Czichos H., Saito T., Smith L.E. (Eds.) Handbook of Metrology and Testing

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688 Part D Materials Performance Testing

[Fe(CN)

]

3−

at the ring or vice versa

N =

. (12.58)

RRDE with different metal discs and even brittle semi-

conductor electrodes have been formed. Usually the

disc is embedded in a thin layer of resin with a cylin-

der of Au or Pt glued by resin to its surface. The

total set is then surrounded by resin within a cylin-

der of a polymer and the electrodes are contacted from

the rear side. This exchangeable RRDE may then be

attached to a disc rotator with rotating contacts for

a reliable connection of the rotating electrodes to a po-

tentiostat (Fig. 12.22) [12.43]. Frequently two isolated

half cylinders are used instead of a full cylinder, which

(μA)

= 0.6V

= –0.23V

0.1 M KOH

dE/dt = 10mV/s

–10

0 200 t (s)15010050

–0.5

–1

–1.5

–2

–2.5

–3

–3.5

0.5

1.5

–1.0 –0.6 –0.2 0.80.60.2

(V) (SHE)

Fig. 12.23 Current of a copper disc I

andringcurrents

and I

of a split RRDE in 0.1 M KOH for a potentio-

dynamic scan of the disc potential dE

/dt = 10 mV/s

i (A/cm

)

E (V)

ΔU

Fig. 12.24 Current densities i

and i

of two surface sites

A and B with an ohmic drop ΔU

within the electrolyte in

front and related rest potentials E



and E



opens the possibility to measure the formation of two

products simultaneously at the split ring. The RRDE

requires a bipotentiostat to set the potential of two

working electrodes independently from each other. An

RRDE with a split ring needs a tripotentiostat. The re-

lated block diagram is depicted in Fig. 12.22. The three

working electrodes WE

,WE

and WE

(disc, ring 1

and ring 2) are connected via a differential ampliﬁer

to avoid grounding problems. The three circuits have

one common reference electrode, RE, and one counter-

electrode, CE, which is grounded. Further details are

similar to those discussed for the block diagram of

E (V) (1) (2)

(3)

BA AB

Fig. 12.25 (a) Current lines (arrows) and curves of equal

potential in the presence of local elements with surface

sites A and B. (b) potential proﬁle with very low (1), low

(2), and very high conductivity (3) of the electrolyte

Part D 12.2

Corrosion 12.2 Conventional Electrochemical Test Methods 689

Fig. 12.4. Figure 12.23 presents as an example the I

the polarization curve of a Cu disc in 0.1 M KOH. Cu

forms a passivating oxide layer at sufﬁciently positive

potentials at the anodic peaks A1 and A2. Figure 12.23

depicts I

and I

of the two analytical ring electrodes,

which are set to appropriate potentials E

= 0.6V

and E

=−0.23 V, respectively. These potentials are

suited to oxidize soluble Cu(I) ions to Cu(II) ions and to

reduce Cu(II) to Cu(I) ions respectively. Thus the meas-

ured analytical ring currents permit the determination of

the kind and the amount of soluble corrosion products

from the disc. The calculation of the related disc cur-

rents I

(CuI) and I

(CuII) of soluble products with

(12.58) and their comparison with the measured total

current I

allow the determination of the charge which

is stored as a passivating oxide ﬁlm on the copper elec-

trode. Thus these measurements with RRDE allow the

determination of the efﬁciency of layer formation and

dissolution. Figure 12.23 shows the close relation of the

current peaks A1 and A2 of I

for Cu(I) oxide and

Cu(II) oxide formation and the dissolution of the related

ions. Even the dissolution of weakly soluble Cu(I) ions

may be detected by I

in 0.1 M KOH.

A further development of the RRDE is its hydrody-

namical modulation of the rotation speed ω. Here the

thickness δ of the Nernst diffusion layer is modulated

according to (12.57) and thus the diffusion of corrosion

products and their transfer to the rings. With a hy-

drodynamical square-wave modulation one may even

distinguish quantitatively between species of the same

kind from the bulk electrolyte and those formed at the

disc. A detailed description of this method and its appli-

cation to corrosion is beyond the scope of this chapter

and the reader is referred to the literature. An example

of its application to the dissolution and ﬁlm forma-

tion has been described for Fe in 1 M NaOH [12.44].

The agreement of experiments and calculation is shown

in [12.45].

