The diffusion of hydrogen through pure iron membranes

Corrosion Science, 1966, Vol. 6, pp. 271 to 285. Pergamon Press Ltd. Printed in Great Britain

THE DIFFUSION OF HYDROGEN THROUGH PURE IRON MEMBRANES* S. WACH, A . P. MIODOWNIK a n d J. MACKOWIAK Department of Metallurgy and Materials Technology, Banersea College of Technology, London S.W. 11 (University of Surrey designate) Abstract--Diffusion coefficients for electrolytic hydrogen in iron membranes have been obtained, using a refined time-lag technique. Results show an initial fast diffusion, followed by a slower secondary stage. The initial stage yields diffusion coefficients of 1.9 x 10-5 cm2s -1 which are independent of the membrane thickness and agree closely with extrapolated high temperature values. The second stage yields considerably lower coefficients which vary with membrane thickness. Results indicate the formation of a barrier to hydrogen flow as diffusion proceeds. Calculations of the effective barrier thickness enable the correction of apparent coefficients reported in the literature, and quantitatively predict the anomalous thickness effect. R~sum~---Des coefficients de diffusion de l'hydrog~ne dlectrolytique dans des membranes de fer, ont 6t6 d6terminds ~t l'aide d'une technique amdliorde du temps de retard. Les rdsultats montrent qu'il existe une diffusion initiale rapide suivie d'une seconde 6tape plus lente. L'6tape initiale conduit ~. des coSfficients de diffusion de 1,9 × l0 -5 cm 2 s-1, qui sont ind6pendants de l'dpaisseur de la membrane et parfaitement en accord avec les valeurs extrapoldes ~t haute temp6rature. La seconde dtape conduit h des coefficients considdrablement plus faibles et qui ddpendent de l'dpaisseur de la membrane. Les rdsultats r6v61ent la formation d'une barri~re s'opposant la diffusion de l'hydrog~ne. Les calculs de l'6paisseur de la barri/~re rendent possible la correction des coefficients repris dans la littdrature et donne des prdvisions quantitatives sur l'effet d'une 6paisseur anormale. Zusammenfassung--Mit einer verbesserten instation§.ren Messtechnik wurde der Diffusionskoefftzient von elektrolytisch erzeugtem Wasserstoff in Eisenmembranen ermittelt. Die Versuche zeigen eine anf/inglich hohe Diffusionsgeschwindigkeit, an die sich ein niedrigerer Diffusionsstrom anschliesst. Der Anfangsteil der Messungen fiihrt zu Diffusionskoeffizienten von 1,9 × l0 -s cm2s-1, die unabhfingig v o n d e r Membrandicke und in guter ~bereinstimmung mit der Extrapolation von Hochtemperaturmesswerten sind. Der zweite Abschnitt der Messungen ergibt bedeutend niedrigere Diffusionskoeffizienten, die mit der Membrandicke varieren. Die Ergebnisse werden mit der Annahme der Bildung einer Diffusionsbarriere durch den Wasserstofffluss gedeutet. Eine Berechnung der wirksamen Dicke dieser Barriere ermSglicht die Korrektur der scheinbaren Diffusionskoeffizienten, die in der Literatur angegeben sind, und fiihren zu quantitativen Angaben fiber nine anomale Dickenabhfingigkeit des Diffusionskoeffizienten. Pe~epaT - - B u r n onpeaeaeHu H0aqb~nlDleHTbI RPt~yarll{ RJIrt aaeHTpo,a~ITnqecHoro n0;Iopoaa n me.aeanofl MeMSpaHe no yconepmeHcTnonannoMy MevoRy aanaaJIunanvtn. Peay.abTaTr~l noKaaar:,n, q'ro 3a Haqa~bnoa 6ucvpo~ ewaRi,lefi avtqbqbyar~vtczte~yew Bw0paA, 6onee Me~neHHaA. H a q a a b n a A CTa~DIA ~Iaew Hoaqbq~ienT~i Rnqb~ayar~rl 1,9.10 -5 CM2 cer~-a, Howopr~m He 3aBnC~W 0W 'ro.rlmrlHr~ MeM5paHu t4 xopotuo corstacy~omnecn c a~c'rpano.m~poBaHHUMn ae..rtnqrinaMrt nprl m,moHofi weMneparype. Bwopan cva~n~ Raew cpanHnwe.rtbHO 6oJ~ee Hnamte H0aqbCnlll'IeHWbI, MeHnmi~aeca c T0.aUlrtHO~ MeM6paHbI. Peay.ar~'rawb~ yHaa~aamT Ha TO, q'ro B xoRe anqbCyamt nO.~HHHaew 6apr~ep, npenaTcTBymumfl noroHy noaopo~ia. Pacqewu aqbq~er~THBHOt~ WOJHllrlHbt 6apLepa Ramw BOaM0mHOCTb ncnpaBl,tWb gamyul~teca HOa~r, ttu,lenw~, CO06IlleHHhle B anTepawype n l-¢O.rlI4qeCTBeHUO npeacraaa'r~, aHoMa,rlbHbll~ aq~q~eHTTOSIII~HHbI. INTRODUCTION THE ANOMALOUS d i f f u s i o n o f h y d r o g e n in i r o n a n d steel a t t e m p e r a t u r e s b e l o w 4 0 0 ° C h a s b e e n r e v i e w e d b y S m i a l o w s k i , ~ a n d g e n e r a l l y a t t r i b u t e d t o t h e p r e s e n c e o f t r a p s , a, a o r d u e t o t h e d e l a y o f h y d r o g e n a t fixed sites. ~ T h e f a c t t h a t h y d r o g e n e m b r i t t l e m e n t o c c u r s o n l y b e l o w 150°C, a n d t h a t d i f f u s i o n a n o m a l i e s i n c r e a s e m a r k e d l y b e l o w t h i s t e m p e r a t u r e is c o n s i d e r e d b y H e w i t t s t o b e d u e t o t h e r a p i d d e c r e a s e in t h e s o l u b i l i t y * Manuscript received 1 February 1966. 271

