Corrosion Science, Vol. 28, No. 10, pp. 969-986,1988 Printed in Great Britain
0010-938X/88 $3.00 + 0.00 @ 1988 Pergamon Press pic
THE KINETICS OF PIT GENERATION ON STAINLESS STEELS B. BAROUX Ugine Research Center, 73400 Ugine, France
Abstract-A kinetic approach is used to investigate pit generation on two types of mechanically polished 3()4austenitic stainless steel, immersed in NaCI containing neutral aqueous solutions. From measurements ?it initiation times under potentiostatic conditions and pitting potentials under potentiokinetic conditions, pitting probability (ar) per unit area and the pit generation rate (g = darldt) were determined. Both for short holding times and for high scanning rates, g does not de pend on the scanning rate: g
= K.cn.exp
(naqElkBT)
where n = 3, a = 0.5, c is the chloride concentration, q the eIectron charge, kB the Boltzmann constant, T the Kelvin tempe rature (3000K), and the constant K de pends on the steel studied. For longer tests, the passive film properties vary during the test and g decreases with time, and therefore the measured pitting potentials must be considered very cautiously. Pits preferentially initiated on non-metallic inclusions, which were not the same in the two steels. Pitting mechanisms consistent with these results were reviewed. The calculated incubation times were related to the probabilistic measured pit generation rates. A general pit initiation model is proposed which accounts for pit generation kinetics, whatever the effective passive film breakdown mechanism.
INTRODUCTION PrITINGcorrosion susceptibility in neutral chloride-containing aqueous media has formed the subject of a lot of investigations. Several mechanisms have been proposed to account for the pit initiation; these mechanisms are described in several r~view artic1est4 it is now very likely that, depending upon the experimental ~nditions, each of them in turn may become more effective. 4More recently, kinetic5 or statisticaI6,7,8aspects of pit initiation were taken into account, but the problem mains of correlating these phenomenological models with the microscopie mitiation mechanisms. ln ail these models, the potential E of the steel plays a major l'ole and acts as a driving force for pit initiation; usually the pit initiation time increases when E decreases and becomes infinite when E cornes close to a critical potential referred to as the pitting potential. However, this point of view is no longer sufficient, if the stochastic aspects of pit initiation are taken into account: the relevant pitting criterion is then the pit generation rate (PGR) peI' unit area and the true pitting potential is that for which this PGR reduces to zero. Moreover, when the PGR is low enough, the pit occurrence is a low probability event and the measured pitting potential& are scattered on a rather large range of potentials, depending on the sample area and on the potential holding time.
Manuscript
received 30 October
1987.
969
970
B.
BAROUX
It is quite possible that a lot of critic al potentials exist, corresponding to the different stages9 of pitting corrosion. The initiation of a stable pit tirst needs a nucleation process, then the propagation, as a result of the development and maintenance of an elevated local acidity;8,JO.11 it is probable that the critical potentials are not the same for those different pit initiation stages. From a practical viewpoint, it is often easier to measure the pitting probabilities in a large enough series of tests, from which some parameters characterizing the pit initiation propensity can be drawn. The pitting frequency is: lIT
= -dP/P
dt
(1)
wherê Pis the survival probability6 [then (1 - P) is the pitting probability], and Tis referred to as the pitting period. ln a potentiostatic test, the pit inititiation time, t, is a probabilistic quantity who se average value is:
J>
dP
= - J~ P dt = J~
T
dP.
~~
Thus, if Tdoes not change during the test, it is equal to the average pit initiation time. ln a potentiokinetic test, the probability density of the pitting potential is: -dP/dE = PITv (3) with v being the scanning rate. The most probable pitting potential Ë is that for which -dP/dE is maximum; then
= dTlT
(4)
(dTldE)E=Ë = -llv.
(5)
dP/P and
The sample area, S, must be taken into account; for this purpose, the pitting probability woS is considered for an intinitesimal are a oS, where wis referred to as the elementary pitting probability3 (EPP) per unit area. If the surface is homogeneous, at least from a macroscopic point of view, the survival probability6 is: P
=
(1
-
WOS)SIOS
= exp
(-wS).
(\.y'
Such a formalism was tirst introduced by Weibull to account for the size effect ('failures in solids; it also gives the appropriate mathematical expression for 0: principle of the weakest link in a chain. 12Lastly, the PG R has to be considered as the EPP time derivative: g
= dw/dt =
-dP/(PS
dt)
=
lI(TS).
