Electrochemical noise at passive iron

ELECTROCHEMICAL

NOISE

Korrosion

and Korrosionsschutz, Universitiit Clausthal, (Received

27 April

lnstitut fiir Metallkunde D 3392 Clausthal-Zellerfeld, 1987;

IRON

K. E. HEUSLER

KNACHSTEDT~~~ Abteilung

AT PASSIVE

in revised

form

29 July

und Metallphysik, F.R.G.

Technische

1987)

Abstract-With the apparatus described it was possible to measure under potentiostatic conditions at frequencies up to about 1 kHz spectral densities of current noise comparable to the thermal noise at resistances of the order M Ohm. The spectral densities of the current noise at passive iron microelectrodes in neutral borate or acetate buffer solutions were nearly frequency independent at frequencies below 10 Hz and increased with the square of the frequency at higher frequencies. The results are described by a nearly frequency independent voltage noise source of an intensity about one order of magnitude larger than the thermal noise at the electrode impedance. The spectral densities of the current noise and the corresponding rms noise currents were found to decrease with time during the approach to the steady state, with electrode potential due to the changes of the electrode impedance, and with electrode area. The current noise was increased by small heat flows through the electrode. At constant temperature, the noise was not affected by the exchange of electrolytes not containing ions causing pitting corrosion. The replacement of such inert electrolytes by electrolytes containing chloride resulted in an immediate increase of the spectral density of the current noise and a subsequent decrease towards a steady state before the end of the incubation time. The rms noise current in presence of chloride normalized to the noise current in absence of chloride was independent of electrode potential and proportional to the logarithm of the ratio between the actual chloride concentration and the critical chloride concentration below which pitting never occurs. The voltage noise source became frequency dependent with a maximum at about 5 Hz. After onset of pitting the low frequency noise of the l/p-type grew by several orders of magnitude. The results are explained in terms of local fluctuations of the thickness of the passivating film due to local adsorption of chloride followed by currentless dissolution of oxide monolayers and subsequent growth or further dissolution of the oxide film at random sites.

INTRODUCTION During charge transfer at an electrode random fluctuations of the current are expected[ l-41 due to elementary processes both in equilibrium and during irrever-

sible charge transfer. Such fluctuations are difficult to observe. There is a better chance for the observation of electrochemical noise, if fluctuations originate from macroscopic events, which may be triggered by molecular events. Examples are noise at biological membrdnes[5,6] or noise due to nucleation and growth of a phase[7]. Several workers found electrochemical noise connected to pitting corrosion before stable pits started to grow[& 121. Current spikes with amplitudes of the order @A were observed above the critical pitting potential in chloride solutions at various steels, but also at aluminum. Usually no visible pits were produced. However, the charges of 10 to 500 PAS associated to one event correspond to iron volumes of the order lo3 gm3[12]. Consequently, the results were interpreted as breaking of the passivating film followed by repassivation. During the growth of stable pits the noise increased to relatively high values. On the other hand, much smaller fluctuations are expected from local changes of the thickness of the passivating layer. Such fluctuations of the anodic current without spikes were found with passive iron in preliminary experimentsC13, 141. It was observed earlierCl51 that the dependence of pit incubation times on the electrode potential is

formally described by a law expected for 2-D nucleation. In these experiments iron was kept passive for some time at constant electrode potential, and chloride was added to the electrolyte at the beginning of the incubation time. Chloride addition caused currentless dissolution of the oxide and thinning of the passivating film. It was concluded that local variations of film thickness due to oxide dissolution catalyzed by chloride and subsequent film growth or further dissolution eventually resulted in complete removal of the passivating film at some arbitrary site. At such a site a pit may grow, if a dislocation is present[ 16, 173, or repassivation may occur. The pit incubation time is not a deterministic quantity. A characteristic distribution function of the pit incubation times measured under identical conditions existsC14, 17-20) which appears to hold also for other metallic materials than pure iron.

