Chemical and electrochemical behaviour of indium ions in the ZnCl22NaCl melt at 450 °C

Electrochrmica

Acre, Vol. 40. No. 17, pp. 2711

2738. 1995

CopyrIght I( 1995 Elwvicr Sc~cnceLtd. Prmed in Great Britam. All rtghts reserved a313-4686/95 $9.50 + 0.00

Pergamon 0013-4686(95)00256-l

CHEMICAL INDIUM

AND ELECTROCHEMICAL IONS IN THE ZnCl,-2NaCl

BEHAVIOUR OF MELT AT 450°C.

Y. CASTRILLEJO,* M. A. GARCIA,E. BARRADO,P. PASQUIER~and G. PICARD~ Dpto de Quimica Analitica, Facultad de Ciencias. Universidad de Valladolid, Prado de la Magdalena s/n. 47005 Valladolid. Spain t Laboratoire d’Electrochimie Analytique et Appliquee. Ecole Nationale Superieure de Chimie de Paris, 11 rue Pierre et Marie Curie. 75231 Paris Cedex 05, France. (Received 22 February 1995, in revisedform

23 May 1995)

Abstract-The stability of indium chloride and oxide as well as the electrochemical behaviour of the In3+ and In+ ions have been studied in the ZnCl,-2NaCI melt at 450°C by X-ray diffraction (XRD), potentiometry, cyclic voltammetry, chronoamperometry and chronopotentiometry. The standard potential of the redox couple In(III)/In(I) and the solubility products of indium oxides have been determined (E”In(III)/In(I) = - 1.006 f 0.001 V (vs. CI,(l atm)/Cl-), pK, = 12.9 f 0.2 in molality scale), finding that In(O) is not stable in these mixtures according with the reaction: ZnCl,(dis) + Zln(liq)ti 2InCl(dis) + Zn(liq) These results have allowed the construction of E-PO’- equilibrium diagrams. Using a tungsten electrode, we observed that the In(III)/In(I) exchange is quasireversible; log(k$m s- ‘) and a values for this reaction are (- 1.92 k 0.09) and (0.51 + 0.06) respectively at 450°C. The average diffusion coefficients D,,,,,,, and D,,,,, are (5.7 k 0.7) x 10e6, and (6.2 + 0.9) x 10e6 cm2 s- 1 respectively. Key words: Molten chlorides, indium chlorides, zinc chlorides, kinetic parameters.

1. INTRODUCTION The mixtures of ZnCl, with alkali chlorides at temperatures ranging from 500 to 700°C appear to be promising method for the electrolytic production of zinc, and could be of valuable interest on an economic point of view due to the higher current den-

sities and lower energy consumptions compared to the aqueous process (reduction of a zinc sulphate solution). However the effect of other elements present in the cell feed (ZnCI,) must be determined, as well as the possibility of using these mixtures for the treatment of metals contained in ores and industrial wastes of zinc. Indium is usually associated with zinc-containing minerals such as blende; therefore, after having studied the electroreduction of ZnCl:ions in a particular bath, ZnCl,-2NaCl at 45o”C[l], as well as the oxoacidity and purification of the melt[2], we have undertaken a study of the chemical and electrochemical behaviour of indium compounds in that medium. Several aspects concerning the properties of indium ions have been investigated in molten chlorides, the more usual solvents being the eutectic

concluded that the In(II1) species were reduced to the metal through a single three electron reaction process, whereas Shafir and Plambeck[S] and more recently Bouteillon et a/.[63 found a two-step process involving the In(I) species, these last authors also proved the InCl disproportionation, as well as the formation of monovalent indium species resulting from the reaction between metallic In and InCI,. In the equimolar NaCl-KC1 mixture, Barbier et a[.[71 observed the possible coexistence of In(O), In(I) and In(III) species, determined the diffusion coefficient of In(II1) and concluded that the In(III)/In(I) exchange was very fast, whereas in the NaCl-KCI-AlCI, mixture Anders and Plambeck[8] observed that indium metal is not stable, being oxidiced by the melt yielding In(I) solutions. In this paper we have investigated the stability of the different oxidation states of indium, as well as the standard potential of the In(III)/In(I) couple and the solubility product of In,O, on the molality scale, these results allow us the construction of E-p02equilibrium diagrams. The properties of the In(III)/ In(I) exchange were studied by using voltammetric and pulse techniques.

