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Transport of hydrogen and deuterium in the reduced activation martensitic steel ARAA
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Transport of hydrogen and deuterium in the reduced activation martensitic steel ARAA S.J. Noh a,∗ , S.K. Lee a , W.J. Byeon a , Y.B. Chun b , Y.H. Jeong b a b
Department of Applied Physics, Dankook University, Yongin-si 448-701, Gyeonggi-do, Republic of Korea Nuclear Materials Division, Korea Atomic Energy Research Institute, 989-111 Daedeok-daero,Yuseong-gu, Daejeon 305-353, Republic of Korea
h i g h l i g h t s • Transport of H2 and D2 in advanced reduced activation alloy was measured. • Appreciable trapping effects are observed only at low temperatures (250–350 ◦ C). • Isotope effect ratio for the diffusivity differs from the classical prediction.
a r t i c l e
i n f o
Article history: Received 9 May 2014 Received in revised form 17 June 2014 Accepted 21 July 2014 Available online xxx Keywords: Reduced activation steel Hydrogen Deuterium Permeation Diffusion
a b s t r a c t Advanced reduced activation alloy (ARAA) is a reduced activation ferritic/martensitic (RAFM) steel under development at the Korea Atomic Energy Research Institute. The transport of hydrogen and deuterium in ARAA was investigated in an elevated temperature range of 250–600 ◦ C. A continuous-flow method, a time-dependent gas-phase technique, was used for the measurements. Complete sets of transport parameters (permeability, diffusivity, solubility, trap site density, and trapping energy) of hydrogen and deuterium in ARAA were successfully obtained. We show that appreciable trapping effects are observed only at low temperatures (250–350 ◦ C) and that the isotope effect ratio for the diffusivity differs from the classical prediction. However, the measured values of permeability, effective diffusivity, and effective solubility of ARRA were within the range of results reported for other RAFM steels. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Advances in fusion technology will rely heavily on advances in materials, and the Korea Atomic Energy Research Institute has been developing an advanced reduced activation alloy (ARAA). ARAA is a reduced activation ferritic/martensitic (RAFM) steel, which is considered as a candidate material for the fusion reactor structure. The permeation of hydrogen isotopes through other RAFM steels has been studied by many investigators [1–9]. In this study, the transport of hydrogen isotopes in ARAA was investigated using hydrogen and deuterium gases. Complete sets of transport parameters (permeability, diffusivity, solubility, trap site density, and trapping energy) of hydrogen and deuterium in ARAA were obtained, and the trapping and isotope effects on the permeability, diffusivity, and solubility were evaluated. These results are
∗ Corresponding author. Tel.: +82 3180053211. E-mail address: [email protected] (S.J. Noh).
compared with those of previously reported results for other RAFM steels [1–7]. 2. Experimental A 45-kg heat (ARAA-1, heat number F211) was produced using vacuum-induction melting and hot rolled in a two-high mill at 1200 ◦ C to a total thickness reduction of 80%. The plate thickness after the hot-roll process was 15 mm. The plate was then normalized at 980 ◦ C for 40 min and tempered for 70 min at 760 ◦ C. The plate was fabricated into a disk (3-mm thickness; 15-mm diameter), and the surface was polished to minimize surface process effects arising from any surface roughness. The chemical composition of the ARAA is given in Table 1. A time-dependent gas-phase technique, the continuous-flow method [10,11] in which the partial pressure of the permeated gas is proportional to the permeation flux through a membrane, was employed for the measurements. The permeation flux of hydrogen isotopes (hydrogen and deuterium) was obtained as a function of time using a hydrogen-isotope permeation measurement
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Please cite this article in press as: S.J. Noh, et al., Transport of hydrogen and deuterium in the reduced activation martensitic steel ARAA, Fusion Eng. Des. (2014), http://dx.doi.org/10.1016/j.fusengdes.2014.07.013
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Table 1 Analyzed composition of ARAA. Element
Concentration (wt%)
C Cr W Mn V Ta Si N Ti Zr Fe
0.09 9.33 1.05 0.46 0.21 0.09 0.07 0.024 0.018 0.009 Balance
system (HPMS) that was designed and constructed in-house, where the partial gas pressure was measured using a residual gas analyzer (in a unit of Pa or Torr) and the effective pumping speed for the permeated gas was determined using a high-precision mass flow controller. The feed pressure was fixed at 100 kPa (1 bar), and the temperature range was 250–600 ◦ C. The system has measurement uncertainties in the temperature. These uncertainties become
1.7 ◦ C at 250 ◦ C and 2.3 ◦ C at 600 ◦ C, which can induce errors of ∼3% for determining the permeation flux. The system also has uncertainties in the pumping speed that corresponds to a 2% error level. Details of the HPMS and the experimental method can be found in Lee et al. [11,12]. 3. Theory Fick’s first law states that the permeation flux of hydrogen atoms through a membrane is proportional to the concentration gradient. We consider hydrogen transport through a membrane of uniform thickness d and assume that the initial concentration throughout the membrane is zero. At time t = 0, the hydrogen pressure on the feed side is increased instantaneously from zero to pf . Then, at any given time t > 0, the hydrogen concentrations on the feed side Cf and permeate side Cp are assumed to be constant according to Sieverts’ law: Cf = S p0.5 , f
(1)
Cp = 0,
(2)
Fig. 1. Arrhenius plots of the (a) permeability, (b) effective diffusivity, and (c) effective solubility of hydrogen and deuterium in ARAA.
