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Hydrogen deposition at iron from liquid ammonia
Elecrrochimica Am,
Vol. 36, No. 2,
pp. 283-290,
1991
Printed in Great Britain.
0013-4686/91 $3.00 + 0.00 199 I. Pergamon Press pk.
0
HYDROGEN
DEPOSITION AT IRON FROM LIQUID AMMONIA M. KLEMM and K. E. HEUSLER
Abteilung Korrosion und Korrosionsschutx, Institut fur Metallkunde und Metallphysik, Technische Universitlt Clausthal, D 3392 Clausthal-Z., F.R.G. (Received 8 March 1990; in revised form 23 April 1990) Abstract-The nermeation of hydrogen through iron sheets from a solution of ammonium chloride in liquid ammonia to an aqueous solution of 0.1 M sodium hydroxide was studied. The square of the hydrogen activity was proportional to the cathodic current density of hydrogen deposition as expected for a Volmer-Tafel mechanism. Exchange rates of the Tafel reaction were around ~r,~= 4 pmol/cm-* s-’
corresponding to j, = 0.4 pA/cm-*. The dependence of the hydrogen activity on the free corrosion potential can also be explained by a Volmer-Tafel mechanism, but not by a Volmer-Heyrovsky mechanism. Slow changes of the surface properties apparently due to a chemical reaction of ammonia with iron decrease the hydrogen activity and catalyse the Tafel recombination with respect to the Volmer reaction. Key words: hydrogen electrode, iron, liquid ammonia.
INTRODUCTION
the activity a of atomic hydrogen at the iron surface is expressed by
In liquid ammonia iron and steel corrode slowly by deposition of hydrogen[ 1,2] resulting in hydrogen embrittlementp, 41. In acidic solutions the charge transfer is rate determining. The Tafel slopes for hydrogen formation decrease with temperature from about 180 mV/decade at 233 K to about 100 mV at 293 K[5]. An analogous strong temperature dependence of the Tafel slope was also observed for hydrogen deposition at platinum[6]. No definite conclusions regarding the mechanism of the hydrogen electrode could be drawn from the earlier experiments. However, the susceptibility of steel to hydrogen embrittlement grew with the cathodic current density of hydrogen deposition indicating a Volmer-Tafel mechanism as for the hydrogen electrode in aqueous electrolytes. In the present work, measurements of hydrogen permeation are used to elucidate the mechanism of hydrogen deposition at iron in liquid ammonia. The Volmer reaction in liquid ammonia can be written NH: +e-
$ H,,+NH,.
It is followed by three competing steps, the Tafel reaction
(1) parallel reaction
2H,, * Hz,
(2)
the Heyrovsky reaction H,,+NH$ and the dissolution
+e-
eHz+NH3,
(3)
of hydrogen into iron H,, * H,b.
(4)
The rates can be expressed using the exchange current densities j,, the coverage 8 with adsorbed hydrogen atoms and their activity a. For a Langmuir isotherm
a = (P(H,)W’(H,)Y’* = ((1 - @,)/@,){@/(l
- 6% (5)
where 8 is the coverage and coverage at any partial pressure hydrogen in the electrolyte and activity. One finds[7,8] for the iv =j,,{(l
8, the equilibrium p ‘(Hz) of molecular at any hydrogen ion rate of step (1)
- W/(1 - @,)1
x {a exp(1 - a,)qF/RT
- exp - a&/RI’},
(6)
of step (2) jT=jro{(l
- @)/(l - @,)}*(l -a*),
(7)
and of step (3) j, =jH,O{(l - @)/(l - @,)> x {exp(l - a,)qF/RT
-a
exp -a,qF/RT},
(8)
with the respective exchange current densities iv,,, j,,, and j,,. The rate of the Tafel recombination IS grven in terms of a current density jr = Fv,, although it is a chemical reaction with the rate or. The value of (1 - S)/(l - 8,) is very close to one, since the hydrogen coverage on iron always remains 8 6 1. The small coverages also justify the use of the Langmuir isotherm. In the subsequent equations (1 - S)/(l - 8,) = 1 will be assumed. The rate of step (4) is determined by diffusion of hydrogen into the iron, while the equilibrium between adsorbed and absorbed hydrogen is maintained at the surface. For steady state diffusion through a sheet of the thickness d and the hydrogen activity a +O at the exit side the permeation current becomes jP = FDc, up, Id, 283
(9)
M. KLEMM and K. E. HEUSLER
284
with the diffusion coefficient D = 9.3 low5 cm2 s-’ of hydrogen, its concentration c, = 2.12 low9 mol cm-’ for p(H,) = 1 bar, both at 2O”C[9], and the dimensionless equilibrium pressure p, related to 1 bar. Since p. was not known in solutions to which hydrogen was not added, the activity uH = ap, will be used. With the general relation[8] for the total cathodic current density 1j 1 Ij I -j, = JhJ + IAl
(10)
one obtains from equation (7) for the Volmer-Tafel mechanism with j, $ j, the hydrogen activity at the entry surface a = (1 + (Ijl -j,)/j,,Y”
(11)
and for the Volmer-Heyrovsky mechanism j, < j, using equation (8) far from equilibrium a = I(lj 1-jpY2jH,bw
wP’/RT.
with (12)
If jp < j and cly= CL~ = 0.5, for the Volmer-Tafel mechanism the hydrogen activity increases with the cathodic overpotential according to a = (jy,,/j2,0)‘/2 exp -a,Fq/2RT. For the Volmer-Heyrovsky activity a = (j,,/j&exp
(13)
mechanism the hydrogen -(a,
- Q)F~IRT
becomes independent of the overpotential,
(14) if ay = aH.
EXPERIMENTAL The cell used for the permeation experiments is shown in Fig. 1. According to the principle of Devanathan and Stachurski[lO] there were two compartments divided by a metal sheet with an area A = 6.8 cm2 as the working electrode. The left compartment was filled with liquid ammonia from which hydrogen was deposited using as the counter electrode a platinum sheet with A = 6 cm*. The stainless steel cell wall or a platinum wire insulated by
Fig. I. Permeation cell with membrane M separating the left comnartment filled with liauid ammonia (NH,) from the righi compartment filled wiih an aqueous s&&n of 0.1 M NaOH. Gl and G2 are the Pt counter electrodes, RI a Pt reference electrode and R2 a Ni reference electrode in the respective cells. After distillation of ammonia into the left compartment, valve Vl is closed and valve V2 is opened to establish the pressure above the left compartment to the right compartment via a PTFE bellow.
