Corrosion mechanism of nickel in hot, concentrated H2SO4

Article abstract of DOI:10.1149/1.1393952

Electrochemical techniques, complemented by weight change and ex situ X-ray spectroscopic measurements, were employed to characterize the corrosion of nickel in concentrated H₂SO₄ solutions. By use of a rotating cylinder electrode, it was found that corrosion is a mass-transport controlled process with the convective diffusion of nickel cations from a saturated NiSO₄ layer as its rate-determining step. The oxidizing nature of the acid solution leads to the formation of additional corrosion products including metastable NiS, and elemental sulfur along with NiSO₄, none of which is protective. When present on the surface, NiS establishes a galvanic interaction with the uncovered metal, significantly polarizing the anodic metal dissolution reaction. Since corrosion is mass-transport controlled, the resultant corrosion rate of the metal is unaffected during the galvanic-induced polarization.

Full text of DOI:10.1149/1.1393952

Corrosion Mechanism of Nickel in Hot, Concentrated ?H?2
SO?4
?
J. R. Kish, M. B. Ives and J. R. Rodda
J. Electrochem. Soc. 2000, Volume 147, Issue 10, Pages 3637-3646.
doi: 10.1149/1.1393952
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Journal of The Electrochemical Society, 147 (10) 3637-3646 (2000)
3637
S0013-4651(99)12-003-2 CCC: $7.00 © The Electrochemical Society, Inc.
Corrosion Mechanism of Nickel in Hot, Concentrated H SO4
2
J. R. Kish,a,z M. B. Ives, * and J. R. Rodda
b,
b
a
b
Pulp and Paper Research Institute of Canada, Vancouver, British Columbia, Canada V6S 2L9
W. W. Smeltzer Corrosion Laboratory, McMaster University, Hamilton, Ontario, Canada L8S 4L7
Electrochemical techniques, complemented by weight change and ex situ X-ray spectroscopic measurements, were employed to
characterize the corrosion of nickel in concentrated H SO solutions. By use of a rotating cylinder electrode, it was found that cor-
2
4
rosion is a mass-transport controlled process with the convective diffusion of nickel cations from a saturated NiSO layer as its
4
rate-determining step. The oxidizing nature of the acid solution leads to the formation of additional corrosion products including
metastable NiS, and elemental sulfur along with NiSO , none of which is protective. When present on the surface, NiS establish-
4
es a galvanic interaction with the uncovered metal, significantly polarizing the anodic metal dissolution reaction. Since corrosion
is mass-transport controlled, the resultant corrosion rate of the metal is unaffected during the galvanic-induced polarization.
©
2000 The Electrochemical Society. S0013-4651(99)12-003-2. All rights reserved.
Manuscript submitted December 2, 1999; revised manuscript received June 21, 2000.
Sulfuric acid (H SO ) is a highly corrosive, yet important, indus-
terized and involves a mass-transport-controlled process where the
rate-controlling step is the convective diffusion of ferrous ions from
2
4
trial inorganic chemical, being used at some stage in the manufacture
of a vast array of industrial products. The specification of appropri-
ate construction materials for containment of this acid is a continu-
ing challenge, especially for its production, where the nominal com-
position of the H SO -H O solution is between 93 and 98.5 wt %
2
3-27
a saturated layer of FeSO и7H O on the alloy surface.
Several
4
2
works have been reported on the anodic behavior of nickel in con-
2
8-30
centrated H SO ;
all show anodic polarization results in the for-
2
4
mation of a salt layer, which can impede the anodic current to a con-
siderable extent, depending on the temperature and concentration.
X-ray diffraction analysis of the crystalline phase formed during
polarization in concentrated H SO indicates that the film is most
2
4
2
H SO . Nickel is a major alloying element in the austenitic stainless
2
4
steels used as a construction material for various critical components
1-3
required for the production of H SO . Although primarily alloyed
2
4
2
4
2
9
to retain the austenite phase, nickel has a significant beneficial influ-
ence on the resulting corrosion resistance of stainless steel to con-
likely ␤-NiSO и6H O, which forms because of the decreased nick-
el sulfate solubility in the more concentrated solutions.
4 2
3
1
4,5
centrated H SO . Alloyed nickel promotes a spontaneous cyclic
The objective of this study was to characterize the electrochemi-
cal behavior of nickel in 93.5 wt % H SO in a attempt to elucidate
2
4
passivation and depassivation of the stainless steel alloy, which oth-
2
4
4,5
erwise would not occur. A fundamental understanding of the role
of nickel in stabilizing passivity is essential in the development of
more corrosion-resistant stainless steel alloys required to improve
both the thermal efficiency and the reliability of the production
its corrosion mechanism. The procedures used involved mostly
potentiodynamic polarization and corrosion potential measurements
complemented by weight change determinations, all under the
hydrodynamic condition provided by a rotating cylinder electrode,
and ex situ X-ray spectroscopic measurements.
6,7
process. Elucidating the corrosion mechanism of nickel in concen-
trated H SO should help considerably in this regard.
2
4
Corrosion in concentrated H SO solutions is a more complex
2
4
Experimental
process than in dilute H SO solutions because of the change in
2
4
Corrosion of nickel in 93.5 wt % H SO was studied under the
2
4
chemical structure. Molecular H SO appears in solutions contain-
2
4
hydrodynamic condition provided by a rotating cylinder electrode
(RCE). Test cylinder electrodes were prepared from a Nickel 270
UNS N02270) rod of stated purity >99.97%; all had areas of
ing about 70 wt % H SO and continues to increase in concentration
2
4
8
,9
as the mixture approaches 100 wt % H SO . Above about 84 wt
2
4
(
2
%
H SO , no free H O molecules exist since in the presence of an
2 4 2
2
.5 cm . A test electrode was mounted and rotated using a Pine
excess of molecular H SO , H O acts as a strong base, reacting with
2
4
2
Ϫ
4
ϩ 10-12
Instrument Company model AFMSRX rotator and MSRX speed
control unit. All electrodes used were wet-ground with emery paper
up to 400 grit, cleaned in soap solution, rinsed with methanol, dried
with absorbent paper, and then weighed immediately prior to im-
mersion. On removal, the electrodes were rinsed with distilled water,
cleaned in soap solution, rinsed with methanol, dried with absorbent
paper, and then weighed.
H SO to produce HSO and H O .
