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Hydrogen transport in plasma nitrided iron
Acta Materialia 52 (2004) 2637–2643 www.actamat-journals.com
Hydrogen transport in plasma nitrided iron Z. Wolarek, T. Zakroczymski
*
Electrochemistry, Corrosion and Applied Surface Science, Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44-52, 01 224 Warsaw, Poland Received 14 April 2003; received in revised form 30 January 2004; accepted 10 February 2004 Available online 11 March 2004
Abstract Hydrogen permeation through membranes prepared from various parts of the nitrided iron specimens was investigated by an electrochemical technique. The membranes were charged with hydrogen by galvanostatic cathodic polarisation in 0.1 M NaOH. The successive partial decay and build-up transients were performed and analysed to determine the diffusivities of hydrogen in the outer compound layer, the inner diffusion zone, and the unmodified iron substrate. Hydrogen transport in the diffusion zone proved to be the most complex. It was found that hydrogen diffused mainly through the ferrite matrix and bypassed the nitride precipitates. Therefore, the real diffusion paths in the diffusion zone had various lengths and were longer than the membrane thickness. 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Iron; Plasma nitriding; Hydrogen; Diffusion; Hydrogen permeation
1. Introduction Among various methods for avoiding or decreasing hydrogen degradation of iron and its alloys, plasma nitriding seems to be especially promising. This process involves chemical and metallurgical changes of the surface/near surface region. Therefore, the nitrided layers, besides their beneficial wear properties, may reduce hydrogen absorption by the substrate metal. In general, this effect may be considered in terms of the hindrance of the entry of hydrogen from a surrounding environment into the outer nitrided layer (the surface effect), and the hindrance of the transport of hydrogen through the whole nitrided layer (the barrier effect). This barrier effect is the subject of this work. There are some reports showing that outer nitrided layers on iron [1,2], carbon steels [3,4] and low alloy high strength steel [5,6] act as barriers for hydrogen transport. The effectiveness of such barriers was evaluated using the electrochemical permeation technique and it was characterized by a decrease of hydrogen diffusivity. *
Corresponding author. Tel.: +48-226-323-221; fax: +48-226-311619. E-mail address: [email protected] (T. Zakroczymski).
Since the way of evaluation of the hydrogen diffusivity and, consequently, its meaning differed, the literature data are scattered and inadequate. Bruzzoni et al. [4] found that the apparent diffusion coefficient of hydrogen in nitrided AISI 4140 steel membranes was 0.053–0.19 106 cm2 /s, while that in the non-nitrided membrane was 30–10 times higher (1.7–1.9 106 cm2 /s). The decrease in hydrogen diffusivity was attributed to the compound layer together with the diffusion one. Fassini et al. [5] applied the model of a two-layer membrane to nitrogen ion-implanted API X65 type pipeline steel. It was found that the apparent hydrogen diffusivity in the modified layer was 5.3 1012 cm2 /s, i.e. about six orders of magnitude lower than that in the steel substrate (1.5 106 cm2 /s). In turn, the model of a three-layer membrane was applied for nitrided Armco iron membranes consisting of the outer compound layer, the inner diffusion layer and the substrate one [1]. The following values of hydrogen diffusivity were found: the compound layer – 4.1 108 cm2 /s, the diffusion layer – 6.1 106 cm2 /s, and the unmodified substrate – 7.3 105 cm2 /s. The predominant role of the compound layer in the hindrance of hydrogen transport through the nitrided steel was even more emphatic in the work of Lesage et al. [6].
1359-6454/$30.00 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2004.02.011
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Nomenclature Cc;0 D D# D" Dc Ds Dd;eff
Dd;x
Da;d DðcþdÞ
hydrogen concentration in the nitrided compound layer at its entry side hydrogen diffusivity hydrogen diffusivity evaluated from the partial decay hydrogen diffusivity evaluated from the partial build-up hydrogen diffusivity in the nitrided compound layer hydrogen diffusivity in the unnitrided iron substrate the effective hydrogen diffusivity for the membrane prepared from the nitrided diffusion zone the section-dependent hydrogen diffusivity for the membrane prepared from the nitrided diffusion zone hydrogen diffusivity in the ferrite matrix of the diffusion zone the effective hydrogen diffusivity for the membrane comprising the nitrided compound and diffusion layer
The diffusion coefficient in the compound layer was found to be 1.26 1011 cm2 /s, while that in the steel substrate 3.1 106 cm2 /s. At the same time, however, the hydrogen diffusivity in the diffusion zone was slightly larger (4.7 106 cm2 /s) than that for the substrate. In the present work, the transport of hydrogen in nitrided Armco iron was examined using specifically prepared membranes and measuring the permeation rate of hydrogen. The main objective was to determine the real diffusivities of hydrogen and the real diffusion paths in the nitrided compound layer, in the diffusion zone, and in the unnitrided iron substrate. Since the permeation of hydrogen through the membrane is complex, it may be altered by slow surface processes (affecting hydrogen entry) and hydrogen trapping (affecting hydrogen transport). Therefore, an effort was made to arrange suitable experimental conditions, under which the role of the surface and trapping effects was diminished, and the measured changes in the permeation rate of hydrogen may be interpreted as changes in the rate of hydrogen diffusion.
2. Experimental The material used was a commercial Armco iron (C 0.031, Mn 0.12, Si 0.01, P 0.008, S 0.015, Cr 0.01, Ni 0.01, Cu 0.02, Al 0.03 wt%) in the form of a hot-drawn, 25 mm diameter rod. Plate specimens, 19 mm in diameter and 3 mm in thickness, were machined out from the rod perpendicularly to its axis.
