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Transfer of ions and electrons at anodic cadmium sulphide films
101
J. Electrounal. Chem., 301 (1991) 101-115 Elsevier Sequoia S.A., Lausanne
Transfer of ions and electrons at anodic cadmium sulphide films M. Krebs I, M.I. Sosa 2 and K.E. Heusler Abteilung Korrosion und Korrosionsschutz, Institut ftir Metallkunde und Metaliphysik, Technische Uniuersittit Clawthai, Agricolasir. 2, W-3392 Clausthai-Z. (FRG) (Received 9 October 1990)
AbSbWt Steady state polarization curves of cadmium in NaHS solutions exhibit a maximum current density at low overpotentials with respect to the equilibrium potential of cadmium sulphide formation, a potential region of about 1 V with nearly potential independent current density and a steep rise of the current density at high overpotentials. The current densities increase with the sulphide concentration and are nearly independent of the pH value between pH 9 and pH 11. During anodic polarization of activated cadmium at constant current density, a CdS film is nucleated at small overpotentials. The film becomes compact when it is a few monolayers thick. The compact film grows by high field conduction. The current efficiencies for film growth and dissolution of cadmium ions are about 20% and SO%, respectively. The current efficiency for film growth drops to about 3% beyond a characteristic electrode potential and the current efficiency for oxidation of sulphide to polysulphide grows accordingly, while the current efficiency for dissolution of cadmium ions remains unaffected. The rate determining steps of the ion transfer reactions at the interface between the sulphide and the electrolyte are the dissolution of CdSH+ formed by reaction of cadmium ions from CdS and HS- from the electrolyte, and the transfer of HS- ions yielding sulphide ions to build up the CdS film and hydrogen ions in the electrolyte. The correlation between sulphide ion transfer during film growth and electron transfer during sulphide oxidation is explained by the semiconductor properties of the film together with sulphide surface states.
INTRODUCTION
Cadmium sulphide layers can be grown on cadmium in neutral and basic aqueous sulphide solutions in which the equilibrium potential of formation of the sulphide is negative to the respective formation potential of cadmium oxide or cadmium hydroxide. The standard potentials of the respective reactions are [l]:
i Present address: Varta AG, Ellwangen, FRG. ’ Present address: Instituto de Investigaciones Fisicoquimicas Argentina. 0022-0728/91/$03.50
0 1991 - Elsevier Sequoia S.A.
Te&icas y Aplicadas (INIFIA),
La Plata,
_
102
CdS + 2 e-= Cd + S2-
ET = -1.225 V
(1)
E; = -0.824
(2)
and Cd(OH),
+ 2 e-=
Cd + 2 OH-
V
The hydroxide is more stable in water than the oxide with CdO+2e-=Cd+2OH-
E; = -0.183 V
(3)
From the dissociation constants of hydrogen sulphide in water H,S = H++ HS-
K, = 9.1 x 1O-8 M
(4)
and HS-=
H++ S*-
K 2 = 12* x lo-l2
the equilibrium potential Ef = ET + (RT/2F)
M
(9
Ee of formation of CdS becomes
ln{ 1 + (h/K,)
+ ( h2/K,K2)}/a
(6)
where h is the activity of hydrogen ions and a the sum of the activities of S2-, HS-, and H,S. Thus, in aqueous sulphide solutions the equilibrium potential of formation of cadmium sulphide is negative to the equilibrium potential of formation of Cd(OH), even at very small activities of sulphide. Sulphide ions S*- are oxidized to polysulphide ions S,“-. The equilibrium potentials for x >, 2 are only slightly more positive than for Si-
+ 2 e-=
2 S2-
Ez = -0.483
V
(7)
Little is known about the acid-base equilibria of the polysulphides. According to cyclic voltammetric measurements, one or two monolayers of CdS were formed close to the equilibrium potential of formation [2]. In a potential region of almost 1.2 V the film grew at constant current density while the potential increased linearly with time. This behaviour is expected for rate determining potential-independent ionic conduction in high electric fields. The current density began to increase steeply at an overpotential of about 1.4 V vs. the equilibrium potential of formation. It was concluded that a porous film was formed. The film was reduced at potentials negative to the equilibrium potential of formation. A later study of film growth in the region of high field ion conduction arrived at the conclusion that interfacial charge transfer of sulphide ions was rate determining 131. Three current peaks were observed in voltammograms close to, but positive of the equilibrium potential of formation [4]. There was no underpotential deposition of adsorbed sulphur. The first peak was interpreted as being due to the deposition of half a monolayer of S, the second to the completion of the full monolayer, and the third to the formation of one further monolayer of CdS. In all the earlier investigations of the anodic sulphidation of cadmium, a 100% current efficiency for film growth was assumed. However, theory predicts that, in principle, the current efficiency for film growth is always less than 100% due to the
103
irreversible dissolutiop. of cations, even if the rate of electron transfer reactions is zero [5]. The kinetics oi g : ,+th and dissolution of oxide films on several metals like iron, titanium and aluminium were observed as expected from the theory. The experiments reported below yield low current efficiencies for the formation of cadmium sulphide on cadmium, both because of the dissolution of cadmium ions from the film into the electrolyte and because of the oxidation of sulphide to polysulphide by electron transfer. The relative importance of the parallel reactions depends, on e.g. the electrode potential and the composition of the electrolyte. EXPERIMENTAL
A rotating ring-disc electrode with a mechanically polished 0.5 cm’ cadmium disc and a gold ring was used. The collection efficiency was N, = 0.36. The whole apparatus was enclosed by a black box, shielding the working electrode from any inadvertent light. The electrolyte solutions, containing 1 M or 0.5 M sodium carbonate + bicarbonate buffer with pH values between pH 7 and pH 13 and sodium sulphide at different concentrations, were prepared with deoxygenated water and kept under nitrogen in order to prevent the formation of polysulphide. After the preparation of the electrolyte, oxygen cannot be removed, because any oxygen is consumed to oxidize sulphide to polysulphide. Cadmium sulphide films were grown and dissolved at 25 o C under galvanostatic or potentiostatic conditions. Electrode potentials were measured vs. HgS(red)/Hg in 1 M NaHCO, + 0.1 M NaHS, pH 9, with E, = -0.74V vs. the standard hydrogen electrode, or vs. Ag,S/Ag in 0.5 M NaHCO, + 0.1 M NaHS, pH 9, with E, = -0.575V. Capacities were usually determined from the voltage transients during 2 rnA/cm’ current pulses lasting 1 ms after an interruption of the polarization for 0.3 s. A computer was programmed to change the experimental parameters and to take the data at predetermined tunes. RESULTS
Diffraction patterns of cadmium anodized in 0.1 M NaHS, pH 9, were obtained by transmission electron microscopy. Cadmium was etched away from the back side until holes appeared in the thin Cd sheet. Three diffuse rings characteristic of hexagonal CdS were observed apart from two rings of Cd and an unidentified ring. A depth profile obtained by Auger analysis is shown in Fig. 1. Both the signals for cadmium and sulphur remained independent of the sputter time for almost 1 min. The oxygen signal was always very small. One concludes that the film consisted of pure CdS not contaminated by oxide. Steady state current densities were established at constant electrode potentials after times up to several days. The long times were necessary for small steady state current densities. The steady state polarization curves shown in Fig. 2 exhibited a peak of the current density at small positive overpotentials vs. the equilibrium potential of CdS formation. The height of the peaks grew with the concentration of
60 \o t 4
tlmin
Fig. 1. Relative with Ar+.