Therefore, concentrated
2
4
3
H SO solutions (>84 wt % H SO ) are essentially a solution con-
2
4
2
4
Ϫ
4
ϩ
sisting of molecular H SO and HSO and H O ions. The change
2
4
3
in chemical structure has a pronounced influence on the relationship
between the redox potential and acidity, which changes significant-
1
3,14
ly at about 70 wt % H SO .
This change coincides with the
2
4
appearance of undissociated H SO molecules, which can behave as
2
4
Concentrated 93.5 wt % H SO solutions were prepared from
2
4
oxidizing species and become reduced to various potential-depen-
1
5-18
British Drug House reagent grade 97-98 wt % H2SO4 and distilled
H O. The concentration of the prepared solutions was confirmed by a
dent sulfur-containing species with a valence lower than ϩ6.
Concentrated H SO solutions can act as either a reducing acid
2
2
4
sound velocity measurement. No attempt was made to aerate or deaer-
ate the acid solutions. A fresh acid solution was used for each test.
Test solutions were contained in a glass electrolysis cell, 80 mm diam
and 50 mm in high, capable of holding 250 mL of solution. The cell
was mounted in a water thermostat bath set at 60ЊC, which maintained
the acid solution temperature to within Ϯ0.5ЊC in all experiments.
The systems of electrodes employed in this study is described
schematically in Fig. 1. The counter electrode was a wire immersed
in its own glass compartment, 10 mm diam and 70 mm high, which
was connected to the electrolysis cell containing the test RCE
through the use of a porous glass plug. Isolation of the counter elec-
trode was used as a precautionary measure to prevent the possible
contamination of the test RCE with reduced sulfur-containing
or an oxidizing acid depending on the material exposed. For exam-
ple, in contact with carbon steel, the cathode reaction involved in
1
9
corrosion is hydrogen evolution, which is typical for a reducing
acid. In contact with copper, the cathode reaction involved in corro-
sion is the reduction of undissociated H SO molecules to various
2
4
2
0,21
reduced sulfur-containing species (SO , S, H S).
Regardless of
2
2
the cathodic reaction, the formation of solid corrosion products
2
2
FeSO иnH O for carbon steel and CuSO , Cu S, and CuS for cop-
4
2
4
2
1
8
per retard the corrosion rate to some degree. The corrosion mech-
anism of carbon steel in concentrated H SO has been well charac-
2
4
*
Electrochemical Society Active Member.
E-mail: jkish@paprican.ca
z
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3
638
Journal of The Electrochemical Society, 147 (10) 3637-3646 (2000)
S0013-4651(99)12-003-2 CCC: $7.00 © The Electrochemical Society, Inc.
Figure 1. Schematic of the electrolysis
cell employed in the study. WE ϭ working
electrode (RCE), CE ϭ counter electrode,
and RE ϭ reference electrode.
species, in particular elemental sulfur, which can form during the
cathodic electrolysis of the sulfuric acid solution.
tric electrodes (see Fig. 1), has successfully reproduced the mass-
transport-controlled corrosion of ferritic stainless steel in 93 wt %
1
5-18
3
8
The electrochemical behavior of nickel was measured using a
computer-controlled EG&G PARC model 273 potentiostat. All
potentials were measured against a platinum wire electrode, which
in 93.5 wt % H SO at 60ЊC has a measured potential of ϩ0.604 Ϯ
H SO at 60ЊC previously reported for a system of concentric
2 4
electrodes.
3
9
X-ray spectroscopic techniques, X-ray fluorescence (XRF) spec-
troscopy, and X-ray photoelectron spectroscopy (XPS) were em-
ployed to characterize the solid corrosion products. The XRF meas-
urements were carried out on a Philips PW 1480 XRF spectrometer.
This technique was employed to characterize the elemental compo-
sition of insoluble nonadherent corrosion products. The procedure
to collect the insoluble nonadherent products involved removing the
deposit from the surface of the electrode by rinsing the covered elec-
trode with distilled water and subsequent filtering. All deposits col-
lected in this manner were dried in air for at least 24 h prior to analy-
sis. The XPS measurements were carried out on a Perkin Elmer PHI
5500 system with a monochromated Al K␣ source. This technique
was employed to characterize the composition of insoluble adherent
corrosion products. The system collected the data using a pass ener-
gy of 29.4 eV with a takeoff angle of 75Њ. Sample preparation prior
to analysis involved rinsing the electrodes with methanol, cleaning
in an ultrasonic methanol bath, and drying using high purity nitro-
gen gas.
2
4
0
.006 V against a standard calomel electrode (SCE). A platinum ref-
erence electrode was chosen because it was used with success in the
1
8,32-34
oleum and concentrated H SO research of Arvía et al.
Fur-
2
4
thermore, a platinum wire was been successfully employed in com-
mercial anodic protection systems for containing concentrated
3
5
H SO . A platinum wire was employed as the counter electrode in
2
4
all polarization measurements. The scan rate was 20 mV/s for all
polarization measurements.
The procedure employed to verify a mass-transport-controlled
anodic dissolution involved comparing an estimated Sh, the Sher-
wood number (dimensionless mass-transfer rate), with that calculat-
ed from a correlation for the expected geometry as a function of the
Re, Reynolds number (dimensionless rotational velocity). See the
List of Symbols for definitions.
A correlation applicable to turbulent flow for a system of con-
centric electrodes with a central rotating electrode has been derived
3
6
by Eisenberg et al. and is expressed as
Results
Sh ϭ 0.079Re0.7Sc0.356
[1]
Corrosion of nickel in stagnant 93.5 wt % H SO at 60ЊC.—Fig-
2
4
ure 2 shows the corrosion potential of a nickel electrode in stagnant
3.5 wt % H SO at 60ЊC as a function of time. The potential quick-
where Sc, the Schmidt number, is a dimensionless fluid property char-
acterizing the relative thickness of the momentum and mass-transfer
boundary layers. This correlation has been confirmed for corrosion
studies of mild steel in 68 wt % H SO at 27ЊC for a system of con-
9
2
4
ly reaches a maximum of ϳϪ0.30 V within the first 2 h of expo-
Pt
sure, after which it begins a two-stage decay over a period of about
2
4
6
h before stabilizing at ϳϪ0.50 V . The two-stage decay consists
24
Pt
centric electrodes. Using a system of nonconcentric electrodes,
of an initial slow decay over a period of about 300 min (5 h) fol-
lowed by a fast decay over a period of about 60 min. The noncon-
tinuous nature of the slow decay is an artifact of the in situ SO2
analysis, which requires the periodic removal of a 10 mL solution
sample. The sensitivity of the potential during its decay to the dis-
turbance induced by solution removal provided an early indication
of the strong dependence on solution agitation as reported later.