PTFE except for the tip ending at a distance of about 3 mm from the center of the working electrode were used as reference electrodes. Both electrodes had time dependent potentials of 0.0 (kO.05) V us the Tl/TlCl electrode in 0.1 M ammonium chloride. During long term experiments the Tl/TlCl reference electrode was avoided because of the danger to deposit thallium on the working electrode from thallium chloride leaking into the cell electrolyte. The right compartment ended in a PTFE bellow in a metal casing in which the vapour pressure of the liquid ammonia above the left compartment was maintained. Hydrogen permeating through the metal sheet was oxidized at the working electrode. The counter electrode of the right compartment was a platinum sheet and the reference electrode an oxidized nickel wire. The whole permeation cell was electrically insulated by a polyethylene bag from the mixture of water and glycol in the thermostat. Potentiostats (Jaissle 1031A and 1001 T-NC, respectively) were used for polarization at the left and right compartments. Cathodic polarization was also performed under galvanostatic conditions. The metal sheets of 40 mm diameter with a thickness between 0.2 and 0.6mm were made from pure iron with 99.998% Fe (Johnson-Matthey) or from the steel StE 500 (Thyssen). The cathodic side was polished mechanically down to 0.25 pm aluminium oxide. The anodic side was roughened. The metal sheet was washed with methanol and dried with pressurized air. After covering the cathodic side with vinyl lacquer (Wirtz) palladium was deposited by dipping the sample from an insulated palladium wire for 3 s into an aqueous solution of 30 g I- ’ PdCI, and 3Ogl-’ NH,Cl. The deposit was uniform and nonporous according to microscopic inspection. The lacquer and the palladium wire were removed, the thickness of the sample was measured and three copper wires were fastened to the side by spot welding. After filling the right compartment with a deaerated aqueous solution of 0.1 M sodium hydroxide the cell was assembled. The desired amount of dry salt was filled into the left compartment through a window which was subsequently closed. This compartment was connected to the ammonia supply system and evacuated to a pressure of about 2 Pa. The valve towards the metal casing around the right compartment was closed and the valve towards the ammonia supply opened. The cell was then cooled down in order to distill ammonia into the left compartment from a supply vessel kept at room temperature. The ammonia (Chemogas) was originally contaminated by water which was removed together with oxygen by keeping the ammonia for 4-7 days in contact with sodium. After filling the left compartment with purified ammonia the cell was disconnected from the supply, the valve towards the casing opened and the whole cell thermostatted to usually 20°C or 25°C.
RESULTS The permeation current was independent of the electrode potential at the working electrode of the right compartment in the range between 0.15 and 0.55 V us the nickel reference electrode in an aqueous solution with 0.1 M sodium hydroxide. Below 0.15 V
Hydrogen deposition at iron from liquid ammonia 1 l-
I
I
I
1
285
I - -160
6-
% \
--120 lLY
- -100 I
I
I
I
1
I
10
20
30
40
50
60
2 0
70
t/h Fig. 2. Fluctuations of the free corrosion potential E, USstainless steel and of the hydrogen activity II” with time at an iron membrane, d = 0.47 mm, in liquid ammonia with 0.1 M NH,Cl at 25°C.
the hydrogen oxidation was determined by charge transfer. At potentials above the 0.55 V oxygen was evolved. A potential of 0.35 V was applied during all further permeation experiments. At this potential the current was measured before filling the left compartment with ammonia. The currents dropped with time. A steady state was attained after about one day. The steady state current densities between 0.1 PA cm-’ and 0.2 PA cmm2 at 20°C and the smaller ones at lower temperatures were used to correct the permeation currents. At later times when the left compartment was filled with ammonia, the anodic current was determined by the much shorter permeation time of the hydrogen. During galvanostatic polarization of steel membranes, electrode potentials and permeation currents became independent of time only after several days. At the free corrosion potential steady states were not observed even after such long times. Otherwise the results with steel were the same as with pure iron, Figure 2 shows the fluctuations of the free corrosion potential of iron and the corresponding hydrogen activities during almost 70 h. The measurements were started after filling the cell with ammonia for about 2 h and establishing a constant temperature 6
I
I
for about 6 h. The fluctuations continued for several days. According to Fig. 3, during the fluctuations the logarithm of the activity was linearly related to the potential. The slope is about dE,/d Ig aH = -0.175 Vdec-‘. Figure 2 is an extreme example of the fluctuations. The usual fluctuations of the free corrosion potential were much smaller corresponding to changes Aa, < 1 of the hydrogen activity. The hydrogen activity aH at the free corrosion potential grew with the concentration of ammonium chloride. Measurements referring to short times after immersion of the sample into the liquid ammonia are shown in Fig. 4. A linear relation between the logarithms of the hydrogen activity and the activity of ammonium chloride was observed the slope being d In a,/d In a(NH,Cl) = 0.8 (kO.3). The activities of ammonium chloride at different concentrations were taken from the work of Ritchey and Hunt[l I]. After stepping the current to some cathodic value the permeation current rose to an apparent steady state value within a few minutes. Figure 5 shows an example. At the membrane with the thickness d = 0.44 mm half of the effect was established after t,,r = 97 s independent of the applied current density and of the solution composition. If the cathodic polarization at constant current was continued, the permeation current dropped to a
I
5
5
4
3 ,’ 2
1
2 -180
-160
-140
-120
1 -100
E,/mV
Fig. 3. Linear correlation of the logarithm of the hydrogen activity aa with . the . free corrosion potential E, LXstainless steel in the experiment shown in Fig. 2.
0.003
d__i_ 0.005
0.01
0.02 0.03
a(NH,,CI)
Fig. 4. Dependence of the hydrogen activity uu at the free corrosion potential of an iron membrane during a few hours after immersion on the activity a(NH,CI) of ammonium chloride in liquid ammonia at 20°C.
