Permeability, solubility and diffusivity of hydrogen isotopes in stainless steels at high gas pressures

International Journal of Hydrogen Energy 32 (2007) 100 – 116 www.elsevier.com/locate/ijhydene

Permeability, solubility and diffusivity of hydrogen isotopes in stainless steels at high gas pressures C. San Marchi∗ , B.P. Somerday, S.L. Robinson Sandia National Laboratories, 7011 East Ave, Livermore, CA 94550, USA Received 17 November 2005; received in revised form 25 April 2006; accepted 1 May 2006 Available online 3 July 2006

Abstract In this report, we provide a framework for describing the permeability, solubility and diffusivity of hydrogen and its isotopes in austenitic stainless steels at temperatures and high gas pressures of engineering interest for hydrogen storage and distribution infrastructure. We demonstrate the importance of using the real gas behavior for modeling permeation and dissolution of hydrogen under these conditions. A simple oneparameter equation of state (the Abel–Noble equation of state) is shown to capture the real gas behavior of hydrogen and its isotopes for pressures less than 200 MPa and temperatures between 223 and 423 K. We use the literature on hydrogen transport in austenitic stainless steels to provide general guidance on and clarification of test procedures, and to provide recommendations for appropriate permeability, diffusivity and solubility relationships for austenitic stainless steels. Hydrogen precharging and concentration measurements for a variety of austenitic stainless steels are described and used to generate more accurate solubility and diffusivity relationships. 䉷 2006 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. Keywords: High-pressure hydrogen gas; Hydrogen isotopes; Permeability; Diffusivity; Solubility

1. Introduction Hydrogen dissolves in and permeates through most materials, thus it is important to understand the permeation, diffusion and dissolution of atomic hydrogen in materials used to contain hydrogen gas. The permeation of hydrogen and its isotopes is important to the vacuum industry for optimizing high-vacuum systems and to the fusion energy community for recovering tritium. More recently, this topic has received attention from the hydrogen energy community: hydrogen dissolution and permeation can be significant at high pressure and may affect the integrity of structural components used for hydrogen gas storage and distribution since hydrogen can embrittle metals. Thus it is also necessary to understand the real gas behavior of hydrogen at the high pressures expected for hydrogen gas infrastructure. The aim of this report is to describe the framework necessary for extrapolating literature data for permeability, solubility, and diffusivity of hydrogen isotopes in stainless steels from high temperature and low gas pressure to engineering ∗ Corresponding author. Tel.: +1 925 294 4880; fax: +1 925 294 3410.

E-mail address: [email protected] (C. San Marchi).

conditions that are relevant to hydrogen storage and distribution. In addition, we want to address inconsistencies in data and make specific recommendations for permeability, solubility, and diffusivity relationships for near-ambient temperature and high pressure, i.e., conditions relevant to the nascent hydrogen energy infrastructure. As will be shown below, deviations from ideal gas behavior are important when extrapolating low pressure “ideal gas” experiments (such as permeation experiments) to engineering analysis of hydrogen storage and distribution systems where operating pressures are expected to approach 100 MPa in some cases. In this report, we review the fundamental thermodynamics necessary for treating real gas behavior and describe the Abel–Noble equation of state for hydrogen, a one-parameter relationship that captures the real behavior of hydrogen and its isotopes at relevant engineering conditions, i.e., pressures less than 200 MPa and temperatures between 223 and 423 K. The relationships for permeation, diffusion and dissolution of hydrogen in metals are then reviewed with attention to the real gas behavior of hydrogen. These fundamental relationships provide an analytical basis for characterizing the transport of hydrogen in metals that contain high-pressure hydrogen gas.

0360-3199/$ - see front matter 䉷 2006 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2006.05.008

C. San Marchi et al. / International Journal of Hydrogen Energy 32 (2007) 100 – 116

The literature on permeation, diffusion and dissolution of hydrogen in austenitic stainless steels is then reviewed, with emphasis on outlining the important phenomena that should be considered when interpreting and using data from the literature. Finally, experimental data are provided to supplement literature data and provide relationships appropriate for high pressure and ambient temperature. Specific recommendations are then given for quantifying equilibrium hydrogen dissolution and transport in austenitic stainless steel exposed to high-fugacity gaseous hydrogen.

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though other equations of state with additional parameters can better fit real gas behavior over a wide range of pressure and temperature, the correlations that are found in the literature are not particularly good at relevant engineering pressures or of limited utility for analytical calculations due to their transcendental form [1–4]. 2.2. Relationship between pressure and fugacity

2. Background

From basic thermodynamic relationships, the chemical potential of any system can be expressed as

2.1. Equation of state: gases



The equation of state describes the thermodynamic state of a system. For gases this requires knowledge of two variables such as the pressure and temperature of the system. Ideal gases are described by the ideal gas law: Vm0 =

RT , P

(1)

d dP

 T

= Vm .

(4)

Substituting Eq. (1) into Eq. (4), the chemical potential of an ideal gas can be written in the form (d)T = RT (d lnP )T .

(5)

Vm0

where is the molar volume of the ideal gas, P and T are the absolute pressure and absolute temperature of the system, respectively, and R is the universal gas constant equal to 8.31447 J mol−1 K −1 . Real gas behavior is often characterized by the compressibility factor Z = P V m /RT , where Vm is the molar volume of the real gas. The compressibility factor equals 1 for the ideal gas and generally shows a positive deviation (Z > 1) at high pressure. There are numerous models and empirical relationships that account for the real behavior of gases, however, these are often complicated transcendental equations that cannot be easily manipulated analytically [1–5]. The Abel–Noble equation of state, on the other hand, is a single parameter relationship of the form RT Vm = + b, (2) P where b is a constant. The Abel–Noble equation of state originates from the van der Waals equation of state for gases, however, the pressure correction term is approximated as zero (i.e., no intermolecular forces). The parameter b represents the finite volume of the gas molecules, which is a weak function of pressure and temperature for general engineering conditions, and thus approximated as constant [6]. The simplicity of the Abel–Noble equation of state is notable when compared to other equations of state for real gases, such as virial equations, which may include upwards of ten parameters, many of which are themselves functions of temperature [1–3]. At pressures of general engineering significance (< 200 MPa) and temperatures near-ambient, the compressibility factor Z can be tracked well using the Abel–Noble equation of state and has the form Pb Z=1+ . (3) RT For a number of real gases the Abel–Noble equation of state predicts real gas behavior to better than a few percent [6]. Al-

This is the familiar form of the chemical potential where the pressure can be thought of as the “activity” of the ideal gas. It should be noted also that the pressure term, d ln P , has no units since it represents dP /P . Deviations from ideal behavior arise, for example, from electronic interactions between molecules and the finite volume of gas. This is particularly apparent at high pressure and low temperature, thus the fugacity f is introduced. The form of the fugacity is chosen for convenience to have a form analogous to that of the ideal case, that is (d)T = RT (d ln f )T .

(6)

Fugacity is often described as the activity of the real gas. It is generally assumed that all gases behave ideally at infinitely low pressure, therefore as P → 0 then f → P . With knowledge of the fugacity the thermodynamics of real gases can be rigorously treated. By combining Eqs. (1) and (4)–(6) and integrating, the fugacity can be related to the equation of state and the properties of the ideal gas: 

f ln f0





P − ln P0



1 = RT



P

P0

(Vm − Vm0 ) dP ,

(7)

where f0 and P0 are the fugacity and pressure, respectively, at some reference pressure. Using the limiting behavior of fugacity (f0 → P0 → 0) and the equation of state for an ideal gas, Eq. (1), the fugacity can be expressed in the form:  ln

f P





P

= 0



Vm 1 − RT P

 dP .

(8)

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Eq. (8) is sometimes referred to as the definition of fugacity and relates the equation of state (embodied in the Vm term) and the fugacity. As such, any equation of state, Vm = f (P , T ), can be substituted into Eq. (8) and solved to determine the fugacity for a given set of conditions. For conditions where the Abel–Noble equation of state is appropriate, fugacity can be expressed as a simple function of pressure and temperature by substituting Eq. (2) into the “definition” of fugacity (Eq. (8)):   Pb f = P exp . (9) RT The ratio of the fugacity to the pressure is often called the fugacity coefficient. This simple closed form of the fugacity allows for analytical determination of thermodynamic phenomena such as permeability and solubility while accurately incorporating the real behavior of the gas phase. This is particularly useful for treating the thermodynamics of high-pressure gaseous systems. 2.3. Solubility In this section, we review the relationship for solubility K assuming equilibrium between the diatomic hydrogen molecule and hydrogen atoms in a metal: 1 2

H2 ↔ H.

(10)

Although we assume hydrogen in this analysis, these relationships are general for any diatomic gas, including isotopes of hydrogen. At equilibrium, the chemical potential of the gas must equal the chemical potential of hydrogen dissolved in the material: 21 H2 =H . We assume that atomic hydrogen dissolved in the material behaves as a dilute solution, and that the real behavior of the hydrogen gas must be considered, therefore 1 0 2 (H2

+ RT ln f ) = 0H + RT ln cL ,

(11)

where cL is the equilibrium concentration of hydrogen dissolved in the metal lattice and the superscript 0 refers to the standard state. The difference in chemical potential between the standard states is related to the enthalpy of formation of H-atoms in the metal H and the entropy of formation S: (0H −

1 2

0H2 ) = H − T S.