A solid black deposit formed immediately after immersion and
covered most of the electrode surface. The black deposit remained
on the surface until the potential transition, after which is subse-
37
Rahmani and Strutt confirmed the Eisenberg et al. correlation 1 for
the corrosion of mild steel in 68 wt % H SO at 27ЊC, but found a sig-
2
4
nificant variation in the velocity exponent at higher acid concentra-
tions and temperatures. Analysis of the data results in the following
37
correlation for the corrosion in 93 and 98 wt % H SO at 40ЊC
2
4
Sh ϭ 0.079Re0.81Sc0.356
[2]
Both correlations were used as a basis for this study. Use of the cor-
relations is justified since the adopted RCE assembly of nonconcen-
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Journal of The Electrochemical Society, 147 (10) 3637-3646 (2000)
3639
S0013-4651(99)12-003-2 CCC: $7.00 © The Electrochemical Society, Inc.
Figure 2. Corrosion potential of a nickel electrode and the dissolved SO2
concentration in stagnant 93.5 wt % H SO at 60ЊC as a function of time
immediately after immersion.
Figure 3. Weight change of nickel electrode in stagnant 93.5 wt % H SO at
60ЊC as a function of time. Superimposed is the corrosion potential transient
2
4
2
4
from Fig. 1.
quently dissolved. After the potential transition, the nickel surface
has a film-free, dull gray appearance for about 120 min (2 h) until
the subsequent formation of a stable, yellow surface deposit. Al-
though the acid solution remained clear, after the 30 h exposure, it
have developed a yellow color. No visible gas evolution occurred
during the corrosion of nickel at either potential plateau. Hydrogen
gas evolution is unlikely since both potential plateaus are more pos-
itive than the equilibrium potential of the hydrogen evolution reac-
acid, but each removed after different exposure times. The weight
loss-time dependence of nickel consisted of an initial, apparent par-
abolic kinetic stage followed by a linear kinetic stage. All six sam-
ples removed during the apparent parabolic stage (10 h) consisted of
an adhered noncontinuous black deposit; the adherence decreasing
as the exposure time approached 10 h. The remaining three samples
removed during the linear stage were covered with a loosely adher-
ent yellow surface film. Therefore, the weight loss measurements of
samples containing the adhered black deposit are misleading since
they include the weight gained from the adherent black deposit.
Nonetheless, the weight loss data show that neither the black deposit
nor the yellow film is significantly protective.
1
3,14
tion, which is Ϫ0.607 V in 93.5 wt % at 25ЊC.
Therefore, some
Pt
cathode reaction other than H evolution occurred during the corro-
2
sion of the nickel electrode.
Superimposed on the corrosion potential-time plot in Fig. 2 is the
dissolved SO concentration in the acid solution as a function of
2
When comparing the release of SO with the weight loss as a
2
time during the corrosion of the same nickel electrode in stagnant
function of time, it is evident that the corrosion of nickel continues
9
3.5 wt % H SO at 60ЊC. The concentration of dissolved SO was
2
4
2
at an appreciable rate despite the absence of further SO generation.
2
analytically measured in situ during corrosion using iodometry as
4
0
Therefore, the cathode reaction involved in the linear stage of corro-
sion must involve the formation of products other than SO2.
Comparing the measured concentration of dissolved SO2 with an
expected concentration calculated from the weight loss of the single
nickel electrode after 30 h exposure provided additional evidence
that the cathodic process involved the formation of additional prod-
uct. Assuming that the corrosion of the single nickel electrode pro-
ceeds according to the reaction sequence
described by Hall. The SO concentration increased monotonical-
2
ly with time for 10 h before it became constant at 0.051 g/L (2.78 ϫ
Ϫ3
1
0
wt %). Since this steady-state concentration is significantly
4
1
lower than the equilibrium solubility of ϳ18 g/L, it is unlikely that
the acid became saturated with respect to SO . When comparing the
2
release of SO with the corrosion potential as a function of time, it
2
is evident that the release of SO occurred during the period prior to
2
the potential transition and not during the period after the transition.
Although the presence of SO in the acid supports a cathodic reac-
Ni ϭ Ni2ϩ ϩ 2eϪ
2
Anode:
tion involving the reduction of H SO to SO , it is not conclusive. It
2
4
2
Cathode: 4H SO ϩ 2e ϭ SO 42 Ϫ ϩ SO ϩ 2HSO ϩ 2H Oϩ [3]
Ϫ
Ϫ
is unclear whether SO was produced as a reaction product of nick-
2
4
2
4
3
2
el corrosion and/or the black deposit dissolution. For reasons dis-
Ni ϩ 4H SO ϭ NiSO ϩ SO ϩ 2HSO ϩ 2H Oϩ
Ϫ
Total:
2 4 4 2 4 3
cussed below, SO is believed to be produced as the main cathodic
2
product involved in a galvanic corrosion process taking place at this
potential plateau.
where 1 mol of nickel reacted to produce 1 mol of SO , with a 100%
2
current efficiency, then the SO concentration can be calculated from
2
The weight loss of the single nickel electrode measured after the
0 h exposure is 6.72 mg/cm . Such a measurement provides no
the weight loss using Faraday’s law. According to Reaction 3, the
2
2
3
30 h weight loss of 6.72 mg/cm corresponds to a theoretical SO
2
information regarding the protective nature of either the black or yel-
low surface. It is possible that the majority of weight loss occurred
during the period prior to the potential transition corrosion or during
the period after the transition. Making weight loss measurements
using multiple nickel coupons as a function of time provided more
information in this regard.
concentration of 0.160 g/L, which is significantly higher than the
measured 0.051 g/L and less than the equilibrium solubility of
18 g/L. Chemical analysis conducted to characterize the elemental
composition of the various solid corrosion products demonstrates
that other possible reduction products include sulfide ions and ele-
mental sulfur.
4
1
Figure 3 shows the weight loss of nickel in stagnant 93.5 wt %
H SO at 60ЊC as a function of time. The curve was constructed by
measuring the weight loss of nine nickel samples, all immersed at
approximately the same time in a glass cell containing 2000 mL
An XPS analysis conducted on a nickel sample after a 15 min
exposure provided information regarding the strongly adherent non-
continuous black deposit. Figure 4 shows the sulfur 2p spectrum.
