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Text S1
Experimental Methods
The experimental studies were conducted using an 8 mm diameter AISI 316
stainless steel disk electrode. The nominal composition was 0.13 % C, 0.31% Co,
18.18% Cr, 0.38% Cu, 1.75% Mn, 2.40% Mo, 12.25% Ni, 0.016% S, 0.35% Si, and the
balance Fe. It was grinded and polished to 600 grit polishing paper followed by a 1 µm
diamond paste polish. The sample was then cleaned with ethanol in an ultrasonic bath.
To ensure that the current peaks can be associated with events detectable by EMSI and
contrast enhanced microscopy, the entire sample was coated, excluding the imaged area
varying between 1x1 mm2 and 130 µm diameter, with Apiezon wax. The specimen was
submerged at 22°C in 0.05 M NaCl solution made with reagent grade chemicals in
Milli-Q (18 MΩ resistance) water.
Experiments have been carried out both potentiostatically and
potentiodynamically and the distribution of pitting sites on the electrode surface
analyzed after both types of experiments. The experiments in which simultaneous in
situ real-time microscopic visualizations and current recordings were made were
obtained under potentiodynamic conditions. A potentiostat controlling the
electrochemical potential was used to scan the electrode from -400 mV to +600 mVAgCl
(i.e. -93 mV to +907 mVNHE) at 1 mV/s. The total sample current was measured and
stored on a computer and simultaneously on the sound track of a video recorder, by
means of a voltage to frequency converter. Great care was taken to synchronize the
video and the current measurements with flashes of 1/2000s easily identified on the
videos and the computer.
The sample was placed in a vertical configuration in an electrochemical cell
containing a AgCl reference electrode and a platinum counter electrode. The cell is a
cuvette with specially arranged windows, which allow the light of a HeNe-Laser (20
mW) to pass perpendicularly through the glass. Light propagates through the
electrolyte, is reflected at about 70° off the sample, and exits the system perpendicularly
through the opposite side, as indicated in Fig. S1. The laser beam is elliptically
polarized by a combination of a Glan-Thompson prism and a quarter wave plate in such
a way that after reflection from the sample surface only linearly polarized light is
leaving the cuvette. A second Glan-Thompson prism is oriented such that nearly all
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intensity is removed from the imaging path. The sample is magnified 8 times by a lens
onto a CCD chip. The CCD chip is tilted about 75° away from the optical axis, thereby
compensating for most of the distortion.
A plane homogeneous sample will display a uniform blank image, the "null"
image. However, local changes on the surface, e.g. areas with a different oxide layer
thickness, are detected as locally brighter spots by the CCD camera. To improve the
quality and contrast of the images we employ an image-processing unit, the Argus 20,
from Hamamatsu. It is capable of real time background subtraction, so that most of the
inhomogeneities of the surface and interference patterns originating from the laser light
are not visible. The subtracted and contrast-enhanced video signal is stored on a S-VHS
video recorder.
The origin of contrast for EMSI can be described in the following way: Light,
when reflected from a surface, changes its polarization. The magnitude of change,
expressed by the complex reflection coefficients rp and rs , (p, s denoting parallel and
vertical direction of the electric field) depends on the angle of incidence and the index
of refraction and can be calculated from the Fresnel equations. These equations define
these reflection coefficients as the ratio of the amplitude of the reflected wave to the
amplitude of the incident wave for a single interface. The reflectance, R, is defined as
the ratio of reflected intensity to the incident intensity. In any ellipsometric experiment,
the principal values to be determined are the phase change ∆, and the ratio of incident to
reflected amplitudes, Ψ.
The change in phase, ∆, which occurs upon reflection is defined as ∆ = 1 - 2
where i are the phase differences between the p and s components of the incoming and
outgoing waves, respectively. It is safe to assume that changes of the phase due to ion
concentrations differences in the electrolyte in the vicinity of a pit can be neglected
because the change in refractive index occurs on a length scale well above the
wavelength of the imaging light and causes no reflection. Therefore, the phase changes
occurring upon reflection of the light result only from the stainless steel and its oxide
layer. Generally, changes in ∆ are much more significant so that amplitude changes
expressed by their ratio Ψ are commonly neglected. This line of argument leads to the
interpretation of the bright areas in the EMSI images as changed oxide films. Careful
inspection of Movie S1A further strengthens this view of an apparent depletion of the
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oxide film during pitting: during the rise of the electrochemical current the brighter
regions enhance the underlying surface features, like scratches and roughness of the
stainless steel, indicating directly that the EMSI signal is originating from the surface
and not from the electrolyte in front of it.
Simultaneously the sample was 8-times magnified onto a CCD chip with a
microscope, therefore being sensitive to local changes of the reflectivity of the sample.
By using a Schwarzschild objective we were able to provide both the necessary large
working distance (~ 20mm) and a diffraction limited spatial resolution of 2 µm at a field
of view of appr. 200 µm. In order to improve the contrast we again used a downstream
Argus 20 image processing unit. The enhanced microscopic image was stored on a
video recorder.
The Model
The employed model has previously been formulated (S1). A variant of the
original model with modified mathematical notations is presented here. The model is
phenomenological and focuses on an interpretation of the interactions among metastable
pitting events and the effects of these interactions on the transition to pitting corrosion
rather than the growth of individual pits. Many details of the complicated process
cannot be included at this stage but will be included in subsequent work; nevertheless,
the primary features of the transition process are successfully seen, even in this
simplified model.
