M. S:FOSTER, C. E. CROUTHAMEL, AND S. E. WOOD
3042
Thermodynamics of Binary Alloys.
11. The Lithium-Tin System1
by Melvin S. Foster, Carl E. Crouthamel, and Scott E. Wood Chemical Engineering Division, Argonne National Laboratory, Argonne, Illinois
(Received January 10, 1966)
Electromotive force measurements have been made on cells which may be represented as ~ atom fraction of Li). The alloy compositions varied from LilLiC1-LiFILi in Sn (1, X L = XL= ~ 0.1 to Sn saturated with solid Li5Sn2. The temperature range was 800 to 1050°K. A secondary reference electrode which consisted of liquid Bi saturated with solid Li3Bi was used in many of the measurements. An equation relating the excess chemical potential of Li in binary Li-Sn alloys as a function of temperature and composition for the region studied was derived by a least-squares treatment. The standard free energy of formation of solid Li5Sn2has also been calculated.
Introduction Concentration cells without transference consisting of a lithium anode and a lithium-tin alloy cathode may be applicable either in a regenerative galvanic cell system or as a primary or secondary battery. The merits of lithium as the most active component of the binary system have been discussed in an earlier work.2 The ability of lithium to form relatively stable intermetallic compounds with many of the more noble elements is one of its chief advantages. The stability of these compounds produces cell voltages in concentration cells without transference which are substantially larger than those predicted from ideal solution theory. One of the elements which forms stable stoichiometric intermetallic compounds with lithium is tin. The phase diagram of the lithium-tin systems as given by Hansen and Anderko3 shows that six stoichiometric compounds are formed. The compound Li7Sn2is reported to have the highest melting point, 783". The potentials of cells without transference have been measured, using cathode compositions between pure tin and 0.30 atom fraction tin in lithium and in the temperature range between 502 and 720". In this region, the cathode consisted of either a one-phase liquid alloy or a liquid alloy of tin saturated with pure solid Lib.
Experimental Section Materials. The electrolyte used in these studies was the same as described in ref 2. The eutectic composition of 70 mole % LiC1-30 mole % LiF was made The Journal of Phyaieal Chemistry
by weighing reagent grade and relatively anhydrous salts in air and further purified by chlorine treatment of the melt, flushed with pure helium, and then evacuated, sealed, and transferred in a Pyrex container to an inert-atmosphere box. The helium atmosphere in the box was continuously recirculated and repurified during the course of the experiments as previously described.2 Lithium metal was obtained from the Foote Mineral Go., Philadelphia, Pa., in the form of 1-lb ingots sealed in cans under an argon atmosphere. The impurity analysis supplied by the Foote Mineral Go. was 0.003y0 Wa, 0.0028% K, 0.003% C1, and 0.0031% N2. From the J. T. Baker Chemical Go., Phillipsburg, N. J., tin metal was obtained in shot form. The impurity analysis supplied by Baker was As, 0.2 ppm; Cu, 5 ppm; Fe, 30 ppm; Pb, 30 ppm; and Zn, 5 ppm. Apparatus and Procedures. The cells used in this investigation were the same as those described in ref 2. A porous beryllia crucible was used to contain the anode or cathode and to minimize the effect of lithium and intermetallic compound solubility in the electrolyte. All electrode alloys used were prepared by combining appropriate weighed quantities of the elements in the inert-atmosphere box. Because of the previously observed experimental (1) This work was performed under the auspices of the U. S. Atomic Energy Commission. (2) M. S. Foster, S. E. Wood, and C. E. Crouthamel, Inorg. Chem., 3,1428 (1964). (3) M. Hansen and K. Anderko, "Constitution of Binary Alloys," McGraw-Hill Book Co., Inc., New York, N. Y.,1958, p 904.