(7)
It is intended in this work to measure the pitting probabilities and the PGR, as a function of the metal-solution potential and of the solution chloride content, c, for. two types of 304 stainless steel, which differ by the nature of the non-metallic inclusions that they contain. The pit generation rate and the induction time, which are probabilistic parameters, will be related to the incubation time needed for the initiation of the tirst pit, which is a deterministic parameter. Next, some possible pitting mechanisms are reviewed, which are consistent with the tindings, and a general model is presented, accounting for the pit initiation kinetics, independent of the precise microscopic mechanisms which have to be considered in each particular experimental case.
-
Pit generation
971
on stainless steels
EXPERIMENTAL Testing apparatus For this study, an apparatus and an experimental elsewhere,13.14 was developed. The testing apparatus detector.
METHOD method, that is described more completely inc1udes electrochemical equipment and a pit
The electrochemical equipment comprises two vessels (Fig. 1). ln the preparation vessel, the test solution is thoroughly de-aerated, using a nitrogen-hydrogen (NH) gas fluxing. A connection tube transfers this solution to a second vesse!. This work vessel consists of a multichannel electrolytic cell, connected to a potentiostatic set. This cell contaÎns a counter electrode and 12 specimen holders are set on four levels, each inc1uding three holders. They are specially designed
holders. These to ho Id 15 mm
diameter sheet samples, whose exposed areas were restricted to a 10 mm diameter disk. A potentiostatic set assigns the sa me metal solution potential for each sample, with reference to an external electrode connected to the cell by a capillary tube. The anodic current is measured individually for each channel by a pit detector. It consists of an electronic device (Fig. 2) which supplies a signal when the anodic current on one channel exceeds a preset value corresponding to the onset of a stable pit. The circuit connected to thp' pit-formed specimen is th en open and the measurement goes on, until ail the samples are pitted. It was observed that the following factors were of lirst importance for the reproductibility of results: ~
(a) The solution must be carefully de-aerated, both in the preparation vessel (for 4 h at least) and in
the electrochemical
cell.
(b) The agitation induced by this flux must be kept as slight as possible, in order to avoid an artilicial increase of the pitting potentials. (c) The value of the anodic current, above which a channel is disconnected, must be chosen carefully. ln this work a critical current of 50 A was used, which fairly weil characterizes the onset of a stable pit. Test conditions The behaviour
of two types of 304 stainless
steel was investigated,
whose composition
(weight %) is
given in Table 1.
to reference electrode NH fluxing
Transfer tube NH
NH
double shell vessels
ev
\
-
\
~ / /
working electrodes
samples sam pie contact screw
ev
joint Specimen-holder(s)
Top view (working vessel)
FIG. 1. Schematic illustration of the electrochemical equipment. (a) Front view of preparation vessel and eIectrochemical cell (working vessel); (b) electrolytic cell, top view; (c) details of the specimen holders.
972
B. BAROUX
TABLE1. Steel
Cr
Ni
Si
Mn
C
S
A B
17.5 19
9 8.9
0.4 0.5
1.7 0.9
0.02 0.05
0.002 0.007
Mg (ppm) 74 0
The test medium was de-aerated NaCI aqueous solution (0.02-0.1-0.5 M and 2 M) at room temperature. Both potentiostatic and potentiokinetic tests (with various scanning rates from 1 to 1000 mY/min) were performed. The samples were disks, whose exposed area, S, was equal to 0.785 mm2 (10 mm diameter). Their surfaces were mechanically wet polished using a SiC paper (grade 1200), then air (aged for 24 hr before the test). The samples were maintained for 15 min at rest potential before the potentiostatic or potentiokinetic tests. Data analysis The pitting probabilities may be calculated at each time, using the number, i, of non-pitted samplh':" The survival probability may be estimated using P = ilN, where N is the total number of samples under consideration. Generally N = 36 was used (obtained by three successive measurements), a good approximation of P. The elementary pitting probability (EPP), is then:
fil = -(lIS)Ln(ilN).
which provides
(8)
ln potentiostatic conditions, the pit generation rate (PGR) is obtained by measuring the w(t) slope; in potentiokinetic
mode,
it is more
precise
to plot
g
Lnfilversus
E and to determine
({!
= dE/dLnw;
= Vdfil/dE = Vfil/({!.
one obtains:
(9)
Lastly, it is useful to consider a conventional pitting potential El (depending on the scanning rate v), for which fil = 1 cm-2; El can be measured with a better accuracy than the true pitting potential, Eo, for
Working electrodes
Electrochemicalcell
POTENTIOSTAT
1
r
-- - - -
1 1 1 Working electrode
VISU
FIG. 2.
Principle of the pits detector.
r - - lx 12)1
973
Pit generation on stainless steels which fIl
= O. If q;remains constant
in a range of potentials, fIl
Combining
equations
fIl
depends exponentially on E:
= exp«E - E1)/q;).
