ARTICLE pubs.acs.org/JPCC
Hydrogen Permeation through fcc PdAu Alloy Membranes Ted B. Flanagan* and D. Wang Material Science Program and Department of Chemistry, University of Vermont, Burlington, Vermont 05405, United States ABSTRACT: H permeabilities have been measured for a series of fcc PdAu alloy membranes in the temperature range from 393 to 573 K. The maximum permeability is found at the atom fraction of Au, XAu = 0.11 ( 0.01, which closely agrees with a theoretically predicted value (Sonwane, C.; Wilcox, J.; Ma, Y. J. Chem. Phys. 2006, 125, 184714). For a series of PdAu alloy membranes with different Au contents, diffusion constants, activation energies, and pre-exponential factors have been determined as a function of H content. H concentration-independent values of these parameters have been obtained by extrapolation to Hf0 where the H solution behaves ideally.
’ INTRODUCTION Because the Pd0.77Ag0.23 alloy is employed industrially as a H2 purification membrane, H diffusion in PdAg alloys has been the subject of many studies;19 however, there have been few studies of H diffusion in the closely related PdAu alloys. Sonwane et al.1 have calculated H solubilities and diffusivities in Pd, PdAg, and PdAu alloys. Density functional theory (DFT) was employed to determine the solubilities and also the activation energies which, when combined with Monte Carlo simulations, yielded diffusion constants; the permeabilities were obtained as a product of the solubility and diffusion constant. The maximum permeability was calculated to occur at the atom fraction of Au, XAu = 0.12, at temperatures from 456 to 1095 K. The permeability of H at 456 K in the XAu = 0.12 membrane was calculated to be about 4.8 times that of Pd, which is greater than the calculated permeability for the XAg = 0.20 alloy, which is 3.1 times that of Pd. It has been found that PdAu membranes have increased resistance to poisoning by sulfur compounds,10 and this has prompted some recent interest in these membranes.12 For example, Coulter et al.11 have recently employed DFT to predict the H permeability of a Pd0.95Au0.05 and several ternary Pd þ Au þ Cu membranes. Using electrochemical breakthrough times in the range from 273 to 389 K, Maestas and Flanagan13 found that the diffusion constants of H in PdAu alloys did not change much from that of H in Pd up to about XAu = 0.20, and then for XAu > 0.20, DH fell with XAu. Sakamoto and co-workers also employed electrochemical methods and found similar trends of DH with XAu.14 The same technique was employed by Yoshihara and McLellan,15 but they did not report data between XAu = 0.20 and 0.50; however, from 0 to 0.20 there was very little effect of XAu on DH. The value of DH found by Yoshihara and McLellan15 is somewhat larger than that reported by Sakamoto et al.14 for the XAu ≈ 0.20 alloy. More recently, Way and co-workers16 determined permeabilities r 2011 American Chemical Society
in PdAu membranes prepared by sequential electroplating and electroless plating. H is assumed to occupy octahedral interstices in fcc Pd-rich alloys as it does in pure Pd. Indirect evidence for this is that the inelastic vibrational frequency of H in an alloy, Pd0.80Ag0.20, of the closely related PdAg alloys, is characteristic of H in octahedral rather than tetrahedral interstices.17