THERMODYNAMICS OF BINARY ALLOYS
3043
fact that lithium metal transferred from an anode of 17.STANDARD DEVIATION OF POINTS FROM CURVE pure liquid lithium to a liquid alloy cathode a t rates A ALLOY SATURATED WITH Li5 S n L ( s ) sufficient to preclude stable, reproducible cell potential measurement, the original intent was to use as a -----DI . . .... . . reference electrode a tin alloy saturated with solid xLi= ai Li5Sn2 (over-all composition of 0.30 atom fraction of Q* 3 mv. tin). This is analogous to the reference electrode of a Q bismuth alloy saturated with LisBi (over-all compoIz sition of 0.40 atoni fraction of bismuth) that had been XLi.O.2 used in studies of the Li-Bi system.2 When cells conJ sisting of a lithium anode and a saturated cathode alloy (over-all composition of 0.30 atom fraction of tin) were operated, the voltages observed appeared to be stable at constant temperature, but the reversible cell voltage was difficult to ascertain because of the slow response of cell voltage with change of temperature. Many points required 10 hr to achieve equilibrium. Before doing further experimental work in this system, it was decided to check the electrode consisting of liquid tin saturated with solid Li5Snzagainst the electrode of liquid bismuth saturated with Li3Bi and, if possible, to apply the latter as the reference 30 IIO 900 io00 electrode in further studies. This check was accomTEMRRATURE (*IO plished without any difficulty other than the slow apFigure 1. Voltage-temperature-composition data for the cell proach to equilibrium mentioned above. The voltages Li(l)/LiCl-LiFlLi in Sn(1, X L ~()X L ~ = atom fraction of Li). obtained, combined with the reference electrode potentials established,* yielded identical results, within experimental error, when compared with those obtained Also shown in the figure (the experimental points are with a pure lithium anode. Thus, the reference in triangles) is the potential of type 4 cell: (4)Li(1)ILielectrode used in these studies consisted of an alloy of C1-LiFiSn saturated with Li5Sn2(s). bismuth saturated with LioBi. In this cell, a species The smooth curve for each composition represents of Li3Bi is the most soluble entity in the electrolyte the cell potential as a linear or quadratic function of (approximately one order of magnitude greater than temperature. This function was derived by a leastany Li-Sn species). Lithium metal solubility in the squares treatment of the data. The standard deviation, electrolyte, however, was negligible in the absence of u, of the individual experimental points from the the pure liquid lithium anode. The stability of the smooth curve is indicated. cell potential with time and with temperature cycling The cell reaction for type 3 cells may be written as indicated thai changes of electrode potential by any the transfer of lithium from pure lithium (saturated irreversible transfer of these species was negligible. with electrolyte) to the alloy, for which the change in the Gibbs free energy is Results
P
The cell potential-temperature-composition data for single-phase 1iqu:d lithium-tin alloys were obtained from two types of cell: (1) Bi(1) saturated with ~ (atom Li3Bi(s)lLiCl-LiF]Li in Sn(1, XI,,),where X L = fraction of Li in Sn) = 0.10, 0.20, 0.30, 0.40, 0.50, 0.60 and 0.65; and (2) Li(l)ILiCl-LiFIBi(l) saturated with Li3Bi(s). Adding the potentials of type 1 and type 2 cells at a given temperature yields the potential of a third type of cell: (3) Li(l)ILiCl-LiFILi in Sn(1, XL,). The potentials of cells of type 3 are shown in Figure 1 as a function of temperature a t several cathode compositions (the experimental points are in circles).
AG
=
-FE = RT In
aLi
(1)
where F is the value of the Faraday, E is the cell potential, R is the gas constant, T is the absolute temperature, and a ~is, the ~ activity of lithium in liquid tin alloy. The standard state of lithium is taken to be the pure liquid metal in the cell environment, L e . , saturated with electrolyte, at the temperature of interest. The excess chemical potential of lithium in the liquid alloy is then given by the relationship ApLiE =
-FE - RT In XI,^ Volume 70, Number 10
(2) October 1966
3044
M. S. FOSTER, C. E. CROUTHAMEL, AND S. E. WOOD
The values so calculated were fitted by a least-squares method to the equation
-6 -I
-7
where the data for each composition were weighted equally according to the number of experimental values for that composition. The values of the constants are shown in Table I. The standard deviation of the observed cell potentials from the values indicated by this equation was 0.5 mv.