12.2.12 Ohmic Drops

High current densities cause ohmic drops within the

electrolyte. For a planar electrode with a current density

i the voltage drop ΔU

changes according to (12.59)

with the electrolyte resistance R

, the speciﬁc con-

ductivity κ of the electrolyte, and the distance d from

the electrode surface. The ohmic drop ΔU

in front

of a hemispherical electrode of radius a at distance r

isgivenby(12.60). For r →∞, ΔU

obtains a max-

imum value ΔU

Ω,max

related to the maximum ohmic

resistance R

Ω,max

. Similar to the concentration gradient

related to diffusion in front of a hemispherical electrode

a small radius a reduces R

Ω,max

and ΔU

Ω,max

to very

small values. For i = 1A/cm

a distance of d = 5mm,

and κ =22 Ω

−1

for an electrolyte with good con-

ductivity such as 0.5MH

, one obtains for a planar

electrode at a distance d = 0.5 cm, a value of ΔU

0.023 V =23 mV (12.59). ΔU

will be much larger for

less-conducting electrolytes and higher current densi-

ties. These values are characteristic of the ohmic drop

between the Haber–Luggin capillary of a reference elec-

trode and the working electrode of a potentiostatic

circuit. It may be compensated automatically to about

90% by an electronic feedback loop, a unit built into

potentiostats. However, this may still be a problem

for electrochemical measurements at very high cur-

rent densities of i ≥10 A/cm

or electrolytes with low

conductivity. Large electrodes will also be submitted

to a nonhomogeneous potential distribution due to the

presence of large local differences of the ohmic drops.

In the case of a microelectrode with a radius of

a =10

−4

cm one obtains ΔU

Ω,max

=4.5×10

−3

mV for

conditions otherwise the same as given above (12.60).

Furthermore the potential will be uniform in front of

its surface even for high current densities. Similar con-

ditions will hold for concave hemispherical surfaces

such as small corrosion pits with μm dimensions. Here

again the potential drop will be three times larger, i. e.

13.5×10

−3

mV for a =1 μm, due to the concave geom-

etry

ΔU

=iR

with R

, (12.59)

ΔU

=iR

, R

κ(r +a)

;

Ω,max

for r →∞. (12.60)

Microelectrodes are of increasing interest. Many pro-

cesses occur on a very small scale so that micro- and

nanoelectrochemistry are actively developing branches

in electrochemistry. These ﬁelds are also important for

corrosion studies. Many corrosion processes occur on

a small scale and still cause huge damage. Mecha-

nistic studies of localized corrosion of passive metal

electrodes may follow the formation and growth of cor-

rosion pits to micrometer and nanometer scales with

appropriate methods such as scanning force microscopy

(SFM) and scanning tunneling microscopy (STM).

These methods use very sharp tips that may also be

seen as ultramicroelectrodes. Another important exam-

ple is corrosion of integrated circuits, which is a serious

problem for their life time and reliability. There are al-

Part D 12.2

690 Part D Materials Performance Testing

ways electrolyte residues on metallic connections on

chips and the encapsulent gives imperfect protection

against the ingress of moisture. The voltage supply of

5 or 15 V is large for any electrochemical process and

thus dissolution of metal at positive potentials and its re-

deposition at negative potential causes disconnection of

vapor-deposited metal connections with μm dimensions

and short circuits by the deposition of dendrites. The in-

vestigation of biological processes and the development

of sensors also need electrochemistry on a micrometer

scale. Further miniaturization pushes electrochemistry

to a nanometer scale. Thus micro- and nanotechnol-

ogy require studies of electrochemical processes with

the help of micro- and ultramicroelectrodes. Corro-

sion research necessarily has to address these small

and extremely small scales. Modern electroanalytical

chemistry uses these micro- and ultramicroelectrodes

for scanning electrochemical microscopes (SECM). It

should also be mentioned that the tip of an STM or an

SFM may be used for highly localized electrochemical

studies and surface structuring in combination with the

imaging of the electrode surface with mesoscopic and

atomic resolution. One possible application of these ul-

tramicroelectrodes is the structuring of metal surfaces

by dissolution and deposition of metal on a submicrom-

eter and nanometer scale.

12.2.13 Measurement of Ohmic Drops and

Potential Proﬁles Within Electrolytes

The ohmic drop in front of an electrode may be used

as a measure of localized electrochemical processes, as

e.g. in the case of local elements and other localized

corrosion phenomena. For an electrolyte with good con-

ductivity the potential in front of an electrode does not

change if the current densities assume moderate values,

although the rate of electrode reactions change locally

with the surface sites A and B due to their physical or

chemical differences. This leads to local anodes A and

cathodes B as discussed in Sect. 12.2.9 with no potential

drop between them (Fig. 12.16). However for a low-

conductivity electrolyte large potential drops ΔU

may

occur, which shift the rest potentials of these sites to the

values E



and E



apart from each other (Fig. 12.24).