’ EXPERIMENTAL SECTION The PdAu alloys were obtained from Engelhard Inc., and membranes were prepared by arc-melting the alloys and then annealing at 1123 K for 72 h and rolling into the appropriate thicknesses, 100150 μm. Fluxes were determined from the decreases of pH2 on the upstream side of the membranes using an MKS gauge, while the downstream side was maintained at pH2 ≈ 0.18 Steady state fluxes were established very rapidly for these PdAu alloy membranes at the temperatures employed. There was a small falloff in flux during the measurements due to the decrease in pup in the upstream volume; however, this was generally small because the upstream volume was large, and in any case, the fluxes can be corrected for such small decreases. Generally, however, the fluxes were taken as the initial ones before any appreciable decreases of pup occurred. The areas of the membranes which were active for permeation after being mounted within the diffusion apparatus were 1.77 cm2. The membranes were enclosed by a tube furnace controlled to (1 K. The temperatures were set by an electronic controller and were found to be in good agreement with those measured by a temperature sensor placed in contact with the mounted membrane before the diffusion measurements were carried out. Received: March 1, 2011 Revised: May 10, 2011 Published: May 19, 2011 11618
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The membranes were oxidized in the atmosphere for ≈30 min at 953 K before mounting them in the diffusion apparatus since this procedure has been shown to improve the reproducibility of Pd-based membranes.18 Since oxides formed by Pd do not penetrate into the alloy appreciably and are rapidly reduced in the presence of H2, the membrane thicknesses are taken as those measured before oxidation. Some higher Au content membranes were palladized, i.e., electrochemically coated with a fine layer of Pd, to improve their reproducibility, but this procedure did not significantly alter the thickness of the membranes. There was no indication of any degradation of the membranes over time. In the present experiments where the downstream side is maintained at pH2 ≈ 0, the steady-state H flux, J, is given by J ¼ DH ðdcH =dxÞ ¼ DH cup =d
ð1Þ
where d is the membrane thickness. The diffusion constants were determined from the fluxes using isotherms to determine cup.19 The normalized flux,20 which for convenience will be referred to as the permeability, will be defined as P ¼ J d ¼ DH ðΔcH =dÞ d ¼ DH cup
ð2Þ
when pdown = 0. Equations for the Dependence of DH on H Content. It has been shown for Pd3,6,21,22 and some Pd alloy membranes, e.g., PdAg,2,7,9 that Fick’s diffusion constant, DH, is a function of the H content of the membrane. Under conditions where the H content is nearly constant, e.g., in time breakthrough experi* , Einstein’s concentraments, DH can be employed to obtain DH tion-independent diffusion constant, using the relationship DH = (d ln p1/2/d ln r)TD*H21 where r = H-to-metal atom ratio and (d ln p1/2/d ln r)T is generally referred to as the thermodynamic factor, f(r), which is a function of the H content. An advantage of Pd and its alloyH2 systems is that thermodynamic factors can be readily evaluated from independently measured equilibrium isotherms.3,6,21,22 Under typical H permeation conditions where r, and therefore f(r), are functions of the distance through the membrane, the thermodynamic factor can be allowed for using eq 39,22 ! Z rup DH ¼ DH f ðrÞdr =rup ¼ DH Fðrup Þ=rup ð3Þ 0