Please cite this article in press as: S.J. Noh, et al., Transport of hydrogen and deuterium in the reduced activation martensitic steel ARAA, Fusion Eng. Des. (2014), http://dx.doi.org/10.1016/j.fusengdes.2014.07.013
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where S is the Sieverts’ constant (or the solubility) of the membrane. The hydrogen permeation flux through the membrane J(t) is given by J(t) =
˚ p0.5 f
∞
1+2
d
n
(−1) exp
n=1
D n2 2 t − d2
Q (t) = A
J t 0
=A
˚ p0.5 f
,
(3)
d
Q (t) = A
dt
t−
d
d2
−
6D
2 d2 2 D
,
∞ (−1)n n=1
n2
exp
−
D n2
2
d2
t
d
d2 6D
t−
.
(6)
−E ϕ
RT
−E d
D = D0 exp Deff =
RT
,
(7)
,
(8)
D
1 + Nt /N exp Et /RT
S = S0 exp
−E
Seff = S 1 +
s
RT
N t
N
,
, exp
S,H (mol m
−3
−0.5
Pa
) = 1.25 exp
−34.7 × 103 RT
, (12)
,
(13)
,
(14)
Nt,H (sites m−3 ) = 1.0 × 1024 , Et,H (J mol
−1
(15)
3
) = 59.4 × 10 ,
(16) (J mol−1
where the subscript H refers to hydrogen, and R K−1 ) is equal to 8.314472. The deuterium transport parameters were determined as
˚D (mol m−1 s−1 Pa−0.5 ) = 9.61 × 10−8 exp
In the experiments, the hydrogen permeation flux through the membrane was measured as a function of time. The permeability ˚ was obtained from Eq. (5) when the permeation flux reached a saturated level. A fit of the asymptotic region of Q(t) as given in Eq. (4) approximates the relationship in Eq. (6), and this line intersects the time axis at tlag = d2 /6D, where tlag is commonly defined as the time lag. The diffusion coefficient is then determined by D = d2 /6tlag [3,12–15], and S can be calculated directly from S = ˚/D. The capture and release of hydrogen atoms occur at trapping centers distributed throughout the membrane [3,5,7]. The trapping process provides additional sites for accommodating hydrogen and increases the time taken for hydrogen to move into the membrane. Thus, the trapping effect leads to an increase in the effective solubility Seff with respect to the lattice solubility S and a decrease in the effective diffusivity Deff with respect to the lattice diffusivity D . However, the permeability is not affected by trapping. As a result, the transport parameters are dependent on the absolute temperature T: ˚ = ˚0 exp
−12.7 × 10 RT
,
−47.4 × 103 RT
3
D,H (m2 s−1 ) = 7.59 × 10−8 exp
(5)
˚ p0.5 f
where A is the membrane area [3,12–15]. In the steady-state (i.e., t → ∞), Eqs. (3) and (4) become J=
Arrhenius plots of the permeability, effective diffusivity, and effective solubility of hydrogen and deuterium for ARAA are shown in Fig. 1. The hydrogen transport parameters in ARAA were determined as follows: ˚H (mol m−1 s−1 Pa−0.5 ) = 9.45 × 10−8 exp
(4)
˚ p0.5 f
assuming that the ARAA has a body-centered cubic structure with six tetrahedral lattice sites available per host atom [3,5,7,16]. 4. Results and discussion
where ˚ = DS is defined as the permeability of the membrane, and D is the diffusion coefficient (or diffusivity) of the membrane [3,12–15]. The total amount of hydrogen Q (t) that has passed through the membrane after time t is given by t
3
D,D (m2 s−1 ) = 7.33 × 10−8 exp
−14.0 × 10 RT
S,D (mol m−3 Pa−0.5 ) = 1.31 exp
−50.1 × 103 RT
3
−36.1 × 103 RT
, (17)
,
(18)
,
(19)
Nt,D (sites m−3 ) = 1.0 × 1024 ,
(20)
Et,D (J mol−1 ) = 59.0 × 103 ,
(21)
(9)
(10)
E t
RT
,
(11)
where ˚0 , D0 , and S0 are pre-exponential factors of the permeability, lattice diffusivity, and lattice solubility, respectively; Eϕ and Ed are the activation energies for permeation and lattice diffusion, respectively; Es is the heat of solution (i.e., the enthalpy of formation of hydrogen atoms in the membrane); Nt and N are the trap and lattice site densities, respectively; Et is the trapping energy; and R is the gas constant [3,5,7]. The lattice site density N is 5.1 × 1029 m−3
Fig. 2. Arrhenius plot of the isotope effect ratios of hydrogen and deuterium for the permeability, effective diffusivity, and effective solubility in ARAA.