(10)
(5), (7), (9) and (10) leads to: Ë
= El
- q;LnS,
(11)
then
and
w(Ë) = liS Relationship (10) is no more suit able when E
failswhenS
cc;in these two casesdr/dE
P(Ë) = 0.368.
Eo, since both g and
(12) 0; in the same way, (11) cIearly
-cc and (5) issatisfiedwith E == Eo.
EXPERIMENTAL
RESULTS
Potentiostatic tests These tests were performed on steel A in NaCI (0.5 M); the EPP time dependence ... shown for several potentials (E) in Fig. 3a and 3b: when the potential is low enough, the PGR is a decreasing function of time. It is assumed that this decrease is due to a modification of the surface during the test, resulting in a lower pitting sensitivity. By contrast, for short potentiostatic holding times, g is an exponential function of E (Fig. 4). g
=H
exp (Ekp)
(13)
where cp = 17 mV and H do es not depend on E.
a 5 ..1
/
(10mV
'" 3 -..,E 2 a: a: ui 2
.i
b
a: a: ui
.
U
"-"
210mV
.. +
210mV
~x_xx
100
200
o
Il 1
1
1
1
1
time{sl Fm. 3. Potentiostatic tests in NaCI (0.5 M) on steel A: time dependence pitting probability (EPP) at different electrode potentials (V(SCE». times, (b) long holding times.
1111111111
10000 time/s) of the eIementary (a) Short holding
1
20000
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B. BAROUX
10'
./ 'O"'O"'l
i'0 ,,-' "-I 10-3b,.
10-41
/
./
1 200
l '-"
,
1
300
1
1
400
E(mV/SCE)
FIG. 4.
Potentiostatic tests in NaCI (0.5 M) on steel A: potential de pend ence of the pit generation rate (PGR) at t = O.
Potentiokinetic tests The results of the potentiokinetic tests depend on the scanning rate, v. Figures Sa and Sb show that, for steel A, the EPP may be approximated by an exponential function (see equation 10). Moreover, when the scanning rate, v, is higher than a critical value vc, comprising between 45 and 100 mY/min for steel A, ep remains constant and close to 17 mV (Fig. Sb). For lower values of v, epbecomes larger (Fig. Sa). Figure 6 shows the scanning rate dependence of El' For v < vc, El is a decreasir function of v; by contrast, when v > vc, El increases linearly with log v. For steel B, it was also found that rois an exponential function of E, with the samp ep value. However, the critic al scanning rate was found to be much smalk.. (vc < 10 mV/min) than for steel A. These results become clearer by considering the pit generation rate g. Figures 7a and 7b show that, for sufficiently high scanning rates, the PGR does not depend on v, and is the same both in potentiokinetic and short potentiostatic tests: with g = H exp (E/ep) ep = 17 mV (14) where H depends on the steel under consideration. Therefore ro
and El
= (Hep/v) exp
E/ep
= -epLn(Hep/v) = EII+epLnv
(15)
(16)
where EII = -epLnHep does not depend on v.
Figure 6 showsthat this relation is perfectly obeyed when v is larger than vc (dark line); for smaller v values, el is much higher (dotted line); it is assumed that, as in the
Pit generation 10
975
on stainless steels
a
N 1
E ~ a: a: ui
10mV/mn
10-2 100
200
300
400
E(mV/SCE)
b 10
N 1
E ~ a: a: ui
400mV/mn
10-2 100
200
300 E(mV/SCE)
400
FIG. 5. Potentiokinetic tests in NaCI (0.5 M): potential dependence of the elementary pitting probability, determined on steel A for various scanning rates, v; (a) v = 1-45 mV/min; (b) V = 100 mV/min-l V/min.
976
B.
350
-
BAROUX
--0
wu en > 300
o
0 0
.s w
000 '0_.....
/
0 0
250
10
100
1000
SCANNING RATE (mV/mn) FIG. 6.