Equation 3 can be employed to calculate DH * from the average DH measured from eq 1 and using F(r) evaluated as a function of r from the equilibrium isotherms. This method does not require any knowledge of the fraction of interstices occupied in the alloys as does the approximate method given below. As an approximation for the dependence of DH on r, the following equation has been derived,22 which is valid at small r, from an expression for the chemical potential of H in Pd using mean field theory23 g r ð4Þ RT ln DH ¼ RTln DH þ 1 2 where g1 is the first-order term in a polynomial expansion of the excess chemical potential of H and r is rup. Plots of RT ln DH against r give g1 from the slope, and these agree reasonably well for PdH with the value of g1 obtained independently from thermodynamic data.22 The situation is more complex for Pd alloys because, unlike in Pd, the octahedral interstices are not all equivalent, and consequently, there is expected to be selective site occupation of the
interstices by H. In this case, the mean field model at low r values where only one type of interstice is occupied, e.g., those surrounded only by nearest neighbor Pd atoms, is given as ln p1=2 ¼
g r ΔμoH r þ 1 þ ln ðβ rÞ RT RT
ð5Þ
where β is the fraction of octahedral sites in the alloy available for occupation by H. This equation is appropriate only at small r values where one type of site is occupied or else where two or more sites can be occupied which have very similar energies for H occupation. From eq 5, we obtain for f(r) ! g r d ln p1=2 β þ 1 f ðrÞ ¼ ¼ ð6Þ ðβ rÞ RT d ln r T
If this equation is integrated to obtain F(r), defined by eq 3, eq 7 is obtained Z Z rup g 1 rup β dr þ FðrÞ ¼ rdr ¼ β lnðβ rÞ ðβ rÞ RT 0 0 g r2 ð7Þ þ β ln β þ 1 2RT where r refers to rup. Inserting this expression for F(r) into eq 3, and taking logarithms of both sides, eq 8 is obtained ! g 1 r2 ln DH ¼ ln DH þ ln β lnðβ rÞ þ β ln β þ ln r 2RT ð8Þ or ln DH ¼ ln
DH
! g 1 r2 r þ ln β ln 1 þ ln r ð9Þ β 2RT
using ln((1 r)/β) ≈ r/β. If the approximation r r r 1þ ln 1 β β 2β
ð10Þ
is employed in eq 9 and the further approximation ln(1 þ (r/2)((1/β) þ g1/RT)) ≈ (r/2)((1/β) þ g1/RT) is then employed, eq 11 is obtained r 1 g1 þ ln DH ¼ ln DH þ ð11Þ 2 β RT Therefore, the slope of a plot of ln DH against r should be (1/2) (1/β þ g1/RT) where r is rup. For the PdAu alloys, values of β have been estimated previously from equilibrium experiments by assuming they can be obtained by adjusting β values so that ° for the alloys becomes equal to ΔSH ° of pure PdH.19 ΔSH
’ RESULTS AND DISCUSSION H Permeability. The permeabilities or normalized fluxes for alloy membranes from XAu = 0 to 0.35 at temperatures from 423 to 573 K are shown in Figures 1 and 2 measured at pup = 50.6 and 101.3 kPa, respectively. Although continuous curves have been drawn through the points in these two figures, the finer details are probably not of significance. The important point is that there is a maximum at XAu = 0.10 for pup = 50.6 kPa and at about XAu = 0.12 for 11619
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Table 1. Experimental and Calculated Values of n from Equations 12 and 13 for the XAu = 0.12 (r = 0.02) and 0.21 (r = 0.03) Alloys (473 K) Where g1 Is in Units of kJ/mol H XAu = 0.21, n (slope) evaluated at r = 0.03 β = 1.0, g1 = 18.2 β = 0.29, g1 = 29.4 β = 0.243, g1 = 33.8 n(exp) n(eq 12) = 0.528
n(eq 12) = 0.534
n(eq 12) = 0.536
0.538
n(eq 13) = 0.537
n(eq 13) = 0.563
n(eq 13) = 0.574
0.538
XAu = 0.12, n (slope) evaluated at r = 0.02 β = 1.0, g1 = 28.9 β = 0.54, g1 = 32.6 β = 0.46, g1 = 34.0 n(exp)
Figure 1. Permeabilities as a function of XAu at 423, 473, 523, and 573 K all with pup = 50.65 kPa.
n(eq 12)=0.534
n(eq 12)=0.534
n(eq 12)=0.535
0.548
n(eq 13)=0.547
n(eq 13)=0.545
n(eq 13)=0.547
0.548
Figure 3. Plot of ln P against ln pup for the XAu = 0.19 alloy at 473 K. The dashed line indicates ideal behavior with a slope of 0.50. Figure 2. Permeabilities as a function of XAu at 423, 473, 523, and 573 K all with pup = 101.3 kPa.