ic ip i0p i1 p L Lc Ls Ld LðcþdÞ La;d La;min La;max t X
cathodic (charging) current density permeation rate of hydrogen initial steady-state permeation rate of hydrogen a new steady-state permeation rate of hydrogen thickness of a membrane thickness of the nitrided compound layer thickness of the membrane prepared from the unnitrided iron substrate thickness of the membrane prepared from the nitrided diffusion zone thickness of the membrane comprising the nitrided compound and diffusion zone length of diffusion paths in the ferrite matrix of the diffusion zone the shortest diffusion path in the ferrite the longest diffusion path in the ferrite time distance
The specimens were plasma nitrided on one side using a nitriding plasma chamber. The nitriding conditions were as follows: gas composition 80% N2 + 20% H2 , pressure of 670 Pa, temperature 540 C, nitriding time 6 h. After this treatment, the specimens were cooled slowly in the chamber. The nitriding treatment produced a modified layer of about 1.3 mm in thickness (Fig. 1(a)) which consisted of a thin, about 10 lm, outer compound layer composed of nitrides Fe2–3 N (e-phase) and Fe4 N (c0 -phase), and an inner, much thicker, diffusion zone with the dispersed Fe4 N precipitates and a solid solution of nitrogen in the metal matrix (Fig. 1(a) and (b)). The following membranes (Fig. 1(a)) were prepared by abrading the nitrided specimens: • One-layer membranes of thickness Ls ¼ 1 mm, comprising only the unmodified iron substrate. • One-layer membranes with varying thickness Ld ¼ 0:4, 0.6, 0.8 and 1 mm, comprising various sections of the diffusion layer. In this case, the compound layer was removed and the specimen was abraded from the other side to the corresponding depth. • Two-layer membranes of thickness LðcþdÞ ¼ 1 mm, comprising the compound layer and the major part of the diffusion zone. The prepared membranes were used for the hydrogen permeation measurements by an electrochemical technique [7]. They were mounted between two electrochemical cells using a holder made of methyl polymetacrylate (Perspex) having flanges and rubber gaskets. The circular area exposed to solution was 0.5 cm2 .
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3. Analysis of permeation transients The non-stationary transport of hydrogen in a nonhomogeneous membrane like that made from the nitrided diffusion layer, and especially in that including both the compound and diffusion layers, is difficult to treat. Nevertheless, for a start, a simple diffusion model for hydrogen permeation through a homogeneous membrane can be used to determine the apparent diffusivity of hydrogen. The following equations, valid for the membrane thickness L, constant diffusion coefficient D, and under the boundary condition of constant hydrogen concentration beneath the entry side of the membrane [8], have been employed to analyse the experimental partial transients: Decay 1 ip i1 2L X p ¼ 1 pffiffiffiffiffiffiffiffi exp 0 1 ip ip pDt n¼0
ð2n þ 1Þ2 L2 4Dt
Build-up 1 ip i0p 2L X p ffiffiffiffiffiffiffiffi ¼ exp 0 i1 pDt n¼0 p ip
2
ð2n þ 1Þ L2 4Dt
! ;
ð1Þ
! ;
ð2Þ
where ip is the measured permeation rate at time t, i0p is the initial steady-state permeation rate (t ¼ 0), i1 p is the new steady-state permeation rate (t ! 1Þ. For the 0 partial decay 0 < i1 p < ip ; for the successive partial 0 1 build-up 0 < ip < ip . The hydrogen diffusivity was evaluated by fitting of a suitable equation to the entire run of the experimental transient by adjusting the diffusion coefficient D. The least square method was employed for the fitting procedure. Fig. 1. SEM micrographs of the etched cross-section surface of the nitrided iron specimen and the way of preparing various membranes.
45
Initially the membranes were charged at their one (entry) side with hydrogen cathodically generated from 0.1 M NaOH at a current density ic ¼ 20 mA/cm2 . The entry side of the nitrided membranes corresponded to the outer surface of the compound layer (two-layers membranes) or to the diffusion layer just beneath the compound layer (one-layer membranes). The membrane exit side, previously coated with a thin layer of Pd, was polarised at the constant anodic potential of 0.15 0.15 VHgjHgOj0:1 M NaOH (0.32 VNHE ) and the anodic current was a measure of the permeation rate of hydrogen. After 24 h, when the permeation rate achieved a steady-state, the successive partial decay and build-up transients were measured after changes of the cathodic current density from 20 to 10 mA/cm2 and then back to the previous value of 20 mA/cm2 . The permeation experiments were carried out at 30 C.
H Permeation Rate, ip (µA/cm2)
ic = 20 10 mA/cm2
unnitrided Fe substrate Ls = 1 mm 40
ic = 10 20 mA/cm2 35 1
10
100
Time, t (s) exper. decay
exper. buildup fitted by Eq. (2) D↑ = 8.2x10-5 cm 2/s
fitted by Eq. (1) -5 2 D = 7.8x10 cm /s ↓
Ds = 8.0 x10-5 cm2/s
Fig. 2. Partial decay and build-up transients for the pre-charged unnitrided iron substrate membrane. Solid lines with open symbols represent the experimental transients; dashed lines with solid symbols represent the model equations fitted to the experimental data.
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4. Results 4.1. Unmodified iron substrate The successive partial decay and build-up permeation transients and the best fittings of Eqs. (1) and (2), respectively, for the unnitrided iron substrate membrane Ls ¼ 1 mm are shown in Fig. 2. The experimental and computer fitted transients overlap each other and the hydrogen diffusivity, taken as an average value of those resulting from the fitting procedure of the decay (D# ) and build-up (D" ) transients, equals Ds ¼ 8:0 105 cm2 /s.
H Permeation Rate, ip (µA/cm2)
0.090 ic = 20
10 mA/cm 2
ic = 10
20 mA/cm
0.085
0.080
2
compound layer + diffusion zone L(c+d) = 1 mm
0.075 100
1000
10000
Time, t (s) exper. decay
exper. buildup
fitted by Eq. (1) -6 2 D = 1.5x10 cm /s
fitted by Eq. (2) -6 2 D↑ = 1.5x10 cm /s
↓
ic = 20
10 mA/cm
-6
2
D(c+d) = 1.5x10 cm /s
2
H Permeation Rate, ip (µA/cm )
35
2
Fig. 4. Partial decay and build-up transients for the pre-charged membrane consisting of the nitrided compound and diffusion layers. Solid lines with open symbols represent the experimental transients; dashed lines with solid symbols represent the model equations fitted to the experimental data.
diffusion zone Ld = 1 mm
30
4.2. Diffusion layer 25
ic = 10
20 mA/cm2
10
100
(a)
1000
Time, t (s) exper. decay
exper. buildup fitted by Eq. (2) D↑ = 7.3x10-6 cm 2/s
fitted by Eq. (1) D↓ = 7.1x10-6 cm 2/s
Dd = 7.2x10-6 cm2/s
10 mA/cm2
2
H Permeation Rate, ip (µA/cm )
ic = 20 90
diffusion zone Ld = 0.4 mm
Two examples of the decay and build-up transients for the nitrided membranes Ld ¼ 1 and 0.4 mm, i.e. comprising various sections of the diffusion zone, are shown in Fig. 3(a) and (b), respectively. In contrast to the iron substrate membranes, there were considerable discrepancies between the fit and the experimental decay and build-up transient curves. The fitting procedure leads to an effective diffusivity Dd;eff , characterising the transport of hydrogen through the whole membrane. The values of Dd;eff , including those for other membranes Ld ¼ 0:6 and 0.8 mm, are depicted in Fig. 5. It can be seen that the thinner membrane has the lower effective diffusivity. Generally, the values of Dd;eff are more than one order of magnitude lower than the value of Ds .