The sulfur region possessed a strong peak and shoulder at 161.12
2
4
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3
640
Journal of The Electrochemical Society, 147 (10) 3637-3646 (2000)
S0013-4651(99)12-003-2 CCC: $7.00 © The Electrochemical Society, Inc.
Table I. Binding energy (BE) of sulfur in selected compounds.
Compound
Peak
Measured BE (eV)
Literature42 Be (eV)
NiS
NiSO4
2p3/2
2p
162.1
169.3
162.2
169.2
increased the maximum potential attained. The steady-state potential
after the transition has a more complex dependence of the rotational
speed. An increase in the rotational speed from 0 to 250 rpm in-
creased the potential from ϳϪ0.50 to ϳϪ0.45 V , where it re-
Pt
mained constant with a further increase to 500 rpm. The increase in
the rotational speed from 500 to 1000 rpm changed the stable poten-
tial after the transition from ϳϪ0.50 to ϳϪ0.62 V , where it re-
Pt
mained constant with a further increase to 2000 rpm.
Several qualitative observations regarding the rate control of the
various processes can be made by associating the potential behavior
with the formation and subsequent dissolution of a NiS deposit.
Since the time required for the potential of the nickel RCE to reach
its maximum is independent of the rotational speed, the formation of
NiS is likely not a mass-transport-controlled process. In contrast,
since the potential transition time is clearly sensitive to the rotation-
al speed, the dissolution of NiS is likely a mass-transport-controlled
process.
Figure 4. XPS sulfur 2p spectrum obtained from the surface of a nickel elec-
trode after 15 min exposure in stagnant 93.5 wt % H SO at 60ЊC.
Table II shows the influence of the rotational speed on the weight
2
4
loss of a nickel RCE during corrosion in 93.5 wt % H SO at 60ЊC.
2
4
An increase in the rotational speed from 250 to 2000 rpm increases
2
the weight loss from 0.44 to 12.12 mg/cm . Although a direct corre-
and 162.63 eV, respectively, and a small peak at 169.25 eV. Table I
lation between weight loss and the rotational speed cannot be con-
cluded from this data alone since the increase in weight loss may be
attributed to a higher rate of weight loss for a NiS-free surface, it can
be concluded when considering the anodic polarization behavior.
Figure 6 superimposes the potentiodynamic anodic polarization
behavior of a nickel RCE (1000 rpm) with and without a NiS surface
deposit in 93.5 wt % H SO at 60ЊC. Polarizing the potential in the
4
2
presents a literature comparison of the binding energies of sulfur
in the most probable species that may have appeared in this study.
Based on the comparison, it is concluded that a NiS deposit covered
the majority of the nickel surface. The presence of NiSO was like-
4
ly due to oxidation of the NiS deposit during exposure to the atmos-
phere prior to the XPS measurement. The most likely source of the
sulfide ion is the reduction of H SO molecules.
2
4
2
2
4
anodic direction produced a limiting current density (ϳ1 mA/cm )
Anticipating a subsequent chemical analysis, the loosely adher-
ent yellow film that formed during the 30 h single nickel electrode
corrosion test was collected. The yellow precipitate consisted of a
water-soluble component and a water-insoluble component.
The soluble component produced a green solution when dis-
solved in water, consistent with the formation of a hydrated nickel
2
ϩ
43
ion (Ni ). The yellow water-soluble component is consistent
aq
with anhydrous NiSO . If the solubility of NiSO in 93.5 wt %
4
4
H SO at 60ЊC is 0.12 wt %, extrapolated from the data reported by
2
4
4
4
Halstead and Lovey, then the time required for a nickel electrode,
with a dissolution rate of 0.24 mg/cm /h, to saturate the solution
2
with NiSO4 is about 17 h. This is consistent with experimental
observation.
The chemical composition of the yellow water-insoluble corro-
sion product was analyzed by XRF. The analysis showed that the
deposit consisted of >99 wt % sulfur (S) and <1 wt % nickel (Ni),
indicating that the yellow water-insoluble corrosion product is ele-
mental sulfur. Considering that the steady-state corrosion of nickel
did not involve the evolution of SO , the reformation of NiS, or the
2
evolution of H , it is reasonable to postulate that the cathodic process
2
involved the reduction of H SO molecules to sulfur.
2
4
Corrosion of nickel in agitated 93.5 wt % H SO at 60ЊC.—Fig-
2
4
ure 5 shows the influence of the rotational speed on the corrosion
potential of a nickel RCE in 93.5 wt % H SO at 60ЊC as a function
2
4
of time. Superimposed on the plot is the corrosion potential of the
nickel electrode in otherwise stagnant 93.5 wt % H SO at 60ЊC
2
4
reported above. The curves show that the rotational speed signifi-
cantly influences the potential transition time, the maximum poten-
tial attained prior to the transition, and the steady-state potential
attained after the transition. An increase in the rotational speed pro-
gressively decreased the potential transition time and progressively
Figure 5. Influence of the rotational speed on the corrosion potential of a
nickel RCE in 93.5 wt % H SO at 60ЊC as a function of time immediately
after immersion. represents steady-state potential in stagnant (0 rpm) acid
measured after 30 h exposure.
2
4
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Journal of The Electrochemical Society, 147 (10) 3637-3646 (2000)
3641
S0013-4651(99)12-003-2 CCC: $7.00 © The Electrochemical Society, Inc.
on a nickel RCE with an NiS deposit on its surface through the fol-
lowing relation
Table II. Influence of rotational speed on the weight loss of nick-
el RCE in 93.5 wt % H SO at 60ЊC.
2
4
il 


1


 d 


*
[4]
Sh ϭ
Rotational speed
rpm)
Exposure time
(min)
Weight loss
(mg/cm )
nF Cs Ϫ C  D
2

b

(
The nickel ion diffusion coefficient was calculated from the Wilke-
4
7
24
1
1
1
2
250
500
000
000
150
150
150
150
10.44
15.44
17.84
12.12
type extrapolation formulas as proposed by Ellison and Schmeal.
Figure 7 indicates that the anodic dissolution process of the nick-
el RCE with a NiS deposit on its surface is mass transport controlled
with the diffusion of nickel cations from a saturated NiSO layer as
4
its rate-determining step; the limiting anodic currents increased with
flow. An analysis of the data results in the following expression for
the mass-transfer process
over the potential range examined, independent of the starting poten-
tial and, thus the surface state. The limiting anodic current density
shows that anodic dissolution is the mass-transport-controlled pro-
cess involved in the corrosion of nickel conjectured above. Further-
more, this comparison shows that the NiS deposit has no protective
capability, consistent with the weight change measurements reported
above (see Fig. 3 and Table II).
