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Influence of molybdenum on the transpassivity of a Fe + 12%Cr alloy in H2SO4 solutions
d O U t ~ OF
ELSEVIER
Journal of Electroanalytical Chemistry 430 (1997) 169-178
Influence of molybdenum on the transpassivity of a Fe + 12%Cr alloy in H2SO 4 solutions M. Bojinov a.,, I. Betova a, R. Raicheff b a Central Laboratory. of Electrochemical Power Sources, Bulgarian Academy of Sciences, ! 113 Sofia, Bulgaria b Department of Electrochemical Engineering and Corrosion Protection, Unil,ersityof Chemical Technology and Metallurgy, ! 756 Sofia, Bulgaria Received 7 November 1996; revised 26 February 1997; accepted 4 March 1997
Abstract
The influence of Mo addition (5-10 wt.%) on the transpassive dissolution, secondary passivation and oxygen evolution on a Fe + 12%Cr alloy in IM H2SO4 is studied by voltammetric and AC impedance measurements within the frame of an investigation of the impact of Mo on the stability of the passive state of ferrous alloys in acidic media. A semi-quantitative model of the processes is proposed, based on the experimental results obtained and model approaches presented in the recent literature. It was found to be consistent with the experimental data and could serve as a first approximation to a generalized model of transpassivity. © 1997 Elsevier Science S.A. Keywords: Transpassive dissolution; Secondary passivation; Surface charge; Iron + chromium alloy; Kinetic model
1. Introduction
Molybdenum additive to stainless steels is known to improve significantly their resistance to localized corrosive attack in media containing aggressive anions such as chloride. In spite of the numerous recent publications on the subject [1-14], there is still no agreement on the mechanism of its action. The two most detailed approaches to the prob!cm are the bipolar passive film model, proposed by Clayton et al. [9-12] and the solute-vacancy interaction model (SVIM) advanced by Macdonald and co-workers [13,14,20] on the basis of the point defect model (PDM) for the growth and breakdown of passive films on metals [15-20]. Within the frame of the first approach, it is assumed that the incorporation of Mo (and to a lesser extent Cr) in the outer part of the passive film as MoO42(respectively CrO42- ) causes the film to behave as an ionic flow rectifier which hampers the chloride ion adsorption and ingress thus suppressing the localized corrosion process. The SVIM, on the other hand, assumes segregation of Mo in the inner part of the passive film as high-valency cations (solutes Mo 6÷) which form 1-1 complexes with cation vacancies reducing both their concentration and
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diffusivity and hence retarding passivity breakdown (within the frames of the PDM, it is shown that an enhanced flow of cation vacancies is the cause of breakdown). Implicitly both models assume that: (i) There is a separation of charges in the barrier sublayer of the passive film since according to Clayton et al. [9-12] injected metal ions (positive carders) are accumulated at the metal lfilm interface and molybdate (chromate) ions (negative charges) at the film lsolution interface, whereas Macdonald et al. [18-20] show that there is an accumulation of injected oxygen vacancies (positive carriers) at the metal lfilm interface and a corresponding accumulation of injected cation vacancies (negative charges) at the filmlsolution interface. (ii) Oxidation of molybdenum (and chromium) to their highest valency state of 6 occurs either by a solid state mechanism at the metal lfilm interface (segregation of high-valency solutes in the barrier layer) or by electrochemical dissolution of the film at its boundary with the electrolyte (transpassive dissolution of Mo and Cr). Syrett et al. [21] have shown that transpassive dissolution proceeds already at potentials slightly higher than the breakdown potential for stainless steels. Thus it is evident that both the formation of surface charges and transpassivity play an important role in the corrosion mechanism and the stability of stainless steels
M. Bojinov et al. / Jounzal of Electroanalytical Chemistry 430 (1997) 169-178
170
and deserve special attention. In the present investigation, we explore the transpassive dissolution, secondary passivation and oxygen evolution on Fe + Cr alloys, emphasizing the impact of Mo additive on the kinetics of the processes. This work could be regarded as a next step in the study of the influence of Mo on the stability of passive state of ferrous alloys initiated recently in our group by modelling the transpassive dissolution and secondary passivation of pure Mo [22,23], as well as the active dissolution of binary Fe + Mo alloys in acidic media [24]. The paper is presented in two parts. The objective of the first one is to study the behavior of a Fe + 12%Cr alloy and the role of Mo additions (5 and 10 wt.%) in it using voltammetric and AC impedance measurements. The work attempts to present a generalized model of the transpassivity, secondary passivation and oxygen evolution on anodic films based on the obtained experimental results and recently published kinetic models. Results on a Fe + 25%Cr alloy and the impact of Mo additions, as well as some reference results on pure Cr, will be presented in the second part of this investigation [25].
influence of nitrogen purging on the results was found during preliminary work). 2.2. Apparatus and procedure Potentiodynamic and potentiostatic current/potential curves, as well as AC impedance spectra, were obtained by a PAR 273/5301 system driven by a PC XT computer via an IEEE 488 interface using the PAR M270 and M378 software. At each potential of measurement, the current vs. time curve was recorded until a steady state current was reached (its variation during an experiment did not exceed 2%). All the potential values were IR-drop corrected. At this steady state the impedance spectra were taken in a frequency range 0.01 to 10 000 Hz at an AC amplitude of 10 mV (rms). Equivalent circuit elements were computed by the Equivalent Circuit program of Boukamp [26].
3. Results 3.1. Polarization curves Fig. I a shows potentiodynamic polarization curves (scan rate, 1 mV s -~) of the Fe + 12%Cr, Fe + 12%Cr + 5%Mo and Fe + 12%Cr + 10%Mo alloys in 1M H2SO4, respectively, in Tafel coordinates. The regions of active dissolution 1, passivation 2, passivity 3, transpassive dissolution 4, secondary passivation 5 and oxygen evolution 6 are clearly defined. In accordance with earlier results [6,7], Mo additive greatly (by one order of magnitude for 5%Mo and about two orders for 10%Mo) reduces the current density both in the active dissolution 1 and the passivation 2 regions, has a small impact on the passivity range 3 and leads to a significant increase in the transpassive disso|ution and oxygen evolution rates. Steady state Tafel polarization curves of the alloys in the transpassive dissolution, secondary passivation and oxygen evolution regions are presented in Fig. I b. A curve for spectroscopically pure Fe in the same medium is presented for comparison. All samples were polarized at 0.55 V until a steady state current was reached (this lasted several hours). Then the polarization curves were measured step-by-step in the positive direction and at each point of measurement the current/time curve was recorded until a new steady state was reached (in the transpassive region, this is achieved far more quickly in comparison to the passive one).
2. Experimental 2.1. Electrodes and electrolyte The composition of the alloys studied which were prepared in the Institute of Metal Science, Bulgarian Academy of Sciences, is shown in Table 1. The samples were shaped in cylindrical form and sealed in PTFE holders with acid resistant epoxy resin in order to expose to the electrolyte a planar area of 0.2 cm 2. Their pretreatment consisted of mechanical polishing on a finer grade emery paper followed by a soft clet.h with alumina as grinding paste, degreasing with methanol and washing with bidistilled water. No cathodic reduction of the natural oxide film produced was performed, since it was found to have little influence on the processes studied in the present paper. A three electrode glass cell was employed, featuring a large area Pt sheet as a counter electrode and a saturated K 2SOn mercury sulfate electrode (SSE, Ess~ = 0.67 V vs. SHE) as a reference. All the potentials in the paper are given vs. this kind of reference electrode. The electrolyte (IM H2SO4) was prepared from analytical grade 97% H2SO4 (Merck) and bidistilled water. All the experiments were carried out at 20 + I°C in naturally aerated solutions (no
Table I Composition of the alloys employed in the present investigation Alloy
Cr (wt.%)
Mo (wt.%)
C (wt.%)
Si (wt.%)
Mn (wt.%)
Fe (wt.%)
Fe + 12%Cr Fe + 12%Cr + 5%Mo Fe .4- 12%Cr + lO%Mo
11.85 12.00 11.90
5.15 9.50
0.015 0.030 0.025
0.15 0.16 0.12
0.14 0.14 0.10
balance balance balance
M. Bojinov et aL / Journal of Electroanalytical Chemist~. 430 (1997) 169-178 J Fe+12%Cr Fe+12%Cr+5%Mo Fe+12%Cr+10%Mo [
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.
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I
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E/V Fig. 1. (a) Linear sweep voltammograms of the Fe + 12%Cr, Fe + 12%Cr + 5 % M o and F e + 12%Cr+ 10%Mo alloys in IM HzSO 4 in the potential range - 1 to + 1.2 V (sweep rate, 1 mV s - i ); (b) steady state polarization curves of pure Fe atilt the Fe + 12%Cr, Fe + 12%Cr+ 5%Mo and F e + 12%Cr+ l O%Mo alloys in the ranges of transpassive dissolution, secondary passivation and oxygen evolution in I M H a SO 4.
The results show that transpassive dissolution and secondary passivation are features due to alloy additives since no such processes are observed for pure Fe. The role of Mo is deafly emphasized on this figure, an addition of 5%Mo to the Fe + 12%Cr alloy causes the transpassive dissolution and secondary passivation current to increase with an order of magnitude. The addition of 10%Mo leads to a further increase, but it is not as pronounced (about three times). The current density of oxygen evolution is increased as well. In the transpassive dissolution region, all three curves pertinent to the alloys have similar Tafel slopes ( ~ 40 mV), then a curvature is observed and finally a current plateau is reached (for the Fe + 12%Cr and Fe + 12%Cr + 5%Mo alloys at ~ 0.8 V, whereas for the Fe + 12%Cr+ 10%Mo alloy at ~ 0.9 V). This current plateau indicates that probably a secondary film is formed which chemically dissolves at its interface with the electrolyte thereby defining a potential independent cmTent. The Tafel slopes for the oxygen evolution reaction are comparable for Fe, Fe + 12%Cr and Fe + 12%Cr + 5%Mo alloys (62 -I- 4 mV) and are smaller than that expected for oxygen evolution on conductive oxides. The s!ope for the
1? 1
Fe + 12%Cr + 10%Mo alloy is greater than the other three slopes ( ~ 150 mV). Summarizing, a strong impact of Mo on the transpassive dissolution and secondary passivation processes is observed. It seems to be more of a quantitative nature for the 5%Mo addition (no alteration of the sht,pe of the polarization curve of Fe + 12%Cr), but some qualitative differences are observed for the 10%Mo addition (less well expressed current plateau and different slope of oxygen evolution reaction).