(12)

Combining Eqs. (11) and (12), the concentration of hydrogen that is dissolved in the metal lattice and in equilibrium with the hydrogen gas can be expressed as cL = Kf 1/2 , where K = K0 exp

(13) 

−H RT

 .

(14)

Eq. (13) can also be written directly by following basic procedures for expressing chemical equilibrium of the reaction shown in Eq. (10), where K is the equilibrium coefficient.

Sievert’s Law is a special case of chemical equilibrium for the reaction expressed in Eq. (10) in the limit of ideal gas behavior (f → P ), in which case K is the so-called Sievert’s parameter. Data fit to an Arrhenius-type relationship for solubility (Eq. (14)) is commonly reported in the literature for materials exposed to hydrogen gas or its gaseous isotopes; to a first approximation the solubility is equivalent for all isotopes of hydrogen (Section 2.5). It is important to make the distinction between solubility and concentration: the solubility K of a species from a gas is independent of the fugacity (pressure) but a function of temperature (Eq. (14)), while the concentration cL depends on both the temperature and fugacity (pressure) as in Eq. (13). Solubility of a gas in a solid should always have a pressure unit associated with it. Often in the literature the term solubility is incorrectly used to refer to concentration, as determined, for example, from hydrogen extraction methods. Hydrogen extraction measures the total concentration of hydrogen, which is the sum of trapped and lattice hydrogen. In metals, hydrogen can be trapped at microstructural features (e.g., point defects, line defects, and surface defects) and this trapped hydrogen does not participate in the dynamic equilibrium, which distinguishes lattice hydrogen. Therefore, hydrogen concentrations determined by techniques that do not distinguish between hydrogen that diffuses through the lattice and hydrogen trapped in the microstructure should not be indiscriminately used to determine solubility; moreover, the term solubility should be reserved for measures of lattice hydrogen. Under specific circumstances as described below, trapped hydrogen is negligible compared to the lattice hydrogen, and solubility can be determined from concentration measurements. Incidentally, being related to the lattice, the solubility (as well as permeability and diffusivity) should be viewed as a physical property of the material and, to a firstorder approximation, should be independent of microstructure. Like all physical properties, however, apparent hydrogen solubility and transport can be dependent on additional variables, such as composition and stress state. Once dissolved in a metal lattice, atomic hydrogen can interact with elastic stress fields: hydrostatic tension dilates the lattice and increases the concentration of hydrogen, while hydrostatic compression decreases the hydrogen concentration. The relationship that describes this effect [7–9] is written as   cS VH  , (15) = exp cL RT where cL is the hydrogen concentration in the unstressed lattice, cS is the concentration of hydrogen in the lattice subjected to a hydrostatic stress =ii /3, and VH is the partial molar volume of hydrogen in the lattice, which for steel is on the order of 2 × 10−6 m3 mol−1 [9,10]. The effect of stress on hydrogen dissolved in the lattice is greatest at low temperature (due to the positive exponential term and its inverse proportionality to temperature). For steels at room temperature this translates to an increase in hydrogen concentration of about 50% for high hydrostatic tension near 500 MPa. For hydrostatic compression of 500 MPa ( = −500 MPa), a reduction in hydrogen concentration of about 30% can be expected. Such

C. San Marchi et al. / International Journal of Hydrogen Energy 32 (2007) 100 – 116

changes in hydrogen concentration are relatively small for the bulk with respect to ordinary applied and residual stresses, especially considering the uncertainty in solubility (Section 4.7). However, hydrogen will interact with stress fields at cracks and other defects, which can be significant, locally increasing the hydrogen content and facilitating the effects of hydrogen on deformation and fracture processes if hydrogen is given sufficient time to diffuse into regions of high hydrostatic tension. The hydrogen concentration in metals can also be increased through trapping at microstructural features including grain boundaries, phase boundaries, second phases (such as hydrides), and dislocations [10–12]. Trap sites are generally categorized by the thermal energy required to remove the hydrogen atom from the trapping site, e.g., “weak” or “strong” traps. For a given microstructural feature, the equilibrium concentration of trapped hydrogen can be expressed as [10]   nT nL HB , (16) = exp 1 − nT 1 − nL RT where nT is the fraction of trapping sites filled with hydrogen, nL is the fraction of available lattice sites filled with hydrogen, and HB is the binding energy of hydrogen to the trap site. For a metal exposed to high-pressure hydrogen gas, nL can be determined from Eq. (13) and the total available lattice sites. The total concentration of hydrogen atoms in a metal cH is then given by [10]  (ZnT )j , (17) cH = cL + j

where Zj is the number of trap sites per microstructural feature of type j and j is the density of microstructural features of type j. Eq. (16) demonstrates the exponential dependence of trapping on the binding energy and the inverse exponential dependence on temperature: low binding energy traps (< 20 kJ mol−1 ) are not highly populated at room temperature, and at high temperature (> 500 K) the concentration of trapped hydrogen is small for virtually all binding energies. In addition, the trap density (Eq. (17)) is important since the density varies over many orders of magnitude depending on the nature of the trap. The reader is referred to Ref. [10] for a more comprehensive and quantitative review of trapping. 2.4. Diffusion and permeability Permeability of hydrogen and its isotopes is generally defined as the steady-state diffusional transport of atoms through a material that supports a pressure difference. Assuming steady state, a semi-infinite plate, and Fick’s first law for diffusion J = −D(dc/dx), we can write J∞ = D

(cx=0 − cx=t ) , t

(18)

where J∞ is the steady-state diffusional flux, D is the diffusivity, c is the concentration and x is the position in a plate of thickness t. Using chemical equilibrium (Eq. (13)) for a real gas and assuming that the hydrogen partial pressure is

103

negligible on one side of the plate (cx=t = 0), the diffusional flux can be expressed as J∞ =

DK 1/2 f . t

(19)

The product DK is defined as the permeability . There are numerous conditions under which this relationship, sometimes called Richardson’s Law, may not be valid (under very high vacuum, at very high pressure or temperature; see Ref. [13] for an extensive discussion of permeation); however, under most engineering conditions, this relationship is well established [13]. The majority of studies on permeation use a direct measurement technique to determine the flux of hydrogen or deuterium permeating through a membrane or disk of the material of interest. In one manifestation of this technique, a constant pressure of hydrogen (or deuterium) is maintained on one side of the membrane and a vacuum on the other side. The rate of hydrogen escape on the vacuum side of the membrane is measured at steady state with a leak detector or other suitable instrumentation. Diffusivity in the membrane material is determined by analyzing flux transients and back calculating a diffusion coefficient from solutions to the flux equation [11]. Both permeability and diffusivity are thermally activated processes, thus they feature an Arrhenius-type dependence on temperature and, like solubility, they can be expressed in the general form   −H  = 0 exp , (20) RT   −HD , (21) D = D0 exp RT respectively. Since  ≡ DK, solubility can be determined from the ratio of the direct measurements of permeability and diffusivity as   −(H − HD ) 0 exp . (22) K= D0 RT For metals, the solubility can be thought of as the pressurenormalized equilibrium concentration of hydrogen within the crystal lattice. The typical method for determining permeability, diffusivity and solubility assumes that hydrogen transport is governed by diffusion in the bulk; therefore, care must be taken to ensure that surface chemistry (oxide layers for example) or other phenomena do not intervene as rate limiting processes. 2.5. Mass/isotope effects It is commonly assumed that the ratio of diffusivity of hydrogen isotopes is equivalent to the inverse ratio of the square root of the masses of the isotopes:  mD DH = , (23) DD mH where D and m are the diffusivity and mass of the respective isotope, and the subscripts H and D refer to hydrogen and deu-

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C. San Marchi et al. / International Journal of Hydrogen Energy 32 (2007) 100 – 116

terium, respectively. Similar expressions written for tri√ can be √ tium and can be simplified as DH = 2DD = 3DT , where the subscript T refers to tritium. These relationships between isotopes stem from classical rate theory, which relates diffusivity to atomic vibrational frequencies and these frequencies are inversely proportional to mass. The activation energy for diffusion is also assumed to be independent of the mass of the isotope. Diffusion data at subambient temperatures do not support Eq. (23) for a number of metals [14], however, permeability data at elevated temperatures generally support the inverse square root dependence on mass for nickel [15] and stainless steels [16–19]. For the purposes of this report we assume that Eq. (23) is a good approximation for both permeability and diffusivity; implicitly then the solubility (K = /D) is assumed to be independent of the mass of the isotope. 2.6. Mixed gases For mixtures of hydrogen gas and chemically stable gases (such as methane, which neither dissociates nor reacts in the mixture), the chemical equilibrium between molecular hydrogen and atomic lattice hydrogen is essentially unaffected. Thus, the hydrogen concentration within the metal lattice can be determined from Eq. (13) using the fugacity of hydrogen at the partial pressure of the hydrogen gas fH2 . Alternately, the hydrogen concentration in the lattice can be determined if we assume an ideal solution of the gases. In this case, fH2 reads fH2 = xH2 fH∗2 ,

(24)

where xH2 is the mole fraction of hydrogen gas in the gas mixture, and fH∗2 is the fugacity of hydrogen at the total system pressure. Substituting into Eq. (13), the concentration of hydrogen cL dissolved in the lattice from the mixed gas can be expressed as a function of the fugacity of hydrogen at either the partial pressure of hydrogen fH2 or the total system pressure fH∗2 coupled with the mole fraction of hydrogen gas xH2 : cL = Kf H2 = xH2 (Kf ∗H2 1/2 ). 1/2

1/2

(25)

If, however, the gas is a mixture of two or more phases that can contribute atomic hydrogen or hydrogen isotopes to the metal lattice (e.g., hydrogen sulfide or deuterium), the partial pressure of hydrogen gas must be established from thermodynamic equilibrium of the gas mixture. An equilibrium mixture of hydrogen and deuterium gas, for example, requires consideration of the isotopic exchange between the molecules: 1 2

D2 +

1 2

H2 ↔ HD.

