Stable and Metastable Phase Equilibria in the Salt-Water Systems

Salt lakes are widely distributed in the world, and some famous salt lake resources are shown in Tables 1 and 2. In China, salt lakes are mainly located in the area of the Qinghai-Xizang (Tibet) Plateau, and the Autonomous Regions of Xinjiang and Inner Mongolia (M.P. Zheng et al., 1989). The composition of salt lake brines can be summarized to the complex salt-water multicomponent system (Li Na – K – Ca Mg H Cl – SO4 – B4O7 – OHHCO3 – CO3 H2O).

Carbonate type: this type belongs to the system (Na -K -Cl -CO 3 -SO 4 -H 2 O), and Atacama Salt Lake in Chile and Zabuye Salt Lake in Tibet are the famous carbonate type of salt lake.The main precipitated minerals are thermonatrite (Na 2 CO 3 •10H 2 O), baking soda (NaHCO 3 ), natron (Na 2 CO 3 •10H 2 O), glauber salt, and halite.
Nitrite type: the brine composition of this type salt lake can be summarized as the system (Na -K -Mg -Cl -NO 3 -SO 4 -H 2 O).The type salt lake main locates in the salt lake area in the northern of Chile among the salt lake group of Andes in the South-America, semi and dry salts in Luobubo and Wuzunbulake Lakes in Xinjiang, the northern of China.There are natratime saltier (NaNO 3 ), niter (KNO 3 ), darapskite ( Borate type: it can be divided into carbonate-borate hypotype and sulphate-borate hypotype.Searles Salt Lake in America, Banguo Lake and Zabuye Salt Lakes in Tibet, China belong to the former, and the brines mostly belong to the system (Na -K -Cl -B 4 O 7 -CO 3 -HCO 3 -SO 4 -H 2 O).In order to prove the industrial development of Searles Lake brines, Teeple (1929) published a monograph after a series of salt-water equilibrium data on Searles lake brine containing carbonate and borate systems.The latter includes Dong-xi-tai Lake, Da-xiao-chaidan Lake and Yiliping Lake in Qinghai Province, Zhachangchaka Lake in Tibet, China.In those lake area, the natural borate minerals of raphite (NaO ) and hydroborate were precipitated (Zheng et al., 1988;Gao et al., 2007).In addition, the concentration of lithium ion exists in the surface brine of salt lakes.

Phase equilibria of salt-water systems
It is essential to study the stable and metastable phase equilibria in multi-component systems at different temperatures for its application in the fields of chemical, chemical engineering such as dissolution, crystallization, distillation, extraction and separation.

The stable phase equilibria of salt-water systems
The research method for the stable phase equilibria of salt-water system is isothermal dissolution method.It is worthy of pointing out that the status of the stable phase equilibrium of salt-water system is the in a sealed condition under stirring sufficiently, and the speed of dissolution and crystallization of equilibrium solid phase is completely equal with the marker of no change for the liquid phase composition.As to the thermodynamic stable equilibrium studies aiming at sea water system (Na -K -Mg -Cl -SO 4 -H 2 O), J.H. Vant'hollf (1912) was in the earliest to report the stable phase diagram at 293.15 K with isothermal dissolution method.
In order to accelerate the exploiting of Qaidam Basin, China, a number of the stable phase equilibria of salt-water systems were published at recent decades (Li et al., 2006;Song, 1998Song, , 2000;;Song & Du, 1986;Song & Yao, 2001, 2003).

The metastable phase equilibria of salt-water systems
However, the phenomena of super-saturation of brines containing magnesium sulfate, borate is often found both in natural salt lakes and solar ponds around the world.Especially for salt lake brine and seawater systems, the natural evaporation is in a autogenetic process with the exchange of energy and substances in the open-ended system , and it is controlled by the radiant supply of solar energy with temperature difference, relative humidity, and air current, etc.In other word, it is impossible to reach the thermodynamic stable equilibrium, and it is in the status of thermodynamic non-equilibrium.
For the thermodynamic non-equilibrium phase diagram of the sea water system as called "solar phase diagram" in the first, N.S.Kurnakov (1938) was in the first to report the experimental diagrams based on the natural brine evaporation, and further called "metastable phase diagram" for the same system (Na -K -Mg -Cl -SO 4 -H 2 O) at (288.15, 298.15, and 308.15)K was reported on the basis of isothermal evaporation method (Jin, et al., 1980(Jin, et al., , 2001(Jin, et al., , 2002;;Sun, 1992).Therefore, the metastable phase equilibria research is essential to predict the crystallized path of evaporation of the salt lake brine.Therefore, in order to separate and utilize the mixture salts effectively by salt-field engineering or solar ponds in Qaidam Basin, studies on the phase equilibria of salt-water systems are focused on the metastable phase equilibria and phase diagrams at present years (Deng et al., 2011;Deng et al., 2008a-g;Deng, et al., 2009a-c;Wang & Deng, 2008, 2010;Li & Deng, 2009;Li et al., 2010;Liu et al., 2011;Meng & Deng, 2011;Guo et al., 2010;Gao & Deng, 2011a-b;Wang et al., 2011a-b).