Please cite this article in press as: S.J. Noh, et al., Transport of hydrogen and deuterium in the reduced activation martensitic steel ARAA, Fusion Eng. Des. (2014), http://dx.doi.org/10.1016/j.fusengdes.2014.07.013
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Fig. 3. Arrhenius plots of the hydrogen (a) permeability, (b) effective diffusivity, and (c) effective solubility in ARAA and other reference RAFM steels: (1) this work, (2) EUROFER 97 [7], (3) OPTIFER-IVb [5], (4) MANET [1], and (5) F82H [4].
where the subscript D refers to deuterium. As shown in Fig. 1(a), the Arrhenius plots of both ˚H and ˚D reveal a linear relationship over the whole temperature range of 250–600 ◦ C. There are no apparent trapping effects because ˚ was obtained from Eq. (5) when the permeation flux through the membrane reached the saturated level, i.e., when the trapped population reached equilibrium. The relationship between ˚ and T was determined by a least-squares fit of the data. In contrast, both Deff,H and Deff,D have non-linear Arrhenius dependences: Deff exhibits a linear relationship at high temperatures (400–600 ◦ C) but deviates from this relationship at low temperatures (250–350 ◦ C). At high temperatures, the trapping effect is assumed to be negligible, and so Deff becomes equal to D , and the activation energy of Deff is constant. However, at low temperatures, the trapping effect predicted by Eq. (9) is apparent; Deff drops below D , and the activation energy of Deff increases with decreasing temperature. The relationship between D and T was determined by a linear least-squares fit of the data obtained at high temperatures (400–600 ◦ C). The trap site density Nt and trapping energy Et were evaluated by a non-linear leastsquares fit of the measured diffusivity data using the theoretical expression for Deff [Eq. (9)], where D is given by Eqs. (13) and (18) for hydrogen and deuterium, respectively. The values of Et,H and
Et,D [Eqs. (16) and (21), respectively] are close to those corresponding to high-angle grain boundaries (59 kJ mol−1 ) and surfaces of coarse secondary particles, e.g., AIN (65 kJ mol−1 ), Fe2–3 C (ε carbide; 65 kJ mol−1 ), MnS (72 kJ mol−1 ) [3,5,7,17]. Fig. 1(c) shows Arrhenius plots of Seff,H and Seff,D . It should be noted that we did not perform separate experiments for measuring Seff,H and Seff,D ; these were calculated as Seff = ˚/Deff . The effects of hydrogen isotopes on the transport parameters were also estimated, and Fig. 2 shows Arrhenius plots of the isotope effect ratios of hydrogen and deuterium for ˚, Deff , and Seff . The isotope effect on Deff was estimated from Deff,H /Deff,D , the ratio of Deff,H and Deff,D . Classical rate theory assumes that atomic vibration frequencies are inversely proportional to (mass)0.5 and that the activation energy for diffusion is independent of the mass of the isotope. Thus, in classical rate theory, the isotope effect ratio of the diffusivity, DH /DD , is predicted to be a constant: DH = DD
m 0.5 D
mH
=
√
2,
(22)
where mD and mH are the masses of deuterium and hydrogen, respectively. However, we found that the value of Deff,H /Deff,D determined in this work differed from that predicted by classical rate
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Fig. 4. Arrhenius plots of the deuterium (a) permeability, (b) effective diffusivity, and (c) effective solubility in ARAA and other reference RAFM steels: (1) this work, (2) EUROFER 97 [6], (3) OPTIFER-IVb [5], (4) MANET [2,3,7], and (5) F82H [3].
theory. The ratio of the pre-exponential diffusivity factors D0,H /D0,D was calculated to be 1.04, and we found that at high temperatures (400–600 ◦ C), Deff,H /Deff,D increased with decreasing temperature (1.24 at 600 ◦ C to 1.30 at 400 ◦ C), which there was little change at low temperatures (Deff,H /Deff,D was 1.31 at 350 ◦ C and 1.32 at 250 ◦ C). This departure from the classical rate theory prediction may be attributed to the quantum effect [18,19]. Furthermore, ˚H /˚D increased with decreasing temperature, from 1.43 at 600 ◦ C to 1.83 at 250 ◦ C, as did Seff,H /Seff,D (1.15 at 600 ◦ C to 1.39 at 250 ◦ C).
These results for ARAA were compared with those of other RAFM steels [1–7]. Fig. 3(a)–(c) shows Arrhenius plots of the permeability, effective diffusivity, and effective solubility of hydrogen in the materials, respectively. We found that the values of ˚H , Deff,H , and Seff,H for ARAA were within the range of results for other RAFM steels and had temperature dependences similar to those of other steels. Fig. 4 shows the corresponding Arrhenius plots for deuterium transport, and these findings are similar to the hydrogen results.