S. WACH, A. P. MIODOW'~aX and J. M.ACKOWIAK

272

of hydrogen with temperature a n d its consequent precipitation into dislocations, cracks or voids. Yet n o r m a l diffusivity values c o r r e s p o n d i n g to those expected by extrapolation from higher temperature data have also been observed, e-s The mathematical analysis a n d experimental technique of Veysseyre, A z o u a n d Bastien 9 yield very reproducible diffusion coefficients, but somewhat lower t h a n would be expected from high temperature work. 1°-1~ C o e ~ c i e n t s obtained by J o h n s t o n a n d Hill a between 2 0 0 ° C and 400°C show a high degree of scatter, while curves o b t a i n e d by Eschbach, Gross a n d Schulienis show two distinct diffusion effects below 400°C. A n associated a n o m a l y is the so-called 'thickness effect'; diffusion experiments with plates t h i n n e r t h a n 1.0 m m (approx.) yield progressively lower diffusion coefficients the lower the thickness 6,7,t4-xe a n d corresponding higher p e r m e a t i o n values t h a n would be expected from the theoretical considerations.V, 17 Characteristic values o f the diffusion coefficients determined u n d e r these various conditions are shown in Table 1. TABLE 1.

DIFFUSION COEFFICIENTS FOR HYDROGEN IN IRON AND MILD STEEL

D = Doexp (-- Q/RT) cmSs-1

D25cC (cm's-b

Material

Source

Ref.

( --2280~ 7-6 x 10-4 exp \._----~-~/

1"5 x 10-5

iron

Sykes, Burton and Gegg

(11)

2-2 x 10-s exp (--2900~

1"4 x 10-5

iron

Geller and Sun

(I0)

8"8 x 10-' exp (--3050~

4'2 x 10- e

iron

Stross and Tompkins

(31)

9-3 x 10-4 exp (--2700~

8.2 × 10-e

iron

(12)

6.4 × l0 -e

mild steel mild steel

Eichenauer, Kunzig and Pebler Srnialowski Frank, Swets and Fry

(6)

\

RT /

2.1 x 10-Sexp (--3300~ \

RT /

(30)

(--3400 / 5.3 x 104 exp ~, ~

5.0 x 10- e

1-4 × 10-s exp (--3200~

4"4 × 10-e

iron

Johnston and Hill

(3)

2.2 × 10-7

iron

Johnston and Hill

(3)