amplitudes
A of Auger lines of cadmium,
sulphur,
and oxygen
vs. time r of sputtering
NaHS. The current densities were nearly potential independent in a range of several tenths of a volt. This range shrank with increasing sulphide concentration. The potential independent current densities grew with the sulphide concentration as shown in Fig. 3. The apparent reaction order {a In j,/a In c(NaHS)}, = 0.64( f 0.6) was obtained from measurements at different constant electrode potentials between E, = -0.54 V and E, = 0.26 V. At constant sulphide concentration the steady state current densities were nearly independent of the pH value from pH 8 to pH 11. At higher pH values the steady state current densities decreased with PH. In order to reduce any preformed films before galvanostatic anodization, the electrode was kept at an overpotential 77= -0.3 V vs. the equilibrium potential of formation of CdS. The capacitance in this initial state was around 50 pF/cm2. Upon an interruption of the circuit the potential rose towards positive overpotentials, while the capacities decreased at rates increasing with the concentration of residual polysulphide. The rate of increase of the reciprocal capacitance became constant after about 1000 s. With the relative dielectric constant cr = 8.6 [6] for CdS, the film thickness after 3000 s was typically estimated at 1.7 nm assuming a double layer capacitance Co = 50 pF/cm2 in series with the film capacitance. Film growth at constant anodic current densities was started 20 s after interruption of the cathodic prepolarization. At this time, overpotentials 0.07 < n/V < 0.12 were established. The capacitances were still in the range 34 < C/(pF cmw2) < 59,
105
25
20
Y
E
15
2 I . ._
10
5
J/
0
__4
I
-0.5
-1
0
0.5
1
EHlV Fig. 2. Steady state current densities j as a function of the electrode potential E, vs. the standard hydrogen electrode for cadmium in 1 M sodium carbonate+ bicarbonate buffer, pH 9, with (A) 10K4 M NaHS, (0) 10m3 M NaHS, (A) 10s2 M NaHS, (0) 10-t M NaHS, and (0) 1 M NaHS, at 25°C.
1
I
I -4
-3
-2
-1
Log (c/M) Fig. 3. Steady state current density j at E u = 0.26 V vs. the standard hydrogen electrode as a function the NaHS concentration c in 1 M sodium carbonate + bicarbonate buffer, pH 9, at 25 o C.
of
106
-0.6
%5
D ImCcrnm2
1.0
1.5
Fig. 4. Electrode potential E, vs. the standard hydrogen electrode as a function of charge Q for cadmium in 0.5 M sodium carbonate+bicarbonate buffer, pH 12, with c = 0.01 M NaHS at 25O C for different anodic current densities.
indicating that a film did not yet grow. The potential transients after applying an anodic current density exhibited four characteristic regions. The first two regions are shown in Fig. 4. The potential first started to grow at an increasing rate. In the second region the rate became constant, as indicated by the linear dependence of the potential on time. Defining the end of the first region by the intercept between the tangent to the steepest potential rise in the first region and the linear potential rise in the second region, one finds that the first region ends at 71- 0.35 V. The charges in the first region grew with the applied current density from 0.07 mC/cm* at 5 PA/cm* to 0.22 mC/cm* at 40 PA/cm* and 0.82 PC/cm* at 400 PA/cm*. There was not sufficient time for capacitance measurements in the first region. As shown in Fig. 5, the reciprocal capacitance C-’ was a linear function of the charge Q. The reciprocal capacitance for Q -+ 0 yielded estimates of the film thickness at the beginning of the galvanostatic experiment. The initial reciprocal capacitances thus determined grew with decreasing current density and with time in the same manner as described above for j = 0. The current efficiency L=
(aQ/ac-')(nFc/V)
(8)
for film growth was calculated from the derivative aQ/aC-’ of the charge with respect to the reciprocal capacitance, and with the charge number n = 2, the
107
0.24
“E
u 0.18
h
Y
\
7
u
0.12
0.06
0
2
4
6
8
10
PI mC cK2
Fig. 5. Reciprocal capacitance C- ’ vs. charge Q in the second region for cadmium in 0.5 M sodium carbonate+ bicarbonate buffer, pH 12, with c = 0.01 M NaHS at 25O C for an anodic current density j = 12 pA/cm2.
Faraday constant F, the dielectric constant e = ~(6~)and the molar volume V= 29.97 cm3/mol of CdS. The potential independent current efficiencies in the second region were around L c- 0.2 for sulphide concentrations between 0.01 and 1 M at 9 < pH < 11. The current efficiencies dropped at smaller sulphide concentrations and larger pH values. The transition from the second region to the third region occurred at potentials E, = 0.4( f. 0.2) or over-potentials q = lS( L-0.2) V. The same transition potentials were obtained from intercepts of the linear dependences of the electrode potential on the time or on the reciprocal capacitance. Figure 6 shows that in the third region the potential, like the reciprocal capacitance, rose at a lower rate than in the second region. The electronic current densities of the oxidation of sulphide to polysulphide were determined from the limiting currents of polysulphide reduction at the ring electrode. Sulphide was oxidized in the first region, but in the second region the respective current efficiencies were usually very small for total current densities exceeding a few r_lA/cm2, as shown in Fig. 7. As mentioned above, the current efficiencies for film growth were also rather small. Most of the current density was used for dissolution of cadmium ions. They precipitated quickly close to the cadmium electrode but also within the electrolyte by formation of CdS powder. A yellow deposit adhering loosely to the electrode became visible after prolonged
108
> I W
200
400
800
600
101 10
t/S
Fig. 6. Electrode potential EH vs. the standard hydrogen electrode as a function of time r for cadmium in 0.5 M sodium carbonate+ bicarbonate buffer, pH 9. with c = 0.1 M NaHS at 25 o C for an anodic current density j = 12 aA/cm2.
