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Electrochemical behaviour of iron in the presence of sulphide ions dissolved in molten LiCl-KCl eutectic at 450°C
ELECTROCHEMICAL BEHAVIOUR OF IRON IN THE PRESENCE OF SULPHIDE IONS DISSOLVED IN MOLTEN LiCl-KC1 EUTECTIC AT 450°C G. SANTARINI Commissariat
B 1’Energie Atomique,
DCAEA-SCECF,
(Received 20 November
Boite postale 6,92260
Fontenay-aux-Roses,
France
1980; in revised form 2 June 1981)
Abstract-From some electrochemical experiments and from thermodynamic considerations a potential - pS’- diagram is proposed for solid speciesrelativeto the ironsulphur system in the presence of molten LiCl-KC1 eutectic at 450°C. On the basis of this study the following values may be adopted: - Gibbs free energy of formation of the Li,FeS, phase (from LirS and FeS): -0.7 kcal (- 2.9 kJ); - Gibbs free energy of formation of the LiK,Fe,,S,,CI phase (from FeS, Li,S and the LiCI-KC1 eutectic: -16kcal (-67kJ); -solubility product of sulphide FeS: 1.5 x lo-‘* (in the molar fraction scale); - sotubility of sulphide LilS: 5.28x lo-* (molar fraction). It is shown in addition that the experimental results point to the existence in solution of species other than Fe’+ and Sr- ions.
qualitative theoretical potential - pS2- diagrams representing fields of relative stabihty. This representation is similar in every way to that of the potential -pH diagrams inaqueous solution or the potential - PO’diagrams in fused salts and may be obtained by the same methods[30-32-J. These diagrams can be used as guides when investigating the conditions of formation of the various species. Figure 1 shows for example a possible qualitative representation for the relative stability regions of the solid compounds mentioned above, neglecting any solid solutions which may be present. Table 1 lists the reactions considered, the equilibrium conditions of which are represented by the numbered straight-line segments of Fig. 1, and gives the slopes of these segments in (RTln 10)/F unit. The bracketed species are very highly concentrated in the eutectic and their activities may therefore be considered as constant. The triple points of the figure correspond to constant Fe” and S’- ion concentrations, as shown for example by reactions A, B and C in Table 1. Configurations other than the one represented are possible: vertical 7 could intersect branches 2 and 4 in two triple points Li,S, J, X and Li,S, Fe, J; the regions of the compounds Li,Fes$ and LiK,Fe2,S,,Cl could have a common boundary __ For a quantitative representation certain thermodynamic data must be known, for example the standard potential of the Fe-Fe*+ couple, the solubility product K, of the sulphide FeS and the concentrations or potentials relative to certain triple points, Table 2 gives some bibliographical data. The potentials are referred to the Ag-Ag+ 3 x lo-‘. reference electrode used in our experimental work*. The potentials noted E” are the standard potentials
INTRODUCTION
This work is part of a general thermodynamic and electrochemical study of reactions between the different species liable to be generated by the elements iron and sulphur in the presence of fused LiCl-KCI eutectic at 45O”C[l, 23. A bibliographical approach leads us to take into consideration: -for the ions in solution in the eutectic: cations Fe’+ and Fe” (solvated)*, anions sulphide S2 -, polysulphides and polyhyposulphides such as Sq- , St-, S;, S;, and complexed iron cations such as FeS:-[3-201; -for the solid phases: LiaS, FeS, Fe&, Li,FeS,, LiJFe,S,, LiK,Fez,S,,Clt[2W29]. Stability and predominance of these species depend on two parameters: -an oxido-reduction factor: the potential E,; -an acido-basicity factor: for example the S2sulphide ion concentration. It is therefore possible, knowing only the stoichiometry of the species liable to be formed, to draw * Throughout this work the possible solvation of ions is not accounted for in the terminology used. The standard state for the ions in solution is taken as the state obtained by extrapolation, in the reference state, to unit molar fraction. The reference state is that of the ion in infinitely dilute solution. Potentials and concentrations are expressed in the molar fraction scale. t These phases, encountered during the running of high energy density batteries (Li-AI/FeS or FeS2) have been studied repeatedly at the Argonne National Laboratory (USA) where their formulae are replaced by letters: Li,FeS1 LilFetS, LiK6Fes+Sr6Cl
* For this we use Nernst’s equation and the standard potential values given by the tables 1343. The junction potential differences and those of the thermoelectric couples are neglected.
=x =z = J 495
G. SANTARINI
496
corresponding to thermodynamic equilibria, are not coherent: they fail to satisfy the inter-relationships authorized by thermodynamic considerations. To gain a better understanding of this system an experimental study was therefore undertaken. Special attention was devoted to solid phases in equilibrium with the liquid eutectic at 450” C and to the lower part of the diagram mentioned above. 1. EXPERIMENTAL
1_iz
-pS*diagram of iron in Fig. 1. Qualitative potential molten LiCI-KC1 eutectic. Relative stability regions of solid compounds. Table
1. Reactions
LiK,Fe,,S,,Cl
The experimental device used consists of a tight cell suitable for standard electrochemical experiments, with a three electrodes system[33]. With this set-up the salt can be- dehydrated in situ by anhydrous hydrochloric gas bubbling and kept under vacuum or under inert atmosphere. Most of the experiments however were performed with already purified salt provided by the Anderson Physics Laboratory, Champaign, Illinois. The LiCl-KC1 eutectic (or a solution of L&S in this eutectic) is contained in an alumina crucible. A light bubbling of dehydrated and deoxygenated argon is kept up m the salt throughout the experiment. The potential of the working eiectrode (iron, or Fe-FeS mixture) is measured against a reference electrode made up of a silver rod in contact with a solution of silver chloride in the eutectic, at concentration 3 x lo-’ (in molar fraction). The electrical contact is made through a thin-ended Pyrex tube.
considered for the establishment
FeS+2e- =Fe+S’-
:
+(Li’
+ 46rm +24Fe+26Szm
METHOD
of the potential
+6K+ +CI-)
- pS2-
diagram
of Fig. 1
l/2 13/23
3
Li,FeS, + 2e- *Fe+2S’-+(ZLi+)
4
24Li,FeS, + (6K* +ClV)+ 2e- eLiK,Fe,,S,,Cl+
5
24FeS+
6
Li,FeS z~FeS+S2-+(2Lic)
cc
7
LizS*(2Li+)+Sz-
m
8
Li,Fe,S,
0
9 10 11
(Li+ + 6K+ +Cl-)
+2Sf-
1
+2e-
22S’-
+(47Li+)
+LiK,Fez4Sz6CI
+ (Lie) + P- +ZLi,FeS,
Li,Fe,S, + e- eZFeS+ZS’-+(3Li+) Fe& + 2e- =Z=FeS+S’2FeS, + (3Li
l
+6K+ +6K+
A B
LiK6Fe,.&,Cl LiK6Fe24S26Cl
C
(2Li+)+SZm *Li,S Li,FeS, + (2Li+) *ZLi,S
-1
$2 0
) + 3em G= Li,Fe,S,
23FeS+Fe+(Li+ 26FeS+ Fe+(Li+
11
+Cl-)+ 3Sz- G+L~K~F~~~S~~CI +C1-)=+LiK6Fe2~S2&l + 3Fez+
=23Li,FeS, + Fc + (6K+ + Cl-) + (45Li+)+20S2+ (25Li’) *13LizFeS1+Fe+(6K++Cl-)+lOFG+
+ Fe’*
of the electrochemical couples represented in lower indices. The symbols E and x represent the potentials and molar fractions of S2- ions at the triple points given in lower-index form. ;L,,s is the solubility of ions in solution in Li,S (molar fraction of S equilibrium with the L&S solid phase). Unfortunately we find that these data of Table 2, if
Several types of auxiliary electrode were used: Pyrex or porous alumina tube containing a silver wire dipping in an LiCI-KCl-AgCI mixture, boron nitride tubecontaining a tubular iron electrode dipping in tbe LiCl-KC1 eutectic. For the coulometric experiments a potentiostat used in a constant-current set-up allows an anodic or
Electrochemical
behaviour of iron in the
Table 2. Some bibliographical
-0.316(~0.007)V (Ag-Ag+ 3 x lo-‘)
c341
-0.53ov (Ag-Ag+)
-0.311v (A&Ag+
3 x W2)
PO1
-
- 0.362 V (Ag-Ag+
3 x lo-‘)
PI
(4-&+
)
1.219v (Pt-PtZ+) 1.58 x lo-’ 1.56(+0.05)x 1.3 x lo-”
K, (FcS)
2.3 x io-‘2
Fe. X
xJ, Fe. FeS xX,
Fe. J
AND
[it] PO1
1.625 V (Li-Li+)
-0.93ov
1.629V (Li-Lit)
- 0.926 V (Ag-Ag+
(Ag-Ag+
3.8 (*0.2)
x 10-4
1.5( fO.l)
x 10-A
RESULTS
2.1. Standard patenciul oJ the Fe-Fe2+
PI
10-S
cathodic current of given intensity to be passed through the working electrode. 2. EXPERIMENTS
497
l
SLi,S
ELi,S.
of sulphhide ions
data useful for this research (T = 450” C)
- 0.535 ( * 0.007) v ‘%tFc’
presence
couple
In this experiment the potential of an iron electrode dipping in pure LiCI-KC1 eutectic at 450” C is followed during the coulometric generation of Fe2+ ions.
3 Y lo-‘)
c273
3 x 1O-2)
c2*1 c201 PO1
Stabilisation of the potential after each electrolysis is reached in a few minutes under these conditions. Curve 1 of Fin. 2 shows the result of a test. The abscissae represeit the decimal logarithm of the molar fraction y of Fez + ions produced by electrolysis (calculated assuming the validity of Faraday’s law) and the ordinates the eouilibrium ootential difference between the iron electrode and the kg-AgCI 3 x 1O- ’ reference electrode. The points correspond to the experimental values,
- 0.500
,)
-0.600
Y P rz
-0.000
-8
-7
-6
-5
-4
-3
-2
log,, Fig. 2. Potential of an iron electrode versuslogarithm of the molar fraction of Fez’ ions produced electrolysis: (1) in pure LiCI-KC1 (at 450°C) (2) in a solution of Li,S in LiCI-KC1 (at 450°C).
by
G. SANTARINI
498
the solid line plots the equation:
K, = 1.5 x 10-l’
= 11.P
Under present experimental conditions the stabilization of the potential after each electrolysis is reached in a few minutes. Radiocrystallographic analysis shows that only the FeS phase is present on the iron electrode after the test.
in the case: E;+zs
= --0_294V
z.
= 3.5 x 10-6
Excellent agreement is therefore observed between theory (Nernst’s equation) and experiment if we assume the presence in the salt, soon after immersion of the iron eiectrode, of a 3.5 x 10e6 molar fraction of Fe*+ ions due to the attack of iron by various oxidising impurities (0,. H,O). The validity of the method is thus confirmed, and this within a wide concentration range (molar fractions between 4 x 1W6 and lo-“). Five tests all gave Z, values between 3 x 10m6 and 12 x lob6 and potential values E&sz+ within the interval: E;c:slFe~+ = - 0.302 f 0.008 V (with respect to Ag-Ag+ 3 x 10-2) or: E&z.
or: pL K, = -log,,K,
= - 0.521+ 0.008 V (with respect to Ag-Ag+ standard state)
This result agrees within the limits of experimental error, with those given in Table 2 which concern a narrower Fe2 + ion molar fraction range.
