# Solid-Liquid Phase Equilibria of the Quaternary System (LiCl + LiBO2 + Li2B4O7 + H2O) at 308.15 K: Experimental and Theoretical Prediction

Authors: Hongya Shen; Qi Liu; Xiuxiu Yang; Yafei Guo; Dan Li; Lingzong Meng; Tianlong Deng
Journal: Journal of Chemistry
 (2022)

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## Abstract

The isothermal dissolution equilibrium method was employed to obtain the solubilities and physicochemical properties of the quaternary system (LiCl + LiBO2 + Li2B4O7 + H2O) at 308.15 K in this work. The dry-salt phase diagram, water-phase diagram, and physicochemical properties, including density, refractive index, and pH against composition in the quaternary system, were established for the first time. The dry-salt phase diagram includes two invariant points, five univariate solubility curves, and four single salt crystalline phase regions (LiCl·H2O, LiBO2·2H2O, LiBO2·8H2O and Li2B4O7·3H2O), respectively. In addition, the physicochemical properties of density, refractive index, and pH in the system change regularly with the changing of the lithium metaborate concentration. Based on the Pitzer model, the mixing ion parameters of θCl,B4O5(OH)4, θB(OH)4,B4O5(OH)4 and Ψ(Li,Cl,B4O5(OH)4, ΨLi,B (OH)4,B4O5(OH)4 and the predictive solubilities in the quaternary system were fitted. Although there is a slight deviation between the calculated and experimental values, the solubility of boron in the quaternary system agrees well, which provides data support for the study of the solubility of boron.


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## Body

## 1. Introduction

Qinghai Salt Lake is rich in lithium and boron resources, which have high mining value [1]. After the brine evaporates, a large amount of NaCl and KCl are precipitated [2], and the composition of brine can be regarded as a complex brine system (Li+, Mg2+//Cl−, SO42−, Borate–H2O) [3]. The exploitation of lithium from brine resources has become a hot research spot [4, 5]. Since boron in brine is usually borate, it also changes correspondingly with the difference in pH value, coexisting ions, and solution concentration [6]. Therefore, studying the phase equilibria of brine systems with different forms of lithium boron components, especially the deep processing of lithium borate resources, has important strategic significance for the development and utilization of salt lake resources to create high-value-added products and realize the diversification of salt lake products [7–9].In recent years, owing to the existence of various forms of borate in solution, extensive literature reports have been done on the phase equilibria of boron-containing complex brine systems at different temperatures, for example, (KBO2 + K2SO4 + H2O) system at 288.15 and 308.15 K [10], (Li2SO4 + LiBO2 + Li2B4O7 + H2O) system at 288.15 K [11], (Li2B4O7 + K2B4O7 + RbB5O8 + H2O) system at 323 K [12], (LiCl + LiB5O8 + H2O) and (Li2SO4 + LiB5O8 + H2O) systems at 298.15 K [13]. The temperature in the Qinghai salt lake region can reach 308.15 K in summer [14]. Therefore, the phase equilibria study of this brine system has a certain theoretical reference value for the rational development of salt lake resources with solar ponds technology. Although some subsystems such as (LiCl + LiBO2 + H2O) at 288.15, 298.15, 308.15 K and 323.15 K [15–17] and (LiBO2 + Li2B4O7 + H2O) at 288.15, 298.15 and 323.15 K [11, 18] have been reported, the phase equilibrium of the quaternary system (LiCl + LiBO2 + Li2B4O7 + H2O) has not been reported in the literature. On the other hand, the Pitzer model based on binary and ternary systems has been widely used to calculate the theoretical solubility of salt–water systems [18–20]. Unfortunately, the literature did not report several ion-interaction parameters for the system (LiCl + LiBO2 + Li2B4O7 + H2O). Therefore, this paper not only presents the solubility and physicochemical properties of the system (LiCl + LiBO2 + Li2B4O7 + H2O) at 308.15 K but also presents a predictive calculation of the solubility after obtaining the mixing ion-interaction parameters using the Pitzer model.


## 2. Experimental

### 2.1. Apparatus and Materials

It can be seen from Table1 that the purity of the reagents used in this experiment was analytically pure. During this work, deionized distilled water (DDW) was used to prepare a series of artificially synthesized brines and chemical analyses, with conductivity (κ) less than or equal to 1.2 × 10−4 S·m−1.Table 1
Relevant reagents used in this work.
Chemical nameCAS reg. NO.GradeInitial mass fraction purityPurification methodFinal mass fraction purityAnalysis methodaLiCl·H2O10102-25-7AR.0.99Recrystallization0.992Titration for Cl-bLiBO2·8H2O63454-43-3AR.0.99Recrystallization0.992Titration for BO2-cLi2B4O712007-60-2AR.0.99Recrystallization0.992Titration for B4O72-aAR from Shanghai Macklin Biochemical Technology Co., Ltd. bAR from Sinopharm Chemical Reagent Co., Ltd. cAR from Sinopharm Chemical Reagent Co., Ltd.The solution reached solid-liquid equilibrium by the constant temperature magnetic stirring thermostat (HXC-500-6A, Beijing Fortune Joy Sci. Technology. Co., Ltd.) with a measurement accuracy of 0.1 K. The densities of solution and water were measured by a densitometer (DMA 4500, Anton Paar, Austria) with a measurement accuracy of 0.5 mg·cm−3, and the refractive index (nD) was measured using an Abbe refractometer (Abbemat 550, Shanghai Trading Co., Ltd.) having an instrument deviation of 0.0003. A high sensitivity pH meter (PH-7310, WTW Co., Ltd. Germany) accurately measured pH values with an error of ±0.001. X-ray powder diffraction with a scan rate of 400°·min−1 and a test range of 10–80° (Smartlab, Rigaku, Japan) is used to identify the solid phases. In this work, all experimental data was measured in triplicate and the average was chosen.


### 2.2. Experimental Methods

After checking the solubility data of the common saturation point of the subsystem in this system, the third salt was mixed in a series of Teflon bottles with a volume of 250 cm3 from the common saturation point of the ternary system with a certain gradient by isothermal solution equilibrium method. LiCl with mass gradient and the quantitative water were added from the common saturation point of LiBO2·8H2O and Li2B4O7·3H2O to form a complex. It was put into a constant temperature water bath magnetic stirring tank. The water bath temperature was controlled at (308.15 ± 1) K. Set the stirring speed at 200 rpm to accelerate the formation of the equilibrium. After continuous stirring for about 50 days, when the liquid and solid phases were separated, an appropriate amount of sample was subsequently taken with a clean pipette for analysis. After the remaining samples were continuously stirred for about 60 days, an aliquot of the supernatant solution was taken for reanalysis. When the relative error of the analytical results for the sampling of different solutions (the concentrations of Li+, Cl−, BO2− and B4O72−) was within 0.003 [21], it proved that the brine reached equilibrium. Subsequently, the physicochemical properties of the liquid phase were analyzed by refractive index, density, and pH, corresponding to those of the solid phase studied by X-ray powder diffraction, respectively.