Solubility prediction for the phase equilibria of salt-water systems
Pitzer and co-workers have developed an ion interaction model and published a series of papers (Pitzer, 1973a(Pitzer, -b, 1974a(Pitzer, -b, 1975(Pitzer, , 1977(Pitzer, , 1995(Pitzer, , 2000;;Pabalan & Pitzer, 1987) which gave a set of expressions for osmotic coefficients of the solution and mean activity coefficient of electrolytes in the solution.Expressions of the chemical equilibrium model for conventional single ion activity coefficients derived are more convenient to use in solubility calculations (Harvie & Weare, 1980;Harvie et al.1984;Felmy & Weare, 1986;Donad & Kean, 1985).
In this chapter, as an example, the stable and metastable phase equilibria in the salt-water system (NaCl -KCl -Na

Apparatus for the stable phase equilibria in the salt-water system
Stable phase equilibria are the thermodynamic equilibria.In order to reach the isothermal dissolve equilibrium, the apparatus mainly contains two parts i.e. constant temperature installing and equilibrator.Therefore, experimental apparatus depends on the target of temperature.Generally, thermostatic water-circulator bath is used under normal atmospheric temperature, and thermostatic oil-circulator bath is chosen at higher level www.intechopen.com Stable and Metastable Phase Equilibria in the Salt-Water Systems 403 temperature.Under low temperature, the refrigerator or freezing saline bath is commonly used.Figure 1 shows the common used equalizer pipe with a stirrer.The artificial synthesis complex put in the pipe to gradually reach equilibria under vigorous stirring.In order to avoid the evaporation of water, the fluid seal installing is needed, and the sampling branch pipe is also needed to seal.Usually, for aqueous quaternary system study, a series of artificial synthesis complex, normally no less than 30, was needed to be done one by one the experimental time consume is equivalence large.At present, a thermostatic shaker whose temperature could controlled with temperature precision of ± 0.1 K can be used for the measurement of stable phase equilibrium (Deng et al., 2002;Deng, 2004).The advantage is that a series artificial synthesis complexes which is loading in each sealed bottle can be put in and vigorous shaking together.
In this study, the stable phase equilibria system (NaCl -KCl -Na 2 B 4 O 7 -K 2 B 4 O 7 -H 2 O) at 298.15 K, a thermostatic shaker (model HZQ-C) whose temperature was controlled within 0.1 K was used for the measurement of phase equilibrium.

Apparatus for the metastable phase equilibria in the salt-water system
The isothermal evaporation method was commonly used, and Figure 2 is our designed isothermal evaporation device in our laboratory (Guo et al., 2010).The isothermal evaporation chamber was consisted of evaporating container, precise thermometer to keep the evaporating temperature as a constant and electric fan to simulate the wind in situ, and the solar energy simulating system with electrical contact thermograph, electric relay and heating lamp.The temperature controlling apparatus is made up of an electric relay, an electrical contact thermograph and heating lamps.In this example of the metastable phase equilibria system (NaCl -KCl -Na 2 B 4 O 7 -K 2 B 4 O 7 -H 2 O) at 308.15 K, the isothermal evaporation box was used.In an air-conditioned laboratory, a thermal insulation material box (70 cm long, 65 cm wide, 60 cm high) with an apparatus to control the temperature was installed.When the solution temperature in the container was under (308.15± 0.2) K, the apparatus for controlling the temperature formed a circuit and the heating lamp began to heat.Conversely, the circuit was broken and the heating lamp stopped working when the temperature exceeded 308.15 K. Therefore, the temperature in the box could always be kept to (308.15 ± 0.2) K.An electric fan installed on the box always worked to accelerate the evaporation of water from the solutions.Of course, the experimental conditions of an air flow velocity, a relative humidity, and an evaporation rate were controlled as similar as to those of the climate of reaching area in a simulative device.