2.2. Potentiometric solubility product
determination
of the iron sulphide
A coulometric generation of Fe2* ions has been carried out in a solution of Li2S in LiCI-KC1 at 450” C. A very low concentration was chosen in order to avoid formation of the LiK,Fe2J&,CI phase (Fig. 1). If we assume Fe and FeS to be the only stable solid compounds under these conditions, and Fez+ and S2 the predominant ionic species in solution, the equilibrium FeS ti Fe’ + + S2- is expressed by the equation: E = E”F@+ +4K,]}
+
g
In
{Y
-Yyo+Jc(Y-Yyo)2
ln2
-g
with K, the solubility product of FeS and y0 the difference between the initial molar fraction of S2ions and the initial molar fraction of Fez+ ions produced by the action of oxidising impurities. The result of this test is given by curve 2, Fig. 2 where the points represent the experimental values, the solid line the graph of equation (1) in the case: E&/@
= -0.3oov y, = 1.26 x IO-’
K, = 1.5 x IO-” with the hypotheses considered this test thus gives the value:
2.3. Cotclomerric generation of Fe2+ ions in a concentrated solution of S ‘- ions in the LiCl-KC1 eutectic To reveal any potential plateaux which would express the equilibria between solid phases Li,S-Fe-Li,FeS,, Li,FeS,-Fe-LiK,Fe,,S2,CL LiK,Fez,&,Cl-Fe-FeS the same experiments as abode were performed in the presence ofconcentrated Li,S * solutions in the LiCl-KCI eutectic at 450°C (molar fractions above 10e3). Under these conditions the stabilization of the potential after each electrolysis is found to be extremely slow, taking several hours. The results obtained are then noticeably affected by small leaks on the gas circuit or by diffusion through the cathode compartment. No potential plateau appears clearly. It is observed however that in each case the initial potential lies around -0.93OV (with respect to Ag-Ag + 3 x 10 - ‘), never falling below this value even for highly concentrated Li,S solutions. Figure 3 gives an example of a test result: the points between - 0.920 and - 0.6OOV certainly do not correspond to equilibrium states (in spite of stabilization periods longer than 1 h); the potential fluctuations in this zone may be attributed to poor contact between the iron and the solid phases formed. As a matter of fact, the reactions between the LiK,Fe,,S,,Cl phase and the Li2FeS2 or FeS phase are very slow and involve the presence of metallic iron (triple points A and B of Fig. 1). 2.4. Coulometry on electrodes consisting of an Fe-FeS mixture To speed up the kinetics of reactions involving the LiK6Fe2,S,,CI phase, electrodes were made from an intimate mixture of iron and sulphide FeS powders surmonted by an iron rod in contact with this mixture and placed in a porous alumina tube. (a) Figure 4 shows the result of a series of potentiostatic reductions of this mixture followed by potentiostatic oxidations. The potential of the electrode is plotted against the quantity of electricity needed for the intensity at this potential to decrease, in absolute value, to 40 PA. This quantity is expressed in molar fraction x of Fe’+ ions reduced (assuming the validity of Faraday’s law and referring this molar fraction to all the Li+ and K* ions present in the cell). Here again the experiments are very long and the molar fraction determination is certainly falsified by diffusion through the auxiliary compartment and oxidation by impurities. Two potential plateaux are observed for the values - 0.900 and -0.930 V. l Henceforward the symbol pX placed before a thermodynamic quantity reprcscntesthe decimal cologaritha T’he concentrations are always expressed in molar fractions. We thus avoid possible confusion with the symbol p (pO-,
pS-. . , ) which molarizy (in 02-,
usually refers to the coloprithm S2-. . .).
of the
Electrochemical
Fig. 3. Coulometric
behaviour
of iron in the presence
of sulphide ions
generation of Fe ‘+ ions in a concentrated solution of Sz- ions in LiCI-KC1 4soT).
Fig. 4. Coulometry on an electrode consisting of an Fe-FeS mixture (x& = 2.9 x lo-“).
499
eutectic (at
(b) Figure 5 concerns the same kind of experiment, but here the electrolysis was interrupted and the potential allowed to stabilize in each case. On this figure the dark circles represent the potentials of the electrode during the potentiostatic coulometry operations and the light circles the potentials after stabilization. A potential plateau appears temporarily for - 0.930 V and a plateau is observed for - 0.900 V. (c) Figure 6 shows the result of a series of cathodic then anodic constant-current cycles carried out at low intensities (0.2 mA, 0.25 mA, 93 mA). The ordinates represent the potential during the test; the quantity of electricity plotted as abscissae is still expressed in molar fraction of Fe2 + ions reduced (number of moles of electron pairs involved divided by the total number of moles of cations or anions present in the eutectic): with the mass of salt used (19.3 g) the constant current durations needed to reach a molar fraction of 10- 3 are 94 h, 75 h and 63 h for intensities of 0.2, 0.25 and 0.30 mA respectively. The anodic and cathodic branches of each cycle display shoulders encompassing the values - 0.900 V and - 0.930 V, but also two others which reveal the existence of a solid phase transformation for potentials between - 0.7ODand - 0.900 V. The potential gaps of
G. SANTARINI
500
-0.500 i -0.600
,’
I
-o.,oo_\
i-7
I
I
hx pr)
-0.100-
B \
4” i;
-o.soo-
I I I 1 I
, -0.70C 1 Y o_
: ,
," + w < 3 w
-
0.3
--__
0.25mA
_.........-
0. 2 m*
rnA
-0.800
Fig. 5. Coulometry on an electrode consisting of an Fe-F& mixture (x& = 2.8 x 10m3). -0.900
these pairs of anodic and cathodic shoulders suggest that the reactions which occur for potentials - 0.900 and -0.930 V are relatively fast, whereas those responsible for the shoulders between -0.700 and - 0.900 V are very slow. Before attempting to interpret all these results we must examine the data given by thermodynamic considerations.
In the following it will be assumed that the predominant ionic species in solution are Fe”+ and S2ions. This hypothesis is certainly all the more valid as the potential and the S ‘- ion concentration are low. dictated
10-S
X Fig. 6. Cathodic and anodic constant-current cycles on an electrodeconsisting ofan Fe-FeS mixture(r& = 3 x lo-‘).
gas) QL,+, E&,z+ the standard potentials of the Li/Li + *, and Fe/Fe’* couples, the consideration of a simple thermodynamic cycle shows that:
3. DISCUSSION
3.1. Relationships
sure-4
0
or, at 723 K and adopting the values of free energies and potentials given by[34] and[35]:
by thermodynamics
pxK,
-pxS)&s
= 8.450.7
Thermodynamic considerations show that the equilibrium quantities mentioned above (solubility product, solubility, interphase equilibrium potentials) are not independent, and a quantitative representation of the equilibrium conditions must account for these
(b) Furthermore, geometrical considerations on the lower part of Fig. 1 diagram, combined with the equilibrium conditions for the reactions Fe e Fez+ + 2e- and FeS s Fez+ + S2- give the relation:
relations. For the lower part of the diagram on figure 1 we can establish the existence of three sets of relationships:
or again, bringing in the triple point D relative to the metastable equilibrium amongst the three phases Li,Fe$, Fe and FeS:
P&
- ~xs~its
(a) With &s and &s being the standard Gibbs free energies of formation of the solid compounds FeS and Li2S (from solid iron, liquid lithium and S2
= &
(2 EkFc'+
* For Lif the standard LiCl-KC1 eutectic.
--x,F~,F~s-ELI,s.F~,x)
(4)
state is that of the ion in the
Electrochemical behaviour of iron in the presence of sulphide ions (c) The same kind of reasoning can show that the potentials of equilibria (stable or metastable) between solid phases are inter-related. We thus have: 3E,,,,.,s =EJ.FCF~S
3.2. Calculation
+ 1OEx,,,,
-
13EX,~e.~es = 0
(5)
- 20EX.Fe.J - 13EX.J.FeS = '
(6)
of coulometric
titration
curues
Let us consider the cathodic reduction of a mixture of metallic iron and solid sulphide FeS under a constant current low enough for electrochemical equilibrium to be taken as reached at each moment; let us suppose moreover that the configuration of the relative stability regions is that of Fig. 1. The potential starts by decreasing exponentially: the figurative point of the system describes branch 1 of the diagram; as soon as the potential reaches the value EJ,Fc.Fss, the FeS phase reacts to give the LiK,Fe,,S,,Cl phase: 26FeS-+(Li+t6K+fCl-)+6e---fLiK,Fe2&,Cl
+ 2 Fe
During this transformation the potential remains constant at E J,Fs.FsS_When all the FeS phase has reacted the potential decreases along a new exponential: the figurative point describes branch 2 of the diagram. We observe a new potential plateau for the value E,.Fc,FcS, a new exponential decrease (branch 3), a plateau for the value EL,s,Fc.Xr and finally a vertical decrease to the lithium deposit. These curves can only be observed in their entirety if the sulphide FeS is present originally in excess. If we call x& the initial molar fraction of the sulphide FeS (number of moles of FeS introduced divided by the total number of moles of cations in the eutcctic) and x the molar fraction of Fe2 ’ ions reduced, by writing the conservation equations for each equilibrium we can express x a function of a, molar fraction of Fe2+ ions in solution, xsl-, molar fraction of S2- ions in solution and x&. In addition a is related to the potential E by Nernst’s equation and from the above geometrical considerations xsl- can be related to the potential E. In this way the relationship between x and E is determined completely. Table 3 gives the equations obtained-with f = (F/RT).
501
The same curves are described backwards if the direction of the current is reversed. Similar arguments could lead to equations for the titration curves of an Li,S solution by addition of FeClz or an FeQ solution by addition of Li,S. 3.3. Interpretation
o~experimental
results
3.3.1. Solubiliry producr K, oJ’ FeS. The solubility product value K, = 1.5 x lo-l2 determined here is close to that obtained during the work reported in[20f: K, = 2.3 x lo- I’. The latter value however is probably less accurate than the former: this value (K, = 2.3 x lo- ’ ‘) is derived from the result of a potentiometric titration of a chloride FeCl, solution by addition of sulphide Li,S and the conditions of this titration (initial molar fraction of FeCl, about 1Om4) are such that the potential zone used for the determination of the constant overlaps that of the thermodynamic possibility of formation of the LiK6Fe2.+!&Cl phase, as found from the interpretation of our own results below. This experiment ought therefore to reveal the existence of potential plateaux and their absence may be attributed to the great slowness of reactions involving the LiK,Fe,,S&l phase, resulting in very long stabilization times; the values used may not have been equilibrium values. In our experiment (initial molar fraction of Li,S about 10m5) stabilization was obtained in a few minutes. 3.3.2. Potential plateaux. The lowest potential plateau value revealed in this study, - 0.930 V, can only be attributed to the precipitation of lithium sulphide Liz& and agrees in fact with other results given in the literature (Table 2). The value -0.900 V may then be assigned to either the equilibrium X, Fe, J or the metastable equilibrium X, Fe, FeS. Calculation of the equilibrium curves by the method described earlier (Section 3.2) shows that the latter hypothesis accounts better for the experimental results than the former. We should then have: E X.Fe.J
=
ELi,S,Fc.X=
-
0.930 v
and using (7): E J.Fs.FeS=
-0.800
v
Table 3. Equations of coulometric titration curves 1
Fe, FeS
A J, Fe, FeS
X = SLi~sexPCf(ELi2s.Fc,x E = EJ, Fe.FeS
+#Ezc,F~.J+
J
~Li,Se~PCf(~LiIS,~s,x++SEx,~c.
&EJ.
F~,F~S--ZWI
-;MEJ.F~.FAI
-exPC2f(E-Ekr@+)l
--~P[~~(EJ.FS,F~S-E~~F~~')I
< x
2 J, Fe B X, Fe, J 3
X,Fe
E = EX.Fe.J &X~CS+~sL~~scxP[~(EL~~s,F~.
x -
Ex,F,J)]
X <~Xb,s
ffS~i~seXP[f(E~~~~e,x
x = Ix&s
+f~~i~~exp[f(E~i,~, F~,X -WI
--~P[~~(Ex.F~,J -
-Ex.F~.J)]
-exP[2f(Ex.Fe.~
E~F~z+)]
-E~F~‘*)]
-expC2f(E-EER-~~~+)l
E = ELiIS,Fe.x C Li,S, Fe, X Liz?+,Fe
)(X&s+ SLi,s)-exPC21(EL*S,FS.X-E~~-~S x = x&s E&i-Li* < E < ELiIs, Fe.x
z*)I < X -= x~~s--XpC2f(Eu,s,F=.x
-EKvI+~*)I
G. SANTARINI
502
This value fits in well with the shoulders observed on the potential us time curves obtained during cathodic and anodic constant current maintenance! cycles on a mixed Fe-FeS electrode (Fig. 6). The following interpretation (accounting for equations 5 and 6) is therefore proposed: E,. Fs., = fiLi,S.Fs,x = - 0.930 V EX, Fe. FeS = - 0*900 v E J, Fe, FeS = -0.8OOV E X. J, FeS = - 0.600 V EkeFet * = - 0.302 V
Px K -
p, sLi,s = 8.55
K, = 2.842 x 10 - 9 sLizs
(8)
in excellent agreement with the thermodynamic relationship 2. Moreover equations obtained by the method of paragraph 3.1(b) give: P,
xX, Fe. J -
Px sLi,S = O
Px XJ, Fe. FsS - Px sLi,s = 1.603
or: xX, Fe.