### 2.3. Analytical Methods

For the quaternary system (LiCl + LiBO2 + Li2B4O7 + H2O), the mercury titration method was used to measure the concentration of chloride ions with diphenylazocarbazide and bromophenol blue as indicators, and the error of the measurement value was less than 0.003 in a mass fraction [22]. The content of boron was analyzed by a modified mannitol titration with a relative uncertainty of ±0.0005 and recorded as a mass fraction [22]. And the lithium-ion concentration in the solution was measured by ICP-OES (Prodigy, Teledyne Leeman Labs, USA) [11]. Due to the diverse existence of boron in aqueous solutions [6], only the total boron concentration can be measured. However, lithium metaborate and lithium tetraborate as the initial reagents are also the solid equilibrium phases in this experiment. Therefore, we assume that only B(OH)4− and B4O5(OH)42− are present in the solution to measure solubility. Combining the concentrations of lithium and boron, the concentrations of two borates LiBO2 and Li2B4O7 are calculated with Eqs. (1) and (2).(1)x+2y=nLi−nLiCl,(2)x+4y=nB,where x, y and nLiCl are the molar concentrations of LiBO2, Li2B4O7 and LiCl, respectively, and nLi is the total molar concentration of Li+ in the system. Similarly, nB is boron (BO2−, B4O72−) ions of the total molar concentration. Considering the influence of reagent impurity, temperature fluctuation and concentration measurement errors, the standard uncertainty of LiCl concentration was less than 0.003. The uncertainty of LiBO2 and Li2B4O7 concentrations did not exceed 0.005.


## 2.1. Apparatus and Materials

It can be seen from Table1 that the purity of the reagents used in this experiment was analytically pure. During this work, deionized distilled water (DDW) was used to prepare a series of artificially synthesized brines and chemical analyses, with conductivity (κ) less than or equal to 1.2 × 10−4 S·m−1.Table 1
Relevant reagents used in this work.
Chemical nameCAS reg. NO.GradeInitial mass fraction purityPurification methodFinal mass fraction purityAnalysis methodaLiCl·H2O10102-25-7AR.0.99Recrystallization0.992Titration for Cl-bLiBO2·8H2O63454-43-3AR.0.99Recrystallization0.992Titration for BO2-cLi2B4O712007-60-2AR.0.99Recrystallization0.992Titration for B4O72-aAR from Shanghai Macklin Biochemical Technology Co., Ltd. bAR from Sinopharm Chemical Reagent Co., Ltd. cAR from Sinopharm Chemical Reagent Co., Ltd.The solution reached solid-liquid equilibrium by the constant temperature magnetic stirring thermostat (HXC-500-6A, Beijing Fortune Joy Sci. Technology. Co., Ltd.) with a measurement accuracy of 0.1 K. The densities of solution and water were measured by a densitometer (DMA 4500, Anton Paar, Austria) with a measurement accuracy of 0.5 mg·cm−3, and the refractive index (nD) was measured using an Abbe refractometer (Abbemat 550, Shanghai Trading Co., Ltd.) having an instrument deviation of 0.0003. A high sensitivity pH meter (PH-7310, WTW Co., Ltd. Germany) accurately measured pH values with an error of ±0.001. X-ray powder diffraction with a scan rate of 400°·min−1 and a test range of 10–80° (Smartlab, Rigaku, Japan) is used to identify the solid phases. In this work, all experimental data was measured in triplicate and the average was chosen.


## 2.2. Experimental Methods

After checking the solubility data of the common saturation point of the subsystem in this system, the third salt was mixed in a series of Teflon bottles with a volume of 250 cm3 from the common saturation point of the ternary system with a certain gradient by isothermal solution equilibrium method. LiCl with mass gradient and the quantitative water were added from the common saturation point of LiBO2·8H2O and Li2B4O7·3H2O to form a complex. It was put into a constant temperature water bath magnetic stirring tank. The water bath temperature was controlled at (308.15 ± 1) K. Set the stirring speed at 200 rpm to accelerate the formation of the equilibrium. After continuous stirring for about 50 days, when the liquid and solid phases were separated, an appropriate amount of sample was subsequently taken with a clean pipette for analysis. After the remaining samples were continuously stirred for about 60 days, an aliquot of the supernatant solution was taken for reanalysis. When the relative error of the analytical results for the sampling of different solutions (the concentrations of Li+, Cl−, BO2− and B4O72−) was within 0.003 [21], it proved that the brine reached equilibrium. Subsequently, the physicochemical properties of the liquid phase were analyzed by refractive index, density, and pH, corresponding to those of the solid phase studied by X-ray powder diffraction, respectively.


## 2.3. Analytical Methods

For the quaternary system (LiCl + LiBO2 + Li2B4O7 + H2O), the mercury titration method was used to measure the concentration of chloride ions with diphenylazocarbazide and bromophenol blue as indicators, and the error of the measurement value was less than 0.003 in a mass fraction [22]. The content of boron was analyzed by a modified mannitol titration with a relative uncertainty of ±0.0005 and recorded as a mass fraction [22]. And the lithium-ion concentration in the solution was measured by ICP-OES (Prodigy, Teledyne Leeman Labs, USA) [11]. Due to the diverse existence of boron in aqueous solutions [6], only the total boron concentration can be measured. However, lithium metaborate and lithium tetraborate as the initial reagents are also the solid equilibrium phases in this experiment. Therefore, we assume that only B(OH)4− and B4O5(OH)42− are present in the solution to measure solubility. Combining the concentrations of lithium and boron, the concentrations of two borates LiBO2 and Li2B4O7 are calculated with Eqs. (1) and (2).(1)x+2y=nLi−nLiCl,(2)x+4y=nB,where x, y and nLiCl are the molar concentrations of LiBO2, Li2B4O7 and LiCl, respectively, and nLi is the total molar concentration of Li+ in the system. Similarly, nB is boron (BO2−, B4O72−) ions of the total molar concentration. Considering the influence of reagent impurity, temperature fluctuation and concentration measurement errors, the standard uncertainty of LiCl concentration was less than 0.003. The uncertainty of LiBO2 and Li2B4O7 concentrations did not exceed 0.005.