Sh ϭ 0.079Re0.76Sc0.356
[5]
The best fit correlation lies between the Eisenberg et al. correlation
(Eq. 1) and the Rahmani and Strutt correlation (Eq. 2).
3
7
The similar magnitude of the limiting current indicates that the
rate-determining step in mass-transport-controlled anodic dissolu-
tion of nickel is identical, regardless of whether a NiS surface de-
posit is present on the surface. Therefore, the dissolution rate of NiS
is controlled by the rate-determining step in the anodic dissolution of
nickel. Since nickel has a similar response to anodic polarization in
concentrated H SO as does iron in its well-known sulfation
As discussed by Rahmani and Strutt, a possible explanation of
the observed increase in mass-transfer rate in highly concentrated
H2SO4, as compared to the Eisenberg et al. correlation (Eq. 1), in-
volves the extrapolation formula suggested by Ellison and
2
4
Schmeal to calculate the diffusion coefficient. The formula was
arrived at through measurements of the diffusion coefficient for fer-
rous ion in 68 wt % H2SO4 using a rotating platinum disk electrode.
Although an agreement between the model (Eq. 1) and the experi-
2
4
4
5,46
stage,
and forms a similar sulfate salt film, it is reasonable to
2
4
postulate that nickel has a similar rate-determining step as does iron;
the convective mass transfer of the metal cation from the saturated
metal sulfate layer.
mental results was found in 68 wt % H2SO4 using the formula, it
is possible that the formula underpredicts the diffusion coefficient of
ferrous ion (and nickel ion) acids of higher concentration. A possi-
ble explanation for the lack of agreement of the correlation of Eq. 5,
as compared to the Eisenberg et al. correlation (Eq. 1) and the Rah-
Mass transfer correlation.—To confirm whether the NiS dissolu-
tion process is controlled by the convective mass transfer of nickel
mani and Strutt correlation (Eq. 2), involves the solubility of NiSO4.
2
ϩ
cations (Ni ) from a saturated NiSO layer, an estimated Sherwood
4
The NiSO solubility used to estimate the Sherwood number was
4
number was compared to that calculated using the Eisenberg et al.
correlation (Eq. 1) and the Rahmani and Strutt correlation (Eq. 2)
and as a function of the Reynolds number (see Fig. 7). Table III lists
the magnitudes of all parameters used to estimate the Sherwood,
Schmidt, and Reynolds numbers for the comparison. The Sherwood
number was estimated from the limiting anodic current density made
Figure 7. Influence of rotational speed on the limiting anodic current densi-
Figure 6. Influence of NiS on the potentiodynamic anodic polarization be-
0.356
ty of a nickel RCE in 93.5 wt % H SO at 60ЊC, expressed as a Sh/Sc
-
2
4
havior of nickel RCE (1000 rpm) in 93.5 wt % H SO at 60ЊC.
2
4
Re relationship.
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3
642
Journal of The Electrochemical Society, 147 (10) 3637-3646 (2000)
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Table III. Hydrodynamic data for nickel mass-transfer correlation in 93.5 wt % H SO at 60ЊC.
2
4
3
53
D ϭ 7.05 ϫ 10Ϫ7 cm /s
2
␳
ϭ 1.785 g/cm
Ϫ2
Ϫ5
3 44
␮
ϭ 7.935 ϫ 10 g/cm s 54
d ϭ 1.27 cm
C ϭ 1.39 ϫ 10 mol/cm
s
3
C ϭ 0 mol/cm
b
n ϭ 2
F ϭ 96,485 C/mol
␻
rpm)
v
il
Re
Sh*
Sc
2
(
(cm/s)
(A/cm )
Ϫ3
1
500
000
500
000
133.23
166.46
199.70
132.93
1.01 ϫ 10
1.57 ϫ 10
2.34 ϫ 10
2.86 ϫ 10
1952
1904
2855
3807
1680
1056
1571
1919
62,900
62,900
62,900
62,900
Ϫ3
Ϫ3
Ϫ3
1
1
2
extrapolated from existing data, and it is possible that this value
under- or overpredicts the real solubility.
oxidative dissolution of the deposit and an appreciable bulk elec-
tronic conductivity. Metal sulfides such as galena (PbS), pyrite
Further support of the proposed mass-transfer correlation (Eq. 5)
was provided by measuring the corrosion potential transient behav-
ior as a function of the bulk nickel cation concentration (see Fig. 8).
An increase in the bulk concentration from 0 to 500 ppm progres-
sively increased the potential transition time from ϳ40 to ϳ150 min.
This is the expected response for a mass-transport-controlled NiS
dissolution process with the diffusion of nickel cations as the rate-
limiting step. An increase in the bulk concentration from 0 to
(FeS ), and covellite (CuS) oxidatively dissolve in the presence of
2
an oxidant with the formation of a metal cation and elemental sul-
4
8-50
fur.
their respective resistivity is sufficiently low to permit participation
The aforementioned metal sulfides are semiconductors, and
5
1
in galvanic dissolution couples. Peters et al. demonstrated that a
galvanic-induced enhanced leaching of galena (PbS) occurs when in
electrical contact with pyrite (FeS ). Another excellent example of a
2
galvanic interaction involving mineral sulfides is the enhanced
2
50 ppm by weight had no effect on the stable potential after the
leaching of a chalcopyrite (CuFeS ) bearing material when in elec-
2
5
2
plateau. A further increase in the bulk concentration to 500 ppm by
weight, however, increased the stable potential after the transition
from ϳϪ0.60 to ϳϪ0.45 V . Again, this is consistent with a mass-
trical contact with pyrite (FeS2).
Considering the difference in the equilibrium dissolution poten-
o
tials, E ϭ ϩ0.35 V
for the anodic dissolution of NiS
Pt
SHE
transport-controlled corrosion process with the diffusion of nickel
cations as the rate-limiting step. It is unclear whether the bulk con-
centration has an effect on the maximum potential attained since the
variance may be experimental uncertainty. The time required to
reach the maximum potential is essentially independent of the bulk
nickel ion concentration.