Reagents
For phase equilibrium study, reagents used should be high-purity grade otherwise the recrystallized step was needed.For the stable and metastable phase equilibria in the salt-water system (NaCl -KCl -Na  ) with conductivity less than 1.2×10 -4 S•m -1 and pH 6.60 at 298.15 K was used to prepare the series of the artificial synthesized brines and chemical analysis.

The chemical analysis of the components in the liquids
For phase equilibrium study in this phase equilibrium system (NaCl -KCl -Na 2 B 4 O 7 -K 2 B 4 O 7 -H 2 O), the composition of the potassium ion in liquids and their corresponding wet solid phases was analyzed by gravimetric methods of sodium tetraphenyl borate with an uncertainty of ≤ ±0.0005 in mass fraction; Both with an uncertainty of ≤ ± 0.003 in mass fraction, the concentrations of chloride and borate were determined by titration with mercury nitrate standard solution in the presence of mixed indicator of diphenylcarbazone and bromphenol blue, and by basic titration in the presence of mannitol, respectively (Analytical Laboratory of Institute of Salt Lakes at CAS, 1982).The concentration of sodium ion was calculated by subtraction via charge balance.

The measurements of the physicochemical properties
For the physicochemical properties determinations, a PHS-3C precision pH meter supplied by the Shanghai Precision & Scientific Instrument Co. Ltd was used to measure the pH of the equilibrium aqueous solutions (uncertainty of ± 0.01).The pH meter was calibrated with standard buffer solutions of a mixed phosphate of potassium dihydrogen phosphate and sodium dihydrogen phosphate (pH 6.84) as well as borax (pH 9.18); the densities (ρ) were measured with a density bottle method with an uncertainty of ± 0.2 mg.cm -3 .The viscosities (η) were determined using an Ubbelohde capillary viscometer, which was placed in a thermostat at (308.15 ± 0.1) K.No fewer than five flow times for each equilibrium liquid phase were measured with a stopwatch with an uncertainty of 0.1 s to record the flowing time, and the results calculated were the average.An Abbe refractometer (model WZS-1) was used for measuring the refractive index (n D ) with an uncertainty of ± 0.0001.The physicochemical parameters of density, refractive index and pH were also all placed in a thermostat that electronically controlled the set temperature at (308.15 ± 0.1) K.

Stable phase equilibria
For the stable equilibrium study, the isothermal dissolution method was used in this study.
The series of complexes of the quaternary system were loaded into clean polyethylene bottles and capped tightly.The bottles were placed in the thermostatic rotary shaker, whose temperature was controlled to (298.15 ± 0.1) K, and rotated at 120 rpm to accelerate the equilibrium of those complexes.A 5.0 cm 3 sample of the clarified solution was taken from the liquid phase of each polyethylene bottle with a pipet at regular intervals and diluted to 50.0 cm 3 final volumes in a volumetric flask filled with DDW.If the compositions of the liquid phase in the bottle became constant, then equilibrium was achieved.Generally, it takes about 50 days to come to equilibrium.

Metastable phase equilibria
The isothermal evaporation method was used in metastable phase equilibria study.
According to phase equilibrium composition, the appropriate quantity of salts and DDW calculated were mixed together as a series of artificial synthesized brines and loaded into clean polyethylene containers (15 cm in diameter, 6 cm high), then the containers were put into the box for the isothermal evaporation at (308.15 ± 0.2) K.The experimental conditions with air flowing velocity of 3.5-4.0m/s, relative humidity of 20-30%, and evaporation rate of 4-6 mm/d are presented, just like the climate of the Qaidam Basin.For metastable evaporation, the solutions were not stirred, and the crystal behavior of solid phase was observed periodically.When enough new solid phase appeared, the wet residue mixtures were taken from the solution.The solids were then approximately evaluated by the combined chemical analysis, of XP-300D Digital Polarizing Microscopy (Shanghai Caikon Optical Instrument Co,. Ltd., China) using an oil immersion, and further identification with X-ray diffraction (X'pert PRO, Spectris.Pte. Ltd., The Netherlands).Meanwhile, a 5.0 cm 3 sample of the clarified solution was taken from the liquid phase of each polyethylene container through a filter pipette, and then diluted to a 250.0 cm 3 final volume in a volumetric flask filled with DDW for the quantitative analysis of the compositions of the liquid phase.Some other filtrates were used to measure the relative physicochemical properties individually according to the analytical method.The remainder of the solution continued to be evaporated and reached a new metastable equilibrium.