## 3. Results and Discussion

### 3.1. Phase Diagram of the Quaternary System (LiCl + LiBO2 + Li2B4O7 + H2O)

Table2 shows the solubility of the liquid equilibrium phase in the quaternary system (LiCl + LiBO2 + Li2B4O7 + H2O) at 308.15 K, where the Jänecke dry-salt index (Zi) is calculated from the mass fraction (w) using equations (3)–(6). Z (B) is calculated based on 100 g of total dry salt, and the specific calculation method is shown in the following formula [22].(3)ZLiCl=wLiClwLiCl+wLiBO2+wLi2B4O7,(4)ZLiBO2=wLiBO2wLiCl+wLiBO2+wLi2B4O7,(5)ZLi2B4O7=wLi2B4O7wLiCl+wLiBO2+wLi2B4O7,(6)ZH2O=wH2OwLiCl+wLiBO2+wLi2B4O7.Table 2
Solubilities in the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K and 0.1 MPa.a
No.Composition of the liquid phase, 100wbComposition of the liquid phase, 100Z/[(g/100 g of salt)]Solid phasedLiClLiBO2Li2B4O7Z (LiCl)Z (LiBO2)Z (Li2B4O7)Z (H2O)1, Ae44.258.250.0084.2915.710.0090.48LC + LB2244.117.470.1285.3214.450.2393.42LC + LB2343.587.060.2085.7213.890.3996.70LC + LB24, Be3.745.180.0041.9358.070.001021.08LB2 + LB853.654.430.1244.5154.031.461119.51LB2 + LB863.564.090.1745.5352.302.171178.77LB2 + LB87, C46.660.000.2199.550.000.45113.36LC + LB4845.701.430.2396.493.020.49111.15LC + LB4944.943.090.2293.146.400.46107.25LC + LB41044.354.950.2489.529.990.49101.86LC + LB411, F143.696.440.2586.2913.220.4997.51LC + LB4 + LB21224.865.970.2480.0119.220.77221.85LB4 + LB21315.075.490.2372.4826.411.11381.00LB4 + LB2149.584.990.2464.6933.691.62575.22LB4 + LB2156.624.370.2558.9038.882.22789.68LB4 + LB216, F23.363.870.2644.8651.673.471235.11LB4 + LB2 + LB8172.333.970.2835.4160.334.261419.76LB4 + LB8181.414.660.3521.9672.595.451457.63LB4 + LB819, De0.006.180.450.0093.216.791408.30LB4 + LB8aStandard uncertainties u, u (T) = 0.02 K, u (p) = 0.005 MPa, u (LiCl) = 0.003, u (LiBO2) = 0.005, and u (Li2B4O7) = 0.005. bw, mass fraction. cZ = Jänecke index. dLC: LiCl·H2O; LB8: LiBO2·8H2O; LB4: Li2B4O7·3H2O; LB2: LiBO2·2H2O. eThe solubilities were cited from ref. [16, 18].The boundary points A, B, C and D on the dry basis diagram of the quaternary system are the saturation points of the three ternary subsystems (LiCl + LiBO2 + H2O), (LiCl + Li2B4O7 + H2O) and (LiBO2 + Li2B4O7 + H2O) shown in Figure 1(a). The dry-salt phase diagram in Figure 1 includes two invariant points F1 saturated with LiCl·H2O, LiBO2·2H2O and Li2B4O7·3H2O and F2 saturated with LiBO2·8H2O, LiBO2·2H2O and Li2B4O7·3H2O, five univariant solubility curves corresponding to F1A (LiCl·H2O + LiBO2·2H2O), CF1 (LiCl·H2O + Li2B4O7·3H2O), F1F2 (LiBO2·2H2O + Li2B4O7·3H2O), BF2 (LiBO2·2H2O + LiBO2·8H2O), F2D (LiBO2·8H2O + Li2B4O7·3H2O), and four crystallization fields corresponding to single salts LiCl·H2O, LiBO2·2H2O, LiBO2·8H2O, and Li2B4O7·3H2O. The size of the crystallization area decreases in the order Li2B4O7·3H2O, LiBO2·2H2O, LiBO2·8H2O, and LiCl·H2O. The results show that Li2B4O7·3H2O has the smallest solubility and is easy to crystallize from brine. Figure 1(b) is a partial enlargement of the phase diagram in the quaternary system (LiCl + LiBO2 + Li2B4O7 + H2O). Figure 2shows the X-ray diffraction patterns of the invariant points F1 and F2. Comparing with the characteristic peaks of the standard PDF card, it shows that the salts LiCl·H2O + LiBO2·2H2O + Li2B4O7·3H2O and LiBO2·2H2O + LiBO2·8H2O + Li2B4O7·3H2O coexist at the invariant points F1 and F2.Figure 1
Dry-salt phase diagram of the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K (a) phase diagram; (b) part-enlargement diagram.
(a)(b)Figure 2
XRD patterns of the invariant point F1 (a) and F2 (b) in the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K. (a) Li2B4O7·3H2O + LiBO2·2H2O + LiCl·H2O. (b) Li2B4O7·3H2O + LiBO2·2H2O + LiBO2·8H2O.
(a)(b)Figure3 plots the water content diagram with Z(LiBO2) and Z(H2O) as the abscissa and ordinate. In the univariant solubility curve CA, Z(H2O) has not significantly changed from 113.36 to 90.48. The Z(H2O) in the univariate solubility curve F2B decreases with the increase of Z(LiBO2). The 100Z (H2O) in the curves F1F2 and F2D increases as 100Z (LiBO2) increases, reaching the maximum value of 1471.67 at point D. The 100Z (H2O) is 97.51 and 1235.11 at the invariant points F1 and F2. In general, the concentration of the solution can be judged by the changing trend of the univariant curves.Figure 3
Water content diagram of the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K.