4.6 x 10-6

iron

Wagner and Sizman

2-5 × 10-5

iron

present work

mild steel mild steel iron iron iron

Schuetz and Robertson

(27)

Palczewska and

(14)

\

RT/

1.2 x 10-I exp (--7820~ \

RT /

1.42 x 10-s exp (--3270~ \

1-1

X

10-s

exp

(--3610~ 1

\ --

--

1

RT I

2 × 10-s

---

3 × 10-7 2 x 10-6 1 × I0 -s 1-39 x 10-s 8-3 × 10-5

--

5 x 10-s

-

-

--

(29)

RT /

--

2.9 × 10-s

--

2.3 × 10-'

mild steel iron mild steel

Ratajczyk

Raczynski Alikin Devanathan, Stachurski and Beck Eschbach, Gross and Schulien Veysseyre, Azou and Bastien Davis

(17) (28) "(8) (13) (9)

(16)

The diffusion of hydrogen through pure iron membranes

273

The present study indicates a possible explanation for the anomalous results obtained at room temperature in both permeation and diffusivity experiments using thin membranes. The present results show the formation of a barrier to hydrogen diffusion during electrolysis. A calculation of the effective barrier th.ickness and its variation with current density in the electrolyte yields a quantitative prediction of.the thickness effect, and allows an estimation of the real hydrogen diffusion coefficient from anomalous values obtained in experiments using thin membranes. Apparent diffusion coefficients ranging from 1.4 × 10-acmZs-1 to 5 x 10-%m2s -x, yield a corrected D value of 0.8 × 10-Scm2s -1 with a scatter of not more than a factor of 2 for pure iron and mild steel. This value is in good agreement with the value of 1.9 X 10-Scm2s -1 obtained before the barrier forms, and 2.5 x 10-Scm2s -~ obtained by extrapolation from high temperature measurements. The real nature of the barrier is currently the subject of further investigation. EXPERIMENTAL TECHNIQUE Diffusion coefficients were determined using the time-lag technique. 1 This technique is based on measurement of the time taken to attain a constant rate of flow through a membrane. With one side of the membrane exposed to hydrogen and the other exposed to pre-evacuated system, changes in the concentration gradient will take place until attainment of steady state conditions. Measurement of the pressure rise in the vacuum side of the system yields characteristic curves of the type shown schematically in Fig. 1. The value of the intercept (to), on the time axis allows the calculation of the diffusion coefficient, D cm2/s, from the following equation: d2 D -(1) 6to

a.

t2=

/7

=

7

¢o---~ Time, sec FIG. I. Theoretical time-lag curve (schematic). D

= ~ (cms s-l)

274

S. WACH, A. P. MIODOWmK and J. MACKOWIAK

where D = diffusion coefficient (cm~s-0 d = thickness (cm) and to = time required to establish constant flow (s). As a result o f a mathematical analysis o f the time-lag method, Rogers, Buritz and Alpert 18 derived a linear representation o f the pressure-time curve: In # . dp dt Setting In t j . dp _ Y; dt

d~ 1 -- ×4D t

K--

_

(2)

d2

1 - - m and - -----x, 4D t

a plot of x vs. y, yields a straight line of slope m. D can then be calculated from the relationship: O

d2 - -

1 ×

4

-

(cm2s -t)

(3)

m

This method was used for the determination o f D values for hydrogen in iron and steels by Eschbach, Gross and Schulien. 13 It allows an accurate check o f the simpler graphical extrapolation method and also shows whether any experimental curve obtained represents a true diffusion, as any anomalies result in a departure from lineality. A n example o f data replotted according to this method is given in Fig. 2.

10-3

,_c: E I0"

i0-5

0

I I

I 2

I 3 ~-

I

I

4

5

rain - I

Fro. 2. Logarithmic method of analysing the time-lag data of FIo. 1. (Schematic). D = -- ~ × 4

1

m×2.303

(cm' s -~)

The diffusion of hydrogen through pure iron membranes TABLE 2.

275

ANALYSIS OF THE HIGH PURITY IRON

Element*

ppm

Carbon Silicon Manganese Aluminium Magnesium Nickel Copper Silver Oxygen Nitrogen

25 7 5 2 2 1 < ! < 1 84 42

*Other elements were either absent or below the limit of detection.