80
4.3. Compound layer together with diffusion layer
70 ic = 10
20 mA/cm2
1
10
(b)
100
Time, t (s) exper. decay
exper. buildup
The successive partial decay and build-up permeation transients recorded for the membrane LðcþdÞ ¼ 1 mm, consisting of the compound and diffusion layers, are shown in Fig. 4. A resulting value of the effective diffusivity DðcþdÞ is almost two orders of magnitude lower than that for the unnitrided membrane, Ds .
fitted by Eq. (2) D ↑ = 4.8x10-6 cm2/s
fitted by Eq. (1) D↓ = 4.8x10-6 cm2/s -6
2
Dd = 4.8x10 cm /s
Fig. 3. Partial decay and build-up transients for the pre-charged membrane prepared from the nitrided diffusion zone: (a) Ld ¼ 1 mm, (b) Ld ¼ 0:4 mm. Solid lines with open symbols represent the experimental transients; dashed lines with solid symbols represent the model equations fitted to the experimental data.
5. Discussion 5.1. Hydrogen diffusivity in the unmodified iron substrate The excellent agreement between the experimental and computer fitted transients for the unnitrided iron
Z. Wolarek, T. Zakroczymski / Acta Materialia 52 (2004) 2637–2643
5.2. Hydrogen diffusivity in the compound layer Although it was impossible to prepare and examine a membrane composed of only the compound layer, the hydrogen diffusivity in this layer can be determined indirectly. One can assume that there are no barriers for hydrogen passing between the compound layer and the diffusion zone (Fig. 1), i.e. there is continuity in the hydrogen concentration at the boundary between these layers. The steady state permeation rate of hydrogen, i1 p , through a membrane consisting of the compound and diffusion layers, LðcþdÞ , can be expressed by the following relationships: i1 p ¼
DðcþdÞ Cc;0 F Dc ðCc;0 Cc=d ÞF Dd;eff Cc=d F ¼ ¼ ; Lc Ld LðcþdÞ
ð3Þ
where Lc is the thickness of the compound layer, Cc;0 is the concentration of hydrogen in the compound layer at its entry side, Cc=d is the concentration of hydrogen at the boundary of the nitrided layer and the diffusion zone, and Dc is the diffusivity of hydrogen in the compound layer. In the steady state, the fall in H concentration through the membrane is the sum of the falls through the component layers: Cc;0 ¼ ðCc;0 Cc=d Þ þ Cc=d . Consequently, the following equation follows from (3) LðcþdÞ Lc Ld ¼ þ : ð4Þ DðcþdÞ Dc Dd;eff Since for the membrane LðcþdÞ ¼ 1 mm, Lc 0:01 mm and Ld 0:99 mm, the effective diffusivity Dd;eff ¼ 7:2 106 cm2 /s found for the membrane Ld ¼ 1 mm (Fig. 3(a)) is basically that for the diffusion layer of the composite membrane considered. Substituting DðcþdÞ ¼ 1:5 106 cm2 /s (Fig. 4) into Eq. (4), a value of Dc ¼ 1:9 108 cm2 /s is obtained. Thus, the diffusivity of hydrogen in the nitrided compound layer is more than 4000 times lower than that in a-iron. The value of Dc obtained is close to that found earlier [1], but it is considerably higher than other data [5,6]. The compound layer nitrided under the applied conditions was composed of c0 -phase and e-phase. Besides, the e-phase was present in the outermost sublayer of the compound layer. The mobility of hydrogen in these phases may be different because of the different metal-atom arrangement: a close-packed hexagonal for e-phase, and a face-centred cubic for c0 -phase [15]. Therefore, the evaluated diffusivity Dc should
be regarded as characteristic for the whole compound layer.
5.3. Hydrogen diffusivity in the diffusion zone Hydrogen transport in the nitrided diffusion zone seems to be more complex and at the same time intriguing than that in the substrate and compound layers. The effective diffusivity Dd;eff characterises the transport of hydrogen through the whole membrane and it increases with the membrane thickness (Fig. 5). However, taking into account irregular distribution of the nitride precipitates in the diffusion zone and remembering that the membranes comprised various sections of this zone (Fig. 1(a)), the thicker membrane the lower the average density of nitride precipitates and their different distribution across the membrane. Therefore, it is reasonable to ascribe the value of Dd;eff to a distance X , corresponding to the middle of the given membrane of thickness Ld (Fig. 5). In this way, the section-dependent hydrogen diffusivity, designated as Dd;x , as a function of the distance in the diffusion zone is shown in Fig. 5. It is useful to note that the extrapolated Dd;x X curve intersects the level of hydrogen diffusivity specific for the unnitrided iron substrate just at the depth of nitriding (Fig. 1(a)). Although the section-dependent diffusivity Dd;x characterizes the transport of hydrogen more exactly than the effective diffusivity Dd;eff , it does not explain the role of the nitride precipitates in hindering hydrogen transport. Generally, the observed inconsistency of the experimental and fitted partial transients for the nitrided membranes (Fig. 3(a) and (b)) indicates that the transport of hydrogen is perturbed. A possible reason can be hydrogen trapping. However, it has been shown that the effect of trapping, distinctly revealed on 10-4
Ds Hydrogen Diffusivity (cm2/s)
substrate membranes (Fig. 2) proves that the boundary conditions required by Eqs. (1) and (2), including that Ds ¼ const, were fulfilled. Therefore the permeation of hydrogen through the membrane was controlled by the rate of hydrogen diffusion inside the membrane. The value of Ds obtained is consistent with the literature data for the lattice diffusivity of hydrogen in a-iron at room temperature [9–14].
2641
10-5
Dd,x Dd,eff
nitrided diffusion zone 10-6 0.0
0.5
unnitrided iron substrate
1.0
1.5
2.0
3.0
Distance, X (mm)
Fig. 5. The effective (Dd;eff ) and section-dependent (Dd;x ) hydrogen diffusivities for the membranes prepared from the nitrided diffusion zone, and the hydrogen diffusivity in the unnitrided iron substrate as a function of the distance in the nitrided specimen.