-B 5
+a
-8
x
-9-
-10
-
-11
-
-I2
-
-13
-
-14
-
Table I : Coefficients Used in Evaluating Eq 3 i = 2
i = l
ai
b, Ci
2018.75 - 35,5044 0,021445
-38,187.4 84.9183 -0.044818
i = 3
33,403.92 -53.6456 0.030409
The curves shown in Figure 2 represent the calcui ~ eq 3 as a function of comlated values for A p ~ from position a t temperatures of 800 and 950°K. The experimental points shown were calculated from the smooth curves in Figure 1. Also shown for comparison in Figure 2 are the values for A ~ L calculated ~ ~ , from the composition of the liquid phase indicated by the published phase diagram3 and the cell potential obtained from a type 4 cell (cathode saturated with solid Li5Sn,). It must be emphasized that the region of the applicability of eq 3 extends only over that portion of the phase diagram in which tin-rich, unsaturated alloys exist, and only for temperatures between 800 and 1050°K.
Discussion The solubility of Li5Snz in liquid tin has been calculated a t chosen temperatures. Equations 3 and 2 were equated at a given temperature. The corresponding potential of a type 4 cell (cathode saturated with solid Li5Snz)B-as used in the calculation of X L a~t the saturation point. The results are shown in Figure 3 and are compared with the phase diagram given by Hansen and Anderko.3 Several attempts were made to fit the data to a function of the form ApLiE = Xsn2f(T,XLi) where f(T,XLi) is a function of the temperature and composition. These attempts failed in that the calculated values deviated widely from the observed values at the lower values of the concentration of tin in the alloy. Apparently, this behavior is forced in the particular way in which the function attempts to reach zero point of the curve (at a composition of pure Li). The Journal of Physical Chemistry
-
0.0
0 A
I
I
I
I
I
I
0.1
0.2
0.3
a4
a5
0.6
0.7
0.6
0.9
1
1
I
I
I
I
'8" .-1
I
I
1.0
I
I
IO50
IO00 950
-z
900
W
9
850
Id -
a
!
800
W c
750
roo 650
600
ao ai
a2
~4 0.5 0.6 0.7 a8 ATOM FRACTION TIN IN LITHIUM
0.3
as
1.0
Figure 3. Partial phase diagram of the L i S n system showing calculated solubility points.
I n reality, for an equilibrium system the curve representing the excess chemical potential of lithium in the binary liquid at constant temperature as a function
THERMODYNAMICS OF BINARY ALLOYS
3045
of the mole fraction of the liquid phase must be discontinuous through the composition range where solid LisSn2 is present in equilibrium with a liquid alloy, since no liquid of these compositions exists. Because of these difficulties and the experimental difficulties noted, it was decided to use the simpler, but empirical, function given in eq 3. If the cell reaction for a type 4 cell may be written as Li(1)
+ 2/6Sn(l)(satd with Li5Snz)+
'/~Li~Snds) (4) then one may represent the Gibbs free energy change for the cell reaetion as
AG
=
-FE = l/;AGt"
- 2/5RTIn asn
(5)
where E is the voltage of the cell of type 4, AGt" is the standard Gibtls free energy of formation of Li5Snz(s) from the element.s, and asn is the activity of tin in the saturated alloy. Li(1) and Li5Sn2(s) are said to exist in their st,andard state in the cell environment.
The activity of tin was calculated by applying the Gibbs-Duhem relationship and eq 3. Values of AGt" for the formation per mole of LiSSn2a t various temperatures are given in Table 11. The estimated error of these values is 1.O kcal/mole.
Table 11: Standard Free Energy of Formation of LisSn*(s) Temp, OK
A@@, kcal/mole
800 850 900 950 1000
-61.4 -59.8 -57.9 -55.3 -52.4
Acknowledgments. The aid of A h . Richard E. Eppley and Mrs. Gene H. McCloud in obtaining the experimental data is gratefully acknowledged.
Volume 70, Number 10 October 1966