~[T~I~I~Au plated

side

Pdplafed soln. 12s04

w-,ro-

,~ ~j~--°T~ hyudPmPl yn g

S

gauges andpumps

(b)

o~--aTn°d pg°utg;ss d.c,o._._.~~ FIG. 3.

Diffusion cells (a) for the higher temperatures (b) for lower temperature work.

The material employed was a high purity iron (Table 2). Membranes of 1, 0.5, and 0.25 mm nominal thickness were produced by rolling with a final cold reduction of approximately 50 per cent, and annealed at 880°C in vacuum. The surface preparation after annealing consisted of abrading with emery papers, a polish with a 6 ~t and 1 ~t diamond compound, followed by degreasing in trichloroethylene. The specimens were then sealed into the diffusion cell as shown in Fig. 3(b). The solution side of the membrane was coated with 1-1.5 ~t of palladium by an electroless plating method. The palladium plating was found essential to prevent corrosion of the membrane by the electrolyte and the consequent side effects of ferrous ions. It also facilitates easier

276

S. WACH,A. P. MIODOWNIKand J. MACKOWIAK

detachment of hydrogen bubbles from the membrane surface, thus minimizing errors due to a reduction in its effective area, as is the case when bare iron is used. u/3 H2SO4 (Analar) was used as the electrolyte and a constant current method chosen for the electrolysis using a stabilized d.c. unit. The evacuated collecting cell (Cell B. Fig. 3b) has a capacity of 200 cm 3 but an additional pre-evacuated volume of a forther 100 cm a was available when the pressure rise appeared too high to be recorded accurately. Pressure measurements were made using a modified Edwards Pirani gauge, G5B-2, in conjunction with a Sefram Graphispot recorder. This n~ultiple-range recorder allows a high degree of accuracy with the most sensitive range setting giving a full-scale deflection equivalent to a pressure of approximately 1 ~z. The recorder was calibrated using a McLeod gauge down to 1 ~t, and constant permeation rate experiments performed at higher temperatures allowed accurate calibration below this value. Determination of D values in the temperature range of 80°C to 180°C were also made using the diffusion cell shown in Fig. (3a). Specimens of pure iron with 55 p.p.m. of carbon supplied by B.I.S.R.A. (Iron A H N 20) were used in rod form. The rods, 0.3 cm dia. and 0.75 cm long, with a hole drilled along the axis from one end, were annealed in vacuum at 880°C for 8 h and then sealed into a special graded glass. After thoroughly descaling with a 20 Yo H2SO4--quinoline solution, the remaining exposed curved surface of the iron was plated with gold; according to Eichenauer and Liebscher 19 gold has a D value for hydrogen equal to 4 × 10-Tcm2s-1 at 100°C, approximately three orders of magnitude lower than the pure iron and therefore serves as an effective barrier to hydrogen. The end of the specimen was palladium coated in order to simulate the conditions employed at the room temperature in the membrane series of experiments (Fig. 3).

The pretreatment of membrane specimens Pretreatment of membranes a,°,14 with hydrogen is essential in order to obtain reproducible results for diffusion coefficients and permeation rates. In the present study, membranes which were prepared mechanically as previously described and subjected to a dynamic vacuum for about 12-16 h, invariably yielded low initial diffusion coefficients, sometimes as much as two orders of magnitude lower than subsequent reproducible values. It was found essential to pre-charge the membranes initially for approximately half an hour at a current density of 5-10 mA/cm 2, then outgas and again pre-charge before each experiment for a time equivalent to the duration of the subsequent test, and finally outgas to reach a pressure < 10-6 mm Hg. Even under these conditions a slight background evolution still occurred and was measured just before each test run, the experimental results being adjusted accordingly. It is assumed that this pretreatment results in the filling of all pre-existing traps with hydrogen, and that no further hydrogen is absorbed by such traps during the subsequent experiment as a result of a state of dynamic equilibrium. RESULTS Curves obtained in practice were generally more complex than the simple theoretical curve shown schematically in Fig. 1. A typical pressure-time curve is illustrated in Fi~. 4, and can be seen to exhibit two distinct portions. These are eouivalent to

The diffusion of hydrogen through pure iron membranes

277

°

t//

/

vt o

FIG. 4.

