*2.2. Maintenance and Mechanism of Metastable State of the Neodymium Dissolved in Na2CO<sup>3</sup> Solution*

2.2.1. Maintaining Metastable State by NaCl

Following on from our previous research [19], the effect of additional NaCl on the maintenance of the metastable state of a solution of dissolved Nd3+ was investigated. The neodymium concentration in 2 mol·L <sup>−</sup><sup>1</sup> Na2CO<sup>3</sup> solution was controlled at 2.621 g·<sup>L</sup> −1 . The ionic strength of the solution was controlled by adding NaCl to Na2CO<sup>3</sup> solution to create a mixed electrolyte NaCl/Na2CO<sup>3</sup> solution. The concentration of the additional NaCl ranged from 0 to 0.5 mol·L −1 . During the experiment, the volume of the Na2CO<sup>3</sup> (or mixed electrolyte NaCl/Na2CO3) solution was fixed at 25 mL, and the NdCl<sup>3</sup> solution was added to it drop by drop with oscillation. The time was set from 0 to 480 min. When the experiment finished, the solution containing precipitates was further centrifuged at 6000 rpm for 5 min. After that, the obtained supernatant was split into two parts; one was selected as aqueous sample for the further testing, and the another was completely acidulated by using dilute hydrochloric acid, after which complexometric titration was used to determine the concentration of Nd3+ .

#### 2.2.2. Effect of NaCl on Neodymium Coordination and Solid Phase Precipitates

The metastable state solution in each representative stationary period was scanned by ultraviolet-visible light (UV-vis) full-wavelength scanning. In order to provide an experimental comparison, a blank solution (Na2CO<sup>3</sup> and NdCl<sup>3</sup> solution only addition with water) was also scanned by UV-vis full wavelength. The precipitates were collected as solid samples and detected by Fourier transform infrared spectroscopy (FTIR). Because drying could cause the sample to decompose [20], producing errors in the results, the samples were all stored in deionized water. Before determination, the water was filtered, the samples dried with filter paper, and the analysis carried out immediately.

#### 2.2.3. Mechanism of Maintaining the Metastable State by NaCl

In order to find the maintenance mechanism of the additional NaCl on the metastable state, a molecular dynamics (MD) calculation was carried out using Materials Studio 8.0 [21] software. The solution model was established by using an Amorphous Cell module, and the model was geometry optimized using a Forcite module. Finally, MD calculation and radial distribution function (RDF) analysis [22] were carried out to reveal the relationship between the RDF and the coordination number of each component in the solution. The average coordination number of each component was calculated by Equation (1).

$$\mathbf{N(L)} = \int\_0^L \mathbf{g(r)} \,\rho \, 4\pi r^2 d\mathbf{r} \tag{1}$$

where N(L) refers to the number of coordination atoms(molecules) in the 0−L spherical shell around the target atom, *ρ* refers to the number density of coordination atoms (molecules), where the value is the ratio of the number of atoms (molecules) to the volume of space, g(r) refers to the RDF value, and indicates the probability of the occurrence of coordination atoms(molecules) within a certain distance, and r refers to the cutoff radius. shell around the target atom, ρ refers to the number density of coordination atoms (molecules), where the value is the ratio of the number of atoms (molecules) to the volume of space, g(r) refers to the RDF value, and indicates the probability of the occurrence of coordination atoms(molecules) within a certain distance, and r refers to the cutoff radius.

#### *2.3. Induced Precipitation of Neodymium Carbonates in Metastable State Solution* The precipitation process of neodymium carbonates by introducing CO2 gas into the

where N(L) refers to the number of coordination atoms(molecules) in the 0−L spherical

*2.3. Induced Precipitation of Neodymium Carbonates in Metastable State Solution* 

The precipitation process of neodymium carbonates by introducing CO<sup>2</sup> gas into the metastable state solution was studied. The procedure of the dissolution of Nd3+ in the solution was as previously described. Further, the dissolved Nd3+ solution was transferred to an autoclave for introducing CO<sup>2</sup> gas. The solution contained a large amount of halogen Cl−, so a corrosion-resistant polytetrafluoroethylene tank was selected as the inner tank of the autoclave. During the experiment, the input pressure of CO<sup>2</sup> was uniformly controlled at 0.2 Mpa. The time was set from 0–60 min. When the set time was reached, the solution containing precipitate was centrifuged at 6000 r·min−<sup>1</sup> for 5 min, then the supernatant obtained after centrifugation was split in two parts. One was acidified, and the concentration of neodymium in the supernatant was determined by inductively coupled plasma emission spectrometer (ICP-OES). The other was analyzed by CO<sup>3</sup> <sup>2</sup><sup>−</sup> and HCO<sup>3</sup> − acid-base titration to determine the concentration of CO<sup>3</sup> <sup>2</sup><sup>−</sup> and HCO<sup>3</sup> −. metastable state solution was studied. The procedure of the dissolution of Nd3+ in the solution was as previously described. Further, the dissolved Nd3+ solution was transferred to an autoclave for introducing CO2 gas. The solution contained a large amount of halogen Cl−, so a corrosion-resistant polytetrafluoroethylene tank was selected as the inner tank of the autoclave. During the experiment, the input pressure of CO2 was uniformly controlled at 0.2 Mpa. The time was set from 0–60 min. When the set time was reached, the solution containing precipitate was centrifuged at 6000 r·min−1 for 5 min, then the supernatant obtained after centrifugation was split in two parts. One was acidified, and the concentration of neodymium in the supernatant was determined by inductively coupled plasma emission spectrometer (ICP-OES). The other was analyzed by CO32− and HCO3− acid-base titration to determine the concentration of CO32− and HCO3−.