For a vanishingly small conductivity κ the potential

proﬁle parallel to the electrode surface within the elec-

trolyte follows the shape of the related areas A and

B with steep changes at their contact (Fig. 12.25). For

0 <κ<∞ a smoothed proﬁle is found which disap-

pears for κ →∞. Thus the potential in close vicinity to

the electrode surface will change within the electrolyte

Metal

Electrolyte

ΔU

Fig. 12.26 Measurement of the potential proﬁle ΔU

within the electrolyte with two reference electrodes RE

and RE

with location. However, these differences will smear out

with increasing distance from the electrode due to the

spread of the current lines.

The related ohmic potential drop ΔU

may be

measured with two reference electrodes, e.g. two

calomel electrodes, one close to the surface moving to

the locations of interest (RE

) and the other at large dis-

tance within the bulk electrolyte (RE

). This arrange-

ment measures the total drop ΔU

with superimposed

changes when moving the sampling electrode parallel

to the surface (Fig. 12.26). More sensitive measure-

ments of small changes of ΔU

are performed when

two reference electrodes are ﬁxed with their Haber–

Luggin capillaries close to each other (Fig. 12.27). If

they are moved together across the metal surface one

measures the potential difference referring to their close

Metal

Electrolyte

d(ΔU

)

Fig. 12.27 Measurement of the proﬁle of the potential gra-

dient d(ΔU

)/dx within the electrolyte with two close

reference electrodes RE

and RE

Part D 12.2

Corrosion 12.2 Conventional Electrochemical Test Methods 691

distance as a function of position. Their potential dif-

ference changes with their common position in front

of the electrode surface and thus samples local poten-

tial gradients without a large background voltage. In

conclusion, with the second electrode separation within

the bulk electrolyte one measures the integral poten-

tial drop ΔU

whereas with two closely interconnected

reference electrodes, i. e. with the so called scanning

reference electrode technique (SRET) [12.46–48], the

local potential gradient dΔU

/dx is obtained. One

may improve the spatial resolution with two small plat-

inum tips that are isolated at their sides and which may

be arranged closer to each other.

An even better arrangement works with a vibrating

reference electrode, i. e. the scanning vibrating elec-

trode technique (SVET) [12.46, 47]. Here one uses

a small vibrating metal tip and a second reference

electrode far away in the bulk electrolyte. The small

amplitude of vibration measures the related local poten-

tial gradient corresponding to the small local changes

during vibration. The measurement of the related small

potential changes may be improved by a lock-in tech-

nique that separates the signal from the background and

disturbing signals of different frequencies from other

sources. With an applied scan of the vibrating electrode

parallel to the electrode surface one samples the related

potential proﬁle and thus images the sites of different

electrochemical activity. The potential change may also

be investigated perpendicular to the surface and thus

three-dimensional potential proﬁles may be obtained.

Useful SVET equipment is available commercially. One

may even calculate from these potential gradients the lo-

cal current densities when the size of the surface sites of

different activity and a possible change of the conduc-

tivity of the electrolyte in front are taken into account.

At present the vibrating electrode is used mainly to map

surface sites of different activity. Examples of frequent

interest are local elements on a corroding metal surface

with cathodic and anodic areas, inclusions at a metal

surface causing localized corrosion or corrosion pits

with high metal dissolution rates within a passivated

metal surface.

WTW

e(φ

– φ

)

eφ

eΔU

Fig. 12.30a,b Contact of specimen W

and tip T with work functions eΦ

and eΦ

and (a) the resulting contact

potential difference e (Φ

−Φ

(b) compensation of e (Φ

−Φ

)by

eΔU. E

and E

are the Fermi

levels of the specimen and the tip

Ground

Pipeline

Fig. 12.28 Detection of localized corrosion sites on under ground

pipelines by measurement of potential proﬁles with two reference

electrodes (RE)

d(t)

ΔU

Fig. 12.29 Equivalent circuit of

a Kelvin probe with the capacity C

of the vibrating tip/specimen combi-

nation, the compensation voltage ΔU

and current measurement A

In industry the investigation of local corrosion dam-

age by potential measurements is a very important

method. Corrosion damage of metal constructions un-

der ground may be detected by screening with two

reference electrodes (Fig. 12.28). Similarly to the above

discussion, localized corrosion of a pipeline will cause

a spread of currents and related potential drops within

the ground. The center of the damage may be found by

two references which are in contact with the ground.