1.0
Cd2’
0.8
o---o--o \
o--o--o---D-
/
‘D /
\ \
O,/“\
0.6
J
/ 0
0.L
0.2
0.0 -0.5
0
0.5
1.0
1.5 E,.,tV
2.0
2.5
3.0
Fig. 7. Current efficiencies L for anodic transfer of sulphide ions (0) resulting in film growth, cadmium ions (0) leading to precipitation of CdS in the bulk of the electrolyte, and of electrons resulting in oxidation of sulphide to polysulphide during anodic polarization at j = 382 PA/cm* cadmium in 0.5 M sodium carbonate+ bicarbonate buffer, pH 10, with c = 10e3 M NaHS at 25 o C.
of (A)
of
109
2.4
N
k 1.8 4
3 D
.Y ? 1.2
0.6
-0,4
02
log ljSlpA
0.8
cm21
I (bl
2,4
Oh
-0,4
0,2
0.8 log ( j,
IpA
1.4
cme2)
Fig. 8. Double logarithmic plot of the current density jcd of cadmium ion transfer vs. the current density j, of sulphide ion transfer during the formation of cadmium sulphide fiis on cadmium in 0.5 M sodium carbonate + bicarbonate buffer, pH 10, at 25 o C with c = (a) 10K3 M NaHS ( 0), lo-* M NaHS (0). (b) 10-l M NaHS (o), and 1 M NaHS (+).
110
electrolysis. Only at pH values G 7 did the life-time of the cadmium ions exceed the transfer time to the ring electrode, and cadmium could be deposited there. Figure 8 shows for the second region a double logarithmic plot of the cadmium ion current density vs. the sulphide ion current density during film growth at different total current densities. The slope was {a In j(Cd’+)/a In j(S2-)}c(Nans) = 1 both for 1 M and 0.1 M NaHS, but decreased to 0.87 for 0.01 M and to 0.72 for 1O-3 M NaHS. There was no systematic dependence of j(S*-) on the NaHS concentration at constant j(Cd2’) for c(NaHS) 2 0.01 M, but at smaller sulphide concentrations j(S*-) decreased with c(NaHS), in particular at low current densities. The current efficiency for film growth decreased accordingly. The slopes {a In in the third region were not significantly different j(Cd2’)/a ln j(S’-)J,,,,ns, from those in the second region. According to Fig. 7, in the third region at potentials E, > 0.3 V, the current efficiency for film growth dropped to values between 1.5% and 5% and there was an equivalent increase of the current efficiency for sulphide oxidation, but the current efficiency for dissolution of cadmium ions did not change much. At high concentrations of sulphide in the electrolyte the current efficiencies remained independent of the overpotential up to 115: 3.5 V. The electronic current density j, grew with the total current density j according to a In j&3 In j = 0.71, as shown in Fig. 9. If the concentration of sulphide in the electrolyte was low, high electronic current densities of sulphide oxidation flowed in a region at potentials above E, > 1.2 V or overpotentials 1 > 2.3 V. There were one or two maxima of the electronic current corresponding to one or, as in Fig. 10, two arrests in the time dependence of the voltage at constant current density. At sufficiently positive potentials the rate of potential change and all the current efficiencies returned to the values characteristic
-G -
-5
-4
logij/Acm-21
Fig. 9. Double logarithmic plot of the electronic current density j, of sulphide oxidation vs. the total current density j during the growth of cadmium sulphide films in the third (0) and fourth (0) regions on cadmium in 0.5 M sodium carbonate+ bicarbonate buffer, pH 10, with 10V3 M NaHS, at 25O C.
111
2
1 > lJ.f
0
-1 5w
0
low
tls
Fig. 10. Electrode potential E, vs.the standard hydrogen electrode as a function of time t for cadmium in 0.5 M sodium carbonate+ bicarbonate buffer, pH 10, with c = 10W3 M NaHS at 25 o C for an anodic current density j = 400 pA/cn?.
3.0
;::c:rf
2.L
3
2
P 0
/
I> .
0
,”
0
0
0 0.6 -1 0 0
50
100
150
Q/mC cmm2
Fig. 11. Electrode potential E, vs.the standard hydrogen electrode and reciprocal capacitance C-’ as a function of the total charge Q during anodic polarization with j = 40 PA/cm2 of cadmium in 0.5 M sodium carbonate + bicarbonate buffer, pH 10, with 0.01 M NaHS, at 25 o C.
112
of the third region. The ratio of the two ionic currents was not affected by the increase of the electronic current, within the limits of experimental accuracy. According to Fig. 11, both the electrode potential and the reciprocal capacitance decreased in the fourth region after having passed a maximum. Film growth stopped completely at a potential of E, = 3.0 V or an overpotential n = 4.2 V when the thickness was about 20 nm. The decrease of both the electrode potential and the reciprocal capacitance indicates a slow thinning of the film. The nearly steady state potentials changed with the logarithm of total current density according to a Tafel slope of about 1.3 V/decade. The current efficiency for sulphide oxidation was about 72% independent of the applied current density as shown in Fig. 9. The remaining part of the current must be due to cadmium ion dissolution. DISCUSSION
The formation kinetics of cadmium sulphide at small positive overpotentials in the first region corresponds qualitatively to nucleation and lateral growth until the film becomes compact and direct contact between the metal and the electrolyte is interrupted. The charges in the first region were equivalent to a few tenths to 3 or 4 monolayers of CdS, if a charge Q, = 0.23 mC/cm2 was assumed [2,4] for one monolayer. It was not possible to subdivide the first region into several stages. A substantial part of film growth in the first region was due to the reduction of polysulphide which cannot be excluded completely from the electrolyte. The relative contribution to film growth of polysulphide reduction occurring at potentials negative to EHss = -0.3 V becomes larger at smaller anodic current densities. Therefore, it is not surprising that the charges in the first region increased with the applied current density. As soon as the film is compact at a film thickness of a few monolayers, polysulphide is not reduced any more. During growth of the compact film, cadmium ions are transferred from the metal into the film at the inner Cd/CdS interface and sulphide ions are transferred from the electrolyte into the film at the outer CdS/electrolyte interface. Within the film there is ion transport in high electric fields. At any constant rate of film growth the mean field was estimated from the dependence of the electrode potential on film thickness derived from capacitance measurements. For current densities between 4 and 400 pAA/cm2 the field strengths E in the second region rose from 5 MV/cm to 11 MV/cm. The relation j’ = ji exp pE/RT
(9)
yielded the exchange current density of ionic conduction log( jh/A cms2) = - 10.8 ( + 0.2) and the activation dipole p = 42 PA s m/mol with a 95% confidence level of +_21 PA s m/mol. From the activation dipole p = ar.zFa the jump
(10) distance
is estimated
at a = 0.44( A 0.22) nm assuming
a transfer
coeffi-
113