I

I

I

I

3

6

9

12

Time,

min

Pressure--time curve for 0-043 em membrane at 25"0°C. a~ (cm2 s-x) Dtrae = ~-o D=pp. = ~7 ° (orris s-x)

an initial fast diffusion stage, followed by a much slower secondary stage. The primary fast diffusion curve was generally supplanted by the secondary diffusion region before reaching a constant slope of reasonable length, hence extrapolation to zero pressures was often di~eult. However the logarithmic method of handling the data to yield a straight line proved useful in these cases, since every part of the pressure-time curve can be used and not just the asymptotic portion. This method was also found particularly useful for the calculation of low secondary diffusion coefficients, where the full curve needs to be recorded for two or more hours. A typical two stage curve plotted logarithmically is given in Fig. 5. It is very similar to the curves obtained by Eschbach e t aL as

Values of D corresponding to the fast and slow diffusion regimes obtained for each membrane, with the associated current and voltage conditions in the electrolyte, are given in Table 3. The primary fast diffusion region could only be detected with difficulty on the 1 m m membrane, as the total pressure rise was not more than 1.0 ~t for the total effect over a period of 2 to 4 min; it was however well pronounced in the case of thinner membranes. The values so obtained cover approximately one order of magnitude.

S. WAC8, A. P. MIODOWNIK a n d J. MACKOWIAK

278 10-2

-IN

10-6

E

m2

\

10-4

I 4

10-6 O

I 8

T 12 ~,

F I G . 5.

I 16

I 20

24

min -t

Logarithmic m e t h o d o f analysing the time-lag d a t a o f FIG. 4. d = 0"043 c m ds 1 - 1"2 × 10- s (cm 2 s -l) Dtrae = -- ~ - X ml X 2'303 D.~.

=

ds

1

4

m ~ X 2.303

-- -- X

-

2.9

× 10 - 6 ( c m 6 s - t )

[ -\(~m/ 6 y -- 1 ] (cm Fe) Ad = d L TABLE 3.

VARIATION OF DIFFUSION COEFFICIENTS AND DIMENSIONS OF THE EFFECTIVE BARRIER WITH MEMBRANE THICKNESS

Conditions of electrolysis

Membrane thickness d (cm)

D fast D slow (10 -5 c m 6 s - q

Effective barrier d (cm Fe)

1'7 m A / c m 6 2'2 V

0"0265

1 "67

0" 17

0-059

1-95 m A / c m 6 2.25 V

0.0265

1 "95

0-20

0.055

3.7 m A / c m t 2-3 V

0.0265

2.6

0.22

0.065

8.3 m A / c m s 2-42 V

0-0438

1.98

0-34

0.055

26 m A / c m 6 2.52 V

0"0438

1.88

0-24

0-0835

61 m A / c m 6 2"85 V

0"10

1"99

0"37

0"13

The diffusion of hydrogen through pure iron membranes

279

DISCUSSION

The barrier hypothesis The initial branch of the composite curves yields values of D of 1-9 × 10-Scm~s -z which are independent of the thickness of the membrane over a range of.voltages and currents. The D value agrees very well with the extrapolated high temperature valt&e from the current work (Fig. 6) and those reported in the literature, l°-z~ which average 1.5 x 10-Scm%-t. The second branch of the pressure-time curves yields considerably lower values, and these vary with membrane thickness, current density and possibly with voltage conditions in the electrolyte. The values obtained in the initial stages make it fairly certain that the hydrogen diffuses in accordance with the accepted activation energy for high temperature diffusion. It follows that some kind of barrier must be created during the experiment to give an effectively slower coefficient in the later stages. The secondary branch of the composite pressure-time curve is however of identical mathematical form to the first branch, differing only in the higher value of the intercept (to). Normally, if D remains unchanged, an increase in (to) can only be obtained by increasing the thickness of the specimen. Whatever the cause of the observed phenomena may be, it can be considered in terms of the formation of a barrier that builds up during the initial stages of diffusion and which causes an iron membrane of thickness (d) to behave °c 10-3