LiCl-KCl, the equimolar mixture KCl-NaCl, and the NaCI-KCI-AICI, mixtures, and some differences have been found on the stability and the electro-

chemical properties of indium in its different oxidation states in these media. In this way in the eutectic LiCI-KCI, Laitinen er a/.[33 and Popov et a!.[41 l

Author to whom correspondence should be addressed.

2. EXPERIMENTAL 2.1 Preparation and purijication of the melt The ZnCl,-NaCl melt, (analytical grade Merck products) was contained in a 100cm3 Pyrex crucible 2731

2132

Y.

placed in a Pyrex cell. The temperature was maintained constant within k2”C by means of a Taner furnace and a West 3200 programmable device. The mixture was fused under vacuum, purified by bubbling hydrogen chloride and then kept under a dry argon atmosphere, a procedure used previously[ 1, 2, 91. 2.2 Electrochemical apparatus The emf measurements were performed with a high impedance voltammeter (Crison). Cyclic voltammetry and pulse techniques were recorded with a PAR EG&G Model 273A potentiostat-galvanostat controlled by a computer using the Model 270/250 research electrochemistry 4.10 software. Ohmic drop compensation was employed during voltammetric and chronoamperometric experiments.. Two tungsten wires (1 mm diameter) were used as working and counter electrodes respectively. The reference electrode consisted of a Pyrex glass tube filled with liquid zinc and covered with molten ZnCl,-2NaCl. A tungsten wire was immersed into the liquid zinc to ensure electrical connection with the reference electrode (Zn(II)/Zn(liq) redox couple). 2.3. Procedure The In(III) solutions were always prepared by direct addition of weighed amounts of InCl, in the fused ZnCl,-2NaCl melt, whereas the In(I) solutions were prepared by addition of In(O) which was oxidiced to In(I) by the melt. pKs(In,O,) determination. With the reference and zirconia electrodes placed into the melt, a known amount of In(II1) was titrated with solid sodium carbonate. Continuous stirring with dried argon was required, and near the end-point the titrant was added every 15 min. All the reagents were analytical grade products.

3.

RESULTS

et al.

CASTRILLEJO

AND DISCUSSION

3.1 Electrochemical study of the In(III)/In(I) electrochemical system on a tungsten electrode 3.1.1. Stable oxidation states. After the purification of the ZnCl,-2NaCI melt, and using tungsten electrodes, the electrochemical window of the melt was 1.78OV, extending from 1.78OV (chlorine evolution) to 0.000 V (zinc deposition) with respect to the Zn(II)/Zn reference electrode (Fig. la)[l]. Figure lb shows a voltammogram for the reduction of Indium trichloride at a tungsten electrode. The electroreduction occurred through only one electrochemical step characterized by the cathodic wave. A associated with the anodic wave A’. The peak potentials are approximately 0.488 and 0.588 V, respectively, and its shape was characteristic of a soluble-soluble exchange presumably related to the In(III)/In(I) couple. Similar conclusion can be derived from chronopotentiograms obtained for In(II1) reduction. Only one transition time can be observed, and by current reversal chronopotentiometry it was found that the

0.15. 0.10.050

<

L

.O.M4.1 O.lS-

0.25 0.24

(al 0.25

0.75

125

-1Gi--

2

EN

0.02 0.015 0.01

-0.01 -0015 402

(bl

0025 4

Fig. 1. (a) Cyclic voltammogram obtained at a tungsten electrode in a pure ZnCl,-2NaCI melt. (b) Voltammogram related to the reduction of InCI, in the fused ZnCI,P2NaCl at 450°C [InCI,] = 3.284 x lO~‘mol kg-‘. Sweep rate: 0.2OOvs-’

ratio oft,, to trcdwas close to one-third whatever the imposed current (Fig. 2), indicating that the electrochemical exchange ocurred between two soluble species. When we examined the voltammograms acquired with a solution of In(I) in the same fashion as those illustrated in Fig. 3, we obtained the same waves A

I

094

US

Fig. 2. Chronopotentiogram with current with a InCI, solution.

reversal obtained

Electrochemical behaviour of indium ions

amount of Zn(0) obtained, it was ascertained In(I) was formed in solution by the reaction:

O’03S k

2733

that

Zn(I1) + 2In(O) G=Zn(0) + 2In(I)

A’