pup = 101.3 kPa at T g 473 K. These findings are close to the predictions of the calculated results of Sonwane et al. shown in their Figure 7(c).1 The maximum in H permeabilities for PdAg alloy membranes found earlier in this laboratory that lies close to XAg = 0.239 is also in agreement with the predictions.1 There is little difference in the permeabilities of the PdAg alloys at the various temperatures, 423, 473, and 523 K,9 whereas there is a steady increase of the permeabilities with temperature for the PdAu alloys (Figures 1 and 2). The permeabilities found here at the maxima are slightly smaller for the PdAu alloys than those for the PdAg alloy with the maximum permeability, XAg = 0.23. Plots of permeability, P, or flux against (pnup pndown) are frequently made where n is determined by trial and error,24 where pup and pdown refer to the upstream and downstream sides of the membrane. In the case where pdown = 0, plots of ln P against ln pup give n from the slope; instead of P, the flux, J, at a constant d can be employed for such plots to determine n. In the case of ideal solubility when Sieverts’ law is followed,23 n = 0.5. It can be shown25 using eqs 4 and 7 that an approximate value of n is given by ! ! D ln FðrÞ D ln r 0:5 n¼ ð12Þ r 1 D ln p D ln p 1 þ ðβ þ g 1 =RTÞ 2
The values of β1 and g1/RT cancel to some extent in eq 12; i.e., the more negative the latter, the more positive the former (Table 1). Since β is usually small compared to g1/RT, a further approximation is to omit β1, simplifying eq 12 to ! ! D ln Fðr D ln r 0:5 ð13Þ n¼ D ln p D ln p 1 þ ðg 1 r=2RTÞ which has the advantage that n does not depend on β which may not be known precisely. Pressure Exponents for the Dependence of Flux on pup. A plot is shown in Figure 3 at 473 K of ln P against ln pup with pdown = 0 for the XAu = 0.19 alloy. The slope is n = 0.546 which is greater than the ideal slope of 0.50 and indicating nonideality in the H solution. Using the value of g1 determined from thermodynamics of 28.0 kJ/mol H9 in eq 12, we obtain n = 0.53 as an average value over the interval of rup values employed for Figure 3 which is close to the experimental value. In an earlier paper concerning the thermodynamics of the PdAuH system,19 it was shown for the XAu = 0.21 alloy that g1 values, derived from the slopes of plots of RT ln((β r)/r) against r from a rearranged form of eq 5, depend, as might be expected, on the value of β chosen. Results are summarized in Table 1 where the g1 values become increasingly negative as the value of β chosen decreases. More detailed analyses are carried out here for the XAu = 0.12 and 0.21 alloys. H2 isotherms for the XAu = 0.12 alloy were 11620
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Table 2. E*D and D°H* for Diffusion Through PdAu Alloys , * Is in Units of kJ/mol and D°H* and (393 to 523 K) Where ED DH at 473 K Are in Units of cm2/s ,
XAu
DH * (473 K)
ED *
D°H*
0.00
11.6 106
23.7 ( 0.2
4.8 103
21.3
3.1 103
22.5
4.1 103
21.3
2.7 103
0.09 0.12 0.19
6
13.8 10
6
13.2 10
6
12.1 10
0.21 0.265
10.1 10 7.28 106
21.9 22.6
2.6 103 2.3 103
0.30
3.46 106
26.8
3.3 103
35.2
9.9 103
0.35
6
,
6
1.29 10
Figure 5. Plot of ED * as a function of XAu.
Figure 4. Diffusion constants at infinite dilution of H, D*H, for PdAu and PdAg9 alloys as a function of XM at 473 K.
employed for plots of RT ln((β r)/r) against r with β chosen as 1.0, 0.46, and 0.54 where 0.46 is the fraction of Pd-rich interstices and β = 0.54 is obtained from the partial entropy of solution.19 The different β values all give quite linear plots for this alloy with the derived g1 values shown in Table 1, and similarly, linear plots were found for the XAu = 0.21 alloy using different values of β.19 The g1 values are more similar to each other for the XAu = 0.12 alloy than for the 0.21 alloy (Table 1), and the n values are all about the same and within error of the experimental values. This illustrates that for the PdAu alloys with XAu e 0.12 it does not seem necessary to know β in order to calculate n. Diffusion Parameters at Infinite Dilution of H. Diffusion constants were measured as a function of r and extrapolated to r = 0 to obtain concentration-independent constants, D*H, and the results are shown in Table 2 and Figure 4 at 473 