J = %i,S
K, = 4.43 x lo- “, a value higher than either that of[20]: 2.3 x lO_ l2 or that determined in this work: 1.5 x lo- “. Moreover the theoretical titration curves (Table 3) calculated with these values are not in keeping with the experimental results (Section 2.4): in particular the x values necessary to obtain plateaux are too large: On the other hand if we take K, = 1.5 x IO-l2 we obtain:
(7)
The temperature 450°C would therefore correspond to the special case where the potential and pS2 _ conditions relative to the LilS, Fe, X and X, Fe, J equilibria coincide. This result agrees with that of reference[25] where it is shown that a mixture of the solid species LizS, LizFeE& and Fe in contact with LiCl-KCI eutectic only reacts to form a new phase, LiK, Fez4 Sz6Cl, at temperatures above 455 i 4” C. With the accepted hypotheses, (4) gives: or:
3.3.3. Potential - pS ’ _ diagram/or solid species. If sLi s in (8) takes the value given in[20]: sLiss= 1.58 X ‘lo-3 , we obtain for K,:
sLils = 5.28 x 10 - 4. This value disagrees with that of[ZO], but theoretical curves calculated on the basis of its validity (Fig. 7) fit the experimental results if the possibility of a metastable equilibrium between the X, Fe, and FeS phases on the one hand, and over-voltages due to the slowness of reactions involving the LiKsFe14S2,Cl phase on the other, are taken into account. It is shown later (Section 3.7) that the presence of certain ionic species in soluion other than Fez+ and S3 - can explain an apparent solubility of Liz S greater than the molar fraction of S - ions in solution in equilibrium with the solid Li,S, though the measurement of the FeS solubility product K, is not affected. We shall therefore take the value sLIzs= 5.28 x 1Om4 and can then present the solid phases equilibrium conditions in the form of the diagram on Fig. 8. Solid (with pLbFes, = - 36.3 kcal[37], FeS, @FaS = -26.8 kcal[35]) was taken into consideration for the drafting of this diagram, but not solid Li, Fe, S,. The dotted lines refer to metastable equilibria. The molar fractions of S2- ions relative to the different triple points are as follows:
x J,Fe,Fcs= 2.493 x lo- 2 sL,,$
sLi,S
=
xL,,S,Fe,X
=
--
xX.Fe,J
5.28 x 1O-4
i
-0.900
J
Fig. 7. Cathodic
X, Fe. Fe5 _---_---________--------~
‘.
reduction
of an Fe-F&
mixture:
curve calculated
\
\
\ \
for: SLAMS = 5.28 x 10e4 X&S = 3 x 10-3.
Electrochemical xX.Fc,F&
=
xX,J,FcS
XJ,F~,F~
=
1.32
X
=
behaviour of iron in the presence
of sulphide
503
ions
or, for the reaction:
3.26 x IO-*
L&S + FeS --* LirFeS,,
lo- ’
The value of xJ,reres agrees with that obtained from the results given on Figs 4,5 and 6, but not with that of reference[20]: 3.8 ( f 0.2) x 1Oe4. This difference is probably due to the slowness of reactions involving the J phase and to a poor contact between the metallic iron and the FeS phase in the experiment of reference[ZO]. 3.4. Gibbs free energies qfformation Li&Fe,,S,, Cl phases
of the L&Fe&
and
With the above hypotheses the Gibbs free energies of formation of the Liz Fe!& and LiK, Fez&e Cl phases at 450” C may be calculated from thermodynamic cycles. (a) For the Gibbs free energy of formation of Li,FeS,:
whence, adopting values of&and
&,
given by [35]:
P’E = - 129.6 kcal ( - 542.1 kJ)
AGg = RTfn xx,Fes sLi,s AGox = - 0.7 kcal (-
2.9 kJ)
to bc compared with that of reference[20] ( - 0.33 ( k 0.20) kcal). (b) Similarly for the Gibbs free energy of formation of LiK, Fe,, S,, Cl: value
~5 = F (6 E&+ + 3 &IS
- 5 Eti-Li*
-E&,I)
+ 23 pE=s
+ 3 RT In %!!QZ
sLi*s The standard potential of the K-K+ couple is not measurable directly but may be calculated from the activity of KC1 in LiCl-KC1 eutectic at 450” C and from that of superfused liquid KC1 at 450” C: with numerical values given by[34], [35] and [38], we obtain:
- 0.500
-0.600
Fe S
2 p: 0 I;I
2
-o.rw
\ 8 iz
- 0.800
-0.90(
Fig. 8. Potential -
pS’-
diagram af iron in fused LiCI-KCI eutectic at 450°C. Relative stability regions of solid compounds.
504
& = - 1045 kcai (-4371
kJ)
or, for the reaction: 23FeS+3LiZS+Fe+6(K+,CI-) -+ LiK6FeZrlSZ6CI + 5 (Li+, Cl-): AG; = 3 RTh, !%%!%? SLi,S
AG”, = - 16 kcal (-67
kJ)
Reference[20] gives: A G; = - 6.1 f 0.3 k-1. This study therefore reveals a greater stability of the LiKeFeZ SZ6Cl phase. 3.5. Composition
of the solid phase at equilibrium
Let us take a solid compound mixture Fe, FeS, Li, S in contact with an LiCl-ICC1 eutectic. Let X& xFcS and ~E,S be the molar fractions of these compounds in the eutectic with: XR + x& +x&s = xg, XL being the molar fraction of the solid mixture components as a whole, These components react with each other and with the eutectic and at thermodynamic equilibrium new phases appear: J, X or Liz!% The new molar fractions are: xx, x&. ’ n;, xk. By writing the iron and sulphur conservxu*s, ation equations for all the reactions possible we can calculate X’F~, X&s, X~irs, x’, and xk with respect to the initial molar fractions x&, x&, x&_ We thus obtain the diagram of Fig. 9 which represents the compositions of the solid mixture at equilibrium as a function of the initial compositions. For clarity of representation the proportions are not respected (stoichiometry of the J phase and ratios between and xz), but Table 4 gives xJ,F~,FeS, xX,Fe,J . . . the mequalities which define the zones represented. In this calculation the molar fractions of the Fe2+ ions are taken to be always negligible compared with those of the Samions, which is quite justified once x$,s is not negligible. It is also limited to cases where xg IS small enough for the molar fractions to be assumed additive. Figure 12 calls for the following remarks: (a) As xoO increases (without reaching excessive values inconsistent with the assumed additivity of the molar fractions) the regions with two solid phases, shaded on the diagram, become narrower until finally only the four zones with three solid phases are observed: Table 4. Inequalities
defining the regions of Fig. 12
amb (J, Fe, FeS), bmd (X, J, FeS),amd (X, Fe, J), udc (Li,S, Fe, X). (b) The diagram concerns the case where the temperature is slightly above 450” C: in the potential -ps=diagram the Li2S, Fe, X and J phases are then distributed as shown on Fig. 1.If the temperature falls, points hand k approach points i and 1.At 450” C the X, Fe, J and L&S, Fe, X regions merge. As the temperature continues to drop this X, Fe, J, Li,S region separates along the segment mc into two regions Li,S, Fe, J and Li2S, J, X. In potential - pS2- coordinates we are then in the situation where the psLias abscissa vertical intersects branches 2 and 4 (Fig. l)*. Figure 10 shows the area representing potential at electrochemical equilibrium versus initial composition of the solid mixture. This diagram is qualitative, but the exact calculation raises no particular difficulty and may be conducted by the method explained in Section 3.2. The diagram refers to the case where the temperature is slightly above 450” C. At 450” C the X, Fe step disappears. The presence of the high-potential X, J, FeS plateau has surprising consequences, meaning that in titrations with an inert electrode the possible sequence: potential rise, plateau (X, J, FeS), fall may be predicted. Such curves correspond to cases of iron deficiency in the Fe, FeS mixture used since the consumption of iron is necessary to the formation of the LiIC,Fe24S26CI phase. We should also mention that in the diagram of figure 10 the titration curves obtained by addition (FeCI, to Li,S or L&S to FeCI,) are the intersections of the surface represented by planes parallel to the plane a b e d. The coulometric titration curves on the other hand are the intersections of this surface by the set of planes passing through the edge symmetrical to the edge a d with respect to the plane b c fe. This comment allows a rapid visualization of the shape of these curves. 3.6. Standard
potential
of the S2--S2
couple
Knowing sLiZsit is possible to calculate the standard potential of the S2--S, couple. Writing:
We obtain: E;z--~~ - B;,_Li+ = 1.978 v V (with whence: E$_s, = -0.577 Ag-Ag+ 3 x lo-’ electrode)
respect to the
This value is quite different from that obtainable by direct measurement ([39], Table 2). We can explain this divergence by allowing that sulphur is highly
X,
Fe
Xx,Fe,J
< ~&S-xkeS
4
XLiIS.Fr.
X
l This study is confinedto the temperature450°C that of most determinations of thermodynamic and electrochemical quantities found in the literature.
Electrochemical
be Fe5 Fig. 9
soluble
in a sulphide
3.7. Ionic species
of iron in the presence of sulphide
d
f
solution
*s:-([lo],
in solution were solvated). If other species are present in significant concentrations they may affect the determination of the Sz- ion equilibrium concentrations (for example sLizs) and the FeS solubility product K,. Henceforward we shall call x’ and K: the molar fractions and solubility products calculated from the experimental results without accounting for these additional species, and x and K, the real values. A large number of extra ionic species may be involved (Fig. 11, Fig. 12): Hitherto
the predominant
a function
of initial composition.
index ri can be positive, negative or nil*. The reaction of formation of a species EC may be written: +sis-
in solution species
assumed to be Fe’+ and S2 - ions (possibly
- polysulphide and polyhyposulphide ions can predominate in certain potential and pS’zones. Some authors have thus suggested the formation of S:- and S; ions to explain potential measurements for sulphur in contact with a sulphide solution in eutectic or to account for the colour of these soIutions[3-191. - Fe2 + ions may be complexed by S2- ions, giving rise to species of the FeS”, FeSz I, Fe%type, or
associate with polysulphide or polyhyposulphide ions. The resulting species may be solvated; - S2- ions may similarly combine with Fez+ ions to give species of the Fe2SZC or Fe&‘* type. - Fe3+ ions only appear for high potentials (E;E”IFe’. = 0.835 V with respect to the Ag-Ag+ 3 x 1O-2 electrode[34] but might be stabilized by complexing with formation of ions such as FeS+,
FeS; , FeS: -. We shall call Fei,Sz these species E,, possibly solvated. One of the two indices J and si may be nil; the
50s
S2
of the solid mixture nt equilibrium in the form:
ions
phi
Liz k
Composition
3s + s=-
hchaviour
+Fef.S2,+
(si+;-.fi)Fe
If we call Kj the equilibrium
constant for this reaction the molar fraction of species Ei is related to those of Fez+ and S 2- by the equation:
xa, = K&$.‘2.X~,_ We shall demonstrate
(9)
that:
- the presence of such extra ionic species given in the generalized form of Fe&S:J permits an explanation for the apparent discrepancies between experimental results. - assuming that only one of these species predominates, it cannot be indeterminate.