0.01

I

Y

-0.01

-o.o!d-

1

-0.25

0.25

0.75

1.25

1.k

d

2.25

EN

Fig. 3. Voltammogram plotted when In(O) was added to fused the ZnCl,-2NaCI 450°C [In(I)] = 5.939 x 10-2mol kg-‘. Scan ratz:0.200Vs-1

and A’, confirming that In(I) is indeed oxidized to In(III), and the half-wave potential, Eliz, was estimated from the relationship E,,, = (E”, + &)/2. Notwithstanding, and in order to confirm the nature of the electrode process, the standard potential of the In(III)/In(I) system was determined by measuring the equilibrium potential of a tungsten wire in different solutions containing In(II1) and In(I). During these experiments In(I) concentration was determined from the amount of In(O) added, whereas the concentration of In(II1) was calculated from the weighed amount of InCl,. A total of 18 concentration-potential data points were taken in 3 separate experiments, the concentration ratio of In(III)/In(I) ranging from 0.49 to 1.89. A plot of the cell emf as a function of the logarithm of the concentration ratio was linear and had a slope of 0.069 k 0.004 V/log unit, in agreement with the theoretical value of O.O72V/log unit expected for a two electron process at this temperature (Fig. 4). The standard potential obtained from the intercept was, in a first approaching, 0.546 + 0.006V (vs. the Zn(II)/Zn(liq) reference electrode). We can then conclude that the In(I)/In(O) couple must be more negative in potential than in Zn(II)/ Zn(0) couple, therefore Indium metal in contact with the melt reacts quantitatively to give zinc metal. From the amount of In(O) put into the melt and the

A’

3.1.2 Reversibility of the In(III)/In(I) electrochemical system on a tungsten electrode. Cyclic voltammograms yielded more information about the electrochemical behaviour of indium ions. The study of the voltammetric curves recorded with a solution of In(II1) (Fig 5a), or a solution of In(I), for potential sweep rates ranging from 0.05 to 1.5Vs-’ shows the linear dependence of the cathodic peak current, I,, and the anodic peak current, I,, on the square root of the sweep rate (Fig. 5b), and it becomes clear that the reduction step of In(II1) and the oxidation step of In(I) consist of a simple diffusion-controlled charge transfer process. On the other hand, the peak potentials do not change with increasing sweep rates for values lower than 2.0 Vs- ’ (Fig. 6a), a behaviour expected for a diffusion controlled process, and the slope of the plot of log(i, - i)/i vs. E, over the approximate current range 0.35ip-0.7i,, approaches the theoretical value of 2.2 nF/RT corresponding to a fast electrochemical process[lO], whereas for higher sweep rates the slope deviates from the theoretical value (Fig. 6b) and the peak potential is shifted towards negative potentials, indicating that in these conditions the electron transfer rate is significantly lower than that of mass transport.

‘,

0 .t

./

,.?

0 55.

..,*

.‘A

.’

z

/ 05

.’

// 1 / I/

0.454 -1 2

-0 8

-04 log

0

04

I 08

lInW)l/[ln(l)l

Fig. 4. Equilibrium potential of a tungsten wire in different solutions containing In(IlI) and In(l).

Fig. 5. A series of voltamograms related to the In(III)/In(I) sweep rates. exchange different [In(III)] = 6.88 ?IO-s mol cme3, s = 0.202cm2 (b) Variation of the cathodic current density with the square root of the sweep rate at 450°C.

Y. CASTRILLUO

2734

et al. O,Ol-

-

1.1 1

1 0,9

0,008-

03

o,w2< g -o.w2-

0.7

. E

0.6

P .’ E 8 7

0.5 0.4

-O.W6-

0.3 0.2

-O.Ol-

0.1

Fig. 7. Semi-integral curve of a voltammogram recorded with a solution of In(II1) at OXVs-’ (b) Logarithmic analysis based on the soluble-soluble reversible hypothesis.

F c b z 8 -

-0.6

-0.6

-1

-1,2t 0.46

0,46

0,5

0852

0.54

0.56

0

EN

Fig. 6. (a) Variation of the cathodic potential peak with the logarithm of the sweep rate. (b) Plot of the log [(i,-i)/i] against E for In(III) reduction. Sweep rates: (1) 0.05, (2) 3.ooVs~‘.