#### **3. Results and Discussion 3. Results and Discussion**

*Solution* 

in (**b**).

*Minerals* **2021**, *11*, x FOR PEER REVIEW 5 of 13

#### *3.1. Maintenance and Mechanism of the Metastable State of Neodymium Dissolved in Na2CO<sup>3</sup> Solution 3.1. Maintenance and Mechanism of the Metastable State of Neodymium Dissolved in Na2CO3*

3.1.1. Maintaining Metastable State by NaCl 3.1.1. Maintaining Metastable State by NaCl

The metastable period of the solution with the addition of NaCl was greater than that of the solution without NaCl due to neodymium being dissolved stably in solution for a longer time. As shown in Figure 2a, the metastable period was sustained only for about 120 min without the addition of NaCl. However, the metastable period reached 240 min when the concentration of the additional NaCl was 0.2 mol·L −1 . Moreover, the amount of dissolved neodymium in the solution reached 2.578 g·L −1 , which was only 1.64% lower than the initial amount of 2.621 g·L −1 . Surprisingly, when the additional concentration of sodium chloride in the solution reached 0.5 mol·L −1 , the metastable period was extended to 480 min, i.e., twice as long as before. The metastable period of the solution with the addition of NaCl was greater than that of the solution without NaCl due to neodymium being dissolved stably in solution for a longer time. As shown in Figure 2a, the metastable period was sustained only for about 120 min without the addition of NaCl. However, the metastable period reached 240 min when the concentration of the additional NaCl was 0.2 mol·L−1. Moreover, the amount of dissolved neodymium in the solution reached 2.578 g·L−1, which was only 1.64% lower than the initial amount of 2.621 g·L−1. Surprisingly, when the additional concentration of sodium chloride in the solution reached 0.5 mol·L−1, the metastable period was extended to 480 min, i.e., twice as long as before.

**Figure 2.** The effect of the concentration of the additional NaCl in (**a**) and Ionic strength of solution **Figure 2.** The effect of the concentration of the additional NaCl in (**a**) and Ionic strength of solution in (**b**).

The molar concentration in the above solution was converted into mass molar concentration according to Equation (2). Then, the ionic strength of each solution was calculated

state effectively.

ter only.

lution.

by using Equation (3). The results are shown in Figure 2b which shows that the addition of NaCl effectively improved the ionic strength of the solution. the ionic strength of the solution. In the case of the equivalent concentration of Na2CO3, the addition of NaCl resulted in neodymium dissolving stably in Na2CO3 solution for a longer time. The higher the con-

*C=bB·ρ* (2)

*<sup>2</sup>* (3)

The molar concentration in the above solution was converted into mass molar concentration according to Equation (2). Then, the ionic strength of each solution was calculated by using Equation (3). The results are shown in Figure 2b which shows that the ad-

<sup>2</sup>*Ci bBi*

*bB* refers to the molar concentration, *ρ* refers to the density of the solution, and *I* refers to

*Minerals* **2021**, *11*, x FOR PEER REVIEW 6 of 13

dition of NaCl effectively improved the ionic strength of the solution.

*I* = 1

$$\mathcal{C} = b\mathcal{B} \cdot \rho \tag{2}$$

$$I = \frac{1}{2} \sum \mathbf{C}\_i b B\_i^2 \tag{3}$$

*bB* refers to the molar concentration, *ρ* refers to the density of the solution, and *I* refers to the ionic strength of the solution. 3.1.2. Effect of NaCl on Neodymium Coordination and Solid Phase Precipitates To confirm whether the coordination reaction between Nd3+ and CO32− still occurred

In the case of the equivalent concentration of Na2CO3, the addition of NaCl resulted in neodymium dissolving stably in Na2CO<sup>3</sup> solution for a longer time. The higher the concentration of NaCl in solution, and the stronger the ionic strength, resulting in a longer metastable period of the solution. Hence, the additional NaCl maintained the metastable state effectively. in the mixed electrolyte solution of NaCl/Na2CO3, the aqueous samples in each period of the above experiments were collected and scanned by UV-vis with full wavelength. As shown in Figure 3, the characteristic peak of neodymium was not found in the UV-vis spectra of the sample of the blank NaCl/Na2CO3 mixed electrolyte solution with only added water. Characteristic peaks of neodymium at the 340–370 nm and 500–620 nm

#### 3.1.2. Effect of NaCl on Neodymium Coordination and Solid Phase Precipitates wavebands [23] were observed in the spectra of the blank NdCl3 solution with added wa-

To confirm whether the coordination reaction between Nd3+ and CO<sup>3</sup> <sup>2</sup><sup>−</sup> still occurred in the mixed electrolyte solution of NaCl/Na2CO3, the aqueous samples in each period of the above experiments were collected and scanned by UV-vis with full wavelength. As shown in Figure 3, the characteristic peak of neodymium was not found in the UV-vis spectra of the sample of the blank NaCl/Na2CO<sup>3</sup> mixed electrolyte solution with only added water. Characteristic peaks of neodymium at the 340–370 nm and 500–620 nm wavebands [23] were observed in the spectra of the blank NdCl<sup>3</sup> solution with added water only. As shown in Figure 3, characteristic peaks of neodymium were obtained at 349 and 357 nm wavelengths in the spectra of the NaCl/Na2CO3 mixed electrolyte solution with dissolved neodymium. Compared with the blank neodymium solution spectrum, it is worth noting that the characteristic peaks of neodymium obtained from the NaCl/Na2CO3 solutions with dissolved neodymium were slightly red-shifted from the initial 347 and 354 nm wavelengths due to the high alkalinity of the NaCl/Na2CO3 mixed electrolyte so-