200 I

175 I

150 I

125 I

IO0 I

75 I

50 I

25 I

%%. %%

NUE 10-4

%%% %% %% %%%%

--.%

10-2. 05

l

I 2-5

[ I03

T,

I " 3.0

f

°K-t

FiG. 6. The variation of diffusion coefficient with temperature. --8610

D =1"1 X lO-me Je (cm 2 s - l )

3-5

S. WACH,A. P. M]ODOWNIK and J. MACKOWIAK

280

effectively as if it had an increased thickness (d -t- Ad). Such a barrier must be considered quite distinct from any form of preexistent traps since these would lead to a reduction in the primary diffusion region. The fast initial rate observed indicates that the pretreatment used in this work removed any interference from preexistent traps. The effective thickness of the postulated barrier can be calculated in terms of an additional laminar increment of iron Ad(cm) as follows: d2 d~ From equation (1) a~nd (3) the true initial D = - - or - - - 6to 4mx Likewise the secondary apparent

d2 --~ or 6t 0

D =

(la and 3a)

d2 -

-

-

(lb and 3b).

-

4m:

Assuming the presence of a barrier Ad in the latter case, real D

-

(d -I- Ad): or 6t o

-

(d -t- Ad) 2 4m:

We then have from (la and lc): Ad = [ ( t ° ~ ~ L\tel

(lc and 3c).

-

-

1] cm Fe (approximate}

Ad----[(m--~:~ ½- 1] cm Fe (accurate) LXmx/

or from (3a and 3c):

Values of Ad obtained in this way are listed in column four of Table 3.

0"16 0-14

sS S f,j

E

0-12

.~<~

0.I0

0.08

0"06 0

.3

0-04 0.02

?

I IO

I 20

J I I I I 30 40 riO 60 70 Current d e n s i t y , mA crn -z

60

FIG. 7. Variation of the barrier thickness with current density in the electrolyte.

(4) (5)

The diffusion of hydrogen through pure iron membranes

281

When the thickness of the postulated barriers Ad cm Fe, is plotted against the current density in the electrolyte a straight line is obtained (Fig. 7). The straight line when extrapolated to zero current density, does not pass through the origin, but makes an intercept of approximately 0.05 cm. So it appears that a finite extra barrier would be produced in the course of diffusion even without the use of an electrolytic means of hydrogen introduction.

Explanation of the membrane thickness effect As previously mentioned, numerous authors have reported a membrane thickness effect, that is increasingly lower D values are obtained for iron and steel membranes of progressively decreasing thickness and a simultaneous abnormal increase in the rate of permeation is observed. Figure 8 shows the correlation between D values and the corresponding membrane thickness obtained by RaczynskF at 90°C, who also used the time-lag method for calculation of his results. If it is assumed that the great majority of the values reported in the literature have been computed from the secondary effect, then these values are all subject to an error induced by the formation of a barrier. Under similar charging conditions the effective barrier thickness should be the same for thick and thin membranes. In the case of thick membranes this contribution may be insignificant; however, the effective barrier thickness may be larger than the actual membrane thickness if the membranes are much thinner than 1 mm. The equations used to obtain diffusion coefficients (equations 1 and 3) are of second order with respect to the thickness of the membrane---if the contribution of the barrier is disregarded, the diffusion coefficient obtained from the second regime, using the actual membrane thickness alone, will invariably be abnormally low. If the barrier hypothesis is valid values can be corrected by assuming diffusion through a composite 10-4

T u~

iO-S

4-"

+ i0-~

10- 08

I 0"8

I 1'6

Membrane

FIG. 8.

1 2-4 thickness,

I 3'0

3'6

mm

The effect of membrane thickness on the apparent diffusion coefficients at 90°C (after Raczynski, ref. 7).

282

S. WACH, A. P. MIODOWNIKand J. MACKOWIAK

m e m b r a n e w h o s e thickness is the s u m o f the a c t u a l m e m b r a n e t h i c k n e s s a n d a b a r r i e r thickness. F r o m e q u a t i o n s l b a n d l c o r 3b a n d 3c it f o l l o w s t h a t :

T r u e Dx = D.~ ×

(d + Ad) z

(6)

d~ Since a v a r i e t y o f c o n d i t i o n s w e r e used by the a u t h o r s to o b t a i n t h e i r D values, a n a v e r a g e v a l u e for 4 d =- 0" 1 cm, has been used f r o m Fig. 7 to c o r r e c t values o b t a i n e d f r o m e x p e r i m e n t s using electrolytic m e t h o d s o f h y d r o g e n c h a r g i n g . T h e z e r o extrap o l a t e d v a l u e o f Ad o = 0-05 c m was used w h e r e h y d r o g e n has been i n t r o d u c e d in by o t h e r means.