Another reversibility test consisting of the computation of the semi-integral of the current m(t) = (l/n)-*‘* r0 i(u) (t-u)-“*du was applied. The convoluted curves obtained at different sweep rates were very similar but do not remain identical from the direct to reverse scan as it can be observed in Fig. 7. For a reversible charge transfer, the convoluted curves should obey the equation[ 11, 123 :

E = E,,, = (RT/nf) ln[(m* - m)/m] where m is the semi-integral of the current density and m* the cathodic limiting value of these functions. The logarithmic analysis of a convoluted curve corresponding to a solution of In(II1) at a sweep rate of 0.8 V s-l according with this model is given in Fig. 7. The electrode potential varies linearly with log[m* - m)/m], but the slope of the linear part of this curve is 0.068 V, a value slightly different to that

expected for a reversible exchange process of 2 electrons (0.072 V). A further study of the electrochemical behaviour of indium ions was carried out using chronopotentiometry. The analysis of the transition time variation as a function of the imposed current density, j,, indicated that the fluxes of In(M) species were diffusion controlled (Sand’s law) (see Fig. 8). Under these conditions, the logarithmic analysis of chronopotentiograms is possible; the electrode potential varies linearly with lg[(r/t)“’ - 11, but the slope of the linear part of the curve (0.065) is slightly different from the theoretical value for a two electron reversible exchange process at 450°C (0.072), for which we can consider the electrochemical system to be quasi-reversible under the experimental conditions employed here. The same procedure was used to analyse the experimental curves obtained with a solution of In(I) and similar results were found. All these criteria show that, in our experimental conditions, we can consider the electrochemical process as quasi-reversible, and presumably the kinetics of the In(III)/In(I) are near to the limit for a

-0.004-

-0.006-

5 -O.C06-0.01~ -0.012-0,014, 0.2

0,4

0,6

0,6 1 1,2 s-'=/s-l,2

Fig. 8. Chronopotentiometric study of InCI, Sand’s law verification.

1.4

6

reduction.

Electrochemical

behaviour

reversible response, which will be confirmed below, them justifying why the slope values obtained with different diagnostic criterias are only slightly different from the theoretical value for a reversible behaviour. 3.2.2 Study of indium ions diffusion. The indium ions diffusion coefficients were computed from chionopotentiometric and voltammetric data and from the boundary semi-integral values according to the following relations.: ir1/2 -= C

nFSD”%r’/’ 2

m* = nFSCD”*

where C is the bulk concentration of the electroactive species (In(III) or In(I)), D the diffusion coefflcient, S the electrode surface and 5 the transition time. Results are summarised in Table 1. A further study of the electrochemical reduction of In(III) on the tungsten electrode was made using chronoamperometry between E = 570mV and E = 450mV. It was observed that chronoamperograms show constant current, for time values greater than 2s, due to thermal convection (Fig. 9). By plotting the variation of the current vs. Z/t”’ at the potential corresponding to the diffusion limiting current of the i-E reduction curve, it can be shown that the experimental data obey the Cottrell law. nFSD”‘C nl/ztl’2

The diffusion coefficient DIn(II1) ion was calculated from the slope of the straight line obtained for a number of exchanged electrons n = 2 (see Table 1). Table 1. In(III) and In(I) diffusion coeflicients different Technique

Voltammetry Semi-integral Chronopotentiometry Chronoamperometry

obtained

by

techniques IO6 &,,a,/ cm* SK1 5.8 5.1 6.4 5.3

k + k +

0.3 0.3 0.2 0.7

IO6 D,“,, / cm’s_’ 6.1 7.2 6.2 5.5

ions

2735

Determination of the charge-transfer parameters.

kinetic

According to these results, the electro-reduction of In(II1) involves one diffusion step (diffusion of In(II1) ions from the bulk solution to the electrode, characterized by the diffusion coefficient D), one twoelectron transfer step (characterized by the intrinsic rate constant k: and the charge-transfer coeficient I), and other diffusion step (diffusion of In(I) ions electrogenerated from the electrode surface to the bulk). The kinetic parameters are derived in practice

from the analysis of the semi-integral of the current[ll, 12, 131. The curve can then be analyzed by using the following equation

i, = 0.4463(nF)3/2SCD1’2u1’2(RT)- ‘j2

id(t) =

of indium

+ * + *

0.4 0.5 0.8 0.3

E = Ei + 2

ln(K”/D$2) + $

-m-mexp(g)(E--E&]/i} The logaritmic analysis according to this equation is presented in Fig. 10, and the charge transfer coeflicient tl and the rate constant kp may be determined from the slope and intercept, respectively, of the logaritmic plot (E vs. log(B), being B = [m* -- m - m exp

WIRTXE-E,,2)l14.