**Figure 3.** UV-vis spectrum of NdCl3/Na2CO3 solution with the addition of 0.5M NaCl, wavelength in 340 to 370 nm in (**a**), and 510 to 600 nm in (**b**). **Figure 3.** UV-vis spectrum of NdCl3/Na2CO<sup>3</sup> solution with the addition of 0.5M NaCl, wavelength in 340 to 370 nm in (**a**), and 510 to 600 nm in (**b**).

There were also neodymium characteristic peaks at 524 and 575 nm wavelengths in the UV-vis spectrum of the neodymium-dissolving solution, as in our previously results [19]. In addition, a new peak with higher intensity was observed at 583 nm. This indicates that neodymium could still coordinate with CO32− in the Na2CO3 solution with the addition As shown in Figure 3, characteristic peaks of neodymium were obtained at 349 and 357 nm wavelengths in the spectra of the NaCl/Na2CO<sup>3</sup> mixed electrolyte solution with dissolved neodymium. Compared with the blank neodymium solution spectrum, it is worth noting that the characteristic peaks of neodymium obtained from the NaCl/Na2CO<sup>3</sup> solutions with dissolved neodymium were slightly red-shifted from the initial 347 and 354 nm wavelengths due to the high alkalinity of the NaCl/Na2CO<sup>3</sup> mixed electrolyte solution.

> There were also neodymium characteristic peaks at 524 and 575 nm wavelengths in the UV-vis spectrum of the neodymium-dissolving solution, as in our previously results [19]. In addition, a new peak with higher intensity was observed at 583 nm. This indicates that neodymium could still coordinate with CO<sup>3</sup> <sup>2</sup><sup>−</sup> in the Na2CO<sup>3</sup> solution with the addition of NaCl. The precipitate sample generated from the solution after 480 min was collected and analyzed by FTIR. The results shown in Figure 4.

non-existent.

and analyzed by FTIR. The results shown in Figure 4.

of NaCl. The precipitate sample generated from the solution after 480 min was collected

Figure 4 shows that the characteristic infrared peak position of the precipitate generated from the NaCl/Na2CO3 solution with dissolved neodymium was consistent with that of the blank sample NaNd(CO3)2 solid phase. This was consistent with results reported in previous studies [11,24]. These reports and our results confirm that in the presence of additional NaCl in a highly concentrated CO32<sup>−</sup> solution, the insoluble rare earth existed only in the form of an NaNd(CO3)2 double salt, while Nd2(CO3)3 was almost

3.1.3. Mechanism of Maintaining the Metastable State by NaCl In order to investigate the mechanism of the maintenance of the metastable state by the additional NaCl, molecular dynamic (MD) calculations were carried out. The construction and optimization of the solution components were consistent with our previous study [19]. The model of the solution with the addition of 0.5 mol·L−<sup>1</sup> NaCl (with the better metastable condition), and the corresponding blank solution (Na2CO3/NaCl Figure 4 shows that the characteristic infrared peak position of the precipitate generated from the NaCl/Na2CO<sup>3</sup> solution with dissolved neodymium was consistent with that of the blank sample NaNd(CO3)<sup>2</sup> solid phase. This was consistent with results reported in previous studies [11,24]. These reports and our results confirm that in the presence of additional NaCl in a highly concentrated CO<sup>3</sup> <sup>2</sup><sup>−</sup> solution, the insoluble rare earth existed only in the form of an NaNd(CO3)<sup>2</sup> double salt, while Nd2(CO3)<sup>3</sup> was almost non-existent.

#### solution with the only additional water) was also established by using the Amorphous 3.1.3. Mechanism of Maintaining the Metastable State by NaCl

Cell module. After that, geometry optimization and the MD calculation were carried out. The components in the model and calculation parameters are shown in Table 3. The energy changed during the geometry optimization process is presented in Figure 5a. **Table 3.** Modeling parameters of the solutions. **Components The Metastable State Solution Corresponding Blank Solution** *ρ***: 1.164 g·L−<sup>1</sup>** *ρ***: 1.148 g·L−<sup>1</sup> Number Mass Fraction (%) Number Mass Fraction (%)** H2O 10,590 84.7 10,590 85.0 Na+ 630 6.4 630 6.5 In order to investigate the mechanism of the maintenance of the metastable state by the additional NaCl, molecular dynamic (MD) calculations were carried out. The construction and optimization of the solution components were consistent with our previous study [19]. The model of the solution with the addition of 0.5 mol·L <sup>−</sup><sup>1</sup> NaCl (with the better metastable condition), and the corresponding blank solution (Na2CO3/NaCl solution with the only additional water) was also established by using the Amorphous Cell module. After that, geometry optimization and the MD calculation were carried out. The components in the model and calculation parameters are shown in Table 3. The energy changed during the geometry optimization process is presented in Figure 5a.