(26)

In this special case, at equilibrium the partial pressure of hydrogen gas will be less than the initial hydrogen gas pressure (due to the formation of HD gas), therefore the concentration of atomic hydrogen in the metal will be less than estimates based on the initial pressure of hydrogen gas. The same is true of deuterium gas and atomic deuterium dissolved in the metal. The total lattice concentration of “hydrogen-like” atoms will be the sum of the concentrations of the isotopes determined individually from Eq. (25).

3. Experimental procedures and results A custom-built facility was used to thermally charge austenitic stainless steels in hydrogen gas. This facility consists of a series of pressure vessels that can accommodate stainless steel test specimens and operate at gas pressure up to 138 MPa at 573 K. A computer code called DIFFUSE [20,21], which solves the diffusion equations for a chosen geometry, physical properties (diffusivity and solubility) and environmental conditions (hydrogen pressure and temperature), is used to estimate the exposure time required to achieve uniform hydrogen saturation in stainless steel specimens. The actual precharging time varied, but was at least as long as predicted by the DIFFUSE code. For austenitic stainless steel, the estimated time to reach uniform saturation of hydrogen in a cylindrical test piece 6 mm in diameter is about 14 days for 138 MPa hydrogen gas at 573 K. Moreover, the diffusivity is sufficiently low at room temperature that the thermally charged specimens can be handled without loss of hydrogen. Typically, thermally precharged specimens are tested in air to estimate the effects of hydrogen on deformation and fracture. After testing, non-deformed portions of these specimens are sectioned from the test piece and shipped on dry ice to a commercial facility (Oremet-Wah Chang in Albany, OR) for hydrogen analysis by hot extraction (also called LECO analysis). Thermally precharged specimens are stored at 253 K prior to testing and analysis. The hydrogen solubility calculated from hydrogen concentration measurements are presented in Table 1 for two 300-series austenitic stainless steels (type 304 and type 316 stainless steels), two Fe–Cr–Ni–Mn austenitic stainless steels (21Cr–6Ni–9Mn and 22Cr–13Ni–5Mn stainless steels, also referred to as nitrogen-strengthened stainless steels) and a family of precipitation-strengthened stainless steels (A-286 and JBK75 are treated as a single alloy for the purposes of this study). Although all the type 304 alloys analyzed here are actually designated type 304L, the small difference in carbon content between type 304 and type 304L is not expected to affect the solubility and the broader type 304 designation is used for discussion. The 21Cr–6Ni–9Mn and 22Cr–13Ni–5Mn alloys are referred to as 21–6–9 and 22–13–5, respectively, in the remainder of this report. The hydrogen solubility is calculated for each measured hydrogen concentration using the fugacity determined for the thermal precharging conditions (Eq. (9)); average values for solubility are given for each material, along with the standard deviation in the calculated values. Generally, the precharging conditions used in this study were 138 MPa hydrogen gas at 573 K, although in a few cases lower pressures were used. Hydrogen solubility calculated from measured hydrogen concentrations reported in other studies that used gas precharging techniques [22–24] are also reported for comparison (Table 1). Thermal precharging was performed at 10 MPa hydrogen gas at 573 K in Refs. [23,24] and 69 MPa hydrogen gas at 470 K in Ref. [22]. The hydrogen concentration was measured in several heats of steel for each grade after thermal precharging. Materials in various microstructural conditions were precharged: annealed, cold-worked, or warm-worked (forged) conditions. Generally,

C. San Marchi et al. / International Journal of Hydrogen Energy 32 (2007) 100 – 116

105

Table 1 Calculated hydrogen solubility of stainless steels after thermal precharging in high-pressure hydrogen gas (pressures ranged from 10 to 138 MPa) Material

304 304L 316 21–6–9 21–6–9 21–6–9 22–13–5 A-286/JBK-75 aged JBK-75 aged Modified JBK-75, HERF (aged) Modified JBK-75, annealed

Number

Different

Saturation

of measurements

microstructures

temperature (K)

10 6 12 19 1 6 9 5 1 2 2

5 3 4 8 1 3 4 3 1 1 1

573 470 573 573 573 470 573 573 573 470 470

−1/2 Solubility

K = cL f

Reference

38.0 ± 6 31.1 ± 2 36.2 ± 2 63.1 ± 8 78.5 50.3 ± 2 57.8 ± 6 30.3 ± 1 30.5 21.8 33.1

This [22] This This [24] [22] This This [23] [22] [22]

mol √ H2 m3 MPa

study study study

study study

HERF = high energy rate forged. The value of solubility is the average and the quoted uncertainty is the standard deviation.

the hydrogen concentration is unaffected by differences in composition from heat to heat and differences in microstructure due to final processing. A few welds of 304L with 308L filler have also been analyzed, and no significant change in hydrogen solubility was observed. 4. Discussion 4.1. Equation of state: hydrogen and its isotopes If the Abel–Noble equation of state is to provide a good prediction of the real gas behavior of hydrogen and its isotopes, the compressibility factor Z should be a linear function of pressure (Eq. (3)). McLennan and Gray [3] plot data for hydrogen and deuterium from Michels et al. [25], which indeed appear linear for temperatures in the range of 273–423 K, and for pressures from ambient to 200 MPa, i.e., high pressures of engineering relevance. As part of this work, all of the hydrogen data of Michels et al. [25] for temperature 223 K and pressure < 200 MPa was fit to the Abel–Noble equation of state (Eq. (2)). The constant b was determined to be 15.84 cm3 mol−1 for hydrogen. The error associated with b depends on the range of pressure and temperature of interest; fitting the experimental data of Michels et al. at a given temperature (in the range 223–423 K) for pressures < 200 MPa shows that b varies by less than 1%. The compressibility factor from measured data Zmeas is plotted in Fig. 1 as a function of hydrogen pressure and temperature for data from Michels et al. [25] and Vargaftik [26]. The lines in Fig. 1 represent the calculated compressibility factor Zcalc for the given temperature from Eq. (3) with b = 15.84 cm3 mol−1 . Fig. 2 shows a plot of the ratio of the calculated to measured compressibility factor (Zcalc /Zmeas ) for selected data of Michels et al. [25] and Vargaftik [26], showing that the Abel–Noble equation of state provides a good representation of real hydrogen gas behavior in the temperature range from 273 to 423 K for pressure 200 MPa. At elevated temperature, experimental data is incomplete; however, there are data [26] to

Fig. 1. Compressibility factor as a function of pressure and temperature. Lines are calculated using the Abel–Noble equation of state, and the symbols represent data from Refs. [25,26].

Fig. 2. The ratio of the calculated to the measured compressibility factor using data from Fig. 1.

support this equation of state to pressures as high as 100 MPa at temperature of 800 K and for pressure up to 50 MPa at temperature of 1000 K. For all of the experimental data fit to the

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C. San Marchi et al. / International Journal of Hydrogen Energy 32 (2007) 100 – 116

Abel–Noble equation of state, the calculated values of Z are within 2% of the measured values; for temperatures 273 K and pressure < 150 MPa, the calculated values are within about 0.5%. Available standard reference data from the National Institute of Standards and Technology for these temperature and pressure ranges [27] also fall within about 0.5% of Zcalc determined from the Abel–Noble equation of state with b equal to 15.84 cm3 mol−1 . The range of applicability quoted above for elevated temperature is limited by the available data, however, based on trends for real gases, it is expected that the Abel–Noble equation of state with b equal to 15.84 cm3 mol−1 can be applied to higher pressures at elevated temperature, probably as high as 200 MPa for temperature from ambient to 1000 K. A relatively large divergence of Zcalc /Zmeas was noted for pressure > 200 MPa near-ambient temperature; thus an upper bound on pressure of 200 MPa was chosen for fitting the Abel–Noble equation of state. No attempt was made to fit data at very low temperature (< 223 K) or to quantify the Abel–Noble relationship at these low temperatures. It is, however, clear from the plots of McLennan and Gray [3] that Z is not a linear function of pressure at subambient temperature and the experimental data of Michels et al. [25] at 223 K show the largest difference from Zcalc (Fig. 2). The constant b is expected to be appropriate for deuterium and tritium as well. Indeed, the value of 15.84 cm3 mol−1 determined here is in good agreement with the report of Chenoweth for deuterium [6]: Chenoweth reports a value of 15.5 cm3 mol−1 , which was determined using the data of Michels et al. [25]. We confirm Chenoweth’s fit for deuterium for all the data of Michels et al. in the temperature range of 273–423 K and pressure < 200 MPa (a value of 15.45 cm3 mol−1 was found if the data in the temperature range from 223 to 423 K is considered). The difference between Zcalc for hydrogen and the experimental data for deuterium are generally less than 2% for the range of conditions identified here. McLennan and Gray plot the data of Michels et al. for hydrogen and deuterium [3] showing that the compressibility of these gases is within about 1% for most engineering conditions (for temperatures in the range of 273–423 K and pressures from ambient to 200 MPa). Differences in compressibility between hydrogen and deuterium, however, increase as temperature is decreased, as well as at a very high pressure. The Abel–Noble equation of state with b in the range of 15.5–15.8 cm3 mol−1 is expected to provide a good estimate (within a few percent) of real behavior of tritium gas (as well as hydrogen and deuterium) over these same pressure and temperature ranges.