Z. Wolarek, T. Zakroczymski / Acta Materialia 52 (2004) 2637–2643 ip∞
diffusion layer Ld = 1 mm
35
2
ic = 10 20 mA/cm
Dα ,d ∼ Ds = 8.0x10-5 cm2/s 2
H Permeation Rate (µA/cm )
the permeation transients during the first charging [16–18] or the complete desorption [18], is insignificant in regard to partial transients [18,19]. Presumably, the changes in the hydrogen concentration are too small to initiate trapping or de-trapping of hydrogen, because these processes are not fully reversible. Moreover, the decay and build-up transients altered by trapping should not coincide [20], whereas those shown in Fig. 3(a) and (b) do. In any case, trapping effects were not apparent in the partial transients recorded for the unnitrided iron substrate membrane (Fig. 2). Thus, the trapping of hydrogen should not be an important factor in the observed discrepancies between the experimental and model partial transients. The actual model of hydrogen transport in the nitrided diffusion zone must take into account the presence of the nitride precipitates in the ferrite matrix. Undoubtedly, the diffusivity of hydrogen in the nitride precipitates is close to that as found for the nitrided compound layer (Dc ). On the other hand, taking into consideration the relatively small solubility of nitrogen in the ferrite at the room temperature (about 0.001%), one can assume that the actual diffusivity in this phase (Da;d ) is very close to that for the unitrided iron substrate (Ds ). Since the ratio Ds =Dc is about 4000, hydrogen should diffuse through the ferrite matrix bypassing the nitride precipitates. An approach proposed earlier [21] to characterise hydrogen transport in a duplex stainless steel can be adapted. Taking into account the lengthened shape and the anisotropy of the nitride precipitates (Fig. 1) it is evident, that the transport (diffusion) paths through the ferrite phase (La;d ) must be longer than the membrane thickness Ld , and that they may have various lengths. The experimental decay or build-up transients can be analysed in terms of the lattice diffusion through the ferrite phase (Da;d Ds ), in which the actual diffusion paths La;d range from the shortest path La;min to the longest path La;max . To this end, n partial paths may be distinguished, and remembering that the steady-state flux of hydrogen should be inversely proportional to the length of path, the 0 entire change of the permeation rate Dip ¼ i1 p ip can be divided into appropriate partial increases Dip;d for each path. Then, using the Eq. (1) or (2) the partial permeation rate with time may be reproduced for each path ip;d ¼ f ðtÞ. If the La;d are correctly chosen, the sum of the partial permeation rates should coincide with the experimental permeation rate curve. Usually, the above procedure must be repeated one or more times for different sets of La;d using the trial-and-error method. As an example, the build-up transient from Fig. 3(a) was re-plotted and analysed in detail in Fig. 6. In this case 5 partial paths were distinguished with an increment DLa;d ¼ 0:5 mm, and values of La;min ¼ 2:5 and La;max ¼ 4:5 mm were evaluated. A satisfactory agreement between the experimental build-up transient and
ip, experimental ip,d Σ ip,d 30
Lα,min = 2.5 mm ∆Lα,d = 0.5 mm
Lα,max = 4.5 mm
ipo 25
10
100
1000
Time (s)
Fig. 6. A detailed analysis of the partial build-up transient from Fig. 3(a). A solid line with open circles represents the experimental permeation rate. Fine dotted represent the predicted permeation rates of hydrogen corresponding to chosen diffusion paths, whereas a coarse dotted line represents the sum of the predicted permeation rates.
the sum of the partial build-ups confirms the correctness of these values. Using the above fitting procedure to the permeation transients for the others membranes with thickness Ld ¼ 0:4, 0.6 and 0.8 mm, the appropriate values of La;min and La;max were determined. The values of La;min and La;max for all studied membranes are shown as a function of the membrane thickness in Fig. 7, as open and solid circles, respectively. An extrapolation of these relationships to the origin of the coordinate system and to the thickness corresponding to the end of the diffusion zone, specify the range of the real diffusion paths in the diffusion zone. Finally, assuming that the length of 8 nitrided diffusion zone
Length of Diffusion Paths (mm)
2642
unitrided iron substrate
Lα,max 6
Lα,min
4
2
0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Membrane Thickness (mm)
Fig. 7. The real lengths of diffusion paths in the nitrided iron membranes as a function of their thickness.
Z. Wolarek, T. Zakroczymski / Acta Materialia 52 (2004) 2637–2643
diffusion paths in the unnitrided iron substrate is practically equal to the thickness of this layer, the span of real diffusion paths may extend over the whole nitrided specimen (Fig. 7). 6. Conclusions 1. An analysis of the partial decay or build-up transients for membranes prepared from nitrided iron specimens enables both the real diffusivity of hydrogen and the real lengths of diffusion paths in each layer of the nitrided iron to be evaluated. 2. The diffusivity of hydrogen in the compound layer is more than 4000 times lower than that in the unnitrided iron. Therefore, the compound layer, in spite of its relatively low thickness, can effectively impede the flux of hydrogen. 3. The transport of hydrogen in the nitrided diffusion zone occurs mainly through the ferrite matrix and can be characterised by a diffusion coefficient close to that for the unnitrided iron, however hydrogen has to bypass the nitride precipitates and, therefore, the real diffusion paths are increased. 4. The real diffusion paths in the nitrided diffusion layer have various lengths. Therefore an equation corresponding to a simple diffusion model cannot be satisfactorily fitted to the experimental partial permeation decay and build-up transient curves.