CO3 <sup>2</sup>- 280 7.5 280 7.5 Nd3+ 3 0.2 0 0.0 **Table 3.** Modeling parameters of the solutions.

state.

randomly and uniformly distributed in the model box, and no agglomeration existed.

**Figure 5.** Geometry optimization process of the solution model (**a**). Temperature change during the MD calculation in (**b**). Geometry optimization and after MD calculation of the solution model (**c**) and (**d**). In the figures, (**i**) refers to the metastable state solution and (**ii**) is the corresponding blank solution. **Figure 5.** Geometry optimization process of the solution model (**a**). Temperature change during the MD calculation in (**b**). Geometry optimization and after MD calculation of the solution model (**c**,**d**). In the figures, (**i**) refers to the metastable state solution and (**ii**) is the corresponding blank solution.

The models after the MD calculation are presented in Figure 5d, which shows that the solution was generally homogeneous. However, in the local region, the components of the solution model had different degrees of agglomeration due to the interaction between ions (or molecules). Among them, the CO32− distribution exhibited local agglomeration. A large number of Na+ ions were distributed around the CO32−. This can be attributed to the incomplete dissociation of Na+ and CO32− at the high concentration of the NaCl/Na2CO3 mixed electrolyte solution. We speculate that the concentration of carbonate that could move freely (called free CO32−) in the solution was limited and at a low level. As shown in Figure 5a, the overall energy decreased gradually with increase in the number of optimization steps without large energy disturbances. At the end of optimization, the energy tended to be relatively minimized and achieved convergence. Change of the temperature is presented in Figure 5b, which shows that the temperature of the models decreased gradually with the increase of simulation time. At the end of the calculation, it was stable at about 298 K ± 10% and there was no significant disturbance. This result is very reliable. The optimized models are presented in Figure 5c, which shows that after the geometry optimization step, the Na<sup>+</sup> , CO<sup>3</sup> <sup>2</sup>−, Nd3+, Cl<sup>−</sup> ions in each solution model were randomly and uniformly distributed in the model box, and no agglomeration existed.

Moreover, Nd3+ was also almost surrounded by CO32− in that Nd3+ was coordinated with about three CO32−. This shows that Nd3+ can coordinate with carbonate despite the addition of NaCl to Na2CO3 solution. In addition, all kinds of complex ions in the form of Ndn(CO3)m3n−2m (m ≥ 2) existed, but in different proportions. As shown in Figure 6a, there was a specific Cl− ion around some Nd3+ ions, indicating that, unlike in previous studies, Cl− might also coordinate with Nd3+. Previous studies of steady-state dissolution of rare earths in CO32− solution [11,24], showed that the coordination between Cl− and Nd3+ could almost be ignored under the condition of steady-state solution equilibrium because of The models after the MD calculation are presented in Figure 5d, which shows that the solution was generally homogeneous. However, in the local region, the components of the solution model had different degrees of agglomeration due to the interaction between ions (or molecules). Among them, the CO<sup>3</sup> <sup>2</sup><sup>−</sup> distribution exhibited local agglomeration. A large number of Na<sup>+</sup> ions were distributed around the CO<sup>3</sup> <sup>2</sup>−. This can be attributed to the incomplete dissociation of Na<sup>+</sup> and CO<sup>3</sup> <sup>2</sup><sup>−</sup> at the high concentration of the NaCl/Na2CO<sup>3</sup> mixed electrolyte solution. We speculate that the concentration of carbonate that could move freely (called free CO<sup>3</sup> <sup>2</sup>−) in the solution was limited and at a low level.

weak Cl− coordination ability, which does not agree with our study. The difference could be ascribed to the difference between metastable and steady states. Besides, it is reasonable to speculate that Cl− occupied the coordination layer of Nd3+, delaying the formation of carbonate precipitation. Therefore, the addition of NaCl maintained the metastable In order to further quantify the interaction from the microscopic level, the main ion pairs of Nd3+-CO32−, Na+-CO32− and Nd3+-Cl− in the solution were analyzed by radial distribution function (RDF), and their coordination numbers were calculated. Figure 6b shows that the RDF peak position of Nd3+ and CO32− in the NaCl/Na2CO3 mixed electrolyte solution was almost the same as that in the single Na2CO3 solution in the chemical bond range (r < 2.6 Å) [25]. This directly proves that Nd3+ can coordinate with CO32− even in the presence of NaCl. At the same time, the RDF peak intensity of Nd3+-CO32− in the presence of Moreover, Nd3+ was also almost surrounded by CO<sup>3</sup> <sup>2</sup><sup>−</sup> in that Nd3+ was coordinated with about three CO<sup>3</sup> <sup>2</sup>−. This shows that Nd3+ can coordinate with carbonate despite the addition of NaCl to Na2CO<sup>3</sup> solution. In addition, all kinds of complex ions in the form of Ndn(CO3)<sup>m</sup> 3n−2m (m <sup>≥</sup> 2) existed, but in different proportions. As shown in Figure 6a, there was a specific Cl<sup>−</sup> ion around some Nd3+ ions, indicating that, unlike in previous studies, Cl<sup>−</sup> might also coordinate with Nd3+. Previous studies of steady-state dissolution of rare earths in CO<sup>3</sup> <sup>2</sup><sup>−</sup> solution [11,24], showed that the coordination between Cl<sup>−</sup> and Nd3+ could almost be ignored under the condition of steady-state solution equilibrium because of weak Cl− coordination ability, which does not agree with our study. The difference could be ascribed to the difference between metastable and steady states. Besides, it is reasonable to speculate that Cl<sup>−</sup> occupied the coordination layer of Nd3+, delaying the formation of carbonate precipitation. Therefore, the addition of NaCl maintained the metastable state.