Potentiostatic
tests in NaCI (0.5 M): effect of the scanning
pitting potential,
El' for which tir = 1 cm-2 (determined
rate on the conventional on steel A).
case of the long potentiostatic tests, this behaviour is due to a decrease in the pitting sensitivity, occurring during the long duration tests. The true pitting potential, Eo (for which g = 0), cannot be assessed by these experiments; however, estimating Eo by the lowest observed pitting potential, it is found that El - Eo ~ rp;as S = 0.785 cm-2 in this work, equation (11) can be used and then Ë
=
El'
The effect of the solution ch/oride content Both for steel A (Fig. 8) and steel B, so long as the scanning rate is greater than the critic al value, vc, the slope does not depend on the chloride content, c. Figure 9 shows the concentration dependance of El for some potentiokinetic tests performed on steels A and B, with v = 100 mY/min; for this scanning rate both w= 1 cm-2 and g = 0.1 cm-2 sec-l. AIso, it was found (Fig. 9): El
= El -
3rpLnc = El - 120 mV log c
(1'1)
where rp = 17 mV has the same value as before, and El is the conventional pittÏ1 potential for c = 1 M and depends on the scanning rate. Combining equations (16) and (17): EH
= Eli -
3rpLnc
(18)
where Eli is a standard pitting potential, independent of c and v. The PGR is then: g = K2 exp (E/rp)
(19)
where K does not depend on c and v. Then: Eli
= -rpLnKrp.
(20)
Some measurements on steel A at v = 10 mY/min (which is smaller than the critical scanning rate for this steel) were also performed; in this case, rpis close to 30 mV and it was found that: dEI/dLnc
= -2.5rp.
(21)
Pit generation
977
on stainless steels
a
10-1
1
U
:
'"
1
1:
10-2
cr:
ci c.: ro-3
200
300
400
E(mVlSCEI
b .10
" 100 D400 mVlmn " 1000 1
I!I potentiostatic
1 U ID III
'"
../ 1
'e
~ cr: ci c.:
1
.'. / ,.
.
.le steel B
1
/ 200
300
400
E(mVISCE)
FIG. 7.
Potentiokinetic tests in NaCI (0.5 M): potential dependence of the pit generation rate (PGR) under different scanning rates: (a) steel A; (b) steels A and B.
978
B. BAROUX
10
./ ./
./2M
.1
,
N
1
E
x.x
x.x
a: a: u.i 10-1
/ 0
'-'"'
1
1.
10-2 150
200
300
400
500
E(mV/SCE)
FIG. 8. Potentiokinetic tests: effects of the solution NaCI content on the elementary pitting probability (EPP), determined for steel A with a 100 mY/min scanning rate.
The same measurements performed on steel b at 10 mY/min give cp= 17 mV and: (22) which shows that the steel B critical scanning rate is smaller than 10 mY/min for ail the tested chloride concentrations. The effect of the steel cleanliness It is weil known that, for industrial steels, pits are initiated on non-metallic inciusions3,1S,16,17 but that not ail inclusion types act as nucleating points. UsÜ~ optical and scanning electron microscopy, it was verified that, both for steels A and B, pits occurred on inclusions or at the inclusion-matrix interfaces. Steel A, containing 74 ppm Mg, con tains about 20 inclusions per mmz, mainly of the MgO type, partially surrounded by Mg or Mn sulphides. Steel B con tains 30 inclusions per mmz, mainly of the CrzOrMnO type. These inclusion densities are not very different, despite the very large PGR difference between the two steels. For example, for E = 300 mV(SCE) in NaCI (0.5 M): '-'"'
gA = 2.10-1 cm-z ç1 gB = 10-4 cm-Z S-I,
corresponding
to E1A-EIB
= LoggA/gB = 130 mV;
itshows clearly that the inclusions
contained in steel A are much more harmful than those contained in steel B. If the pitting frequency 1IT1for a single pitting site is considered: (23)
Pit generation
979
on stainless steels
CHLORIDE CONTENT
600
500
300
10
FIG. 9. Potentiokinetic tests: effect of the solution NaCI content on the conventional pitting potential, El' determined with a 100 mY/min scanning rate (steels A and B).
where (} is the number of inclusions per unit area (2. 103 cm -2 for steel A and 3.103 cm-2 for steel B). For E = 300 mV(SCE), in NaCI (0.5 M), il = 104sec was found for steel A and 3.107 sec was found for steel B; it shows that the inclusion pitting sensitivity is 3 .103times largerin steel A th an in steel B. Moreover, the pitting probability for a single pitting site is very small, and it is only because the number of inclusions is very large that pitting may occur within a short time; from equations (7) and (23): (24) 'lere i and il are the pitting periods, respectively, for the whole sample and for a SIngle pitting site. jnthesÎS Equation (19) strongly suggests that three chloride ions are involved in the rate-determining initiation process, so that (19) may be rewritten as: g
= K[c exp (E/3cp)J3.
(25a)
With q as the electron charge, kB the Boltzman constant, and T the Kelvin temperature, e = kBT/q ==:25 mV at room temperature, cp= 17 mV may be simply expressed as: cp ==: 2Ef3.
(25b)
ln order ta simplify the following discussion, for each value of E and c, the function r( a) (whose argument a is a positive real number) is now considered and defined by:
r(a)
= c exp
(aE/e).