### 3.2. Physicochemical Properties

The relevant physicochemical properties of the electrolyte solution in the quaternary system (LiCl + LiBO2 + Li2B4O7 + H2O), such as density, refractive index and pH value, are shown in Table3. Figure 4 reflects the variation trend of the physicochemical properties in this system with Z(LiBO2). The change rule of densities in Figure 4(a) is roughly consistent with the refractive indices in Figure 4(b). As Z(LiBO2) increases, the values also increase in the curves of CF1 and F1A, reaching their maximum (1.3846 g·cm−3 and 1.4594) at point A. But values sharply decrease in the curves of F1F2, and there are minimums (1.0633 and 1.3454) at point F2. Moreover, the changing trend of the pH curve in Figure 4(c) is different from that of the former two. The pH value in the liquid phase gradually increases from point C (4.14) to point D (10.65). The specific trend of the pH value increases from C to F2 and decreases in the F1A and F2B curves with the increase of Z(LiBO2). The densities, refractive indices, and pH values in the curve of F2D have almost the same trend.Table 3
Physicochemical properties of the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K and 0.1 MPa.a
No.bρ/g·cm−3nDpHExperimental ValueCalculated ValueRelative Error, %Experimental ValueCalculated ValueRelative Error, %1, Ac1.38461.38550.071.45941.4554−0.285.4921.37561.37760.151.45311.45310.005.9331.37031.37080.041.45201.4509−0.086.174, Bc1.07181.07400.201.36071.3556−0.3710.3551.06701.06850.141.35681.3537−0.2310.4261.06421.06560.131.35481.3527−0.1610.477, C1.28151.29180.801.43721.4339−0.234.1481.30981.3059−0.301.44471.4367−0.564.8991.32881.3237−0.391.44741.4406−0.475.51101.34841.3470−0.101.44891.4457−0.226.1211, F11.36751.3644−0.221.45031.4493−0.076.25121.22521.2244−0.071.40771.4054−0.168.39131.15571.1542−0.131.38961.3823−0.539.15141.11391.11440.041.36361.36880.389.79151.09151.0895−0.191.35781.36050.2010.3216, F21.06331.06470.141.34541.35200.4910.50171.06501.0605−0.421.34741.35020.2110.55181.06701.0653−0.161.34831.35090.1910.5619, D1.07261.07780.481.35211.35320.0810.65a Standard uncertainties u, u (T) = 0.02 K, u (p) = 0.005 MPa, u (ρ) = 0.005 g cm−3. u (nD) = 0.002, u (pH) = 0.01. b The no. Column corresponds to the no. Column in Table 2. c The physicochemical properties were cited from ref. [16].Figure 4
Physicochemical properties versus composition diagram of the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K (a) density versus 100Z (LiBO2); (b) refractive index versus 100Z (LiBO2); (c) pH versus 100Z (LiBO2).
(a)(b)(c)Calculate density (ρ) and refractive index (nD) from reported empirical equations [23].(7)lnnDnD0=∑Biwi,lnρρ0=∑Aiwi.In the above formula,ρ and nD are the density values and the refractive indices in the solution. Correspondingly, ρ0 and nD0 represent pure water at 308.15 K, while ρ0 is 0.99484 g·cm−3 and nD0 is 1.33131. Wi expressed the mass fraction of the i-th component in the solution. Ai and Bi, denote constants for the i-th component of the density and refractive index in solution, which can be fitted with the experimental data. For LiCl, LiBO2 and Li2B4O7, Ai is 0.005466, 0.01083, and 0.02935, and Bi is 0.001574, 0.002357, and 0.003915, respectively. Except for a few complicated points, the difference between the calculated results and the measured densities and refractive index do not exceed 0.0080 and 0.0056, respectively, which proves the reliability of the data.


## 3.1. Phase Diagram of the Quaternary System (LiCl + LiBO2 + Li2B4O7 + H2O)

Table2 shows the solubility of the liquid equilibrium phase in the quaternary system (LiCl + LiBO2 + Li2B4O7 + H2O) at 308.15 K, where the Jänecke dry-salt index (Zi) is calculated from the mass fraction (w) using equations (3)–(6). Z (B) is calculated based on 100 g of total dry salt, and the specific calculation method is shown in the following formula [22].(3)ZLiCl=wLiClwLiCl+wLiBO2+wLi2B4O7,(4)ZLiBO2=wLiBO2wLiCl+wLiBO2+wLi2B4O7,(5)ZLi2B4O7=wLi2B4O7wLiCl+wLiBO2+wLi2B4O7,(6)ZH2O=wH2OwLiCl+wLiBO2+wLi2B4O7.Table 2
Solubilities in the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K and 0.1 MPa.a
No.Composition of the liquid phase, 100wbComposition of the liquid phase, 100Z/[(g/100 g of salt)]Solid phasedLiClLiBO2Li2B4O7Z (LiCl)Z (LiBO2)Z (Li2B4O7)Z (H2O)1, Ae44.258.250.0084.2915.710.0090.48LC + LB2244.117.470.1285.3214.450.2393.42LC + LB2343.587.060.2085.7213.890.3996.70LC + LB24, Be3.745.180.0041.9358.070.001021.08LB2 + LB853.654.430.1244.5154.031.461119.51LB2 + LB863.564.090.1745.5352.302.171178.77LB2 + LB87, C46.660.000.2199.550.000.45113.36LC + LB4845.701.430.2396.493.020.49111.15LC + LB4944.943.090.2293.146.400.46107.25LC + LB41044.354.950.2489.529.990.49101.86LC + LB411, F143.696.440.2586.2913.220.4997.51LC + LB4 + LB21224.865.970.2480.0119.220.77221.85LB4 + LB21315.075.490.2372.4826.411.11381.00LB4 + LB2149.584.990.2464.6933.691.62575.22LB4 + LB2156.624.370.2558.9038.882.22789.68LB4 + LB216, F23.363.870.2644.8651.673.471235.11LB4 + LB2 + LB8172.333.970.2835.4160.334.261419.76LB4 + LB8181.414.660.3521.9672.595.451457.63LB4 + LB819, De0.006.180.450.0093.216.791408.30LB4 + LB8aStandard uncertainties u, u (T) = 0.02 K, u (p) = 0.005 MPa, u (LiCl) = 0.003, u (LiBO2) = 0.005, and u (Li2B4O7) = 0.005. bw, mass fraction. cZ = Jänecke index. dLC: LiCl·H2O; LB8: LiBO2·8H2O; LB4: Li2B4O7·3H2O; LB2: LiBO2·2H2O. eThe solubilities were cited from ref. [16, 18].The boundary points A, B, C and D on the dry basis diagram of the quaternary system are the saturation points of the three ternary subsystems (LiCl + LiBO2 + H2O), (LiCl + Li2B4O7 + H2O) and (LiBO2 + Li2B4O7 + H2O) shown in Figure 1(a). The dry-salt phase diagram in Figure 1 includes two invariant points F1 saturated with LiCl·H2O, LiBO2·2H2O and Li2B4O7·3H2O and F2 saturated with LiBO2·8H2O, LiBO2·2H2O and Li2B4O7·3H2O, five univariant solubility curves corresponding to F1A (LiCl·H2O + LiBO2·2H2O), CF1 (LiCl·H2O + Li2B4O7·3H2O), F1F2 (LiBO2·2H2O + Li2B4O7·3H2O), BF2 (LiBO2·2H2O + LiBO2·8H2O), F2D (LiBO2·8H2O + Li2B4O7·3H2O), and four crystallization fields corresponding to single salts LiCl·H2O, LiBO2·2H2O, LiBO2·8H2O, and Li2B4O7·3H2O. The size of the crystallization area decreases in the order Li2B4O7·3H2O, LiBO2·2H2O, LiBO2·8H2O, and LiCl·H2O. The results show that Li2B4O7·3H2O has the smallest solubility and is easy to crystallize from brine. Figure 1(b) is a partial enlargement of the phase diagram in the quaternary system (LiCl + LiBO2 + Li2B4O7 + H2O). Figure 2shows the X-ray diffraction patterns of the invariant points F1 and F2. Comparing with the characteristic peaks of the standard PDF card, it shows that the salts LiCl·H2O + LiBO2·2H2O + Li2B4O7·3H2O and LiBO2·2H2O + LiBO2·8H2O + Li2B4O7·3H2O coexist at the invariant points F1 and F2.Figure 1
Dry-salt phase diagram of the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K (a) phase diagram; (b) part-enlargement diagram.
(a)(b)Figure 2
XRD patterns of the invariant point F1 (a) and F2 (b) in the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K. (a) Li2B4O7·3H2O + LiBO2·2H2O + LiCl·H2O. (b) Li2B4O7·3H2O + LiBO2·2H2O + LiBO2·8H2O.
(a)(b)Figure3 plots the water content diagram with Z(LiBO2) and Z(H2O) as the abscissa and ordinate. In the univariant solubility curve CA, Z(H2O) has not significantly changed from 113.36 to 90.48. The Z(H2O) in the univariate solubility curve F2B decreases with the increase of Z(LiBO2). The 100Z (H2O) in the curves F1F2 and F2D increases as 100Z (LiBO2) increases, reaching the maximum value of 1471.67 at point D. The 100Z (H2O) is 97.51 and 1235.11 at the invariant points F1 and F2. In general, the concentration of the solution can be judged by the changing trend of the univariant curves.Figure 3
Water content diagram of the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K.