NaCl was slightly lower than that in the single Na2CO3 solution. The difference of RDF peak intensity indicated that the additional NaCl had an influence on the interaction between Nd3+ and CO32−. From the point of view of coordination number, with the presence of the additional NaCl the average coordination number around Nd3+ was about 1.83 CO32−, which was lower than the average coordination number of 2.50 in the single Na2CO3

cupied the coordination layer of Nd3+ in the metastable period, causing the decrease in the average coordination number between Nd3+ and CO32−. This is consistent with Figure 6a.

**Figure 6.** Coordination between Nd3+, Cl<sup>−</sup> & CO32<sup>−</sup> (**a**). RDF of the ion pairs Nd3+-CO32−, Nd3+-Cl<sup>−</sup> & Na+-CO32<sup>−</sup> and their coordination number (**b**–**d**), respectively. **Figure 6.** Coordination between Nd3+, Cl<sup>−</sup> & CO<sup>3</sup> <sup>2</sup><sup>−</sup> (**a**). RDF of the ion pairs Nd3+-CO<sup>3</sup> <sup>2</sup>−, Nd3+-Cl<sup>−</sup> & Na<sup>+</sup> -CO<sup>3</sup> <sup>2</sup><sup>−</sup> and their coordination number (**b**–**d**), respectively.

To quantitatively explain the coordination between Nd3+ and Cl− in the mixed electrolyte, the RDF and the coordination number were further analyzed and calculated. Figure 6c shows that the RDF peak at 2.275 Å within the range of chemical bond (<2.6 Å) was clearly observed from the spectrum of the Nd3+-Cl− ion pair in the mixed electrolyte solution of NaCl/Na2CO3. One Nd3+ was coordinated with about one Cl−. In contrast to the single Na2CO3 solution, there was insignificant evidence of an interaction existing between Cl− and Nd3+. Hence, it was proved that that Cl− could coordinate with Nd3+ in the presence of NaCl during the metastable period. It is worth noting that the RDF peak position of Nd3+-CO32− was earlier than that of Nd3+-Cl−. The result indicates that CO32− tends to occupy the coordination layer of Nd3+ and reacted with it first, then Cl− entered the coordination layer of Nd3+, although, previous studies [11,24] showed that in an environment of high concentration of CO32− solution, Cl− did not coordinate with Nd3+ in a steady state. However, our result does not conflict with these previous studies because of the difference between metastable and steady states. In addition, when the placement time exceeded the metastable period, the precipitate was still consistent with that obtained in the steady state. Therefore, there is sufficient In order to further quantify the interaction from the microscopic level, the main ion pairs of Nd3+-CO<sup>3</sup> <sup>2</sup>−, Na<sup>+</sup> -CO<sup>3</sup> <sup>2</sup><sup>−</sup> and Nd3+-Cl<sup>−</sup> in the solution were analyzed by radial distribution function (RDF), and their coordination numbers were calculated. Figure 6b shows that the RDF peak position of Nd3+ and CO<sup>3</sup> <sup>2</sup><sup>−</sup> in the NaCl/Na2CO<sup>3</sup> mixed electrolyte solution was almost the same as that in the single Na2CO<sup>3</sup> solution in the chemical bond range (r < 2.6 Å) [25]. This directly proves that Nd3+ can coordinate with CO<sup>3</sup> 2− even in the presence of NaCl. At the same time, the RDF peak intensity of Nd3+-CO<sup>3</sup> 2− in the presence of NaCl was slightly lower than that in the single Na2CO<sup>3</sup> solution. The difference of RDF peak intensity indicated that the additional NaCl had an influence on the interaction between Nd3+ and CO<sup>3</sup> <sup>2</sup>−. From the point of view of coordination number, with the presence of the additional NaCl the average coordination number around Nd3+ was about 1.83 CO<sup>3</sup> <sup>2</sup>−, which was lower than the average coordination number of 2.50 in the single Na2CO<sup>3</sup> solution. The reason for the decrease of coordination number may be that part of Cl<sup>−</sup> occupied the coordination layer of Nd3+ in the metastable period, causing the decrease in the average coordination number between Nd3+ and CO<sup>3</sup> <sup>2</sup>−. This is consistent with Figure 6a.

reason to speculate that in the metastable state, Cl− participated in the coordination reaction and temporarily occupied the coordination layer of Nd3+, and then was re-released into the solution with the passage of time. When the metastable period ended, the Cl− in the coordination layer of Nd3+ had been exhausted. A diagram of Nd3+, Cl− and CO32− coordination in the metastable state is shown in Figure 7. To quantitatively explain the coordination between Nd3+ and Cl<sup>−</sup> in the mixed electrolyte, the RDF and the coordination number were further analyzed and calculated. Figure 6c shows that the RDF peak at 2.275 Å within the range of chemical bond (<2.6 Å) was clearly observed from the spectrum of the Nd3+-Cl<sup>−</sup> ion pair in the mixed electrolyte solution of NaCl/Na2CO3. One Nd3+ was coordinated with about one Cl−. In contrast to the single Na2CO<sup>3</sup> solution, there was insignificant evidence of an interaction existing between Cl− and Nd3+. Hence, it was proved that that Cl<sup>−</sup> could coordinate with Nd3+ in the presence of NaCl during the metastable period.