. 286
M. KLEMMand K. E. HEUSLER 0.8
0,s . 0
1
2
3
4
5
6
t/ min Fig. 5. Dependence of the permeation current density jP at an iron membrane, d = 0.44mm, in liquid ammonia with 1 M ammonium chloride at 20°C after applying a cathodic current density of j = 0.15 ~Acm-*.
steady state during a few hours. As shown in Fig. 6 the electrode potential became more negative during this time by a few mV, only. The difference of the permeation current to its steady state value decayed exponentially. The characteristic time of about 120 min was independent of the electrode potential and of the concentration of ammonium chloride, but became shorter with the temperature corresponding to an activation enthalpy of about AH: = 60 kJ mol-‘. After interruption of the cathodic current the permeation current usually dropped within about 15 min to the value corresponding to the free cor3.0
0.1’
1 0
I
,
I
1
2
3
t/h
Fig. 6. Dependence on time I of the permeation current density j,, of the electrode potential E us stainless steel (a), and of the difference, iP-j& (b) between the permeation current density jP and -its steady state ialue j) = 2.35 ~Acrnat an iron membrane, d = 0.47 mm, in liouid ammonia with 0.1 M ammonium chloride at 20°C ifter applying a cathodic current density of j = IO~Acm-*.
rosion potential, but sometimes, in particular at high concentrations of ammonium chloride, it dropped to a slightly smaller value from which it recovered during a few hours. After a potentiostatic step the cathodic current decreased during the first few hours, but increased again at later times as shown in Fig. 7. The initial decrease of the current corresponds to the increase of the cathodic polarization in the galvanostatic experiment. The permeation current dropped monotonously. Both the cathodic current and the permeation current can be described by two parallel processes with the same respective characteristic times. The characteristic time of the fast process was about 120 min and equal to the one observed during galvanostatic polarization. The characteristic time of the slow process was about 10.5 h. The increase of the permeation current in Fig. 7 at very long times indicates the beginning of chaotic long term fluctuations which were observed with 0.1 M ammonium chloride solution at cathodic current densities exceeding IO p A cm-* close to a limiting current density. Figure 8 shows a cathodic polarization curve measured during nearly 70 h by the galvanodynamic method. The current density was increased at the rate of O.l5pAcm-*h-l to j=4pAcm-*, at 0.30pAcm-‘h-’ to 10pAcm-2, and at 0.45 p A cmm2 h- ’ for higher current densities. The polarization curve followed a Tafel line with the slope dE/d lg j = 0.13 V dec-’ from the corrosion current density up to about 10 PA cm-*. In other measurements Tafel slopes between 0.10 V dec-’ and 0.14 V dec-’ were observed. A limiting current density of about 20 p A cm-2 was approached in these long term experiments. It is probably a diffusion limited current density fluctuating slowly due to natural convection. It was not possible to stir the liquid ammonia in the permeation cell. The hydrogen activities uH corresponding to Fig. 8 are shown in Fig. 9. The square of the hydrogen activity increased nearly proportional to j-j,,. The deviations from linearity were completely absent when the experiment was repeated with the same electrode. An experiment with another electrode is shown in Fig. 10. The linear relationship between uh
20
30
10
50
t/h Fig. 7. Dependence on time t of the cathodic current densityj (a) and of the difference,j, -i; (b) between the permeation current density jP and its steady state value fP = 2.5 PA cm-*, or of the corresponding hydrogen activities, uu - 021, at an iron membrane, d = 0.49mm, in liquid ammonia with 0.02 M ammonium chloride at 20°C after applying an electrode potential E = -0.30 V USplatinum. j, and j2 show the contributions to the cathodic current density with characteristic times equal to those of the respective permeation current densities j,, and j,+r. 20.00 10.00 -
I . lm .rn O 00
I
I
I I
00
5.00
I I I
2.00
1,oo 2.00 0,50
% i;i 1.00 . =
d' 0,20
0.50 -
0.10 0.20 0.05 0,lO 0 0.05 -LOO
I -300
1 -200 F/mV
I -100
I 01
0.02
0
Fig. 8. Cathodic current density j and hydrogen activity an at an iron membrane, d = 0.47 mm, in liquid ammonia with 0. I M ammonium chloride at 2OC as a function of the electrode potential E LXstainless steel measured by the galvanodynamic method as described in the text.
288
M. KLEMMand K. E. HEUSLER
40
r 0.
30 0
0
0
0
0
6
0
/
5
sp 00
“Z 20
I:/o/-,
d’
,,,,,
A0
4 3 2
2
4
6
8
10
12
Ij I-j,/f~Acm-’
Fig. 9. Hydrogen activity ua us the difference, j -j,, between the cathodic current density j and the permeation current density jP, (1) according to measurements in Fig. 8 (O), and (2) during a second experiment under the same conditions (a).
and j - jP is again observed up to j - jP x 10 n A cm-‘. At higher current densities the hydrogen activities fluctuated slowly with time. Figure 10 shows mean values taken during < 8 h scattering around aH = I.
in[9]. the activity was obtained by also considering the temperature dependence of the solubility c, . From the mean slopes in Fig. 11 one finds apparent enthalpies AH, = 47 kJ mol-’ and AH, = 20 kJ mol-‘, respectively.
Figure 11 shows that both the hydrogen concentration at the iron surface and the corresponding hydrogen activity measured at the free corrosion potential in 0.1 M ammonium chloride solution increased with the temperature. The measurements were taken, when a constant temperature was established, within about 6 h. The hydrogen concentration was calculated from equation (9) using the temperature dependence of the diffusion coefficient D,, given
The strong dependence of the permeation current density or of the corresponding hydrogen activity on the electrode potential or on the cathodic current density is almost certainly due to a Volmer-Tafel mechanism. From the linear dependence between ai and j - jP one calculates with equations (9) and (11) for aH = 1 exchange current densities of the Tafel
DISCUSSION
70 -
0 -8
a
60 -
0
50 -
0
0
0
-7 aI:
40 0
0
-6
0
30 -
-5 20 -4 10 0
-3 0
10
20
30
40
1j 1-j, /pActi*
Fig. 10. Hydrogen activity uH (;s the difference, j - jP, between the cathodic current density j and the permeation current density j, at an iron membrane, d = 0.47 mm, in liquid ammonia with 0.1 M ammonium chloride at 20°C. The fluctuating values correspond to measurements with cathodic current densities exceeding the limiting current density.