EXPERIMENTAL Reliable quantitative measurements of electrochemical noise require an apparatus optimally free of spurious noise which may originate from the electrochemical cell and its components, from the electronics and from the surroundings as the principal noise sources. The cell with a volume of less than 20 cm’ developed for noise measurements is shown in Fig. 1. The working electrode was zone refined iron with 99.98% Fe (quality Sl, Vacuumschmelze AG, Hanau). The 311

312

K. NACHSTEDTAND

Fig. I. Cross section of the cylindrical electrochemical cell for noise measurements with working electrode W, counter electrode C and reference electrode R connected to the cell via an electrolyte bridge with a Pt wire in the Habe-Luggin capillary. The solution flows from the bottom to the top through an inlet parallel or perpendicular to the working electrode. The ratio of the flow rates in the two directions can be regulated in wide limits. In some experiments a temperature difference across the working electrode was established

by a flow of water from a thermostat through the heat exchanger

TN at the rear end of the working

electrode.

mean grain size was 1.5 mm. Rods of various diameters between 0.6 and 10 mm were insulated with alkyd lacquer and embedded into an epoxy polymer disc. The plane of the disc with the cross section of the iron rod in its center was polished and cleaned in distilled water in an ultrasonic field. The counter electrode was a platinum sheet with an area of about 3 cm2 at a distance of about 20 mm from the working electrode. A Hg/HgzSOd-electrode in 0.1 M potassium sulfate was used as the reference electrode. For conversion to potentials as other reference electrodes a potential E = 0.636 V us the standard hydrogen electrode was used. The Haber-Luggin capillary with a length of 35 mm connecting the reference electrode to the cell contained the cell electrolyte and a Pt-wire for lowering the impedance. The distance from the tip of the capillary to the working electrode was 3 mm. All components were firmly mounted in mechanically stable positions. The cell electrolytes were either 0.4 M borate or 0.3 M acetate buffers adjusted to various pHvalues with and without additions of other salts. About 130 cm3 of the electrolyte deaerated with a stream of pure nitrogen as shown in Fig. 2 were circulated through the cell via a water thermostat by a pulsationfree rotary pump. The flow velocity in the cell’ usually was about 0.3 m s- ’ but could be increased to several m s I. The pump was driven by a shaft to the dc-motor outside the outer shield. Using a piston pump with a volume of about 500 cm3 the cell electrolyte could be exchanged within less than 1 s. The electrolyte taken from a supply vessel was kept in a stream of nitrogen at the same temperature as the cell electrolyte. Both the inner shield around the cell and the outer

K.E.

H EUSLER

shield were made from 3 mm soft iron sheet. The inner shield was covered with a thermal insulation and was mounted on a 40 mm layer of polyurethane foam to absorb mechanical shocks and vibrations. A heat exchanger connected to the thermostat kept the inner shield at the same temperature as the electrolyte. A battery powered potentiostat and a battery powered output amplifier as well as the equipment to exchange the cell electrolyte were surrounded by the outer shield. Most of the measurements were performed at 25.O”C. A low noise battery potentiostat (Jaissle 1001 T-NC) with the circuit schematically shown in Fig. 3 was used. The digital instrument for the electrode potential was disconnected, because it caused small fluctuations in the potentiostatic circuit. The commercially available potentiostat was further modified by using specially selected low noise amplifiers. The maximal bandwidth of the potentiostatic circuit for high cell impedances was about 20 kHz at - 3 dB. The current was measured as a voltage with respect to ground via a current to voltage converter. At a sensitivity of 10 pA V-’ the bandwidth for current measurements with the l/U-converter was about 20 kHz at - 3 dB. The bandwidth decreased with the sensitivity down to about 20 Hz for the maximum current sensitivity of Therefore, a 3-stage low noise cascade 10 nAV_‘. amplifier with up to lOOO-fold amplification was built which allowed to operate the potentiostat at the current sensitivity of 10 PA V _ ’ and correspondingly higher bandwidth. The current to voltage amplifier and the cascade amplifier together had a - 3 dB bandwidth of 20 kHz for the sensitivity of 10 nA V 1 as shown in Fig. 4. A further problem was the decrease of the bandwidth of the potentiostat with growing current, or for a given input ac voltage, with decreasing cell impedance. This effect is shown in Fig. 5. The - 3 dB bandwidth for ac voltages with the amplitude 1 mV at the input was about 0.4 kHz for a resistance R of 15 Ohms, 1.65 kHz for 105 Ohms and 5 kHz for 1100 Ohms. The resistance R, = 50 Ohm was similar to the corresponding electrolyte resistance in the experimental cell. In the range of frequency independent amplification at low frequencies the observed current noise from a dummy circuit as shown in Fig. 5 was independent of frequency in the Hz to kHz region for resistors of the order 0.1 M Ohm. The spectral density of this noise exceeded the calculated thermal noise by less than one order of magnitude. Figure 6 shows the spectral density of the current noise measured in the frequency region between about 1 Hz and about 50 Hz which was predominantly used in the experiments reported below. The experimental noise approached the thermal noise with increasing resistance R between the inputs at the potentiostat for the reference electrode and the working electrode. As expected for ideal potentiostatic conditions, the resistance R, between the inputs for the counter electrode and the reference electrode did not significantly influence the spectral density of the current noise. The l/finstrumental noise was usually detectable only at very low frequencies. At 1 Hz its spectral density was of the order 10eZ4 A2 Hz- ‘. This instrumental noise could be measured up to increasingly higher frequencies and lower spectral densities as the resistance R was made larger and over several