## 3.2. Physicochemical Properties

The relevant physicochemical properties of the electrolyte solution in the quaternary system (LiCl + LiBO2 + Li2B4O7 + H2O), such as density, refractive index and pH value, are shown in Table3. Figure 4 reflects the variation trend of the physicochemical properties in this system with Z(LiBO2). The change rule of densities in Figure 4(a) is roughly consistent with the refractive indices in Figure 4(b). As Z(LiBO2) increases, the values also increase in the curves of CF1 and F1A, reaching their maximum (1.3846 g·cm−3 and 1.4594) at point A. But values sharply decrease in the curves of F1F2, and there are minimums (1.0633 and 1.3454) at point F2. Moreover, the changing trend of the pH curve in Figure 4(c) is different from that of the former two. The pH value in the liquid phase gradually increases from point C (4.14) to point D (10.65). The specific trend of the pH value increases from C to F2 and decreases in the F1A and F2B curves with the increase of Z(LiBO2). The densities, refractive indices, and pH values in the curve of F2D have almost the same trend.Table 3
Physicochemical properties of the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K and 0.1 MPa.a
No.bρ/g·cm−3nDpHExperimental ValueCalculated ValueRelative Error, %Experimental ValueCalculated ValueRelative Error, %1, Ac1.38461.38550.071.45941.4554−0.285.4921.37561.37760.151.45311.45310.005.9331.37031.37080.041.45201.4509−0.086.174, Bc1.07181.07400.201.36071.3556−0.3710.3551.06701.06850.141.35681.3537−0.2310.4261.06421.06560.131.35481.3527−0.1610.477, C1.28151.29180.801.43721.4339−0.234.1481.30981.3059−0.301.44471.4367−0.564.8991.32881.3237−0.391.44741.4406−0.475.51101.34841.3470−0.101.44891.4457−0.226.1211, F11.36751.3644−0.221.45031.4493−0.076.25121.22521.2244−0.071.40771.4054−0.168.39131.15571.1542−0.131.38961.3823−0.539.15141.11391.11440.041.36361.36880.389.79151.09151.0895−0.191.35781.36050.2010.3216, F21.06331.06470.141.34541.35200.4910.50171.06501.0605−0.421.34741.35020.2110.55181.06701.0653−0.161.34831.35090.1910.5619, D1.07261.07780.481.35211.35320.0810.65a Standard uncertainties u, u (T) = 0.02 K, u (p) = 0.005 MPa, u (ρ) = 0.005 g cm−3. u (nD) = 0.002, u (pH) = 0.01. b The no. Column corresponds to the no. Column in Table 2. c The physicochemical properties were cited from ref. [16].Figure 4
Physicochemical properties versus composition diagram of the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K (a) density versus 100Z (LiBO2); (b) refractive index versus 100Z (LiBO2); (c) pH versus 100Z (LiBO2).
(a)(b)(c)Calculate density (ρ) and refractive index (nD) from reported empirical equations [23].(7)lnnDnD0=∑Biwi,lnρρ0=∑Aiwi.In the above formula,ρ and nD are the density values and the refractive indices in the solution. Correspondingly, ρ0 and nD0 represent pure water at 308.15 K, while ρ0 is 0.99484 g·cm−3 and nD0 is 1.33131. Wi expressed the mass fraction of the i-th component in the solution. Ai and Bi, denote constants for the i-th component of the density and refractive index in solution, which can be fitted with the experimental data. For LiCl, LiBO2 and Li2B4O7, Ai is 0.005466, 0.01083, and 0.02935, and Bi is 0.001574, 0.002357, and 0.003915, respectively. Except for a few complicated points, the difference between the calculated results and the measured densities and refractive index do not exceed 0.0080 and 0.0056, respectively, which proves the reliability of the data.