3.2. AC impedance spectra AC impedance spectra of pure Fe in the potential region covered by the voltammetric curve from Fig. I b are presented in Fig. 2. The spectrum at 0.85 V is qualitatively identical to that published in a series of papers by Gabrielli et al. [27,28]. According to these authors it expresses the passive film growth under high-field conditions and the relaxation of the concentration of mobile Fe 3+ in the fi!~m [27,28]. At higher potentials, the high-frequency semicircle is four~d to be composed of two overlapped capacitive time constants (second spectrum in Fig. 2) and in the oxygen evoh~tion region, two overlapped inductive time constants gradually appear in the spectra as the potential increases (last two spectra in Fig. 2). Thus in this region a multistep process is taking place somewhat analogous to that described by Rerolle and Wiart [29] for the oxygen evolution on lead and lead alloys in H2SO 4. AC impedance spectra for the alloys covering the potential ranges of interest in the present work are shown in Fig. 3 (Fe + 12%Cr), Fig. 4 (Fe + 12%Cr + 5%Mo) and Fig. 5 (Fe + 12%Cr + lC%Mo), respectively. In the transpassive dissolution region, one capacitive and one inductive time constants are observed. In the secondary passivation region, a capacitive behavior at low frequencies is consistent with the growth of a secondary film. As the potential
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i
I
2
Fig. 2. AC impedance spectra of pure Fe in IM H2SO 4 in the region of transpassive dissolution, secondary passivation and oxygen evolution of the alloys employed in the present study. Parameter is frequency in Hz.
M. Bojinov et al. / Journal of Electroanalytical Chemistry 430 (1997) 169-178
172
Fe+12%Cr
M H,2SO4
I 1
Fe+12%Cr+5%Mo
I 1 M H2S04
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2
Fig. 4. AC impedance spectra of a Fe+ 12%Cr+5%Mo alloy in IM H 2 SO 4 in the region of transpassive dissolution, secondary passivation and oxygen evolution, Parameter is frequency in Hz.
Fig. 3, AC impedance spectra ofa Fe+ 12%Cr alloy in IM H2SO 4 in the region of transpassive dissolution, secondary passivation and oxygen evolution, Parameter is frequeacy in Hz.
increases, the inductive time constant almost disappears at 1.0 V and by the same potential the high-frequency semicircle becomes a combination of two overlapping time constants in analogy to Fe (see Fig. 2). They are discemible for the 5%Mo (Fig. 4) and clearly observed for the 10%Mo alloy (Fig. 5). For Fe + 12%Cr and Fe + 12%Cr + 5%Mo alloys, the spectra in the oxygen evolution region comprise two inductive time constants in analogy to Fe (Fig. 2), although they are better distinguished (Figs. 3 and 4). For the 10%Mo alloy, conversely, the capacitive time constant at intermediate frequencies persists to the upper potential limit of the measurements and only one inductive semicircle is observed (Fig. 5). Geaerally, the absolute values of the impedance for the Mo-containing alloys are far smaller than for the Fe + 12%Cr alloy (Figs. 3-5), which is in accordance with the polarization results depicted in Fig. l b and further confirm the impact of Mo on the rate of both transpassive dissolution and secondary passivation. In conclusion, it can be stated that a 5%Mo addition changes only quantitatively the picture observed for Fe + 12%Cr. Several qualitative differences are observed for a lO%Mo addition in the secondary passivation and oxygen evolution ranges.
Fe+12%Cr+10%Mo 1Q~ 11.0
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Fig. 5. AC impedance spectra of a Fe+12%Cr+ 10%Mo alloy in IM H2SO 4 in the region of transpassive dissolution; secondary passivation and oxygc~l evolution. Parameter is frequency in Hz.
M. Bojinov et aL / Jounuff of Electroanalytical Chemist~. 430 (1997) 169-178
For a preliminary treatment of experimental data in the transpassive and secondary passive regions, the equivalent electrical circuit of Fig. 6a was found to be appropriate. In this circuit, C is the high-frequency capacitance of the metallfilmlelectrolyte system, R t is the defect migration resistance, R~ and L~ are elements associated with the inductive loop observed throughout the investigated potential range (the subscripts will be explained in detail in Section 4), Co is the Faradaic pseudocapacitance due to the growth of the secondary oxidation product layer and R a is the electrolyte resistance. These parameters should by no means be regarded as independent electrical elements. Their values characterize the properties of the interface and the rates of the reaction steps involved and are used to derive intermediate information for the system under study. They acquire clear physical meaning only when related to a specific kinetic model. The dependences of these parameters on the potential for the three alloys studied are presented in Fig. 6b-f.
zoo
L sc
l
--- MO~
|
~
~
~%_
I
2-~
+
,~-Haq
H: e-
. n-SC ~regioni
~O 2
insulator p-SC region j . . ~ region
C O d F ()~ h
+ ®
X=0
Fig. 7. (a) Scheme of the processes in the metallfilmlsolution system during transpassivity and secondary passivation; (b) distribution of defect concentration as depending on the distance from the filmlsolution interface.
_=__
100
"~-- 2O tw
I
I
®
m
x=d F
®
200
l-~ V V "
electrolyte + secondary film
Co(O)
I no Mo5%Mo10%Mo I • ,O .e. Rsc
negative surface charge
barrier film bulk
metal
Fe+12%Cr I 1 M H;pSO4
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I ooMooyo,o .oI 5000 2000i
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1
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1
11
010
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'
'
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Fig. 6. (a) Equivalent circuit of the electrode system: C, high-frequency capacitance of the metallfilm[electrolytesystem, R,, resistance of defect migration, R~c,Lsc,elementsassociated to the negativesurface charge at the filmlsolution interface, C0, Faradaic pseudocapacitance, Rn, electrolyte ~esistance; (b) R t vs. potential dependence for the three alloys studied; (¢) R~ vs. potential dependence for the three alloys studied; (d) L~ vs. potential dependence for the three alloys studied; (e) C .s. potential dependence for the three alloys studied; (f) Co vs. potential dependence for the three alloys studied.
They seem to confirm the general picture that emerges from the qualitative analysis of polarization curves and AC impedance spectra. The potential dependences of R t (Fig. 7b) can be directly taken as inversely proportional to the polarization curves from Fig. lb. For the Fe + 12%Cr alloy, Rsc changes slightly in the transpassive dissolution region and increases smoothly in the secondary passivation one (Fig. 6c). For a 5% and 10% Mo addition, a steep decrease of this parameter is observed in the transpassivity range (Fig. 6c). The increase of R~ in the secondary passive range is not as evident for the Mo-containing alloys as it is for Fe + 12%Cr (Fig. 6c). The pseudoinductance Lsc decreases in the transpassivity region, this trend being more pronounced for the Mo-containing alloys (Fig. 6d), and is roughly constant in the secondary passivation range (Fig. 6d). The values of the high-frequency capacitance for the Fe + 12%Cr alloy are fax lower than those for the Mo-containing alloys (Fi~. 6e) which is consistent with the considerably higher transpassive dissolution rate of the latter. The values of the Faradaic pseudocapacitance for the Mo-containing a!loys are about an order of magnitude higher than that for the Fe + 12%Cr alloy implying lower current efficiency for secondary film formation [23]. A more detailed explanation of the potential evolution of the circuit elements will be attempted in the Section 4 on the basis of a kinetic model.
M. Bofinov et al. / Journal of Electroanalytical Chemistry 430 (1997) 169-178
174
Then the balance of fluxes at the interface gives [19]
4. Discussion
4.1. Transpassive dissolution and secondary passivation domains A simplified scheme of the alloy Ifilmlelectrolyte interface during transpassivity is presented in Fig. 7a and the corresponding distribution of defects as depending on the distance from the filmlsolution interface is depicted in Fig. 7b. This scheme is constructed to be consistent either with a bipolar rectifier structure of the passive film as proposed by Claytoi~ et al. [9-12] or the p - i - n tunnel diode structure as suggested by the PDM [19]. The chemistry of the PDM [15-20] is used to describe the inteffaeial reactions of generation and annihilation of vacancies within the frame of the present approach and the concept of independence of the electric field strength on potential and film thickness advanced therein is also adopted. Conversely, the vacancy motion is treated according to the generalized theory of Fromhold which is valid at any value of the field strength [31], instead of using Nernst-Planck equations as proposed by the PDM [15-20] which are applicable in the low-field limit only. There is enough evidence that highfield assisted migration governs the anodic film growth on a range of passive metals [23,27,28,30,32]. The chemistry and physics of the proposed model are summarized briefly below and for a detailed definition of quantities involved we refer to the list of symbols at the end of the paper. At steady state, the continuity equation for the metal[anodic film Ielectrolyte system imposes
JMIF----"JF -- JFIs ffiJ.~ ffi const.