2643
References [1] Zakroczymski T, Lukomski N, Flis J. J Electrochem Soc 1993;140:3578. [2] Zakroczymski T, Lukomski N, Flis J. Corros Sci 1995;37: 811. [3] Brass AM, Chene J, Pivin JC. J Mater Sci 1989;24:1693. [4] Bruzzoni P, Br€ uhl SP, Gomez JAB, Nosei L, Ortiz M, Feugeas JN. Surf Coat Technol 1998;110:13. [5] Fassini FD, Zampronio MA, de Miranda PEV. Corros Sci 1993;35:549. [6] Lesage J, Chicot D, Bartier O, Zampronio MA, de Miranda PEV. Mater Sci Eng A 2000;282:203. [7] Devanathan MAV, Stachurski Z. Proc Roy Soc A 1962;270: 90. [8] McBreen J, Beck W, Nanis L. J Electrochem Soc 1966;113:1218. [9] Devanathan MAV, Stachurski Z. J Electrochem Soc 1964;111: 619. [10] Beck W, Bockris JOÕM, McBreen J, Nanis L. Proc Roy Soc A 1966;290:220. [11] Radhakrishnan TP, Shreir LL. Electrochim Acta 1967;12:889. [12] Dillard JL, Talbot-Besnard S. Compt Rend Acad Sci (Paris) Ser C 1969;269:1173. [13] Raczy nski W, Talbot-Besnard S. Compt Rend Acad Sci (Paris) Ser C 1969;269:1253. [14] Quick NR, Johnson HH. Acta Metall 1978;26:903. [15] Jack DH, Jack KH. Mater Sci Eng 1973;11:1. [16] Kumnick AJ, Johnson HH. Metall Trans 1974;5:1199. [17] Pressouyre GM, Bernstein IM. Metall Trans A 1978;9:1571. [18] Zakroczymski T. J Electroanal Chem 1999;475:82. [19] Zakroczymski T, Szklarska-Smialowska Z. J Electrochem Soc 1985;132:2548. [20] Caskey Jr GR, Pillinger WL. Metall Trans A 1975;6:467. [21] Owczarek E, Zakroczymski T. Acta Mater 2000;48:3059.
Hydrogen transport in plasma nitrided iron Z. Wolarek, T. Zakroczymski
*
Electrochemistry, Corrosion and Applied Surface Science, Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44-52, 01 224 Warsaw, Poland Received 14 April 2003; received in revised form 30 January 2004; accepted 10 February 2004 Available online 11 March 2004
Abstract Hydrogen permeation through membranes prepared from various parts of the nitrided iron specimens was investigated by an electrochemical technique. The membranes were charged with hydrogen by galvanostatic cathodic polarisation in 0.1 M NaOH. The successive partial decay and build-up transients were performed and analysed to determine the diffusivities of hydrogen in the outer compound layer, the inner diffusion zone, and the unmodified iron substrate. Hydrogen transport in the diffusion zone proved to be the most complex. It was found that hydrogen diffused mainly through the ferrite matrix and bypassed the nitride precipitates. Therefore, the real diffusion paths in the diffusion zone had various lengths and were longer than the membrane thickness. 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Iron; Plasma nitriding; Hydrogen; Diffusion; Hydrogen permeation
1. Introduction Among various methods for avoiding or decreasing hydrogen degradation of iron and its alloys, plasma nitriding seems to be especially promising. This process involves chemical and metallurgical changes of the surface/near surface region. Therefore, the nitrided layers, besides their beneficial wear properties, may reduce hydrogen absorption by the substrate metal. In general, this effect may be considered in terms of the hindrance of the entry of hydrogen from a surrounding environment into the outer nitrided layer (the surface effect), and the hindrance of the transport of hydrogen through the whole nitrided layer (the barrier effect). This barrier effect is the subject of this work. There are some reports showing that outer nitrided layers on iron [1,2], carbon steels [3,4] and low alloy high strength steel [5,6] act as barriers for hydrogen transport. The effectiveness of such barriers was evaluated using the electrochemical permeation technique and it was characterized by a decrease of hydrogen diffusivity. *
Corresponding author. Tel.: +48-226-323-221; fax: +48-226-311619. E-mail address: [email protected] (T. Zakroczymski).
Since the way of evaluation of the hydrogen diffusivity and, consequently, its meaning differed, the literature data are scattered and inadequate. Bruzzoni et al. [4] found that the apparent diffusion coefficient of hydrogen in nitrided AISI 4140 steel membranes was 0.053–0.19 106 cm2 /s, while that in the non-nitrided membrane was 30–10 times higher (1.7–1.9 106 cm2 /s). The decrease in hydrogen diffusivity was attributed to the compound layer together with the diffusion one. Fassini et al. [5] applied the model of a two-layer membrane to nitrogen ion-implanted API X65 type pipeline steel. It was found that the apparent hydrogen diffusivity in the modified layer was 5.3 1012 cm2 /s, i.e. about six orders of magnitude lower than that in the steel substrate (1.5 106 cm2 /s). In turn, the model of a three-layer membrane was applied for nitrided Armco iron membranes consisting of the outer compound layer, the inner diffusion layer and the substrate one [1]. The following values of hydrogen diffusivity were found: the compound layer – 4.1 108 cm2 /s, the diffusion layer – 6.1 106 cm2 /s, and the unmodified substrate – 7.3 105 cm2 /s. The predominant role of the compound layer in the hindrance of hydrogen transport through the nitrided steel was even more emphatic in the work of Lesage et al. [6].
1359-6454/$30.00 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2004.02.011
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Z. Wolarek, T. Zakroczymski / Acta Materialia 52 (2004) 2637–2643
Nomenclature Cc;0 D D# D" Dc Ds Dd;eff
Dd;x
Da;d DðcþdÞ
hydrogen concentration in the nitrided compound layer at its entry side hydrogen diffusivity hydrogen diffusivity evaluated from the partial decay hydrogen diffusivity evaluated from the partial build-up hydrogen diffusivity in the nitrided compound layer hydrogen diffusivity in the unnitrided iron substrate the effective hydrogen diffusivity for the membrane prepared from the nitrided diffusion zone the section-dependent hydrogen diffusivity for the membrane prepared from the nitrided diffusion zone hydrogen diffusivity in the ferrite matrix of the diffusion zone the effective hydrogen diffusivity for the membrane comprising the nitrided compound and diffusion layer
The diffusion coefficient in the compound layer was found to be 1.26 1011 cm2 /s, while that in the steel substrate 3.1 106 cm2 /s. At the same time, however, the hydrogen diffusivity in the diffusion zone was slightly larger (4.7 106 cm2 /s) than that for the substrate. In the present work, the transport of hydrogen in nitrided Armco iron was examined using specifically prepared membranes and measuring the permeation rate of hydrogen. The main objective was to determine the real diffusivities of hydrogen and the real diffusion paths in the nitrided compound layer, in the diffusion zone, and in the unnitrided iron substrate. Since the permeation of hydrogen through the membrane is complex, it may be altered by slow surface processes (affecting hydrogen entry) and hydrogen trapping (affecting hydrogen transport). Therefore, an effort was made to arrange suitable experimental conditions, under which the role of the surface and trapping effects was diminished, and the measured changes in the permeation rate of hydrogen may be interpreted as changes in the rate of hydrogen diffusion.