Electrochemical noise at passive iron TO

313

EXCHANGE WASTE-ELECTROLYTE

OUT

TO THERMOSTAT .-

.& FROM THERMOSTAT

EXCHhNGE ELECTROLYTE

r-l

PRINTER

Fig. 2. Schematic diagram of the apparatus for measurements of electrochemical noise.

Fig. 3. Schematic representation of the potentiostatic circuit with the operational amplifiers OPl and 0P2 and the current to voltage converter with the operational amplifier 0P3. The output U of the current to voltage converter is measured across the resistance R,. The potentiostatic circuit is connected to the electrolytic cell with the working electrode ME, the reference electrode BE and the counter electrode GE.

orders of magnitude at nearly infinite resistance R. It was shown experimentally that the instrumental noise originated mainly from the Z/U-converter. The amplified signal was fed to a two-channel signal analyzer (Iwatsu 2100B) via a notch filter which selectively eliminated the signals at 50 Hz and multiples of this frequency. As another measure to diminish the 50 Hz signal, one protecting transformer connected to the public power supply was u$ed to operate all instruments. Although the residual signal at 50 Hz was very small, it was still the highest one at the input of the signal analyzer. Since this instrument scales the measurements to the highest signal, the resolution of the noise measurements was dramatically improved by the filter.

At the maximal values of the input sensitivity S ( + 0.1 V full scale), of amplification A (10 nA V- ‘) and of the digital resolution D (12 bits) of the signal with 4 K maximum data length in the time domain a maximum digital current resolution of C = AS/D = 0.25 pA was obtained. After Fourier transformation the instrument yielded up to L = 1024 lines in the selected frequency band B up to B = 100 kHz. Power spectra were measured after up to M = 128 times of signal averaging depending on the desired speed and accuracy, eg in the 1 kHz band, after M = 128 averages the digital resolution E of the power spectral density was E = C2L/BM = 5 lo-‘* A2 Hz-‘. The time to obtain an averaged spectrum depended on the frequency range and the frequency resolution, eg 4 min were necessary to measure the time dependence of the current, to calculate the spectral densities in the 20 kHz band at 20 Hz resolution and to average 128 spectra. On the other hand, the same procedure took only about 15 s in the 20 Hz band at 0.4 Hz resolution and 4 averages. Up to 8 spectra could be stored in the analyzer. The data were permanent@ stored on floppy disc via a microcompuar (Commodore 8032 SK). The transfer time for one averaged spectrum of maximal frequency resolution was about 20 s. The computer was also used to operate the signal analyzer, to perform calculations with the data or to transfer them back to the signal analyzer for further processing, and to plot or print the final results.

RESULTS The iron electrodes were first activated for several min at E,,, = - 0.15 V vs the reversible hydrogen electrode in the same solution and subsequently passivated at the potential selected for the later noise measurements. After 5 h the current density in 0.4 M borate

K. NACHSTEDTAND

314

_ .s -< ;= s s

K.E. HEUSLER

-16 -20 -2.5-26 -32 -

)

-36 100

10'

102

103

105

104

f/Hz Fig. 4. converter and ( q)with the sensitivity 10 PA V - ’ at the I/U-converter stage cascade amplifier.