4.2. Effect of pressure and temperature Experimentally, temperature and pressure are varied in permeability studies over some range to determine the exponential temperature dependence and confirm the square root dependence of pressure as predicted by thermodynamic equilibrium (for low pressure, as typical of permeation experiments, ideal gas behavior is assumed and the pressure is used in place of

fugacity). The square root dependence on pressure, however, is often assumed, rather than established. Under some conditions, such as low pressure (on the order of 10 Pa) or specific surface condition, the square root dependence on fugacity has been found to be inappropriate [13,28], thus studies at low pressure or without careful preparation of the exposed surfaces should be viewed critically. In general, permeability studies are performed at temperatures and pressures significantly different from conditions relevant to gaseous hydrogen distribution and storage in engineering applications. Tests are typically performed at pressures near-ambient (or lower) and temperatures greater than 200 ◦ C, while pressurized systems for the storage of gaseous hydrogen operate near-ambient temperature and at pressures potentially up to 138 MPa. The experimental conditions are necessitated by the desire to make measurements in a safe and efficient manner, thus dictating low pressure and high temperature. The measured relationships are then extrapolated to the engineering conditions of interest. It has been shown that permeability data (assuming ideal gas) can be extrapolated with confidence to at least a pressure of 25 MPa for nickel [15], and solubility data to a pressure of 50 MPa at 773 K for stainless steel [29]. Permeation at higher pressures has not been confirmed. The square root dependence of hydrogen transport on fugacity (Eq. (19)) is expected to be a good approximation for all relevant engineering pressures above ambient and temperatures where thermal dissociation of diatomic hydrogen gas can be neglected, i.e., temperature less than about 1273 K [13], since the mechanisms of lattice transport are not expected to change. As shown from first principles, the fugacity should be rigorously applied in solubility and permeability rate calculations, but this has not been consistently acknowledged in the literature in the context of hydrogen effects on material properties [9,10,12,30–33]. The real gas behavior of hydrogen (and its isotopes) becomes apparent in the fugacity function (Eq. (9)) at relatively low pressure and ambient temperature, although real gases tend toward ideal behavior (fugacity tends toward the pressure) as temperature is increased. Thus ideal behavior is a good engineering approximation at elevated temperatures and relatively low pressures and, for this reason, most experimental studies on permeability and solubility have not accounted for fugacity. For pressures as low as 15 MPa at ambient temperature, however, the fugacity is about 10% greater than pressure. In terms of permeability and solubility it is the square root of this value that is relevant, which implies a rather modest correction for real gas behavior near-ambient temperature and pressure < 15 MPa. Consequently, while it is not surprising that the real gas behavior of hydrogen has not been addressed in experimental permeability and solubility studies, when extrapolating these studies to high-pressure gaseous hydrogen, the fugacity must be considered. The fugacity of hydrogen is plotted in Fig. 3 as a function of pressure for several temperatures and assuming the Abel–Noble equation of state with b equal to 15.84 cm3 mol−1 . At 273 K and a pressure of 200 MPa, for example, the fugacity is four times the pressure, demonstrating the importance of fugacity at high pressure. For a comparatively modest pressure of 35 MPa

C. San Marchi et al. / International Journal of Hydrogen Energy 32 (2007) 100 – 116

Fig. 3. Fugacity as a function of pressure using the Abel–Noble equation of state (symbols and lines are both calculations).

the fugacity–pressure ratio is 1.25 at 298 K (while the square root of this ratio is 1.12). The fugacity plotted in Fig. 3 at 298 K falls within a fraction of a percent of the hydrogen fugacity reported by Baranowski [34] for pressure less than 200 MPa (Baranowski’s source appears to be equivalent to Michels et al. [25]). 4.3. Surface effects By definition, permeability and solubility (in addition to diffusivity) of hydrogen in metals are independent of surface condition as these properties assume diffusion-controlled transport of hydrogen through the lattice. In practice, however, experimental measurements are strongly influenced by surface condition. Oxides have been proposed as diffusion barriers for austenitic stainless steels in first wall fusion reactors [35,36]. These oxides, in some cases, have been shown to significantly reduce the apparent permeability [17,37,38]. When these oxides are very thin, the oxide is thought to reduce the kinetics of diatomic hydrogen dissociation on the surface creating a process that is not rate-controlled by diffusion and thus not a true permeability. The permeability of stainless steel with surface oxides was recovered in one study by coating the oxide with palladium [17]. The palladium catalyzes the dissociation of diatomic hydrogen eliminating the kinetic barrier at the surface and establishing conditions of diffusion-controlled transport of hydrogen. The implication of this observation is that the permeability through the oxide is similar to that in the metal. On the other hand, the permeability is relatively unaffected by thick oxides; the interpretation being that once the oxide layer reaches a critical thickness the layers crack exposing metal surface [17,36,37]. It should be emphasized as well that when surface conditions modify the kinetics of hydrogen transport, the square root dependence of pressure is often lost [17,37]. Very low pressure (< 10 Pa) also precludes the square root dependence on pressure and diffusion-controlled transport [13,28]. While oxides and surface films have been reported to reduce the apparent permeability in some metals, it should not be assumed that these surface conditions would persist under different environmental conditions and thus would not offer

107

advantages in engineering systems. Most permeability tests are conducted at pressure on the order of 1 kPa, while the significantly higher fugacity of hydrogen at 100 MPa for example may result in reduction of the oxide and loss of the barrier effect [36,37]. Moreover, the apparent changes in hydrogen transport appear to be the result of changing the rate-controlling step from lattice diffusion to a surface process such as adsorption and dissociation; thus surface layers do not change the intrinsic hydrogen permeability of the material. Oxides and surface films may not have a strong effect on steady-state hydrogen transport, in some cases [37], but may presumably have a substantial effect on hydrogen transport transients and thus diffusivity measurements. In addition, the diffusivity measurement will be significantly affected by the specific method of determination, that is whether the solutions to the diffusion equations are fit to measured flux transients, or whether a single characteristic time is used to calculate a diffusion coefficient. The former method offers some intrinsic averaging of the signal over a range of fluxes, while the latter method is susceptible to signal noise. In either case, these transients are likely to be more sensitive to surface conditions than the steady-state permeability measurement. A number of studies on austenitic stainless steels have attempted to correlate solubility with surface finish and resulting hydrogen embrittlement phenomena [22,39]. As described above, the surface condition by definition cannot affect the solubility of the metal lattice, since solubility assumes thermodynamic equilibrium between the lattice and the gas phase. The condition of the surface can, however, affect the kinetics of surface reactions, which will affect the time for establishment of equilibrium between the gas and the lattice. In addition, plastically deformed surfaces (e.g., by machining) can induce phase changes in some alloys (martensite in 304 stainless steel, for example, and -phase in A-286), which will affect the surface kinetics as well as equilibrium. In summary, the surface condition can have a profound impact on the measured quantities in permeation studies, particularly the measured diffusivity. The nomenclature established in any given study should be carefully considered before interpreting and using results. For values that are true materials properties, the square root pressure dependence should be established and the surface condition should be controlled such that the process of hydrogen transport is indeed governed by lattice diffusion. Surface effects should not play an important role in the measured hydrogen concentration of specimens that are presumed to be uniformly saturated with hydrogen (Section 4.7), provided that sufficient time for saturation of the metal lattice is ensured; our own work and that of Caskey [22] show no discernible effect of surface condition on hydrogen concentration in saturated specimens.

4.4. Effects of microstructure and hydrogen trapping on transport and dissolution of hydrogen Several studies on austenitic steels have shown that hydrogen transport and dissolution are independent of whether the

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microstructure is annealed or heavily cold-worked (when the microstructure is stable with respect to phase change) [22,39,40]. In face-centered cubic (FCC) metals such as stainless steels, trap binding energies are relatively low; e.g., the binding energy of hydrogen to dislocations is approximately 10 kJ mol−1 [41]. Trap binding energies of this magnitude lead to very low concentrations of trapped hydrogen. Thus, the solubility determined from permeability measurements and from hydrogen extraction techniques should provide similar results in austenitic stainless steels, particularly when hydrogen is dissolved at elevated temperatures, since trapped hydrogen decreases as temperature increases. There are occasions, however, when hydrogen transport and solubility may appear to depend on the microstructure of the alloy. Steel phases with a body-centered cubic (BCC) crystal structure, such as ferrite and martensite, have significantly higher hydrogen diffusivity and substantially lower hydrogen solubility than the FCC austenitic phase [9]. In relatively unstable austenitic stainless steel such as 304, cold-work can induce martensitic phase transformations, which then cause the effective transport properties, as well as solubility, to be substantially different from an annealed 304 stainless steel that is free of martensite [42,43]. Ferrite is also common in austenitic stainless steels, particularly in high-chromium 300-series alloys, and can have a significant effect on hydrogen transport if the ferrite is highly oriented, as in long thin stringers, or in high enough concentrations, as for duplex alloys. In contrast to austenitic stainless steels, strong traps and low lattice solubility characterize plain carbon and low alloy steels (indeed any steels with a BCC crystal structure) [10]. The solubility measurement technique (e.g., permeation or hydrogen extraction), as well as the hydrogen trapping characteristics of the microstructure, will strongly influence the apparent hydrogen concentration, particularly at lower temperature. Steady-state experiments, for example, are sensitive only to lattice hydrogen, while hydrogen extraction measurements can access the trapped hydrogen in addition to lattice hydrogen. It is important to consider the measurement technique when assessing the hydrogen concentration in these alloys, and to use the value relevant to the phenomenon of interest. For example, when assessing hydrogen flux through a material, the solubility is of interest, while in studies of hydrogen embrittlement the total hydrogen concentration (or trapped hydrogen concentration) determined by hydrogen extraction could perhaps be of more interest. Moreover, it should be emphasized that for materials with significant hydrogen trapping, the diffusivity measured under transient conditions differs from the true lattice diffusivity, thus the apparent diffusivity must be corrected to eliminate the contribution of trapping prior to calculating solubility (lattice hydrogen).