3.7.1. Determination of the molar fraction of S2ions. Let us suppose that to determine the molar fraction of S2- ions corresponding to an equilibrium amongst three solid phases P’ (of formula Li,. K,, Fe,. S,. Cl,.), P” and Fe we add S2 ions to an Fe2+ ion solution in the presence of metallic iron to form a first solid phase, for example P’, and continue
adding until the first traces of the second phase P” appear. The writing of the conservation equations for iron and sulfur in the case we should ignore the existence of l For the list to be exhaustive the species E, should be noted Lir, gk, S,* Cl:,. not to account for salvation, which needs not be mentroned in writing but to allow for the possible existence of ions such as Li:’ or Cl; and their combinations with Fez’, S’-. This would encumber the calculation without changing the principle, and unnecessarily for the region in question.
G. SANTARINI
Fig. IO. Potential
at equilibrium
versus initial composition
of the solid mixture.
--._
Fe,
5“’
*-‘--_____________________/‘---
,’ I’ /’
Fig. 11. A possible qualitative representation for the regions of relative predominance of polysulphide and polyhyposulphide ions.
-. -.
Fig. 12. A ‘possible qualitative representation for the fields of relative predominance of some FeSi -2X and FefY- * type ions in a solution in contact with metallic iron.
Electrochemical behaviour of iron in the presence of sulphide ions
species Ei, and in the case this existence is accounted for, gives:
I
SO7
We find moreover that the values sli,s = 1.58 x lo-” 203, x;.re.rCs = 3.8 x lo-*[20], K: = 1.5 x lo- I 1 (this work) or 2.3 x lo-i2[20] fail to satisfy these relationships; we have:
1
where y0 represents the initial molar fraction of Fe’+ ions, y the total molar fraction ofadded Szm ions, OL the molar fraction of Fe’+ ions in solution, and putting: (c’ - I’ - k’)/2 = h’. 3.7.2. Determination of rhe FeS solubility produrt. Assuming the non-existence of species E, the titration curve equation for a solution of S2- ions titrated with Fe2+ ions is written, in the FeS formation zone:
y=y,+or_K,
(11)
a
with
El=exp[$(E
1
y,,, the initial molar fraction of S2- ions*, is also the abscissa of the point of inflexion of the curve plotting potential usy, molar fraction of added Fe2 + ions. K: is the constant product ( y - y, + a)a. If species E, are taken into consideration we have:
We see that the curve described by this equation can only coincide with a curve described by (11) in three cases: (a) every ri is nil; we then have: K: = K, (b) every ri equals - 2; we then have: K;
=K,+CK,Ki
(c) within the range of molar fractions CLused for the study the term
i
L
is negligible compared with the other terms of (12). We have:
k, = 2
X;,F~,F~S 'k, kIp3
We have already observed (section 3.3.3) that the slowness of reactions involving the J phase could explain why the x; value obtained by direct determination is excessive, and k; therefore too high. On the other hand, the K: and &,s measurements use relatively fast reactions: the inequality k; c k, is certainly a fact and as shown by previous considerations (sections 3.7.1 and 3.7.2) could be explained by the involvement of species Ei of the Fe,,S; .type. We lack enough experimental data to determme the nature of these species, but an approach could be made with the help of a few hypotheses. It may be assumed for instance that in the potential range - 0.930 to - 0.600 V a single species Fe,.?: predominates: we shall see that if this hypothesis is proved such a species cannot be indeterminate. Equation (10) is written: sLi,S= sLi,S- (S + r)Kor~~2&Xsti,S
and earlier considerations
(15)
(section 3.7.2) show that:
K:=K,+KK:ifr= -2 K: = K, (within the limits of measurement precision) in all other cases. In the first case the inequality k; -c kl can on1 be obtained if s = 0. The corresponding species Fe,Y- is very unlikely. For f = 0 we get a series of species such as Li; or Li,K+ which again cannot appear at noticeable concentration within the potential range considered here. This possibility will therefore be ruled out. In the other cases we have: K’ = K, Equation (12) gives:
K: 1. K,. 3.7.3. Search for a predominant species E,. The considerations of paragraph 3.1(b) show that the .. quantltles sLi,s. K,, x,,~~,~~~.~x.~~., are interrelated by expressions of the type: K
= k, sL,,s
x X,F~.J = &SL,,S
(13)
From experimental results (7) we can assign to kl, k2 and kl the values: k, = 2.842 x 1O-9 k, = 2.493 x 1O-2 k, = 1
(14)
l Or difference between the initial molar fraction of S’ionsand that of Fe’* ions produced by the action of oxidising impurities.
A numerical calculatiot using the values determined in the experiment of Fig. 2 specifies this inequality: for potentials far enough from that of the inflexion point, we have: 5 KK:“@ K: --u u
< 0.1
The K K: values calculated by equations (14) and ( 15) for different values of r and s should verify this inequality. This reasoning considerably limits the number of possibilities for the species Ei investigated. Another remark will help us to narrow the choice: equation (10) applies to metals other than iron. In
_
___.._
..
-0,7kcal(-2.9kJ)
Li2St FeS+ LizFeS2
_-_.
-16kcal(-67kJ)
- 10.8kcal(-45.4kJ)
23FeSt3LilStFet6(Kt,C1-)~LiK,Fe,&,Clt5(Li+,Cl)
1.89x lo3
x lo- I6 217kcal(907kJ) 5028 x 1O-4 2084
23LizFeS2~Fet(6Kt~CI-)~LiK,Fe,,S,,CIt(45Li+)t20S2~
(2Li+)t2S2-$Li,Sf - ?
1.32x lo-’ 2.30x10~1548.4kd(203kJ)
LiK6Fe2&CI~23FeStFet(Lift6Kt +CI-)+3S*-
I.5x IO-l2 39.1kcal(164kJ)
K
kJ) 5.28x 1O-4 5.28x 1O-4 10.8kcal(45.4
xsz-
Li,Se(2Li+)tS’-
-
-0s77v
l/2$ t 2e- s2-
FeSGFe” t S2-
-0.302V
E”(Ag-Ag+3 x W2)
Fe” +2e- $Fe
Reactions
Table5. Thermodynamic dataresulting fromthediscussion (Section 3)
--
._
Electrochemical
behaviour of iron in the presence of sulphide ions
the case of lead for instance we have:
G_I~S =
sLi,S +
[
s1 -
K,as~,+‘~12
x
&(%
Lt>S.Pb.PbS
K, being the equilibrium
+$)I
sS,
Li,S
constant
of the reaction: z+ Pb,, s::
with s; = 1 and hi = 0, since here we find the sulphide PbS in the presence of Li& For iron we have:
si_i,S
=
SLi,S
x
K,
K
+
2
1s2-~(s2+~)]
L,,S.Fc.xe,S
i
s2+$
>
constant
Fe2++s,S2-
of the reaction: eFef2S::
with s; = 2 and hi = - 1 since in this case it is the mixed sulphide LizFeSz which is found in the presence of Li,S. Experience shows that these two sL,~~ values are approximately equal[20], [36]: s& = 1.58 x lo-“. In the general case of any Pbf, SJ: and Fe!, S;; species this result can only be due to a chance comcrdence. If on the other hand this possibility is excluded and it is assumed that for both iron and lead a single species containing neither of these elements: S; is responsible for the result observed, we can write: K, $ (EOpbpbz* - EF,,z*) ; K, = exp c (
S+>I
Showing that the equality of the s& values given by the two determinations can only be obtained for: s + r/2 = 0. The corresponding species Ei is a polymer of the sulphide ion: S; 2s. As a working hypothesis we shall take the existence of the simplest species of this series: the S:- ion, which accounts for all the results. This ion, probably solvated in the form Li,S:for example, increases the apparent solubility of L&S: Li,S+S*-
*
and may be an intermediary mechanism:
Li,Sz-
in the Li,FeS,
Fe2+ +Li,S:-
+
2s2-
=
K
for
the
s:-
and x~,~_~~- = l/K, molar fraction of S2ions relating to the boundary of the relative predominance regions
of Sz-
and S$- ions. We find: K = 1.89 x lo3
xs’- _s:- = 5.30 X 1o-4
This work presents a first attempt to establish a potential - pS 2 - diagram of the solid species relative to the iron-sulphur system in the presence of LiCl-KC1 eutectic at 450°C. This diagram is still incomplete and an interesting complement would be to account for reactions involving the Li,Fe2S, phase. We find moreover that the experimental results as a whole can only be explained by involving ionic species in solution other than Fe’* and S*-. Although the predominance of a single sulphurated anion (in the low-potential zone of the diagram) gives coherence between the thermodynamic values calculated from experiment, the presence of other species in solution is nonetheless highly probable. To find out more on this subject it is necessary to determine the regions of relative predominance of species in solution for sulphur and the iron-sulphur system. Apart from their undoubted theoretical interest for the chemistry of oxido-reduction and acido-basicity reactions in ionic solvents such studies could have important practical applications in the field of high energy density electrochemical batteries. work was supported by the Commissariat B I’Energie Atomique (For&may-am-Roses, France). We are grateful to P. Leveque, H. Coriou and J. Dixmier for encouragement to undertake this study and for their helpful assistance in its course. We wish to thank D. Herpin for electrochemical experiments. Acknowledgemenrs-This
REFERENCES formation
Li,FeS,
Equation (15) can be used to calculate equilibrium:
which means that throughout the accessible pS2range (and for low enough potentials) the S2- ions The correction to be entered into the predominate. titration curve calculation given in section 3.2 to account for the existence of this species hardly applies unless E -=z - 0.850V, which is why the experimental results are well described by the equations of Table 3, in the with sqizs = 5.28 x 10m4 (or K, = 1.5 x lo-I’), potentral range above - 0.850 V. Table 5 shows a list of thermodynamic constants calculated from the experimental results of this study (paragraph 2) from the values of the Gibbs free energies of formation of Li,S and FeS, and the standard potentials of the couples Li-Li + and K-K l calculated from[34], [35] and [38], and from the considerations of paragraph 3.
CONCLUSION
c(“+‘G
being the equilibrium
509
1. G. Santarini, C. r. h&d. s&m.
Acad. Sri., P&s 288,457 (1979). 2. G. Santarini, C. r. hebd, stkronc.Acad. Sri., Paris 289,421
(1979). 3. J. Greenberg, B. S. Sundheim and D. M. Gruen, J. C&m. Phys. 29, 461 (1956). 4. W. Giggenbach, /. inorg. nucl. Chum. 30, 3 189 (1968). 5. F. G. Bodewig and J. A. Plambeck, J. akctrochem. Sot. 117, 904 (1970). 6. M. V. Merritt and D. T. Sawyer, Inorg. Chem. 9, 211 ( 1970). 7. D. M. Gruen, R. L. MC Beth and A. J. Zielen. J. Am. Chem. SOC. 93, 6691 ( 1971). 8. W. Giggenbach, Inorg. Chem. 10, 1306 (1971). 9. W. Giggenbach. Inorg. Chem. 10, 1308 (1971).
G.
510
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10. J. H. Kennedy and F. Adamo, J. Electrochem. SC. 119, 1518 (1972). 11. W. Giggenbach, Inorg. C&em. 11, 1201 (1972). 12. C. H. Liu, A. J. Zielen and D. M. Gruen, J. electrockem. sac. LUI, 67 (1973). 13. I. P. Bernard. A. de Haan and H. Van der Poor-ten. C. r. ’ kebd. sPanc. Acod. Sci., Pari.s 276, 587 (1973). 14. B. Cleaver, A. J. Davies and D. J. Schiefrin, Elecrrochim. Acta 18, 747 (1972). 15. F. See1 and H. J. Guttler, Angew. Chem. ht. Ed 12,420 (1973). 16. W. F. Giggenbach, J. Chem. Sot. I), 729 (1973). 17. R. P. Martin. W. H. Daub. J. L. Roberts and D. T. Sawyer, Znorg1 Chem. It, 1921 (1973). Acta 20,929 18. M. J. Weaver and D. Inman, E/ectrockim. (1975). 19. D. 0. Raleinh. J. T. White and C. A. Oaden. J. I
ekctochem. S%: 126, 1087 (1979).