-20

0.01

0.1

1

’ wasobtained (0) directly at the l/Uand 1CUKLfold amplification with the 3-

10

100

f/kHz Fig. 5. Dependence on frequencyjof the ratio of the output ac current $, to the current ib calculated for frequency independent amplification of the whole potentiostatic cmxit with the resistances R = 15 Ohm( q), R = 105 Ohm (A) and R = 1100 Ohm (0) between the inputs for working electrode ME and reference electrode BE and a resistance R, = 50 Ohm between the inputs for BE and counter electrode GE. The nc voltage at R was 1 mV peak to peak.

buffer, pH 7.4, dropped to 40 (+ 10)nA cm-’ which was considered to be close to the steady state current density. Larger mean current densities or erratic spikes of the current were taken as evidence of crevice corrosion. Such electrodes were discarded. Activation at much more negative potentials resulted in a relatively slow decrease of the anodic current density, probably due to oxidation of hydrogen dissolved into the iron. In 0.3 M acetate buffer, pH 7.2, the steady state current densities were usually, but insignificantly lower than in borate buffer. Spectra of the current noise under potentiostatic conditions were qualitatively different in the low frequency region between about 1 and 100 Hz and in the high frequency region between about 100 and 20 kHz. In the high frequency region the spectra were usually measured in borate buffer solutions. The shape

of the spectra of the current noise was influenced both by the frequency dependent impedance of the cell and by the frequency dependent amplification of the potentiostat. The cell impedance is mainly given by the electrolyte resistance and the electrode impedance. Since the shape of the spectra was not only determined by processes at the electrode, the effect of electrolyte composition on the rms noise current was evaluated. The rms noise current obtained by integration of the spectrum in the high frequency band in general rose with the conductivity or concentration of the electrolyte, but there were also significant differences at constant conductivity or electrolyte concentration between different anions like acetate, nitrate, phosphate, chloride and iodide. The high frequency noise will be discussed in detail elsewhere. It is not correlated to pit incubation.

Electrochemical The acetate

frequency

usually

measured

The conductivity of this buffer is much higher than the conductivity of the borate buffer. Therefore, reliable measurements with borate buffer were more difficult to obtain because of a larger susceptibility to spurious noise, eg from the circulation of the electrolyte. However, at least in a stagnant electrolyte the spectra of the current noise were

;+-I I

IO

m

0

5

8

8

2

iron

identical in the two buffer solutions within the limits of accuracy. The spectral density of the low frequency noise thus is independent of the conductivity of the electrolyte. The noise originating from the electrode grew relative to the mean current with decreasing electrode area. Therefore, measurements were performed with electrodes as small as possible in view of the instrumental resolution. Figure 7 shows spectra of the current noise in the 50 Hz band during the approach to the steady state at different times after passivation. The spectral density increased towards higher frequenciesfwithf2. At frequencies in the range from about 0.5 to 20 Hz the spectral density became less dependent on frequency and was nearly independent of frequency a long time after passivation. Data at very low frequencies were influenced by instrumental l/f-noise and slow drifts of the mean current. The instrumental noise naturally became relatively more important when the electrochemical noise decreased with time. As shown in Fig. 8, the rms noise current in the frequency range from 0.4 to 20 Hz decreased roughly in parallel to the decrease of the mean current towards the steady state, but the rms noise current attained its steady state value much earlier than the mean current. In the steady state the rms noise current became smaller at more positive electrode potentials as shown in Fig. 9, although the mean current was independent of the electrode potential. It should be noted that there was no influence of the flow velocity of the electrolyte on the noise spectra in electrolytes of high conductivity. An increase of the low frequency noise was observed when the buffer solution .without chloride was exchanged for the same buffer solution with chloride. No

‘.:--0

‘0 t

at

OO

1

2

3

R-’ / M fi’

Fig. 6. Spectral density S, of the white current noise in the 1 to 50 Hz frequency band at metal film resistors R betweenthe inputs at the potentiostat for the reference electrode and for the working electrode. (0) short circuit of inputs for reference electrode and counter electrode (two-electrode operation) and (0) second resistor R, = R betweenthe inputs for the counter electrode and for the reference electrode (three-electrode operation). Solid line corresponds to thermal noise calculated for 298.15 K.

Fig. 7. Spectral densities S, of the current noise at passive iron with the area A = 1.33 mm’ in 0.3 M sodium acetate-acetic acid buffer, pH 7.2, at 298.15 K for various times t after a step from the activation potential EHSS = -0.15 V USthe reversible hydrogen electrode in the same solution to E,,, = 1.068 V. (1): t = 3 min. I = 25 nA; (2) t = 65 min, I = 3 nA; (3): t = 300 min. I = 1 nA.