It is clear that equations (19) and (25a) may be rewritten as:
(26)
980
B.
g
BAROUX
= Kfn(a) = Ken exp
(naqE/kBT),
(27)
where n = 3 and a = 0.5. Then, rn acts as a pit initiation driving force. More generaIly, one can determine n and a from the chloride concentration and potential partial derivatives of lng:
= olnf"/oe = n olng/oE = olnrn/oE = 1/cp = nalt:. olng/oe
(28) (29)
Hoar and Jacob,18 working on anodically prepassivated stainless steels, found n = 2.5-4.5 and cp= 110-200 mV, which leads to a = 0.1. This value of n is in good agreement with these results but the very large observed cpvalues show that a heavily depends on the passivation conditions. ln the present work, the passive film is formed by a simple mechanical polishing followed by a 24 h ageing in air, and the corresponding a value is close to 0.5. However, if the test duration increases (e.g. . decreasing the potential scanning rate), cpincreases and a decreases; it appears tha( the passive layer is reinforced during the long duration tests, and that weIl passivated surfaces exhibit lower values than freshly poli shed ones. DISCUSSION
General kinetie model Pit initiation can be considered as a nucleation process followed by stabilization process;8.l6 the first one leads to the passive layer local breakdown, resulting in a direct contact between the base metal and the corrosive solution. Then the stabilization current increases markedly and part of the dissolved metallic cations are hydrolysed, resulting in a local acidification; if this dissolution current is high enough to maintain a sufficient local acidity, despite the cation dissolution towards the bulk solution, the pit nuclei cannot repassivate and a stable pit is generated. g
=
Àp*
(30)
where À is the pit nucleation rateS and p*, the probability of stabilizing the pit nuclel~ According to Crolet,16 a pit nucleus cannot develop when E is smaller than a stabilization potential Ep, very similar to the protection potential defined by Pourbr for pit propagation;19 following this ide a p* is equal to zero below Ep, and one aboV!; Ep. Williams,8 however, assumes that the repassivation is a Poissonian probabilistic process: p*
= exp
(-,uT*)
(31)
where 1/,11is the average pit nucleus lifetime and T* a criticallifetime, which tends toward one when either Eor e increases; as the repassivation process mainly depends on the hydrodynamic conditions in the corrosive solution, it is very likely that, in the case studied, T*= 0 and p * = 1 (otherwise the very simple relation27 would make no sense); then g
= À is both
the pit generation
and nucleation
rate.
. Pit nucleation is generally described as a deterministic process, characterized by an incubation time T'. ln order to explain the pit initiation probabilistic behaviour, we must assume that the incubation process does not necessarily lead to pit nucleation, but rather to a sensitized state from which a pit can occur; let us note p**
Pit generation
981
on stainless stee\s
as the transition probability between this sensitized state and the nucleated state; the pit nucleation frequency is thenp**h', where p** = 0-1. Therefore: À = (lp**h'
(32)
g = (lph'
(33)
and where p = p*p* *. The pitting periods i and il for whole sam pIe and for a single pitting site are then: (34) and i It may be supposed that the nucleation
-~idity variations
= i' /(P(lS). probability,
p**, is due to some local random
at the film solution interface. McDonald and coworkers caIculated the incubation time20 in the case where the passive film is a M203 pure oxide, containing some 02- and M3+vacancies. Following these authors, the passive film breakdown is due to the formation of some cation vacancies in this oxide, up to a critical amount. This ide a may be generalized for other passive film structures or breakdown mechanisms. It must first be assumed that breakdown occurs due to the accumulation, close to the pitting sites, of some critical point defects, the nature of which depends on the experimental conditions. With X being their concentration (per unit area), J+(E, c) their creation rate andr(X) their destruction rate. The net creation rate is: dX/dt = J+(E, c) - r(X).
(35)
ln the stationary state, the equilibrium concentration Xeqis given by: J+(E, c) = r(Xeq)
(36)
and the true pitting potential Eo by: r(Eo,
c) = r(Xcrit)
(37)
Where Xcritis the breakdown concentration of point defects. For E ~ Eo, (dX/dt) is - '1ual to J+(E, c) and the incubation time i' needed for reaching Xcritis then: i' = Xcrit/J+(E, c).
(38)
ln some particular cases, which are discussed in the following section, J+ is found to be proportion al to f"(a) (see equation 27), for some appropriate n and a values:
= const. r"(a) Eo = Eg - ncpLnc 1h'
(39)
(40)
where cp = (nalE) and Eg depends on the tested material.