On the other hand, cyclic voltammograms such as those shown in Fig. 5a were very reproducible, and it was found that the information of interest could be easily extracted from these voltammograms by comparison to simulated voltammograms calculated by using a simulation computer program (M271 COOL kinetic analysis software l.lO), for a quasi-reversible mechanism in which the charge-transfer rate constant, kf, the transfer coefticient, ol, and the half-wave potential, E,,, , were adjusted to give the best fit between the experimental and calculated results. We also tried to fit the system to a reversible process. However the best results were found for a quasireversible process. Representative examples of these simulations are shown in Fig. 11, and the average values obtained are listed in Table 2 where it is possible to see the very good agreement between the values obtained from the different methods employed.

o.015~ 0

0.1 I

0.2 .

0.3

0.4

0.5

0.6 1

0.7 1

0.8 I

0.9 I

to.4

E/v

Fig. 9. Chronoamperometric

study reduction.

of indium

trichloride

Fig. 10. Logarithmic analysis of semi-integral of the voltammograms based on the soluble-soluble quasi-reversible hypothesis. In(II1) solution, sweep rate 0.6 V s - I.

Y. CASTRILLEJ~ et al.

2736

as oxide, and proposed here, In(II1) is precipitated when the reaction is monitored with the zirconia electrode, selective to 02- ions[7, 81, and emfjump occurs at the point corresponding to the stoichiometric precipitation of the oxide. The potential values obtained after successive additions of known amounts of sodium carbonate to a solution of In(II1) with an initial concentration C, = 2.06 x 10-i mol kg-’ are plotted in Fig. 12. Only one equivalence point can be observed, for a stoichiometric ratio c( = [added carbonate]/[Indium (III)] equal to 1.5. This value indicates that the reaction is: 21n3 + + 302 -0.024

0

0.2

0.6

0.4

I 1

0.6

EN

+ In,O,(s)

The X-ray diffractometry analysis of the resulting solid compound recovered at the end of the experiment after dissolution of the melt in water and subsequent filtration has proved the existence of In,O,, confirming the above reaction. From the mass balance equations:

0.025

CO2 -1b”lk =

0.02

C02-Iadd - 3CWM,,,

C~nW~)lbUIk = C1n(lll)li~itid - XIn2W,,,

0.015-

(1)

(2)

and with the expression of the solubility product, K, = [In(III)]Z,,,,[02~]3,,,,, we can derive an equation for the titration curve,

0.01.

[02=15

- 2C,(a - 3/2)[02+J4 + C;(x - 3/2)2[02-]3

- 9/4K, = 0

(3)

Beyond the equivalence point (a > 1.5) there was an excess of carbonate ions which led to ZnO pre-

-O.Ol-0.015-O.M(b) -0.026i 0

0.2

0.4

0.6

-.-a, 1

03

EN Fig. 11. (a) Linear sweep voltammogram of InCI, reduction, sweep rate 1.5 Vs-’ (+-) experimental results; ( + + ) and (---) simulated results corresponding to a reversible and a quasi-reversible process respectively. (b) Linear sweep voltammogram of In(I) oxidation, sweep rate 0.6Vs-‘. (-) experimental results; (t +) and (---) simulated results corresponding to a reversible and a quasireversible process respectively.

were used to analyze the experimental curves obtained with a solution of In(I)[ 141, and the results are given in Table 2. The

same

3.2 E-p@

“a

32

‘. ?

2

23 \

. \

2,4

.

\m .m*_-

methods

> 0

diagram of In.