+
s
(2)
In the following presentation, the contributions of both interfaces and the film bulk to the overall impedance will be discussed. • At the metal lfilm interface, oxygen vacancies are generated according to the reaction of formation of a metal position in the barrier layer network [15-20]
Z~tlF = RMIF+ i toCMIF
(R-l)
and metal vacancies are correspondingly consumed
JF = (2 FDo/2 a)[ Co( d r ) - co(0)exp( - dF/a)] X exp[(2 Fa/RT) dPo/dF]
(R-2)
The interfacial rate constants are assumed to be potential dependent in a Tafel manner ki = ki°exp(bi~MIF)
(3)
(6)
where [ 15-20] ~O =
~MIF -I- Ed v + ~bFiS= E( applied potential)
(7)
~bMiF = ( 1 - a) E - Ed F ~FIS = qn dFIs/Se0 and q. is a negative surface charge [23,30.32] accumulated at the filmlsolution interface by the cation vacancies generated mainly by the transpassive dissolution reaction. As for most cases d F >> a, co(O)exp(--dF/a) << co(dv) and
JF = (2FDo/Ea)co( dv)exp{(EFa/RT) X [(1 - or) E + qndFIs/teo]/dF}
(8)
or setting
A - (2FDo/2a)co(dF) and B - (2Fa/RT) j F f A e x p { B [ ( 1 -ot)E+qndFis/eeo]/dF}
(9) (10)
It is postulated that the build up of the surface charge is a slow process, i.e. it cannot follow instantaneously rapid variations in the applied potential [30]. Then the time dependence of the surface charge is treated in analogy to the surface charge approach [30]
dqn/dt=jsW(qn,s- qn)
;'~1)
The steady state value of the surface charge is defined as t~FIS,sCFIs --"
otEe~o/dFis
(12)
Inserting this in Eq. (11) results in the expression
dqn/dt =JsW( t~eeeo/dFIs - qn)
k,
m + V~- -4 M M + 3 e -
(5)
where R~[F = F[blklcM(dF) + ib 3 2k 2] and CMIF is the interfacial capacitance. • In the anodic film with a thickness d F, oxygen vacancy motion is driven by the electric field at the metal lfilm interface according to the generalized transport equation [31 ]
qn.s =
k:
m ~ M M + Vg + + 2 e -
(4)
Postulating that the small sine perturbation does not lead to a significant deviation of the concentration of metal vacancies at the metal[film interface cu(d,,) from its steady state value, the impedance at the metal[film interfaceTeads as
( 1)
where j~ is the steady state current density for a given applied potential. Accordingly, the impedance of the system will be the sum of the impedances of the two interfaces and the film bulk [33] z = ZM F +
JMIF ----F[ k2CM(dF) + -~kl]
(!3)
From Eqs. (10) and (13) under a small amplitude AC perturbation we obtaha [30]:
Aj=j~B[(I-t~)AE+
AqadFis/eeo]/d F
Aqn =jsWeeoaAE/[ dF~s(i a, +jsW)]
(14) (15)
M. Bojinov et al. / Journal of Electroanalytical Chemistry 430 (1997) 169-178
Accordingly, the Faradaic impedance of the film bulk is
Z F,F -~ = A j / A E =jsB[(1-a)
+j,W,~,~oa/(ioJ+j~W)]/d F
(16)
which is equivalent to Z~,~= l / R t + l/(itoLsc+Rsc ) where
Rt-- dF/LB( I - a) Rsc - dF/j~Bot
(18)
Lsc f dF/j~ WBot To derive the total impedance, the high-frequency capacitance of the film C and the Faradaic pseudocapacitance C O have to be added in the appropriate manner ZF= [1/Rt + 1/(icoLsc + Rsc) + ioJC] -~ + l/io~C o (19) The Faradaic pseudocapacitance C o is defined as
CO= A Q / A E - (
zF/Vm)AdF/AAE
(20)
where A is the current efficiency for secondary film formation. • At the filmlsolution interface, oxygen vacancies react with adsorbed water forming an oxygen position in the barrier layer network k3
V2+ + H20 --* Oo + 2H +
Thus subject to the assumption that the small sine perturbatio does not change significantly the concentration of oxygen vacancies at the film[solution interface co(O), the impedance of that interface becomes ZFI~ = RFI~ + i t°CFis
(17)
(R-3)
Accordingly, metal vacancies are produced at the film lsolution interface leading to metal ion abstraction from the film
175
(22)
Consequently, the total impedance of the system can be calculated from F-xls. (2), (5), (17)-(20) and (22). However, as stated above (see Section 3), the impedance response of the system in the transpassive and the secondary passive domain exhibits only two time constants (one capacitive and the other inductive) and a series capacitive feature at low frequencies, which is consistent with the impedance defined by Eqs. (17)-(20) and the electrical circuit depicted in Fig. 64. Thus for the special case under investigation the contribution of the interracial impedances is thought to be negligible. Further confirmation to this suggestion is searched below on the basis of the potential dependences of the circuit parameters. In order to explore further these dependences within the frames of the present model, the film thickness vs. potential relationship is taken from the PDM [18-20] with the assumption that the applied potential is expressed vs. the potential of zero film thickness (E - 0 when d F - 0) [1
(23)
During transpassive dissolution 8 = 6 and X-- 3 d F = (1 - o t - otots/ot,)E/E
(24)
Inserting this in Eq. (18) it follows that R t = (1 - a -
otols/oq)e/[ Ej~B(I - a ) ]
R,c = (l -
k4
M M ~ VM 3- + M]q+
(R-4)
and transpassive dissolutionof the alloying elements from the film proceeds according to [201 ks
M'M, + 4H20 ~ M'O42- + V~7 + 8H + + 3e-
(R-5)
(M'--Cr,Mo) The transpassive dissolution reaction results in an accumulation of cation vacancies near the filmlsolution interface in a layer with a thickness dFis and to a depletion of this layer in chromium and molybdenum positions in the oxide network. The depletion in Cr of the first atomic layers near the film[electrolyte interface during transpassivity was quantitatively confirmed by Kirchheirn_ et al. for a Fe10%Cr alloy [34]. The balance of fluxes at the filmlsolution interface gives
JFls = 3Fk°exp(3F°t°t~.EI RT) + k3co(0) + k4
(21)
It is unlikely that Eq. (R-5) will proceed via a simultaneous three-electron transfer, but to describe the behavior of Fe + 12%Cr alloy, at this stage it was not necessary to propose a detailed reaction sequence for the transpassive dissolution of Cr.
L~: = (1 - a - a o t s / a l ) E / ( E j 2 W B a )
(25)
The numerators of Eq. (25) increase linearly with potential whereas their denominators increase exponentially with the same parameter because so does the stationary current density is-Thus R t, R~c and Lsc all decrease which is found experimentally (Fig. 6b-d). Due to the higher transpassive dissolution current for the Mo-containing alloys, the values of the elements Rt.. Rs¢ and L~ are far smaller for them than for the Fe + 12%Cr alloy, which is consistent with experiment as well (Fig. 6b-d). From Eq. (25) two important characteristics of the system could be derived, namely
oz-- ( R , / P ~ ) / [ I + ( Rt/Rs~)]
(26)
W=LsoL/R,o These two parameters are plotted in Fig. 8 as depending on the oxidation potential. The obtained dependences are consistent with the physical picture given in Fig. 7a. Due to the accumulation of M'O42- at the film[solution interface and the simultaneous depletion of the interface in Cr and Mo [34], the rate of the transpassive dissolution is slowed down. This leads to a
M. Bojinov et al, / Journal of Electroanalytical Chemistry 430 (1997) 169-178
176
Fe+12%Cr I 1 M H2SO4
4.2. Oxygen evolution region
,.. I no Mo 5%Mo 10%Mo I -0~
0.6
As negative charge carriers (cation vacancies) are accumulated near the filmlsolution interface (Fig. 7a), due to the p - i - n junction structure depicted in Fig. 7b [19] the concentration of captured holes at that interface will increase with the transpassive dissolution current of Eq. (R-5). At a certain potential level ( ~ 1.0 V), water will become oxidized by these holes and oxygen evolution will take place according to the generalized equation:
®
0.5 0.4 0.3 0.2 0.1
%=o16o17 o18'o19' i ' .
I
E/V
l no Mo 5%Mo 10%Mo
H 2 0 + 2h + -> 702 + 2H + ]
2O
®
10 "7
o E
5
~8
2 1 0.5 0.2 - , 0,5 0.6
. , t , t , 0.7 0.8 0.9
1
1.1
EIV
Fig. 8. Potential dependences of the polarizability of the filmlsolution interface ot (a) and the capture cross section per positive defect W (b) as deduced from Eq. (16) for the three alloys studied.
The current of the oxygen reaction increases exponentially and so does the steady state current (Fig. lb). In the oxygen evolution region, in addition to the charge transfer loop, three time constants (one capacitive and the two other inductive) gradually appear in the impedance spectra (Figs. 2-5). To explain their nature, the following hypothetical model is proposed. Oxygen evolution is regarded as a two-step reaction, the oxygen anion acting as adsorbed intermediate with a formal coverage 0~, as emphasized by De Wit and Lenderink [33]: k3
H20
---* O ~ d + 2 H + k6
Vo gradual dissipation of the surface charge qn- The conditions for the formation of a secondary film which is believed to consist mainly of ferric oxide-hydroxide are reached [35]. As a consequence, the parameter a characterizing the part of the applied potential consumed at the filmlsolution interface decreases (Fig. 8a). Simultaneously R t and Lsc tend to become constant and R~c increases. This is the trend observed experimentally in the secondary passivation region (Fig. 6b-d). The gradual formation of a secondary film causes the associated current efficiency to grow with potential and to reach a constant value in the secondary passivation region. This results in a decrease of the Faradaic pseudocapacitance C O to a constant value as well (Fig. 60. Similar speculations could explain the potential trend of the capture cross section per charge carrier W (Fig. 8b). This quantity is related to the surface excess of negative carriers by the equation W= (2F/3)-'
(27)
The observed decrease of W (Fig. 8b) is caused by the increase of the surface excess of negative carders fl due to the gradual dissipation of the surface charge and the associated growth of the accumulation layer thickness from a monoiayer at low potentials to several atomic layers at higher ones. In the secondary passivation region, there is no further increase of the thickness of this layer, hence/3 will tend to constant values and so does W (Fig.
8b).
(R'-3)
-, Oo
(R-6)
In addition to their participation in the film formation, the oxygen anions are oxidized by holes at the film lsolution interface forming another intermediate O~ with a coverage 0 2 k7
O~a- + h + --¢ O~
(R-7)
which in turn is oxidized to produce oxygen gas (the recombination of oxygen atoms is taken as a fast process for the sake of simplicity) t¢8
O~ + h + -, I
(R-S)
At this stage, the important assumption of the anodic layer being electronically conductive is made, thus the main part of the applied potential is thought to occur as a drop at the film[solution interface. If film formation, iron dissolution and oxygen evolution are the processes to be taken into account, the charge balance at the film lsolution interface reads as
+k80
(28)
The corresponding material balances of the intermediates are of the form f l d O l / d t = k 3 ( i - 0 i - 02) - ( k 6 + k T ) 0 !
fl d O 2 / d t = k701 - ksO 2
(29)
M. Bojinov et al. / Journal of Electroanalytical Chemistry 430 (1997) 169-178
The steady statt solution is readily obtained setting d Oi/dt =0 0Is = k 3 k 8 / D
(30)
02s = k3k7/J~
D = (k 3 + k 6 + kT)ks + k3k7
The AC impedance solution is a result of the first order Taylor expansion of Eqs. (28) and (29) around a steady state Z~'Il = R t I + F[(~kc + k 7 - k 4 ) d O l / d r + ( k s - k4)dO2/dE ] + itOCFis
(32)
where
+ ( b 7 + bs)k7]O,. ,,
,
(33)
d O t ~ d E = ( XtZ2 - k3X2)/ZD d O 2 / d E = ( X2ZI + k T X I ) / Z o XI -- [ ( b 3 - b 6 ) k 6 -1- ( b 3 - b7)k7]Ols
X2 = [(
- bs)kTO
principle to perform a numerical simulation of the impedance response according to Eqs. (32) and (33) and to obtain values for the rate constants as is frequently done in the literature. However, as at the present stage of the work there is no direct evidence Ibr the formation of intermediates of the oxygen reaction at the alloy electrodes studied, we confine ourselves to this qualitative treatment.