## 4. Solubility Prediction

### 4.1. Model Parameterization

Among many complex thermodynamic calculation models of water-salt systems, the Pitzer model is widely used in the calculation of solubility of water-salt systems [16, 24]. However, at present, there is no literature on thermodynamic calculations based on the Pitzer ionic interaction model for quaternary systems (LiCl + LiBO2 + Li2B4O7 + H2O). Therefore, we will use the Pitzer model to fit the solubility data of this system at 308.15 K. The primary expressions for calculating solubility in this model are equations (8) to (10) [24].(8)Φ−1=2∑ii−AΦI3/2I+bI1/2+∑c∑amcmaBcaΦ+ZCca+∑c∑<c′mcmc′Φcc′Φ+∑amaΨcc′a,+∑a∑<a′mama′Φaa′Φ+∑cmcΨcaa′,(9)lnγM=ZM2F+∑ama2BMa+ZCMa+∑cmcΦMc+∑amaΨMca+∑a∑<a′mama′ΨMaa′+zM∑c∑amcmaCca,(10)lnγX=ZM2F+∑cmc2BcX+ZCcX+∑amaΦXa+∑cmcΨcXa+∑c∑<c′mcmc′Ψcc′X+zX∑c∑amcmaCca,where the subscripts M, c, and c′ are the cations in the solution, X, a and a′ are the anions in the solution, Zi represents the valence of the ions, mi refers to the concentration of the substance in the solution (mol·kg−1), Φ and i are the permeability coefficient and activity coefficient. Other symbols in the equations, for instance, F, C, Z, AΦ, BΦ, and B are described in references [25, 26]. However, Debye–Hückel parameter AΦ at 308.15 K is 0.398535 in the study.At a specific temperature and pressure, the solubility equilibrium constant (Ksp) of the hydrated salt for the dissolution reaction can be obtained by the following formula [24].(11)MvMXvX·nH2O=vMMv++vXXv−+nH2O,lnKsp=vMlnmMγM+vXlnmXγX+nlnαW,=vMlnmM+vMlnγM+vX+vXlnγ±+nlnαW,where γM and γX are the activity coefficient, and the mean activity coefficient is denoted by γ±.Boron exists in various forms in borate solution, in which B(OH)4− and B4O5(OH)42− are on behalf of the metaborate and tetraborate ions [6, 27]. In addition, other existing forms of boron lack the relevant Pitzer binary and mixing parameters at 308.15 K, so thermodynamic properties cannot be fitted. Therefore, we only selected B(OH)4− and B4O5(OH)42− two ions for solubility calculations. The single salt parameters of LiCl and LiB(OH)4, and the solubility product constants (Ksp) of LiCl·H2O, LiBO2·2H2O and LiBO2·8H2O were obtained from the literature [16, 28]. The single salt parameters of Li2B4O5(OH)4 at 308.15 K were lacking in the literature, and the temperature is close to 298.15 K, so Deng’s parameters at 298.15 K were chosen in the calculation [29]. The Pitzer mixing parameters θCl,B(OH)4 and φLi,Cl,B(OH)4 were cited from our pervious work [16]. The missing Pitzer mixing parameters θCl,B4O5(OH)4 and φLi,Cl,B4O5(OH)4 were fitted with the solubilities of the system LiCl − Li2B4O7 − H2O at 308.15 K [30]. The parameters θB(OH)4,B4O5(OH)4 and φLi,B(OH)4, B4O5(OH)4 were reported in our previous [31]. However, the calculated solubility data with above parameters for points F1 and F2 show great deviation with the experimental results. The parameters θB(OH)4,B4O5(OH)4 and φLi,B(OH)4, B4O5(OH)4 were adjusted again. The single salt parameters and mixing ion parameters of the system used in the study are shown in Tables 4 and 5.Table 4
Pitzer single salt parameters of electrolyte in the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K.
Parametersα1α2β(0)β(1)β(2)C(Ø)Ref.LiCl——0.14690.31340.003240[26]LiCl2.00.00.2016−0.18790.0−0.004044[12]LiB (OH)41.41.5−0.270641.8193−44.34910.007996[12]Li2B4O5 (OH)42.00.0−0.331042−0.1528130.00000.01012000[27]Table 5
Pitzer mixing parameters in the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K.
SpeciesθΨRef.Cl–,B(OH)4−−0.1781[12]Cl−,B4O5(OH)42−−0.1500This workB(OH)4−, B4O5(OH)42−0.0620This workLi+,Cl−,B(OH)4−0.006856[12]Li+,Cl− B4O5(OH)42−0.0233This workLi+,B(OH)4−, B4O5(OH)42−0.0000This workPitzer mixing parametersθCl,B4O5(OH)4, θB(OH)4,B4O5(OH)4, Ψ(Li,Cl,B4O5(OH)4, and ΨLi+,B(OH)4,4O5(OH)4 mixing parameters in the quaternary system.


### 4.2. Solubility Calculation

Before using the Pitzer model to calculate the solubility of the system (LiCl + LiBO2 + Li2B4O7 + H2O) at 308.15 K, it is necessary to obtain the corresponding Pitzer parameters. It can be seen from the existing literature that when LiCl·H2O, LiBO2·2H2O, LiBO2·8H2O, and Li2B4O7·3H2O are in the dissolution equilibrium, the solubility product constants (lnKsp) are 12.0072, −1.0200, −0.5140, and −7.5511, respectively [31]. We calculated the solubility at 308.15 K by combining the above lnKsp values, Pitzer single parameters and the mixing parameters. Table 6 lists the solubilities for the boundary points and invariant points in the quaternary system (LiCl + LiBO2 + Li2B4O7 + H2O) at 308.15 K, and the corresponding phase diagram is shown in Figure 5. The calculated phase diagram indicated by the red dotted line cannot completely coincide with the experimental data curve. There is an obvious deviation, especially in the solubility curves for LiBO2·8H2O and Li2B4O7·3H2O saturation. The calculated saturation solubility isotherms for LiBO2·8H2O and Li2B4O7·3H2O were still significantly inconsistent with the experimental data despite changing the mixing parameters several times. At point C, the experimental value is closest to the calculated value, and the relative error is the smallest. At the invariant points F1 and F2, the deviation of lithium borate content are larger, while the deviation of lithium chloride is smaller. Therefore, the solubility calculated by the Pitzer model cannot exactly match the experimental value. However, except for curve DF2 in Figure 5, the fitted values on other solubility curves are consistent with the experimental data, indicating that the Pitzer model can explain the solubility changes very well.Table 6
Comparison of experimental and calculated values of invariant points in the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K.a
No.bValueComposition of the liquid phase, 100wbEquilibrium solid phaseLiClLiBO2Li2B4O7CExperimental46.660.000.21LiCl·H2O + Li2B4O5(OH)4·H2OExperimental calculatedCalculated46.660.000.25LiCl·H2O + Li2B4O5(OH)4·H2OExperimental calculatedExperimental0.006.180.45LiB(OH)4·6H2O + Li2B4O5(OH)4·H2OCCalculated0.0010.650.55LiB(OH)4·6H2O + Li2B4O5(OH)4·H2ODExperimental43.696.440.25LiCl·H2O + LiB(OH)4 + Li2B4O5(OH)4·H2ODCalculated43.6911.100.30LiCl·H2O + LiB(OH)4 + Li2B4O5(OH)43H2OF1Experimental3.363.870.26LiB(OH)4 + LiB(OH)4·6H2O + Li2B4O5(OH)4·H2OF1Calculated3.366.670.32LiB(OH)4 + LiB(OH)4·6H2O + Li2B4O5(OH)4·H2OaStandard uncertainties u, u (T) = 0.02 K, u (p) = 0.005 MPa, u (LiCl) = 0.003, u (LiBO2) = 0.005, and u (Li2B4O7) = 0.005. bThe no. Column corresponds to the no. Column in Table 2.Figure 5
Experimental and calculated phase diagram in quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K; red dashed lines for the calculated data, solid black lines for the experimental data.At the F1 point, the maximum deviation between the mass fraction of w(LiCl), w(LiBO2) and w(Li2B4O7) and the theoretical value is 0,0.0466, 0.0005, respectively, and the deviation value at the F2 point is 0,0.028, 0.0006, respectively. However, the variation trend of the solubility curve calculated in Figure 5 is consistent with the experimental results, indicating that the Pitzer model can be used to describe solubility. The error between the experimental value and the calculated value is caused for various reasons. The parameters required in the calculations are derived from different kinds of literature and cannot be matched with each other. In addition, assumed only two boron species of B(OH)4− and B4O5(OH)42−, were used in this system for the calculation, but other boron species may be present in the brine, such as B(OH)3, B3O3(OH)52−, and B3O3(OH)4− [6, 27]. The results show that this assumption is not precise enough. The relative errors for the experimental solubility calculated using the concentration of lithium and boron are a little larger. It is worth noting that the errors between experimental solubility and computed results are unavoidable. Thus, a large number of thermodynamic models for boron-containing systems are necessary to fit the Pitzer model. The concentration of various boron species can be obtained similarly using the concentration between different boron species [6], pH value, reaction equilibrium constant, etc. [32, 33]. In the calculation of the boron ion, its activity coefficient is considered to be 1.0 [6]. The existing literature shows that the reaction equilibrium constants between different boron species have not been reported in the lithium borate system. For this work, we have chosen an approximation of the reaction equilibrium constant for calculation [6]. Figure 6 shows the boron species’ calculated distribution in this quaternary system (LiCl + LiBO2 + Li2B4O7 + H2O), and the main boron species in the different curves vary greatly. In curves DF2 and BF2, the main boron species include B(OH)4− and B4O5(OH)42−. Other types of boron can be ignored. In curve F1F2, the B3O3(OH)4− can be ignored. In curve CF1, B(OH)3 is the main boron species, which may be caused by m(LiCl). Licl solution Is acidic, and as m(LiCl) increases, B(OH)3 is formed by combining B(OH)4− and H+. So, calculations assuming two boron species in solution may not be precise enough. The solubility of lithium borate is the main target of our study rather than the concentration of boron species in this study. Therefore, boron species other than B(OH)4− and B4O5(OH)42− were not considered in this solubility calculation due to the lack of parameters for various boron species at 308.15 K.Figure 6
Boron species distribution in solution in the quaternary system LiCl–− LiBO2–− Li2B4O7–− H2O at 308.15 K.