One of these will be placed at different sites, thus mea-

suring the potential difference as a function of location.

The position of large potential differences should be

close to the site of active corrosion damage.

The scanning Kelvin probe provides another pos-

sibility to investigate surface sites with varying elec-

Part D 12.2

692 Part D Materials Performance Testing

trochemical activity. Its application to surface studies

is complementary to the two aforementioned methods

for corrosion studies. Its advantage is that it enables

a potential measurement without direct contact with the

medium of interest. Two different metals, the work-

ing electrode W and a vibrating tip T in its vicinity,

form a condenser (Fig. 12.29). Their direct contact in

the outer circuit produces a contact potential differ-

ence which equals the difference of the work functions

(Φ

−Φ

) = e

ΔΦ of both metals (Fig. 12.30a).

This potential difference ΔΦ causes a small alternat-

ing current during the vibration of the tip to the surface

of the working electrode due to the change of the ca-

pacity C =

εε

with distance d according to (12.62).

This current disappears when an externally applied

voltage ΔU compensates ΔΦ = (Φ

−Φ

)((12.61),

Figs. 12.29, 12.30b). Thus the difference of the work

functions is measured by a disappearing current den-

sity i of a Kelvin probe. The work function is closely

related to the energy of the Fermi level of a metal, which

changes with the potential drop within the electrolyte in

front of an electrode, i. e. due to charging of its dou-

log (

/Ω)

321–1 4 5

log ( f/Hz)

ΔΦ(deg)

Φ phase

Z impedance

Fig. 12.31 (a) Equivalent circuit of an electrode surface with

a double-layer capacity C = 10 μF, a charge-transfer resistance

=1kΩ and an ohmic resistance R

=10 Ω within the elec-

trolyte.

(b) Bode diagram of the impedance Z in dependence on the

frequency of the added alternating voltage (solid) and the related

phase shift ΔΦ (dashed)

ble layer. Any change of the potential drop across the

electrode–electrolyte interface affects the work function

and thus the compensating voltage of the Kelvin probe.

With a vibrating small metal electrode T one may scan

the electrode surface and thus measure the changes of

the difference of the work functions of W and T as

a function of its position and consequently the poten-

tial distribution in front of a corroding metal. The main

advantage is the measurement of potential differences

without making contact with the electrolyte in front of

the electrode. This may be very important when the

electrode–electrolyte interface is buried below a layer

of polymer. For these cases the Kelvin probe allows

one to follow electrochemical reactions and corrosion

processes, including the delamination of polymer lay-

ers on metals via potential measurements that otherwise

would not be accessible [12.49, 50]. Another example

is atmospheric corrosion when only a very thin ﬁlm of

electrolyte covers the surface, to which one cannot eas-

ily make a conducting contact via the Haber–Luggin

capillary of a reference electrode.

ΔU

tot

ΔΦ −ΔU =e

(Φ

−Φ

)−ΔU = 0 ,

(12.61)

εε

ΔU

tot

ΔU

tot

, (12.61a)

i =

ΔU

tot

εε

ΔU

tot

=0 . (12.62)

12.2.14 Nonstationary Methods,

Pulse Measurements

The sequence of several elementary reaction steps and

their inﬂuence on the overall electrochemical corrosion

process requires their separation. This could be done by

electrochemical transient measurements. A very rapid

change of the electrode potential leads to a sequence of

reaction steps (Fig. 12.31) that may be separated in the

time domain. The ohmic drop within the electrolyte be-

tween the reference electrode and the working electrode

is established within less than a microsecond. This may

be measured with fast galvanostatic transients. For this

discussion a useful equivalent circuit for an electrode

within the electrolyte consists of a capacity C in paral-

lel to a charge-transfer resistance R

. A resistance R

in series to this combination takes care of the electrolyte

resistance between the Haber–Luggin capillary and the

working electrode (Fig. 12.31). A galvanostatic pulse

with a rise time in the range of about 100 ns may easily

be applied between working and counter-electrode. As

Part D 12.2

Corrosion 12.2 Conventional Electrochemical Test Methods 693

a consequence the ohmic drop will be detected imme-

diately, within less than 1 μs. The subsequent charging

of the double layer, i. e. of the capacity C with time

causes an increase of the measured voltage across the

equivalent circuit. Extrapolation of this voltage increase

back to t = 0 yields at the intersection the ohmic drop

ΔU

, which should increase linearly with the galvano-

statically applied current density i. The thus measured

ohmic drop ΔU

= R

i may be used for an appropri-

ate setting of the resistance R

at the compensation

unit of a potentiostat. Thus one may compensate ΔU

automatically during potentiostatic transients, which in-

crease proportionally to the current density i.