20. M. L. Saboungi. 21. 22. 23. 24. 2.5.
J. J. Marr and M. Blander, 3. electrochem. SOC. 125, 1567 (1978). F. C. Mruzek and J. E. Battles, J. clectrochem. Sot. 124, 1556 (1977). C. A. Melendres and C. C. SY, B. Tani, J. electrochem. sot. 124, lo60 (1977). 8. S. Tani, Americrrn mineralogist 62.819 (1977). P. A. Nelson er a/., Argonne National Laboratory Progress Report, A.N.L. 78-20. P. A. Nelson e! al., Argonne National Laboratory Progress Report, A.N.L. 78-45.
26. S. K. Preto, S. von Winbush and M. F. Roche, 2nd Int. Symp. Molten Salts. Pit&burg. The Electrochemical Society, (1978). 27. D. 0. Raleigh, J. T. White and C. A. Ogden, J. elecarochem. Sot. 126, 1087 (1979). 28. J. Phillips and H. F. Gibbard, 2nd Int. Symp. Molten Salts, Pittsburg. The Electrochemical Society, (1978). 29. P. A. Nelson Ed al. Argonne National Laboratory Progress Report, A.N.L. 79-39. 30. B. Tremillon, La ckimie en solvunrs non-aqueux, P.U.F., Paris (1971). 31. G. Delarue Bull. Sot. Chim. Fr. 1654 (1960). 32. G. Santarini, 1980 Conference on Ionic &ui& Dead Sea, Israel ( 1980). 33. G. Sanuuin~ 30th Meeting of I&E., Trondheim, Norway (1979). 34. I. A Plambeck, Encyclopedia of Electrochemistry of the Elemenis, Vol. X, Bard, New York (1976). 35. I. Barin, 0. Knacke and 0. Kubaschewski, Thcrmochemical properties of inorganic substances, Springer, Berlin (1977). 36. M. L. Saboungi, J. J. Marr and M. Blander, &ferallurgical Transactions 8, lOB, 477 (1979). 37. R. C. Shamta and Y. A. Chang, Metallurgical Trmsacrims B, lOB, 103 (1979). 38. J. Lumsden, Thermodynamics of Molten Salt Mixtures, Academic Press, London (1966). 39. F. G. Bodewig and J. A, Plambeck, J. efectrochem. Sot. 116, 607 (1969).
B 1’Energie Atomique,
DCAEA-SCECF,
(Received 20 November
Boite postale 6,92260
Fontenay-aux-Roses,
France
1980; in revised form 2 June 1981)
Abstract-From some electrochemical experiments and from thermodynamic considerations a potential - pS’- diagram is proposed for solid speciesrelativeto the ironsulphur system in the presence of molten LiCl-KC1 eutectic at 450°C. On the basis of this study the following values may be adopted: - Gibbs free energy of formation of the Li,FeS, phase (from LirS and FeS): -0.7 kcal (- 2.9 kJ); - Gibbs free energy of formation of the LiK,Fe,,S,,CI phase (from FeS, Li,S and the LiCI-KC1 eutectic: -16kcal (-67kJ); -solubility product of sulphide FeS: 1.5 x lo-‘* (in the molar fraction scale); - sotubility of sulphide LilS: 5.28x lo-* (molar fraction). It is shown in addition that the experimental results point to the existence in solution of species other than Fe’+ and Sr- ions.
qualitative theoretical potential - pS2- diagrams representing fields of relative stabihty. This representation is similar in every way to that of the potential -pH diagrams inaqueous solution or the potential - PO’diagrams in fused salts and may be obtained by the same methods[30-32-J. These diagrams can be used as guides when investigating the conditions of formation of the various species. Figure 1 shows for example a possible qualitative representation for the relative stability regions of the solid compounds mentioned above, neglecting any solid solutions which may be present. Table 1 lists the reactions considered, the equilibrium conditions of which are represented by the numbered straight-line segments of Fig. 1, and gives the slopes of these segments in (RTln 10)/F unit. The bracketed species are very highly concentrated in the eutectic and their activities may therefore be considered as constant. The triple points of the figure correspond to constant Fe” and S’- ion concentrations, as shown for example by reactions A, B and C in Table 1. Configurations other than the one represented are possible: vertical 7 could intersect branches 2 and 4 in two triple points Li,S, J, X and Li,S, Fe, J; the regions of the compounds Li,Fes$ and LiK,Fe2,S,,Cl could have a common boundary __ For a quantitative representation certain thermodynamic data must be known, for example the standard potential of the Fe-Fe*+ couple, the solubility product K, of the sulphide FeS and the concentrations or potentials relative to certain triple points, Table 2 gives some bibliographical data. The potentials are referred to the Ag-Ag+ 3 x lo-‘. reference electrode used in our experimental work*. The potentials noted E” are the standard potentials
INTRODUCTION
This work is part of a general thermodynamic and electrochemical study of reactions between the different species liable to be generated by the elements iron and sulphur in the presence of fused LiCl-KCI eutectic at 45O”C[l, 23. A bibliographical approach leads us to take into consideration: -for the ions in solution in the eutectic: cations Fe’+ and Fe” (solvated)*, anions sulphide S2 -, polysulphides and polyhyposulphides such as Sq- , St-, S;, S;, and complexed iron cations such as FeS:-[3-201; -for the solid phases: LiaS, FeS, Fe&, Li,FeS,, LiJFe,S,, LiK,Fez,S,,Clt[2W29]. Stability and predominance of these species depend on two parameters: -an oxido-reduction factor: the potential E,; -an acido-basicity factor: for example the S2sulphide ion concentration. It is therefore possible, knowing only the stoichiometry of the species liable to be formed, to draw * Throughout this work the possible solvation of ions is not accounted for in the terminology used. The standard state for the ions in solution is taken as the state obtained by extrapolation, in the reference state, to unit molar fraction. The reference state is that of the ion in infinitely dilute solution. Potentials and concentrations are expressed in the molar fraction scale. t These phases, encountered during the running of high energy density batteries (Li-AI/FeS or FeS2) have been studied repeatedly at the Argonne National Laboratory (USA) where their formulae are replaced by letters: Li,FeS1 LilFetS, LiK6Fes+Sr6Cl
* For this we use Nernst’s equation and the standard potential values given by the tables 1343. The junction potential differences and those of the thermoelectric couples are neglected.
=x =z = J 495
G. SANTARINI
496
corresponding to thermodynamic equilibria, are not coherent: they fail to satisfy the inter-relationships authorized by thermodynamic considerations. To gain a better understanding of this system an experimental study was therefore undertaken. Special attention was devoted to solid phases in equilibrium with the liquid eutectic at 450” C and to the lower part of the diagram mentioned above. 1. EXPERIMENTAL
1_iz
-pS*diagram of iron in Fig. 1. Qualitative potential molten LiCI-KC1 eutectic. Relative stability regions of solid compounds. Table
1. Reactions
LiK,Fe,,S,,Cl
The experimental device used consists of a tight cell suitable for standard electrochemical experiments, with a three electrodes system[33]. With this set-up the salt can be- dehydrated in situ by anhydrous hydrochloric gas bubbling and kept under vacuum or under inert atmosphere. Most of the experiments however were performed with already purified salt provided by the Anderson Physics Laboratory, Champaign, Illinois. The LiCl-KC1 eutectic (or a solution of L&S in this eutectic) is contained in an alumina crucible. A light bubbling of dehydrated and deoxygenated argon is kept up m the salt throughout the experiment. The potential of the working eiectrode (iron, or Fe-FeS mixture) is measured against a reference electrode made up of a silver rod in contact with a solution of silver chloride in the eutectic, at concentration 3 x lo-’ (in molar fraction). The electrical contact is made through a thin-ended Pyrex tube.
considered for the establishment
FeS+2e- =Fe+S’-
:
+(Li’
+ 46rm +24Fe+26Szm
METHOD
of the potential
+6K+ +CI-)
- pS2-
diagram
of Fig. 1
l/2 13/23
3
Li,FeS, + 2e- *Fe+2S’-+(ZLi+)
4
24Li,FeS, + (6K* +ClV)+ 2e- eLiK,Fe,,S,,Cl+
5
24FeS+
6
Li,FeS z~FeS+S2-+(2Lic)
cc
7
LizS*(2Li+)+Sz-
m
8
Li,Fe,S,
0
9 10 11
(Li+ + 6K+ +Cl-)
+2Sf-
1
+2e-
22S’-
+(47Li+)
+LiK,Fez4Sz6CI
+ (Lie) + P- +ZLi,FeS,
Li,Fe,S, + e- eZFeS+ZS’-+(3Li+) Fe& + 2e- =Z=FeS+S’2FeS, + (3Li
l
+6K+ +6K+
A B
LiK6Fe,.&,Cl LiK6Fe24S26Cl
C
(2Li+)+SZm *Li,S Li,FeS, + (2Li+) *ZLi,S
-1
$2 0
) + 3em G= Li,Fe,S,
23FeS+Fe+(Li+ 26FeS+ Fe+(Li+
11
+Cl-)+ 3Sz- G+L~K~F~~~S~~CI +C1-)=+LiK6Fe2~S2&l + 3Fez+
=23Li,FeS, + Fc + (6K+ + Cl-) + (45Li+)+20S2+ (25Li’) *13LizFeS1+Fe+(6K++Cl-)+lOFG+
+ Fe’*
of the electrochemical couples represented in lower indices. The symbols E and x represent the potentials and molar fractions of S2- ions at the triple points given in lower-index form. ;L,,s is the solubility of ions in solution in Li,S (molar fraction of S equilibrium with the L&S solid phase). Unfortunately we find that these data of Table 2, if
Several types of auxiliary electrode were used: Pyrex or porous alumina tube containing a silver wire dipping in an LiCI-KCl-AgCI mixture, boron nitride tubecontaining a tubular iron electrode dipping in tbe LiCl-KC1 eutectic. For the coulometric experiments a potentiostat used in a constant-current set-up allows an anodic or
Electrochemical
behaviour of iron in the
Table 2. Some bibliographical
-0.316(~0.007)V (Ag-Ag+ 3 x lo-‘)
c341
-0.53ov (Ag-Ag+)
-0.311v (A&Ag+
3 x W2)
PO1
-
- 0.362 V (Ag-Ag+
3 x lo-‘)
PI
(4-&+
)
1.219v (Pt-PtZ+) 1.58 x lo-’ 1.56(+0.05)x 1.3 x lo-”
K, (FcS)
2.3 x io-‘2
Fe. X
xJ, Fe. FeS xX,
Fe. J
AND
[it] PO1
1.625 V (Li-Li+)
-0.93ov
1.629V (Li-Lit)
- 0.926 V (Ag-Ag+
(Ag-Ag+
3.8 (*0.2)
x 10-4
1.5( fO.l)
x 10-A
RESULTS
2.1. Standard patenciul oJ the Fe-Fe2+
PI
10-S
cathodic current of given intensity to be passed through the working electrode. 2. EXPERIMENTS
497
l
SLi,S
ELi,S.
of sulphhide ions
data useful for this research (T = 450” C)
- 0.535 ( * 0.007) v ‘%tFc’
presence
couple
In this experiment the potential of an iron electrode dipping in pure LiCI-KC1 eutectic at 450” C is followed during the coulometric generation of Fe2+ ions.
3 Y lo-‘)
c273
3 x 1O-2)
c2*1 c201 PO1
Stabilisation of the potential after each electrolysis is reached in a few minutes under these conditions. Curve 1 of Fin. 2 shows the result of a test. The abscissae represeit the decimal logarithm of the molar fraction y of Fez + ions produced by electrolysis (calculated assuming the validity of Faraday’s law) and the ordinates the eouilibrium ootential difference between the iron electrode and the kg-AgCI 3 x 1O- ’ reference electrode. The points correspond to the experimental values,
- 0.500
,)
-0.600
Y P rz
-0.000
-8
-7
-6
-5
-4
-3
-2
log,, Fig. 2. Potential of an iron electrode versuslogarithm of the molar fraction of Fez’ ions produced electrolysis: (1) in pure LiCI-KC1 (at 450°C) (2) in a solution of Li,S in LiCI-KC1 (at 450°C).
by
G. SANTARINI
498
the solid line plots the equation:
K, = 1.5 x 10-l’
= 11.P
Under present experimental conditions the stabilization of the potential after each electrolysis is reached in a few minutes. Radiocrystallographic analysis shows that only the FeS phase is present on the iron electrode after the test.
in the case: E;+zs
= --0_294V
z.