It is worth noting that the RDF peak position of Nd3+-CO<sup>3</sup> <sup>2</sup><sup>−</sup> was earlier than that of Nd3+-Cl−. The result indicates that CO<sup>3</sup> <sup>2</sup><sup>−</sup> tends to occupy the coordination layer of Nd3+ and reacted with it first, then Cl<sup>−</sup> entered the coordination layer of Nd3+, although, previous studies [11,24] showed that in an environment of high concentration of CO<sup>3</sup> 2− solution, Cl<sup>−</sup> did not coordinate with Nd3+ in a steady state. However, our result does not conflict with these previous studies because of the difference between metastable and steady states. In addition, when the placement time exceeded the metastable period, the precipitate

was still consistent with that obtained in the steady state. Therefore, there is sufficient reason to speculate that in the metastable state, Cl− participated in the coordination reaction and temporarily occupied the coordination layer of Nd3+, and then was re-released into the solution with the passage of time. When the metastable period ended, the Cl− in the coordination layer of Nd3+ had been exhausted. A diagram of Nd3+, Cl<sup>−</sup> and CO<sup>3</sup> 2− coordination in the metastable state is shown in Figure 7. *Minerals* **2021**, *11*, x FOR PEER REVIEW 10 of 13

**Figure 7.** Coordination process of Nd3+ in the NaCl/Na2CO3 mixed electrolyte solution. **Figure 7.** Coordination process of Nd3+ in the NaCl/Na2CO<sup>3</sup> mixed electrolyte solution.

The concentration of free CO32− in solution was another key factor affecting the existence of metastable states. To explore the interaction between Na+ and CO32− in the solution in the presence of additional NaCl, the RDF of the Na+-CO32− ion pair and its average coordination number were also analyzed and calculated. The results in Figure 6d show that there was interaction between Na+ and CO32− in the mixed electrolyte solution, and the position of the RDF peak was basically the same as that in single Na2CO3 solution. The average coordination number was about 1.14 CO32− around a Na+ ion in the solution with additional NaCl, which was not much different from the corresponding blank solution number of 1.17. However, the value was lower than the value of 1.30 in a single Na2CO3 The concentration of free CO<sup>3</sup> <sup>2</sup><sup>−</sup> in solution was another key factor affecting the existence of metastable states. To explore the interaction between Na<sup>+</sup> and CO<sup>3</sup> <sup>2</sup><sup>−</sup> in the solution in the presence of additional NaCl, the RDF of the Na<sup>+</sup> -CO<sup>3</sup> <sup>2</sup><sup>−</sup> ion pair and its average coordination number were also analyzed and calculated. The results in Figure 6d show that there was interaction between Na<sup>+</sup> and CO<sup>3</sup> <sup>2</sup><sup>−</sup> in the mixed electrolyte solution, and the position of the RDF peak was basically the same as that in single Na2CO<sup>3</sup> solution. The average coordination number was about 1.14 CO<sup>3</sup> <sup>2</sup><sup>−</sup> around a Na<sup>+</sup> ion in the solution with additional NaCl, which was not much different from the corresponding blank solution number of 1.17. However, the value was lower than the value of 1.30 in a single Na2CO<sup>3</sup> solution.

solution. The existence of this difference does not mean that the degree of dissociation of Na+- CO32− ion pairs in the mixed electrolyte solution was higher because of the introduction of Na+ via the addition of NaCl. The introduced Na+ would also tend to interact with CO32−, reducing the average coordination number. In this regard, the conversion calculation of the number of Na+ ions around the CO32− is a better illustration of the problem, as listed in The existence of this difference does not mean that the degree of dissociation of Na<sup>+</sup> - CO<sup>3</sup> <sup>2</sup><sup>−</sup> ion pairs in the mixed electrolyte solution was higher because of the introduction of Na<sup>+</sup> via the addition of NaCl. The introduced Na<sup>+</sup> would also tend to interact with CO<sup>3</sup> <sup>2</sup>−, reducing the average coordination number. In this regard, the conversion calculation of the number of Na<sup>+</sup> ions around the CO<sup>3</sup> <sup>2</sup><sup>−</sup> is a better illustration of the problem, as listed in Table 4.


Table 4 shows that the distribution of Na+ around CO32− in mixed electrolyte and single Na2CO3 solutions was the same at a cutoff distance of 2.575 Å (within chemical bond range), which was 2.57 Na+ around CO32−. The total number of Na+ was 630 in the mixed

additional NaCl. Even so, the distribution of Na+ around CO32− was almost the same. This means that the dissociation degree of the Na+-CO32− ion pairs with the additional NaCl should be much lower than that in the single Na2CO3 solution. Therefore, the additional

Table 4. **Table 4.** Distribution of Na<sup>+</sup> around CO<sup>3</sup> <sup>2</sup><sup>−</sup> in the solution.

tem.

(**b**).