cient a: = 0.5 and an effective charge 1z ) = 2 of the conducting ions. The jump distance is close to the distance of nearest sites of Cd or S in the CdS lattice. The ion conductivity in the third region is much larger than in the second region. For current densities between 30 PA/cm* and 1 mA/cm* the field strength increased from about 1.7 MV/cm to about 2.7 MV/cm. One finds log(ji/A cm-*) = - 6.6( + 0.2) and p = 76( f 53) PA s m/mol, or a = 0.79( kO.55) nm. Thus, the increase of the ion conductivity is mainly due to the much larger exchange current density resulting from a higher concentration of mobile ions, while the increase of the mean jump distance is not significant. In the third region the electronic current for the oxidation of sulphide ions to polysulpbide shown in Fig. 7 rises to a potential-independent level, while the Fermi level is closer to the valence band than to the conduction band. The transition between the second and third regions occurs at electrode potentials E, = 0.4( + 0.2) V at which the Fermi level is in the middle of the band gap with a width [7] of 2.45( +O.OS) eV. The flat band potential is about E, = -0.95( kO.2) V [8]. At high band bending the following mechanism becomes possible: electrons are transferred to holes in the valence band or to empty (positively charged) surface states at energies close to the valence band. New empty states in the valence band or at the surface can be created only by excitation of the electrons to the conduction band, this step being rate determining. Electrons in the conduction band flow towards the metal easily. According to Fig. 10 the current efficiency for electron transfer decreases with the ionic current density. At the higher ionic current density the interfacial potential difference becomes more positive, i.e. the positive charge in surface states increases. Simultaneously with the increase of the electronic current efficiency the current efficiency for film growth at constant current efficiency for cadmium ion dissolution decreases. This effect can be explained by the presence of sulphide surface states. The rate constant for sulphide ion transfer is decreased by the weaker binding of the sulphide ions at the outer surface of the CdS film due to the tendency to form surface states with an effective positive charge. Otherwise, there were no changes of the transfer kinetics of the cadmium ions and the sulphide ions at the outer interface. Regarding the mechanisms of the interfacial ion transfer reactions, the following conclusions can be drawn: the kinetics depend on the concentration of sulphide, but not on pH in the region 9 G pH G 11. Therefore, HS- and not S*- must participate in the transfer of sulphide ions. In the steady state, electrochemical equilibrium is established between the sulphide ions in the electrolyte and in CdS, because at constant film thickness the current of sulphide ions is zero. The steady state current density is due to dissolution of cadmium ions. Cadmium ions dissolve, although the electrolyte is supersaturated and CdS powder (or a porous film [2]) is eventually deposited. An analogous formation of a secondary layer is often observed with passivating oxide films. Since the interfacial equilibrium potential difference of sulphide ion exchange becomes more negative with the concentration of HS- in the electrolyte, one
114
expects the steady state current density to decrease according to the effective transfer coefficient y. The observed increase of the rate with the sulphide concentration must be due to a positive reaction order r of cadmium ion dissolution with respect to HS-. In analogy to the theory developed for oxide electrodes [9,10] one finds for the steady state a {In j’(Cd*‘)/a
ln a(HS},,
=
r -
y
(11)
During film growth at constant rate the interfacial potential difference remains constant with time. If the sulphide ion current density is much larger than the respective exchange current density, the ratio of the logarithms of the two parallel ion transfer rates changes as the ratio of the effective transfer coefficients. One obtains { 3 ln j(Cd*‘)/a
ln j(HS-)}
o(HS-) = P/Y
(12)
where /3 is the transfer coefficient of sulphide ion transfer. Under the same condition, the anodic rate of sulphide incorporation with reaction order y with respect to HS- depends on the activity of HS- at constant rate of cadmium ion dissolution as {a In j(SH-)/a
In u(SH-)}~(~Z+)
=y -
/3r/y
(13)
Since, from Fig. 8, /3/y = 1, one finds with eqn. (13) y = r. Figure 3 yields r - y = 0.65( f 0.06). A true transfer coefficient being a positive quantity one concludes r > 0.65, and probably r =y = 1 yielding y = p = 0.35. Thus, the most probable mechanism for the cadmium ion transfer is 2(Cd2+) +3 (SH-)
+ ,(CdSH+)
(14)
and for the sulfide ion transfer 3(SH-)
+
2(S2-)
+dH+)
(15)
assigning the numbers 1, 2, and 3 to the three phases Cd, CdS and electrolyte, respectively. The extrapolation of j(SH-) to the steady state current density j,,(Cd*+) yields the exchange current density j,(SH-). The expected theoretical dependence In j,(SH-)
= In j,$(SH-)
+ (1 - /?) In a(SH-)
(16)
is verified by the values calculated from Figs. 3 and 8 from the experiments with 0.01 < c(NaHS)/M < 1 for p = 0.35 with the standard exchange current density j;(SH-) = 10-79(*0.3) A ,.m‘. The exchange current density obtained for c(NaHS) = 10d3 M is about a factor of 10 smaller than expected from the values at the higher concentrations of sulphide. The potential difference in the Hehnholtz layer at the interface between CdS and the electrolyte is determined by the ion transfer kinetics and not by the electric field in the space charge. The changes of the interfacial potential difference require that charges are stored in the surface, e.g. by electrosorption of sulphide ions [8].
115
The large electronic current efficiency at potentials above E, = 1.3 V in dilute sulphide solutions can be attributed to surface states confined to a rather narrow energy region about a few tenths of an eV above the valence band. These surface states are obviously destroyed by adsorption of sulphide, since the effect disappeared at high sulphide concentrations in the electrolyte. In the fourth region the band bending is so high that interband tunnelling can occur [2] explaining the high electronic current efficiency of about 72%. The remaining current is carried by cadmium ions. However, no sulphide ions are transferred to the sulphide film, apparently because these ions are not bound to the surface. ACKNOWLEDGEMENT
M.I.S. acknowledges
a grant from the Alexander
von Humboldt
Foundation.
REFERENCES 1 A.J. Bard, R. Parsons and J. Jordan (Eds.), Standard Potentials in Aqueous Solutions, Marcel Dekker, New York, 1985. 2 L.M. Peter, Electrochim. Acta, 23 (1978) 1073. 3 A. Damjanovic, L.-S. Yeh and P.G. Hudson, J. Appl. Electrochem., 12 (1982) 153, 343. 4 V.I. Birss and L.E. Kee, J. Electrochem. Sot., 133 (1986) 2097. 5 K.E. Heusler, Ber. Bunsenges. Phys. Chem., 72 (1968) 1197; Electrochim. Acta, 28 (1983) 439; Corros. Sci., 29 (1989). 6 B. Segall and D.T.F. Marple in M. Aven and J.S. Prenes (Eds.), Physical Chemistry of II-VI Compounds, North Holland, Amsterdam, 1967, pp. 319ff. 7 R. Memming in B.E. Conway and J.O’M. Bockris (Eds.), Comprehensive Treatise of Electrochemistry, Vol. 7, Plenum Press, New York, 1983, ch 8, pp. 529ff. 8 D. Meissner, Dissertation, University of Hamburg, 1986. 9 K.D. Allard and K.E. Heusler, J. Electroanal. Chem., 77 (1977) 35. 10 K.E. Heusler, Electrochim. Acta, 28 (1983) 439.