= 3.5 x 10-6
Excellent agreement is therefore observed between theory (Nernst’s equation) and experiment if we assume the presence in the salt, soon after immersion of the iron eiectrode, of a 3.5 x 10e6 molar fraction of Fe*+ ions due to the attack of iron by various oxidising impurities (0,. H,O). The validity of the method is thus confirmed, and this within a wide concentration range (molar fractions between 4 x 1W6 and lo-“). Five tests all gave Z, values between 3 x 10m6 and 12 x lob6 and potential values E&sz+ within the interval: E;c:slFe~+ = - 0.302 f 0.008 V (with respect to Ag-Ag+ 3 x 10-2) or: E&z.
or: pL K, = -log,,K,
= - 0.521+ 0.008 V (with respect to Ag-Ag+ standard state)
This result agrees within the limits of experimental error, with those given in Table 2 which concern a narrower Fe2 + ion molar fraction range.
2.2. Potentiometric solubility product
determination
of the iron sulphide
A coulometric generation of Fe2* ions has been carried out in a solution of Li2S in LiCI-KC1 at 450” C. A very low concentration was chosen in order to avoid formation of the LiK,Fe2J&,CI phase (Fig. 1). If we assume Fe and FeS to be the only stable solid compounds under these conditions, and Fez+ and S2 the predominant ionic species in solution, the equilibrium FeS ti Fe’ + + S2- is expressed by the equation: E = E”F@+ +4K,]}
+
g
In
{Y
-Yyo+Jc(Y-Yyo)2
ln2
-g
with K, the solubility product of FeS and y0 the difference between the initial molar fraction of S2ions and the initial molar fraction of Fez+ ions produced by the action of oxidising impurities. The result of this test is given by curve 2, Fig. 2 where the points represent the experimental values, the solid line the graph of equation (1) in the case: E&/@
= -0.3oov y, = 1.26 x IO-’
K, = 1.5 x IO-” with the hypotheses considered this test thus gives the value:
2.3. Cotclomerric generation of Fe2+ ions in a concentrated solution of S ‘- ions in the LiCl-KC1 eutectic To reveal any potential plateaux which would express the equilibria between solid phases Li,S-Fe-Li,FeS,, Li,FeS,-Fe-LiK,Fe,,S2,CL LiK,Fez,&,Cl-Fe-FeS the same experiments as abode were performed in the presence ofconcentrated Li,S * solutions in the LiCl-KCI eutectic at 450°C (molar fractions above 10e3). Under these conditions the stabilization of the potential after each electrolysis is found to be extremely slow, taking several hours. The results obtained are then noticeably affected by small leaks on the gas circuit or by diffusion through the cathode compartment. No potential plateau appears clearly. It is observed however that in each case the initial potential lies around -0.93OV (with respect to Ag-Ag + 3 x 10 - ‘), never falling below this value even for highly concentrated Li,S solutions. Figure 3 gives an example of a test result: the points between - 0.920 and - 0.6OOV certainly do not correspond to equilibrium states (in spite of stabilization periods longer than 1 h); the potential fluctuations in this zone may be attributed to poor contact between the iron and the solid phases formed. As a matter of fact, the reactions between the LiK,Fe,,S,,Cl phase and the Li2FeS2 or FeS phase are very slow and involve the presence of metallic iron (triple points A and B of Fig. 1). 2.4. Coulometry on electrodes consisting of an Fe-FeS mixture To speed up the kinetics of reactions involving the LiK6Fe2,S,,CI phase, electrodes were made from an intimate mixture of iron and sulphide FeS powders surmonted by an iron rod in contact with this mixture and placed in a porous alumina tube. (a) Figure 4 shows the result of a series of potentiostatic reductions of this mixture followed by potentiostatic oxidations. The potential of the electrode is plotted against the quantity of electricity needed for the intensity at this potential to decrease, in absolute value, to 40 PA. This quantity is expressed in molar fraction x of Fe’+ ions reduced (assuming the validity of Faraday’s law and referring this molar fraction to all the Li+ and K* ions present in the cell). Here again the experiments are very long and the molar fraction determination is certainly falsified by diffusion through the auxiliary compartment and oxidation by impurities. Two potential plateaux are observed for the values - 0.900 and -0.930 V. l Henceforward the symbol pX placed before a thermodynamic quantity reprcscntesthe decimal cologaritha T’he concentrations are always expressed in molar fractions. We thus avoid possible confusion with the symbol p (pO-,
pS-. . , ) which molarizy (in 02-,
usually refers to the coloprithm S2-. . .).
of the
Electrochemical
Fig. 3. Coulometric
behaviour
of iron in the presence
of sulphide ions
generation of Fe ‘+ ions in a concentrated solution of Sz- ions in LiCI-KC1 4soT).
Fig. 4. Coulometry on an electrode consisting of an Fe-FeS mixture (x& = 2.9 x lo-“).
499
eutectic (at
(b) Figure 5 concerns the same kind of experiment, but here the electrolysis was interrupted and the potential allowed to stabilize in each case. On this figure the dark circles represent the potentials of the electrode during the potentiostatic coulometry operations and the light circles the potentials after stabilization. A potential plateau appears temporarily for - 0.930 V and a plateau is observed for - 0.900 V. (c) Figure 6 shows the result of a series of cathodic then anodic constant-current cycles carried out at low intensities (0.2 mA, 0.25 mA, 93 mA). The ordinates represent the potential during the test; the quantity of electricity plotted as abscissae is still expressed in molar fraction of Fe2 + ions reduced (number of moles of electron pairs involved divided by the total number of moles of cations or anions present in the eutectic): with the mass of salt used (19.3 g) the constant current durations needed to reach a molar fraction of 10- 3 are 94 h, 75 h and 63 h for intensities of 0.2, 0.25 and 0.30 mA respectively. The anodic and cathodic branches of each cycle display shoulders encompassing the values - 0.900 V and - 0.930 V, but also two others which reveal the existence of a solid phase transformation for potentials between - 0.7ODand - 0.900 V. The potential gaps of
G. SANTARINI
500
-0.500 i -0.600
,’
I
-o.,oo_\
i-7
I
I
hx pr)
-0.100-
B \
4” i;
-o.soo-
I I I 1 I
, -0.70C 1 Y o_
: ,
," + w < 3 w
-
0.3
--__
0.25mA
_.........-
0. 2 m*
rnA
-0.800
Fig. 5. Coulometry on an electrode consisting of an Fe-F& mixture (x& = 2.8 x 10m3). -0.900
these pairs of anodic and cathodic shoulders suggest that the reactions which occur for potentials - 0.900 and -0.930 V are relatively fast, whereas those responsible for the shoulders between -0.700 and - 0.900 V are very slow. Before attempting to interpret all these results we must examine the data given by thermodynamic considerations.
In the following it will be assumed that the predominant ionic species in solution are Fe”+ and S2ions. This hypothesis is certainly all the more valid as the potential and the S ‘- ion concentration are low. dictated
10-S
X Fig. 6. Cathodic and anodic constant-current cycles on an electrodeconsisting ofan Fe-FeS mixture(r& = 3 x lo-‘).
gas) QL,+, E&,z+ the standard potentials of the Li/Li + *, and Fe/Fe’* couples, the consideration of a simple thermodynamic cycle shows that:
3. DISCUSSION
3.1. Relationships
sure-4
0
or, at 723 K and adopting the values of free energies and potentials given by[34] and[35]:
by thermodynamics
pxK,
-pxS)&s
= 8.450.7
Thermodynamic considerations show that the equilibrium quantities mentioned above (solubility product, solubility, interphase equilibrium potentials) are not independent, and a quantitative representation of the equilibrium conditions must account for these
(b) Furthermore, geometrical considerations on the lower part of Fig. 1 diagram, combined with the equilibrium conditions for the reactions Fe e Fez+ + 2e- and FeS s Fez+ + S2- give the relation:
relations. For the lower part of the diagram on figure 1 we can establish the existence of three sets of relationships:
or again, bringing in the triple point D relative to the metastable equilibrium amongst the three phases Li,Fe$, Fe and FeS:
P&
- ~xs~its
(a) With &s and &s being the standard Gibbs free energies of formation of the solid compounds FeS and Li2S (from solid iron, liquid lithium and S2
= &
(2 EkFc'+
* For Lif the standard LiCl-KC1 eutectic.
--x,F~,F~s-ELI,s.F~,x)
(4)
state is that of the ion in the
Electrochemical behaviour of iron in the presence of sulphide ions (c) The same kind of reasoning can show that the potentials of equilibria (stable or metastable) between solid phases are inter-related. We thus have: 3E,,,,.,s =EJ.FCF~S
3.2. Calculation
+ 1OEx,,,,
-
13EX,~e.~es = 0
(5)
- 20EX.Fe.J - 13EX.J.FeS = '
(6)
of coulometric
titration
curues
Let us consider the cathodic reduction of a mixture of metallic iron and solid sulphide FeS under a constant current low enough for electrochemical equilibrium to be taken as reached at each moment; let us suppose moreover that the configuration of the relative stability regions is that of Fig. 1. The potential starts by decreasing exponentially: the figurative point of the system describes branch 1 of the diagram; as soon as the potential reaches the value EJ,Fc.Fss, the FeS phase reacts to give the LiK,Fe,,S,,Cl phase: 26FeS-+(Li+t6K+fCl-)+6e---fLiK,Fe2&,Cl
+ 2 Fe
During this transformation the potential remains constant at E J,Fs.FsS_When all the FeS phase has reacted the potential decreases along a new exponential: the figurative point describes branch 2 of the diagram. We observe a new potential plateau for the value E,.Fc,FcS, a new exponential decrease (branch 3), a plateau for the value EL,s,Fc.Xr and finally a vertical decrease to the lithium deposit. These curves can only be observed in their entirety if the sulphide FeS is present originally in excess. If we call x& the initial molar fraction of the sulphide FeS (number of moles of FeS introduced divided by the total number of moles of cations in the eutcctic) and x the molar fraction of Fe2 ’ ions reduced, by writing the conservation equations for each equilibrium we can express x a function of a, molar fraction of Fe2+ ions in solution, xsl-, molar fraction of S2- ions in solution and x&. In addition a is related to the potential E by Nernst’s equation and from the above geometrical considerations xsl- can be related to the potential E. In this way the relationship between x and E is determined completely. Table 3 gives the equations obtained-with f = (F/RT).
501
The same curves are described backwards if the direction of the current is reversed. Similar arguments could lead to equations for the titration curves of an Li,S solution by addition of FeClz or an FeQ solution by addition of Li,S. 3.3. Interpretation
o~experimental
results
3.3.1. Solubiliry producr K, oJ’ FeS. The solubility product value K, = 1.5 x lo-l2 determined here is close to that obtained during the work reported in[20f: K, = 2.3 x lo- I’. The latter value however is probably less accurate than the former: this value (K, = 2.3 x lo- ’ ‘) is derived from the result of a potentiometric titration of a chloride FeCl, solution by addition of sulphide Li,S and the conditions of this titration (initial molar fraction of FeCl, about 1Om4) are such that the potential zone used for the determination of the constant overlaps that of the thermodynamic possibility of formation of the LiK6Fe2.+!&Cl phase, as found from the interpretation of our own results below. This experiment ought therefore to reveal the existence of potential plateaux and their absence may be attributed to the great slowness of reactions involving the LiK,Fe,,S&l phase, resulting in very long stabilization times; the values used may not have been equilibrium values. In our experiment (initial molar fraction of Li,S about 10m5) stabilization was obtained in a few minutes. 3.3.2. Potential plateaux. The lowest potential plateau value revealed in this study, - 0.930 V, can only be attributed to the precipitation of lithium sulphide Liz& and agrees in fact with other results given in the literature (Table 2). The value -0.900 V may then be assigned to either the equilibrium X, Fe, J or the metastable equilibrium X, Fe, FeS. Calculation of the equilibrium curves by the method described earlier (Section 3.2) shows that the latter hypothesis accounts better for the experimental results than the former. We should then have: E X.Fe.J
=
ELi,S,Fc.X=
-
0.930 v
and using (7): E J.Fs.FeS=
-0.800
v
Table 3. Equations of coulometric titration curves 1
Fe, FeS
A J, Fe, FeS
X = SLi~sexPCf(ELi2s.Fc,x E = EJ, Fe.FeS
+#Ezc,F~.J+
J
~Li,Se~PCf(~LiIS,~s,x++SEx,~c.