TABLE 4.

COMPARISON OF THE APPARENT AND RE-CALCULATED DIFFUSION COEFFICIENTS OBTAINED WITH MEMBRANES OF DIFFERENT THICKNESS

Membrane thickness d cm

Apparent Dz cm ~ s -1

0.008 0-076 0.01 0.012 0'02 0"042

9-2 × -2.9 × 1-4 x 3'8 x 2"0 ×

0.078 0.12 0-16 0.10

3.4 3"1 2 2.8

0.0254 0.077

2.3 × 10-s --

x x × x

10-~°

Re-calculated D1 cm z s -x

Material

Source

Ref.

10-7 10-s 10-7 10-s

1.5 0'5 2-4 1-2 5"2 1"0

× × x x × x

10-~ 10-s 10-s 10-6 10-e 10-s

0.5c steel mild steel iron mild steel

Heath Frank, Swets and Fry Raczynski Alikin

(17) (6) (7) (28)

mild steel

Palczewska and Ratajczyk

(14)

10-6 10-s 10-6 10 -6

I'0 6.5 5.2 1.I

× × × x

10-5 I0 -~ 10-~ 10-~

mild steel mild steel

(27)

5-6 x 10-7 8.3 × 10-5

mild steel iron

Schuetz and Robertson Veysseyre, Azou and Bastien Davis Devanathan, Stachurski and Beck

(9) (16) (8)

T a b l e 4 gives s o m e e x p e r i m e n t a l D v a l u e s t a k e n f r o m the l i t e r a t u r e t o g e t h e r w i t h d e r i v e d D values o b t a i n e d in a c c o r d a n c e with e q u a t i o n (6). T h e latter c a n be seen to fall within t h e s a m e o r d e r o f m a g n i t u d e despite the v a r i e t y o f c o n d i t i o n s u n d e r w h i c h the e x p e r i m e n t a l D values were o b t a i n e d . It w o u l d seem t h e r e f o r e t h a t the h y p o t h e s i s o f a diffusion i n d u c e d b a r r i e r applies a n d c a n explain the a n o m a l o u s thickness effect. A t the s a m e t i m e the w i d e r a n g e o f r e p o r t e d D values c a n be t r a n s f o r m e d to o b t a i n a m o r e c o n s i s t e n t D i f f u s i o n Coefficient for h y d r o g e n at r o o m t e m p e r a t u r e (Fig. 9). Veysseyre, A z o u a n d Bastien 9 also o b t a i n e d v e r y c o n s i s t e n t results a n d a g r e e m e n t o f their e x p e r i m e n t a l c u r v e s with the e x p e c t e d t h e o r e t i c a l p r e d i c t i o n . T h e i r experim e n t s were c o n d u c t e d by p r e t r e a t i n g the m e m b r a n e in a similar w a y to p r e s e n t w o r k , but t h e m e m b r a n e was t h e n c h a r g e d at a high c u r r e n t density a n d they o b t a i n e d l o w D values. It a p p e a r s t h a t such e x p e r i m e n t a l c o n d i t i o n s c o u l d lead to the f o r m a t i o n o f a b a r r i e r b e f o r e m e a s u r e m e n t s were t a k e n , a n d their results are in fact c o n s i s t e n t w i t h the s l o w e r r e g i m e o f diffusion d e s c r i b e d in this p a p e r .

The diffusion of hydrogen through pure iron membranes

]0-4L~ A I0

"n

.

I

"

& .

.

~,

.

.

283

~ v e r a g e of D .

.

.

_

Oo(eorrected)

I/o

10_7

1

0

0 0"2 -0.4 90"6 0"8 ~ Thickness,

FIG.