(31)
jFis,.=F[k4(kt+kT)/k3+~k6+2k7]O,s
R[ I = F[ b4k4(k 6 + k 7 ) i k 3 + d / 3 b t k 6
177
s
Z l = i toil + k 3 + k 6 + k 7 Z 2 = it aft + k s Z D = Z t Z2 + k s k7
and CFIs is the interfacial capacitance. F,q. (32) gives the possibility to explain the three time constants present for all the alloys in the oxygen evolution domain. At the beginning of the oxygen evolution region, if the rate of Eq. (R-7) is greater than that of Eq. (R-8), the coverage of the interface with adsorbed divalent oxygen anions Oa2d will decrease with potential and the corresponding coverage with adsorbed monova~ent oxygen intermediates O~ will increase. This trend is tantamount of a combination between a capacitive and an inductive time constant as found experimentally in the spectra in the potential range 0.95 to 1.15 V (Figs. 2-5). At high potentials, due to the faster increase of the rate of Eq. (R-8) with potential, the coverage of adsorbed monovalent oxygen anions begins to decrease as well and the associated time constant becomes inductive as observed in the experimental spectra (Figs. 2-5). Another explanation of such a time constant could be the experimental fact that during oxygen evolution, the dissolutio~ of Fe as Fe 3+ was found to be strongly potential dependent [36]. This could result once again in the formation of an accumulation layer of iron vacancies and it will comribute to the impedance as an inductive feature as in the case treated in Section 4.1. Although it is not the aim of the present paper to present a complete mechanism of the oxygen evolution reaction, the above hypothetical model helps at explaining the experimentally observed features. It is possible in
5. Conclusions An experimental study of the electrochemical behavior of Fe + 12%Cr alloy in H2SO4 solutions is presented, emphasizing the role of Mo additions on the transpassive dissolution, secondary passivation and oxygen evolution reactions. On the basis of the experimental results and model approaches proposed in the literature, a semiquantitative kinetic model of the transpassive dissolution process is advanced. It is established that the model is consistent with the experimental data and could be regarded as a first approximation to a generalized model of the transpassive process. At the present stage of the work, some unclarified points will be outlined and the limitations of the model will be mentioned as a conclusion. • Significant improvement of the presented kinetic scheme is needed, to account quantitatively for the superposition of secondary passivation and oxygen evolution reactions and to evaluate the impact of Mo additive on these processes. • An independent deterrr,lnation of the oxide and secondary film thickness and composition, as well as the current efficier, cy for the transpassive dissolution, secondary film formation and oxygen evolution could help in determining unequivocally the model parameters. Such a study will be attempted in the near future.
6. List of symbols a
A
B
atomic jump distance, cm constant in the high-field migration equation, A cm -2 field coefficient in the high-field equation, V-i cm
Tafel coefficients of the interfacial reactions (i = 1-8), V -i Co(0) concentration of oxygen vacancies at the film lsolution interface, tool cm-s Co(dF) concentration of oxygen vacancies at the metal lfiim interface, mol cm-3 cM(dF) concentration of metal vacancies at the metal [film interface, mol cm -3 high-frequency capacitance of the film, F cm -2 C capacitance of the metallfilm interface, F cm-2 CMIF capacitance of the cation vacancy accumulation CFIs layer,. F c m - 2 Faradaic pseudocapacitance, F cm-2 Co bi
M. Bojinov et al. / Journal of Eiectroanalytical Chemistry. 430 (1997) 169-178
178
dFIs Do E E i
J JMIF
JF
JFis A ki L,~c
thickness of the barrier layer, cm thickness of the metal vacancy accumulation layer, cm diffusivity of oxygen vacancies, cm 2 s- ! applied potential, V electric field strength, V cm-l i ~ g i r . : ~ , unit c ~ n t density, A cm -2 current density at the metallfilm interface, A cm -~ film formation current density, A c m - : current density at the film lsolution interface, A cm-2 steady state current density, A cm -2 rate constants of the interracial reactions (i - 1-8), mol cm -2 s -t inductance due to surface charge relaxation, H cm 2
m
MM
oo qn qn, s Rt
Ra Rsc
Vm W
metal atom in the metal phase metal position in the barrier layer network oxygen position in the barrier layer network negative surface charge at the film[solution interface, C cm -2 steady state surface charge at the film[solution interface, C cm -2 resistance due to migration of defects, fl cm: electrolyte resistance, 1~ cm z resistance due to surface charge relaxation, 12 cm 2 oxygen vacancy in the barrier film network metal vacancy in the barrier film network molar volume of the phase in the barrier film, cm 3 molcapture cross section for a positive defect, cm" C-!
ZMIF
ZF
Z~ls a
a I
8
A ~M[F ~FIS
impedance of the metal lfiim interface, ~ cm z impedance of the anodic film, fl cm2 impedance of the filmlsolution interface, fl cm 2 polarizability of the filmlsolution interface barrier symmetry factor of the transpassive dissolution reaction (Eq. (R-5)) barrier symmetry factor of the oxygen vacancy generation reaction (Eq. (R- 1)) maximum surface excess, mol cm -2 valency of transpassive dissolution dielectric constant of the film current efficiency for secondary film formation local potential drop at the metallfilm interface, V local potential drop at the film lsolution interface, V valency of the cation in the film
gies under contract CH-330 is gratefully acknowledged. The authors are indebted to Professor Tz. Rashev from the Institute of Metal Science, Bulgarian Academy of Sciences for the preparation of the alloy samples.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [ i 1] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33]
Acknowledgements [34]
The f'mancial support of the National Science Fund, Bulgarian Ministry of Science, Education and Technolo-
[35] [36]
R.C. Newman, E.M. Franz, J. Eleetrochem. Soc. 131 (1984) 223. J.N. Wanklyn, Corr. Sci. 21 (1981) 211. K. Hashimoto, K. Asami, K. Teramoto, Corr. Sci. 19 (1979) 3. R. Goetz, D. LandoR, Electrochim. Acta 29 (1984) 667. C. Leygraf, G. Hultquist, L Olefjord, B.-O. Elfstroem, V. Knyazheva, A. Plaskeyev, Y. Kolotyrkin, Corr. Sci. 19 (1979) 343. P. Marcus, I. Olefjord, Corr. Sci. 28 (1988) 589. K. Sugimoto, Y. Sawada, Corr. Sci. 17 (1977) 425. M. Sakashita, N. Sato, Corr. Sci. 17 (1977) 473. A.R. Brooks, C.R. Clayton, K. Doss, Y.C. Lu, J. Electrochem. Soc. 133 (1986) 2459. C.R. Clayton, Y.C. Lu, J. Electrochem. Soc. 133 (1986) 2465. Y.C. Lu, C.R. Clayton, A.R. Brooks, Corr. Sci. 29 (1989) 863. C.R. Clayton, Y.C. Lu, Corr. Sci. 29 (1989) 881. M. Urquidi, D.D. Macdonald, J. Electrochem. Soc. 132 (1985) 555. M. Urquidi, D.D. Macdonald, J. Electrochem. Soc. 136 (1989) 961. C. Chao, L. Lin, D.D. Macdonald, J. Electrochem. Soc. 128 (1981) 1187. L. Lin, C. Chao, D.D. Macdonald, J. Electrochem. Soc. 128 (1981) 1194. C. Chao, L. Lin, D.D. Macdonald, J. Electrochem. Soc. 129 (1982) 1874. D.D. Macdonald, M. Urquidi-Macdonald, J. Electrochem. Soc. 137 (1990) 2395. D.D. Macdonald, S. Biaggio, H. Song, J. Electrochem. Soc. 139 (1992) 170. D.D. Macdonald, J. Eiectrochem. Soc. 139 (1992) 3434. B.C. Syrett, D.D. Macdonald, H. Shih, Corrosion 36 (1980) 130. M. Bojinov, I. Betova, R. Raicheff, Electrochim. Acta 41 (1996) 1173. M. Bojinov, I. Betova, R. Ralcheff, J. Electroanal. Chem. 411 (1996) 37. M. Bojinov, I. Betova, R. Ralcheff, J. Appl. Electrochem. 24 (1996) 939. M. Bojinov, I. Betova, R. Raicheff, in preparation. B. Boukamp, Equivalent Circuit, University of Twente, The Netherlands, 1989. C. Gabrielli, M. Keddam, F. Minouflet, H. Perrot, Mater. Sci. Forum 185-188 (1995) 631. C. GabrieUi, M. Keddam, F. Minouflet, H. Perrot, Electrochim. Acta 41 (1996) 1121. C. ReroUe, R. Wiart, Electrochim. Acta 41 (1995) 1063. M. Bojinov, L Kanazirski, A. Girginov, Electrochim. Acta 41 (1996) 2695. A.T. Fromhoid Jr., in: J.W. Diggle, A.K. Vijh (Eds.), Oxides and Oxide Films, vol. 3, Marcel Dekkor, New York, 1976, pp. 1-271. M. Bojinov, Mater. Sci. Forum 185-188 (1995) 601. J.H.W. De Wit, H.J.W. Lenderink, Electrochim. Acta 41 (1996) 1111. R. Kirchheim, B. Heine, H. Fischmoister, S. Hofmann, H. Knote, U. Stolz, Corr. Sci. 29 (1989) 899. N. Hara, K. Sugimoto, J. Electrochem. Soc. 126 (1979) 1328. U. Stimming, J.W. Schultze, Electrochim. Acta 24 (1979) 859.