NiS ϭ Ni2 ϩ S ϩ 2eϪ
ϩ
[6]
[7]
o
and E ϭ Ϫ0.25 VSHE, of the anodic dissolution of nickel
Ni ϭ Ni2 ϩ 2eϪ
ϩ
Influence of NiS on resultant corrosion potential.—A possible
mechanism through which the NiS deposit influences the corrosion
potential of nickel involves a galvanic interaction between the de-
posit and the uncovered metal. A galvanic interaction requires an
it is reasonable to assume that the NiS-H SO corrosion potential is
2
4
more noble than the Ni-H SO corrosion potential. Therefore, dur-
2
4
ing a galvanic interaction, NiS would be the cathodic phase and
Figure 9. Anodic polarization behavior of a nickel RCE (1000 rpm) without
NiS on its surface superimposed with cathodic polarization of nickel RCE
Figure 8. Influence of the bulk solution nickel cation concentration on the
corrosion potential of a nickel RCE (1000 rpm) in 93.5 wt % H SO at 60ЊC
as a function of time immediately after immersion.
2
4
(
1000 rpm) with NiS on its surface in 93.5 wt % H SO at 60ЊC.
2 4
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Journal of The Electrochemical Society, 147 (10) 3637-3646 (2000)
3643
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nickel the anodic phase. From an electronic conduction point of
view, NiS should be capable of sustaining a galvanic interaction
since its bulk electrical resistivity is 2-4 ϫ 10 ⍀ m.
NiS formation.—Immediately after immersion, nickel corrodes at a
relatively high rate with the formation of H S according to the fol-
2
Ϫ7
45
lowing reaction sequence
Support for a galvanic interaction is provided by superimposing
the anodic polarization of a nickel RCE without NiS on its surface
ϩ
Anode:
4Ni ϭ 4Ni2 ϩ 8eϪ
Cathode: 9H SO ϩ 8e ϭ 4SO 42 ϩ H S ϩ 4H O ϩ 4HSOϪ [8]
Ϫ
Ϫ
ϩ
with the cathodic polarization of 93.5 wt % H SO on a nickel RCE
2
4
2
4
2
3
4
with NiS on its surface for various magnitudes of the cathode/anode
surface area ratio, ␪ (see Fig. 9). As ␪ is increased from 0.01 to 1, the
4Ni ϩ 9H SO ϭ 4NiSO ϩ H S ϩ 4H O ϩ 4HSO Ϫ
ϩ
Total:
2 4 4 2 3 4
galvanic potential, E , the potential at which the anodic current
g
The cathodic reaction is strongly polarized to achieve the corrosion
current, as indicated by the negative corrosion potential, albeit unsta-
ble, measured immediately upon immersion. The degree of polariza-
equals the cathodic current, increases from ϳϪ0.62 to Ϫ0.28 V .
Pt
The series of curves demonstrates how the potential of nickel could
change in a galvanic interaction with NiS during the growth and dis-
solution of the NiS deposit.
tion is sufficient to promote the formation of H S, which is the pri-
2
mary cathode reaction (H SO reduction) at such a degree of polar-
2
4
1
7
ization. The relatively high reaction rate and solution viscosity
Discussion
result in a rapid buildup of H S at the metal-solution interface. The
2
Corrosion mechanism of nickel in 93.5 wt % H SO .—A possi-
cathode formation of H S from the reduction of H SO molecules
2
4
2
2
4
ble mechanism through which nickel corrodes in 93.5 wt % H SO
provides a source of the required sulfide anions.
2
4
is depicted in Fig. 10. The mechanism consists of the following four
stages.
Once formed, H S provides an alternative reaction path for sur-
face nickel atoms. Thus, during corrosion, nickel atoms can either
2
Figure 10. Schematic of nickel corrosion mechanism in 93.5 wt % H SO at 60ЊC.
2
4
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644
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anodically dissolve with the formation of a soluble cation according
to Reaction 7 or they can anodically dissolve with the formation of
insoluble NiS according to
As NiS dissolves during galvanic corrosion, ␪ decreases and thus
the galvanic potential decreases. Figure 9 demonstrates how the gal-
vanic potential changes with ␪ during the dissolution stage. As ␪ de-
creased from 1 to 0.01, the galvanic potential decreased from
Ni ϩ H S ϭ NiS ϩ 2H ϩ 2eϪ
ϩ
[9]
2
ϳϪ0.28 to Ϫ0.62 V . Considering the potential transients measured
Pt
Therefore, after the initial formation of H S, the corrosion of nickel
during the corrosion of nickel, the finite residence time of NiS re-
sults from its mass-transport-controlled dissolution rate being sig-
nificantly slower than its activation-controlled growth rate.
2
occurs according to the following reaction sequence, which makes
ϩ
2Ϫ
use of the relation 2H ϩ SO4 ϭ H SO
2
4
3Ni ϭ 3Ni2ϩ ϩ 6eϪ
Steady-state stage.—The galvanic interaction no longer exists once
all the NiS dissolves. At this point, the steady-state corrosion of nick-
el occurs, proceeding according to the following reaction sequence
Anode:
Ni ϩ H S ϭ NiS ϩ 2H ϩ 2eϪ
ϩ
2
[10]
Cathode: 9H SO ϩ 8e ϭ 4SO 24 Ϫ ϩ H S ϩ 4H O ϩ 4HSO 4Ϫ
Ϫ
ϩ
3Ni ϭ 3Ni2ϩ ϩ 6eϪ
Anode:
2
4
2
3
4Ni ϩ 8H SO ϭ 3NiSO ϩ NiS ϩ 4H O ϩ 4HSOϪ
ϩ
Cathode: 8H SO ϩ 6e ϭ 3SO 42 Ϫ ϩ S ϩ 4H Oϩ ϩ 4HSOϪ [14]
Ϫ
Total:
2
4
4
3
4
2
4
3
4
3Ni ϩ 8H SO ϭ 3NiSO ϩ S ϩ 4H O ϩ 4HSOϪ
ϩ
resulting in the formation of a NiS surface deposit. The solid-state
mechanism is consistent with the formation of an initial strongly
adhered surface deposit and an initial corrosion potential transient
that is essentially independent of the electrode’s rotational speed.
It is rather difficult to comment on the nucleation process be-
cause heterogeneities may catalyze nucleation, and because of the
complexity of the process when heterogeneities are not involved. It
is reasonable to consider, however, that nucleation involves a num-
ber of nuclei one monolayer thick on the nickel surface from which
the growth stage commences.