J. Electrounal. Chem., 301 (1991) 101-115 Elsevier Sequoia S.A., Lausanne
Transfer of ions and electrons at anodic cadmium sulphide films M. Krebs I, M.I. Sosa 2 and K.E. Heusler Abteilung Korrosion und Korrosionsschutz, Institut ftir Metallkunde und Metaliphysik, Technische Uniuersittit Clawthai, Agricolasir. 2, W-3392 Clausthai-Z. (FRG) (Received 9 October 1990)
AbSbWt Steady state polarization curves of cadmium in NaHS solutions exhibit a maximum current density at low overpotentials with respect to the equilibrium potential of cadmium sulphide formation, a potential region of about 1 V with nearly potential independent current density and a steep rise of the current density at high overpotentials. The current densities increase with the sulphide concentration and are nearly independent of the pH value between pH 9 and pH 11. During anodic polarization of activated cadmium at constant current density, a CdS film is nucleated at small overpotentials. The film becomes compact when it is a few monolayers thick. The compact film grows by high field conduction. The current efficiencies for film growth and dissolution of cadmium ions are about 20% and SO%, respectively. The current efficiency for film growth drops to about 3% beyond a characteristic electrode potential and the current efficiency for oxidation of sulphide to polysulphide grows accordingly, while the current efficiency for dissolution of cadmium ions remains unaffected. The rate determining steps of the ion transfer reactions at the interface between the sulphide and the electrolyte are the dissolution of CdSH+ formed by reaction of cadmium ions from CdS and HS- from the electrolyte, and the transfer of HS- ions yielding sulphide ions to build up the CdS film and hydrogen ions in the electrolyte. The correlation between sulphide ion transfer during film growth and electron transfer during sulphide oxidation is explained by the semiconductor properties of the film together with sulphide surface states.
INTRODUCTION
Cadmium sulphide layers can be grown on cadmium in neutral and basic aqueous sulphide solutions in which the equilibrium potential of formation of the sulphide is negative to the respective formation potential of cadmium oxide or cadmium hydroxide. The standard potentials of the respective reactions are [l]:
i Present address: Varta AG, Ellwangen, FRG. ’ Present address: Instituto de Investigaciones Fisicoquimicas Argentina. 0022-0728/91/$03.50
0 1991 - Elsevier Sequoia S.A.
Te&icas y Aplicadas (INIFIA),
La Plata,
_
102
CdS + 2 e-= Cd + S2-
ET = -1.225 V
(1)
E; = -0.824
(2)
and Cd(OH),
+ 2 e-=
Cd + 2 OH-
V
The hydroxide is more stable in water than the oxide with CdO+2e-=Cd+2OH-
E; = -0.183 V
(3)
From the dissociation constants of hydrogen sulphide in water H,S = H++ HS-
K, = 9.1 x 1O-8 M
(4)
and HS-=
H++ S*-
K 2 = 12* x lo-l2
the equilibrium potential Ef = ET + (RT/2F)
M
(9
Ee of formation of CdS becomes
ln{ 1 + (h/K,)
+ ( h2/K,K2)}/a
(6)
where h is the activity of hydrogen ions and a the sum of the activities of S2-, HS-, and H,S. Thus, in aqueous sulphide solutions the equilibrium potential of formation of cadmium sulphide is negative to the equilibrium potential of formation of Cd(OH), even at very small activities of sulphide. Sulphide ions S*- are oxidized to polysulphide ions S,“-. The equilibrium potentials for x >, 2 are only slightly more positive than for Si-
+ 2 e-=
2 S2-
Ez = -0.483
V
(7)
Little is known about the acid-base equilibria of the polysulphides. According to cyclic voltammetric measurements, one or two monolayers of CdS were formed close to the equilibrium potential of formation [2]. In a potential region of almost 1.2 V the film grew at constant current density while the potential increased linearly with time. This behaviour is expected for rate determining potential-independent ionic conduction in high electric fields. The current density began to increase steeply at an overpotential of about 1.4 V vs. the equilibrium potential of formation. It was concluded that a porous film was formed. The film was reduced at potentials negative to the equilibrium potential of formation. A later study of film growth in the region of high field ion conduction arrived at the conclusion that interfacial charge transfer of sulphide ions was rate determining 131. Three current peaks were observed in voltammograms close to, but positive of the equilibrium potential of formation [4]. There was no underpotential deposition of adsorbed sulphur. The first peak was interpreted as being due to the deposition of half a monolayer of S, the second to the completion of the full monolayer, and the third to the formation of one further monolayer of CdS. In all the earlier investigations of the anodic sulphidation of cadmium, a 100% current efficiency for film growth was assumed. However, theory predicts that, in principle, the current efficiency for film growth is always less than 100% due to the
103
irreversible dissolutiop. of cations, even if the rate of electron transfer reactions is zero [5]. The kinetics oi g : ,+th and dissolution of oxide films on several metals like iron, titanium and aluminium were observed as expected from the theory. The experiments reported below yield low current efficiencies for the formation of cadmium sulphide on cadmium, both because of the dissolution of cadmium ions from the film into the electrolyte and because of the oxidation of sulphide to polysulphide by electron transfer. The relative importance of the parallel reactions depends, on e.g. the electrode potential and the composition of the electrolyte. EXPERIMENTAL
A rotating ring-disc electrode with a mechanically polished 0.5 cm’ cadmium disc and a gold ring was used. The collection efficiency was N, = 0.36. The whole apparatus was enclosed by a black box, shielding the working electrode from any inadvertent light. The electrolyte solutions, containing 1 M or 0.5 M sodium carbonate + bicarbonate buffer with pH values between pH 7 and pH 13 and sodium sulphide at different concentrations, were prepared with deoxygenated water and kept under nitrogen in order to prevent the formation of polysulphide. After the preparation of the electrolyte, oxygen cannot be removed, because any oxygen is consumed to oxidize sulphide to polysulphide. Cadmium sulphide films were grown and dissolved at 25 o C under galvanostatic or potentiostatic conditions. Electrode potentials were measured vs. HgS(red)/Hg in 1 M NaHCO, + 0.1 M NaHS, pH 9, with E, = -0.74V vs. the standard hydrogen electrode, or vs. Ag,S/Ag in 0.5 M NaHCO, + 0.1 M NaHS, pH 9, with E, = -0.575V. Capacities were usually determined from the voltage transients during 2 rnA/cm’ current pulses lasting 1 ms after an interruption of the polarization for 0.3 s. A computer was programmed to change the experimental parameters and to take the data at predetermined tunes. RESULTS
Diffraction patterns of cadmium anodized in 0.1 M NaHS, pH 9, were obtained by transmission electron microscopy. Cadmium was etched away from the back side until holes appeared in the thin Cd sheet. Three diffuse rings characteristic of hexagonal CdS were observed apart from two rings of Cd and an unidentified ring. A depth profile obtained by Auger analysis is shown in Fig. 1. Both the signals for cadmium and sulphur remained independent of the sputter time for almost 1 min. The oxygen signal was always very small. One concludes that the film consisted of pure CdS not contaminated by oxide. Steady state current densities were established at constant electrode potentials after times up to several days. The long times were necessary for small steady state current densities. The steady state polarization curves shown in Fig. 2 exhibited a peak of the current density at small positive overpotentials vs. the equilibrium potential of CdS formation. The height of the peaks grew with the concentration of
60 \o t 4
tlmin
Fig. 1. Relative with Ar+.