CL5

1s

1

4 2

2.5

3

Alpha

3.2.1 Titration of indium trichloride by carbonate ion and pKs(In,O,) determination. In the method Table 2. Kinetic parameters Technique Simulation (In(II1) reduction) (In(I) oxidation) Semi-integral (In(II1) reduction) (In(I) oxidation)

Fig. 12. Potentiometric 0.038 79 mol kg-’ of In(III)/In(I)

[In(III)] titration of by sodium carbonate.

exchange

’

3

E,,,/V

log K,O/cm s -

0.538 k 0.003 0.539 f 0.002

- 1.83 f 0.09 - 1.92 + 0.09

0.52 f 0.06 0.47 * 0.05

- 1.87 + 0.10 - 1.99 + 0.09

0.52 f 0.07 0.55 + 0.04

=

Electrochemical

behaviour

of indium ions

2131

with sodium carbonate with the zirconia electrode we could not see any emfjump corresponding to the In,0 formation, indicating that the In,0 is fully dissociated in this melt. All the calculated data were then used to build up the equilibrium potential-acidity diagrams for indium compounds (Fig. 13).

a5

0

45

4. CONCLUSIONS

> w‘ -1

-1,5

Zn 4 4

I

I

I

I

8

12

16

20

pdFig. 13. Equilibrium potential acidity diagram for indium compounds (solid lines) and the mixtures Cl, + O,, HCI + H,O (dotted lines), for pressures between 1 and lo- 3 atm, in the melt ZnCl,-2NaC1 at 450°C.

cipitation

and: ~0’~

= pK,ZnO

(4)

In order to obtain the value of K,(In,O,) from the experimental results, a simulation method based on these equations was used and led to arbitrary values of the constant. The simulated curve which best fits the experimental data is shown in Fig. 12. The mean value of pK,(In,O,) obtained for three different titrations was 12.9 k 0.2. The solubility product corresponding to the reaction : 2 In(II1) + 302-

= In,O,

allows to calculate the activity related to the equilibrium:

coefficient

of InCl,,

InCl,(s) G InCl,(dissolved) taking into account compounds

the reaction

3ZnO + 21nCl 3 = 2In,O,

between

the pure

= -pK,(In,O,)

- pK*

- log a(ZnC1,) + pK,(ZnO)

3Cl,(g) + In,O,(s)

+ 2InCl,(dissolved)

6HCL(g) + In,O,(s)

+ 2InCl,(dissolved)

+ 3/20,(g) + 3H,O(g)

By using voltammetric, chronopotentiometric and chronoamperometric techniques, it was possible to determine accurately the kinetic parameters characterizing the mass and the charge transfers occurring in the electrochemical reduction of In(II1) and oxidation of In(I). The intrinsic rate constant kf, and the transfer coefficient a can be extracted from voltammograms by comparison to simulated voltammograms calculated by using a simulation computer program, and also by means of the logarithmic analysis of convoluted curves by applying the equation corresponding to a soluble-soluble quasireversible process, finding a very good agreement between both methods. Acknowledgements-The authors are grateful to DGICYT CE93-0017 (Spain) and to Metaleurop Recherche (France) for financial support which enabled this study. Two of the authors (M.A.G. and P.P) thank to Iberdrola S.A. Spain and to Research and Technology Ministry of France for a doctoral grant.

+ 3ZnC1,

by using the relation logf(InC1,)

Indium (I) chloride is normally only slightly solvated in most melt chlorides since it is vaporised as InCl. However, InCl is soluble in the melt ZnCl,-2NaCl where is completely solvated. This fact implies a shift on the standard potential of the couple In(I)/In(O) towards more cathodic potential situated below the reduction potential of Zn(I1) ions. Indium (0) is then inestable in this medium. The chemical properties of indium in the melt ZnCl,.-2NaC1, as well as the mixtures Cl,(g) + O,(g) and HCl(g) + H,O(g) previously determined[2], have been summarized in the form of an equilibrium potential oxoacidity diagram. The In,O, can be chlorinated with the mixture Cl, + O2 for P(C1,) = 1 atm and P(0,) = tom3 atm (quasi-pure chlorine action) and by bubbling HCI containing 1% of water. In the first case, during the chlorinating action, the oxide ions are oxidized to gaseous oxygen, whereas in the second case, oxide ions are transformed into water by action of HCl, according with the following reactions:

(5)

where K*, the constant of the equilibrium between pure compounds, was calculated from the chemical potentials given by Barin et aI.[15] while log determined were and a(ZnC1,) pK,(ZnO) previously[2, 161. It was found that logf(InC1,) is -2.2 + 0.2 at 450°C. When we tried to determine experimentally the stability of In,0 by titration of a solution of In(I)

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2738

Y. CASTRILLEJOel al.

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1 I. A. J. Methods

Bard

and

L.

Fundamentals

R. and

Faulkner,

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