Hydrogen deposition at ron from liquid ammonia
described by two processes with the same characteristic times, ie for the cathodic current density
T IY 30
10
20
289
2.0
j = (j; + (j; -j;)
1
+ (jt+(jp-jqlexp
1.0 *I
u
,’
exp -t/r,
0.5
0.2 3.3
3.4
3.5
3.6
T-1110-31(
Fig. Il. Dependence on temperature T of the concentration CR (0) and of the hydrogen activity uH (0) at the surface of an iron membrane d = 0.47 mm at the free corrosion potential in 0.1 M ammonium chloride solution in liquid
ammonia. recombination jr.” = 0.18 PAcm-* from Fig. 10 and jr.” = 0.35 PA cm-* from curve 2 in Fig. 9. Curve 1 in Fig. 9 yields values betweenj,, = 0.9 PA cmm2 at low cathodic current densities to jr.0 = 0.28 PA cm-* at high current densities. The experiments obeying equation (11) cannot be explained by a VolmerHeyrovsky mechanism. Therefore, such an explanation of curve 1 in Fig. 9 cannot be justified. Also, using equations (6) and (14) a comparison of the slopes in Fig. 8, dE/d lg j = -0.13 V dec-’ and dE/d lg jP = 0.175 V/dec-‘, would yield uy = 0.45 and the rather improbable transfer coefficient LX”= 0.12. The apparent decrease of the exchange current density of the Tafel recombination is obviously due to a time dependent modification of the catalytic properties of the electrode surface during the several days of the experiment. The fast change of the permeation current shown in Fig, 5 is caused by the instationary penetration of hydrogen from the entry side to the exit side. Using the relation D* = 0.138d2/t,,2,
(1%
given by McBreen et a1.[12] one finds for d = 0.044cm and t,,* = 97 s an apparent diffusion coefficient D* = 2.8 10e6 cm* SK’. The apparent diffusion coefficient depends on the density of hydrogen traps in the iron. Chaudhary and Riecke[l3] observed values in the range 8 1Om8< D*/cm* s-’ < 2 10m5depending on the mechanical pretreatment of the iron, ie on the density of grain boundaries and dislocations which act as traps. The slow time dependence of the permeation current in principle must be explained by a change of the hydrogen activity at the entrance side. The results in Fig. 6 are interpreted by an exponential decrease with time of the activity from initially aH = 7.5 to aH = 5.8 in the steady state. With the constant cathodic current density one calculates an increase of the exchange current density of the Tafel recombination from the initial value jr.,, = 13 PA cm-* to the steady state value jr.,, = 0.23 PA cm-‘. Figure 7 shows that the cathodic current density j and the permeation current density j,, both can be
-t/T2},
(16)
with the initial current density jn = jy + jz and the steady state current densityj” =j; +f2. An analogous equation holds for the permeation current density j,. The differences j$., -iR, and jnp2 -j$, both are positive. On the other hand, j; -J ‘is positive, but j; -jg is negative. The effects are relatively small. From Fig. 7 one calculates initial values uH = 8.4 and jr,” = 0.24 PA cm-*, at the minimum cathodic current density aH = 6.9 and jr.0 = 0.37 PA cm-*, and in the steady state uH = 6.4 and jr.0 = 0.4 PA cm-‘. The potentiostatic results mean that the modification of the surface characterized by the characteristic time T, simultaneously increases the exchange current density of the Tafel recombination and decreases the exchange current density of the Volmer reaction. The latter effect is qualitatively indicated in the galvanostatic experiment by the small increase with time of the overpotential. The second process with the longer characteristic time t2 increases both exchange current densities. However, one cannot exclude that in this case the decrease of the activity uH may be due to a contribution of the electrochemical recombination to the total current density. Since both characteristic times are independent of the electode potential and of the concentration of ammonium chloride, the modification of the surface changing the hydrogen deposition kinetics must be due to a chemical process, very probably a chemical reaction between the iron surface and the ammonia. The correlation between the corrosion potential and the activity aH in Fig. 3 is compatible with a Volmer-Tafel mechanism. A Volmer-Heyrovsky mechanism would predict aH being independent of the corrosion potential. Assuming for the hydrogen deposition an electrochemical reaction order y = I with respect to the activity of ammonium chloride, the corrosion current density should depend on the activity a(NH,CI) as dInj,/d
lna(NH,Cl)=a+/(a+
+a_),
(17)
with the apparent transfer coefficients LY+ = 0.82 (+0.04)[2,5] and tl_ =O.SS(+O.l). Since for the Volmer-Tafel mechanism j, = jv x ai j,,,, a value d In an/d In u(NH,CI) = 0.3( f0.02) is predicted. Equation (17) describes the corrosion rate due to hydrogen deposition. In practice, this rate is often only a small part of the actual corrosion rate which is mainly determined by some residual oxidant like oxygen in the solution[2,5]. Then, the corrosion potential and the total corrosion rate become practically independent of the activity of the acid, but the rate of hydrogen deposition jH and the corresponding, relatively small contribution to the total corrosion rate grow linearly with this activity. From this limiting case one predicts d In a,/d In a(NH,CI) z 0.5 which agrees to the experimental value 0.8( kO.3) in view of the relatively large mean deviation. The temperature dependence of the hydrogen activity uH in Fig. 11 is given by the respective
M. KLEMMand K. E. HEUSLER
290
current densities due to hydrogen deposition. The hydrogen activity would remain constant if the current density of hydrogen deposition at the corrosion potential changed with the temperature in the same way as the solubility c,. The increase of the hydrogen activity with temperature indicates that the corrosion current density due to hydrogen deposition at the corrosion potential grows with temperature nearly twice as fast as the solubility.
corrosion
Acknowledgement-This work was supported by a grant of the German Federal Minister of Research and Technology (BMFT) for research and development in the field of corrosion and corrosion protection.
REFERENCES I. M. Ahrens, W. Schmitt and K. E. Heusler, Werksrofi Kerr. 32, 197 (1981). 2. M. Ahrens and K. E. Heusler, Electrochim. Acta 21,239 (1982).
3. W. Schmitt and K. E. Heusler, Werksfofi Korr. 35,329 (1984). 4. M. Klemm and K. E. Heusler, Werksroffe Korr. 39,492 (1988). 5. M. Ahrens, Electrochemical Investigations of the Corrosion of Iron in Liquid Ammonia. Dissertation, Clausthal (I 979). 6. M. H. Miles and C. A. Yates, .I. electrochem. Sot. 121, 230 (1974). 7. K. J. Vetter, in Electrochemical Kinetics, p. 516. Academic Press, New York (1967). 8. E. G. Dafft. K. Bohnenkamn and H. J. Enaell. Corros. Sci. is,591 (1979). . 9. E. Riecke and K Bohnenkamp, Z. Metallkunde 75, 76 (1984).
10. M. A. V. Devanathan and Z. Stachurski, Proc. R. Sot. A270, 90 (1962). 11. H. W. Ritchey and H. Hunt, J. phys. Chem. 43, 407 (1939). 12. J. McBreen, L. Nanis and W. Beck, J. electrochem. Sot. 113, 1218 (1966). 13. R. S. Chaudhary and E. Riecke, Werksrofe Korr. 32,73 (1981).