amplitudes
A of Auger lines of cadmium,
sulphur,
and oxygen
vs. time r of sputtering
NaHS. The current densities were nearly potential independent in a range of several tenths of a volt. This range shrank with increasing sulphide concentration. The potential independent current densities grew with the sulphide concentration as shown in Fig. 3. The apparent reaction order {a In j,/a In c(NaHS)}, = 0.64( f 0.6) was obtained from measurements at different constant electrode potentials between E, = -0.54 V and E, = 0.26 V. At constant sulphide concentration the steady state current densities were nearly independent of the pH value from pH 8 to pH 11. At higher pH values the steady state current densities decreased with PH. In order to reduce any preformed films before galvanostatic anodization, the electrode was kept at an overpotential 77= -0.3 V vs. the equilibrium potential of formation of CdS. The capacitance in this initial state was around 50 pF/cm2. Upon an interruption of the circuit the potential rose towards positive overpotentials, while the capacities decreased at rates increasing with the concentration of residual polysulphide. The rate of increase of the reciprocal capacitance became constant after about 1000 s. With the relative dielectric constant cr = 8.6 [6] for CdS, the film thickness after 3000 s was typically estimated at 1.7 nm assuming a double layer capacitance Co = 50 pF/cm2 in series with the film capacitance. Film growth at constant anodic current densities was started 20 s after interruption of the cathodic prepolarization. At this time, overpotentials 0.07 < n/V < 0.12 were established. The capacitances were still in the range 34 < C/(pF cmw2) < 59,
105
25
20
Y
E
15
2 I . ._
10
5
J/
0
__4
I
-0.5
-1
0
0.5
1
EHlV Fig. 2. Steady state current densities j as a function of the electrode potential E, vs. the standard hydrogen electrode for cadmium in 1 M sodium carbonate+ bicarbonate buffer, pH 9, with (A) 10K4 M NaHS, (0) 10m3 M NaHS, (A) 10s2 M NaHS, (0) 10-t M NaHS, and (0) 1 M NaHS, at 25°C.
1
I
I -4
-3
-2
-1
Log (c/M) Fig. 3. Steady state current density j at E u = 0.26 V vs. the standard hydrogen electrode as a function the NaHS concentration c in 1 M sodium carbonate + bicarbonate buffer, pH 9, at 25 o C.
of
106
-0.6
%5
D ImCcrnm2
1.0
1.5
Fig. 4. Electrode potential E, vs. the standard hydrogen electrode as a function of charge Q for cadmium in 0.5 M sodium carbonate+bicarbonate buffer, pH 12, with c = 0.01 M NaHS at 25O C for different anodic current densities.
indicating that a film did not yet grow. The potential transients after applying an anodic current density exhibited four characteristic regions. The first two regions are shown in Fig. 4. The potential first started to grow at an increasing rate. In the second region the rate became constant, as indicated by the linear dependence of the potential on time. Defining the end of the first region by the intercept between the tangent to the steepest potential rise in the first region and the linear potential rise in the second region, one finds that the first region ends at 71- 0.35 V. The charges in the first region grew with the applied current density from 0.07 mC/cm* at 5 PA/cm* to 0.22 mC/cm* at 40 PA/cm* and 0.82 PC/cm* at 400 PA/cm*. There was not sufficient time for capacitance measurements in the first region. As shown in Fig. 5, the reciprocal capacitance C-’ was a linear function of the charge Q. The reciprocal capacitance for Q -+ 0 yielded estimates of the film thickness at the beginning of the galvanostatic experiment. The initial reciprocal capacitances thus determined grew with decreasing current density and with time in the same manner as described above for j = 0. The current efficiency L=
(aQ/ac-')(nFc/V)
(8)
for film growth was calculated from the derivative aQ/aC-’ of the charge with respect to the reciprocal capacitance, and with the charge number n = 2, the
107
0.24
“E
u 0.18
h
Y
\
7
u
0.12
0.06
0
2
4
6
8
10
PI mC cK2
Fig. 5. Reciprocal capacitance C- ’ vs. charge Q in the second region for cadmium in 0.5 M sodium carbonate+ bicarbonate buffer, pH 12, with c = 0.01 M NaHS at 25O C for an anodic current density j = 12 pA/cm2.
Faraday constant F, the dielectric constant e = ~(6~)and the molar volume V= 29.97 cm3/mol of CdS. The potential independent current efficiencies in the second region were around L c- 0.2 for sulphide concentrations between 0.01 and 1 M at 9 < pH < 11. The current efficiencies dropped at smaller sulphide concentrations and larger pH values. The transition from the second region to the third region occurred at potentials E, = 0.4( f. 0.2) or over-potentials q = lS( L-0.2) V. The same transition potentials were obtained from intercepts of the linear dependences of the electrode potential on the time or on the reciprocal capacitance. Figure 6 shows that in the third region the potential, like the reciprocal capacitance, rose at a lower rate than in the second region. The electronic current densities of the oxidation of sulphide to polysulphide were determined from the limiting currents of polysulphide reduction at the ring electrode. Sulphide was oxidized in the first region, but in the second region the respective current efficiencies were usually very small for total current densities exceeding a few r_lA/cm2, as shown in Fig. 7. As mentioned above, the current efficiencies for film growth were also rather small. Most of the current density was used for dissolution of cadmium ions. They precipitated quickly close to the cadmium electrode but also within the electrolyte by formation of CdS powder. A yellow deposit adhering loosely to the electrode became visible after prolonged
108
> I W
200
400
800
600
101 10
t/S
Fig. 6. Electrode potential EH vs. the standard hydrogen electrode as a function of time r for cadmium in 0.5 M sodium carbonate+ bicarbonate buffer, pH 9. with c = 0.1 M NaHS at 25 o C for an anodic current density j = 12 aA/cm2.
