326
Ind. Eng. Chem. Fundam., Vol. 17, No. 4, 1978
Phase Equilibria in the Li-LiF-Li2S System Edward G. Groff
' and Gerard M. Faeth
Mechanical Engineering Department, The Pennsylvania State University, University Park, Penmylvankr
76802
The phase equilibria characteristics of the immiscible Li-LiF-Lips system are described. Such two-phase liquid mixtures are contained within reaction chambers of thermal energy sources employing Li and SFBas reactants. A thermodynamic model, based on the van Laar expression for the excess Gibbs free energy of mixing, permits prediction of ternary system solubilities from data on constituent binaries. Model parameters were evaluated by application of thermodynamic equilibrium equations to experimentally measured solubility data on the Li-LizS and LiF-Li,S binaries and published data on the Li-LiF binary. Predicted ternary mixture solubilities compared favorably, with data measured in the temperature range of 11 16-1244 K. Over this temperature range, Li mole fractions in the salt-rich phase (LiF and Lipsbeing in stoichiometric ratio) ranged from 0.002 to 0.008, and mole fractions of LiF and Li,S in the Li-rich phase ranged from 0.017 to 0.036 and 0.002 to 0.007, respectively.
Introduction Phase equilibria of molten salt mixtures are of interest in the study of energy storage units, heat-transfer systems, high-temperature batteries, and closed thermal energy sources. Theories for expressing the excess Gibbs free energy of mixing of nonpolar molecular liquids have been applied to these systems. Regular solution theory has been used to predict the liquidus lines of binary alkali halide mixtures from enthalpy of mixing data (Carlson et al., 19771, and the eutectic points of ternary alkali halide mixtures from binary data (Nakanishi, 1970). After examining the data of Bredig and collaborators (1962) for alkali halide-metal binary systems, Pitzer (1962) concluded that such systems display thermodynamic properties similar to mixtures of normal nonpolar molecular liquids; Lumsden (1966) concluded that the most probable model involves the existence of metal atoms and salt molecules. The present study examines these ideas for ternary mixtures of lithium, lithium fluoride, and lithium sulfide. This mixture is formed in a thermal energy source (Groff and Faeth, 1978) using the chemical reaction between Li (fuel) and SF6 gas (oxidant) yielding LiF and LizS as products. In the solubility and temperature ranges of interest, immiscible Li-rich and salt-rich phases exist. Similar ternary systems exist in thermal energy sources employing other alkali metals and halogenated gases as reactants. Solubility data were obtained experimentally for the LiF-Li2S and Li-LiF binaries, and data for the Li-LiF binary were taken from the literature (Dworkin et al., 1962). The binary systems were modeled with the van Laar expression for the excess Gibbs free energy of mixing (Wohl, 1946), with the empirical constants determined from the solubility data. Extension of this model to the ternary mixture provided predictions of solubilities for comparison with data obtained in the study. Experiments Experimental methods are briefly described in the following; details are given elsewhere (Groff and Faeth, 1976). Table I summarizes the source and manufactured purity of the reagents (used without additional purification). All apparatus were constructed of type 316 stainless steel, except for sampling cups which were made of nickel 200 alloy. 'Address correspondence to this author a t General Motors Research Laboratories, Engine Research Department, 12 Mile and Mound Roads, Warren, Mich. 48090.