2. Experimental The material used was a commercial Armco iron (C 0.031, Mn 0.12, Si 0.01, P 0.008, S 0.015, Cr 0.01, Ni 0.01, Cu 0.02, Al 0.03 wt%) in the form of a hot-drawn, 25 mm diameter rod. Plate specimens, 19 mm in diameter and 3 mm in thickness, were machined out from the rod perpendicularly to its axis.
ic ip i0p i1 p L Lc Ls Ld LðcþdÞ La;d La;min La;max t X
cathodic (charging) current density permeation rate of hydrogen initial steady-state permeation rate of hydrogen a new steady-state permeation rate of hydrogen thickness of a membrane thickness of the nitrided compound layer thickness of the membrane prepared from the unnitrided iron substrate thickness of the membrane prepared from the nitrided diffusion zone thickness of the membrane comprising the nitrided compound and diffusion zone length of diffusion paths in the ferrite matrix of the diffusion zone the shortest diffusion path in the ferrite the longest diffusion path in the ferrite time distance
The specimens were plasma nitrided on one side using a nitriding plasma chamber. The nitriding conditions were as follows: gas composition 80% N2 + 20% H2 , pressure of 670 Pa, temperature 540 C, nitriding time 6 h. After this treatment, the specimens were cooled slowly in the chamber. The nitriding treatment produced a modified layer of about 1.3 mm in thickness (Fig. 1(a)) which consisted of a thin, about 10 lm, outer compound layer composed of nitrides Fe2–3 N (e-phase) and Fe4 N (c0 -phase), and an inner, much thicker, diffusion zone with the dispersed Fe4 N precipitates and a solid solution of nitrogen in the metal matrix (Fig. 1(a) and (b)). The following membranes (Fig. 1(a)) were prepared by abrading the nitrided specimens: • One-layer membranes of thickness Ls ¼ 1 mm, comprising only the unmodified iron substrate. • One-layer membranes with varying thickness Ld ¼ 0:4, 0.6, 0.8 and 1 mm, comprising various sections of the diffusion layer. In this case, the compound layer was removed and the specimen was abraded from the other side to the corresponding depth. • Two-layer membranes of thickness LðcþdÞ ¼ 1 mm, comprising the compound layer and the major part of the diffusion zone. The prepared membranes were used for the hydrogen permeation measurements by an electrochemical technique [7]. They were mounted between two electrochemical cells using a holder made of methyl polymetacrylate (Perspex) having flanges and rubber gaskets. The circular area exposed to solution was 0.5 cm2 .
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3. Analysis of permeation transients The non-stationary transport of hydrogen in a nonhomogeneous membrane like that made from the nitrided diffusion layer, and especially in that including both the compound and diffusion layers, is difficult to treat. Nevertheless, for a start, a simple diffusion model for hydrogen permeation through a homogeneous membrane can be used to determine the apparent diffusivity of hydrogen. The following equations, valid for the membrane thickness L, constant diffusion coefficient D, and under the boundary condition of constant hydrogen concentration beneath the entry side of the membrane [8], have been employed to analyse the experimental partial transients: Decay 1 ip i1 2L X p ¼ 1 pffiffiffiffiffiffiffiffi exp 0 1 ip ip pDt n¼0
ð2n þ 1Þ2 L2 4Dt
Build-up 1 ip i0p 2L X p ffiffiffiffiffiffiffiffi ¼ exp 0 i1 pDt n¼0 p ip
2
ð2n þ 1Þ L2 4Dt
! ;
ð1Þ
! ;
ð2Þ
where ip is the measured permeation rate at time t, i0p is the initial steady-state permeation rate (t ¼ 0), i1 p is the new steady-state permeation rate (t ! 1Þ. For the 0 partial decay 0 < i1 p < ip ; for the successive partial 0 1 build-up 0 < ip < ip . The hydrogen diffusivity was evaluated by fitting of a suitable equation to the entire run of the experimental transient by adjusting the diffusion coefficient D. The least square method was employed for the fitting procedure. Fig. 1. SEM micrographs of the etched cross-section surface of the nitrided iron specimen and the way of preparing various membranes.
45
Initially the membranes were charged at their one (entry) side with hydrogen cathodically generated from 0.1 M NaOH at a current density ic ¼ 20 mA/cm2 . The entry side of the nitrided membranes corresponded to the outer surface of the compound layer (two-layers membranes) or to the diffusion layer just beneath the compound layer (one-layer membranes). The membrane exit side, previously coated with a thin layer of Pd, was polarised at the constant anodic potential of 0.15 0.15 VHgjHgOj0:1 M NaOH (0.32 VNHE ) and the anodic current was a measure of the permeation rate of hydrogen. After 24 h, when the permeation rate achieved a steady-state, the successive partial decay and build-up transients were measured after changes of the cathodic current density from 20 to 10 mA/cm2 and then back to the previous value of 20 mA/cm2 . The permeation experiments were carried out at 30 C.
H Permeation Rate, ip (µA/cm2)
ic = 20 10 mA/cm2
unnitrided Fe substrate Ls = 1 mm 40
ic = 10 20 mA/cm2 35 1
10
100
Time, t (s) exper. decay
exper. buildup fitted by Eq. (2) D↑ = 8.2x10-5 cm 2/s
fitted by Eq. (1) -5 2 D = 7.8x10 cm /s ↓
Ds = 8.0 x10-5 cm2/s
Fig. 2. Partial decay and build-up transients for the pre-charged unnitrided iron substrate membrane. Solid lines with open symbols represent the experimental transients; dashed lines with solid symbols represent the model equations fitted to the experimental data.
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4. Results 4.1. Unmodified iron substrate The successive partial decay and build-up permeation transients and the best fittings of Eqs. (1) and (2), respectively, for the unnitrided iron substrate membrane Ls ¼ 1 mm are shown in Fig. 2. The experimental and computer fitted transients overlap each other and the hydrogen diffusivity, taken as an average value of those resulting from the fitting procedure of the decay (D# ) and build-up (D" ) transients, equals Ds ¼ 8:0 105 cm2 /s.