Vol. 36, No. 2,
pp. 283-290,
1991
Printed in Great Britain.
0013-4686/91 $3.00 + 0.00 199 I. Pergamon Press pk.
0
HYDROGEN
DEPOSITION AT IRON FROM LIQUID AMMONIA M. KLEMM and K. E. HEUSLER
Abteilung Korrosion und Korrosionsschutx, Institut fur Metallkunde und Metallphysik, Technische Universitlt Clausthal, D 3392 Clausthal-Z., F.R.G. (Received 8 March 1990; in revised form 23 April 1990) Abstract-The nermeation of hydrogen through iron sheets from a solution of ammonium chloride in liquid ammonia to an aqueous solution of 0.1 M sodium hydroxide was studied. The square of the hydrogen activity was proportional to the cathodic current density of hydrogen deposition as expected for a Volmer-Tafel mechanism. Exchange rates of the Tafel reaction were around ~r,~= 4 pmol/cm-* s-’
corresponding to j, = 0.4 pA/cm-*. The dependence of the hydrogen activity on the free corrosion potential can also be explained by a Volmer-Tafel mechanism, but not by a Volmer-Heyrovsky mechanism. Slow changes of the surface properties apparently due to a chemical reaction of ammonia with iron decrease the hydrogen activity and catalyse the Tafel recombination with respect to the Volmer reaction. Key words: hydrogen electrode, iron, liquid ammonia.
INTRODUCTION
the activity a of atomic hydrogen at the iron surface is expressed by
In liquid ammonia iron and steel corrode slowly by deposition of hydrogen[ 1,2] resulting in hydrogen embrittlementp, 41. In acidic solutions the charge transfer is rate determining. The Tafel slopes for hydrogen formation decrease with temperature from about 180 mV/decade at 233 K to about 100 mV at 293 K[5]. An analogous strong temperature dependence of the Tafel slope was also observed for hydrogen deposition at platinum[6]. No definite conclusions regarding the mechanism of the hydrogen electrode could be drawn from the earlier experiments. However, the susceptibility of steel to hydrogen embrittlement grew with the cathodic current density of hydrogen deposition indicating a Volmer-Tafel mechanism as for the hydrogen electrode in aqueous electrolytes. In the present work, measurements of hydrogen permeation are used to elucidate the mechanism of hydrogen deposition at iron in liquid ammonia. The Volmer reaction in liquid ammonia can be written NH: +e-
$ H,,+NH,.
It is followed by three competing steps, the Tafel reaction
(1) parallel reaction
2H,, * Hz,
(2)
the Heyrovsky reaction H,,+NH$ and the dissolution
+e-
eHz+NH3,
(3)
of hydrogen into iron H,, * H,b.
(4)
The rates can be expressed using the exchange current densities j,, the coverage 8 with adsorbed hydrogen atoms and their activity a. For a Langmuir isotherm
a = (P(H,)W’(H,)Y’* = ((1 - @,)/@,){@/(l
- 6% (5)
where 8 is the coverage and coverage at any partial pressure hydrogen in the electrolyte and activity. One finds[7,8] for the iv =j,,{(l
8, the equilibrium p ‘(Hz) of molecular at any hydrogen ion rate of step (1)
- W/(1 - @,)1
x {a exp(1 - a,)qF/RT
- exp - a&/RI’},
(6)
of step (2) jT=jro{(l
- @)/(l - @,)}*(l -a*),
(7)
and of step (3) j, =jH,O{(l - @)/(l - @,)> x {exp(l - a,)qF/RT
-a
exp -a,qF/RT},
(8)
with the respective exchange current densities iv,,, j,,, and j,,. The rate of the Tafel recombination IS grven in terms of a current density jr = Fv,, although it is a chemical reaction with the rate or. The value of (1 - S)/(l - 8,) is very close to one, since the hydrogen coverage on iron always remains 8 6 1. The small coverages also justify the use of the Langmuir isotherm. In the subsequent equations (1 - S)/(l - 8,) = 1 will be assumed. The rate of step (4) is determined by diffusion of hydrogen into the iron, while the equilibrium between adsorbed and absorbed hydrogen is maintained at the surface. For steady state diffusion through a sheet of the thickness d and the hydrogen activity a +O at the exit side the permeation current becomes jP = FDc, up, Id, 283
(9)
M. KLEMM and K. E. HEUSLER
284
with the diffusion coefficient D = 9.3 low5 cm2 s-’ of hydrogen, its concentration c, = 2.12 low9 mol cm-’ for p(H,) = 1 bar, both at 2O”C[9], and the dimensionless equilibrium pressure p, related to 1 bar. Since p. was not known in solutions to which hydrogen was not added, the activity uH = ap, will be used. With the general relation[8] for the total cathodic current density 1j 1 Ij I -j, = JhJ + IAl
(10)
one obtains from equation (7) for the Volmer-Tafel mechanism with j, $ j, the hydrogen activity at the entry surface a = (1 + (Ijl -j,)/j,,Y”
(11)
and for the Volmer-Heyrovsky mechanism j, < j, using equation (8) far from equilibrium a = I(lj 1-jpY2jH,bw
wP’/RT.
with (12)
If jp < j and cly= CL~ = 0.5, for the Volmer-Tafel mechanism the hydrogen activity increases with the cathodic overpotential according to a = (jy,,/j2,0)‘/2 exp -a,Fq/2RT. For the Volmer-Heyrovsky activity a = (j,,/j&exp
(13)
mechanism the hydrogen -(a,
- Q)F~IRT
becomes independent of the overpotential,
(14) if ay = aH.
EXPERIMENTAL The cell used for the permeation experiments is shown in Fig. 1. According to the principle of Devanathan and Stachurski[lO] there were two compartments divided by a metal sheet with an area A = 6.8 cm2 as the working electrode. The left compartment was filled with liquid ammonia from which hydrogen was deposited using as the counter electrode a platinum sheet with A = 6 cm*. The stainless steel cell wall or a platinum wire insulated by
Fig. I. Permeation cell with membrane M separating the left comnartment filled with liauid ammonia (NH,) from the righi compartment filled wiih an aqueous s&&n of 0.1 M NaOH. Gl and G2 are the Pt counter electrodes, RI a Pt reference electrode and R2 a Ni reference electrode in the respective cells. After distillation of ammonia into the left compartment, valve Vl is closed and valve V2 is opened to establish the pressure above the left compartment to the right compartment via a PTFE bellow.