1.0
Cd2’
0.8
o---o--o \
o--o--o---D-
/
‘D /
\ \
O,/“\
0.6
J
/ 0
0.L
0.2
0.0 -0.5
0
0.5
1.0
1.5 E,.,tV
2.0
2.5
3.0
Fig. 7. Current efficiencies L for anodic transfer of sulphide ions (0) resulting in film growth, cadmium ions (0) leading to precipitation of CdS in the bulk of the electrolyte, and of electrons resulting in oxidation of sulphide to polysulphide during anodic polarization at j = 382 PA/cm* cadmium in 0.5 M sodium carbonate+ bicarbonate buffer, pH 10, with c = 10e3 M NaHS at 25 o C.
of (A)
of
109
2.4
N
k 1.8 4
3 D
.Y ? 1.2
0.6
-0,4
02
log ljSlpA
0.8
cm21
I (bl
2,4
Oh
-0,4
0,2
0.8 log ( j,
IpA
1.4
cme2)
Fig. 8. Double logarithmic plot of the current density jcd of cadmium ion transfer vs. the current density j, of sulphide ion transfer during the formation of cadmium sulphide fiis on cadmium in 0.5 M sodium carbonate + bicarbonate buffer, pH 10, at 25 o C with c = (a) 10K3 M NaHS ( 0), lo-* M NaHS (0). (b) 10-l M NaHS (o), and 1 M NaHS (+).
110
electrolysis. Only at pH values G 7 did the life-time of the cadmium ions exceed the transfer time to the ring electrode, and cadmium could be deposited there. Figure 8 shows for the second region a double logarithmic plot of the cadmium ion current density vs. the sulphide ion current density during film growth at different total current densities. The slope was {a In j(Cd’+)/a In j(S2-)}c(Nans) = 1 both for 1 M and 0.1 M NaHS, but decreased to 0.87 for 0.01 M and to 0.72 for 1O-3 M NaHS. There was no systematic dependence of j(S*-) on the NaHS concentration at constant j(Cd2’) for c(NaHS) 2 0.01 M, but at smaller sulphide concentrations j(S*-) decreased with c(NaHS), in particular at low current densities. The current efficiency for film growth decreased accordingly. The slopes {a In in the third region were not significantly different j(Cd2’)/a ln j(S’-)J,,,,ns, from those in the second region. According to Fig. 7, in the third region at potentials E, > 0.3 V, the current efficiency for film growth dropped to values between 1.5% and 5% and there was an equivalent increase of the current efficiency for sulphide oxidation, but the current efficiency for dissolution of cadmium ions did not change much. At high concentrations of sulphide in the electrolyte the current efficiencies remained independent of the overpotential up to 115: 3.5 V. The electronic current density j, grew with the total current density j according to a In j&3 In j = 0.71, as shown in Fig. 9. If the concentration of sulphide in the electrolyte was low, high electronic current densities of sulphide oxidation flowed in a region at potentials above E, > 1.2 V or overpotentials 1 > 2.3 V. There were one or two maxima of the electronic current corresponding to one or, as in Fig. 10, two arrests in the time dependence of the voltage at constant current density. At sufficiently positive potentials the rate of potential change and all the current efficiencies returned to the values characteristic
-G -
-5
-4
logij/Acm-21
Fig. 9. Double logarithmic plot of the electronic current density j, of sulphide oxidation vs. the total current density j during the growth of cadmium sulphide films in the third (0) and fourth (0) regions on cadmium in 0.5 M sodium carbonate+ bicarbonate buffer, pH 10, with 10V3 M NaHS, at 25O C.
111
2
1 > lJ.f
0
-1 5w
0
low
tls
Fig. 10. Electrode potential E, vs.the standard hydrogen electrode as a function of time t for cadmium in 0.5 M sodium carbonate+ bicarbonate buffer, pH 10, with c = 10W3 M NaHS at 25 o C for an anodic current density j = 400 pA/cn?.
3.0
;::c:rf
2.L
3
2
P 0
/
I> .
0
,”
0
0
0 0.6 -1 0 0
50
100
150
Q/mC cmm2
Fig. 11. Electrode potential E, vs.the standard hydrogen electrode and reciprocal capacitance C-’ as a function of the total charge Q during anodic polarization with j = 40 PA/cm2 of cadmium in 0.5 M sodium carbonate + bicarbonate buffer, pH 10, with 0.01 M NaHS, at 25 o C.
112
of the third region. The ratio of the two ionic currents was not affected by the increase of the electronic current, within the limits of experimental accuracy. According to Fig. 11, both the electrode potential and the reciprocal capacitance decreased in the fourth region after having passed a maximum. Film growth stopped completely at a potential of E, = 3.0 V or an overpotential n = 4.2 V when the thickness was about 20 nm. The decrease of both the electrode potential and the reciprocal capacitance indicates a slow thinning of the film. The nearly steady state potentials changed with the logarithm of total current density according to a Tafel slope of about 1.3 V/decade. The current efficiency for sulphide oxidation was about 72% independent of the applied current density as shown in Fig. 9. The remaining part of the current must be due to cadmium ion dissolution. DISCUSSION
The formation kinetics of cadmium sulphide at small positive overpotentials in the first region corresponds qualitatively to nucleation and lateral growth until the film becomes compact and direct contact between the metal and the electrolyte is interrupted. The charges in the first region were equivalent to a few tenths to 3 or 4 monolayers of CdS, if a charge Q, = 0.23 mC/cm2 was assumed [2,4] for one monolayer. It was not possible to subdivide the first region into several stages. A substantial part of film growth in the first region was due to the reduction of polysulphide which cannot be excluded completely from the electrolyte. The relative contribution to film growth of polysulphide reduction occurring at potentials negative to EHss = -0.3 V becomes larger at smaller anodic current densities. Therefore, it is not surprising that the charges in the first region increased with the applied current density. As soon as the film is compact at a film thickness of a few monolayers, polysulphide is not reduced any more. During growth of the compact film, cadmium ions are transferred from the metal into the film at the inner Cd/CdS interface and sulphide ions are transferred from the electrolyte into the film at the outer CdS/electrolyte interface. Within the film there is ion transport in high electric fields. At any constant rate of film growth the mean field was estimated from the dependence of the electrode potential on film thickness derived from capacitance measurements. For current densities between 4 and 400 pAA/cm2 the field strengths E in the second region rose from 5 MV/cm to 11 MV/cm. The relation j’ = ji exp pE/RT
(9)
yielded the exchange current density of ionic conduction log( jh/A cms2) = - 10.8 ( + 0.2) and the activation dipole p = 42 PA s m/mol with a 95% confidence level of +_21 PA s m/mol. From the activation dipole p = ar.zFa the jump
(10) distance
is estimated
at a = 0.44( A 0.22) nm assuming
a transfer
coeffi-
113