&EJ.
F~,F~S--ZWI
-;MEJ.F~.FAI
-exPC2f(E-Ekr@+)l
--~P[~~(EJ.FS,F~S-E~~F~~')I
< x
2 J, Fe B X, Fe, J 3
X,Fe
E = EX.Fe.J &X~CS+~sL~~scxP[~(EL~~s,F~.
x -
Ex,F,J)]
X <~Xb,s
ffS~i~seXP[f(E~~~~e,x
x = Ix&s
+f~~i~~exp[f(E~i,~, F~,X -WI
--~P[~~(Ex.F~,J -
-Ex.F~.J)]
-exP[2f(Ex.Fe.~
E~F~z+)]
-E~F~‘*)]
-expC2f(E-EER-~~~+)l
E = ELiIS,Fe.x C Li,S, Fe, X Liz?+,Fe
)(X&s+ SLi,s)-exPC21(EL*S,FS.X-E~~-~S x = x&s E&i-Li* < E < ELiIs, Fe.x
z*)I < X -= x~~s--XpC2f(Eu,s,F=.x
-EKvI+~*)I
G. SANTARINI
502
This value fits in well with the shoulders observed on the potential us time curves obtained during cathodic and anodic constant current maintenance! cycles on a mixed Fe-FeS electrode (Fig. 6). The following interpretation (accounting for equations 5 and 6) is therefore proposed: E,. Fs., = fiLi,S.Fs,x = - 0.930 V EX, Fe. FeS = - 0*900 v E J, Fe, FeS = -0.8OOV E X. J, FeS = - 0.600 V EkeFet * = - 0.302 V
Px K -
p, sLi,s = 8.55
K, = 2.842 x 10 - 9 sLizs
(8)
in excellent agreement with the thermodynamic relationship 2. Moreover equations obtained by the method of paragraph 3.1(b) give: P,
xX, Fe. J -
Px sLi,S = O
Px XJ, Fe. FsS - Px sLi,s = 1.603
or: xX, Fe.
J = %i,S
K, = 4.43 x lo- “, a value higher than either that of[20]: 2.3 x lO_ l2 or that determined in this work: 1.5 x lo- “. Moreover the theoretical titration curves (Table 3) calculated with these values are not in keeping with the experimental results (Section 2.4): in particular the x values necessary to obtain plateaux are too large: On the other hand if we take K, = 1.5 x IO-l2 we obtain:
(7)
The temperature 450°C would therefore correspond to the special case where the potential and pS2 _ conditions relative to the LilS, Fe, X and X, Fe, J equilibria coincide. This result agrees with that of reference[25] where it is shown that a mixture of the solid species LizS, LizFeE& and Fe in contact with LiCl-KCI eutectic only reacts to form a new phase, LiK, Fez4 Sz6Cl, at temperatures above 455 i 4” C. With the accepted hypotheses, (4) gives: or:
3.3.3. Potential - pS ’ _ diagram/or solid species. If sLi s in (8) takes the value given in[20]: sLiss= 1.58 X ‘lo-3 , we obtain for K,:
sLils = 5.28 x 10 - 4. This value disagrees with that of[ZO], but theoretical curves calculated on the basis of its validity (Fig. 7) fit the experimental results if the possibility of a metastable equilibrium between the X, Fe, and FeS phases on the one hand, and over-voltages due to the slowness of reactions involving the LiKsFe14S2,Cl phase on the other, are taken into account. It is shown later (Section 3.7) that the presence of certain ionic species in soluion other than Fez+ and S3 - can explain an apparent solubility of Liz S greater than the molar fraction of S - ions in solution in equilibrium with the solid Li,S, though the measurement of the FeS solubility product K, is not affected. We shall therefore take the value sLIzs= 5.28 x 1Om4 and can then present the solid phases equilibrium conditions in the form of the diagram on Fig. 8. Solid (with pLbFes, = - 36.3 kcal[37], FeS, @FaS = -26.8 kcal[35]) was taken into consideration for the drafting of this diagram, but not solid Li, Fe, S,. The dotted lines refer to metastable equilibria. The molar fractions of S2- ions relative to the different triple points are as follows:
x J,Fe,Fcs= 2.493 x lo- 2 sL,,$
sLi,S
=
xL,,S,Fe,X
=
--
xX.Fe,J
5.28 x 1O-4
i
-0.900
J
Fig. 7. Cathodic
X, Fe. Fe5 _---_---________--------~
‘.
reduction
of an Fe-F&
mixture:
curve calculated
\
\
\ \
for: SLAMS = 5.28 x 10e4 X&S = 3 x 10-3.
Electrochemical xX.Fc,F&
=
xX,J,FcS
XJ,F~,F~
=
1.32
X
=
behaviour of iron in the presence
of sulphide
503
ions
or, for the reaction:
3.26 x IO-*
L&S + FeS --* LirFeS,,
lo- ’
The value of xJ,reres agrees with that obtained from the results given on Figs 4,5 and 6, but not with that of reference[20]: 3.8 ( f 0.2) x 1Oe4. This difference is probably due to the slowness of reactions involving the J phase and to a poor contact between the metallic iron and the FeS phase in the experiment of reference[ZO]. 3.4. Gibbs free energies qfformation Li&Fe,,S,, Cl phases
of the L&Fe&
and
With the above hypotheses the Gibbs free energies of formation of the Liz Fe!& and LiK, Fez&e Cl phases at 450” C may be calculated from thermodynamic cycles. (a) For the Gibbs free energy of formation of Li,FeS,:
whence, adopting values of&and
&,
given by [35]:
P’E = - 129.6 kcal ( - 542.1 kJ)
AGg = RTfn xx,Fes sLi,s AGox = - 0.7 kcal (-
2.9 kJ)
to bc compared with that of reference[20] ( - 0.33 ( k 0.20) kcal). (b) Similarly for the Gibbs free energy of formation of LiK, Fe,, S,, Cl: value
~5 = F (6 E&+ + 3 &IS
- 5 Eti-Li*
-E&,I)
+ 23 pE=s
+ 3 RT In %!!QZ
sLi*s The standard potential of the K-K+ couple is not measurable directly but may be calculated from the activity of KC1 in LiCl-KC1 eutectic at 450” C and from that of superfused liquid KC1 at 450” C: with numerical values given by[34], [35] and [38], we obtain:
- 0.500
-0.600
Fe S
2 p: 0 I;I
2
-o.rw
\ 8 iz
- 0.800
-0.90(
Fig. 8. Potential -
pS’-
diagram af iron in fused LiCI-KCI eutectic at 450°C. Relative stability regions of solid compounds.
504
& = - 1045 kcai (-4371
kJ)
or, for the reaction: 23FeS+3LiZS+Fe+6(K+,CI-) -+ LiK6FeZrlSZ6CI + 5 (Li+, Cl-): AG; = 3 RTh, !%%!%? SLi,S
AG”, = - 16 kcal (-67
kJ)
Reference[20] gives: A G; = - 6.1 f 0.3 k-1. This study therefore reveals a greater stability of the LiKeFeZ SZ6Cl phase. 3.5. Composition
of the solid phase at equilibrium
Let us take a solid compound mixture Fe, FeS, Li, S in contact with an LiCl-ICC1 eutectic. Let X& xFcS and ~E,S be the molar fractions of these compounds in the eutectic with: XR + x& +x&s = xg, XL being the molar fraction of the solid mixture components as a whole, These components react with each other and with the eutectic and at thermodynamic equilibrium new phases appear: J, X or Liz!% The new molar fractions are: xx, x&. ’ n;, xk. By writing the iron and sulphur conservxu*s, ation equations for all the reactions possible we can calculate X’F~, X&s, X~irs, x’, and xk with respect to the initial molar fractions x&, x&, x&_ We thus obtain the diagram of Fig. 9 which represents the compositions of the solid mixture at equilibrium as a function of the initial compositions. For clarity of representation the proportions are not respected (stoichiometry of the J phase and ratios between and xz), but Table 4 gives xJ,F~,FeS, xX,Fe,J . . . the mequalities which define the zones represented. In this calculation the molar fractions of the Fe2+ ions are taken to be always negligible compared with those of the Samions, which is quite justified once x$,s is not negligible. It is also limited to cases where xg IS small enough for the molar fractions to be assumed additive. Figure 12 calls for the following remarks: (a) As xoO increases (without reaching excessive values inconsistent with the assumed additivity of the molar fractions) the regions with two solid phases, shaded on the diagram, become narrower until finally only the four zones with three solid phases are observed: Table 4. Inequalities
defining the regions of Fig. 12
amb (J, Fe, FeS), bmd (X, J, FeS),amd (X, Fe, J), udc (Li,S, Fe, X). (b) The diagram concerns the case where the temperature is slightly above 450” C: in the potential -ps=diagram the Li2S, Fe, X and J phases are then distributed as shown on Fig. 1.If the temperature falls, points hand k approach points i and 1.At 450” C the X, Fe, J and L&S, Fe, X regions merge. As the temperature continues to drop this X, Fe, J, Li,S region separates along the segment mc into two regions Li,S, Fe, J and Li2S, J, X. In potential - pS2- coordinates we are then in the situation where the psLias abscissa vertical intersects branches 2 and 4 (Fig. l)*. Figure 10 shows the area representing potential at electrochemical equilibrium versus initial composition of the solid mixture. This diagram is qualitative, but the exact calculation raises no particular difficulty and may be conducted by the method explained in Section 3.2. The diagram refers to the case where the temperature is slightly above 450” C. At 450” C the X, Fe step disappears. The presence of the high-potential X, J, FeS plateau has surprising consequences, meaning that in titrations with an inert electrode the possible sequence: potential rise, plateau (X, J, FeS), fall may be predicted. Such curves correspond to cases of iron deficiency in the Fe, FeS mixture used since the consumption of iron is necessary to the formation of the LiIC,Fe24S26CI phase. We should also mention that in the diagram of figure 10 the titration curves obtained by addition (FeCI, to Li,S or L&S to FeCI,) are the intersections of the surface represented by planes parallel to the plane a b e d. The coulometric titration curves on the other hand are the intersections of this surface by the set of planes passing through the edge symmetrical to the edge a d with respect to the plane b c fe. This comment allows a rapid visualization of the shape of these curves. 3.6. Standard
potential
of the S2--S2
couple
Knowing sLiZsit is possible to calculate the standard potential of the S2--S, couple. Writing:
We obtain: E;z--~~ - B;,_Li+ = 1.978 v V (with whence: E$_s, = -0.577 Ag-Ag+ 3 x lo-’ electrode)
respect to the
This value is quite different from that obtainable by direct measurement ([39], Table 2). We can explain this divergence by allowing that sulphur is highly
X,
Fe
Xx,Fe,J
< ~&S-xkeS
4
XLiIS.Fr.
X
l This study is confinedto the temperature450°C that of most determinations of thermodynamic and electrochemical quantities found in the literature.