K. NACHSTEDTAND

316

were found with acetate, nitrate and sulfate. However, it was very important to keep the temperature exactly constant, since there was also an increase of low frequency noise due to temperature differences. This effect was first observed when the electrolyte circulating through the cell for some time was exchanged by an identical electrolyte. In this particular experiment the temperature in the cell was only regulated by an air thermostat. Due to friction heating the temperature in cell was slightly higher than the temperature of the new electrolyte. Figure 10 shows that the effect is due to a temperature gradient at the electrode. The noise grew with the temperature gradient and quickly attained a steady state, but was independent of the direction of the gradient. Since the effect was independent of whether at the back side of effects

K. E. HEUSLER the electrode a water or air thermostat was used, the noise is not due to the thermostat. According to Fig. 11 the spectral density of the current noise caused by a thermal gradient was only enhanced at frequencies below about 40 Hz. No significant changes of the noise were detected, if the temperature differences were less than about 0.1 K. Figure 12 shows the ac component of the current before and after the exchange of the solution without chloride by a solution with chloride. The increase of the noise immediately after the exchange is clearly apparent. The amplitude of the noise current was of the order 10 pA and several orders of magnitude

0.4 -

. .

7.5

l

7 a ? VI ;e.-

0.3 0.2 -

l9

. 1.0

. . -0.5

..

0 0

05

10

Ig(I/nA) Fig. 8. Double logarithmic plot of the rms noise current i,,, in the frequency band from 1 to 20 Hz vs the dc current I during its slow approach to the steady state. i,, was obtained from power spectra measured under the conditions of Fig. 7 but for A = 0.79 mm’.

I 0.4

I 0.8

I 1.2

1.0

Fig. 9. Dependence of the steady state reciprocal rms noise current i,,, in the frequency band from 1 to 20 Hz on the electrode potential EHss vs the reversiblepotential E” of oxide formation in 0.3 M sodium acetate-acetic acid buffer, pH 7.2, at 298.15 K with a passive iron electrode of the area A = 0.28 mm’, I = 0.11 nA.

0.6 1

0

0.5 (ES,-E’)/V

1.5

1 1.6

1

1

1

I

I 2.0

I

I

,

2.4

2.6

3.2

t/102s Fig. 10. Dependence of the current at passive iron with the area A = 0.95 mm’ in 0.3 M sodium T was changed with acetate-acetic acid buffer, pH 7.2, 298.15 K, at E,,, = 1068 V while the temperature time t at the rear side of the iron electrode.

Electrochemical noise at passive iron smaller than the values published earlier[S-141. It is apparent from the part showing the noise at high time resolution, that the noise is fairly regular and not composed of isolated spikes with fast rise times and slow decay times. According to an intuitive interpretation of the time dependence of the current in Fig. 12, charges associated to one event are of the order of several PAS. The effect of chloride on the noise disappeared immediately after the exchange of the solution with chloride by the solution without chloride. The relative enhancement of the noise by chloride decreased with the area of the electrode and could be measured reliably only at electrodes with areas smaller than about 0.1 cm’.

-27-----l

f /Hz Fig. 11. at both and for and the

Power spectra of the noise current for T = 298.15 K sides of the passive iron electrode (lower spectrum) a temperature gradient of 5 K between the rear side front side of the iron electrode (upper spectrum), other condition being the same as in Fig. 10.

317

In Fig. 13 spectra measured in a solution without chloride and with chloride both during and shortly after the end of the incubation time are compared. During the incubation time the spectra1 density was significantly greater than in the solution without chloride with a maximum of the effect a frequencies around 5 Hz, but there was no effect of chloride on the part of the spectra where the spectral density grew with f2. Shortly after the onset of pit growth the spectral density grew by several orders of magnitude, in particular at low frequencies, and decreased inversely proportional to the square of the frequency. The rms noise current quickly rose to a maximum immediately after the first contact of the passive iron with the solution containing chloride and decayed nearly exponentially towards a steady state value as shown in Fig. 14. In the steady state the rms noise current remained larger than in the solution without chloride. Sometimes pitting occured before the steady state noise current was established. Since the most probable incubation times are inversely proportional to the area of small electrodes[ 14, 173 sutlicient time was often available for the noise measurements even at high concentrations and positive electrode chloride potentials. The potential dependence of the steady state rms noise current was the same in solutions with and without chloride. The ratio of the steady state rms noise currents was independent of the electrode potential, but decreased linearly with the logarithm of the chloride concentration as shown in Fig. 15. At and below a critical chloride concentration of 3 mM in the acetate buffer the influence of chloride on the rms current disappeared. No pitting was ever observed below this critical concentration of chloride. The rms noise current at a given chloride concentration and at

Fig. 12. ac component i of the current at passive iron with the area A = 0.28 mm2 in 0.3 M sodium acetate-acetic acid buffer, pH 7.2, at 298.15 K, E HSS = 1.068 V before and after exchange of the solution for one containing 0.5 M sodium chloride at the time f = 0.