%ble I. Source and Punty of Reagents purity, reagent
supplier
%
Li SF,
Lithium Corporation of America Matheson Gas Products Matheson Gas Products Fisher Scientific Company Research Organic/Inorganic Chemical Company Baker and Adamson Company
99.9 99.8 99.99 99.97 98.0
Ar LiF Li, S
S
99.9
Chrome-alumel thermocouples manufactured to ANSI tolerances, &0.75% in the temperature range of interest, were used to measure temperature. All mixtures were under argon, and access to the baths was accomplished through argon-purged sampling ports. LiF-Li2S Binary. Thermal analysis was used to investigate this binary. Samples weighing 15-20 g were prepared by mixing Li, LiF, and S, and forming LizS by reaction upon heating. A capsule containing the reactants was welded shut under argon and then heated to 1300 K. After standing for 5 h, the cooling curve was recorded. Accuracy was confirmed by measuring the melting temperature of LiF to be 1120 K, in agreement with published values, and reproducing all test conditions within 1 K. Li-Li2S Binary. This binary was investigated by direct sampling and analysis of a bath heated in a furnace. Tests were limited to the solid Li2S and Li-rich liquid region of the phase diagram. The bath consisted of excess solid Lis, about 30 g, and 166 g of Li. The bath was maintained at the test temperature for 23 h, stirred by an argon bubbler for the first 19 h, before samples were removed. Ternary System. A steadily reacting thermal energy source employing the reaction between Li and SF6 was used to investigate the ternary system (Groff and Faeth, 1976,1978). The temperature range of the experiments was 1116-1244 K. Liquid lithium and gaseous SF6flowed into the reaction vessel, which had a volume of approximately 0.025 m3 and reacted according to 8Li + SF6 6LiF + Li2S (1)
-
The products collected in the more dense salt-rich liquid phase contained in a sump, 550 cm3 in volume, at the bottom of the vessel. The product, along with any dissolved Li, was removed from the sump through a trap. The SF6was injected into the Li-rich portion of the bath, and reacts in a two-phase turbulent jet. A flow of argon through the injector, surrounding the flow of SF6,prevented corrosion from contact of hot surfaces with the
0019-7874/78/1017-0326$01.00/00 1978 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 17, No. 4, 1978 327
L
1500
E.,,,,---
I400
i1
1
/ ’
/
1200 *
.
\
i
SOLI0 + LlaUlD
I Iooo
/
1
T W O SOLIDS
t
900 0
I
2
3
5 6 MOLE F R I C T I O N LIPS 4
7
8
9
I100
1000
k
900
w
g
800
5
ONE LIQUID t L12S SOLID
0
700
600
6
3
9
12
15
21
18
24
MOLE FRACTION L12S X IO4
Figure 2. Li-Li2S system; solid lines are model predictions.
IO
Figure 1. LiF-Li2S system; solid lines are model predictions.
halogenated gas, and helped to stir the bath. Analysis of the argon flow leaving the chamber indicated that the reaction was complete. Li-rich samples were extracted through a port in the top of the reaction vessel. Salt-rich samples were obtained a t the exit of the trap. Prior to taking a sample, the system was operated a t a given temperature level long enough to completely refill the sump with product. Proper Li inflow was monitored in this period with an argon bubbler which indicated the liquid level in the vessel. Sampling and Analysis. Li-rich samples were obtained in a 3-cm3 cup sealed with a ball valve. Salt-rich samples were obtained in a 30-cm3cup, extended into the flow leaving the trap of the reaction vessel. Li-rich samples were prepared for analysis by polishing the exterior of the sampling cup, to remove contaminants. The salt-rich samples were ground into a fine powder to enhance subsequent dissolutiori in water. These processes were completed under argon in a vacuum/glove box. After weighing, prepared Li-rich or salt-rich samples were transferred to a distillation apparatus. Water and hydrochloric acid were added to the sample and the hydrogen sulfide evolved! from the acidified solution was carried to an ammoniacal zinc sulfate solution by an argon purge flow where it was trapped, and then titrated with potassium iodate using titarch indicator to determine moles of sulfide. Ethyl alcohol was added to the remaining sample solution which was titrated with thorium nitrate using alizarin Red S indicator to yield fluoride. Lithium was determined in Li-rich samples by difference, but in salt-rich samples such 21 procedure is not acceptable, and the free Li was deterrnined by measuring the evolved hydrogen when water was added to the sample. The hydrogen was detected with a gas chromatograph fitted with an BO/ 100 mesh 5-A molecular sieve. All procedures were calibrated with prepared samples of known composition. The accuracy of the procedures, f 3 % for LiF and Li2S in Li-rich samples and f 8 % for Li in salt-rich samples, was confirmed by analyzing additional known samples.