The electronic properties of the electrode–electro-

lyte interface and its related equivalent circuit may

be determined by measurement of the impedance and

its dependence on frequency, which is presented in

Fig. 12.31 as a so-called Bode plot. For impedance mea-

surements the electrode potential is varied by a small

superimposed amplitude of a few mV in order to jus-

tify the approximation of the electrochemical system

by the proposed equivalent circuit. A linear i–E re-

lation in the sense of Ohm’s law is valid for small

potential changes only. In general the i–E relation

is exponential according to the Butler–Volmer equa-

tion of (12.26). Figure 12.31 also contains the phase

shift ΔΦ. For the presented example R

= 1kΩ,

= 10 Ω and C = 10 μF are chosen. These values

are reasonable for the electrode–electrolyte interface.

At low frequency (ω = 2π f ), i. e. below 1 Hz, the

current passes the ohmic resistances leading to approx-

imately Z = R

because the parallel capacitive

resistance 1/ωC becomes very large. The phase shift

is vanishingly small. At very high frequencies of

f =100 kHz the capacitive resistance is very low with

a short circuit across C. In this case the impedance

equals R

with ΔΦ = 0. At intermediate frequencies

of f =100 Hz, Z =1/ωC will hold approximately with

a maximum of ΔΦ. In the example of Fig. 12.31a,b one

obtains 1/ωC = 100 Ω for f =158 Hz, which refers to

the maximum of the phase shift ΔΦ.

For potentiostatic transients one has to discuss

a sequence of time ranges. Figure 12.32 presents an

example for a rotating Au disc electrode in a solution

of 0.5×10

−3

M, K

[Fe(CN)

]and K

[Fe(CN)

],which

are dominated by the following processes: (1) charging

of the double layer, (2) charge-transfer control of the

electrode process (3) increasing diffusion control and

(4) full diffusion control. This charge-transfer process

of a redox system does not involve complicating chem-

ical reaction steps within the electrolyte and adsorption

and desorption at the electrode surface (Fig. 12.11).

Therefore it is still a relatively simple situation.

1. The charging of the double layer via the R

-C com-

bination in series occurs according to (12.63, 12.64).

The total applied voltage is the sum of the potential

drop at the ohmic resistance R

and the capacity C

of the double layer i. e. ΔU = ΔU

+ΔE. With

a typical capacity of 20 μF/cm

for a free metal

surface and a resistance of R

= 0.1 Ω cm

for

a well conducting electrolyte at the short distance

between the metal surface and the Haber–Luggin

capillary of the reference electrode the charging

of the double layer occurs with a time constant

of R

C =2×10

−6

s =2 μs. For potentiostatic tran-

sients the measured current density drops according

to (12.63) and the voltage across the double layer,

i. e. across the capacitance C, increases according to

(12.64). After about 8 μs the electrode potential ΔE

should be fully established. A larger R

value will

increase the time constant. This is the case for low-

conductivity electrolytes. However in most cases the

charging time for the double layer is short enough

to follow corrosion processes with a sufﬁcient time

resolution

i =

ΔU

exp



−



, (12.63)

ΔE = ΔU



1 −exp



−



. (12.64)

2. After about 10 μs of double-layer charging one

may measure the electrode reaction under charge-

transfer control with the related charge-transfer

overvoltage η

. For these conditions the electrode

process is ruled by the Butler–Volmer equation

(12.26). If the current density is small enough

no further complications are involved. This sit-

uation refers to the plateau currents in time

range 2 of Fig. 12.32. The current density as-

sumes a constant value of 10

−2

A/cm

for about

0.3 ms, which corresponds to a charge of 3 μC/cm

and thus to 3 ×10

−11

mol/cm

of K

[Fe(CN)

For the 5 × 10

−4

M solution this amount of re-

acting ions is within a layer of 600 nm. This

distance is close to the mean diffusion path

x =

√

2Dt =

√

2×5×10

−6

×3×10

−4

√

30 × 10

−10

5.5×10

−5

cm =550 nm of dissolved ions within the

electrolytes.