Table 4 shows that the distribution of Na<sup>+</sup> around CO<sup>3</sup> <sup>2</sup><sup>−</sup> in mixed electrolyte and single Na2CO<sup>3</sup> solutions was the same at a cutoff distance of 2.575 Å (within chemical bond range), which was 2.57 Na<sup>+</sup> around CO<sup>3</sup> <sup>2</sup>−. The total number of Na<sup>+</sup> was 630 in the mixed electrolyte, higher than that of 580 in a single Na2CO<sup>3</sup> solution, due to the existence of additional NaCl. Even so, the distribution of Na<sup>+</sup> around CO<sup>3</sup> <sup>2</sup><sup>−</sup> was almost the same. This means that the dissociation degree of the Na<sup>+</sup> -CO<sup>3</sup> <sup>2</sup><sup>−</sup> ion pairs with the additional NaCl should be much lower than that in the single Na2CO<sup>3</sup> solution. Therefore, the additional NaCl could also affect the interaction of Na<sup>+</sup> -CO<sup>3</sup> <sup>2</sup><sup>−</sup> ion pairs, further reducing the concentration of free CO<sup>3</sup> <sup>2</sup>−. Thus, the delayed the formation of neodymium carbonates was delayed and the metastable period was extended. NaCl could also affect the interaction of Na+-CO32− ion pairs, further reducing the concentration of free CO32−. Thus, the delayed the formation of neodymium carbonates was delayed and the metastable period was extended. *3.2. Induced Precipitation of Neodymium Carbonates in Metastable State Solution*  In theory, if the system dominated by CO32− in the solution could be rapidly transformed into the coexistence of HCO3− and CO32−, a rapid destruction of metastable state could be achieved and most of the dissolved neodymium could be separated from the solution via a self-precipitation. Theoretically, introduction of acidic CO2 gas into the so-

#### *3.2. Induced Precipitation of Neodymium Carbonates in Metastable State Solution* lution, as shown in Equation (4), would neutralize the original alkaline Na2CO3 solution

*Minerals* **2021**, *11*, x FOR PEER REVIEW 11 of 13

In theory, if the system dominated by CO<sup>3</sup> <sup>2</sup><sup>−</sup> in the solution could be rapidly transformed into the coexistence of HCO<sup>3</sup> − and CO<sup>3</sup> <sup>2</sup>−, a rapid destruction of metastable state could be achieved and most of the dissolved neodymium could be separated from the solution via a self-precipitation. Theoretically, introduction of acidic CO<sup>2</sup> gas into the solution, as shown in Equation (4), would neutralize the original alkaline Na2CO<sup>3</sup> solution so that the induction of neodymium carbonate from the metastable solution might be more quickly achieved. so that the induction of neodymium carbonate from the metastable solution might be more quickly achieved. Na2CO3(aq) + CO2(g) + H2O(l) = 2NaHCO3(aq) (4) The specific experimental results in Figure 8a show that the metastable state was rapidly terminated after the introduction of CO2 gas. The concentration of dissolved Nd3+ in the solution fell rapidly, and neodymium carbonate precipitate were generated and separated from the solution. After gassing with CO2 for only 5 min, the Nd3+ concentration in

$$\mathrm{Na\_2CO\_{3(aq)}} + \mathrm{CO\_{2(g)}} + \mathrm{H\_2O\_{(l)}} = 2\mathrm{NaHCO\_{3(aq)}}\tag{4}$$

The specific experimental results in Figure 8a show that the metastable state was rapidly terminated after the introduction of CO<sup>2</sup> gas. The concentration of dissolved Nd3+ in the solution fell rapidly, and neodymium carbonate precipitate were generated and separated from the solution. After gassing with CO<sup>2</sup> for only 5 min, the Nd3+ concentration in the solution decreased from 2.621 to 1.793 g·L −1 , and the precipitation rate reached 31.60%. When the ventilation time was extended to 30 min, only 0.239 g·L <sup>−</sup><sup>1</sup> was left in the solution, and the precipitation rate of Nd3+ reached 90.87%. When the ventilation time reached 60 min, the neodymium concentration in the solution further decreased from 0.239 g·L <sup>−</sup><sup>1</sup> at 30 min to 0.138 g·<sup>L</sup> −1 , and the precipitation rate slowly increased from 90.78% to almost 95%. The results indicate that Nd3+ in the solution entered the insoluble solid phase and was separated from the solution via self-precipitation. and the precipitation rate of Nd3+ reached 90.87%. When the ventilation time reached 60 min, the neodymium concentration in the solution further decreased from 0.239 g·L−1 at 30 min to 0.138 g·L−1, and the precipitation rate slowly increased from 90.78% to almost 95%. The results indicate that Nd3+ in the solution entered the insoluble solid phase and was separated from the solution via self-precipitation. Acid-base titration analysis was carried out to determine the concentration of CO32<sup>−</sup> and HCO3− in the solution after CO2 was injected. Figure 8b shows that the concentration of CO32− in the solution decreased with increasing CO2 introduction time. The concentration of HCO3− showed an upward trend during the introduction of CO2, and the system gradually changed from a single CO32−-dominated to a CO32− and HCO3−-dominated sys-

**Figure 8.** The concentration of dissolved Nd3+ in the solution and the precipitation rate with the ventilation time of CO2 (**a**), and the concentration of CO32<sup>−</sup>/HCO3<sup>−</sup> with the ventilation time of CO2 **Figure 8.** The concentration of dissolved Nd3+ in the solution and the precipitation rate with the ventilation time of CO<sup>2</sup> (**a**), and the concentration of CO<sup>3</sup> <sup>2</sup>−/HCO<sup>3</sup> − with the ventilation time of CO<sup>2</sup> (**b**).