Electrochemical
be Fe5 Fig. 9
soluble
in a sulphide
3.7. Ionic species
of iron in the presence of sulphide
d
f
solution
*s:-([lo],
in solution were solvated). If other species are present in significant concentrations they may affect the determination of the Sz- ion equilibrium concentrations (for example sLizs) and the FeS solubility product K,. Henceforward we shall call x’ and K: the molar fractions and solubility products calculated from the experimental results without accounting for these additional species, and x and K, the real values. A large number of extra ionic species may be involved (Fig. 11, Fig. 12): Hitherto
the predominant
a function
of initial composition.
index ri can be positive, negative or nil*. The reaction of formation of a species EC may be written: +sis-
in solution species
assumed to be Fe’+ and S2 - ions (possibly
- polysulphide and polyhyposulphide ions can predominate in certain potential and pS’zones. Some authors have thus suggested the formation of S:- and S; ions to explain potential measurements for sulphur in contact with a sulphide solution in eutectic or to account for the colour of these soIutions[3-191. - Fe2 + ions may be complexed by S2- ions, giving rise to species of the FeS”, FeSz I, Fe%type, or
associate with polysulphide or polyhyposulphide ions. The resulting species may be solvated; - S2- ions may similarly combine with Fez+ ions to give species of the Fe2SZC or Fe&‘* type. - Fe3+ ions only appear for high potentials (E;E”IFe’. = 0.835 V with respect to the Ag-Ag+ 3 x 1O-2 electrode[34] but might be stabilized by complexing with formation of ions such as FeS+,
FeS; , FeS: -. We shall call Fei,Sz these species E,, possibly solvated. One of the two indices J and si may be nil; the
50s
S2
of the solid mixture nt equilibrium in the form:
ions
phi
Liz k
Composition
3s + s=-
hchaviour
+Fef.S2,+
(si+;-.fi)Fe
If we call Kj the equilibrium
constant for this reaction the molar fraction of species Ei is related to those of Fez+ and S 2- by the equation:
xa, = K&$.‘2.X~,_ We shall demonstrate
(9)
that:
- the presence of such extra ionic species given in the generalized form of Fe&S:J permits an explanation for the apparent discrepancies between experimental results. - assuming that only one of these species predominates, it cannot be indeterminate.
3.7.1. Determination of the molar fraction of S2ions. Let us suppose that to determine the molar fraction of S2- ions corresponding to an equilibrium amongst three solid phases P’ (of formula Li,. K,, Fe,. S,. Cl,.), P” and Fe we add S2 ions to an Fe2+ ion solution in the presence of metallic iron to form a first solid phase, for example P’, and continue
adding until the first traces of the second phase P” appear. The writing of the conservation equations for iron and sulfur in the case we should ignore the existence of l For the list to be exhaustive the species E, should be noted Lir, gk, S,* Cl:,. not to account for salvation, which needs not be mentroned in writing but to allow for the possible existence of ions such as Li:’ or Cl; and their combinations with Fez’, S’-. This would encumber the calculation without changing the principle, and unnecessarily for the region in question.
G. SANTARINI
Fig. IO. Potential
at equilibrium
versus initial composition
of the solid mixture.
--._
Fe,
5“’
*-‘--_____________________/‘---
,’ I’ /’
Fig. 11. A possible qualitative representation for the regions of relative predominance of polysulphide and polyhyposulphide ions.
-. -.
Fig. 12. A ‘possible qualitative representation for the fields of relative predominance of some FeSi -2X and FefY- * type ions in a solution in contact with metallic iron.
Electrochemical behaviour of iron in the presence of sulphide ions
species Ei, and in the case this existence is accounted for, gives:
I
SO7
We find moreover that the values sli,s = 1.58 x lo-” 203, x;.re.rCs = 3.8 x lo-*[20], K: = 1.5 x lo- I 1 (this work) or 2.3 x lo-i2[20] fail to satisfy these relationships; we have:
1
where y0 represents the initial molar fraction of Fe’+ ions, y the total molar fraction ofadded Szm ions, OL the molar fraction of Fe’+ ions in solution, and putting: (c’ - I’ - k’)/2 = h’. 3.7.2. Determination of rhe FeS solubility produrt. Assuming the non-existence of species E, the titration curve equation for a solution of S2- ions titrated with Fe2+ ions is written, in the FeS formation zone:
y=y,+or_K,
(11)
a
with
El=exp[$(E
1
y,,, the initial molar fraction of S2- ions*, is also the abscissa of the point of inflexion of the curve plotting potential usy, molar fraction of added Fe2 + ions. K: is the constant product ( y - y, + a)a. If species E, are taken into consideration we have:
We see that the curve described by this equation can only coincide with a curve described by (11) in three cases: (a) every ri is nil; we then have: K: = K, (b) every ri equals - 2; we then have: K;
=K,+CK,Ki
(c) within the range of molar fractions CLused for the study the term
i
L
is negligible compared with the other terms of (12). We have:
k, = 2
X;,F~,F~S 'k, kIp3
We have already observed (section 3.3.3) that the slowness of reactions involving the J phase could explain why the x; value obtained by direct determination is excessive, and k; therefore too high. On the other hand, the K: and &,s measurements use relatively fast reactions: the inequality k; c k, is certainly a fact and as shown by previous considerations (sections 3.7.1 and 3.7.2) could be explained by the involvement of species Ei of the Fe,,S; .type. We lack enough experimental data to determme the nature of these species, but an approach could be made with the help of a few hypotheses. It may be assumed for instance that in the potential range - 0.930 to - 0.600 V a single species Fe,.?: predominates: we shall see that if this hypothesis is proved such a species cannot be indeterminate. Equation (10) is written: sLi,S= sLi,S- (S + r)Kor~~2&Xsti,S
and earlier considerations
(15)
(section 3.7.2) show that:
K:=K,+KK:ifr= -2 K: = K, (within the limits of measurement precision) in all other cases. In the first case the inequality k; -c kl can on1 be obtained if s = 0. The corresponding species Fe,Y- is very unlikely. For f = 0 we get a series of species such as Li; or Li,K+ which again cannot appear at noticeable concentration within the potential range considered here. This possibility will therefore be ruled out. In the other cases we have: K’ = K, Equation (12) gives:
K: 1. K,. 3.7.3. Search for a predominant species E,. The considerations of paragraph 3.1(b) show that the .. quantltles sLi,s. K,, x,,~~,~~~.~x.~~., are interrelated by expressions of the type: K
= k, sL,,s
x X,F~.J = &SL,,S
(13)
From experimental results (7) we can assign to kl, k2 and kl the values: k, = 2.842 x 1O-9 k, = 2.493 x 1O-2 k, = 1
(14)
l Or difference between the initial molar fraction of S’ionsand that of Fe’* ions produced by the action of oxidising impurities.
A numerical calculatiot using the values determined in the experiment of Fig. 2 specifies this inequality: for potentials far enough from that of the inflexion point, we have: 5 KK:“@ K: --u u
< 0.1
The K K: values calculated by equations (14) and ( 15) for different values of r and s should verify this inequality. This reasoning considerably limits the number of possibilities for the species Ei investigated. Another remark will help us to narrow the choice: equation (10) applies to metals other than iron. In
_
___.._
..
-0,7kcal(-2.9kJ)
Li2St FeS+ LizFeS2
_-_.
-16kcal(-67kJ)
- 10.8kcal(-45.4kJ)
23FeSt3LilStFet6(Kt,C1-)~LiK,Fe,&,Clt5(Li+,Cl)
1.89x lo3
x lo- I6 217kcal(907kJ) 5028 x 1O-4 2084
23LizFeS2~Fet(6Kt~CI-)~LiK,Fe,,S,,CIt(45Li+)t20S2~
(2Li+)t2S2-$Li,Sf - ?
1.32x lo-’ 2.30x10~1548.4kd(203kJ)
LiK6Fe2&CI~23FeStFet(Lift6Kt +CI-)+3S*-
I.5x IO-l2 39.1kcal(164kJ)
K
kJ) 5.28x 1O-4 5.28x 1O-4 10.8kcal(45.4
xsz-
Li,Se(2Li+)tS’-
-
-0s77v
l/2$ t 2e- s2-
FeSGFe” t S2-
-0.302V
E”(Ag-Ag+3 x W2)
Fe” +2e- $Fe
Reactions
Table5. Thermodynamic dataresulting fromthediscussion (Section 3)
--
._
Electrochemical
behaviour of iron in the presence of sulphide ions
the case of lead for instance we have:
G_I~S =
sLi,S +
[
s1 -
K,as~,+‘~12
x
&(%
Lt>S.Pb.PbS
K, being the equilibrium
+$)I
sS,
Li,S
constant
of the reaction: z+ Pb,, s::
with s; = 1 and hi = 0, since here we find the sulphide PbS in the presence of Li& For iron we have:
si_i,S
=
SLi,S
x
K,
K
+
2
1s2-~(s2+~)]
L,,S.Fc.xe,S
i
s2+$
>
constant
Fe2++s,S2-
of the reaction: eFef2S::
with s; = 2 and hi = - 1 since in this case it is the mixed sulphide LizFeSz which is found in the presence of Li,S. Experience shows that these two sL,~~ values are approximately equal[20], [36]: s& = 1.58 x lo-“. In the general case of any Pbf, SJ: and Fe!, S;; species this result can only be due to a chance comcrdence. If on the other hand this possibility is excluded and it is assumed that for both iron and lead a single species containing neither of these elements: S; is responsible for the result observed, we can write: K, $ (EOpbpbz* - EF,,z*) ; K, = exp c (
S+>I
Showing that the equality of the s& values given by the two determinations can only be obtained for: s + r/2 = 0. The corresponding species Ei is a polymer of the sulphide ion: S; 2s. As a working hypothesis we shall take the existence of the simplest species of this series: the S:- ion, which accounts for all the results. This ion, probably solvated in the form Li,S:for example, increases the apparent solubility of L&S: Li,S+S*-
*
and may be an intermediary mechanism:
Li,Sz-
in the Li,FeS,
Fe2+ +Li,S:-
+
2s2-
=
K
for
the
s:-
and x~,~_~~- = l/K, molar fraction of S2ions relating to the boundary of the relative predominance regions
of Sz-
and S$- ions. We find: K = 1.89 x lo3
xs’- _s:- = 5.30 X 1o-4
This work presents a first attempt to establish a potential - pS 2 - diagram of the solid species relative to the iron-sulphur system in the presence of LiCl-KC1 eutectic at 450°C. This diagram is still incomplete and an interesting complement would be to account for reactions involving the Li,Fe2S, phase. We find moreover that the experimental results as a whole can only be explained by involving ionic species in solution other than Fe’* and S*-. Although the predominance of a single sulphurated anion (in the low-potential zone of the diagram) gives coherence between the thermodynamic values calculated from experiment, the presence of other species in solution is nonetheless highly probable. To find out more on this subject it is necessary to determine the regions of relative predominance of species in solution for sulphur and the iron-sulphur system. Apart from their undoubted theoretical interest for the chemistry of oxido-reduction and acido-basicity reactions in ionic solvents such studies could have important practical applications in the field of high energy density electrochemical batteries. work was supported by the Commissariat B I’Energie Atomique (For&may-am-Roses, France). We are grateful to P. Leveque, H. Coriou and J. Dixmier for encouragement to undertake this study and for their helpful assistance in its course. We wish to thank D. Herpin for electrochemical experiments. Acknowledgemenrs-This
REFERENCES formation
Li,FeS,
Equation (15) can be used to calculate equilibrium:
which means that throughout the accessible pS2range (and for low enough potentials) the S2- ions The correction to be entered into the predominate. titration curve calculation given in section 3.2 to account for the existence of this species hardly applies unless E -=z - 0.850V, which is why the experimental results are well described by the equations of Table 3, in the with sqizs = 5.28 x 10m4 (or K, = 1.5 x lo-I’), potentral range above - 0.850 V. Table 5 shows a list of thermodynamic constants calculated from the experimental results of this study (paragraph 2) from the values of the Gibbs free energies of formation of Li,S and FeS, and the standard potentials of the couples Li-Li + and K-K l calculated from[34], [35] and [38], and from the considerations of paragraph 3.
CONCLUSION
c(“+‘G
being the equilibrium
509
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