Mineral identification for the solid phase
For mineral identification when enough new solid phase appeared either in the stable equilibrium system or in the metastable equilibrium system, the wet residue mixtures were taken from the solution according to the experimental method.Firstly, as to the minerals of Na The stable phase equilibrium experimental results of solubilities of the quaternary system (NaCl -KCl -Na 2 B 4 O 7 -K 2 B 4 O 7 -H 2 O) at 298.15 K were determined, and are listed in Table 3, respectively.On the basis of the Jänecke index (J B , J B /[mol/100 mol(2Na + + 2K + )]) in Table 3, the stable equilibrium phase diagram of the system at 298.15 K was plotted and shown in Figure 5.

Metastable phase equilibrium of the quaternary system
The experimental results of the metastable solubilities and the physicochemical properties of the quaternary system (NaCl -KCl -Na 2 B 4 O 7 -K 2 B 4 O 7 -H 2 O) at 308.15 K were determined, and are listed in Tables 4 and 5, respectively.On the basis of the Jänecke index (J B , J B /[mol/100 mol(2Na + + 2K + )]) in Table 4, the metastable equilibrium phase diagram of the system at 308.15 K was plotted (Figure 6). No.
Composition of the solution 100   No.
Composition of the solution 100w B Jänecke index    A comparison of the dry-salt diagrams of the metastable phase equilibrium at 308.15 K and the stable phase equilibrium at 298.15 K for the same system is shown in Figure 8.The metastable crystallization regions of borax and potassium chloride are both enlarged while the crystallized area of other minerals existed is decreased.When compared with the stable system, the solubility of borax in water in the metastable system is increased from 3.13 % to 5.70 %.The metastable phenomenon of borax is obvious in this reciprocal quaternary system.

Ion-interaction model
As to any electrolyte, its thermodynamic prosperity varied from weak solution to high concentration could be calculated through 3 or 4 Pitzer parameters.Pitzer ion-interaction model and its extended HW model of aqueous electrolyte solution can be briefly introduced in the following (Pitzer, 1975(Pitzer, , 1977(Pitzer, , 2000;;Harvie & Wear, 1980;Harvie et al., 1984;Kim & Frederich, 1988a-b).
As to the ion-interaction model, it is a semiempirical statistical thermodynamics model.In this model, the Pitzer approach begins with a virial expansion of the excess free energy of the form to consider the three kinds of existed potential energies on the ion-interaction potential energy in solution.
Where n w is kilograms of solvent (usually in water), and m i is the molality of species i (species may be chosen to be ions); i, j, and k express the solute ions of all cations or anions; I is ion strength and given by 2 1 2 ii Im z =  , here z i is the number of charges on the i-th solute.
The first term on the right in equation ( 1) is the first virial coefficients.The first virial coefficients i.e. the Debye-Hückel limiting law, f(I), is a function only of ionic strength to express the long-range ion-interaction potential energy of one pair of ions in solution and not on individual ionic molalities or other solute properties.
Short-range potential effects are accounted for by the parameterization and functionality of the second virial coefficients, ij , and the third virial coefficients, ijk .The quantity ij represents the short-range interaction in the presence of the solvent between solute particles i and j.This binary interaction parameter of the second virial coefficient does not itself have any composition dependence for neutral species, but for ions it is dependent it is ionic strength.
The quantity ijk represents short-range interaction of ion triplets and are important only at high concentration.The parameters ijk are assumed to by independent of ionic strength and are taken to be zero when the ions i, j and k are all cations or all anions.
Taking the derivatives of equation ?with respect to the number of moles of each components yields expressions for the osmotic and activity coefficients.