ity changes of six orders of magnitude are predicted between ambient temperature and 673 K, the coincidence of permeability data for many austenitic alloys from many studies is rather remarkable, especially considering surface effects as described above. Other reviews of data on stainless steels [44] found similar consensus on permeability data (although the units quoted in Ref. [44] are believed to be incorrect, see Appendix). Exponential relationships with the lowest activation energy terms are recommended for two reasons: (1) as discussed by Louthan and Derrick [39], hydrogen transport through a material is affected by the surface condition, however, the activation energy should approach a minimum in the limit that permeation is purely governed by lattice diffusion through the bulk; and (2) lower activation energy leads to higher extrapolated permeability at ambient temperature, thus providing an upper bound to the permeation rate at ambient temperature. Average permeability relationships determined in studies that considered several austenitic alloys are summarized in Table 2 and plotted in Figs. 4 and 5. LeClaire’s relationship determined from a review of literature data is distinguished by open diamonds in the figures and plots for other stainless steels show similar correlations with the averaged data. The permeability relationship of Louthan and Derrick [39], marked by circles in the figures, appears to be a good average relationship for austenitic stainless steels, particularly since it was generated from data on several alloys in both annealed and cold-worked conditions; three of the alloys were variants of type 304 stainless steel. The Louthan and Derrick relationship was developed for deuterium, but √ it has been corrected here for hydrogen by multiplying by 2. The average relationship of Sun et al. was also generated from six alloys in several conditions (solution heat treated, annealed and cold-worked) [40] and is marked with triangles in Figs. 4 and 5. The average relationship proposed by Perng and Altstetter [42] is distinguished by open squares in these figures. The lines without symbols in Figs. 4 and 5 represent permeability determined from a number of studies for two different alloys: Fig. 4 for type 304 stainless steels [40,42,45–49] and Fig. 5 for type 316 stainless steels [18,19,35,40,46,47,50–54]. For the unstable austenitic stainless steels, such as 304 and 321, strain-induced martensite may form during thermomechanical processing or by deformation at low temperature [42,43]. BCC phases (including martensite) have permeability and diffusivity several orders of magnitude greater than the FCC (austenitic) phases [9]. It has been observed that the presence of martensitic phases in austenitic stainless steel, for example as a consequence of cold-working the alloy, will greatly increase the permeability and diffusivity of hydrogen in the alloy [42,43]. Cold-working stable austenitic alloys, such as 316 and 310 stainless steels, however, does not significantly affect the rate of hydrogen transport [40,43].

4.5. Permeability

4.6. Diffusivity

LeClaire reviewed permeability data [13] and found that the majority of data for austenitic stainless steels is within factors of 1.5 and 1.5−1 of an average curve. Given that permeabil-

Measured values of hydrogen diffusivity in austenitic stainless steels are somewhat less consistent than permeability: Figs. 6 and 7 show the hydrogen diffusivity relationships for several

6.86

7.5 7.5 5.9 5.9 5.9

266

203 345 135 222 103

[29,44] [29,44] This study This study This study

— —

[42]

8.65 488

[13]

5.9 179

[40]

109

49.3

59.8

62.27

65.69

56.1

1.2 × 10−4

2.81 × 10−4

3.27 × 10−4

0.535 × 10−4

0.1

—

1 × 10−4 –0.03

473–703

—

373–623

Determined from hydrogen extraction techniques

0.1–0.3 423–700

Average of several alloys Average of six alloys Based on > 20 studies on 12 austenitic alloys Average of four alloys (301, 302, 304, 310) 304L 21–6–9 304L 21–6–9 A-286/JBK-75 aged

a From

kJ mol

 H

0



mol √ H2 m s MPa



Permeability  = 0 exp(−H /RT ) Pressure range (MPa) Temperature range (K) Alloy

Table 2 Permeability, diffusivity and solubility relationships: average values determined for several austenitic stainless steels

deuterium data: permeability and diffusivity corrected to hydrogen by multiplying by the square root of the mass ratio:

√ 2.

2.01 × 10−7

— —

53.62 5.76 × 10−7

54.0 6.6 × 10−7

Fig. 4. Permeability of 304 stainless steel alloys, solid lines with no symbols: [40,42,45–49]. Circles: [39], average of several different austenitic stainless steels. Triangles: [40], average of six austenitic stainless steels. Squares: [42], average of four alloys. Diamonds: [13], based on more than 20 studies on 12 austenitic alloys.



Diffusivity D = D0 exp(−HD /RT ) 2

 kJ D0 ms HD mol

m

MPa

Solubility, /D, K = K0 exp(−Hs /RT )

 kJ mol √ H2 Hs mol K0 3

[39]a

Reference

C. San Marchi et al. / International Journal of Hydrogen Energy 32 (2007) 100 – 116

Fig. 5. Permeability of 316 stainless steel alloys, solid lines with no symbols: [18,19,35,40,46,47,50–54]. Circles: [39], average of several different austenitic stainless steels. Triangles: [40], average of six austenitic stainless steels. Squares: [42], average of four alloys. Diamonds: [13], based on more than 20 studies on 12 austenitic alloys.

Fig. 6. Diffusivity of 304 stainless steel alloys, solid lines: [40,42,46,48,49]; dotted line: [47], relationship from study that features low solubility, same study dotted in Fig. 8. Circles: [39], average of several different austenitic stainless steels. Triangles: [40], average of six austenitic stainless steels. Squares: [42], average of four alloys.

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Fig. 7. Diffusivity of 316 stainless steel alloys, solid lines: [40,46,52,54]; dotted lines: [18,35,47,51], relationships from studies that feature low solubility, same studies dotted in Fig. 9. Circles: [39], average of several different austenitic stainless steels. Triangles: [40], average of six austenitic stainless steels. Squares: [42], average of four alloys.

type 304 and type 316 stainless steels, respectively, determined from permeation studies (hydrogen permeability for these same studies are plotted in Figs. 4 and 5, although not all studies that report permeability also report diffusivity), as well as the average relationships marked by symbols and summarized in Table 2. While permeability is commonly determined from a steady-state condition and thus can be time-averaged, diffusivity requires analysis of transient data and this leads to larger intrinsic uncertainty in the determination. Additionally, transient data are likely to be more sensitive to surface condition adding further uncertainty, as described above. These considerations explain the large scatter in diffusivity data, which is translated to solubility data (Section 4.7), since solubility is determined from the ratio of permeability to diffusivity. Studies that report the highest diffusivity share a common feature: special precautions were not taken to control the surface condition of the permeation specimens, such as removing oxides or other surface films. The relationships from these studies [18,35,47,51] are plotted as dotted lines in Figs. 6–9. Higher diffusivity implies lower solubility (K = /D), and studies reporting comparatively low solubility are clearly discernible when plotting data from many studies (Figs. 8 and 9). The relative solubility then provides an indirect indication of the accuracy of the diffusion determination. If we neglect the studies that result in low solubility [18,35,47,51] and only consider the studies where the solubility determinations cluster at the highest values [39,40,42,46,48,49,52,54], the hydrogen diffusivity relationships are in good accord with one another. The average relationships [39,40,42], Table 2 and marked by symbols in Figs. 6 and 7, appear to represent reliable averages of diffusivity for austenitic stainless steels. Variables that have second-order effects on permeability determinations, such as microstructure and alloy composition, appear to have a greater effect on diffusivity. Second phases, particularly those with a BCC crystal structure such as martensite and ferrite, for example, can markedly change the apparent diffusivity (Section 4.4). Sun et al. noted that the

Fig. 8. Solubility of 304 stainless steel alloys, solid lines: [40,42,46,48,49]; dotted line: [47], relationship from study distinguished by low solubility, same study dotted in Fig. 6. Circles: [39], average of several different austenitic stainless steels. Triangles: [40], average of six austenitic stainless steels. Squares: [42], average of four alloys.

Fig. 9. Solubility of 316 stainless steel alloys, solid lines: [40,46,52,54]; dotted lines: [18,35,47,51], relationships from studies distinguished by low solubility, same studies dotted in Fig. 7. Circles: [39], average of several different austenitic stainless steels. Triangles: [40], average of six austenitic stainless steels. Squares: [42], average of four alloys.

hydrogen permeability of six austenitic stainless steel alloys were nearly indistinguishable; however, careful consideration of their data reveals that the alloys clustered into two groups with respect to hydrogen diffusivity [40]. Similar trends can be observed from other studies [42,55]. For austenitic alloys it appears that hydrogen diffusivity may scale with the inverse of the chromium content, although the trend is certainly not a simple function of chromium as discussed in Section 4.7. Differences between specific austenitic alloys, such as 300-series stainless steels compared to the Fe–Cr–Ni–Mn stainless steels, are more apparent in hydrogen solubility, and are discussed in the following section. 4.7. Solubility Figs. 8 and 9 show the hydrogen solubility relationships for several type 304 and type 316 stainless steels, respectively, determined from permeation studies. As discussed in Section 4.6,

C. San Marchi et al. / International Journal of Hydrogen Energy 32 (2007) 100 – 116

111

Fig. 10. Solubility of hydrogen in austenitic stainless steels from several studies extrapolated to ambient temperature: this study (304L, Table 2); Louthan and Derrick [39] (Table 2); Perng and Altstetter [42] (Table 2); Mitchell, 304 [48]; Grant, 304 [49].