Results The present measurements for the LiF-Li2S binary are shown in Figure 1 as symbols on a partial phase diagram. A eutectic point was observed at an LizS mole fraction of 0.15 f 0.01 and a temperature of 1065 f 2 K. Two thermal effects were observed a.t LizS concentrations below the eutectic point, but only the lower effect was observed at higher concentrations. Possible reasons for the absence of the higher thermal effect, expected from the solidifi-
RUN SYMBOLS LITHIUM SULFIDE/ L I T H I U M FLUORIDE
E L
r
1
0 2 /
Y
i
t PPC-7 0 PPc-~
ni
L
I
001 1110
4
1 1130
1150 1170 1190 TEMPERATURE l D K l
1210
1230
1250
Figure 3. Salt-rich phase of ternary system; solid lines are model predictions.
cation of Liz& include the presence of an immiscible two-phase region, undercooling of the Liz& or incomplete dissolution of the Li2S in the LiF. The tests were limited to LizS concentrations below 0.3 because heat released by the Li-S reaction, when the sample was prepared, was sufficient to cause failure of the test capsule a t higher concentrations. The measurements for the Li-LizS binary are shown in Figure 2 as symbols on a partial phase diagram. The scale of the Li2S mole fraction is greatly expanded. The low solubility of Li2S in Li suggests that the freezing point of Li will not be depressed appreciably from the pure component value of 454 K. This has been substantiated with tests using a differential thermal analysis technique (Cunningham et al., 1972). The solubility data obtained for the ternary system are presented as symbols in Figures 3 and 4 for the salt-rich and Li-rich phases, respectively. Different tests are distinguished by various symbols. The details of each test are recorded elsewhere (Groff and Faeth, 1976,1978). The salt-rich results are plotted as the ratio of the mole fraction of Li2S to that of LiF, and the mole fraction of Li, as a function of temperature. For steady reaction LiF and LizS must leave the vessel in the salt-rich phase, with the stoichiometric proportions specified by eq 1. This implies X L ~ B / X L ~=F 0.167
(2)
The data illustrated in Figure 3 are in close agreement with eq 2, verifying that steady-state operation was achieved during the tests. The solubility of Li is very low in this phase, less than 0.9% on a mole fraction basis, and in-
Ind. Eng. Chem. Fundam., Vol. 17, No. 4, 1978
328
05
, O N E LIQUID
LITHIUM FLUORIDE
TWO Liauios
1400
$
1300
008
y.
005
*.
I”
-
3
0
I
RUN SYMBOLS
002
,
.
0
I
001 1110
1130
1150
1170 1190 TEMPERATURE ( O K )
1210
PPC-4 PPC-5 PPC-7 PPC-8
1230
/
1100 1000
1250
900
Figure 4. Li-rich phase of ternary system; solid lines are model predictions.
creases with temperature. The ratio of solubilities of LizS and LiF in the Li-rich phase, Figure 4, is not fixed by stoichiometry requirements and is less than the value given by eq 2. This ratio, and the solubility of LiF and LizS all increase with increasing temperature. Model Formulation The excess Gibbs free energy of mixing is modeled by the van Laar expression (Wohl, 1946), and is written for a binary system composed of species i and j’ as follows
DATA OF DWORKIN. IRONSTEIN, AND IREDIG [19621
,
,
,
,
112; O K
,
,
,
,
7
8
9
ONE SOLID-ONE LIQUIO
I
2
3
4
5 6 MOLE FRACTION LIF
1
1 IO
Figure 5. Li-LiF system; solid lines are model predictions.
The five empirical parameters describing the Li-LiF-Li2S ternary system and the three constituent binaries were obtained by evaluating experimental solubility data for the binary systems. During these analyses, it was found that improved characterization of the data was obtained if the parameters Aljand B, were functions of temperature, and a total of eight empirical constants were ultimately used. The temperature dependencies of the parameters appear in the entropy and enthalpy of mixing expressions
(3) Extension of eq 3 to the case of a mixture composed of three or more species (Wohl, 1946) yields
f/z fE
=
i
I
ninlbjbjAi;’ (4)
nTC nibi i
where Ai,’ = Aii’, and Aii’ = A,‘ = 0. The A,’ and bi are empiricai parameters which can be interpreted as interaction energies and quasilattice parameters, respectively. The relation between the activity coefficient and the excess Gibbs free energy of mixing is
Substitution of eq 4 into eq 5 yields a general expression for the activity coefficients of the various species in multicomponent mixtures, in terms of the van Laar parameters. bk
C C (Aik’- ‘/z Ai;?bib;ninj
Equations 3-6 provide three- and six-parameter representations of binary and ternary systems, respectively. However, the parameters can be redefined as follows to eliminate one parameter from each representation A 11, . = b,A..’ 1 11 (7) and
BI = bi/b,;
B2 = bz/b,;
B3 = b i / b ~ (8)
For the ternary case, the B3 = B1 Bz fixes one parameter when the other two are known.