For pure electrolytes
For the pure single-electrolyte MX, the osmotic coefficient defined by Pitzer (2000): φ is the osmotic coefficient; Z M and Z X are the charges of anions and cautions in the solution.
m is the molality of solute; M , X , and ( = M + X ) represent the stiochiometric coefficients of the anion, cation, and the total ions on the electrolyte MX.
In equation ( 1), f φ , B MX and C MX are defined as following equations.In equation (1a), here b is a universal empirical constant to be equal 1.2 kg 1/2 •mol -1/2 .12 12 1 / / AI f bI For non 2-2 type of electrolytes, such as several 1-1-,2-1-, and 1-2-type pure salts, the best form of B MX is following (Pitzer, 1973): For 2-2 type of electrolytes, such as several 3-1-and even 4-1-type pure salts, an additional term is added (Pizter, 1977): A φ is the Debye-Hückel coefficient for the osmotic coefficient and equal to 0.3915 at 298.15 K. Where, N 0 is Avogadro's number, d w and D are the density and static dielectric constant of the solvent (water in this case) at temperature and e is the electronic charge.k is Boltzmann's constant.In equation ( 1b), (0) MX , (1) MX , C φ MX are specific to the salt MX, and are the singleelectrolyte parameters of MX.The universal parameters α = 2.0 kg 1/2 •mol -1/2 and omit (2) MX for several 1-1-,2-1-, and 1-2-type salts at 298.15 K.As salts of other valence types, the values α 1 = 1.4 kg 1/2 •mol -1/2 , and α 2 = 12 kg 1/2 •mol -1/2 were satisfactory for all 2-2 or higher valence pairs electrolytes at 298.15 K.The parameter (2) MX is negative and is related to the association equilibrium constant.
The mean activity coefficient ± is defined as: In equations ( 3), ( 4), ( 5) and ( 6), the subscripts M, c, and c' present cations different cations; X, a, and a' express anions in mixture solution.N c , N a and N n express the numbers of cations, anions, and neutral molecules; r M , Z M , m C and r X , Z X , m a , Ф present the ion activity coefficient, ion valence number, ion morality, and the permeability coefficient; n , m n , nc , and na express activity coefficient of neutral molecule, morality of neutral molecule the interaction coefficient between neutral molecules with cations c and anion a.
The defining equation of F is given by equation ( 7). 3. The function Z in the equation ( 8) is defined by: Where, m is the molality of species i, and z is its charge.

4.
A φ is the Debye-Hückel coefficient for the osmotic coefficient and equal to 0.3915 at 298.15 K, and it is decided by solvent and temperature as equation ( 1d). 5.The third virial coefficients, i,j,k ψ in equations ( 3) to ( 5) are mixed electrolyte parameters for each cation-cation-anion and anion-anion-cation triplet in mixed electrolyte solutions.6.The parameters which describe the interaction of pair of oppositely charged ions represent measurable combinations of the second virial coefficients.They are defined as explicit functions of ionic strength by the following equations (Kim & Frederick, 1988).Where the functions g and g' in equations ( 10), ( 11) and ( 12) are defined by In equations ( 13) and ( 14), x =  1 I 1/2 or =  2 I 1/2 .In Pitzer's model expression in Eqns.( 10) to ( 12),  is a function of electrolyte type and does not vary with concentration or temperature.Following Harvie et al. (1984), when either cation or anion for an electrolyte is univalent, the first two terms in equations ( 10) to ( 12) are considered,

() CA
β can be neglect and α 1 =2.0 kg 1/2 •mol -1/2 , α 2 = 0 at 298.15 K.For higher valence type, such as 2-2 electrolytes for these higher valence species accounts for their increased tendency to associate in solution, the full equations from (10) to ( 12) are used, and ,, φ ΦΦΦwhich depend upon ionic strength, are the second virial coefficients, and are given the following form (Pitzer, 1973).
In equations ( 15), ( 16) and ( 17), i,j θ is an adjustable parameter for each pair of anions or cations for each cation-cation and anion-anion pair, called triplet-ion-interaction parameter.The functions, ij E θ and ' ij E θ are functions only of ionic strength and the electrolyte pair type.Pitzer (1975) derived equations for calculating these effects, and Harvie and Weare (1981) summarized Pitzer's equations in a convenient form as following: In equations ( 18) and ( 19), J(x) is the group integral of the short-range interaction potential energy.J'(x) is the single-order differential quotient of J(x) , and both are independent of ionic strength and ion charges.In order to give the accuracy in computation, J(x) can be fitted as the following function: In equations ( 21) and ( 22), C 1 = 4.581, C 2 = 0.7237, C 3 = 0.0120, C 4 = 0.528.
Firstly, x ij can be calculated according to equation ( 20), and J(x) and J'(x) were obtained from equations ( 21) and ( 22), and then to obtained ij E θ and ' ij E θ from equations ( 18) and ( 19 ,, φ ΦΦΦ, the osmotic and activity coefficients of electrolytes can be calculated via equations from (3) to (6).
Using the osmotic coefficient, activity coefficient and the solubility products of the equilibrium solid phases allowed us to identify the coexisting solid phases and their compositions at equilibrium.On Pitzer ion-interaction model and its extended HW model, a numbers of papers were successfully utilized to predict the solubility behaviors of natural water systems, salt-water systems, and even geological fluids (Felmy & Weare, 1986;Kim & Frederich, 1988a, 1988b;Fang et al., 1993;Song, 1998;Song & Yao, 2001, 2003;Yang, 1988Yang, , 1989Yang, , 1992Yang, , 2005)).
By the way, additional work has centered on developing variable-temperature models, which will increase the applicability to a number of diverse geochemical systems.The primary focus has been to broaden the models by generating parameters at higher or lower temperatures (Pabalan & Pitzer, 1987;Spencer et al., 1990;Greenberg & Moller, 1989).