318

K. NACHSTEDT

05

2

1

3 f

10

45

AND K.

20

/Hz

Fig. 13. Spectral density Sj of the current noise at passive iron with the area A = O.7Y mm’ in 0.3 M sodium acetate-acetic acid buffer, pH 7.2, at 298.15 K, E,,, = 0.28 V (1) in the steady state, 1 = 0.3 nA; (2) during the incubation shortly after exchange of the solution for one containing 0.1 M sodium chloride; (3) during stable pit growth about 1 min after the end of the incubation time.

4.

e

“E

.-L

“0

50

100

E. HEUSLER

150

200

250

t/s

Fig. 14. Dependence on time r of therms noise current &in the frequency range from 1 to 20 Hz at passive iron with the area A = 0.28 mm’ in 0.3 M sodium acetate-acetic acid buffer, pH 7.2, E HsS = 1.068 V, in the the steady state with I = 0.10 nA and after exchanging the solution for one containing 0.5 M sodium chloride. The hatched area signifies the time for exchange of the solution and the subsequent first measurement.

constant electrode potential vs the hydrogen electrode in the same solution decreased with the pH value which was changed in the range between 2.5 and 11.5 pH. At the highest pH value chloride did not cause a significant increase of the rms noise current.

DISCUSSION The fluctuations described in the experimental section are qualitatively and quantitatively different from those reported earlier. As already mentioned, they were rather smooth in the time domain. Isolated spikes of the current were observed only after the end of the incubation time. They apparently result from repassivation of the iron at pits stopping to grow. Not every pit

Fig. 15. Ratio N = i(Cl-) rms/i rnlsof the rrns noise currents in the frequency band between 1 and 20 Hz, i (Cl -),,, with and trmS without chloride, as a function of the concentration c of sodium chloride in 0.3 M sodium acetate-acetic acid buffer, pH 7.2, at passive iron with the area A = 0.28 mm’, E,,, = 1.068 V. 298.15 K.

grows continuously. Thus, the noise found in the earlier work must be attributed to the processes of pit growth and death. The spectral density of the current noise then decreases with frequency according to Si = k/f” with the exponent a close to (I = 2. At low frequencies Si is several orders of magnitude larger than before the end of the incubation time or in absence of ions which cause pitting corrosion. The current noise in absence of chloride ions is related to properties of the electrode. This is apparent from the decrease of Si during the approach to the steady state shown in Figs 7 and 8 or the dependence on electrode potential of the rms noise current shown in Fig. 9. The increase of the noise current upon addition of chloride must be due to electrochemical noise from electrode reactions preceding the formation of the first pit. This conclusion is supported by the time dependence of the rms noise current after addition of chloride and by the dependence of the rms noise current on the chloride concentration which disappears at thecritical chlorideconcentration. It should be noted that the critical concentration in the acetate buffer solution is one order of magnitude larger than the critical concentration found in sulfuric acid or borate buffer solutions. Thus, acetate can be considered as an inhibitor of pitting corrosion. However, the acetate buffer solution also contained minute amounts of some oxidizing substances which may cause the effect. The qualitative conclusions are supported by a quantitative treatment. The spectral density of the current noise is related to the spectral density of the voltage noise by the frequency dependent magnitude 121 of the impedance of the experimental circuit: S”(f)

= S,(f)1 ZU-)I’.

(1)

In the region of frequency-independent amplification of the potentiostatic circuit the impedance of the experimental circuit is mainly given by the faradaic electrode resistance Rand the parallel electrode capacitance C with the electrolyte resistance R, between electrode and the tip of the Luggin capillary in series.

Electrochemical

319

noise at passive iron

with the spectral density of the thermal

noise

Sith= 4kT/R.

C

Fig. 16. Circuit used to calculate the spectral density of the current noise, with faradaic electrode resistance R, electrode capacitance C, resistance R, of the electrolyte between working electrode and tip of the Luggin capillary, and voltage noise source

0.