ELSEVIER
Journal of Electroanalytical Chemistry 430 (1997) 169-178
Influence of molybdenum on the transpassivity of a Fe + 12%Cr alloy in H2SO 4 solutions M. Bojinov a.,, I. Betova a, R. Raicheff b a Central Laboratory. of Electrochemical Power Sources, Bulgarian Academy of Sciences, ! 113 Sofia, Bulgaria b Department of Electrochemical Engineering and Corrosion Protection, Unil,ersityof Chemical Technology and Metallurgy, ! 756 Sofia, Bulgaria Received 7 November 1996; revised 26 February 1997; accepted 4 March 1997
Abstract
The influence of Mo addition (5-10 wt.%) on the transpassive dissolution, secondary passivation and oxygen evolution on a Fe + 12%Cr alloy in IM H2SO4 is studied by voltammetric and AC impedance measurements within the frame of an investigation of the impact of Mo on the stability of the passive state of ferrous alloys in acidic media. A semi-quantitative model of the processes is proposed, based on the experimental results obtained and model approaches presented in the recent literature. It was found to be consistent with the experimental data and could serve as a first approximation to a generalized model of transpassivity. © 1997 Elsevier Science S.A. Keywords: Transpassive dissolution; Secondary passivation; Surface charge; Iron + chromium alloy; Kinetic model
1. Introduction
Molybdenum additive to stainless steels is known to improve significantly their resistance to localized corrosive attack in media containing aggressive anions such as chloride. In spite of the numerous recent publications on the subject [1-14], there is still no agreement on the mechanism of its action. The two most detailed approaches to the prob!cm are the bipolar passive film model, proposed by Clayton et al. [9-12] and the solute-vacancy interaction model (SVIM) advanced by Macdonald and co-workers [13,14,20] on the basis of the point defect model (PDM) for the growth and breakdown of passive films on metals [15-20]. Within the frame of the first approach, it is assumed that the incorporation of Mo (and to a lesser extent Cr) in the outer part of the passive film as MoO42(respectively CrO42- ) causes the film to behave as an ionic flow rectifier which hampers the chloride ion adsorption and ingress thus suppressing the localized corrosion process. The SVIM, on the other hand, assumes segregation of Mo in the inner part of the passive film as high-valency cations (solutes Mo 6÷) which form 1-1 complexes with cation vacancies reducing both their concentration and
* Corresponding [email protected]
author.
Tel.:
003592731552;
e-mail:
0022-0728/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved. PI! S 0 0 2 2 - 0 7 2 8 ( 9 7 ) 0 0 1 6 3 - 0
diffusivity and hence retarding passivity breakdown (within the frames of the PDM, it is shown that an enhanced flow of cation vacancies is the cause of breakdown). Implicitly both models assume that: (i) There is a separation of charges in the barrier sublayer of the passive film since according to Clayton et al. [9-12] injected metal ions (positive carders) are accumulated at the metal lfilm interface and molybdate (chromate) ions (negative charges) at the film lsolution interface, whereas Macdonald et al. [18-20] show that there is an accumulation of injected oxygen vacancies (positive carriers) at the metal lfilm interface and a corresponding accumulation of injected cation vacancies (negative charges) at the filmlsolution interface. (ii) Oxidation of molybdenum (and chromium) to their highest valency state of 6 occurs either by a solid state mechanism at the metal lfilm interface (segregation of high-valency solutes in the barrier layer) or by electrochemical dissolution of the film at its boundary with the electrolyte (transpassive dissolution of Mo and Cr). Syrett et al. [21] have shown that transpassive dissolution proceeds already at potentials slightly higher than the breakdown potential for stainless steels. Thus it is evident that both the formation of surface charges and transpassivity play an important role in the corrosion mechanism and the stability of stainless steels
M. Bojinov et al. / Jounzal of Electroanalytical Chemistry 430 (1997) 169-178
170
and deserve special attention. In the present investigation, we explore the transpassive dissolution, secondary passivation and oxygen evolution on Fe + Cr alloys, emphasizing the impact of Mo additive on the kinetics of the processes. This work could be regarded as a next step in the study of the influence of Mo on the stability of passive state of ferrous alloys initiated recently in our group by modelling the transpassive dissolution and secondary passivation of pure Mo [22,23], as well as the active dissolution of binary Fe + Mo alloys in acidic media [24]. The paper is presented in two parts. The objective of the first one is to study the behavior of a Fe + 12%Cr alloy and the role of Mo additions (5 and 10 wt.%) in it using voltammetric and AC impedance measurements. The work attempts to present a generalized model of the transpassivity, secondary passivation and oxygen evolution on anodic films based on the obtained experimental results and recently published kinetic models. Results on a Fe + 25%Cr alloy and the impact of Mo additions, as well as some reference results on pure Cr, will be presented in the second part of this investigation [25].
influence of nitrogen purging on the results was found during preliminary work). 2.2. Apparatus and procedure Potentiodynamic and potentiostatic current/potential curves, as well as AC impedance spectra, were obtained by a PAR 273/5301 system driven by a PC XT computer via an IEEE 488 interface using the PAR M270 and M378 software. At each potential of measurement, the current vs. time curve was recorded until a steady state current was reached (its variation during an experiment did not exceed 2%). All the potential values were IR-drop corrected. At this steady state the impedance spectra were taken in a frequency range 0.01 to 10 000 Hz at an AC amplitude of 10 mV (rms). Equivalent circuit elements were computed by the Equivalent Circuit program of Boukamp [26].
3. Results 3.1. Polarization curves Fig. I a shows potentiodynamic polarization curves (scan rate, 1 mV s -~) of the Fe + 12%Cr, Fe + 12%Cr + 5%Mo and Fe + 12%Cr + 10%Mo alloys in 1M H2SO4, respectively, in Tafel coordinates. The regions of active dissolution 1, passivation 2, passivity 3, transpassive dissolution 4, secondary passivation 5 and oxygen evolution 6 are clearly defined. In accordance with earlier results [6,7], Mo additive greatly (by one order of magnitude for 5%Mo and about two orders for 10%Mo) reduces the current density both in the active dissolution 1 and the passivation 2 regions, has a small impact on the passivity range 3 and leads to a significant increase in the transpassive disso|ution and oxygen evolution rates. Steady state Tafel polarization curves of the alloys in the transpassive dissolution, secondary passivation and oxygen evolution regions are presented in Fig. I b. A curve for spectroscopically pure Fe in the same medium is presented for comparison. All samples were polarized at 0.55 V until a steady state current was reached (this lasted several hours). Then the polarization curves were measured step-by-step in the positive direction and at each point of measurement the current/time curve was recorded until a new steady state was reached (in the transpassive region, this is achieved far more quickly in comparison to the passive one).
2. Experimental 2.1. Electrodes and electrolyte The composition of the alloys studied which were prepared in the Institute of Metal Science, Bulgarian Academy of Sciences, is shown in Table 1. The samples were shaped in cylindrical form and sealed in PTFE holders with acid resistant epoxy resin in order to expose to the electrolyte a planar area of 0.2 cm 2. Their pretreatment consisted of mechanical polishing on a finer grade emery paper followed by a soft clet.h with alumina as grinding paste, degreasing with methanol and washing with bidistilled water. No cathodic reduction of the natural oxide film produced was performed, since it was found to have little influence on the processes studied in the present paper. A three electrode glass cell was employed, featuring a large area Pt sheet as a counter electrode and a saturated K 2SOn mercury sulfate electrode (SSE, Ess~ = 0.67 V vs. SHE) as a reference. All the potentials in the paper are given vs. this kind of reference electrode. The electrolyte (IM H2SO4) was prepared from analytical grade 97% H2SO4 (Merck) and bidistilled water. All the experiments were carried out at 20 + I°C in naturally aerated solutions (no
Table I Composition of the alloys employed in the present investigation Alloy
Cr (wt.%)
Mo (wt.%)
C (wt.%)
Si (wt.%)
Mn (wt.%)
Fe (wt.%)
Fe + 12%Cr Fe + 12%Cr + 5%Mo Fe .4- 12%Cr + lO%Mo
11.85 12.00 11.90
5.15 9.50
0.015 0.030 0.025
0.15 0.16 0.12
0.14 0.14 0.10
balance balance balance
M. Bojinov et aL / Journal of Electroanalytical Chemist~. 430 (1997) 169-178 J Fe+12%Cr Fe+12%Cr+5%Mo Fe+12%Cr+10%Mo [
100
:
E 10
.
:
:
1.,;
i
,..
..°
;,~-.................-, ,->-----" "L..'',
,:
0.1
- .',.~.. . . . . . . .
':i
, ~ .....
"--Y !
0.01
.--,".."Y
-0.5
,
®
i
,
p
0
0.5
',
~
1
Fe+12%Cr F e + 1 2 % C r ÷ 5 % M o F e + 1 2 % C r + l O % M o
Fe
I
I 100 10
E ..ml,
0.1 0.01 0.4
I
0.6
T
T
I
08.
1
T
I
1.2
r
1.4
E/V Fig. 1. (a) Linear sweep voltammograms of the Fe + 12%Cr, Fe + 12%Cr + 5 % M o and F e + 12%Cr+ 10%Mo alloys in IM HzSO 4 in the potential range - 1 to + 1.2 V (sweep rate, 1 mV s - i ); (b) steady state polarization curves of pure Fe atilt the Fe + 12%Cr, Fe + 12%Cr+ 5%Mo and F e + 12%Cr+ l O%Mo alloys in the ranges of transpassive dissolution, secondary passivation and oxygen evolution in I M H a SO 4.
The results show that transpassive dissolution and secondary passivation are features due to alloy additives since no such processes are observed for pure Fe. The role of Mo is deafly emphasized on this figure, an addition of 5%Mo to the Fe + 12%Cr alloy causes the transpassive dissolution and secondary passivation current to increase with an order of magnitude. The addition of 10%Mo leads to a further increase, but it is not as pronounced (about three times). The current density of oxygen evolution is increased as well. In the transpassive dissolution region, all three curves pertinent to the alloys have similar Tafel slopes ( ~ 40 mV), then a curvature is observed and finally a current plateau is reached (for the Fe + 12%Cr and Fe + 12%Cr + 5%Mo alloys at ~ 0.8 V, whereas for the Fe + 12%Cr+ 10%Mo alloy at ~ 0.9 V). This current plateau indicates that probably a secondary film is formed which chemically dissolves at its interface with the electrolyte thereby defining a potential independent cmTent. The Tafel slopes for the oxygen evolution reaction are comparable for Fe, Fe + 12%Cr and Fe + 12%Cr + 5%Mo alloys (62 -I- 4 mV) and are smaller than that expected for oxygen evolution on conductive oxides. The s!ope for the
1? 1
Fe + 12%Cr + 10%Mo alloy is greater than the other three slopes ( ~ 150 mV). Summarizing, a strong impact of Mo on the transpassive dissolution and secondary passivation processes is observed. It seems to be more of a quantitative nature for the 5%Mo addition (no alteration of the sht,pe of the polarization curve of Fe + 12%Cr), but some qualitative differences are observed for the 10%Mo addition (less well expressed current plateau and different slope of oxygen evolution reaction).