K. The diffusion constants increase slightly with XAu at small XAu values, and start to decrease at XAu ≈ 0.20, and then decrease more sharply at XAu g 0.25 (Figure 4). This is in agreement with previous studies * relative to Pd at small Au except for the small increase of DH contents (Figure 4). Figure 4 also shows data for PdAg alloys,9 and the D*H values for the PdAu alloys are seen to fall off more sharply than those for the PdAg alloys. ° from the Plots of ln DH against 1/T give values of ED and DH ° expED/RT. If the ln DH * values are Arrhenius equation, DH = DH plotted against 1/T, the, corresponding values at infinite dilution are obtained, E*D and D°H*. E*D values are shown in Figure 5 where they can be seen to decrease to values below that of Pd at small * at small XAu and then increase for XAu > 0.265. The increased DH XAu (Figure 4) is reflected by smaller values of E*D (Figure 5). In a
recent study of H diffusion in PdAg alloys,9 there was also a * decreases to below the region at small XAg contents where ED value for Pd; however, the decrease is not as pronounced as for the PdAu alloys shown here, and this may be related to the observation from M€ossbauer studies of Wagner and coworkers26 that Au in Pd is “very repulsive to H which cannot penetrate to their nearest neighbor sites”. , D°H* values are nearly constant (Table 2) except for an , apparent increase at XAu = 0.35. It should be noted that D°H* values appear to be generally of the order of 103cm2/s for Pd and its alloys21 so that the values found here (Table 1) appear to be reasonable. Since the D°H values are obtained from ED and there is more error in DH ° from a DH value at a given temperature, , *. than in ED and thus more in D°H* than in ED , In their review, Wicke and Brodowsky21 report D°H* values for PdAg alloys which decrease steadily with XAg; however, their review also gives pre-exponential values at infinite dilution for these alloys for D and T isotopes where the decrease is insignificant and thus the results are inconsistent. Holleck4 found a steady decrease, i.e., from 2.9 103 cm2/s for Pd to 1.82 103 cm2/s for the Pd 0.50Ag0.50 alloy (533913 K). This is a , smaller decrease in D°H* than reported by Wicke and Brodowsky. In an earlier ,study of H diffusion in PdAg alloys by the present very much with XAg. Although the authors,9 D°H* did not change , detailed variation of D°H* with the fraction of substitutional metal in Pd is not well-established, it seems that any trends with XM do not appear to be very large. Salomons et al.6 have proposed a model for H diffusion in alloys which they applied to the fcc PdCu and PdY alloys. At infinite dilution where the H atoms occupy the energetically most stable sites, e.g., octahedral sites with only Pd nearest , neighbors, Pd6 sites, their model6 predicts that D°H* = nνa2o, where n is a geometric factor, ao the lattice constant, and ν the attempt frequency. The lattice constant, ao, increases with Au content, but the effect is relatively small, e.g., from Pd to the XAu = 0.30 by only 3% which is well within experimental alloy a2o increases , , error of the D°H* values (Table 2). Since the D°H* values do not change very much, it seems that the assumption of Salomons et al.6 that ν is independent of XAu is reasonable and that β is not a factor. Dependence of Diffusion Parameters on H Concentration. Fick’s diffusion constants, DH, depend on r, 3,18,21 and such a dependence is illustrated in Figure 6 for the PdAu alloys at 473 K plotted as ln DH vs rup. It is useful to remember that the average r from the upstream to downstream sides of the membrane, where rdown = 0 for the latter, is ≈rup/2. It can be seen that the slope, (d ln DH/dr), is most negative for Pd and remains negative to 11621
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Table 3. β and g1 (in kJ/mol H) Values at 473 K for PdAu Alloys (393 to 523 K)a XAu
β
g1 (thermo.)
g1 (RT ln DHr plot slopes)
0.00 0.09 0.12
1.0
33.8
34.3
0.68 0.54
30.6 32.6
27.5 28.8
0.19
0.40
28.0
17.9
0.21
0.29
29.4
17.6
0.265
0.24
20.8
9.9
0.30
0.156
19.5
þ1.8
β is determined from the entropy25as explained in the text, and g1 is affected by the choice of β. a
Figure 6. Plot of ln DH as a function of H content for PdAu alloys (473 K).