3. If diffusion becomes rate-determining for a suf-

ﬁciently large current density the change of the

electrolyte composition immediately at the elec-

Part D 12.2

694 Part D Materials Performance Testing

log i (A/cm

)

Charge

transfer

control

Rise time of potentiostatic circuit

Increasing

diffusion

control

Stationary

diffusion

control

–2

–3

–4

–5

–1

–6

–2–3–4–5 –1 102

(η

)

(η

+ η

)

–6

log t (s)

1000 rpm

10 rpm

0rpm

ω =

Fig. 12.32 Potentiostatic transient for an Au RDE, with the dif-

ferent time domains, change of i with the frequency of rotation

ω =2π f/(min

−1

)

trode surface leads to a diffusion overvoltage η

Consequently the reaction rate becomes determined

by the diffusion overvoltage after some time when

the concentrations of the reacting species at the

electrode surface deviate from their bulk values. If

only the diffusion overvoltage is effective, Cottrell

derived the current density as a function of time,

as shown in (12.65) [12.51]. i depends exponen-

tially on the diffusion overvoltage η

and (12.65)

is similar to (12.53), which holds for stationary con-

ditions. For a potentiostatic transient i also depends

on time with 1/

√

t. The bulk concentration c

and

the diffusion constant D refer to a species that is

involved in the electrode process and which causes

diffusion overvoltage by its limited transport. It

could be a reduced or oxidized species and the cur-

rent density then refers to the anodic or cathodic

process, respectively. Equation (12.65) is not valid

for t = 0 because i goes to inﬁnity for this condi-

tion. However, charge-transfer overvoltage cannot

be excluded, which limits the current density for

short times. This however, is not included in this

treatment.

i = nF





exp





−1





(12.65)

If both, charge transfer and diffusion are rate-de-

termining the total overvoltage equals η = η

+η

For these conditions the change of the current den-

sity for potentiostatic transients has been deduced

as (12.66) [12.52, 53]. i(0) is the current density for

t → 0 when the double-layer charging is ﬁnished

and the concentration of any reacting species is still

unchanged. This corresponds to (12.26)whendiffu-

sion control is still not effective. For short times, i.e.

for λ

√

t 1, the approximation of (12.67) has been

derived which may be used to determine i(0) from

i–

√

t plots of the current values of potentiostatic

transients. Thus i(0) is obtained by extrapolation

of i–

√

t plots to

√

t → 0 for each electrode poten-

tial. The i(0) values may then be compared to the

polarization curve for pure charge-transfer control.

For λ

√

t  1 the approximation of (12.68) has been

derived with a t

−0.5

dependence of i. This con-

dition corresponds to dominant diffusion control.

The double logarithmic plot of the current transient

of Fig. 12.32 shows a slope d log i/dlogt =−0.5.

This result is expected for the t

−0.5

dependence of

(12.65). A slope of −0.5 is also expected from the

approximation of (12.68)forλ

√

t  1

i =i(0) exp





erfc



√



, (12.66)

λ =



B,Red

√

Red

exp



αzF



B,Ox

√

exp



−

(

1 −α

)



(12.66a)

i(0) =i

−



exp



αzFη



−exp



−(1 −α)zFη



, (12.26)

i =i(0)



1 −

√





for λ

√

t  1



(12.67)

i =i(0)

√

πλ

√



for λ

√

t  1



(12.68)

4. For times longer than 0.5 s the transients of

Fig. 12.32 are in the regime of total diffusion con-

trol with a current density which depends on the

rotation speed of the RDE. In this time range the

current densities follow the

√

ω dependence accord-

ing to the Levich equation (12.57) demonstrating the

full diffusion control of the process.

Part D 12.2

Corrosion 12.3 Novel Electrochemical Test Methods 695

12.2.15 Concluding Remarks

Corrosion within electrolytes or under the inﬂuence

of thin electrolyte ﬁlms is an electrochemical process.