PTFE except for the tip ending at a distance of about 3 mm from the center of the working electrode were used as reference electrodes. Both electrodes had time dependent potentials of 0.0 (kO.05) V us the Tl/TlCl electrode in 0.1 M ammonium chloride. During long term experiments the Tl/TlCl reference electrode was avoided because of the danger to deposit thallium on the working electrode from thallium chloride leaking into the cell electrolyte. The right compartment ended in a PTFE bellow in a metal casing in which the vapour pressure of the liquid ammonia above the left compartment was maintained. Hydrogen permeating through the metal sheet was oxidized at the working electrode. The counter electrode of the right compartment was a platinum sheet and the reference electrode an oxidized nickel wire. The whole permeation cell was electrically insulated by a polyethylene bag from the mixture of water and glycol in the thermostat. Potentiostats (Jaissle 1031A and 1001 T-NC, respectively) were used for polarization at the left and right compartments. Cathodic polarization was also performed under galvanostatic conditions. The metal sheets of 40 mm diameter with a thickness between 0.2 and 0.6mm were made from pure iron with 99.998% Fe (Johnson-Matthey) or from the steel StE 500 (Thyssen). The cathodic side was polished mechanically down to 0.25 pm aluminium oxide. The anodic side was roughened. The metal sheet was washed with methanol and dried with pressurized air. After covering the cathodic side with vinyl lacquer (Wirtz) palladium was deposited by dipping the sample from an insulated palladium wire for 3 s into an aqueous solution of 30 g I- ’ PdCI, and 3Ogl-’ NH,Cl. The deposit was uniform and nonporous according to microscopic inspection. The lacquer and the palladium wire were removed, the thickness of the sample was measured and three copper wires were fastened to the side by spot welding. After filling the right compartment with a deaerated aqueous solution of 0.1 M sodium hydroxide the cell was assembled. The desired amount of dry salt was filled into the left compartment through a window which was subsequently closed. This compartment was connected to the ammonia supply system and evacuated to a pressure of about 2 Pa. The valve towards the metal casing around the right compartment was closed and the valve towards the ammonia supply opened. The cell was then cooled down in order to distill ammonia into the left compartment from a supply vessel kept at room temperature. The ammonia (Chemogas) was originally contaminated by water which was removed together with oxygen by keeping the ammonia for 4-7 days in contact with sodium. After filling the left compartment with purified ammonia the cell was disconnected from the supply, the valve towards the casing opened and the whole cell thermostatted to usually 20°C or 25°C.
RESULTS The permeation current was independent of the electrode potential at the working electrode of the right compartment in the range between 0.15 and 0.55 V us the nickel reference electrode in an aqueous solution with 0.1 M sodium hydroxide. Below 0.15 V
Hydrogen deposition at iron from liquid ammonia 1 l-
I
I
I
1
285
I - -160
6-
% \
--120 lLY
- -100 I
I
I
I
1
I
10
20
30
40
50
60
2 0
70
t/h Fig. 2. Fluctuations of the free corrosion potential E, USstainless steel and of the hydrogen activity II” with time at an iron membrane, d = 0.47 mm, in liquid ammonia with 0.1 M NH,Cl at 25°C.
the hydrogen oxidation was determined by charge transfer. At potentials above the 0.55 V oxygen was evolved. A potential of 0.35 V was applied during all further permeation experiments. At this potential the current was measured before filling the left compartment with ammonia. The currents dropped with time. A steady state was attained after about one day. The steady state current densities between 0.1 PA cm-’ and 0.2 PA cmm2 at 20°C and the smaller ones at lower temperatures were used to correct the permeation currents. At later times when the left compartment was filled with ammonia, the anodic current was determined by the much shorter permeation time of the hydrogen. During galvanostatic polarization of steel membranes, electrode potentials and permeation currents became independent of time only after several days. At the free corrosion potential steady states were not observed even after such long times. Otherwise the results with steel were the same as with pure iron, Figure 2 shows the fluctuations of the free corrosion potential of iron and the corresponding hydrogen activities during almost 70 h. The measurements were started after filling the cell with ammonia for about 2 h and establishing a constant temperature 6
I
I
for about 6 h. The fluctuations continued for several days. According to Fig. 3, during the fluctuations the logarithm of the activity was linearly related to the potential. The slope is about dE,/d Ig aH = -0.175 Vdec-‘. Figure 2 is an extreme example of the fluctuations. The usual fluctuations of the free corrosion potential were much smaller corresponding to changes Aa, < 1 of the hydrogen activity. The hydrogen activity aH at the free corrosion potential grew with the concentration of ammonium chloride. Measurements referring to short times after immersion of the sample into the liquid ammonia are shown in Fig. 4. A linear relation between the logarithms of the hydrogen activity and the activity of ammonium chloride was observed the slope being d In a,/d In a(NH,Cl) = 0.8 (kO.3). The activities of ammonium chloride at different concentrations were taken from the work of Ritchey and Hunt[l I]. After stepping the current to some cathodic value the permeation current rose to an apparent steady state value within a few minutes. Figure 5 shows an example. At the membrane with the thickness d = 0.44 mm half of the effect was established after t,,r = 97 s independent of the applied current density and of the solution composition. If the cathodic polarization at constant current was continued, the permeation current dropped to a
I
5
5
4
3 ,’ 2
1
2 -180
-160
-140
-120
1 -100
E,/mV
Fig. 3. Linear correlation of the logarithm of the hydrogen activity aa with . the . free corrosion potential E, LXstainless steel in the experiment shown in Fig. 2.
0.003
d__i_ 0.005
0.01
0.02 0.03
a(NH,,CI)
Fig. 4. Dependence of the hydrogen activity uu at the free corrosion potential of an iron membrane during a few hours after immersion on the activity a(NH,CI) of ammonium chloride in liquid ammonia at 20°C.