## 4.1. Model Parameterization

Among many complex thermodynamic calculation models of water-salt systems, the Pitzer model is widely used in the calculation of solubility of water-salt systems [16, 24]. However, at present, there is no literature on thermodynamic calculations based on the Pitzer ionic interaction model for quaternary systems (LiCl + LiBO2 + Li2B4O7 + H2O). Therefore, we will use the Pitzer model to fit the solubility data of this system at 308.15 K. The primary expressions for calculating solubility in this model are equations (8) to (10) [24].(8)Φ−1=2∑ii−AΦI3/2I+bI1/2+∑c∑amcmaBcaΦ+ZCca+∑c∑<c′mcmc′Φcc′Φ+∑amaΨcc′a,+∑a∑<a′mama′Φaa′Φ+∑cmcΨcaa′,(9)lnγM=ZM2F+∑ama2BMa+ZCMa+∑cmcΦMc+∑amaΨMca+∑a∑<a′mama′ΨMaa′+zM∑c∑amcmaCca,(10)lnγX=ZM2F+∑cmc2BcX+ZCcX+∑amaΦXa+∑cmcΨcXa+∑c∑<c′mcmc′Ψcc′X+zX∑c∑amcmaCca,where the subscripts M, c, and c′ are the cations in the solution, X, a and a′ are the anions in the solution, Zi represents the valence of the ions, mi refers to the concentration of the substance in the solution (mol·kg−1), Φ and i are the permeability coefficient and activity coefficient. Other symbols in the equations, for instance, F, C, Z, AΦ, BΦ, and B are described in references [25, 26]. However, Debye–Hückel parameter AΦ at 308.15 K is 0.398535 in the study.At a specific temperature and pressure, the solubility equilibrium constant (Ksp) of the hydrated salt for the dissolution reaction can be obtained by the following formula [24].(11)MvMXvX·nH2O=vMMv++vXXv−+nH2O,lnKsp=vMlnmMγM+vXlnmXγX+nlnαW,=vMlnmM+vMlnγM+vX+vXlnγ±+nlnαW,where γM and γX are the activity coefficient, and the mean activity coefficient is denoted by γ±.Boron exists in various forms in borate solution, in which B(OH)4− and B4O5(OH)42− are on behalf of the metaborate and tetraborate ions [6, 27]. In addition, other existing forms of boron lack the relevant Pitzer binary and mixing parameters at 308.15 K, so thermodynamic properties cannot be fitted. Therefore, we only selected B(OH)4− and B4O5(OH)42− two ions for solubility calculations. The single salt parameters of LiCl and LiB(OH)4, and the solubility product constants (Ksp) of LiCl·H2O, LiBO2·2H2O and LiBO2·8H2O were obtained from the literature [16, 28]. The single salt parameters of Li2B4O5(OH)4 at 308.15 K were lacking in the literature, and the temperature is close to 298.15 K, so Deng’s parameters at 298.15 K were chosen in the calculation [29]. The Pitzer mixing parameters θCl,B(OH)4 and φLi,Cl,B(OH)4 were cited from our pervious work [16]. The missing Pitzer mixing parameters θCl,B4O5(OH)4 and φLi,Cl,B4O5(OH)4 were fitted with the solubilities of the system LiCl − Li2B4O7 − H2O at 308.15 K [30]. The parameters θB(OH)4,B4O5(OH)4 and φLi,B(OH)4, B4O5(OH)4 were reported in our previous [31]. However, the calculated solubility data with above parameters for points F1 and F2 show great deviation with the experimental results. The parameters θB(OH)4,B4O5(OH)4 and φLi,B(OH)4, B4O5(OH)4 were adjusted again. The single salt parameters and mixing ion parameters of the system used in the study are shown in Tables 4 and 5.Table 4
Pitzer single salt parameters of electrolyte in the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K.
Parametersα1α2β(0)β(1)β(2)C(Ø)Ref.LiCl——0.14690.31340.003240[26]LiCl2.00.00.2016−0.18790.0−0.004044[12]LiB (OH)41.41.5−0.270641.8193−44.34910.007996[12]Li2B4O5 (OH)42.00.0−0.331042−0.1528130.00000.01012000[27]Table 5
Pitzer mixing parameters in the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K.
SpeciesθΨRef.Cl–,B(OH)4−−0.1781[12]Cl−,B4O5(OH)42−−0.1500This workB(OH)4−, B4O5(OH)42−0.0620This workLi+,Cl−,B(OH)4−0.006856[12]Li+,Cl− B4O5(OH)42−0.0233This workLi+,B(OH)4−, B4O5(OH)42−0.0000This workPitzer mixing parametersθCl,B4O5(OH)4, θB(OH)4,B4O5(OH)4, Ψ(Li,Cl,B4O5(OH)4, and ΨLi+,B(OH)4,4O5(OH)4 mixing parameters in the quaternary system.