Table 2 Transport parameters for ARAA and reference RAFM steels (activation energies in kJ mol−1 ). Material ARAA(H) ARAA(D) EUROFER 97(H) EUROFER 97(D) OPTIFER-IVb(H) OPTIFER-IVb(D) MANET(H) MANET(D) F82H(H) F82H(D)
˚0
Eϕ −8
9.45 × 10 9.61 × 10−8 1.03 × 10−8 1.53 × 10−8 1.80 × 10−8 1.50 × 10−8 2.93 × 10−8 2.73 × 10−8 4.90 × 10−8 4.03 × 10−8
47.4 50.1 37.4 38.3 39.6 40.3 43.1 39.9 39.3 40.8
D0
Ed −8
7.59 × 10 7.33 × 10−8 4.57 × 10−7 1.50 × 10−7 5.49 × 10−8 4.61 × 10−8 7.17 × 10−8 1.01 × 10−7 1.80 × 10−7 1.07 × 10−7
12.7 14.0 22.3 14.5 10.6 11.3 13.5 13.2 14.1 13.9
S0 1.25 1.31 0.023 0.102 0.328 0.325 0.409 0.270 0.300 0.377
Es
Nt
34.7 36.1 15.1 23.8 29.0 29.0 29.6 26.7 25.8 26.9
1.0 × 10 1.0 × 1024 1.3 × 1025 1.0 × 1024 2.2 × 1024 1.0 × 1024 – 1.5 × 1025 2.6 × 1023 1.6 × 1023 24
Et
T(K)
Refs.
Curve
59.4 59.0 43.2 57.9 52.2 55.2 – 48.5 54.0 55.9
523–873 523–873 373–723 423–723 423–892 423–892 523–873 373–743 373–723 373–723
T. W. T. W. [7] [6] [5] [5] [1] [2,3,7] [4] [3]
Fig. 3. (1) Fig. 4. (1) Fig. 3. (2) Fig. 4. (2) Fig. 3. (3) Fig. 4. (3) Fig. 3. (4) Fig. 4. (4) Fig. 3. (5) Fig. 4. (5)
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For comparison, the transport parameters (permeability, diffusivity, solubility, trap site density, and trapping energy) of hydrogen and deuterium in ARAA and the reference RAFM steels are summarized in Table 2. The values of ˚0 , Eϕ , S0 , and Es of ARAA are the highest, whereas the values of D0 , Ed , and Nt are within the range of values of the reference steels. The values of Et of ARAA are also close to those of other steels. 5. Conclusions Complete sets of parameters for the hydrogen and deuterium transport in ARAA were successfully obtained over a temperature range of 250–600 ◦ C. Appreciable trapping effects were observed only at low temperatures (250–350 ◦ C), and the average trapping energy was found to be close to those of the high-angle grain boundary and coarse secondary particle surfaces. We also found that the isotope effect√ratio for the diffusivity differed from the classical prediction of 2. Although there were some discrepancies in the pre-exponential factors and activation energies between those of the ARAA and other RAFM steels, the measured values of ˚, Deff , and Seff of ARRA were within the range of results reported for other steels. Acknowledgments This work was supported by the National R&D Program through a National Research Foundation of Korea (NRF) grant funded by the Ministry of Science ICT & Future Planning (No. 2008-0061900). References [1] K.S. Forcey, D.K. Ross, J.C.B. Simpson, D.S. Evans, Hydrogen transport and solubility in 316L and 1.4914 steels for fusion reactor applications, J. Nucl. Mater. 160 (1988) 117–124.
