li
2SO
4 solution remains relatively unaffected. This suggests that the microstructure of ion pairs in the MgSO
4 solution undergoes changes, while the microstructure of ion pairs in the Li
2SO
4 solution remains unchanged. These findings widen the differentiation of magnesium–lithium solvent microstructures and provide a basis for strengthening the separation of magnesium and lithium.
Therefore, with increasing temperature, the number of water molecules in the second hydration shell surrounding the contact ion pair in the MgSO4 solution decreases. In Li2SO4 solution, the water structure changes due to variations in hydrogen bond numbers. The structures of MgCl2 and LiCl solutions remain largely unchanged, breaking the structural similarity between magnesium and lithium in solution and aiding in enhancing their separation.
3.2. Microstructure of Mixed Brine at Different Temperatures
To validate the changes in the microstructure of single-salt solutions in a cascaded temperature field, as discussed in
Section 3.1, we investigated the influence of interionic temperature on the magnesium–lithium separation structure in a multi-ion system and examined the microstructural variations in brine with different magnesium–lithium mass ratios.
Figure 3 shows the microstructure of mixed brine with magnesium–lithium mass ratios of 5:1, 10:1, 20:1, 40:1, 80:1, and 160:1 at different temperatures. It can be seen from the combined results that with a decreasing magnesium–lithium mass ratio, the number of Cl
− ions in the solution increases, and the peak intensity and area of water peaks at 3340 cm
−1 and 1090 cm
−1 change less during temperature variation. This is due to the easier formation of a coordination relationship between Li
+ and Cl
− in the solution, resulting in fewer Li
2SO
4 clusters. It was shown in
Section 3.1 that Li
2SO
4 clusters play a major role in the change in water structure in the solution; therefore, the variation in the microstructure of the water structure in the solution is smaller. In a multi-ion system, as the magnesium–lithium ratio increases, the number of Cl
− ions in the solution decreases, and with temperature change, the variation in water structure in the solution with hydrogen bond number becomes more significant. However, with more Cl
− ions in the solution, the change in water structure with temperature is hindered, and the change in water structure around Li
2SO
4 clusters is suppressed, which is not conducive to the change in magnesium–lithium structure in the solution.
Figure 4 shows the radial distribution function of anions in simulated brine with a magnesium–lithium mass ratio of 40:1. Combined with the infrared spectra of brine, it can be seen that the peak areas of the characteristic bands of SO
42− at 1090 cm
−1 and 980 cm
−1 decrease as the temperature increases, indicating that the free ion peak and contact ion peak of SO
42− in the brine decrease with temperature increase. Correspondingly, in
Figure 4, the radial distribution function of SO
42− in the brine has a clear shoulder peak at r = 3.5 Å, and the stronger the shoulder peak, the stronger the interaction energy between SO
42− and H
2O in the solution. In the radial distribution function, the distribution of water molecules around Cl
− in the brine changes less. In the radial distribution function of Mg
2+-SO
42−, it can be clearly seen that with temperature change, the arrangement of SO
42− and H
2O in the second hydration layer changes, and the ionic coordination structure undergoes a significant change. In terms of the radial distribution function of Li
+-SO
42−, with increasing temperature, the distance between Li
+ and the hydration layer around SO
42− first increases and then decreases, the hydrogen bond between SO
42− and H
2O breaks, and the surrounding water structure changes. Based on this, it can be inferred that the microstructure of MgSO
4 ion pairs in the brine changes during the cooling process, and the distribution of water molecules around Li
2SO
4 clusters has a great impact. This is consistent with the microstructure changes in single-salt solutions in
Section 3.1 and reinforces the magnesium–lithium separation.
Therefore, in a multi-ion system, the concentration of Cl− ions in the brine determines the change in water structure in the brine. The lower the concentration of Cl− ions, the greater the variation in the microstructure of the water with the hydrogen bond number during temperature increase, and the more significant the difference in the magnesium–lithium structure in the brine, which is more conducive to strengthening magnesium–lithium separation. This is the reason that Na2SO4 needs to be added to the raw brine to convert it into a sulfate-type solution before the brine is evaporated and separated.