3.2. AC impedance spectra AC impedance spectra of pure Fe in the potential region covered by the voltammetric curve from Fig. I b are presented in Fig. 2. The spectrum at 0.85 V is qualitatively identical to that published in a series of papers by Gabrielli et al. [27,28]. According to these authors it expresses the passive film growth under high-field conditions and the relaxation of the concentration of mobile Fe 3+ in the fi!~m [27,28]. At higher potentials, the high-frequency semicircle is four~d to be composed of two overlapped capacitive time constants (second spectrum in Fig. 2) and in the oxygen evoh~tion region, two overlapped inductive time constants gradually appear in the spectra as the potential increases (last two spectra in Fig. 2). Thus in this region a multistep process is taking place somewhat analogous to that described by Rerolle and Wiart [29] for the oxygen evolution on lead and lead alloys in H2SO 4. AC impedance spectra for the alloys covering the potential ranges of interest in the present work are shown in Fig. 3 (Fe + 12%Cr), Fig. 4 (Fe + 12%Cr + 5%Mo) and Fig. 5 (Fe + 12%Cr + lC%Mo), respectively. In the transpassive dissolution region, one capacitive and one inductive time constants are observed. In the secondary passivation region, a capacitive behavior at low frequencies is consistent with the growth of a secondary film. As the potential
F e l l M Hz.,qO4
1000fI"
1 10
~. "
,vL/
o a o o a o
0 "1
• ;,~ ooo
o.ssv
'.~ . . . . . . 1000 -u
" " " 2000
.,,. . . . . . . .
1
~,.
/
1.15V
%, L? "o.6ff 3000
r,,,)
C ,,....
E "i"
i.0
5 ..'~ "°'"
''~j~'°
. . .1.20 . V" °"~, i . !Y~[ ....
•
o.°ii:'"°" .
Re(Z) / ~ cm
,
,,
o
i
I
2
Fig. 2. AC impedance spectra of pure Fe in IM H2SO 4 in the region of transpassive dissolution, secondary passivation and oxygen evolution of the alloys employed in the present study. Parameter is frequency in Hz.
M. Bojinov et al. / Journal of Electroanalytical Chemistry 430 (1997) 169-178
172
Fe+12%Cr
M H,2SO4
I 1
Fe+12%Cr+5%Mo
I 1 M H2S04
1.10 °=u
°a
°
11~F
J: 0.6V
ff
O~10=
%
=."
° 1,~
=,,
%
0.75 V 0
="....
° °
"0 I"
:
o.,&
r
on
0.011
f o.sv
IO0
"°
1 ~ .... i;
5111° °°""'°'°'" 1 o11: 11o:
°'V"
0.11 =
",.......
r
-'°°.."" 50
o=°%
° ug
, 1.~.°°°
o o°
1 0 0°
0.011
iI
=% 11.0 0 ° ~ o0.011a
lkl~0d
~o,~ I.lO 1t.0 o ° ° o a ° o 0%e
io
="."
~
r .0.75 v ......
4o
0
io
5
10
4 q ~ . . . . ~ o . . . . ~ o . . . . ~ o . . . . 400
~ 0.9~y. - o "
o<
11,Q
.. :L.
11.0
11,(}
o
o
1,1~"
o,111
flier (~ . . . .
...
~
k X"
50
' '
100
150
,.osv I
110
....
110 ° . .% °
S~ 11
60 .... .
0.95 V
•
° • ,
t ~ °'11
110
o.1~'~ Q
oaa
o°O =o
a
oo
....
•
1.0 V
o.,
s .....
1"o . . . . ,"s
11~,~
~o
~
1,;~
":'~"
ooa
Ill0°000
E ~e....
1
a .== 1,~1~°
,o,v
=°0
,Or
5
° °or
5 ..... ,o ....,;
~"
NI
~
° o
5 1110 aa o 11
o~ . . . .
.
a°
~ 1.oy..',.--..
o ° o =
7%...°"~15I
~o
, ....
"'0 :~"
° 110a aa
f:v" "~,
,oo°v ",",,1
} ......
";"
0
o °
lk
.,,No.
4
6
8
[
•
0°0
Z ~:~
:i
2
110
[,fN
I
°
• •
1.193' 1
11(
.o.f I ,
o o = = 110
% o •
o
11k /
0,5
11.,=1
°,;,,~jl Re(Z) / Q crn
1.0
=%
9"
•o
o.11 ,.,°,,/I 1.173V "% .... ="i I
2
Re(Z) / Q cm
2
Fig. 4. AC impedance spectra of a Fe+ 12%Cr+5%Mo alloy in IM H 2 SO 4 in the region of transpassive dissolution, secondary passivation and oxygen evolution, Parameter is frequency in Hz.
Fig. 3, AC impedance spectra ofa Fe+ 12%Cr alloy in IM H2SO 4 in the region of transpassive dissolution, secondary passivation and oxygen evolution, Parameter is frequeacy in Hz.
increases, the inductive time constant almost disappears at 1.0 V and by the same potential the high-frequency semicircle becomes a combination of two overlapping time constants in analogy to Fe (see Fig. 2). They are discemible for the 5%Mo (Fig. 4) and clearly observed for the 10%Mo alloy (Fig. 5). For Fe + 12%Cr and Fe + 12%Cr + 5%Mo alloys, the spectra in the oxygen evolution region comprise two inductive time constants in analogy to Fe (Fig. 2), although they are better distinguished (Figs. 3 and 4). For the 10%Mo alloy, conversely, the capacitive time constant at intermediate frequencies persists to the upper potential limit of the measurements and only one inductive semicircle is observed (Fig. 5). Geaerally, the absolute values of the impedance for the Mo-containing alloys are far smaller than for the Fe + 12%Cr alloy (Figs. 3-5), which is in accordance with the polarization results depicted in Fig. l b and further confirm the impact of Mo on the rate of both transpassive dissolution and secondary passivation. In conclusion, it can be stated that a 5%Mo addition changes only quantitatively the picture observed for Fe + 12%Cr. Several qualitative differences are observed for a lO%Mo addition in the secondary passivation and oxygen evolution ranges.
Fe+12%Cr+10%Mo 1Q~ 11.0
-~.~.
o
o= o
=
•
1.10 = a
N= o
~1V
•0
4
= ""
[ ~II" .o.,""=.
•
[
I 1 M H2SO 4
o.,, ..
t o.e v .... 2",° -'S . . . . ,, . . . . ,,, . . . . 3, . . . . ,o
0.0.,0".,
• •
•
i
".. iI
4.~V
o.745v
o.,,,,1;'._ I
J ,
....
, ....
o1"~'
%-,,,,,s ~11 I
, ....
~'~
2 ° ° = = =11;~.= 1
"~
1~°
°o'
' = 0o888 V o 1~1~:¢
% o°
"'1 . . . .
2....
'~. . . .
11-
4.....
5
C~
?
'~ [ °o....
'1~... ..... ~= 1.....
~'~..1.,o = I ~=~.°'8°° I 2 .....
a .....
11o o o-"
r'~.f'°?/ ,k °o o.s[
""
I=1o %
0.986 V"~' ~..... 3.....
'1..... !1p . . . . .
' .'." t ."
4' -o.o
°
1.'082 V
,qlg, v .... 1
1.0
]
o-!
' I .
•'k. °.. ] 1,5
2.0
%,'"I
2
Re(Z) / Q cm
4
"~, 1o ="~.°.
............. 0.5
' .I
3
2
Fig. 5. AC impedance spectra of a Fe+12%Cr+ 10%Mo alloy in IM H2SO 4 in the region of transpassive dissolution; secondary passivation and oxygc~l evolution. Parameter is frequency in Hz.
M. Bojinov et aL / Jounuff of Electroanalytical Chemist~. 430 (1997) 169-178
For a preliminary treatment of experimental data in the transpassive and secondary passive regions, the equivalent electrical circuit of Fig. 6a was found to be appropriate. In this circuit, C is the high-frequency capacitance of the metallfilmlelectrolyte system, R t is the defect migration resistance, R~ and L~ are elements associated with the inductive loop observed throughout the investigated potential range (the subscripts will be explained in detail in Section 4), Co is the Faradaic pseudocapacitance due to the growth of the secondary oxidation product layer and R a is the electrolyte resistance. These parameters should by no means be regarded as independent electrical elements. Their values characterize the properties of the interface and the rates of the reaction steps involved and are used to derive intermediate information for the system under study. They acquire clear physical meaning only when related to a specific kinetic model. The dependences of these parameters on the potential for the three alloys studied are presented in Fig. 6b-f.
zoo
L sc
l
--- MO~
|
~
~
~%_
I
2-~
+
,~-Haq
H: e-
. n-SC ~regioni
~O 2
insulator p-SC region j . . ~ region
C O d F ()~ h
+ ®
X=0
Fig. 7. (a) Scheme of the processes in the metallfilmlsolution system during transpassivity and secondary passivation; (b) distribution of defect concentration as depending on the distance from the filmlsolution interface.
_=__
100
"~-- 2O tw
I
I
®
m
x=d F
®
200
l-~ V V "
electrolyte + secondary film
Co(O)
I no Mo5%Mo10%Mo I • ,O .e. Rsc
negative surface charge
barrier film bulk
metal
Fe+12%Cr I 1 M H;pSO4
®
173
I
Rt
10 5
2ols'o16 o'.7 0:6'0:9 EIV
I ooMooyo,o .oI 5000 2000i
oo:ooyo,o,yo[ 100000
7@!
1000!
~
5001 200'
,-;o|
,
,
EIV
500 [
-.,,. O
1
.
= 1:
~.5 0:6 0.7 028 019 i
ql E
~ '
1.1
I
,
0.5 . . . . . . EIV
1
I.o:''oo'o o ]
,,u 6.5
0.22~).=5 06 07
08 09 El V
1
11
010
016'0'7
08
'
'
EIV
Fig. 6. (a) Equivalent circuit of the electrode system: C, high-frequency capacitance of the metallfilm[electrolytesystem, R,, resistance of defect migration, R~c,Lsc,elementsassociated to the negativesurface charge at the filmlsolution interface, C0, Faradaic pseudocapacitance, Rn, electrolyte ~esistance; (b) R t vs. potential dependence for the three alloys studied; (¢) R~ vs. potential dependence for the three alloys studied; (d) L~ vs. potential dependence for the three alloys studied; (e) C .s. potential dependence for the three alloys studied; (f) Co vs. potential dependence for the three alloys studied.