[2] E. Serra, A. Perujo, Influence of the surface conditions on permeation in the deuterium—MANET system, J. Nucl. Mater. 240 (1997) 215–220. [3] E. Serra, A. Perujo, G. Benamati, Influence of traps on the deuterium behaviour in the low activation martensitic steels F82H and Batman, J. Nucl. Mater. 245 (1997) 108–114. [4] E. Serra, G. Benamati, Hydrogen behaviour in aged low activation martensitic steel F82H for fusion reactor applications, J. Mater. Sci. Technol. 14 (1998) 573–578. [5] G.A. Esteban, A. Perujo, K. Douglas, L.A. Sedano, Tritium diffusive transport parameters and trapping effects in the reduced activating martensitic steel OPTIFER-IVb, J. Nucl. Mater. 281 (2000) 34–41. [6] A. Aiello, I. Ricapito, G. Benamati, R. Valentini, Hydrogen isotopes permeabillity in EUROFER 97 martensitic steel, Fusion Sci. Technol. 41 (2002) 872–876. ˜ F. Legarda, R. Lindau, Hydrogen transport and trapping [7] G.A. Esteban, A. Pena, in ODS-EUROFER, Fusion Eng. Des. 82 (2007) 2634–2640. [8] A.V. Fedorov, S. van Til, A.J. Magielsen, M.P. Stijkel, Tritium permeation in EUROFER in EXOTIC and LIBRETTO irradiation experiments, Fusion Eng. Des. 88 (2013) 2918–2921. [9] T. Chikada, M. Shimada, R.J. Pawelko, T. Terai, T. Muroga, Tritium permeation experiments using reduced activation ferritic/martensitic steel tube and erbium oxide coating, Fusion Eng. Des., in press. [10] G. Benamati, E. Serra, C.H. Wu, Hydrogen and deuterium transport and inventory parameters through W and W-alloys for fusion reactor applications, J. Nucl. Mater. 283–287 (2000) 1033–1037. [11] S.K. Lee, H.S. Kim, B.H. Chung, S.J. Noh, Study of an experimental system for hydrogen permeation in thin-solid materials for fusion plasma research, Curr. Appl. Phys. 11 (5) (2011) S99–S102. [12] S.K. Lee, Y.G. Ohn, S.J. Noh, Measurement of hydrogen permeation through nickel in the elevated temperature range of 450–850 ◦ C, J. Korean Phys. Soc. 63 (2013) 1955–1961. [13] H.A. Daynes, Diffusion through rubber, Proc. R. Soc. Lond. A97 (1920) 286–307. [14] J. Crank, The Mathematics of Diffusion, Oxford University Press, London, 1975. [15] S.W. Rutherford, D.D. Do, Review of time lag permeation technique as a method for characterisation of porous media and membranes, Adsorption 3 (1997) 283–312. [16] A. Seeger, On the location of positive muons and solute hydrogen atoms in alpha iron, Phys. Lett. 58A (1976) 137–138. [17] J.P. Hirth, Effects of hydrogen on the properties of iron and steel, Metall. Trans. 11A (1980) 861–890. [18] Y. Fukai, H. Sugimoto, Diffusion of hydrogen in metals, Adv. Phys. 34 (1985) 263–326. [19] G. Alefeld, J. Völkl, Hydrogen in Metals I, Springer-Verlag, New York, NY, 1978.
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Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Transport of hydrogen and deuterium in the reduced activation martensitic steel ARAA S.J. Noh a,∗ , S.K. Lee a , W.J. Byeon a , Y.B. Chun b , Y.H. Jeong b a b
Department of Applied Physics, Dankook University, Yongin-si 448-701, Gyeonggi-do, Republic of Korea Nuclear Materials Division, Korea Atomic Energy Research Institute, 989-111 Daedeok-daero,Yuseong-gu, Daejeon 305-353, Republic of Korea
h i g h l i g h t s • Transport of H2 and D2 in advanced reduced activation alloy was measured. • Appreciable trapping effects are observed only at low temperatures (250–350 ◦ C). • Isotope effect ratio for the diffusivity differs from the classical prediction.
a r t i c l e
i n f o
Article history: Received 9 May 2014 Received in revised form 17 June 2014 Accepted 21 July 2014 Available online xxx Keywords: Reduced activation steel Hydrogen Deuterium Permeation Diffusion
a b s t r a c t Advanced reduced activation alloy (ARAA) is a reduced activation ferritic/martensitic (RAFM) steel under development at the Korea Atomic Energy Research Institute. The transport of hydrogen and deuterium in ARAA was investigated in an elevated temperature range of 250–600 ◦ C. A continuous-flow method, a time-dependent gas-phase technique, was used for the measurements. Complete sets of transport parameters (permeability, diffusivity, solubility, trap site density, and trapping energy) of hydrogen and deuterium in ARAA were successfully obtained. We show that appreciable trapping effects are observed only at low temperatures (250–350 ◦ C) and that the isotope effect ratio for the diffusivity differs from the classical prediction. However, the measured values of permeability, effective diffusivity, and effective solubility of ARRA were within the range of results reported for other RAFM steels. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Advances in fusion technology will rely heavily on advances in materials, and the Korea Atomic Energy Research Institute has been developing an advanced reduced activation alloy (ARAA). ARAA is a reduced activation ferritic/martensitic (RAFM) steel, which is considered as a candidate material for the fusion reactor structure. The permeation of hydrogen isotopes through other RAFM steels has been studied by many investigators [1–9]. In this study, the transport of hydrogen isotopes in ARAA was investigated using hydrogen and deuterium gases. Complete sets of transport parameters (permeability, diffusivity, solubility, trap site density, and trapping energy) of hydrogen and deuterium in ARAA were obtained, and the trapping and isotope effects on the permeability, diffusivity, and solubility were evaluated. These results are
∗ Corresponding author. Tel.: +82 3180053211. E-mail address: [email protected] (S.J. Noh).
compared with those of previously reported results for other RAFM steels [1–7]. 2. Experimental A 45-kg heat (ARAA-1, heat number F211) was produced using vacuum-induction melting and hot rolled in a two-high mill at 1200 ◦ C to a total thickness reduction of 80%. The plate thickness after the hot-roll process was 15 mm. The plate was then normalized at 980 ◦ C for 40 min and tempered for 70 min at 760 ◦ C. The plate was fabricated into a disk (3-mm thickness; 15-mm diameter), and the surface was polished to minimize surface process effects arising from any surface roughness. The chemical composition of the ARAA is given in Table 1. A time-dependent gas-phase technique, the continuous-flow method [10,11] in which the partial pressure of the permeated gas is proportional to the permeation flux through a membrane, was employed for the measurements. The permeation flux of hydrogen isotopes (hydrogen and deuterium) was obtained as a function of time using a hydrogen-isotope permeation measurement
http://dx.doi.org/10.1016/j.fusengdes.2014.07.013 0920-3796/© 2014 Elsevier B.V. All rights reserved.