One may have a voltage noise source either between R C or in series to the total impedance. A voltage noise source u with a spectral density S,(f) in series to the total impedance as shown in Fig. 16 has relatively simple properties. One finds for the spectral density of the current noise under potentiostatic conditions

and

S,(f)

= S,/[R,2 + R(R+2R,)(l

+w~R*C~)-~],

(2)

with w = 27cf. In the general case, instead of R one must consider a frequency dependent faradaic impedance. For a white voltage noise source with S, independent of frequency the spectral density of the current noise will be independent of frequency Si = S, j(R + R,)‘,

(2a)

at low frequencies where wRC Q 1. If R, 6 R, there is a frequency region where wR,C e 1 and s, = S”W2C2

(2b)

At the highest frequencies, where wR,C + 1, Si again becomes independent of frequency, but is determined by R,: Si = S,/R,z.

(2c)

The observed spectral densities of the current noise are nearly quantitatively described by equation (2) except for the fact that the high frequency limit already is in the region where the amplification of the potentiostat decreases with frequency. As expected from equation (2b) the spectral density of the current noise is exactly proportional toy2 in the frequency region above about 20 Hz indicating that the spectral density of the voltage noise S, is independent of frequency, at least in this frequency region. Assuming that S, remains white also at somewhat lower frequencies where Si becomes independent of frequency, one can estimate RC from the frequency f* = 1/2xRC at which Si is just twice the value given by equation (2a). From the spectrum in Fig. 7 for t = 300 min one finds f* = 10 Hz. The capacitance of the passive iron is about C’ = 5 PF cm-*. The electrode used in the experiment of Fig. 7 thus has a capacitance of about C = 0.066 PF and a resistance of about R = 0.24 M Ohm, or R’ = 3.2 K Ohm cm’. The spectral densities Spx in Fig. 6 of the current noise measured with dummy circuits instead of the cell are optimally described by the empirical relation Sf”/S;” = 1 + (a + bR’)E* 13:3-a

‘,

(3)

(4)

The parameters are a = 0.71 (t 0.35) and b = (1.4( + 1.1)/M Ohm)‘. The experimental noise at the resistor R is thus by a factor of up to 4 larger than the expected thermal noise. The factor may be less because of some unknown excess noise from the metal film resistors. The correction factor becomes independent of the impedance for low impedances as one also concludes from the fact that the spectral density of the current noise is linearly related to fZ in the region where the impedance is dominated by the electrode capacitance. Applying the factor given by equation (3) as a correction of the measurement at 300 min in Fig. 7 referring to an electrolyte not containing chloride one finds that the experimental noise is 19( f 6) times the thermal noise. The correction factor decreases for smaller electrodes with a higher impedance. A measurement analogous to the one just discussed but at an electrode with an area of A = 2.8 10m3 cm2 yielded the spectral density of the current noise 2.4 10-25 A2 Hz-’ at 10 Hz which after applying the correction corresponds to 4.0 ( + 1.4) times the thermal noise. The frequency dependent correction factor may result in systematically estimating too small resistances R. It appears that at frequencies below 100 Hz the steady state noise is about one order of magnitude larger than the thermal noise at the electrode impedance. With the experiments presented above is not possible to identify the origin of the excess voltage noise. It follows from further experiments[23] that there are two noise sources, an external one and another one in the electrode. The steady state impedance of the passive iron increases aproximately linearly with the electrode potential, because the thickness of the passivating film becomes larger. The capacitance to a first approximation is inversely proportional to film thickness. A quantitative estimate of the resistance R can be obtained from the assumption that R is determined by high field ionic conduction through the film with the rate. ZZ = ZO.z exp B(E - PVQ,

(5)

where exchange the current, /I Z,,, 1s Q = (3.68 10e3 As Vcme2) = 0.074 As V cm-‘[22], (E,, - E”) the charge stored in the film at steady state at the electrode potential E,E” with respect to the equilibrium potential E” of oxide formation.Small variations of E at constant Q correspond to a resistance R = Q/BZz = (0.05 V) (E,,-

E”)/Z,).