3.3. 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-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·6H
2O) during the crystal precipitation process. As is summarized in
Section 3.1 and
Section 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
42− 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
2SO
4 is affected by temperature, leading to the breaking of hydrogen bonds between water molecules and SO
42− 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 7 shows the changes in the magnesium–lithium ratio and ion concentrations of magnesium and lithium in brine with different magnesium–lithium mass ratios after cooling. It can be seen from the figure that the magnesium–lithium ratio of brine decreases by about one-third during the cooling process; when the mass ratio of magnesium to lithium is 5:1, the lithium loss is 25.06%, and when the mass ratio of magnesium to lithium is greater than 5:1, the lithium loss can be controlled within 5%. In addition, the enrichment trend of lithium in the liquid phase is smaller at 40 °C compared to 60–50 °C and 40–25 °C. This can be attributed to the fact that at 40 °C, magnesium ions have a larger charge than lithium ions, enabling them to undergo rapid movement under the influence of an electric field, forming a thicker diffusion layer and resulting in alterations in the microstructure of brine [
2]. As is shown in
Figure 6, LiCl exists in brine in ion form, while Li
2SO
4 exists in cluster form. Combined with the radial distribution function in
Figure 4, the distance between hydration layers around Li
2SO
4 increases as the temperature decreases, promoting Li
2SO
4 crystallization and affecting the concentration of lithium in the solution. As a result, during the cooling process, LiCl exists in the liquid phase in ion form, while Li
2SO
4 clusters exist in an ion pairing structure. Changes in the hydration layers around Li
2SO
4 clusters due to temperature variation promote the formation of lithium sulfate crystals, causing the loss of Li
+ in the liquid phase in the form of Li
2SO
4 clusters, thus affecting the separation of magnesium and lithium.
3.4. Mechanism of Lithium Entrapment into Solid Phase
By referring to the radial distribution function of Li
+-SO
42− in
Figure 4, it can be observed that as the temperature decreases, the distance between hydration layers surrounding Li
+-SO
42− 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 Li2SO4. 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 MgSO
4 crystals is rougher than that of Li
2SO
4 crystals, and according to the scale in
Figure 8c,d, it can be observed that MgSO
4 crystals are larger than Li
2SO
4 crystals. In
Figure 8a, it can be observed that most of the crystals obtained after cooling are MgSO
4 crystals. The MgSO
4 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 MgSO
4 in solution, resulting in a rearrangement of the hydration layers and promoting MgSO
4 crystallization. This alteration in the water structure within the brine facilitates the generation of Li
2SO
4 crystals and thus, the entrapment of lithium salts in the 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
2SO
4·H
2O exists in the solid phases obtained during the variable-temperature crystallization process of brine with different magnesium–lithium mass ratios. Further analysis was carried out by combining scanning electron microscopy (SEM) and XRD results, which confirmed that some of the small granular crystals observed in SEM were Li
2SO
4 crystals. This implies that Li
2SO
4 crystals are entrained in MgSO
4 crystals and adhere to the surface of MgSO
4 in the form of small granules. Consequently, during the brine cooling process, lithium loss occurs in the form of Li
2SO
4·H
2O crystal entrainment into MgSO
4 crystals.
Therefore, during the variable-temperature enhanced magnesium–lithium separation process, the change in the MgSO4 complex structure in solution due to a decrease in temperature results in a rearrangement of the hydration layers and promotes MgSO4 crystallization. This alteration in water structure within brine increases the hydrated layer distance between Li+-SO42− clusters and enhances the generation of Li2SO4 crystals, leading to lithium loss during the magnesium–lithium separation process.
4. Conclusions
This study aims to address the issues associated with enhancing magnesium–lithium separation and reducing lithium loss through variable-temperature treatment. The microscopic structural changes, magnesium–lithium separation efficiency, and lithium loss mechanisms in high-magnesium–lithium-ratio brine solutions at different temperatures during the variable-temperature process were investigated. The following conclusions were drawn:
Through the analysis of FTIR spectra and radial distribution functions of different brine solutions, it was found that temperature can change the structure of MgSO4 solutes and the water structure of Li2SO4 in the liquid phase. The arrangement of SO42− and H2O in the second hydration layer of MgSO4 in the brine solution is changed with temperature. The hydrogen bonding between SO42− and H2O in the Li2SO4 solution is broken, resulting in changes in the surrounding water molecule structure. This change enhances the structural differences in the magnesium–lithium solution in the brine, thereby promoting magnesium–lithium separation. In a multi-ion system, the concentration of Cl− in the brine determines the changes in water structure. A lower Cl− concentration and increasing temperature result in greater changes in the water microstructure in the brine, leading to more pronounced differences in the magnesium–lithium structure and enhancing magnesium–lithium separation. In high-magnesium–lithium-ratio brine, by controlling the temperature and supersaturation state, lithium loss can be controlled within 5%. Therefore, the regulation of temperature and the supersaturation state aids in the separation of high-magnesium–lithium-ratio brine. During the cooling process, the magnesium–lithium separation is enhanced, and the cooling promotes changes in the water structure in the liquid phase, resulting in an increase in the number of hydration layers around Li+-SO42− clusters and the formation of Li2SO4 crystals. Thus, lithium is trapped in the MgSO4 crystals in the form of Li2SO4 crystals.