For n = 3 and a = 0.5, cp= 17mV and then:
Eo= Eg - 120 mV 10glOc. When E ~ Eo, i' ~ 00 andÀ~
O. Moreover,
when E~
(41) +00, À tends towards a limit
value, À"" which does not depend on E and c.s A constant time, iO' must then be added to the incubation time given by equation (38); io may be interpreted as the
982
B. BAROUX
transient time before the beginning of the incubation process20and then: À-oo = p* *ho. Therefore, in the potential range defined by E ~ Eo and T' ~ To, À-and lIT' are proportion al to J+(E, e). The incubation process starts when the metal-solution interface [including the film (f), the metal substrate (m) and the corrosive solution (s) close to the passive film] is shifted from a previous stationary state (for which T' = 00). A relaxation time is needed to reach a new stationary state, during which J+ is larger than its new stationary value; if r does not change during this process, the net point defect creation rate (r - r) is no more equal to zero and the breakdown may occur (if the incub,ation time is shorter than the relaxation time). For instance, in the case (to be discussed more completely later ) where J+ is a function of the potential difference Ers through the film-solution (fs) interface, dErJdE = ars
(42a)
where arsis a parameter between 0 and 1. When E increases quickly, as it does in t........... short duration tests described in the preceding sections, its variations are concentrated at the fs interface and ars = 1; then Ers and J+ increase with E and an incubation
process starts; after a longer time, the potential repartition requilibrates and Ers decreases to its new equilibrium value, resulting in a new Xeqconcentration. If Xeqis smaller th an Xcrit the metal-solution interface is in a new stationary state and no pitting is awaited for; however, before this stationary state is reached, a local breakdown may occur, if the incubation time is shorter th an the relaxation time. The same reasoning may be done for quick local variations of the chloride concentration in the solution.
Ionie fluxes throughout the passive film (Fig. 10) ln this section, some general data are presented which are needed for the following: (a) The potential drop, Ers, across the film-solution interface (fs) is a function of the physical parameters which control the system; it depends on the electro potential, E, and on the solution pH. Assuming a linear dependence on E: ~
Ers = A + arsE
(42,-,
where arswas defined in equation (42a) and A does not depend on E (but may scale with the other parameters controlling the system, such as the passive thickness, the pH of the solution, etc.). (b) After Hoar and Jacob,18the metallic cations (M) can be extracted from the film by forming a transient soluble chloride complex MCln at the film-solution interface (fs), j ~ being the cation flux through fs;
j~ = constante" x exp (na'ErslE)
(43)
where the constant depends on the cation activity in the film, which may be assumed ta remain constant in short enough duration tests. 1::was defined ab ove and a' is a transfer coefficient. Combining (43) and (42b): j~ = K~r"(a)
(44)
where a = a' ars and K~ is independent of e and E, but may change with the solution pH; close to the non-metallic inclusions, this solution pH is lowered and j ~increases.
Pit generation
983
on stainless steels
-
.M
.v lm
1..
l
x,
.C~"
v
a
metal (m)
solution (s)
film (f) fs
mf
FIG. 10. Schema tic representation of the fluxes (j) of the chemical species, throughout the bulk metal (m), the passive film (f), and the corrosive solution (s) (see Discussion). The considered species are M = metal cations, V = cation vacancies (in m or f), Cl- = chio ride ions (in the s orf); their concentrations in m, for s are notedxM, xv, XC1-, with the subscript m, for s; in the paper xc;r is noted c.
(c) Cl- ions may be incorporated in the film; the adsorption rate jfrl- is proportional to eX exp (a' Er.le) (where a' is a transfer coefficient) and then: j'Clsr
=
KCl-r sf ( a )
(45)
where a = a' ars and Kfrl- does not depend on c and E. ln the stationary state, the Cl- desorption rate, j~l-, is obviously equal to the Cl-
adsorption rate, j frl-. After McDonald2o, cation vacancies (V) in the film are in equilibrium with the _fioccupied Cl- adsorption sites A: V + nA ~ null where n
= 3/2 if those
(46)
adsorption sites are some 02- vacancies in a M203 oxide film.