Fig. 11. Solubility derived from hydrogen extraction data (Table 1): open symbols, data from this study; closed symbols, data from Refs. [22,29]. Error bars represent standard deviation and are plotted only for 304L and 21–6–9.

hydrogen solubility determined from permeation studies depends on the quality of the hydrogen diffusivity measurements. It should be emphasized that the studies describing careful and thoughtful experimental techniques report data consistent with one another, with the highest values for solubility and the lowest values for enthalpy of formation of H-atoms in the metal (H ). As with permeability and diffusivity, both Louthan and Derrick [39] and Perng and Altstetter [42] provide reliable solubility relationships that appear conservative (high) at low temperature (Fig. 10). While the solubility at high temperature is certainly of interest, for many engineering applications the solubility at ambient temperature is of more concern. As the extrapolations in Fig. 10 show for the data clustered at high solubility, H (proportional to the slope of the Arrhenius-type plot) has a strong impact on the extrapolated solubility. For studies that determined approximately the same solubility at elevated temperature, the difference in H causes values extrapolated to ambient temperature to differ by an order of magnitude. The relationship with the lowest H will provide upper bounds on both the extrapolated solubility and amount of hydrogen dissolved in the steel. In addition, as described in Section 4.5, the theoretical minimum in the energy terms should be approached as surface effects are reduced, providing a scientific basis for choosing relationships with the lowest energy terms, such as that proposed by Louthan and Derrick for austenitic stainless steels: 5.9 kJ mol−1 [39]. The relationships of Louthan and Derrick [39], however, have been criticized for averaging the data for several austenitic alloys. Other evidence in the literature, for example, suggests that the solubility of 304 stainless steel is significantly less than 21–6–9 [40,55]. Hydrogen concentration data from hydrogen extraction measurements of Caskey and Sission [22] and within our own laboratory also support the observation that the solubility of hydrogen in 21–6–9 and 22–13–5 is greater than in 304 and 316 stainless steels at the same temperature (Fig. 11 and Table 1). Caskey [29,44] proposes two solubility relationships based on hydrogen extraction data and fitting of tritium diffusion profiles to solubility and diffusion relationships. However,

Caskey’s solutions are not unique and no clear justification for the choice of energy terms is given (nor comprehensive study of temperature). These relationships distinguish between 304 and 21–6–9 well enough but do not capture all of his data. The deuterium data of Caskey, in particular, appear to be consistently low [29] and are not considered further here. In addition, the relationships generated by Caskey do not take into account real gas behavior (i.e., the fugacity) when converting concentration to solubility. We have taken the hydrogen concentration data reported by Caskey in Refs. [22,29] as well as our own data (Table 1) and used the lowest energy term (5.9 kJ mol−1 , Ref. [39]), along with the fugacity function (Eq. (9)) determined in Section 4.1, to generate solubility relationships for 304 and 21–6–9, respectively. A more expansive accounting of temperature is one important feature of combining our data with that of Caskey. The average solubility for a number of austenitic alloys determined from hydrogen extraction data are plotted in Fig. 11, and the parameters for the hydrogen solubility relationships are given in Table 2 (as well as Table 3). In addition, the differences in hydrogen diffusivity between alloys can be estimated by dividing the permeability (as measured from Louthan and Derrick [39] for example) by these solubility relationships. The diffusivity relationships for 304 and 21–6–9 as determined by this procedure are given in Table 3. The H term determined by Louthan and Derrick [39] represents a lower limit compared to Caskey [29] and others and is believed to be the most appropriate value for austenitic stainless steels; in addition, from the view of extrapolation it represents an upper bound on hydrogen concentrations. Considering that the data represent two laboratories and in our case data collected over a period of years from numerous hydrogen saturation trials performed for various lengths of time, the fit in Fig. 11 is satisfying. The major assumption in constructing these relationships is that trapping can be neglected for austenitic stainless steels at the temperatures used for hydrogen exposure. In this case, solubility (lattice hydrogen) can be determined from the total hydrogen concentration (i.e., from

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Table 3 Recommended permeability, diffusivity and solubility relationships for austenitic stainless steels Alloy

Permeability  = 0 exp(−H /RT )

0 All austenitic stainless steels 300-series 21Cr–6Ni–9Mn, 22Cr–13Ni–5Mn A-286/JBK-75 aged



mol √ H2 m s MPa

1.2 × 10−4 — — —



H



kJ mol



59.8 — — —

Fig. 12. Hydrogen concentrations determined from solubility relationships in Table 2 at hydrogen pressure of 69 MPa: this study (304L); Louthan and Derrick [39]; Perng and Altstetter [42]; Caskey (304L) [29,44], using pressure, all others use fugacity.

extraction data). The construction of alloy-specific solubility relationships is motivated by the desire to express the hydrogen solubility as a function of temperature (between ambient and a few hundred degrees centigrade) to within 10–20%, compared to diffusivity and permeability, where a factor of two is generally sufficient since these values vary by many orders of magnitude over narrow temperature ranges. The concentrations predicted by several of the solubility relationships for 304 stainless steel from Table 2 are compared in Fig. 12. In this plot the pressure is used in place of fugacity for the Caskey correlation only since this relationship was developed from concentration data without consideration of the real gas behavior of hydrogen. The average relationships of Louthan and Derrick [39] and of Perng and Altstetter [42] predict higher solubility (Fig. 10) and higher concentrations (Fig. 12) than the relationship generated here, while the Caskey relationship [29,44] predicts the lowest concentration. The reason for the higher solubility determined from permeation experiments compared to hydrogen extraction measurements is unclear. Trapping, for example, would cause an opposite trend: that is, the concentration measurements would be higher than predicted from permeation measurements due to the trapped (excess) hydrogen. The most likely explanation for the higher solubility from permeation experiments (Louthan and Derrick [39] and of Perng and Altstetter [42]) is uncertainty in the dif-

Diffusivity D = D0 exp(−HD /RT ) 2

 kJ HD mol D0 ms

Solubility, /D, K = K0 exp(−Hs /RT )

 kJ mol √ H2 Hs mol K0 3

Reference

— 8.9 × 10−7 5.4 × 10−7 12 × 10−7

— 135 222 103

[39] This study This study This study

— 53.9 53.9 53.9

m

MPa

— 5.9 5.9 5.9

fusivity measurements (Section 4.6). The predictions of Caskey are lower than those predicted in this study primarily due to his use of a relatively high value of H (i.e., steeper slope when extrapolating concentrations). The solubility relationships determined here should provide the most accurate estimations for concentration of hydrogen in uniformly saturated stainless steels. Data for 316 and 22–13–5 stainless steels were not used to construct the improved solubility relationships in Fig. 11 and Table 3, but these data follow the trends for 304 and 21–6–9, respectively. This adds further weight to these relationships as data from both permeation experiments and hydrogen extraction studies indicate that the diffusivity and solubility of hydrogen in austenitic alloys seem to cluster into at least two groups. The precipitation-strengthened austenitic stainless steels appear to show a different solubility depending on whether the alloy is annealed or aged. In the annealed condition a “modified A286” [22] (presumably JBK-75) was found to have a hydrogen concentration similar to 304L, while in the forged condition (and presumably aged) the alloy features a significantly lower hydrogen concentration. Our own measurements on peak aged A-286 and JBK-75 alloys also show a lower hydrogen concentration than measured for type 304 and type 316 stainless steels under the same hydrogen exposure conditions (Table 1). Thus, data for the precipitation-strengthened austenitic alloys in the aged condition are used to determine a solubility relationship and a diffusivity relationship (Table 3) in the same manner as described above for 304 and 21–6–9. Permeability studies on JBK-75, however, have shown very little effect of aging on hydrogen diffusivity in this alloy, although hydrogen permeability appears to be slightly higher in the solution heat treated condition, which translates to a higher hydrogen solubility [56]. Alloy composition is generally believed to be the source for differences between the 300-series and the Fe–Cr–Ni–Mn austenitic stainless steels. Nitrogen as well as high manganese and high chromium have been implicated since these are distinguishing characteristics of 21Cr–6Ni–9Mn, 21Cr–9Ni–9Mn and 22Cr–13Ni–5Mn, all of which appear to have significantly higher solubility than the 300-series alloys. Nitrogenstrengthened 300-series alloys, 316N and 304LN, however do not display higher solubility than their counterparts without nitrogen [39,40]. High chromium and manganese may explain elevated solubility in some alloys, but type 321 stainless steel has high solubility and relatively low chromium and man-