Total:
2 4 4 3 4
Without NiS on the surface, the cathode reaction occurs once
again on the nickel surface. Since the anode reaction is now mass
transport controlled, not activation controlled as in the NiS formation
stage, it is the kinetically slowest reaction and controls the overall
rate of corrosion. The cathode reaction in this stage depolarizes, as
compared to the NiS formation stage, since it does not need to be dri-
ven as hard to balance the current. The extent of the depolarization is
sufficient such that the primary cathode reaction product at the cor-
rosion potential now becomes elemental sulfur and not H S, as with
2
NiS growth-galvanic polarization stage.—The growth of NiS fol-
lowing nucleation involves the formation of a thick, noncontinuous
film on the surface. A thick film is a likely result of the reasonable
good electronic and ionic conductivity of the NiS phase. A noncon-
tinuous film is a likely result of the excess of nickel equivalents dis-
the NiS formation stage. Therefore, without the generation of H S as
the primary cathode reaction product, NiS does not reform.
2
Modeling the galvanic potential behavior.—According to the gal-
vanic corrosion model, Eg is a function of ␪, which is a function of
time. Therefore, by modeling the NiS growth and dissolution kinetics
and determining the corresponding Eg transient, the galvanic cou-
pling model can be validated. As pointed out above, the exact NiS
nucleation and growth mechanism is unknown and is rather difficult
to determine experimentally. Nonetheless, an attempt based on the
physical situation described below for nickel corrosion in 93.5 wt %
H SO at 60ЊC successfully reproduced the general form of the E -t
2
ϩ
solving a soluble cations (Ni ) coupled with the limited supply of
the reactant H S at the metal-solution interface (discussed below).
2
Once its growth stage commences, NiS establishes a galvanic
interaction with the nickel substrate. During the interaction, the cath-
ode reaction involved in the corrosion of NiS
Ϫ
ϩ
4
H SO ϩ 2e ϭ SO 42 Ϫ ϩ SO ϩ 2H O ϩ HSOϪ [11]
2 4 2 3 4
2
4
g
dependence and thus supported the concept of a galvanic interaction.
As a first approximation, it is reasonable to consider that the
growth of NiS is controlled by the rate at which nickel atoms anod-
ically dissolve to form NiS according to Reaction 9. The corre-
sponding growth rate of the anodic deposit can be expressed mathe-
matically as follows
is enhanced on NiS sites, whereas the anode reactions involved in
the dissolution of nickel (Reactions 7 and 9) are enhanced on nickel
sites. The growth of NiS continues despite the discontinued cathode
production of H S due to the presence of excess H S at the metal-
2
2
solution interface and terminates once Reaction 9 consumes all the
excess H S. The measured apparent corrosion potential of nickel is
2
now the galvanic potential of the NiS-Ni couple and is a function of
both the cathode and anode kinetic parameters and ␪.
dV
dt
IM
ϭ
[15]
nF␳
NiS dissolution-galvanic depolarization stage.—The magnitude of ␪
at the instant the growth process terminates is relatively large since
the noncontinuous NiS film covers the majority of the nickel surface.
The large ␪ coupled with the high cathodic current for the reduction
of H SO molecules on NiS produce a galvanic situation where the
Assuming that NiS grows as a disk with radius r and constant height
h on a nickel surface with radius r (constant), the change in volume
o
at a constant height is governed by the change in radius according to
dV ϭ ␲hrdr
[16]
2
4
galvanic potential is controlled essentially at the corrosion potential
for the oxidative dissolution of NiS. Therefore, the anode reaction
When metal dissolution controls the anodic growth rate, the current
is given by
NiS ϭ Ni2 ϩ S ϩ 2eϪ
ϩ
[12]
I ϭ i(A Ϫ A)
[17]
o
takes place with a significant rate along with the cathode reaction
Reaction 11) on NiS. The significance of this result is that the dis-
solution of the Ni-NiS galvanic interaction proceeds according to the
following reaction sequence
Substituting Eq. 16 and 17 into Eq. 15, and integrating and rear-
ranging, gives
(



t
r2 ϭ r o2 Ϫ exp Ϫ
[18]
Ni ϭ Ni2 ϩ 2eϪ
ϩ

Anode (Ni):
␶

g 
Anode (NiS):
NiS ϭ Ni2 ϩ S ϩ 2eϪ
ϩ
where ␶ ϭ nF␳h/2iM.
g
Cathode (NiS): 8H SO ϩ 4e ϭ 2SO 24 Ϫ ϩ 2SO2
Ϫ
[13]
Considering now the NiS dissolution kinetics, it is reasonable to
assume that the rate is controlled by the diffusion of nickel ions
2
4
ϩ
Ϫ
4
ϩ 4H O ϩ 4HSO 00 0
2ϩ
3
(Ni ) into solution from the NiSO film-solution interface. The
4
anodic polarization behavior of the nickel RCE and the effect of the
electrode’s rotational speed on the weight loss of a nickel RCE sup-
port the assumption of mass-transport-controlled dissolution. When
Total:
Ni ϩ NiS ϩ 8H SO ϭ 2NiSO ϩ S ϩ 2SO
2 4 4 2
ϩ 4H Oϩ ϩ HSOϪ
3
4
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mass transport controls the dissolution rate, the change in volume
with time is given by
␳
dV
DAo
ϭ
(C Ϫ C )
[19]
s
b
M dt
␦
Assuming NiS dissolves as a disk of initial radius rm and constant
height h on a nickel surface of radius r and C ϭ 0, then substitut-
o
b
ing Eq. 16 and 19, integrating, and rearranging gives
1
t
r2 ϭ r2
Ϫ
[20]
m
2
r
␶
d
o
where ␶ ϭ ␳␦h/DMC .
d
s
The corrosion potential of a nickel RCE, when rotated at
1
000 rpm is 93.5 wt % H SO at 60ЊC, reached a maximum after
2
4
about 12 min exposure and then proceeded to decay, first slowly and
then more rapidly, for about 36 min before attaining its steady state
(Fig. 5). It is reasonable to postulate that the growth of NiS occurred
during the initial 12 min period, whereas the dissolution of NiS
occurred during the next 36 min period. By assuming that the growth
rate is significantly higher than the dissolution rate at all times dur-
ing growth such that the dissolution rate is neglected, then Eq. 18
determines the Eg-t dependence during the initial 12 min exposure
(
(
NiS growth) and Eq. 20 determines the Eg-t during the next 36 min
NiS dissolution). The Eg-t dependence corresponding to either
Eq. 18 or 20 can be determined graphically using the nickel and
NiS(Ni) polarization curves as shown in Fig. 9.
It is believed that the NiS deposit forms a noncontinuous film on
m
the surface of nickel, and, therefore, ␪ attains a maximum value ␪ .
m
Based on the aforementioned assumptions, ␪ reaches ␪ at the point
at which the growth process terminates; i.e., after 12 min exposure.