Differentiation of eq 4 yields the second term in each expression. The result is too long to repeat here, but it is noted that the model cannot be classified as a regular solution model because of the nonzero excess entropy of mixing (Hildebrand et al., 1970). Evaluation of Binary Parameters Li-LiF Binary. The components were labeled such that subscripts 1, 2, and 3 represented Li, LiF, and Li2S, respectively. Employing this convention, the empirical parameters representing the Li-LiF binary are A12and B1, which were determined from the solubility data for the immiscible liquid region reported by Dworkin et al. (1962). At a given temperature, the fugacity of a species is identical in each of two immiscible phases, and since the standard state for each species is the same in each phase (activity of unity for the pure liquid), the equilibrium condition implies that the activity of each species is identical in each of the two phases. This leads to mathematical relations (derived in the Appendix) for the parameters Alz and B1 as functions of the mole fractions of the species in the two phases and the temperature. The solubility data of Dworkin et al. (1962) presented in Figure 5, when substituted into eq A-2 and A-3, provided the parameters plotted vs. temperature in Figure 6. Each parameter is a monotonically decreasing function of temperature. The computed values were fitted as a linear function of temperature using least-squares techniques, and the resulting equations are A12= 121.53 - 0.05730T (kJ/mol) (11) and
B1 = 2.5846 - 8.132 X 10-4T with temperature in K. The estimated standard deviations
Ind. Eng. Chem. Fundam., Vol. 17, No. 4, 1978 60 55
p! 4 0
35
30
14
moL-#1 12
-
I
I O
I
L
08
04
02
I100
I
I200
,
I
1300 1400 TEMPERATURE ( O K 1
,
1500
1600
Figure 6. Model parameters for Li-LiF system; solid lines are least-squares fit of the data.
of A12and B1 about the regression lines are 1.36 k J and 0.08, respectively. Computed equilibrium compositions using the van Laar expression (eq 3) and the fitted parameters are compared to the data in Figure 5; the agreement is good over the complete temperature range including the consolute point. Li-LizS Binary. The empirical parameters AI3 and B3 for the Li-Li2S binary were estimated using the solubility data presented in Figure 2. Equation A-5, developed in the Appendix, was used to represent the equilibrium between solid LizS arid the Li-Li2S liquid solution. The parameter B3 was assumed to be temperature invariant while AI3was taken to be a linear function of temperature. The LizS property data used were: heat of fusion of 45.4 kJ/mol, freezing point of 1645 K (Cunningham et al., 1972), and average heat capacity difference of 4.2 J/mol. Both the heat of fusion and heat capacity values were estimated since data were not available in the literature. The heat of fusion value is discussed in greater detail below, and the heat capacity value has a relatively small effect on the results. The inability to obtain data in the Li2S-rich portion of the phase diagram resulted in the B3 value not being fixed by the analysis. The B3 value was chosen such that the interaction energy par,ameter, AI3,would match that of the Li-LiF binary at a temperature of 1200 K. This decision was based on suspected similar immiscibility characteristics of the two binaries. A value of 1.36 resulted which is less than B1, an expected trend since the molar volume of Li2S is larger than that of LiF. A sensitivity analysis indicated that a B3 variation of k0.05 results in a k5% variation in the Lips solubility in the Li-rich phase prediction of the model 6or the ternary system. The Li-Li2S binary cannot be treated more accurately until additional solubility data are available to include in the analysis. The parameters usled to represent the Li-Li2S binary are A13 = 53.287 - 4.00 X 10-4T(kJ/mol) (12) and B, = 1.36 Figure 2 compares the computed results with the experimental data. LiF-Li2S Binary. The parameters AZ3and B2,for the LiF-Li2S binary, were evaluated using eq A-5 applicable
329