. 286
M. KLEMMand K. E. HEUSLER 0.8
0,s . 0
1
2
3
4
5
6
t/ min Fig. 5. Dependence of the permeation current density jP at an iron membrane, d = 0.44mm, in liquid ammonia with 1 M ammonium chloride at 20°C after applying a cathodic current density of j = 0.15 ~Acm-*.
steady state during a few hours. As shown in Fig. 6 the electrode potential became more negative during this time by a few mV, only. The difference of the permeation current to its steady state value decayed exponentially. The characteristic time of about 120 min was independent of the electrode potential and of the concentration of ammonium chloride, but became shorter with the temperature corresponding to an activation enthalpy of about AH: = 60 kJ mol-‘. After interruption of the cathodic current the permeation current usually dropped within about 15 min to the value corresponding to the free cor3.0
0.1’
1 0
I
,
I
1
2
3
t/h
Fig. 6. Dependence on time I of the permeation current density j,, of the electrode potential E us stainless steel (a), and of the difference, iP-j& (b) between the permeation current density jP and -its steady state ialue j) = 2.35 ~Acrnat an iron membrane, d = 0.47 mm, in liouid ammonia with 0.1 M ammonium chloride at 20°C ifter applying a cathodic current density of j = IO~Acm-*.
rosion potential, but sometimes, in particular at high concentrations of ammonium chloride, it dropped to a slightly smaller value from which it recovered during a few hours. After a potentiostatic step the cathodic current decreased during the first few hours, but increased again at later times as shown in Fig. 7. The initial decrease of the current corresponds to the increase of the cathodic polarization in the galvanostatic experiment. The permeation current dropped monotonously. Both the cathodic current and the permeation current can be described by two parallel processes with the same respective characteristic times. The characteristic time of the fast process was about 120 min and equal to the one observed during galvanostatic polarization. The characteristic time of the slow process was about 10.5 h. The increase of the permeation current in Fig. 7 at very long times indicates the beginning of chaotic long term fluctuations which were observed with 0.1 M ammonium chloride solution at cathodic current densities exceeding IO p A cm-* close to a limiting current density. Figure 8 shows a cathodic polarization curve measured during nearly 70 h by the galvanodynamic method. The current density was increased at the rate of O.l5pAcm-*h-l to j=4pAcm-*, at 0.30pAcm-‘h-’ to 10pAcm-2, and at 0.45 p A cmm2 h- ’ for higher current densities. The polarization curve followed a Tafel line with the slope dE/d lg j = 0.13 V dec-’ from the corrosion current density up to about 10 PA cm-*. In other measurements Tafel slopes between 0.10 V dec-’ and 0.14 V dec-’ were observed. A limiting current density of about 20 p A cm-2 was approached in these long term experiments. It is probably a diffusion limited current density fluctuating slowly due to natural convection. It was not possible to stir the liquid ammonia in the permeation cell. The hydrogen activities uH corresponding to Fig. 8 are shown in Fig. 9. The square of the hydrogen activity increased nearly proportional to j-j,,. The deviations from linearity were completely absent when the experiment was repeated with the same electrode. An experiment with another electrode is shown in Fig. 10. The linear relationship between uh
20
30
10
50
t/h Fig. 7. Dependence on time t of the cathodic current densityj (a) and of the difference,j, -i; (b) between the permeation current density jP and its steady state value fP = 2.5 PA cm-*, or of the corresponding hydrogen activities, uu - 021, at an iron membrane, d = 0.49mm, in liquid ammonia with 0.02 M ammonium chloride at 20°C after applying an electrode potential E = -0.30 V USplatinum. j, and j2 show the contributions to the cathodic current density with characteristic times equal to those of the respective permeation current densities j,, and j,+r. 20.00 10.00 -
I . lm .rn O 00
I
I
I I
00
5.00
I I I
2.00
1,oo 2.00 0,50
% i;i 1.00 . =
d' 0,20
0.50 -
0.10 0.20 0.05 0,lO 0 0.05 -LOO
I -300
1 -200 F/mV
I -100
I 01
0.02
0
Fig. 8. Cathodic current density j and hydrogen activity an at an iron membrane, d = 0.47 mm, in liquid ammonia with 0. I M ammonium chloride at 2OC as a function of the electrode potential E LXstainless steel measured by the galvanodynamic method as described in the text.
288
M. KLEMMand K. E. HEUSLER
40
r 0.
30 0
0
0
0
0
6
0
/
5
sp 00
“Z 20
I:/o/-,
d’
,,,,,
A0
4 3 2
2
4
6
8
10
12
Ij I-j,/f~Acm-’
Fig. 9. Hydrogen activity ua us the difference, j -j,, between the cathodic current density j and the permeation current density jP, (1) according to measurements in Fig. 8 (O), and (2) during a second experiment under the same conditions (a).
and j - jP is again observed up to j - jP x 10 n A cm-‘. At higher current densities the hydrogen activities fluctuated slowly with time. Figure 10 shows mean values taken during < 8 h scattering around aH = I.
in[9]. the activity was obtained by also considering the temperature dependence of the solubility c, . From the mean slopes in Fig. 11 one finds apparent enthalpies AH, = 47 kJ mol-’ and AH, = 20 kJ mol-‘, respectively.
Figure 11 shows that both the hydrogen concentration at the iron surface and the corresponding hydrogen activity measured at the free corrosion potential in 0.1 M ammonium chloride solution increased with the temperature. The measurements were taken, when a constant temperature was established, within about 6 h. The hydrogen concentration was calculated from equation (9) using the temperature dependence of the diffusion coefficient D,, given
The strong dependence of the permeation current density or of the corresponding hydrogen activity on the electrode potential or on the cathodic current density is almost certainly due to a Volmer-Tafel mechanism. From the linear dependence between ai and j - jP one calculates with equations (9) and (11) for aH = 1 exchange current densities of the Tafel
DISCUSSION
70 -
0 -8
a
60 -
0
50 -
0
0
0
-7 aI:
40 0
0
-6
0
30 -
-5 20 -4 10 0
-3 0
10
20
30
40
1j 1-j, /pActi*
Fig. 10. Hydrogen activity uH (;s the difference, j - jP, between the cathodic current density j and the permeation current density j, at an iron membrane, d = 0.47 mm, in liquid ammonia with 0.1 M ammonium chloride at 20°C. The fluctuating values correspond to measurements with cathodic current densities exceeding the limiting current density.