H Permeation Rate, ip (µA/cm2)
0.090 ic = 20
10 mA/cm 2
ic = 10
20 mA/cm
0.085
0.080
2
compound layer + diffusion zone L(c+d) = 1 mm
0.075 100
1000
10000
Time, t (s) exper. decay
exper. buildup
fitted by Eq. (1) -6 2 D = 1.5x10 cm /s
fitted by Eq. (2) -6 2 D↑ = 1.5x10 cm /s
↓
ic = 20
10 mA/cm
-6
2
D(c+d) = 1.5x10 cm /s
2
H Permeation Rate, ip (µA/cm )
35
2
Fig. 4. Partial decay and build-up transients for the pre-charged membrane consisting of the nitrided compound and diffusion layers. Solid lines with open symbols represent the experimental transients; dashed lines with solid symbols represent the model equations fitted to the experimental data.
diffusion zone Ld = 1 mm
30
4.2. Diffusion layer 25
ic = 10
20 mA/cm2
10
100
(a)
1000
Time, t (s) exper. decay
exper. buildup fitted by Eq. (2) D↑ = 7.3x10-6 cm 2/s
fitted by Eq. (1) D↓ = 7.1x10-6 cm 2/s
Dd = 7.2x10-6 cm2/s
10 mA/cm2
2
H Permeation Rate, ip (µA/cm )
ic = 20 90
diffusion zone Ld = 0.4 mm
Two examples of the decay and build-up transients for the nitrided membranes Ld ¼ 1 and 0.4 mm, i.e. comprising various sections of the diffusion zone, are shown in Fig. 3(a) and (b), respectively. In contrast to the iron substrate membranes, there were considerable discrepancies between the fit and the experimental decay and build-up transient curves. The fitting procedure leads to an effective diffusivity Dd;eff , characterising the transport of hydrogen through the whole membrane. The values of Dd;eff , including those for other membranes Ld ¼ 0:6 and 0.8 mm, are depicted in Fig. 5. It can be seen that the thinner membrane has the lower effective diffusivity. Generally, the values of Dd;eff are more than one order of magnitude lower than the value of Ds .
80
4.3. Compound layer together with diffusion layer
70 ic = 10
20 mA/cm2
1
10
(b)
100
Time, t (s) exper. decay
exper. buildup
The successive partial decay and build-up permeation transients recorded for the membrane LðcþdÞ ¼ 1 mm, consisting of the compound and diffusion layers, are shown in Fig. 4. A resulting value of the effective diffusivity DðcþdÞ is almost two orders of magnitude lower than that for the unnitrided membrane, Ds .
fitted by Eq. (2) D ↑ = 4.8x10-6 cm2/s
fitted by Eq. (1) D↓ = 4.8x10-6 cm2/s -6
2
Dd = 4.8x10 cm /s
Fig. 3. Partial decay and build-up transients for the pre-charged membrane prepared from the nitrided diffusion zone: (a) Ld ¼ 1 mm, (b) Ld ¼ 0:4 mm. Solid lines with open symbols represent the experimental transients; dashed lines with solid symbols represent the model equations fitted to the experimental data.
5. Discussion 5.1. Hydrogen diffusivity in the unmodified iron substrate The excellent agreement between the experimental and computer fitted transients for the unnitrided iron
Z. Wolarek, T. Zakroczymski / Acta Materialia 52 (2004) 2637–2643
5.2. Hydrogen diffusivity in the compound layer Although it was impossible to prepare and examine a membrane composed of only the compound layer, the hydrogen diffusivity in this layer can be determined indirectly. One can assume that there are no barriers for hydrogen passing between the compound layer and the diffusion zone (Fig. 1), i.e. there is continuity in the hydrogen concentration at the boundary between these layers. The steady state permeation rate of hydrogen, i1 p , through a membrane consisting of the compound and diffusion layers, LðcþdÞ , can be expressed by the following relationships: i1 p ¼
DðcþdÞ Cc;0 F Dc ðCc;0 Cc=d ÞF Dd;eff Cc=d F ¼ ¼ ; Lc Ld LðcþdÞ
ð3Þ
where Lc is the thickness of the compound layer, Cc;0 is the concentration of hydrogen in the compound layer at its entry side, Cc=d is the concentration of hydrogen at the boundary of the nitrided layer and the diffusion zone, and Dc is the diffusivity of hydrogen in the compound layer. In the steady state, the fall in H concentration through the membrane is the sum of the falls through the component layers: Cc;0 ¼ ðCc;0 Cc=d Þ þ Cc=d . Consequently, the following equation follows from (3) LðcþdÞ Lc Ld ¼ þ : ð4Þ DðcþdÞ Dc Dd;eff Since for the membrane LðcþdÞ ¼ 1 mm, Lc 0:01 mm and Ld 0:99 mm, the effective diffusivity Dd;eff ¼ 7:2 106 cm2 /s found for the membrane Ld ¼ 1 mm (Fig. 3(a)) is basically that for the diffusion layer of the composite membrane considered. Substituting DðcþdÞ ¼ 1:5 106 cm2 /s (Fig. 4) into Eq. (4), a value of Dc ¼ 1:9 108 cm2 /s is obtained. Thus, the diffusivity of hydrogen in the nitrided compound layer is more than 4000 times lower than that in a-iron. The value of Dc obtained is close to that found earlier [1], but it is considerably higher than other data [5,6]. The compound layer nitrided under the applied conditions was composed of c0 -phase and e-phase. Besides, the e-phase was present in the outermost sublayer of the compound layer. The mobility of hydrogen in these phases may be different because of the different metal-atom arrangement: a close-packed hexagonal for e-phase, and a face-centred cubic for c0 -phase [15]. Therefore, the evaluated diffusivity Dc should
be regarded as characteristic for the whole compound layer.
5.3. Hydrogen diffusivity in the diffusion zone Hydrogen transport in the nitrided diffusion zone seems to be more complex and at the same time intriguing than that in the substrate and compound layers. The effective diffusivity Dd;eff characterises the transport of hydrogen through the whole membrane and it increases with the membrane thickness (Fig. 5). However, taking into account irregular distribution of the nitride precipitates in the diffusion zone and remembering that the membranes comprised various sections of this zone (Fig. 1(a)), the thicker membrane the lower the average density of nitride precipitates and their different distribution across the membrane. Therefore, it is reasonable to ascribe the value of Dd;eff to a distance X , corresponding to the middle of the given membrane of thickness Ld (Fig. 5). In this way, the section-dependent hydrogen diffusivity, designated as Dd;x , as a function of the distance in the diffusion zone is shown in Fig. 5. It is useful to note that the extrapolated Dd;x X curve intersects the level of hydrogen diffusivity specific for the unnitrided iron substrate just at the depth of nitriding (Fig. 1(a)). Although the section-dependent diffusivity Dd;x characterizes the transport of hydrogen more exactly than the effective diffusivity Dd;eff , it does not explain the role of the nitride precipitates in hindering hydrogen transport. Generally, the observed inconsistency of the experimental and fitted partial transients for the nitrided membranes (Fig. 3(a) and (b)) indicates that the transport of hydrogen is perturbed. A possible reason can be hydrogen trapping. However, it has been shown that the effect of trapping, distinctly revealed on 10-4
Ds Hydrogen Diffusivity (cm2/s)
substrate membranes (Fig. 2) proves that the boundary conditions required by Eqs. (1) and (2), including that Ds ¼ const, were fulfilled. Therefore the permeation of hydrogen through the membrane was controlled by the rate of hydrogen diffusion inside the membrane. The value of Ds obtained is consistent with the literature data for the lattice diffusivity of hydrogen in a-iron at room temperature [9–14].