Other n values would be found for other film structures: for example, n = 3 if the adsorption sites are some OH- vacancies in a M(OH)3 hydroxide film. ln the stationarystate, the A sites are in equilibriumwith the solution Cl- ions; x1c x exp (Er.le) = constant;
xy(x1t = constant
(47)
and therefore: x y = constant
r"( ars)
(48)
with x1 and xy being the A and V concentrations in the film, at the fs interface (the activity coefficients are included in the constants). Furthermore, the flux of the cation vacancies throughout the film (j y) is found to be proportional to x y; then: jY = KYr"(ars) where KYdepends on the solution acidity.2o
(49)
984
B. BAROUX
(e) If the metal-film (mf) and the film-solution (fs) interfaces do not move, the vacancies are created at the fs interface by the cation fluxjt: and consumed at the mf interface, by submerging into the metal bulk (x~ being the vacancies concentration in the metal substrate close to the mf interface and j ~(x~) their submergence rate towards the bulk). ln the stationary state: (50) otherwise a critical amount of vacancies may be reached either in the film or in the metal substrate and thus cause the passive film breakdown. (f) Assessment of the acs and a' coefficients is not very easy. ln the first approximation, the transfer coefficient a' may be taken equal to 1/2. On the other hand, for short potentiostatic tests or high scanning rate potentiokinetic tests, the variations of E may be assumed to be concentrated at the fs interface; then, as far as quick variations of the electrode potential are concerned, acs may be taken to be equal to 1. Of course, for longer tests, the potential distribution inside the passi' film may change and acsdecreases.
Breakdown mechanisms (a) The case when the passivefilmbreakdown is due to an accumulationof metal vacanciesin the metal substrate willbe firstconsidered. Followingthe general mode!,
J+ = jt: andr = j~. For E ~ Eo, i' is given by equation (39), which is consistent with the present results if n = 3 (Hoar and Jacob mechanism), acs = 1 (potential variations concentrated at fs interface), a' = 0.5 (transfer coefficient) and thus a =
0.5. (b) The breakdown may also be due to an accumulation of vacancies in the passive film itse!f; then J+
= jt: andr = j{m'
For E ~ E(), relation
again; this mechanism is then also consistent with our results if n
(39) is found
= 3 and a = 0.5.Lin
et al.20studied the case where an accumulation ofvacancies is produced in the filmat the mf interface,
due to a difference
between j
present results, it must be postulated that n
n
= 3/2 as proposed by Lin et al.20
y and
j im; in order to explain
= 3 in the jY expression
the
(49) rather than
(c) From another viewpoint, the cations produced at the fs interface diffus,towards the bulk solution (flux j~) or are hydrolysed; the acidification rate is proportion al to Ut: - j~). Assuming that the film breakdown is produced b a local increase of acidity, J+ = j t: and r = j ~. The relation (39) remains valid for E ~ Eo. Following this view, the pit nucleation mechanism is the same as for crevice corrosion and is then enhanced at the metal-inclusion interfaces, which act as occluded cells. (d) Some workers2I.22feel that Cl- ions, which are incorporated in the passive film, may cause its breakdown, when their concentration xfJ- exceeds a critical value. ln this case J+ = j~r andr = /{. For E ~ Eo, one finds then that lh' is proportion al to r( a) (see eq uation 45). Such a Cl- dependence of i' cannot explain the present experimental results. Lastly, a MCl" chloride formation inside the passive film was also put forward;23,24the formation rate of the chloride is obviously proportion al to r"(a), with the appropriate a value, and a critical size of chloride is formed after an incubation time i' which is proportional to 1/r"(a). (e) It was seen above that several mechanisms are consistent with the present results, assuming n = 3 and a = 0.5 for short duration tests. For longer tests, the passive film composition or structure may change, resulting in other a values.
"
Pit generation
on stainless steels
985
Moreover, it is possible that the critical pitting mechanism becomes different when the passive film reinforces. More generally, several pitting mechanisms may be effective in the pit nucleation process; for example, Cl- adsorption can precede the MCln formation inside the film, or the film mechanical breakdown due to electrostriction forces;25similarly, penetration throughout the film must precede an eventual MCln formation at the mf interface, etc.; a chain of elementary pitting mechanisms has then to be considered and the rate determining step is the slowest of those successive mechanisms; several chains may compete and the rate determining process is then the fastest among ail the possible ones; following the more effective mechanism, the" E and e pit nucleation rate dependence may change from one experimental situation to another; then relation (27) cannot be generalized without caution to other experimental situations. SUMMARY AND CONCLUSIONS Using a statistical determination of the pitting potentials for two types of 304 stainless steel, the pit generation rate was determined, both in potentiostatic and potentiokinetic conditions, in neutral aqueous solutions with various NaCI concentrations. (1) Both the for short potentiostatic holding times and potentiokinetic scanning rates larger than a critical value Vc>the pit generation rate g is an exponential function of the metal-solution potential difference E and does not depend on the scanning rate: g
=Kx
en exp (naE/kBT)
(51)
where e is the chloride concentration, q the electron charge, kB the Boltzmann constant, Tthe Kelvin temperature, and n = 3 and a = 0.5; the constant, K, depends on the noxious non metallic inclusions contained in the steel. For long potentiostatic tests or for potentiokinetic scanning rate smaller than the critical value, g also depends on the test duration and the obtained pitting potentials have to be considered ry cautiously. - (2) The pit initiation process is the succession of a determistic incubation nrocess, characterized by an incubation time ri and of some probabilistic processes .aracterized by a pitting probability p ~ 1. If Qis the density of pitting sites, the pit nucleation rate is:
~
g
= Qp/T'.