Please cite this article in press as: S.J. Noh, et al., Transport of hydrogen and deuterium in the reduced activation martensitic steel ARAA, Fusion Eng. Des. (2014), http://dx.doi.org/10.1016/j.fusengdes.2014.07.013
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Table 1 Analyzed composition of ARAA. Element
Concentration (wt%)
C Cr W Mn V Ta Si N Ti Zr Fe
0.09 9.33 1.05 0.46 0.21 0.09 0.07 0.024 0.018 0.009 Balance
system (HPMS) that was designed and constructed in-house, where the partial gas pressure was measured using a residual gas analyzer (in a unit of Pa or Torr) and the effective pumping speed for the permeated gas was determined using a high-precision mass flow controller. The feed pressure was fixed at 100 kPa (1 bar), and the temperature range was 250–600 ◦ C. The system has measurement uncertainties in the temperature. These uncertainties become
1.7 ◦ C at 250 ◦ C and 2.3 ◦ C at 600 ◦ C, which can induce errors of ∼3% for determining the permeation flux. The system also has uncertainties in the pumping speed that corresponds to a 2% error level. Details of the HPMS and the experimental method can be found in Lee et al. [11,12]. 3. Theory Fick’s first law states that the permeation flux of hydrogen atoms through a membrane is proportional to the concentration gradient. We consider hydrogen transport through a membrane of uniform thickness d and assume that the initial concentration throughout the membrane is zero. At time t = 0, the hydrogen pressure on the feed side is increased instantaneously from zero to pf . Then, at any given time t > 0, the hydrogen concentrations on the feed side Cf and permeate side Cp are assumed to be constant according to Sieverts’ law: Cf = S p0.5 , f
(1)
Cp = 0,
(2)
Fig. 1. Arrhenius plots of the (a) permeability, (b) effective diffusivity, and (c) effective solubility of hydrogen and deuterium in ARAA.
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where S is the Sieverts’ constant (or the solubility) of the membrane. The hydrogen permeation flux through the membrane J(t) is given by J(t) =
˚ p0.5 f
∞
1+2
d
n
(−1) exp
n=1
D n2 2 t − d2
Q (t) = A
J t 0
=A
˚ p0.5 f
,
(3)
d
Q (t) = A
dt
t−
d
d2
−
6D
2 d2 2 D
,
∞ (−1)n n=1
n2
exp
−
D n2
2
d2
t
d
d2 6D
t−
.
(6)
−E ϕ
RT
−E d
D = D0 exp Deff =
RT
,
(7)
,
(8)
D
1 + Nt /N exp Et /RT
S = S0 exp
−E
Seff = S 1 +
s
RT
N t
N
,
, exp
S,H (mol m
−3
−0.5
Pa
) = 1.25 exp
−34.7 × 103 RT
, (12)
,
(13)
,
(14)
Nt,H (sites m−3 ) = 1.0 × 1024 , Et,H (J mol
−1
(15)
3
) = 59.4 × 10 ,
(16) (J mol−1
where the subscript H refers to hydrogen, and R K−1 ) is equal to 8.314472. The deuterium transport parameters were determined as
˚D (mol m−1 s−1 Pa−0.5 ) = 9.61 × 10−8 exp
In the experiments, the hydrogen permeation flux through the membrane was measured as a function of time. The permeability ˚ was obtained from Eq. (5) when the permeation flux reached a saturated level. A fit of the asymptotic region of Q(t) as given in Eq. (4) approximates the relationship in Eq. (6), and this line intersects the time axis at tlag = d2 /6D, where tlag is commonly defined as the time lag. The diffusion coefficient is then determined by D = d2 /6tlag [3,12–15], and S can be calculated directly from S = ˚/D. The capture and release of hydrogen atoms occur at trapping centers distributed throughout the membrane [3,5,7]. The trapping process provides additional sites for accommodating hydrogen and increases the time taken for hydrogen to move into the membrane. Thus, the trapping effect leads to an increase in the effective solubility Seff with respect to the lattice solubility S and a decrease in the effective diffusivity Deff with respect to the lattice diffusivity D . However, the permeability is not affected by trapping. As a result, the transport parameters are dependent on the absolute temperature T: ˚ = ˚0 exp
−12.7 × 10 RT
,
−47.4 × 103 RT
3
D,H (m2 s−1 ) = 7.59 × 10−8 exp
(5)
˚ p0.5 f
where A is the membrane area [3,12–15]. In the steady-state (i.e., t → ∞), Eqs. (3) and (4) become J=
Arrhenius plots of the permeability, effective diffusivity, and effective solubility of hydrogen and deuterium for ARAA are shown in Fig. 1. The hydrogen transport parameters in ARAA were determined as follows: ˚H (mol m−1 s−1 Pa−0.5 ) = 9.45 × 10−8 exp
(4)
˚ p0.5 f
assuming that the ARAA has a body-centered cubic structure with six tetrahedral lattice sites available per host atom [3,5,7,16]. 4. Results and discussion