For an understanding of its leading mechanisms the

application of electrochemical methods is a necessary

requirement. They allow the simulation of corrosion

phenomena under well-controlled electrochemical con-

ditions with a systematic variation of the related

parameters. For a detailed understanding of the mecha-

nisms and the condition of the metal surfaces one needs

additional information, which is obtained through the

application of surface analytical methods. For a chem-

ical analysis of corroding surfaces and surface ﬁlms

methods working in the ultrahigh vacuum such as x-ray

photoelectron spectroscopy (XPS) [12.54, 55] or Auger

electron spectroscopy (AES) [12.56] are valuable an-

alytical tools that provide qualitative and quantitative

information. The structure of surfaces and surface lay-

ers may be investigated with synchrotron methods such

as x-ray diffraction (XRD) and x-ray absorption spec-

troscopy (XAS), which yield the parameters of the long-

or short-range order of surfaces or surface ﬁlms, respec-

tively [12.57]. A direct image of surface structures even

down to atomic resolution is obtained by the in situ ap-

plication of scanning methods such as scanning force

microscopy (SFM) and scanning tunneling microscopy

(STM). There are numerous other in situ methods such

as infrared (IR) or laser Raman spectroscopy, each of

them having its speciﬁc advantages and providing some

insight into a corroding system. All these methods to-

gether give information on the chemical composition,

structure and the properties of surfaces and surface

ﬁlms. Electrochemistry remains incomplete and rather

arbitrary without the surface methods, whereas these

analytical tools without a detailed understanding of the

electrochemical reactions and a well-controlled electro-

chemical specimen preparation give no reliable results.

One therefore has to apply many of these methods in

combination in order to get reliable results without too

much speculation for the usually complicated systems

in corrosion, whether in theory or practice.

12.3 Novel Electrochemical Test Methods

During the last 30 years new electrochemical techniques

have arisen which give more and faster information

about corrosion reactions and also provide data on

corrosion in geometric orders at the nanoscale. An-

alyzing the dynamic behavior of a corrosion system

requires special techniques, which are essentially dif-

ferent from conventional direct-current (DC) techniques

(Sect. 12.1), such as measurement of the open-circuit

potential, polarization curves, weight loss, or other

physicochemical parameters. Based on linear system

theory (LST), electrochemical impedance spectroscopy

(EIS) is one of the most powerful techniques.

Electrochemical noise analysis (ENA) is a relatively

new method. Stochastic ﬂuctuations of the electrode

potential or the cell current are often referred to as

electrochemical noise, analogous to the word noise,in-

dicating random ﬂuctuations of incoherent acoustic or

electrical signals. Noise analysis is a well-developed

technique in many ﬁelds, and it is being applied in-

creasingly to electrochemical systems, in particular in

corrosion science and engineering.

Another important and widely used tool for corro-

sion investigations is the scanning electrode technique.

The inherent advantage of scanning reference electrodes

is the possibility to measure the initiation, distribution,

and rate of local corrosion processes in situ with spatial

resolutiondownto20μm.

12.3.1 Electrochemical Noise Analysis

Within corrosion research, the analysis of electro-

chemical noise offers a simple, sensitive and virtually

nondestructive measuring technique for assessment of

the corrosion susceptibility of metallic materials and

for the investigation of corrosion processes. The present

status of knowledge concerning noise diagnostics in

corrosion processes permits the application of this

method not only to experimental tasks in the laboratory,

but also to special problems in the context of practical

corrosion monitoring. Furthermore, speciﬁc advantages

of the technique enable its use to an increasing extent

in supporting or improving conventional corrosion test-

ing. The advantages here include obtaining additional

information and shortening testing times, thus resulting

in state-of-the art corrosion testing.

ENA is an electrochemical method that offers great

potential for measuring and monitoring localized corro-

sion. This technique needs no external signal to obtain

corrosion data. The principle is based on the fact that

two identical electrodes exposed to the same medium

Part D 12.3

696 Part D Materials Performance Testing

(Current noise)

Current

output

(Potential

noise)

Zero resistance

ammeter (ZRA)

Reference

electrode

Identical

electrodes

Multi-

meter

100 kΩ 100 kΩ

E1 E2

Fig. 12.33 Experimental set up for potential and current

noise measurements

(environment) under free corrosion conditions show

stochastic ﬂuctuations of the open-circuit potential in

the μV range and of the galvanic coupling current in the

nA range, generated by corrosion reactions on the elec-

trode surfaces [12.58–61]. These potential and current

ﬂuctuations are known as electrochemical noise.

The experimental set up for measuring electro-

chemical noise is relatively simple (Fig. 12.33). The

two identical electrodes (made, e.g., from mild steel)

are connected over a zero-resistance ammeter (ZRA),

which feeds the current output (current noise) via a mul-

timeter into a computer. The two electrodes can be con-

nected over two ultraaccurate metal resistors (100 kΩ

each) in series to provide an average potential point:

since the resistance of the two resistors is much larger

than the solution resistance (generally not more than

100 Ω) no measurable disturbance is introduced into the

system by the potential and current measurements. The

potential between this average point and the reference

electrode (e.g. Saturated Calomel Electrode (SCE))

is sampled. For potential and current measurements

a 2 points/s sampling rate for 500 s (8.3min)ofmea-

suring time is sufﬁcient. For corrosion monitoring this

procedure will be repeated in appropriate time intervals.