Model parameterization and solubility predictions
As to the borate solution, the crystallized behavior of borate salts is very complex.The coexisted polyanion species of borate in the liquid phase is difference with the differences of boron concentration, pH value, solvent, and the positively charged ions.The ion of B 4 O 7 2-is the general statistical express for various possible existed borates.Therefore, the structural formulas of Na respectively.Borate in the liquid phase corresponding to the equilibrium solid phase maybe coexists as B 4 O 5 (OH) 4 2-, B 3 O 3 (OH) 4 -, B(OH) 4 -, and son on due to the reactions of polymerization or depolymerization of boron anion.Therefore, in this part of predictive solubility of the quaternary system (NaCl -KCl -Na 2 B 4 O 7 -K 2 B 4 O 7 -H 2 O), the predictive solubilities of this system were calculated on the basis of two assumptions: Model I: borate in the liquid phase exists all in statistical form of B 4 O 7 2-i.e.B 4 O 5 (OH) 4 2-; Model II: borate in the liquid phase exists as various boron species of The necessary model parameters for the activity coefficients of electrolytes in the system at 298.15 K were fit from obtained osmotic coefficients and the sub-ternary subsystems by the multiple and unary linear regression methods.

Model I for the solubility prediction
Model I: Suppose that borate in solution exists as in the statistical expression form of B 4 O 7 2- i.e.B 4 O 5 (OH) 4 2-, and the dissolved equilibria in the system could be following: So, the dissolved equilibrium constants can be expressed as: , respectively.Then, the equilibria constants K are calculated with 0 /RT and shown in Table 6.
According to the equilibria constants and the Pitzer ion-interaction parameters, the solubilities of the quaternary system at 298.15 K have been calculated though the Newton's Iteration Method to solve the non-linearity simultaneous equations system, and shown in Table 9.

Model II for the solubility prediction
Model II: Suppose that borate in solution exists as in various boron species of B 4 O 5 (OH) 4 2-, B 3 O 3 (OH) 4 -, B(OH) 4 -to further describe the behaviors of the polymerization and depolymerization of borate anion in solution, and the dissolved equilibria in the system could be following:  8.According to the equilibria constants and the Pitzer ion-interaction parameters, the solubilities of the quaternary system at 298.15 K have been calculated though the Newton's Iteration Method to solve the non-linearity simultaneous equations system, and shown in Table 10.In fact, this theoretic calculation for the reciprocal quaternary system is equivalence of the calculated solubilities for the six-component system (Na There were two possible reasons: one is that the structure of borate in solution is very complex, an the Pitzer's parameters of borate salts is scarce; the other one is the high saturation degree of borate, the difference between the experimental equilibrium constant and the theoretic calculated equilibrium constant was large enough.

References
Analytical Laboratory of Institute of Salt Lakes at CAS. (1988).The analytical methods of brines and salts, 2nd ed., Chin. Sci. Press,Beijing
Fig. 3. Identification of the invariant points for the solid phase in the reciprocal system (NaCl -KCl -Na 2 B 4 O 7 -K 2 B 4 O 7 -H 2 O) with a polarized microscopy using an oil-immersion method.(a), the invariant point (NaCl + KCl + Na 2 B 4 O 7 •10H 2 O); (b), the invariant point(KCl + Na 2 B 4 O 7 •10H 2 O + K 2 B 4 O 7 •4H 2 O).The metastable equilibria solid phases in the two invariant points are further confirmed with X-ray diffraction analysis, and listed in Figure4, except in the invariant points (NaCl + KCl + Borax) in Figure4awhich shows that the minerals KCl, NaCl, Na 2 B 4 O 7 •10H 2 O and a minor Na 2 B 4 O 7 •5H 2 O are existed.The minor of Na 2 B 4 O 7 •5H 2 O maybe is formed due to the dehydration of Na 2 B 4 O 7 •10H 2 O in the processes of transfer operation and/or grinding.