(52)
Using a general point defects model the incubation kinetics are described by: dX/dt
= constant
[j+(E, c)
-
r(X)]
(53)
where X, j+ and j- are the concentrations, the creation rate and the destruction rate of the point defects; if Xcritis the critical concentration of point defects, the true pitting pitential, Eo, is given by: j+(Eo, e) = r(Xcrit).
(54)
When E ~ Eo, the incubation time may be approximated to: ri = Xcrit/J+(E, e), and then g is proportional to j+(E, e).
(55)
986
B. BAROUX
(3) ln the studied experimental case, J+ and gare (naqE/KBT). For short duration tests:
proportion al to r\a)
= en exp
a
= 0.5
and
n
= 3.
(56)
For longer tests, a and n decrease. This dependence is consistent with several possible incubation mechanisms, one ofthem being the accumulation ofvacancies in the metal substrate close to the metal-film interface. Under other experimental conditions, other incubation mechanisms may become effective and therefore other E and e dependences of pit generation rate are expected. (4) From a more general viewpoint, it is postulated that the incubation process occuis when the metal-solution interface is not in a stationary state, and that a defect creation rate J+ becomes much larger th an the corresponding destruction rate J-. Wh en ageing, the film may tend to another stationary state, resulting in a decrease of the pit generation rate. Acknowledgements-The author gratefully acknowledges G. Beranger and C. Lemaitre (Compiègne, France), F. Dabosi (Toulouse, France) and Prof. M. Pourbaix (Bruxelles, Belgium) for fruitful suggestions on this work. REFERENCES 1. Z. SZLARSKA-SMIALOWSKA,Corrosion-NA
CE 27,223
(1971).
2. M. JANIK-CZACHOR, G. C. WOOD and G. E. THOMSON, Br. Corr. J. 15,154 (1980). 3. B. BAROUX, Passivation and localized corrosion of stainless steels, in Passivity Semi-conductors (ed. M. FROMENT), 531. Elsevier, Holland (1983). 4. H. H. STREHBLOW,Werkst. und Korrosion 35, 437 (1984).
of Metals
and
5. K. E. HEUSLER and L. FISHER, Werkst. und Korrosion 27, 551 (1976). 6. T. SHIBATAand T. TAKEYAMA,Corrosion-NA CE 33,243 (1977). 7. T. SHIBATAand T. TAKEYAMA,8th 1. C.M. C. Maïnz, Vol. 1,246 (1981). 8. 9. 10. 11.
D. E. WILLIAMS, G. WESTCOIT and M. FLEISHMANN,J. Electrochem. 9th LC.M.C. (Toronto), 180 (1984). J. R. GALVELE, J. Electrochem. Soc. lI8, 529 (1976). J. L. CROLET, Rev. Coat. Corrosion 3,159 (1979).
12. W. WEIBULL, Proceedings Stockholm (1939).
of the Royal
Swedish
lnstitute
for
13. B. BAROUX, B. SALA, T. JOSSIC and J. PINARD, Mat. et Techn. French). 14. B. BAROUXand B. SALA, 7th Eur. Corr. Congress, Nice, France, 15. Z. SZKARSKA-SMIALOWSKA, Corrosion-NA CE 28,388 (1972).
Soc. 132,1787-1796
Engineering
(SIRPE
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No.
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Paris), 211 (1985) (fi
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16. J. L. CROLET, L. SERAPHINand R. TRICOT, Mem. Sei. Rev. Met. 74,647 17. P. POYET,P. COUCHINAVE,J. HAHN, B. SAULNIERandJ. (in French).
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Research,
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Y. Boos, Mem. Sei. Rev. Metal. 76,489(1979)
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F. LIN, C. Y. CHAO and D. D. MCDONALD, J. Electrochem. Soc. 1286,1194 P. HOAR, D. C. MEARS and G. P. ROTHWELL, Corros. Sei. 5,279 (1965). H. STREHBLOWand B. TITZE, Corros. Sei. 17,468 (1977). A. VERMILYEA,J. Electrochem. Soc. lI8, 529 (1971). OKADA, J. Electrochem. Soc. 131,241 (1984). SATO, Electrochim. Acta 16,1683 (1971).
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