Figure 12.34 shows potential and current noise ver-

sus time plots of mild steel in two cooling waters with

different salt concentration [12.61]. Cooling water 2

contained higher chloride and sulfate levels, which ob-

viously resulted in a signiﬁcantly different ﬂuctuation

pattern of the electrochemical noise at mild steel in

these two waters. The electrochemical noise signals can

be processed in a digital or analogue manner. The digital

signal-processing technique involves the acquisition of

raw data and their subsequent numerical analysis, while

the analog processing method produces an output sig-

nal proportional to the root mean square (RMS)ofthe

noise using electronic ﬁlters and ampliﬁers. From these

data the noise resistance R, can be deﬁned as

=δV/δI , (12.69)

where δV is the RMS of the corrosion potential ﬂuctua-

tion and δI is the RMS of the current ﬂuctuation [12.62,

63].

Data processing can also include transformation in

the frequency-domain (spectral density) curves using

the maximum-entropy method (MEM) or fast Fourier

transformation (FFT). The MEM inherently produces

smoother spectra without apparent loss of informa-

tion [12.64] and is simpler to use when the number

of data points is not a power of two. Analysis in the

frequency domain needs simultaneous collection of po-

tential and current noise data.

With FFT the spectral noise response R

n( f ) can be

calculated at each frequency f by

R( f ) = V ( f )/l( f )and (12.70)

R( f )



R( f )

+R( f )



1/2

, (12.71)

where V( f )andI( f ) are complex numbers obtained

from the FFT. The spectral noise resistance R

is de-

ﬁned as the value of

( f )at f =0 , (12.72)

=lim f →0



( f )



. (12.73)

An analysis in the frequency domain can yield informa-

tion on the type of corrosion at the electrodes.

The electrochemical current-noise power-spectral

density [PSD(I)] at high frequencies (100–1000 MHz)

can be indicative for general corrosion while the shape

and the repetition rate of transients of the electrochem-

ical potential and current determine the type of cor-

rosion [12.61]. The slope of the power-spectrum den-

Part D 12.3

Corrosion 12.3 Novel Electrochemical Test Methods 697

Voltage (mV)

1.22

–0.96

1.14

Time (h)

0 0.57

Current (nA)

660

–476

1.14

Time (h)

0 0.57

Cooling water 1

Voltage (mV)

0.236

–0.447

1.14

Time (h)

0.570

Current (nA)

–43.5

1.14

Time (h)

0 0.57

Cooling water 2

Fig. 12.34 Potential and current noise

at mild steel in different cooling

waters (after [12.61])

sity of the electrochemical voltage-noise relationship

[PSD(U)] after the removal of the linear trend was rec-

ognized as a signiﬁcant parameter for distinguishing be-

tween uniform and local corrosion. The electrochemical

noise generated by uniform corrosion is, white noise,

and therefore the slope is close to zero. Electrochem-

ical noise generated by localized corrosion consists of

PSD(U) [dB(V

/Hz)]

–120

–60

1000

Frequency (mHz)

0.1

PSD(U) [dB(V

/Hz)]

–120

–60

1000

Frequency (mHz)

0.1

PSD(I) [dB(A

/Hz)]

–60

–240

–120

1000

Frequency (mHz)

0.1

PSD(I) [dB(A

/Hz)]

–60

–240

–120

1000

Frequency (mHz)

0.1

Cooling water 1 Cooling water 2

PSD(U) = –73.8dB(V

/Hz)

Slope = 6.3dB(V

/Hz) decade

–1

PSD(I) = –140.1dB(A

/Hz)

Slope = 8.2dB(A

/Hz) decade

–1

PSD(U) = –94.8 dB(V

/Hz)

Slope = 15.3dB(V

/Hz) decade

–1

PSD(I) = –164.9dB(A

/Hz)

Slope = 3.1dB(A

/Hz) decade

–1

Fig. 12.35 Power-spectral density

(PSD) for potential and current noise

at mild steel in different cooling

waters (after [12.61])

exponentially decreasing transients and the slope of the

PSD(U) curve is higher (> 12 dB (V

−1

)) decade

−1

Figure 12.35 shows PSD(U) graphs that, for the

uniformly corroding steel in cooling water 1, the

slope is 6.3dB(V

−1

) decade

−1

, while the slope is

15.3dB(V

−1

) decade at the locally corroding steel

in cooling water 2.

Part D 12.3