where ˚ = DS is defined as the permeability of the membrane, and D is the diffusion coefficient (or diffusivity) of the membrane [3,12–15]. The total amount of hydrogen Q (t) that has passed through the membrane after time t is given by t
3
D,D (m2 s−1 ) = 7.33 × 10−8 exp
−14.0 × 10 RT
S,D (mol m−3 Pa−0.5 ) = 1.31 exp
−50.1 × 103 RT
3
−36.1 × 103 RT
, (17)
,
(18)
,
(19)
Nt,D (sites m−3 ) = 1.0 × 1024 ,
(20)
Et,D (J mol−1 ) = 59.0 × 103 ,
(21)
(9)
(10)
E t
RT
,
(11)
where ˚0 , D0 , and S0 are pre-exponential factors of the permeability, lattice diffusivity, and lattice solubility, respectively; Eϕ and Ed are the activation energies for permeation and lattice diffusion, respectively; Es is the heat of solution (i.e., the enthalpy of formation of hydrogen atoms in the membrane); Nt and N are the trap and lattice site densities, respectively; Et is the trapping energy; and R is the gas constant [3,5,7]. The lattice site density N is 5.1 × 1029 m−3
Fig. 2. Arrhenius plot of the isotope effect ratios of hydrogen and deuterium for the permeability, effective diffusivity, and effective solubility in ARAA.
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Fig. 3. Arrhenius plots of the hydrogen (a) permeability, (b) effective diffusivity, and (c) effective solubility in ARAA and other reference RAFM steels: (1) this work, (2) EUROFER 97 [7], (3) OPTIFER-IVb [5], (4) MANET [1], and (5) F82H [4].
where the subscript D refers to deuterium. As shown in Fig. 1(a), the Arrhenius plots of both ˚H and ˚D reveal a linear relationship over the whole temperature range of 250–600 ◦ C. There are no apparent trapping effects because ˚ was obtained from Eq. (5) when the permeation flux through the membrane reached the saturated level, i.e., when the trapped population reached equilibrium. The relationship between ˚ and T was determined by a least-squares fit of the data. In contrast, both Deff,H and Deff,D have non-linear Arrhenius dependences: Deff exhibits a linear relationship at high temperatures (400–600 ◦ C) but deviates from this relationship at low temperatures (250–350 ◦ C). At high temperatures, the trapping effect is assumed to be negligible, and so Deff becomes equal to D , and the activation energy of Deff is constant. However, at low temperatures, the trapping effect predicted by Eq. (9) is apparent; Deff drops below D , and the activation energy of Deff increases with decreasing temperature. The relationship between D and T was determined by a linear least-squares fit of the data obtained at high temperatures (400–600 ◦ C). The trap site density Nt and trapping energy Et were evaluated by a non-linear leastsquares fit of the measured diffusivity data using the theoretical expression for Deff [Eq. (9)], where D is given by Eqs. (13) and (18) for hydrogen and deuterium, respectively. The values of Et,H and
Et,D [Eqs. (16) and (21), respectively] are close to those corresponding to high-angle grain boundaries (59 kJ mol−1 ) and surfaces of coarse secondary particles, e.g., AIN (65 kJ mol−1 ), Fe2–3 C (ε carbide; 65 kJ mol−1 ), MnS (72 kJ mol−1 ) [3,5,7,17]. Fig. 1(c) shows Arrhenius plots of Seff,H and Seff,D . It should be noted that we did not perform separate experiments for measuring Seff,H and Seff,D ; these were calculated as Seff = ˚/Deff . The effects of hydrogen isotopes on the transport parameters were also estimated, and Fig. 2 shows Arrhenius plots of the isotope effect ratios of hydrogen and deuterium for ˚, Deff , and Seff . The isotope effect on Deff was estimated from Deff,H /Deff,D , the ratio of Deff,H and Deff,D . Classical rate theory assumes that atomic vibration frequencies are inversely proportional to (mass)0.5 and that the activation energy for diffusion is independent of the mass of the isotope. Thus, in classical rate theory, the isotope effect ratio of the diffusivity, DH /DD , is predicted to be a constant: DH = DD
m 0.5 D
mH
=
√
2,
(22)
where mD and mH are the masses of deuterium and hydrogen, respectively. However, we found that the value of Deff,H /Deff,D determined in this work differed from that predicted by classical rate
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Fig. 4. Arrhenius plots of the deuterium (a) permeability, (b) effective diffusivity, and (c) effective solubility in ARAA and other reference RAFM steels: (1) this work, (2) EUROFER 97 [6], (3) OPTIFER-IVb [5], (4) MANET [2,3,7], and (5) F82H [3].