During the corrosion of stainless steel many ions enter the solution from an
active pit including Fe, Cr, Mo, etc. and hydrolysis reactions lower the pH of the
solution; Cl ions are also attracted to the site in order to maintain electroneutrality. We
do not attempt to model the transport of all these species. Rather, as a simplification,
we introduce a single local concentration c of aggressive species in the diffusion
boundary layer at the surface whose temporal evolution is described by the equation
∂
c
∂
t=−
γ
c+D∇2c+K
l0
gt−ti
()
δ
r−ri
()
i
∑.
Here, the first term on the right side takes into account the loss of aggressive species
because of their diffusion into the bulk of the electrolyte, and the rate constant of this
process is
γ
= 2D/l02 where D is the diffusion constant and l0 is the diffusion boundary
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layer thickness. The second term describes lateral diffusion within the boundary layer.
The last term corresponds to the release of aggressive species by the pits. An active pit,
located at point ri at time ti, releases into solution within its lifetime a total number K
moles of such ions. All pits are identical. The function g(t) is defined as
g(t)=
1
τ
0
exp(−t/
τ
0), t>0
0, t < 0
where
τ
0 is the lifetime of a pit. Note that in the model the lifetimes of all active pits are
thus identical and do not depend on the reaction conditions. Moreover, an active pit
after its disappearance leaves no passive trace on the surface.
Aggressive solution around a pit produces local weakening of the nearby oxide
film. In the simplest approximation, the rate of weakening can be taken to be directly
proportional to the concentration of the aggressive species at the electrode surface.
Introducing a phenomenological variable s that specifies the degree of local film
damage the equation for its temporal evolution is written as
∂
s
∂
t=−
κ
s+
ν
c.
Here,
ν
is a rate constant for the oxide film damage in the presence of aggressive ions
and
κ
is the rate constant determining how fast the oxide film can repair itself when
such ions are absent. The corresponding recovery time of the oxide layer is T0 = 1/
ν
.
The use of a recovery time for the repair of the film neglects such second order effects
such as the subsequent reaction of Fe+2 to Fe+3 which can lead to film thickening in the
vicinity of a pit. All cathodic reaction is assumed to take place on the counter electrode;
thus no local cathodic reaction, which can favor a protected zone around each active pit,
is included. However, the ohmic potential drop
Φ
(r) in the solution around a pit has
been taken into account and this potential drop does reduce the probability of pitting up
to radial distances r about a few diameters from a pit. Although under the conditions of
the simulations presented here the potential drop in solution has only a small effect, in
the presence of a stable pit with higher current the potential drop can have a strong
influence and can inhibit metastable pit growth in its vicinity (see (S1)).
The local generation rate w of active pits at the metal surface depends on the
combined effects of the concentration of aggressive species in the ionic conducting
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phase (electrolyte) and the damage to the protective oxide film on the metal surface;
both effects increase the rate of generation. On the other hand, the local potential drop
decreases the pitting probability. Thus, the dependence is phenomenologically chosen in
the form
w(c,s)=wmax
1+exp M0−
α
cc−
α
ss+
α
ΦΦ
()
/H
[]
.
The rate of spontaneous pit generation for a damage-free film (s = 0) in absence of
aggressive ions (c = 0) is w0=wmax 1+exp(M0/H)
[]
−1. The pitting rate monotonously
increases with s and c and reaches saturation at w = wmax. The coefficients
α
c,
α
s and
α
Φ
determine the sensitivity of the pitting rate to the presence of aggressive ions, the film
damage, and the potential drop. The quantity M0 specifies the threshold, at which a
steep increase of the pitting rate sets in, and the parameter H determines how steep this
increase is. The generation rate w depends on the overall parameters such as applied
potential, electrolyte concentration, temperature, and metal alloy properties through the
maximum generation rate wmax; although explicit dependences are not specified in the
model, an increase in applied potential, temperature, electrolyte corrosiveness such as
lowered pH, or alloy susceptibility is accounted for in the simulations by an increase in
the value of wmax.
The pits likely nucleate at preferred sites such as at sulfide inclusions; this is
consistent with our experiments that show that there appears to be a fixed number of
sites, at defects and inclusions, for pit nucleation. We have carried out our simulations
in two ways, by taking a homogeneous surface where all sites are equally probable and
by taking a surface with a number of active sites distributed over the surface. (The
details of the effects of surface defects and inclusions will be published in a future
publication.) Although the distribution of pit locations is influenced by the use of active
sites, the main conclusions of the simulations are not affected and the explosive growth
in the number of pits at the transition to pitting corrosion is again seen.
Parameter values used in simulation shown in Fig. 4:
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wmax = 5 x 103 cm-2s-1,
γ
= 0.8 s-1, D = 10-5 cm2s-1, K = 2.1 x 10-12 mol,
κ
= 0.033 s-1,
ν
=
103 mol-1cm3s-1, M0 = 50,
Η
= 10, αc = 8.78 x 106 cm3mol-1, lo = 0.005 cm,
τ
0 = 1 s,
α
s
= 7210, and
α
Φ = 400 V-1.
Figure for supporting online material
Fig. S1.
Figure Caption
Fig. S1. Sketch of experimental imaging setup
Reference for supporting online material.
S1. T. T. Lunt, J. R. Scully, V. Brusamarello, A. S. Mikhailov, J. L. Hudson,
J. Electrochem. Soc. 149, B163 (2002).