to solid-liquid equilibria data, and the solubility data presented in Figure 1. The property data used for LiF (Stull and Prophet, 1971) were: freezing point of 1121 K, heat of fusion of 27.1 kJ/mol, and average heat capacity difference of 2.7 J/mol. The analysis showed that the freezing point depression of LiF was equivalent to an ideal solution. Ideal solution behavior is indicated by A23 = 0 (13) with B2 fixed by eq 8, although B2 has no effect on the binary results since A23 is zero. It is estimated that A23 is accurate to within fl kJ/mol in the region of the phase diagram investigated experimentally. In the absence of additional data, it was assumed that the remainder of the phase diagram would be a simple eutectic type. Using eq A-5, with A23 set to zero, the heat of fusion of Lips could be estimated to be the value required to match the experimental eutectic point. The average heat capacity difference for Li2S was estimated to be 1.1kJ/mol in this temperature range, and the heat of fusion value determined was 49.4 kJ/mol. LizS solubility predictions in the Li-rich phase of the ternary system are affected significantly by the estimated heat of fusion since this quantity is also used to determine the parameters for the Li-Li2S binary. The computed solubility characteristics of the LiF-Li2S binary are compared to the experimental data in Figure 1. Evaluation of T e r n a r y Mixture Equilibrium of the immiscible mixture composed of Li-rich and salt-rich phases requires that the activity of each component is the same in both phases, eq A-1. The sum of the mole fractions in each phase must also be unity. A final equilibrium condition, for the present ternary data, is that the product materials must be present in stoichiometric proportions in the salt-rich phase as prescribed by eq 2. The resulting set of six nonlinear equations were solved simultaneously to yield the six unknown mole fractions, using a Newton-Raphson procedure (Groff and Faeth, 1976). The predictions of the model are compared with the measurements in Figures 3 and 4. In the salt-rich phase, Figure 3, the stoichiometric product ratio is closely satisfied, as noted earlier; the predicted Li concentrations are within 5-870 of the measured values. For the Li-rich phase, Figure 4, the results of the model are in good agreement with the data. The largest differences are 25% for LiF and 39% for Li2S at the low and high temperature extremes of the data, respectively. In all cases, the trends of the data are given correctly by the model. S u m m a r y a n d Conclusions The solubility characteristics of a ternary mixture of Li, LiF, and Li2S were modeled using simple solution theory. The eight empirical constants required by the model were evaluated from binary solubility data. Dworkin et al. (1962), provided data for the Li-LiF binary. Data for the LiF-Li2S and Li-Li2S binaries were obtained in this investigation. The predicted ternary mixture solubility results compared favorably with data obtained during the study. The accuracy of the ternary solubility predictions depends upon the accuracy and completeness of the data available for the constituent binary systems used to evaluate the empirical parameters. More extensive data were available for the Li-LiF binary, and since these are major species in the range of the ternary data, their solubilities were predicted most accurately. The results substantiate the conclusions of Pitzer (1962) and Lumsden (1966) that mixtures of alkali metals and molten salts have mixing characteristics similar
330
Ind. Eng. Chem. Fundam., Vol. 17, No. 4, 1978
to normal nonpolar molecular liquids. Appendix Immiscible Liquid Equilibria. Mathematical expressions for the van Laar parameters as functions of mole fractions in each of two equilibrated phases, xi and yi, and the mixture temperature, T, are derived below. Equilibrium in a multicomponent system requires ai(xi) = ai(yi) (A-1) For the case of a binary system composed of species 1 and 2, two expressions result upon substitution of the van Lam expressions for the activity coefficients, eq 6 into eq A-1. These equations can be solved to yield A12 and B1 as functions of temperature and equilibrium compositions as follows