Hydrogen deposition at ron from liquid ammonia
described by two processes with the same characteristic times, ie for the cathodic current density
T IY 30
10
20
289
2.0
j = (j; + (j; -j;)
1
+ (jt+(jp-jqlexp
1.0 *I
u
,’
exp -t/r,
0.5
0.2 3.3
3.4
3.5
3.6
T-1110-31(
Fig. Il. Dependence on temperature T of the concentration CR (0) and of the hydrogen activity uH (0) at the surface of an iron membrane d = 0.47 mm at the free corrosion potential in 0.1 M ammonium chloride solution in liquid
ammonia. recombination jr.” = 0.18 PAcm-* from Fig. 10 and jr.” = 0.35 PA cm-* from curve 2 in Fig. 9. Curve 1 in Fig. 9 yields values betweenj,, = 0.9 PA cmm2 at low cathodic current densities to jr.0 = 0.28 PA cm-* at high current densities. The experiments obeying equation (11) cannot be explained by a VolmerHeyrovsky mechanism. Therefore, such an explanation of curve 1 in Fig. 9 cannot be justified. Also, using equations (6) and (14) a comparison of the slopes in Fig. 8, dE/d lg j = -0.13 V dec-’ and dE/d lg jP = 0.175 V/dec-‘, would yield uy = 0.45 and the rather improbable transfer coefficient LX”= 0.12. The apparent decrease of the exchange current density of the Tafel recombination is obviously due to a time dependent modification of the catalytic properties of the electrode surface during the several days of the experiment. The fast change of the permeation current shown in Fig, 5 is caused by the instationary penetration of hydrogen from the entry side to the exit side. Using the relation D* = 0.138d2/t,,2,
(1%
given by McBreen et a1.[12] one finds for d = 0.044cm and t,,* = 97 s an apparent diffusion coefficient D* = 2.8 10e6 cm* SK’. The apparent diffusion coefficient depends on the density of hydrogen traps in the iron. Chaudhary and Riecke[l3] observed values in the range 8 1Om8< D*/cm* s-’ < 2 10m5depending on the mechanical pretreatment of the iron, ie on the density of grain boundaries and dislocations which act as traps. The slow time dependence of the permeation current in principle must be explained by a change of the hydrogen activity at the entrance side. The results in Fig. 6 are interpreted by an exponential decrease with time of the activity from initially aH = 7.5 to aH = 5.8 in the steady state. With the constant cathodic current density one calculates an increase of the exchange current density of the Tafel recombination from the initial value jr.,, = 13 PA cm-* to the steady state value jr.,, = 0.23 PA cm-‘. Figure 7 shows that the cathodic current density j and the permeation current density j,, both can be
-t/T2},
(16)
with the initial current density jn = jy + jz and the steady state current densityj” =j; +f2. An analogous equation holds for the permeation current density j,. The differences j$., -iR, and jnp2 -j$, both are positive. On the other hand, j; -J ‘is positive, but j; -jg is negative. The effects are relatively small. From Fig. 7 one calculates initial values uH = 8.4 and jr,” = 0.24 PA cm-*, at the minimum cathodic current density aH = 6.9 and jr.0 = 0.37 PA cm-*, and in the steady state uH = 6.4 and jr.0 = 0.4 PA cm-‘. The potentiostatic results mean that the modification of the surface characterized by the characteristic time T, simultaneously increases the exchange current density of the Tafel recombination and decreases the exchange current density of the Volmer reaction. The latter effect is qualitatively indicated in the galvanostatic experiment by the small increase with time of the overpotential. The second process with the longer characteristic time t2 increases both exchange current densities. However, one cannot exclude that in this case the decrease of the activity uH may be due to a contribution of the electrochemical recombination to the total current density. Since both characteristic times are independent of the electode potential and of the concentration of ammonium chloride, the modification of the surface changing the hydrogen deposition kinetics must be due to a chemical process, very probably a chemical reaction between the iron surface and the ammonia. The correlation between the corrosion potential and the activity aH in Fig. 3 is compatible with a Volmer-Tafel mechanism. A Volmer-Heyrovsky mechanism would predict aH being independent of the corrosion potential. Assuming for the hydrogen deposition an electrochemical reaction order y = I with respect to the activity of ammonium chloride, the corrosion current density should depend on the activity a(NH,CI) as dInj,/d
lna(NH,Cl)=a+/(a+
+a_),
(17)
with the apparent transfer coefficients LY+ = 0.82 (+0.04)[2,5] and tl_ =O.SS(+O.l). Since for the Volmer-Tafel mechanism j, = jv x ai j,,,, a value d In an/d In u(NH,CI) = 0.3( f0.02) is predicted. Equation (17) describes the corrosion rate due to hydrogen deposition. In practice, this rate is often only a small part of the actual corrosion rate which is mainly determined by some residual oxidant like oxygen in the solution[2,5]. Then, the corrosion potential and the total corrosion rate become practically independent of the activity of the acid, but the rate of hydrogen deposition jH and the corresponding, relatively small contribution to the total corrosion rate grow linearly with this activity. From this limiting case one predicts d In a,/d In a(NH,CI) z 0.5 which agrees to the experimental value 0.8( kO.3) in view of the relatively large mean deviation. The temperature dependence of the hydrogen activity uH in Fig. 11 is given by the respective
M. KLEMMand K. E. HEUSLER
290
current densities due to hydrogen deposition. The hydrogen activity would remain constant if the current density of hydrogen deposition at the corrosion potential changed with the temperature in the same way as the solubility c,. The increase of the hydrogen activity with temperature indicates that the corrosion current density due to hydrogen deposition at the corrosion potential grows with temperature nearly twice as fast as the solubility.
corrosion
Acknowledgement-This work was supported by a grant of the German Federal Minister of Research and Technology (BMFT) for research and development in the field of corrosion and corrosion protection.
REFERENCES I. M. Ahrens, W. Schmitt and K. E. Heusler, Werksrofi Kerr. 32, 197 (1981). 2. M. Ahrens and K. E. Heusler, Electrochim. Acta 21,239 (1982).
3. W. Schmitt and K. E. Heusler, Werksfofi Korr. 35,329 (1984). 4. M. Klemm and K. E. Heusler, Werksroffe Korr. 39,492 (1988). 5. M. Ahrens, Electrochemical Investigations of the Corrosion of Iron in Liquid Ammonia. Dissertation, Clausthal (I 979). 6. M. H. Miles and C. A. Yates, .I. electrochem. Sot. 121, 230 (1974). 7. K. J. Vetter, in Electrochemical Kinetics, p. 516. Academic Press, New York (1967). 8. E. G. Dafft. K. Bohnenkamn and H. J. Enaell. Corros. Sci. is,591 (1979). . 9. E. Riecke and K Bohnenkamp, Z. Metallkunde 75, 76 (1984).
10. M. A. V. Devanathan and Z. Stachurski, Proc. R. Sot. A270, 90 (1962). 11. H. W. Ritchey and H. Hunt, J. phys. Chem. 43, 407 (1939). 12. J. McBreen, L. Nanis and W. Beck, J. electrochem. Sot. 113, 1218 (1966). 13. R. S. Chaudhary and E. Riecke, Werksrofe Korr. 32,73 (1981).