C. San Marchi et al. / International Journal of Hydrogen Energy 32 (2007) 100 – 116

ganese (and no nitrogen). Titanium has been implicated to explain the solubility of type 321 stainless steel. Composition does not explain, however, the relatively low solubility of hydrogen in annealed (single-phase) A-286 and JBK-75 (Fig. 8) as these alloys have among the highest chromium, nickel and titanium contents of all the alloys that have been discussed. In the aged condition, the solubility of hydrogen in A-286 is reduced. Aging substantially changes the matrix composition of A-286; nickel and titanium in particular are depleted in the matrix as Ni3 Ti precipitates during aging. It is not clear, however, if the lower solubility is due to the precipitates having very low solubility (perhaps due to the ordered structure of the precipitated phases) or if the loss of nickel and titanium in the matrix contributes to the reduction in hydrogen solubility. Further study is necessary to clarify solubility trends due to compositional differences in austenitic stainless steels. 5. Recommendations and conclusions 5.1. High-pressure gas: hydrogen and its isotopes The Abel–Noble equation of state provides a simple analytical relationship that describes the real gas behavior of hydrogen for conventional engineering pressures above ambient (0.1 MPa < P < 200 MPa) and temperatures near-ambient (223 K < T < 423 K). The real gas behavior of deuterium is nominally equivalent to hydrogen for the same range of pressure and temperature and tritium is expected to follow the same relationship. This equation of state is appropriate to higher temperature (< 1000 K) for pressures to at least 50 MPa and is probably accurate to pressures as high as 200 MPa; however, experimental validation is lacking. The Abel–Noble parameter b was determined to be 15.84 cm3 mol−1 using data previously published for hydrogen. The fugacity of hydrogen should be used in thermodynamic relationships in place of the pressure. Assuming the Abel–Noble equation of state, the fugacity has a simple analytical form: f =P exp(P b/RT ) (Eq. (9)), which can easily be incorporated in permeation, diffusion, and solubility calculations. The ratio of fugacity to pressure (often called fugacity coefficient) is about 1.1 at 15 MPa and 298 K, thus at industrial gas cylinder pressure (∼ 14 MPa) the real behavior of the gas is important. The fugacity coefficient decreases as temperature increases. 5.2. Permeability, diffusivity and solubility of hydrogen The permeability measurements for austenitic stainless steels that have been reported in the literature are generally quite consistent. These reports show that for austenitic stainless steels the permeability is independent of the alloy and the microstructure; BCC phases, such as strain-induced martensite, however, can substantially increase permeation. The relationships of Louthan and Derrick [39] or Perng and Altstetter [42] are recommended for extrapolation to ambient temperature. Diffusivity, on the other hand, appears to depend on the alloy; in addition, there may be considerable errors in reported values due to the role of

113

surface condition. The Fe–Cr–Ni–Mn stainless steels, such as 21Cr–6Ni–9Mn and 22Cr–13Ni–5Mn, for example, have lower diffusivity of hydrogen and higher solubility for hydrogen than the 300-series stainless steels (while the permeability is the same for the two alloy groups). Since the permeability is essentially the same for all stainless steels, the accuracy of the solubility measured from permeation experiments will depend primarily on the accuracy of the diffusion measurement, which generally has large uncertainty. For stainless steels the lattice solubility can be approximated by the total hydrogen concentration since hydrogen is not strongly trapped and equilibrium lattice concentrations are very high, particularly at elevated temperature. Therefore, hydrogen extraction techniques provide good estimates for solubility. In this report, hydrogen extraction data were used, taking into consideration fugacity, to determine solubility relationships for type 304 and 21Cr–6Ni–9Mn stainless steels. Similar hydrogen extraction data for type 316 and 22Cr–13Ni–5Mn stainless steels correlate well with these relationships for type 304 and 21Cr–6Ni–9Mn, respectively. These solubility relationships were developed to provide conservatively high values when extrapolated to ambient temperature and to account for the pressure and temperature dependence of real gas behavior. Appropriate diffusivity relationships for these two alloy groups can be determined using D = /K. The recommended relationships for permeation, diffusion and solubility are given in Table 3. Existing tools for hydrogen transport in stainless steels, such as the DIFFUSE code [20,21], should be re-evaluated to confirm the appropriateness of its database of transport parameters, and the use of appropriate thermodynamics of the gas (namely the real gas behavior of hydrogen). Acknowledgment The authors wish to thank Steve Rice and Richard Larson of Sandia National Laboratories for useful discussions on the thermodynamics of gases. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DEAC04-94AL85000. Appendix A. Units The units that are used for permeability and solubility of hydrogen vary substantially in the literature, often leading to confusion. Solubility units are a measure of concentration normalized by the square root of pressure (or fugacity). These units are a direct consequence of defining solubility such that K ∝ cL ∝ J∞ . Permeability units are more difficult to visualize: flux normalized by a characteristic distance (thickness) and the square root of pressure. The flux is concentration per time per surface area. The concentration unit varies according to the motivation of the discipline making use of the information. For relatively low concentrations of interstitial atoms, the metallurgist prefers parts per million (ppm) and to complicate matters, two variants are commonly used: atomic ppm and weight ppm. Systems engineers, on the other

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C. San Marchi et al. / International Journal of Hydrogen Energy 32 (2007) 100 – 116

Table A1 Unit conversions for quantities commonly encountered in permeability, diffusivity and solubility studies To convert from

To

Multiply by

atm mol H2 mol H2

MPa g cm3

0.101325 2.016 22414a

eV cal mol−1

kJ mol−1 kJ mol−1

96.486 0.004184

mol H2 m3 atm1/2

mol H2 m3 MPa1/2

3.14153

cm3

mol H2 m3 MPa1/2

140.16a

cm3 atm1/2

gH g MPa1/2

mol H2 m3 MPa1/2

3.9 × 106b

wt ppm H MPa1/2

mol H2 m3 MPa1/2

3.9b

at ppm H MPa1/2

mol H2 m3 MPa1/2

0.0718b,c

cm2 s−1

m2 s−1

0.0001

mol H2 m s atm1/2

mol H2 m s MPa1/2

3.14153

cm3 cm s atm1/2

mol H2 m s MPa1/2

0.014016a

Energy

Solubility

Diffusivity

Permeability

Note that a number of conversions require knowledge of the physical properties of the material (density, molecular weight) or a clear definition of the standard state chosen for the gas, therefore some of the conversions are not universal. a At STP, standard pressure and temperature: P = 0.101325 MPa, T = 273.15 K. bAssumes density of solid to be 7.9 g cm −3 (stainless steel), and limit of small H content. cAssumes equivalent molecular weight of solid to be 55 g mol−1 (stainless steel), and limit of small H content.

hand, prefer standard gas volumes (cubic centimeters or liters) per volume of material. Others in the scientific community have settled on moles of H2 gas per volume (cubic meter) of material. In addition, gas equivalence requires a standard reference state (standard temperature and pressure), but in practice there is no universal definition of standard temperature and pressure. When not stated we assume standard temperature and pressure to be 273 K and 0.101325 MPa. Older studies typically used atmospheres for pressure units, but recent studies have settled

on the megapascal (MPa). The recommended units for solubility and permeability are then Solubility:

mol H2 , m3 MPa1/2

Permeability:

mol H2 . m s MPa1/2

Table A1 provides conversion factors for a number of commonly reported units.

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There are several inconsistencies in the data reported by Caskey. The pressure units reported in Ref. [44] √ for permeability and solubility are believed to be incorrect; MPa should be √ replaced with atm (i.e., the values reported by Caskey have units of mol m−1 s−1 atm−1/2 and mol m−3 atm−1/2 for permeability and solubility, respectively). In Ref. [29], Caskey quotes hydrogen charging temperature as 740 K, while plots seem to indicate that the temperature was in fact 470 K as described in another reference [22]. Finally, it must be kept in mind when converting between units that two atoms make a molecule of hydrogen gas, but when dissolved in the lattice of a metal the hydrogen exists as atomic hydrogen, therefore a factor of two is necessary when converting between atoms of hydrogen dissolved in the material (e.g., ppm) and the equivalent amount of hydrogen gas (e.g., mol H2 ). This issue is distinct from the factor of two sometimes associated with the enthalpy of formation of H-atoms dissolved in the metal (sometimes called the heat of solution [44]), although their origin is the of the  same: stoichiometry reaction expressed in Eq. (10) 21 H2 ↔ H . The stoichiometry of the reaction in Eq. (10) leads to the linear expression for permeability:  = DK. The hydrogen dissolution reaction could also be expressed as H2 ↔ 2H. The equilibrium constant for this reaction is K ∗ = cL2 /f = K 2 , and the enthalpy associated with this reaction is twice the enthalpy of formation of H-atoms (from Eq. (10)). One could express the permeabil√ ity in terms of this equilibrium constant as  = D K ∗ , but obviously the linear relationship is lost. The enthalpy of this reaction (H2 ↔ 2H) could be used in the conventional form of solubility (Eqs. (10)–(14)), provided that a factor of two is added to the denominator of Eq. (14), since Eq. (14) implicitly assumes that the reaction is expressed as 21 H2 ↔ H (Eq. (10)). This is the source of the factor of two in the exponential term for solubility given in Ref. [44]. References [1] Hemmes H, Driessen A, Griessen R. Thermodynamic properties of hydrogen at pressures up to 1 Mbar and temperatures between 100 and 1000 K. J Phys C Solid State 1986;19:3571–85. [2] Zhou L, Zhou Y. Determination of compressibility factor and fugacity coefficient of hydrogen in studies of adsorptive storage. Int J Hydrogen Energy 2001;26:597–601. [3] McLennan KG, Gray EM. An equation of state for deuterium gas to 1000 bar. Meas Sci Technol 2004;15:211–5. [4] Tkacz M, Litwiniuk A. Useful equations of state of hydrogen and deuterium. J Alloy Compd 2002;330–332:89–92. [5] Peress J. Working with non-ideal gases. Chem Eng Prog 2003;99:39–41. [6] Chenoweth DR. Gas transfer analysis: section H-real gas results via the van der Waals equation of state and virial expansion extensions of its limiting Abel–Boble form (SAND83-8229). Livermore, CA: Sandia National Laboratories; 1983. [7] Wriedt HA, Oriani RA. Effect of tensile and compressive elastic stress on equilibrium hydrogen solubility in a solid. Acta Metall 1970;18: 753–60. [8] van Leeuwen HP. The kinetics of hydrogen embrittlement: a quantitative diffusion model. Eng Fract Mech 1974;6:141–61. [9] Moody NR, Robinson SL, Garrison WM. Hydrogen effects on the properties and fracture modes of iron-based alloys. Res Mech 1990;30:143–206. [10] Hirth JP. Effects of hydrogen on the properties of iron and steel. Metall Trans 1980;11A:861–90.