2641
10-5
Dd,x Dd,eff
nitrided diffusion zone 10-6 0.0
0.5
unnitrided iron substrate
1.0
1.5
2.0
3.0
Distance, X (mm)
Fig. 5. The effective (Dd;eff ) and section-dependent (Dd;x ) hydrogen diffusivities for the membranes prepared from the nitrided diffusion zone, and the hydrogen diffusivity in the unnitrided iron substrate as a function of the distance in the nitrided specimen.
Z. Wolarek, T. Zakroczymski / Acta Materialia 52 (2004) 2637–2643 ip∞
diffusion layer Ld = 1 mm
35
2
ic = 10 20 mA/cm
Dα ,d ∼ Ds = 8.0x10-5 cm2/s 2
H Permeation Rate (µA/cm )
the permeation transients during the first charging [16–18] or the complete desorption [18], is insignificant in regard to partial transients [18,19]. Presumably, the changes in the hydrogen concentration are too small to initiate trapping or de-trapping of hydrogen, because these processes are not fully reversible. Moreover, the decay and build-up transients altered by trapping should not coincide [20], whereas those shown in Fig. 3(a) and (b) do. In any case, trapping effects were not apparent in the partial transients recorded for the unnitrided iron substrate membrane (Fig. 2). Thus, the trapping of hydrogen should not be an important factor in the observed discrepancies between the experimental and model partial transients. The actual model of hydrogen transport in the nitrided diffusion zone must take into account the presence of the nitride precipitates in the ferrite matrix. Undoubtedly, the diffusivity of hydrogen in the nitride precipitates is close to that as found for the nitrided compound layer (Dc ). On the other hand, taking into consideration the relatively small solubility of nitrogen in the ferrite at the room temperature (about 0.001%), one can assume that the actual diffusivity in this phase (Da;d ) is very close to that for the unitrided iron substrate (Ds ). Since the ratio Ds =Dc is about 4000, hydrogen should diffuse through the ferrite matrix bypassing the nitride precipitates. An approach proposed earlier [21] to characterise hydrogen transport in a duplex stainless steel can be adapted. Taking into account the lengthened shape and the anisotropy of the nitride precipitates (Fig. 1) it is evident, that the transport (diffusion) paths through the ferrite phase (La;d ) must be longer than the membrane thickness Ld , and that they may have various lengths. The experimental decay or build-up transients can be analysed in terms of the lattice diffusion through the ferrite phase (Da;d Ds ), in which the actual diffusion paths La;d range from the shortest path La;min to the longest path La;max . To this end, n partial paths may be distinguished, and remembering that the steady-state flux of hydrogen should be inversely proportional to the length of path, the 0 entire change of the permeation rate Dip ¼ i1 p ip can be divided into appropriate partial increases Dip;d for each path. Then, using the Eq. (1) or (2) the partial permeation rate with time may be reproduced for each path ip;d ¼ f ðtÞ. If the La;d are correctly chosen, the sum of the partial permeation rates should coincide with the experimental permeation rate curve. Usually, the above procedure must be repeated one or more times for different sets of La;d using the trial-and-error method. As an example, the build-up transient from Fig. 3(a) was re-plotted and analysed in detail in Fig. 6. In this case 5 partial paths were distinguished with an increment DLa;d ¼ 0:5 mm, and values of La;min ¼ 2:5 and La;max ¼ 4:5 mm were evaluated. A satisfactory agreement between the experimental build-up transient and
ip, experimental ip,d Σ ip,d 30
Lα,min = 2.5 mm ∆Lα,d = 0.5 mm
Lα,max = 4.5 mm
ipo 25
10
100
1000
Time (s)
Fig. 6. A detailed analysis of the partial build-up transient from Fig. 3(a). A solid line with open circles represents the experimental permeation rate. Fine dotted represent the predicted permeation rates of hydrogen corresponding to chosen diffusion paths, whereas a coarse dotted line represents the sum of the predicted permeation rates.
the sum of the partial build-ups confirms the correctness of these values. Using the above fitting procedure to the permeation transients for the others membranes with thickness Ld ¼ 0:4, 0.6 and 0.8 mm, the appropriate values of La;min and La;max were determined. The values of La;min and La;max for all studied membranes are shown as a function of the membrane thickness in Fig. 7, as open and solid circles, respectively. An extrapolation of these relationships to the origin of the coordinate system and to the thickness corresponding to the end of the diffusion zone, specify the range of the real diffusion paths in the diffusion zone. Finally, assuming that the length of 8 nitrided diffusion zone
Length of Diffusion Paths (mm)
2642
unitrided iron substrate
Lα,max 6
Lα,min
4
2
0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Membrane Thickness (mm)
Fig. 7. The real lengths of diffusion paths in the nitrided iron membranes as a function of their thickness.
Z. Wolarek, T. Zakroczymski / Acta Materialia 52 (2004) 2637–2643
diffusion paths in the unnitrided iron substrate is practically equal to the thickness of this layer, the span of real diffusion paths may extend over the whole nitrided specimen (Fig. 7). 6. Conclusions 1. An analysis of the partial decay or build-up transients for membranes prepared from nitrided iron specimens enables both the real diffusivity of hydrogen and the real lengths of diffusion paths in each layer of the nitrided iron to be evaluated. 2. The diffusivity of hydrogen in the compound layer is more than 4000 times lower than that in the unnitrided iron. Therefore, the compound layer, in spite of its relatively low thickness, can effectively impede the flux of hydrogen. 3. The transport of hydrogen in the nitrided diffusion zone occurs mainly through the ferrite matrix and can be characterised by a diffusion coefficient close to that for the unnitrided iron, however hydrogen has to bypass the nitride precipitates and, therefore, the real diffusion paths are increased. 4. The real diffusion paths in the nitrided diffusion layer have various lengths. Therefore an equation corresponding to a simple diffusion model cannot be satisfactorily fitted to the experimental partial permeation decay and build-up transient curves.
2643
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