cient a: = 0.5 and an effective charge 1z ) = 2 of the conducting ions. The jump distance is close to the distance of nearest sites of Cd or S in the CdS lattice. The ion conductivity in the third region is much larger than in the second region. For current densities between 30 PA/cm* and 1 mA/cm* the field strength increased from about 1.7 MV/cm to about 2.7 MV/cm. One finds log(ji/A cm-*) = - 6.6( + 0.2) and p = 76( f 53) PA s m/mol, or a = 0.79( kO.55) nm. Thus, the increase of the ion conductivity is mainly due to the much larger exchange current density resulting from a higher concentration of mobile ions, while the increase of the mean jump distance is not significant. In the third region the electronic current for the oxidation of sulphide ions to polysulpbide shown in Fig. 7 rises to a potential-independent level, while the Fermi level is closer to the valence band than to the conduction band. The transition between the second and third regions occurs at electrode potentials E, = 0.4( + 0.2) V at which the Fermi level is in the middle of the band gap with a width [7] of 2.45( +O.OS) eV. The flat band potential is about E, = -0.95( kO.2) V [8]. At high band bending the following mechanism becomes possible: electrons are transferred to holes in the valence band or to empty (positively charged) surface states at energies close to the valence band. New empty states in the valence band or at the surface can be created only by excitation of the electrons to the conduction band, this step being rate determining. Electrons in the conduction band flow towards the metal easily. According to Fig. 10 the current efficiency for electron transfer decreases with the ionic current density. At the higher ionic current density the interfacial potential difference becomes more positive, i.e. the positive charge in surface states increases. Simultaneously with the increase of the electronic current efficiency the current efficiency for film growth at constant current efficiency for cadmium ion dissolution decreases. This effect can be explained by the presence of sulphide surface states. The rate constant for sulphide ion transfer is decreased by the weaker binding of the sulphide ions at the outer surface of the CdS film due to the tendency to form surface states with an effective positive charge. Otherwise, there were no changes of the transfer kinetics of the cadmium ions and the sulphide ions at the outer interface. Regarding the mechanisms of the interfacial ion transfer reactions, the following conclusions can be drawn: the kinetics depend on the concentration of sulphide, but not on pH in the region 9 G pH G 11. Therefore, HS- and not S*- must participate in the transfer of sulphide ions. In the steady state, electrochemical equilibrium is established between the sulphide ions in the electrolyte and in CdS, because at constant film thickness the current of sulphide ions is zero. The steady state current density is due to dissolution of cadmium ions. Cadmium ions dissolve, although the electrolyte is supersaturated and CdS powder (or a porous film [2]) is eventually deposited. An analogous formation of a secondary layer is often observed with passivating oxide films. Since the interfacial equilibrium potential difference of sulphide ion exchange becomes more negative with the concentration of HS- in the electrolyte, one
114
expects the steady state current density to decrease according to the effective transfer coefficient y. The observed increase of the rate with the sulphide concentration must be due to a positive reaction order r of cadmium ion dissolution with respect to HS-. In analogy to the theory developed for oxide electrodes [9,10] one finds for the steady state a {In j’(Cd*‘)/a
ln a(HS},,
=
r -
y
(11)
During film growth at constant rate the interfacial potential difference remains constant with time. If the sulphide ion current density is much larger than the respective exchange current density, the ratio of the logarithms of the two parallel ion transfer rates changes as the ratio of the effective transfer coefficients. One obtains { 3 ln j(Cd*‘)/a
ln j(HS-)}
o(HS-) = P/Y
(12)
where /3 is the transfer coefficient of sulphide ion transfer. Under the same condition, the anodic rate of sulphide incorporation with reaction order y with respect to HS- depends on the activity of HS- at constant rate of cadmium ion dissolution as {a In j(SH-)/a
In u(SH-)}~(~Z+)
=y -
/3r/y
(13)
Since, from Fig. 8, /3/y = 1, one finds with eqn. (13) y = r. Figure 3 yields r - y = 0.65( f 0.06). A true transfer coefficient being a positive quantity one concludes r > 0.65, and probably r =y = 1 yielding y = p = 0.35. Thus, the most probable mechanism for the cadmium ion transfer is 2(Cd2+) +3 (SH-)
+ ,(CdSH+)
(14)
and for the sulfide ion transfer 3(SH-)
+
2(S2-)
+dH+)
(15)
assigning the numbers 1, 2, and 3 to the three phases Cd, CdS and electrolyte, respectively. The extrapolation of j(SH-) to the steady state current density j,,(Cd*+) yields the exchange current density j,(SH-). The expected theoretical dependence In j,(SH-)
= In j,$(SH-)
+ (1 - /?) In a(SH-)
(16)
is verified by the values calculated from Figs. 3 and 8 from the experiments with 0.01 < c(NaHS)/M < 1 for p = 0.35 with the standard exchange current density j;(SH-) = 10-79(*0.3) A ,.m‘. The exchange current density obtained for c(NaHS) = 10d3 M is about a factor of 10 smaller than expected from the values at the higher concentrations of sulphide. The potential difference in the Hehnholtz layer at the interface between CdS and the electrolyte is determined by the ion transfer kinetics and not by the electric field in the space charge. The changes of the interfacial potential difference require that charges are stored in the surface, e.g. by electrosorption of sulphide ions [8].
115
The large electronic current efficiency at potentials above E, = 1.3 V in dilute sulphide solutions can be attributed to surface states confined to a rather narrow energy region about a few tenths of an eV above the valence band. These surface states are obviously destroyed by adsorption of sulphide, since the effect disappeared at high sulphide concentrations in the electrolyte. In the fourth region the band bending is so high that interband tunnelling can occur [2] explaining the high electronic current efficiency of about 72%. The remaining current is carried by cadmium ions. However, no sulphide ions are transferred to the sulphide film, apparently because these ions are not bound to the surface. ACKNOWLEDGEMENT
M.I.S. acknowledges
a grant from the Alexander
von Humboldt
Foundation.
REFERENCES 1 A.J. Bard, R. Parsons and J. Jordan (Eds.), Standard Potentials in Aqueous Solutions, Marcel Dekker, New York, 1985. 2 L.M. Peter, Electrochim. Acta, 23 (1978) 1073. 3 A. Damjanovic, L.-S. Yeh and P.G. Hudson, J. Appl. Electrochem., 12 (1982) 153, 343. 4 V.I. Birss and L.E. Kee, J. Electrochem. Sot., 133 (1986) 2097. 5 K.E. Heusler, Ber. Bunsenges. Phys. Chem., 72 (1968) 1197; Electrochim. Acta, 28 (1983) 439; Corros. Sci., 29 (1989). 6 B. Segall and D.T.F. Marple in M. Aven and J.S. Prenes (Eds.), Physical Chemistry of II-VI Compounds, North Holland, Amsterdam, 1967, pp. 319ff. 7 R. Memming in B.E. Conway and J.O’M. Bockris (Eds.), Comprehensive Treatise of Electrochemistry, Vol. 7, Plenum Press, New York, 1983, ch 8, pp. 529ff. 8 D. Meissner, Dissertation, University of Hamburg, 1986. 9 K.D. Allard and K.E. Heusler, J. Electroanal. Chem., 77 (1977) 35. 10 K.E. Heusler, Electrochim. Acta, 28 (1983) 439.