Fig. 6 .Fig. 7 .
Fig. 6.Metastable phase diagram of the quaternary system (NaCl -KCl -Na 2 B 4 O 7 -K 2 B 4 O 7 -H 2 O) at 308.15 K. (a), dry-salt phase diagram; (b), water-phase diagram.On the basis of physicochemical property data of the metastable system (NaCl -KCl -Na 2 B 4 O 7 -K 2 B 4 O 7 -H 2 O) at 308.15 K in Table5, the diagram of physicochemical properties versus composition was drawn and shows in Figure7.The physicochemical properties of the metastable equilibrium solution vary regularly with the composition of borate mass fraction.The singular point on every curve of the composition versus property diagram corresponds to the same invariant point and on the metastable solubility.

Fig. 8 .
Fig. 8.Comparison of the metastable phase diagram at 308.15 K in solid line and the stable phase diagram at 298.15 K in dashed line for the quaternary system (NaCl -KCl -Na 2 B 4 O 7 -K 2 B 4 O 7 -H 2 O).--, metastable experimental points; -○-, stable experimental points.
single-electrolyte third virial coefficient, C MX , account for short-range interaction of ion triplets and are important only at high concentration.These terms are independent of ionic strength.The parameters C MX and MX C φ , the corresponding coefficients for calculating the osmotic coefficient, are related by the equation (1 Fig. 9. Comparison of the experimental and calculated phase diagram of the quaternary system (NaCl -KCl -Na 2 B 4 O 7 -K 2 B 4 O 7 -H 2 O) at 298.15 K. -•-, Calculated based on Model I; -▲-, Calculated based on Model II; -○-, Experimental.

Financial
support from the State Key Program of NNSFC (Grant.20836009), the NNSFC (Grant.40773045), the "A Hundred Talents Program" of the Chinese Academy of Sciences (Grant.0560051057), the Specialized Research Fund for the Doctoral Program of Chinese Higher Education (Grant 20101208110003), The Key Pillar Program in the Tianjin Municipal Science and Technology (11ZCKFGX2800) and Senior Professor Program of Tianjin for TUST (20100405) is acknowledged.Author also hopes to thank all members in my research group and my Ph.D. students Y.H. Liu, S.Q.Wang, Y.F.Guo, X.P. YU, J. Gao, L.Z.Meng, DC Li, Y. Wu, and D.M. Lai for their active contributions on our scientific projects.

Table 2 .
Stable and Metastable Phase Equilibria in the Salt-Water Systems Statistical distribution of the lithium reserves in the world The isothermal evaporation phase diagrams of the sea water system at different temperature show a large difference with Vant'hoff stable phase diagram.The crystallization fields of leonite (MgSO 4 .K 2 SO 4 .4H 2 O), and kainite (KCl.MgSO 4 .3H 2 O) are all disappear whereas the crystallization field of picromerite (MgSO 4 .K 2 SO 4 .6H 2 O) increases by 20-fold, which is of great importance for producing potassium sulfate or potassium-magnesium fertilizer.

Table 4
Corresponding to the no.column in Table 4; ** not determined. *

Table 10 .
Calculated solubility data of the system (NaCl -KCl -Na 2 B 4 O 7 -K 2 B 4 O 7 -H 2 O) at 298.15 K on the basis of Model II.* B4, B3, B express for B 4 O 5 (OH) 4 2-, B 3 O 3 (OH) 4 -, B(OH) 4 -; N10, Na 2 B 4 O 7 •10H 2 O; K4, K 2 B 4 O 7 •4H 2 O.In Figure 9, compared with Models I and II, the calculated values in the boundary points and the cosaturated point of (Na 2 B 4 O 7 •10H 2 O + KCl + NaCl) based on model II were in good agreement with the experimental data.However, in the cosaturated point of (Na 2 B 4 O 7 •10H 2 O + K 2 B 4 O 7 •4H 2 O + KCl), a large difference on the solubility curve still existed.Reversely, the predictive result based on model II closed to the experimental curve.