For the graphical determination of the Eg-t dependence, it is assumed
that ␪m ϭ 3, which corresponds to a surface coverage, A/A ϭ 0.75.
o
Figure 11 shows ␪, derived from Eq. 18 and 20 using the assump-
tions described above and Eg, determined graphically using Fig. 9, as
a function of time during the growth and subsequent dissolution of the
NiS deposit. Superimposed in the Eg-t plot is the measured potential
transient of nickel when rotated at 1000 rpm in 93.5 wt % H SO at
Figure 11. Theoretical changes during growth and dissolution of NiS deposit
on nickel in 93.5 wt % H2SO4 at 60ЊC (1000 rpm). (a) ␪ as a function of time,
(b) NiS-nickel galvanic potential as a function of time superimposed with the
2
4
measured corrosion potential of a nickel RCE under identical conditions.
60ЊC. The theoretical and experimental curves are clearly of the same
form, and the agreement is good except at long times. It appears that
the galvanic interaction theory fit the facts reasonably well despite the
fact that the exact NiS nucleation and growth process is unknown.
Schmuki of the National Research Council Canada and J. McAn-
drew of McMaster University during the XPS and XRF analyses,
respectively, is gratefully appreciated.
Conclusions
Potentiodynamic polarization and corrosion potential studies on
a nickel RCE complemented with ex situ X-ray spectroscopic meas-
urements led to the following conclusions regarding the corrosion
The Pulp and Paper Research Institute of Canada assisted in meeting the
publication costs of this article.
List of Symbols
mechanism of nickel in hot concentrated H SO .
2
4
Mass transfer correlation
1
. Concentrated 93.5 wt % H SO acts as an oxidizing acid when
3
2
4
Cb
Cs
d
bulk solution concentration, mol/m
saturation concentration, mol/m
diameter of RCE, m
in contact with nickel. The cathodic process involves the reduction
of H SO molecules to various sulfur-containing species, SO , ele-
3
2
4
2
2
mental sulfur, and H S. Corrosion leads to the formation of several
D
F
diffusion coefficient, m /s
Faraday’s constant, 9.6485 ϫ 10 C/equiv
2
4
surface products including NiS, NiSO , and elemental sulfur, none
4
2
of which is protective.
il
limiting anodic current density, A/m
k
n
Re
Sc
Sh
v
mass transfer coefficient, m/s
number of electrons in reaction
Reynolds number, ␳vd/␮
Schmidt number, ␮/␳d
2. Corrosion of nickel is a mass-transport-controlled process with
the convective diffusion of nickel cations from a saturated layer of
NiSO as its rate-determining step.
4
3
. Prior to establishing a steady-state, the corrosion of nickel pro-
Sherwood number, kd/D
fluid velocity, ␻d/2, m/s
fluid viscosity, poise
ceeds with the formation and subsequent dissolution of a NiS
deposit. When present on the surface, NiS establishes a galvanic
interaction with the uncovered metal, significantly polarizing the
nickel anodic dissolution reaction. The anodic dissolution rate is
essentially unaffected during the galvanic-induced polarization since
the rate is mass transport controlled.
␮
␳
3
fluid density, kg/m
␻
rotational speed, rad/s
Kinetic modeling
2
A
area covered by deposit, m
2
Ao
total area, m
Acknowledgments
3
Cb
Cs
D
bulk solution concentration, mol/m
The financial support of the Natural Science and Engineering
Council of Canada is gratefully appreciated, both in the provision of
experimental supplies and in the provision of a student stipend. The
experimental assistance of M. J. Graham, G. I. Sproule, and P.
3
saturation concentration, mol/m
2
diffusion coefficient, m /s
Eg
F
galvanic potential, V
Faraday’s constant, 9.6485 ϫ 10 C/equiv
4
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3
646
Journal of The Electrochemical Society, 147 (10) 3637-3646 (2000)
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h
i
I
M
n
r
rm
ro
t
V
␦
␳
␪
height of disk cap, m
20. C. W. Rogers, J. Chem. Soc., 254 (1926).
21. E. G. Kremko, I. A. Kakovskii, and L. D. Sheveleva, Prot. Met., 20, 73 (1985).
2
anodic current density of uncovered metal, A/cm
anodic current of uncovered metal, A
molecular weight of deposit, kg/mol
number of electrons in reaction
radius of disk deposit, m
maximum radius of disk deposit, m
radius of metal surface, m
time, s
volume of disk deposit, m
diffusion layer thickness, m
density of deposit, kg/m
surface area ratio, A/(A -A)
2
2. G. Gilli and F. Zucchii, Corros. Sci., 8, 801 (1968).
2
3. L. A. Poluboyarteseva, P. I. Zarubin, and V. M. Vobakovskii, J. Appl. Chem. USSR,
3
6, 1210 (1963).
2
2
4. B. T. Ellison and W. R. Schmeal, J. Electrochem. Soc., 125, 524 (1978).
5. T. N. Andersen, N. Vanorden, and W. J. Schlitt, Met. Trans. A., 11A, 1421 (1980).
26.
S. W. Dean and G. D. Grab, Mater. Perform., 24, 22 (1985).
27. S. L. Pohlman and T. N. Andersen, Mater. Perform., 26, 41 (1987).
28. U. Ebersbach, K. Schwabe, and K. Ritter, Electrochim. Acta, 12, 927 (1967).
29. G. Gilli, P. Borea, F. Zucchi, and G. Trabanelli, Corros. Sci., 9, 673 (1969).
3
3
0. M. Turner, G. E. Thomson, and P. A. Brook, Corros. Sci., 13, 985 (1973).
3
31. W. D. Halsted and B. F. Lovey, J. Appl. Chem. Biotechnol., 27, 585 (1977).
3
2. A. J. Arvía and J. W. S. Carrozza, Electrochim. Acta, 11, 1641 (1966).
o
3
3. J. W. S. Carrozza, H. A. Garrera, and A. J. Arvía, Electrochim. Acta, 14, 205 (1969).
␶
dissolution time constant, ␳␦h/DMCs
growth time constant, nF␳h/2iM
d
34. A. J. Arvía, H. A. Garrera, and J. W. S. Carrozza, Electrochim. Acta, 16, 79 (1971).
35. O. L. Riggs, Jr. and C. E. Locke, Anodic Protection Theory and Practice in the Pre-
vention of Corrosion, Plenum Press, New York (1981).
␶
g
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