theory. The ratio of the pre-exponential diffusivity factors D0,H /D0,D was calculated to be 1.04, and we found that at high temperatures (400–600 ◦ C), Deff,H /Deff,D increased with decreasing temperature (1.24 at 600 ◦ C to 1.30 at 400 ◦ C), which there was little change at low temperatures (Deff,H /Deff,D was 1.31 at 350 ◦ C and 1.32 at 250 ◦ C). This departure from the classical rate theory prediction may be attributed to the quantum effect [18,19]. Furthermore, ˚H /˚D increased with decreasing temperature, from 1.43 at 600 ◦ C to 1.83 at 250 ◦ C, as did Seff,H /Seff,D (1.15 at 600 ◦ C to 1.39 at 250 ◦ C).
These results for ARAA were compared with those of other RAFM steels [1–7]. Fig. 3(a)–(c) shows Arrhenius plots of the permeability, effective diffusivity, and effective solubility of hydrogen in the materials, respectively. We found that the values of ˚H , Deff,H , and Seff,H for ARAA were within the range of results for other RAFM steels and had temperature dependences similar to those of other steels. Fig. 4 shows the corresponding Arrhenius plots for deuterium transport, and these findings are similar to the hydrogen results.
Table 2 Transport parameters for ARAA and reference RAFM steels (activation energies in kJ mol−1 ). Material ARAA(H) ARAA(D) EUROFER 97(H) EUROFER 97(D) OPTIFER-IVb(H) OPTIFER-IVb(D) MANET(H) MANET(D) F82H(H) F82H(D)
˚0
Eϕ −8
9.45 × 10 9.61 × 10−8 1.03 × 10−8 1.53 × 10−8 1.80 × 10−8 1.50 × 10−8 2.93 × 10−8 2.73 × 10−8 4.90 × 10−8 4.03 × 10−8
47.4 50.1 37.4 38.3 39.6 40.3 43.1 39.9 39.3 40.8
D0
Ed −8
7.59 × 10 7.33 × 10−8 4.57 × 10−7 1.50 × 10−7 5.49 × 10−8 4.61 × 10−8 7.17 × 10−8 1.01 × 10−7 1.80 × 10−7 1.07 × 10−7
12.7 14.0 22.3 14.5 10.6 11.3 13.5 13.2 14.1 13.9
S0 1.25 1.31 0.023 0.102 0.328 0.325 0.409 0.270 0.300 0.377
Es
Nt
34.7 36.1 15.1 23.8 29.0 29.0 29.6 26.7 25.8 26.9
1.0 × 10 1.0 × 1024 1.3 × 1025 1.0 × 1024 2.2 × 1024 1.0 × 1024 – 1.5 × 1025 2.6 × 1023 1.6 × 1023 24
Et
T(K)
Refs.
Curve
59.4 59.0 43.2 57.9 52.2 55.2 – 48.5 54.0 55.9
523–873 523–873 373–723 423–723 423–892 423–892 523–873 373–743 373–723 373–723
T. W. T. W. [7] [6] [5] [5] [1] [2,3,7] [4] [3]
Fig. 3. (1) Fig. 4. (1) Fig. 3. (2) Fig. 4. (2) Fig. 3. (3) Fig. 4. (3) Fig. 3. (4) Fig. 4. (4) Fig. 3. (5) Fig. 4. (5)
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For comparison, the transport parameters (permeability, diffusivity, solubility, trap site density, and trapping energy) of hydrogen and deuterium in ARAA and the reference RAFM steels are summarized in Table 2. The values of ˚0 , Eϕ , S0 , and Es of ARAA are the highest, whereas the values of D0 , Ed , and Nt are within the range of values of the reference steels. The values of Et of ARAA are also close to those of other steels. 5. Conclusions Complete sets of parameters for the hydrogen and deuterium transport in ARAA were successfully obtained over a temperature range of 250–600 ◦ C. Appreciable trapping effects were observed only at low temperatures (250–350 ◦ C), and the average trapping energy was found to be close to those of the high-angle grain boundary and coarse secondary particle surfaces. We also found that the isotope effect√ratio for the diffusivity differed from the classical prediction of 2. Although there were some discrepancies in the pre-exponential factors and activation energies between those of the ARAA and other RAFM steels, the measured values of ˚, Deff , and Seff of ARRA were within the range of results reported for other steels. Acknowledgments This work was supported by the National R&D Program through a National Research Foundation of Korea (NRF) grant funded by the Ministry of Science ICT & Future Planning (No. 2008-0061900). References [1] K.S. Forcey, D.K. Ross, J.C.B. Simpson, D.S. Evans, Hydrogen transport and solubility in 316L and 1.4914 steels for fusion reactor applications, J. Nucl. Mater. 160 (1988) 117–124.
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