They seem to confirm the general picture that emerges from the qualitative analysis of polarization curves and AC impedance spectra. The potential dependences of R t (Fig. 7b) can be directly taken as inversely proportional to the polarization curves from Fig. lb. For the Fe + 12%Cr alloy, Rsc changes slightly in the transpassive dissolution region and increases smoothly in the secondary passivation one (Fig. 6c). For a 5% and 10% Mo addition, a steep decrease of this parameter is observed in the transpassivity range (Fig. 6c). The increase of R~ in the secondary passive range is not as evident for the Mo-containing alloys as it is for Fe + 12%Cr (Fig. 6c). The pseudoinductance Lsc decreases in the transpassivity region, this trend being more pronounced for the Mo-containing alloys (Fig. 6d), and is roughly constant in the secondary passivation range (Fig. 6d). The values of the high-frequency capacitance for the Fe + 12%Cr alloy are fax lower than those for the Mo-containing alloys (Fi~. 6e) which is consistent with the considerably higher transpassive dissolution rate of the latter. The values of the Faradaic pseudocapacitance for the Mo-containing a!loys are about an order of magnitude higher than that for the Fe + 12%Cr alloy implying lower current efficiency for secondary film formation [23]. A more detailed explanation of the potential evolution of the circuit elements will be attempted in the Section 4 on the basis of a kinetic model.
M. Bofinov et al. / Journal of Electroanalytical Chemistry 430 (1997) 169-178
174
Then the balance of fluxes at the interface gives [19]
4. Discussion
4.1. Transpassive dissolution and secondary passivation domains A simplified scheme of the alloy Ifilmlelectrolyte interface during transpassivity is presented in Fig. 7a and the corresponding distribution of defects as depending on the distance from the filmlsolution interface is depicted in Fig. 7b. This scheme is constructed to be consistent either with a bipolar rectifier structure of the passive film as proposed by Claytoi~ et al. [9-12] or the p - i - n tunnel diode structure as suggested by the PDM [19]. The chemistry of the PDM [15-20] is used to describe the inteffaeial reactions of generation and annihilation of vacancies within the frame of the present approach and the concept of independence of the electric field strength on potential and film thickness advanced therein is also adopted. Conversely, the vacancy motion is treated according to the generalized theory of Fromhold which is valid at any value of the field strength [31], instead of using Nernst-Planck equations as proposed by the PDM [15-20] which are applicable in the low-field limit only. There is enough evidence that highfield assisted migration governs the anodic film growth on a range of passive metals [23,27,28,30,32]. The chemistry and physics of the proposed model are summarized briefly below and for a detailed definition of quantities involved we refer to the list of symbols at the end of the paper. At steady state, the continuity equation for the metal[anodic film Ielectrolyte system imposes
JMIF----"JF -- JFIs ffiJ.~ ffi const.
+
s
(2)
In the following presentation, the contributions of both interfaces and the film bulk to the overall impedance will be discussed. • At the metal lfilm interface, oxygen vacancies are generated according to the reaction of formation of a metal position in the barrier layer network [15-20]
Z~tlF = RMIF+ i toCMIF
(R-l)
and metal vacancies are correspondingly consumed
JF = (2 FDo/2 a)[ Co( d r ) - co(0)exp( - dF/a)] X exp[(2 Fa/RT) dPo/dF]
(R-2)
The interfacial rate constants are assumed to be potential dependent in a Tafel manner ki = ki°exp(bi~MIF)
(3)
(6)
where [ 15-20] ~O =
~MIF -I- Ed v + ~bFiS= E( applied potential)
(7)
~bMiF = ( 1 - a) E - Ed F ~FIS = qn dFIs/Se0 and q. is a negative surface charge [23,30.32] accumulated at the filmlsolution interface by the cation vacancies generated mainly by the transpassive dissolution reaction. As for most cases d F >> a, co(O)exp(--dF/a) << co(dv) and
JF = (2FDo/Ea)co( dv)exp{(EFa/RT) X [(1 - or) E + qndFIs/teo]/dF}
(8)
or setting
A - (2FDo/2a)co(dF) and B - (2Fa/RT) j F f A e x p { B [ ( 1 -ot)E+qndFis/eeo]/dF}
(9) (10)
It is postulated that the build up of the surface charge is a slow process, i.e. it cannot follow instantaneously rapid variations in the applied potential [30]. Then the time dependence of the surface charge is treated in analogy to the surface charge approach [30]
dqn/dt=jsW(qn,s- qn)
;'~1)
The steady state value of the surface charge is defined as t~FIS,sCFIs --"
otEe~o/dFis
(12)
Inserting this in Eq. (11) results in the expression
dqn/dt =JsW( t~eeeo/dFIs - qn)
k,
m + V~- -4 M M + 3 e -
(5)
where R~[F = F[blklcM(dF) + ib 3 2k 2] and CMIF is the interfacial capacitance. • In the anodic film with a thickness d F, oxygen vacancy motion is driven by the electric field at the metal lfilm interface according to the generalized transport equation [31 ]
qn.s =
k:
m ~ M M + Vg + + 2 e -
(4)
Postulating that the small sine perturbation does not lead to a significant deviation of the concentration of metal vacancies at the metal[film interface cu(d,,) from its steady state value, the impedance at the metal[film interfaceTeads as
( 1)
where j~ is the steady state current density for a given applied potential. Accordingly, the impedance of the system will be the sum of the impedances of the two interfaces and the film bulk [33] z = ZM F +
JMIF ----F[ k2CM(dF) + -~kl]
(!3)
From Eqs. (10) and (13) under a small amplitude AC perturbation we obtaha [30]:
Aj=j~B[(I-t~)AE+
AqadFis/eeo]/d F
Aqn =jsWeeoaAE/[ dF~s(i a, +jsW)]
(14) (15)
M. Bojinov et al. / Journal of Electroanalytical Chemistry 430 (1997) 169-178
Accordingly, the Faradaic impedance of the film bulk is
Z F,F -~ = A j / A E =jsB[(1-a)
+j,W,~,~oa/(ioJ+j~W)]/d F
(16)
which is equivalent to Z~,~= l / R t + l/(itoLsc+Rsc ) where
Rt-- dF/LB( I - a) Rsc - dF/j~Bot
(18)
Lsc f dF/j~ WBot To derive the total impedance, the high-frequency capacitance of the film C and the Faradaic pseudocapacitance C O have to be added in the appropriate manner ZF= [1/Rt + 1/(icoLsc + Rsc) + ioJC] -~ + l/io~C o (19) The Faradaic pseudocapacitance C o is defined as
CO= A Q / A E - (
zF/Vm)AdF/AAE
(20)
where A is the current efficiency for secondary film formation. • At the filmlsolution interface, oxygen vacancies react with adsorbed water forming an oxygen position in the barrier layer network k3
V2+ + H20 --* Oo + 2H +
Thus subject to the assumption that the small sine perturbatio does not change significantly the concentration of oxygen vacancies at the film[solution interface co(O), the impedance of that interface becomes ZFI~ = RFI~ + i t°CFis
(17)
(R-3)
Accordingly, metal vacancies are produced at the film lsolution interface leading to metal ion abstraction from the film
175
(22)
Consequently, the total impedance of the system can be calculated from F-xls. (2), (5), (17)-(20) and (22). However, as stated above (see Section 3), the impedance response of the system in the transpassive and the secondary passive domain exhibits only two time constants (one capacitive and the other inductive) and a series capacitive feature at low frequencies, which is consistent with the impedance defined by Eqs. (17)-(20) and the electrical circuit depicted in Fig. 64. Thus for the special case under investigation the contribution of the interracial impedances is thought to be negligible. Further confirmation to this suggestion is searched below on the basis of the potential dependences of the circuit parameters. In order to explore further these dependences within the frames of the present model, the film thickness vs. potential relationship is taken from the PDM [18-20] with the assumption that the applied potential is expressed vs. the potential of zero film thickness (E - 0 when d F - 0) [1
(23)
During transpassive dissolution 8 = 6 and X-- 3 d F = (1 - o t - otots/ot,)E/E
(24)
Inserting this in Eq. (18) it follows that R t = (1 - a -
otols/oq)e/[ Ej~B(I - a ) ]
R,c = (l -
k4
M M ~ VM 3- + M]q+
(R-4)
and transpassive dissolutionof the alloying elements from the film proceeds according to [201 ks
M'M, + 4H20 ~ M'O42- + V~7 + 8H + + 3e-
(R-5)
(M'--Cr,Mo) The transpassive dissolution reaction results in an accumulation of cation vacancies near the filmlsolution interface in a layer with a thickness dFis and to a depletion of this layer in chromium and molybdenum positions in the oxide network. The depletion in Cr of the first atomic layers near the film[electrolyte interface during transpassivity was quantitatively confirmed by Kirchheirn_ et al. for a Fe10%Cr alloy [34]. The balance of fluxes at the filmlsolution interface gives
JFls = 3Fk°exp(3F°t°t~.EI RT) + k3co(0) + k4
(21)
It is unlikely that Eq. (R-5) will proceed via a simultaneous three-electron transfer, but to describe the behavior of Fe + 12%Cr alloy, at this stage it was not necessary to propose a detailed reaction sequence for the transpassive dissolution of Cr.
L~: = (1 - a - a o t s / a l ) E / ( E j 2 W B a )
(25)
The numerators of Eq. (25) increase linearly with potential whereas their denominators increase exponentially with the same parameter because so does the stationary current density is-Thus R t, R~c and Lsc all decrease which is found experimentally (Fig. 6b-d). Due to the higher transpassive dissolution current for the Mo-containing alloys, the values of the elements Rt.. Rs¢ and L~ are far smaller for them than for the Fe + 12%Cr alloy, which is consistent with experiment as well (Fig. 6b-d). From Eq. (25) two important characteristics of the system could be derived, namely
oz-- ( R , / P ~ ) / [ I + ( Rt/Rs~)]
(26)
W=LsoL/R,o These two parameters are plotted in Fig. 8 as depending on the oxidation potential. The obtained dependences are consistent with the physical picture given in Fig. 7a. Due to the accumulation of M'O42- at the film[solution interface and the simultaneous depletion of the interface in Cr and Mo [34], the rate of the transpassive dissolution is slowed down. This leads to a
M. Bojinov et al, / Journal of Electroanalytical Chemistry 430 (1997) 169-178
176
Fe+12%Cr I 1 M H2SO4
4.2. Oxygen evolution region
,.. I no Mo 5%Mo 10%Mo I -0~
0.6
As negative charge carriers (cation vacancies) are accumulated near the filmlsolution interface (Fig. 7a), due to the p - i - n junction structure depicted in Fig. 7b [19] the concentration of captured holes at that interface will increase with the transpassive dissolution current of Eq. (R-5). At a certain potential level ( ~ 1.0 V), water will become oxidized by these holes and oxygen evolution will take place according to the generalized equation:
®
0.5 0.4 0.3 0.2 0.1
%=o16o17 o18'o19' i ' .