When the CO2 introduction time reached 5 min, the concentration of HCO3− in the solution approached 0.286 mol·L−1 and the corresponding concentration of CO32− was 1.331 mol·L−1, which was much lower than the initial value of 2 mol·L−1. After 60 min, the concentration of HCO3− in the solution increased than several times and reached about 0.816 Acid-base titration analysis was carried out to determine the concentration of CO<sup>3</sup> 2− and HCO<sup>3</sup> − in the solution after CO<sup>2</sup> was injected. Figure 8b shows that the concentration of CO<sup>3</sup> <sup>2</sup><sup>−</sup> in the solution decreased with increasing CO<sup>2</sup> introduction time. The concentration of HCO<sup>3</sup> − showed an upward trend during the introduction of CO2, and the system gradually changed from a single CO<sup>3</sup> <sup>2</sup>−-dominated to a CO<sup>3</sup> <sup>2</sup><sup>−</sup> and HCO<sup>3</sup> −-dominated system.

mol·L−1. Besides, the corresponding concentration of CO32− was reduced to 1.018 mol·L−1, and the solution system could no longer be considered to be dominated by single CO32−,

When the CO<sup>2</sup> introduction time reached 5 min, the concentration of HCO<sup>3</sup> − in the solution approached 0.286 mol·L <sup>−</sup><sup>1</sup> and the corresponding concentration of CO<sup>3</sup> <sup>2</sup><sup>−</sup> was 1.331 mol·L −1 , which was much lower than the initial value of 2 mol·L −1 . After 60 min, the concentration of HCO<sup>3</sup> − in the solution increased than several times and reached about 0.816 mol·L −1 . Besides, the corresponding concentration of CO<sup>3</sup> <sup>2</sup><sup>−</sup> was reduced to 1.018 mol·L −1 , and the solution system could no longer be considered to be dominated by single CO<sup>3</sup> <sup>2</sup>−, but both CO<sup>3</sup> <sup>2</sup><sup>−</sup> and HCO<sup>3</sup> −. The reason was that the solution of NaCl/Na2CO<sup>3</sup> mixed electrolyte with higher basicity spontaneously absorbed acidic CO<sup>2</sup> gas, resulting in the conversion of CO<sup>3</sup> <sup>2</sup><sup>−</sup> to HCO<sup>3</sup> − in a short time.

After introducing CO2, the concentration of CO<sup>3</sup> <sup>2</sup><sup>−</sup> in the solution decreased, but the solution volume was almost unchanged. In other words, it was equivalent to diluting the solution. It is well known that ion pairs dissociate more completely in dilute solution. Thus, there is no doubt that the concentration of free CO<sup>3</sup> <sup>2</sup><sup>−</sup> in the solution was increased, and it is important that CO<sup>2</sup> could induce the precipitation of neodymium carbonate in the metastable state solution. In addition, the concentration of CO<sup>3</sup> <sup>2</sup><sup>−</sup> decreased as CO<sup>2</sup> introduction time and the precipitation rate of neodymium carbonate increased. Therefore, the introduction of carbon dioxide into metastable solutions is a new potential method for the separation of rare earths. This is because carbon dioxide is nonpolluting and does not introduce other ion impurities as with the use of precipitants (e.g., ammonium carbon, which is commonly used in industry, introduces ammonium ions). In addition, the separation is achieved by the rapid production of rare earth precipitation in a short time after its entry into the solution.

#### **4. Conclusions**

We chose neodymium as an example of a rare earth element and studied the maintenance of the metamorphic state of Na2CO<sup>3</sup> solution with dissolved Nd3+. The results show that the metastable state can be successfully prolonged by adding sodium chloride. In addition, the introduction of carbon dioxide is an effective way to terminate the metastable state and generate neodymium carbonate.

The main conclusions are as follows. (1) The higher the additional NaCl concentration, the longer the metastable period, because the additional NaCl affects the interaction of Na<sup>+</sup> - CO<sup>3</sup> <sup>2</sup>−-ion pairs and influences the concentration of free CO<sup>3</sup> <sup>2</sup><sup>−</sup> in the solution. (2) The Cl− introduced by the high concentration of NaCl can occupy the coordination layer of Nd3+ temporarily and delay the formation of rare earth carbonate precipitation. (3) After introduction of CO<sup>2</sup> gas, the existing environment of the solution directly changes in a short time from a single CO<sup>3</sup> <sup>2</sup>−-dominated system to a predominantly CO<sup>3</sup> <sup>2</sup><sup>−</sup> and HCO3− dominated system. As a result, the metamorphic state of the solution is quickly terminated and the precipitation of Nd carbonate is advanced.

**Author Contributions:** Conceptualization, K.L.; data curation, X.Z.; formal analysis, Y.M.; funding acquisition, Y.Y.; investigation, K.L.; methodology, K.L.; project administration, Y.Y.; validation, F.N.; visualization, K.L.; writing—original draft, K.L.; writing—review & editing, L.W. and D.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China, grant number 51774155, and The APC was funded by 51774155.

**Data Availability Statement:** Not Applicable.

**Acknowledgments:** The authors gratefully acknowledge the financial supports of the Program of National Natural Science Foundation of China (51774155).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

1. Takagi, K.; Hirayama, Y.; Okada, S.; Yamaguchi, W.; Ozaki, K. Novel powder processing technologies for production of rare-earth permanent magnets. *Sci. Technol. Adv. Mater.* **2021**, *22*, 150–159. [CrossRef] [PubMed]