Use of eq A-2 and A-3 in conjunction with solubility data in the immiscible liquid region permits the van Laar parameters for a particular system to be evaluated. Solid-Liquid Equilibria. Lumsden (1966) suggests that solid solutions are not formed with an ionic size ratio greater than 1.13 for the large to small cations. The values for the solutions considered in this study exceed this limit, and in the following, equations are developed which permit evaluation of van Laar parameters for solid-liquid equilibria data for mixtures which do not form solid solutions. The equilibrium between a solid and a liquid solution requires f l ( s ) = 7l(solu, x i ) (A-4) The effects of composition and temperature changes are separated by evaluating eq A-4 a t temperature T and a t the freezing temperature of the pure component, Tfi After rearrangement and integration (see Chapter 26 of Lewis and Randall (1961)), the following expression results R In a,lTf. =
with Oi = Tfi- T. In the above k1 is the relative molal heat content defined by ki = hi (solu,xi) - hio, AHfiis the heat of fusion of the pure component a t its freezing point, and Acpi is the average difference between the partial molal heat capacity of the component in solution and the molar heat capacity of the solid. The left-hand side of eq A-5 is evaluated from eq 6, and the relative molal heat content is derived from eq 10. Considering a binary mixture consisting of components 1 and 2 with both van Laar parameters being linear functions of temperature, A12 = A + BT and B1= a + bT, the following terms will result for equilibrium between solid component 1 and component 1 in solution
R In allT,, = R In x1 + 'I2( Tfl
x2
BlXl
+ x2
)
(A-6)
and
b B P [ (Blxl 2x1x2 + x2)3
]
(A-7)
These terms are substituted into eq A-5 which is then solved for the unknown parameters. Nomenclature a = model parameter, dimensionless ai = chemical activity, dimensionless A, A , . = model parameter, J/mol A,' 2 model parameter, J/cm3 b = model parameter, K-' bi = model parameter, cm3/mol B = model parameter, J/mol K Bi = model parameter, dimensionless cp = specific heat, J/mol K f = molar Gibbs free energy, J/mol h = molar enthalpy, J/mol H = enthalpy, J ki = relative heat content, J/mol ni = number of moles p = pressure, kPa R = gas constant (8.3147 J/mol K) S = entropy, J/K T = temperature, K xi, yi = mole fraction, dimensionless Greek Letters y = activity coefficient, dimensionless 0 = temperature difference, K Superscripts O = pure component _ -- partial molal quantity E = excess thermodynamic quantity Subscripts f = property at freezing point mix = change due to mixing Literature Cited Bredig, M. A.. Bronstein, H. R., J . fhys. Chem., 64, 64 (1960). Bredig, M. A., Johnson, J. W., J . fhys. Chem., 64, 1699 (1960). Carlson, A,, Howard, J. B., Reid, R. C., Ind. Eng. Chem. Fundam., 16, 157 (1977). Cunningham, P. T.. Johnson, S.A,, Cairns, E. J., J . Electrochem. SOC.,119, 1448 (1972). Dworkin, A. S., Bronstein, H. R.. Bredi, M. A,, J . ftys. Chem., 66, 572 (1962). Groff, E. G.. Faeth, G. M., Technical Report to Defense Advanced Research Projects Agency, "Char. of a Steadily Operating Metal Combustor," Contract N00600-74-0033, Program Code. 2N10, ARPA Order No. 2150 (1976). Groff, E. G., Faeth, G. M., AIAA, J . Hydro,, 12, 63 (1976). Hiklebrand, J. H., Prausnitz, J. M., Scott, R. L., "Regular and Related Solutions," Van Nostrand-Reinhold Co., New York, N.Y., 1970. Lewis, G. H., Randall, M., "Thermodynamics." 2nd ed, revised by K. S. Pitzer and L. Brewer, McGraw-Hili, New York, N.Y., 1961. Lumsden, J., "Thermodynamics of Molten Salt Mixtures,''Academic Press, New York, N.Y., 1966. Nakanishi, K., Ind. Eng. Chem. Fundam., 9, 449 (1970). Pitzer, K. S.,J . Am. Chem. SOC.,64, 2025 (1962). Stuii, D.R., Prophet, H., "JANAF Thermochemical Tables,'' NSRDS-NBS 37, U S . Govt. Printing Office, Washington, D.C., 1971.
Received for review April 7 , 1978 Accepted July 20, 1978 Work supported by the David W. Taylor Naval Ship Research
and Development Center, Annapolis Laboratory, as Technical Agent for the Defense Advanced Research Projects Agency, and conducted in the Mechanical Engineering Department of The Pennsylvania State University.