## 4.2. Solubility Calculation

Before using the Pitzer model to calculate the solubility of the system (LiCl + LiBO2 + Li2B4O7 + H2O) at 308.15 K, it is necessary to obtain the corresponding Pitzer parameters. It can be seen from the existing literature that when LiCl·H2O, LiBO2·2H2O, LiBO2·8H2O, and Li2B4O7·3H2O are in the dissolution equilibrium, the solubility product constants (lnKsp) are 12.0072, −1.0200, −0.5140, and −7.5511, respectively [31]. We calculated the solubility at 308.15 K by combining the above lnKsp values, Pitzer single parameters and the mixing parameters. Table 6 lists the solubilities for the boundary points and invariant points in the quaternary system (LiCl + LiBO2 + Li2B4O7 + H2O) at 308.15 K, and the corresponding phase diagram is shown in Figure 5. The calculated phase diagram indicated by the red dotted line cannot completely coincide with the experimental data curve. There is an obvious deviation, especially in the solubility curves for LiBO2·8H2O and Li2B4O7·3H2O saturation. The calculated saturation solubility isotherms for LiBO2·8H2O and Li2B4O7·3H2O were still significantly inconsistent with the experimental data despite changing the mixing parameters several times. At point C, the experimental value is closest to the calculated value, and the relative error is the smallest. At the invariant points F1 and F2, the deviation of lithium borate content are larger, while the deviation of lithium chloride is smaller. Therefore, the solubility calculated by the Pitzer model cannot exactly match the experimental value. However, except for curve DF2 in Figure 5, the fitted values on other solubility curves are consistent with the experimental data, indicating that the Pitzer model can explain the solubility changes very well.Table 6
Comparison of experimental and calculated values of invariant points in the quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K.a
No.bValueComposition of the liquid phase, 100wbEquilibrium solid phaseLiClLiBO2Li2B4O7CExperimental46.660.000.21LiCl·H2O + Li2B4O5(OH)4·H2OExperimental calculatedCalculated46.660.000.25LiCl·H2O + Li2B4O5(OH)4·H2OExperimental calculatedExperimental0.006.180.45LiB(OH)4·6H2O + Li2B4O5(OH)4·H2OCCalculated0.0010.650.55LiB(OH)4·6H2O + Li2B4O5(OH)4·H2ODExperimental43.696.440.25LiCl·H2O + LiB(OH)4 + Li2B4O5(OH)4·H2ODCalculated43.6911.100.30LiCl·H2O + LiB(OH)4 + Li2B4O5(OH)43H2OF1Experimental3.363.870.26LiB(OH)4 + LiB(OH)4·6H2O + Li2B4O5(OH)4·H2OF1Calculated3.366.670.32LiB(OH)4 + LiB(OH)4·6H2O + Li2B4O5(OH)4·H2OaStandard uncertainties u, u (T) = 0.02 K, u (p) = 0.005 MPa, u (LiCl) = 0.003, u (LiBO2) = 0.005, and u (Li2B4O7) = 0.005. bThe no. Column corresponds to the no. Column in Table 2.Figure 5
Experimental and calculated phase diagram in quaternary system LiCl − LiBO2 − Li2B4O7 − H2O at 308.15 K; red dashed lines for the calculated data, solid black lines for the experimental data.At the F1 point, the maximum deviation between the mass fraction of w(LiCl), w(LiBO2) and w(Li2B4O7) and the theoretical value is 0,0.0466, 0.0005, respectively, and the deviation value at the F2 point is 0,0.028, 0.0006, respectively. However, the variation trend of the solubility curve calculated in Figure 5 is consistent with the experimental results, indicating that the Pitzer model can be used to describe solubility. The error between the experimental value and the calculated value is caused for various reasons. The parameters required in the calculations are derived from different kinds of literature and cannot be matched with each other. In addition, assumed only two boron species of B(OH)4− and B4O5(OH)42−, were used in this system for the calculation, but other boron species may be present in the brine, such as B(OH)3, B3O3(OH)52−, and B3O3(OH)4− [6, 27]. The results show that this assumption is not precise enough. The relative errors for the experimental solubility calculated using the concentration of lithium and boron are a little larger. It is worth noting that the errors between experimental solubility and computed results are unavoidable. Thus, a large number of thermodynamic models for boron-containing systems are necessary to fit the Pitzer model. The concentration of various boron species can be obtained similarly using the concentration between different boron species [6], pH value, reaction equilibrium constant, etc. [32, 33]. In the calculation of the boron ion, its activity coefficient is considered to be 1.0 [6]. The existing literature shows that the reaction equilibrium constants between different boron species have not been reported in the lithium borate system. For this work, we have chosen an approximation of the reaction equilibrium constant for calculation [6]. Figure 6 shows the boron species’ calculated distribution in this quaternary system (LiCl + LiBO2 + Li2B4O7 + H2O), and the main boron species in the different curves vary greatly. In curves DF2 and BF2, the main boron species include B(OH)4− and B4O5(OH)42−. Other types of boron can be ignored. In curve F1F2, the B3O3(OH)4− can be ignored. In curve CF1, B(OH)3 is the main boron species, which may be caused by m(LiCl). Licl solution Is acidic, and as m(LiCl) increases, B(OH)3 is formed by combining B(OH)4− and H+. So, calculations assuming two boron species in solution may not be precise enough. The solubility of lithium borate is the main target of our study rather than the concentration of boron species in this study. Therefore, boron species other than B(OH)4− and B4O5(OH)42− were not considered in this solubility calculation due to the lack of parameters for various boron species at 308.15 K.Figure 6
Boron species distribution in solution in the quaternary system LiCl–− LiBO2–− Li2B4O7–− H2O at 308.15 K.


## 5. Conclusion

In this paper, the isothermal solution equilibrium method carried out the phase equilibrium study in the system (LiCl + LiBO2 + Li2B4O7 + H2O) at 308.15 K. According to each experimental data of the measured equilibrium solution, the corresponding phase diagrams were obtained. The dry-salt diagram of the quaternary system includes two invariant points, four single salt crystallization fields for LiCl·H2O, LiBO2·2H2O, LiBO2·8H2O and Li2B4O7·3H2O, and five univariant solubility curves. The densities, refractive indices, and pH values of this system show certain regularity with the increased concentration of lithium metaborate in the solution. In addition, the results calculated by the empirical equation are highly identical to the experimental data. The solubility of this system was calculated based on the Pitzer model combined with the corresponding Pitzer parameters and the solubility product constant of the solid equilibrium phase. There is a certain deviation in the calculated solubility compared with the experimental value in this system. Although the assumption that there are only two boron species in the brine cannot be fully applied to solubility calculations, the results of such calculations are still able to explain the experimental values well. The phase diagrams and thermodynamic model results in the quaternary system (LiCl + LiBO2 + Li2B4O7 + H2O) can not only supplement the database of such boron resources but also provide a theoretical basis for their comprehensive utilization and provide a good theoretical reference value for the construction of general thermodynamic models.



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