(6)

The reciprocal rms noise current is proportional to R and should therefore also be proportional to E,, - E”. Fig. 9 shows that the experiments are in agreement with this expectation. However, the absolute values of the resistance derived from the spectral densities of the current noise are more than 3 orders of magnitude larger than R = 1.3 M Ohm cm2 predicted by (6) from E,-EE”=1.068VandI,=Z,,=40nAcm-2forthe experimental conditions of Fig. 7. A possible reason for this discrepancy is a frequency dependence of R in the region below 1 Hz. During the approach to the steady state after passivation the spectral density of the current noise

K. NACHSTEDTAND

320

determined by the capacitance quickly becomes constant. This is expected because both the anodic current and the current efficiency for film growth initially are high. When the current is already of the same order of magnitude as the steady state current, the current efficiency drops to zero. The film thickness and the capacitance then are already very close to their steady state values. The spectral density of the current noise determined by the resistance R approaches its steady state value relatively slowly as expected from equation (6), but becomes independent of time already before the steady state current I, is established as shown in Fig. 8. The spectral density of the current noise in the corresponding frequency region indicates a frequency dependence of the spectral density of the voltage noise in the spectrum in Fig. 7 taken after 3 min. A quantitative evaluation would require separate measurements of the frequency dependence of the electrode impedance. During the incubation time after addition of chloride the spectral density of the current noise at the capacitance is little affected in agreement with the observation that there is only a decrease up to 1 “/, of the mean thickness of the passivating film[23] by currentless dissolution[15]. Apparently, the intensity of the voltage noise source does not change significantly in this region. The enhancement of Si determined by S, and the resistance clearly has a maximum at frequencies of a few Hz which becomes more prominent at higher chloride concentrations. Because there are only small changes of the film thickness and because the specific conductance of the film is independent of the chloride concentration in the electrolyte[lS], the decrease of the resistance R will be negligible. The increase of Si with the chloride concentration must be attributed to a growing intensity of a frequency dependent voltage noise source S,. The shape of its spectrum can be described by a Lorentz function with a maximum around 5 Hz[23]. The enhanced voltage noise in presence of chloride ions or an equivalent current noise cannot be caused by instrumental sources. The origin of the enhanced noise can be understood by the mechanism proposed earlier [15,17,20,24]. Currentless dissolution due to adsorbed chloride proceeds locally by formation of an iron(W) complex with chloride. The local potential will drop, if no current flows. Under potentiostatic conditions a current will flow to restore the steady state film thickness, but the locally more positive interfacial potential also enhances the probability of chloride adsorption and further film thinning at the same site. This type of model involving random opening and closing of current channels is known to yield a Lorentz function of the noise spectrum with a central frequency Jo = 0[5]. The result that there is a maximum in the noise spectrum at a central frequency f0 z 0 Hz indicates oscillations around the mean current[25], eg a coupling between the opening and closing of channels. A rough estimate of the charges Qi consumed for local film growth after currentless thinning is obtained from the rms current of the noise in the frequency band from 1 to 20 Hz around the central frequency of about _& = 5 Hz for the maximum of Si:

Qi = L,,Jfo.

(7)

In agreement with the intuitive guess the charges Qi are

K.E.

HEUSLER

about 2 pAs for the experimental conditions of Fig. 12 corresponding to thickness fluctuations of one atomic layer of oxide on an area of the order 0.01 to 0.1 pm2 on an electrode with a total area A = 2.8 lo6 pm’. It would be possible to estimate the number of sites by considering the dependence of the enhancement of the mean steady state current[15] and of the noise by chloride on the electrode area. This problem will be considered elsewhere in detail. However, the qualitative result that the relative enhancement of the noise decreases with the electrode area indicates that there is a large number of individual sites. The low frequency of maximal noise enhancement and the estimated charges point towards sites of macroscopic size. The relative enhancement of the noise is independent of the electrode potential, but grows with the chloride concentration only above a critical concentration. Apparently, a high rate of local oxide dissolution becomes possible, if above the critical concentration a condensed two-dimensional phase of adsorbed chloride may form which, however, is prevebted to cover the whole surface by the chloride desorption associated with the currentless oxide dissolution. The independence of the electrode potential is expected, because in the steady state the mean potential difference at the interface between the oxide and the electrolyte is independent of the electrode potential[21]. Acknowledgements-This work was supported by the SPP ‘Corrosion Research’ of Deutsche Forschungsgemeinschaft. The authors are indebted to A. Jaissle, D 7051 Waiblingen, for permanent and invaluable help in designing and fabricating special electronic equipment for the noise measurements.

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