I
E/V
l no Mo 5%Mo 10%Mo
H 2 0 + 2h + -> 702 + 2H + ]
2O
®
10 "7
o E
5
~8
2 1 0.5 0.2 - , 0,5 0.6
. , t , t , 0.7 0.8 0.9
1
1.1
EIV
Fig. 8. Potential dependences of the polarizability of the filmlsolution interface ot (a) and the capture cross section per positive defect W (b) as deduced from Eq. (16) for the three alloys studied.
The current of the oxygen reaction increases exponentially and so does the steady state current (Fig. lb). In the oxygen evolution region, in addition to the charge transfer loop, three time constants (one capacitive and the two other inductive) gradually appear in the impedance spectra (Figs. 2-5). To explain their nature, the following hypothetical model is proposed. Oxygen evolution is regarded as a two-step reaction, the oxygen anion acting as adsorbed intermediate with a formal coverage 0~, as emphasized by De Wit and Lenderink [33]: k3
H20
---* O ~ d + 2 H + k6
Vo gradual dissipation of the surface charge qn- The conditions for the formation of a secondary film which is believed to consist mainly of ferric oxide-hydroxide are reached [35]. As a consequence, the parameter a characterizing the part of the applied potential consumed at the filmlsolution interface decreases (Fig. 8a). Simultaneously R t and Lsc tend to become constant and R~c increases. This is the trend observed experimentally in the secondary passivation region (Fig. 6b-d). The gradual formation of a secondary film causes the associated current efficiency to grow with potential and to reach a constant value in the secondary passivation region. This results in a decrease of the Faradaic pseudocapacitance C O to a constant value as well (Fig. 60. Similar speculations could explain the potential trend of the capture cross section per charge carrier W (Fig. 8b). This quantity is related to the surface excess of negative carriers by the equation W= (2F/3)-'
(27)
The observed decrease of W (Fig. 8b) is caused by the increase of the surface excess of negative carders fl due to the gradual dissipation of the surface charge and the associated growth of the accumulation layer thickness from a monoiayer at low potentials to several atomic layers at higher ones. In the secondary passivation region, there is no further increase of the thickness of this layer, hence/3 will tend to constant values and so does W (Fig.
8b).
(R'-3)
-, Oo
(R-6)
In addition to their participation in the film formation, the oxygen anions are oxidized by holes at the film lsolution interface forming another intermediate O~ with a coverage 0 2 k7
O~a- + h + --¢ O~
(R-7)
which in turn is oxidized to produce oxygen gas (the recombination of oxygen atoms is taken as a fast process for the sake of simplicity) t¢8
O~ + h + -, I
(R-S)
At this stage, the important assumption of the anodic layer being electronically conductive is made, thus the main part of the applied potential is thought to occur as a drop at the film[solution interface. If film formation, iron dissolution and oxygen evolution are the processes to be taken into account, the charge balance at the film lsolution interface reads as
+k80
(28)
The corresponding material balances of the intermediates are of the form f l d O l / d t = k 3 ( i - 0 i - 02) - ( k 6 + k T ) 0 !
fl d O 2 / d t = k701 - ksO 2
(29)
M. Bojinov et al. / Journal of Electroanalytical Chemistry 430 (1997) 169-178
The steady statt solution is readily obtained setting d Oi/dt =0 0Is = k 3 k 8 / D
(30)
02s = k3k7/J~
D = (k 3 + k 6 + kT)ks + k3k7
The AC impedance solution is a result of the first order Taylor expansion of Eqs. (28) and (29) around a steady state Z~'Il = R t I + F[(~kc + k 7 - k 4 ) d O l / d r + ( k s - k4)dO2/dE ] + itOCFis
(32)
where
+ ( b 7 + bs)k7]O,. ,,
,
(33)
d O t ~ d E = ( XtZ2 - k3X2)/ZD d O 2 / d E = ( X2ZI + k T X I ) / Z o XI -- [ ( b 3 - b 6 ) k 6 -1- ( b 3 - b7)k7]Ols
X2 = [(
- bs)kTO
principle to perform a numerical simulation of the impedance response according to Eqs. (32) and (33) and to obtain values for the rate constants as is frequently done in the literature. However, as at the present stage of the work there is no direct evidence Ibr the formation of intermediates of the oxygen reaction at the alloy electrodes studied, we confine ourselves to this qualitative treatment.
(31)
jFis,.=F[k4(kt+kT)/k3+~k6+2k7]O,s
R[ I = F[ b4k4(k 6 + k 7 ) i k 3 + d / 3 b t k 6
177
s
Z l = i toil + k 3 + k 6 + k 7 Z 2 = it aft + k s Z D = Z t Z2 + k s k7
and CFIs is the interfacial capacitance. F,q. (32) gives the possibility to explain the three time constants present for all the alloys in the oxygen evolution domain. At the beginning of the oxygen evolution region, if the rate of Eq. (R-7) is greater than that of Eq. (R-8), the coverage of the interface with adsorbed divalent oxygen anions Oa2d will decrease with potential and the corresponding coverage with adsorbed monova~ent oxygen intermediates O~ will increase. This trend is tantamount of a combination between a capacitive and an inductive time constant as found experimentally in the spectra in the potential range 0.95 to 1.15 V (Figs. 2-5). At high potentials, due to the faster increase of the rate of Eq. (R-8) with potential, the coverage of adsorbed monovalent oxygen anions begins to decrease as well and the associated time constant becomes inductive as observed in the experimental spectra (Figs. 2-5). Another explanation of such a time constant could be the experimental fact that during oxygen evolution, the dissolutio~ of Fe as Fe 3+ was found to be strongly potential dependent [36]. This could result once again in the formation of an accumulation layer of iron vacancies and it will comribute to the impedance as an inductive feature as in the case treated in Section 4.1. Although it is not the aim of the present paper to present a complete mechanism of the oxygen evolution reaction, the above hypothetical model helps at explaining the experimentally observed features. It is possible in
5. Conclusions An experimental study of the electrochemical behavior of Fe + 12%Cr alloy in H2SO4 solutions is presented, emphasizing the role of Mo additions on the transpassive dissolution, secondary passivation and oxygen evolution reactions. On the basis of the experimental results and model approaches proposed in the literature, a semiquantitative kinetic model of the transpassive dissolution process is advanced. It is established that the model is consistent with the experimental data and could be regarded as a first approximation to a generalized model of the transpassive process. At the present stage of the work, some unclarified points will be outlined and the limitations of the model will be mentioned as a conclusion. • Significant improvement of the presented kinetic scheme is needed, to account quantitatively for the superposition of secondary passivation and oxygen evolution reactions and to evaluate the impact of Mo additive on these processes. • An independent deterrr,lnation of the oxide and secondary film thickness and composition, as well as the current efficier, cy for the transpassive dissolution, secondary film formation and oxygen evolution could help in determining unequivocally the model parameters. Such a study will be attempted in the near future.
6. List of symbols a
A
B
atomic jump distance, cm constant in the high-field migration equation, A cm -2 field coefficient in the high-field equation, V-i cm
Tafel coefficients of the interfacial reactions (i = 1-8), V -i Co(0) concentration of oxygen vacancies at the film lsolution interface, tool cm-s Co(dF) concentration of oxygen vacancies at the metal lfiim interface, mol cm-3 cM(dF) concentration of metal vacancies at the metal [film interface, mol cm -3 high-frequency capacitance of the film, F cm -2 C capacitance of the metallfilm interface, F cm-2 CMIF capacitance of the cation vacancy accumulation CFIs layer,. F c m - 2 Faradaic pseudocapacitance, F cm-2 Co bi
M. Bojinov et al. / Journal of Eiectroanalytical Chemistry. 430 (1997) 169-178
178
dFIs Do E E i
J JMIF
JF
JFis A ki L,~c
thickness of the barrier layer, cm thickness of the metal vacancy accumulation layer, cm diffusivity of oxygen vacancies, cm 2 s- ! applied potential, V electric field strength, V cm-l i ~ g i r . : ~ , unit c ~ n t density, A cm -2 current density at the metallfilm interface, A cm -~ film formation current density, A c m - : current density at the film lsolution interface, A cm-2 steady state current density, A cm -2 rate constants of the interracial reactions (i - 1-8), mol cm -2 s -t inductance due to surface charge relaxation, H cm 2
m
MM
oo qn qn, s Rt
Ra Rsc
Vm W
metal atom in the metal phase metal position in the barrier layer network oxygen position in the barrier layer network negative surface charge at the film[solution interface, C cm -2 steady state surface charge at the film[solution interface, C cm -2 resistance due to migration of defects, fl cm: electrolyte resistance, 1~ cm z resistance due to surface charge relaxation, 12 cm 2 oxygen vacancy in the barrier film network metal vacancy in the barrier film network molar volume of the phase in the barrier film, cm 3 molcapture cross section for a positive defect, cm" C-!
ZMIF
ZF
Z~ls a
a I
8
A ~M[F ~FIS
impedance of the metal lfiim interface, ~ cm z impedance of the anodic film, fl cm2 impedance of the filmlsolution interface, fl cm 2 polarizability of the filmlsolution interface barrier symmetry factor of the transpassive dissolution reaction (Eq. (R-5)) barrier symmetry factor of the oxygen vacancy generation reaction (Eq. (R- 1)) maximum surface excess, mol cm -2 valency of transpassive dissolution dielectric constant of the film current efficiency for secondary film formation local potential drop at the metallfilm interface, V local potential drop at the film lsolution interface, V valency of the cation in the film
gies under contract CH-330 is gratefully acknowledged. The authors are indebted to Professor Tz. Rashev from the Institute of Metal Science, Bulgarian Academy of Sciences for the preparation of the alloy samples.
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Acknowledgements [34]
The f'mancial support of the National Science Fund, Bulgarian Ministry of Science, Education and Technolo-
[35] [36]
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