I'0 1.2 mm

1.4

I-6

9. Comparison of the apparent and corrected diffusion coefficients for different membrane thicknesses. (Data from Table 4). D~e

=

Dapp. X

(d +d 2Ad)~ (cm s-l)

© apparent coefficients z~ corrected coefficients Curves obtained between room temperature and 400°C by Eschbach et al. 13 show a similar dual nature to those obtained in the present work, although these authors did not interpret their results in the same way. However if the barrier hypothesis is applied to their results, an effective barrier thickness at 253°C can be calculated for their ferritic-pearlitic steel (0-12 ~o, 0.53 Mn, 0.1 Si) of 0.3 cm wall thickness. The apparent D of 1.2 × 10-Scm2s-1, then yields a corrected D of 3.2 × 10-Scm2s -1 and a barrier thickness Ad of 0.11 cm Fe. Location o f the diffusion induced barrier From the assumptions made in deriving corrected D values, it is not possible to deduce the precise location of the diffusion induced barrier. It is likely that an appreciable part of the barrier may be situated on the input side of the membrane, since the thickness of the barrier varies with current density in the electrolyte. However the finite (Ado) value obtained by extrapolation to zero current density must be also considered. In this respect it is interesting to note that Heath 17 and Raczynski 7 have shown that permeability increases with decrease in membrane thickness. Curve I in Fig. 10 shows the values Heath obtained at a current density of 200 m A / c m ~. According to Smialowski x and Frank 2° the rate of flow q~ (cma/cm~s) is proportional to the reciprocal of the membrane thickness (d): ~0 = K/d

(7)

A plot of the rate of flow versus the reciprocal of the thickness should therefore result

284

S. WACH, A. P. MaODOWNIK and J. MACKOWIAK

~o E

uncorrecfed d)

~E o

/ i nc

~b, . . . . . . . . . . -)<

/

'

///

.,/," / / l r (corrected for A dn=0"0125era)

~./

/ /

// s"

//

~ '~2 - - -

~

I~

I

2

I

4

I

6

8

d '

I

I0

I

12

mm-=

FIG. 10. Variation of permeation rate with reciprocal of thickness of iron membranes. Curve I shows experimental data obtained by Heath (ref. 17). Curve II obtained by

subtracting Ad' from the real thickness of the membrances. Ad' was calculated by comparing two experimental flow rate values ¢~ and ¢=. At/'

qhdl-qh

cp~/=

(cmFe)

--

de.~t,.

=

d --

Ad'

in a straight line through the origin. If the same correction is attempted for the rate of flow data as was made for the D values (i.e. adding 0.1 cm to the membrane thickness) the departure from theoretical expectations increases. In fact the permeability anomaly is removed by a reduction rather than an increase in the effective thickness of the membrane (Fig. 10, curve I10. If part of the finite (Ado) value as obtained from the diffusion experiments lies inside the membrane, this could contribute to the permeability anomaly, but further work is clearly required to relate the two effects. All that can be said at this stage is that the barrier is likely to be composite in nature, and straddles the input side of the membrane.

Nature, origin and properties of the barrier The hypothesis of an effective barrier or series of barriers clarifies quantitatively the diffusion behaviour of hydrogen, but the formulation used is to some extent only a matter of mathematical convenience. The real nature and real dimensions of the barrier are still a matter for further research. The internal part of the barrier may be due to a high local hydrogen concentration, 2e but whether this is present as a very thin layer of the 13-phase mentioned by Smialowski 1 and found in Ni-Cr steel, zl whether it is merely a hydrogen saturated layer is not yet known. Experiments currently in progress show that the part of the barrier controlled by current density conditions in the electrolyte is extremely sensitive to temperature. This work will be published in a separate paper.

The diffusion of hydrogen through pure iron membranes

285

Acknowledgements~Thc work reported in this paper forms part of a general investigation into the state of hydrogen in steel sponsored by the Ministry of Aviation. We wish to thank Mr. G. H. Cole for interest shown and helpful suggestions, Prof. F. C. Thompson for many helpful discussions, Mr. E. White and Mr. B. C. Wigzell for help in the construction of the apparatus, and Battersea College of Technology for providing space and facilities for the research. The authors also wish to thank The British Iron and Steel Research Association'for supplying the pure iron (AHN20) and its complete analysis. I. 2. 3. 4. 5. 6. 7. 8. 9. 10. I I. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.

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