115

[11] Perkins WG. Permeation and outgassing of vacuum materials. J Vac Sci Technol 1973;10:543–56. [12] Oriani RA. The physical and metallurgical aspects of hydrogen in metals. Fusion Technol 1994;26:235–66. [13] LeClaire AD. Permeation of gases through solids: 2. An assessment of measurements of the steady-state permeability of H and its isotopes through Fe, Fe-based alloys, and some commercial steels. Diffus Defect Data 1983;34:1–35. [14] Voelkl J, Alefeld G. Hydrogen diffusion in metals. In: Nowick AS, Burton JJ, editors. Diffusion in solids: recent developments. Materials science and technology. New York: Academic Press; 1975. [15] Louthan MR, Derrick RG. Permeability of nickel to high pressure hydrogen isotopes. Scr Metall 1976;10:53–5. [16] Quick NR, Johnson HH. Permeation and diffusion of hydrogen and deuterium in 310 stainless steel, 472 K to 779 K. Metall Trans 1979;10A:67–70. [17] Swansiger WA, Bastasz R. Tritium and deuterium permeation in stainless steels: influence of thin oxide films. J Nucl Mater 1979;85&86:335–9. [18] Forcey KS, Ross DK, Simpson JCB, Evans DS. Hydrogen transport and solubility in 316L and 1.4914 steels for fusion reactor applications. J Nucl Mater 1988;160:117–24. [19] Shiraishi T, Nishikawa M, Tamaguchi T, Kenmotsu K. Permeation of multi-component hydrogen isotopes through austenitic stainless steels. J Nucl Mater 1999;273:60–5. [20] Baskes M. DIFFUSE-83 (SAND83-8231). Livermore, CA: Sandia National Laboratories; 1983. [21] Hardwick MF, Robinson SL. Diffuse II: a hydrogen isotope diffusion and trapping simulation program upgrade (SAND99-8202). Livermore, CA: Sandia National Laboratories; 1998. [22] Caskey GR, Sisson RD. Hydrogen solubility in austenitic stainless steels. Scr Metall 1981;15:1187–90. [23] Ma LM, Liang GJ, Li YY. Effect of hydrogen charging on ambient and cryogenic mechanical properties of a precipitate-strengthened austenitic steel. In: Fickett FR., Reed RP, editors. Proceedings of the international cryogenic materials conference, Huntsville, AL, 1991. Advances in cryogenic engineering, vol. 38A. New York: Plenum Press; 1992. p. 77–84. [24] Ma L, Liang G, Tan J, Rong L, Li Y. Effect of hydrogen on cryogenic mechanical properties of Cr–Ni–Mn–N austenitic steels. J Mater Sci Technol 1999;15:67–70. [25] Michels A, De Graff W, Wassenaar T, Levelt JMH, Louwerse P. Compressibility isotherms of hydrogen and deuterium at temperatures between −175 ◦ C and +150 ◦ C (at densities up to 960 Amagat). Physica 1959;25:25–42. [26] Vargaftik NB. Tables on the thermophysical properties of liquids and gases: in normal and dissociated states. London: Hemisphere Publishing Corporation; 1975. [27] Lemmon EW, McLinden MO, Friend DG. Thermophysical properties of fluid systems. In: Linstrom PJ, Mallard WG, editors. NIST chemistry webbook, NIST standard reference database number 69 (http://webbook.nist.gov). Gaithersburg MD: National Institute of Standards and Technology; 2005. [28] Zarchy AS, Axtmann RC. Tritium permeation through 304 stainless steel at ultra-low pressures. J Nucl Mater 1979;79:110–7. [29] Caskey GR. Hydrogen solution in stainless steels (DPST-83-425). Aiken, SC: Savannah River Laboratory; 1983. [30] Oriani RA. Hydrogen embrittlement of steels. Ann Rev Mater Sci 1978;8:327–57. [31] van Leeuwen HP. Fugacity of gaseous hydrogen. In: Oriani RA, Hirth JP, Smialowski M, editors. Hydrogen degradation of ferrous alloys. Park Ridge, NJ: Noyes Publications; 1985. p. 16–35. [32] Moody NR, Stoltz RE, Perra MW. Effect of hydrogen on fracture toughness of the Fe–Ni–Co superalloy IN903. Metall Trans 1987;19A:1469–82. [33] Schefer RW, Houf WG, San Marchi C, Chernicoff WP, Englom L. Characterization of leaks from compressed hydrogen dispensing systems and related components. Int J Hydrogen Energy 2006; 31:1247–60. [34] Baranowski B. Thermodynamics of metal/hydrogen systems at high pressures. Ber Bunsen Ges 1972;76:714–24.

116

C. San Marchi et al. / International Journal of Hydrogen Energy 32 (2007) 100 – 116

[35] Fedorov VV, Pokhmursky VI, Dyomina EV, Prusakova MD, Vinogradova NA. Hydrogen permeability of austenitic steels proposed for fusion reactor first wall. Fusion Technol 1995;28:1153–8. [36] Strehlow RA, Savage HC. Formation and use of oxide films to impede outgassing of metals. J Nucl Mater 1974;53:323–7. [37] Swansiger WA, Musket RG, Weirick LJ, Bauer W. Deuterium permeation through 309S stainless steel with thin, characterized oxides. J Nucl Mater 1974;53:307–12. [38] Ishikawa Y, Yoshimura T, Arai M. Effect of surface oxides on the permeation of deuterium through stainless steel. Vacuum 1996;47:701–4. [39] Louthan MR, Derrick RG. Hydrogen transport in austenitic stainless steel. Corros Sci 1975;15:565–77. [40] Sun XK, Xu J, Li YY. Hydrogen permeation behaviour in austenitic stainless steels. Mater Sci Eng 1989;A114:179–87. [41] Thomas GJ. Hydrogen trapping in FCC metals. In: Bernstein IM, Thompson AW, editors. Proceedings of the international conference on effect of hydrogen on behavior of materials: hydrogen effects in metals, 1980. Moran, WY: The Metallurgical Society of AIME; 1981. p. 77–85. [42] Perng T-P, Altstetter CJ. Effects of deformation on hydrogen permeation in austenitic stainless steels. Acta Metall 1986;34:1771–81. [43] Sun XK, Xu J, Li YY. Hydrogen permeation behavior in metastable austenitic stainless steels 321 and 304. Acta Metall 1989;37:2171–6. [44] Caskey GR. Hydrogen effects in stainless steels. In: Oriani RA, Hirth JP, Smialowski M, editors. Hydrogen degradation of ferrous alloys. Park Ridge, NJ: Noyes Publications; 1985. p. 822–62. [45] Gorman JK, Nardella WR. Hydrogen permeation through metals. Vacuum 1962;12:19–24.

[46] Gromov AI, Kovneristyi YK. Permeability, diffusion, and solubility of hydrogen in Cr–Ni and Cr–Mn austenitic steels. Met Sci Heat Treat 1980;22:321–4. [47] Tanabe T, Tamanishi Y, Sawada K, Imoto S. Hydrogen transport in stainless steels. J Nucl Mater 1984;122&123:1568–72. [48] Mitchell DJ, Edge EM. Permeation characteristics of some iron and nickel based alloys. J Appl Phys 1985;57:5226–35. [49] Grant DM, Cummings DL, Blackburn DA. Hydrogen in 304 steel: diffusion, permeation and surface reaction. J Nucl Mater 1987;149: 180–91. [50] Van Deventer EH, Maroni VA. Hydrogen permeation characteristics of some austenitic and nickel-base alloys. J Nucl Mater 1980;92:103–11. [51] Hashimoto E, Kino T. Hydrogen permeation through type 316 stainless steels and ferritic steel for fusion reactor. J Nucl Mater 1985;133&134:289–91. [52] Kishimoto N, Tanabe T, Suzuki T, Yoshida H. Hydrogen diffusion and solution at high temperatures in 316L stainless steel and nickel-base heat-resistant alloys. J Nucl Mater 1985;127:1–9. [53] Gautsch O, Hoddap G. Deuterium permeability of the austenitic stainless steel AISI 316. J Nucl Mater 1988;152:35–40. [54] Grant DM, Cummings DL, Blackburn DA. Hydrogen in 316 steel—diffusion, permeation and surface reaction. J Nucl Mater 1988;152:139–45. [55] Perng T-P, Altstetter CJ. Hydrogen effects in austenitic stainless steels. Mater Sci Eng A 1990;129:99–107. [56] Xu J, Sun XK, Chen WX, Li YY. Hydrogen permeation and diffusion in iron-base superalloys. Acta Metall Mater 1993;41:1455–9.