Table 4. ED and D°H as a Function of r for Diffusion Through PdAu Alloy Membranes (393523 K) ED (kJ/mol H) XAu 0
r = 0.010
0.015
XAu = 0.265 where it becomes ≈0 and then becomes positive for the XAu = 0.30 alloy. The dependence of RT ln DH on rup at different temperatures is shown for two representative PdAu alloys, XAu = 0.12 and 0.21, in Figures 7 and 8, respectively. There is a clear trend for the slopes to become more negative with decrease of temperature which is in agreement with eq 9 or 12. According to eq 11 the slopes are given approximately by g1/2RT and using β values evaluated , from thermodynamics19 and the assumption that ΔS°H* for the alloys should be the same as that for Pd if the appropriate values of β are employed. g1 values have been calculated (Table 3).
0.025
0.030 -
24.01
24.13
24.2
-
0.09
-
21.92
21.90
22.01
-
0.12
-
22.52
22.56
22.62
22.71
0.19 0.21
-
21.51 22.04
21.56 22.08
21.61 22.17
21.68 22.20
0.265
-
22.46
22.54
22.59
22.62
0.30
-
26.95
26.76
26.64
26.69
0.35
-
-
35.2
-
-
Figure 7. RT ln DH plotted against rup for the XAu = 0.12 alloy at a series of temperatures.
Figure 8. ln DH plotted against rup for the XAu = 0.21 alloy at a series of temperatures.
0.020
D°H 103 (cm2/s)
0
-
-
-
-
0.09
-
3.50
3.44
3.48
-
0.12 0.188
-
3.92 2.80
3.92 2.83
3.94 2.85
3.99 2.88
0.21
-
2.73
2.74
2.79
2.81
0.265
-
2.20
2.25
2.30
2.33
0.30
-
3.56
3.49
3.45
3.55
The agreement of the g1 values evaluated from thermodynamics and from the plots of ln DH vs r is reasonably good for alloys with small values of XAu but poor for those with XAu g0.19 (Table 3). One problem is that the slopes (Figures 7 and 8) are not very accurate for the higher content alloys because of the small range of r employed, but there may be some additional factor which enters into the determination of the slopes for these alloys. Equation 3 can be employed to obtain D*H from DH, i.e., by integration using experimental values of f(r) to obtain F(r). For a * are representative alloy, XAu = 0.19, and the values of DH somewhat greater at 423 and 473 K than the values obtained by extrapolation to r = 0 (Table 2). For example, the values at 423 and 473 K from extrapolation are 6.3 10 and 12.1 106 cm2/s, respectively, and the average values from integration of eq 1 are 6.7 106 and 12.5 106 cm2/s. The values from eq 9 are similar to those from integration of eq 3. The values from integration of eq 3 or from eq 9 increase with r by about 3% (473 K) from r = 0.01 to 0.04 and about 4% (423 K) from r = 0.015 to 0.05. 11622
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The Journal of Physical Chemistry C With regard to H diffusion in PdAg alloys9 the H contents attained were much greater than for the present alloys, and * can be calculated from DH therefore the range over which DH using eq 1 is much larger and the relative constancy of the former was reasonably good and in good agreement with the value obtained by extrapolation of DH to r = 0. ° values as a function of r from 0 to Table 4 shows ED and DH about 0.03. It can be seen that ED increases with r for the lower Au content alloys, and then for the XAu = 0.30 alloy ED decreases ° with r. An increase of ED with r. There are no clear trends of DH with r is also found for the PdAg alloys up to XAg = 0.23, but for those alloys it appears that D°H decreases somewhat with r.9
’ CONCLUSIONS Permeabilities have been measured for a series of PdAu alloys in the temperature range from 393 to 573 K, and the maximum permeability occurs at XAu = 0.100.12 which agrees with the theoretically predicted maximum in permeability.1 Diffusion constants and activation energies increase and decrease, respectively, with XAu at quite small values of XAu. Although it is not seen in Figure 4, there is an extended horizontal region in the plot of D*H against XAu, and for the PdAg alloys, * at the data of Z€uchner5 at 303 K clearly show a maximum in DH about XAg = 0.10. This may be a characteristic of expanded Pd alloys, i.e., those which expand upon alloying. Contracted alloys do not appear to show the same phenomenon, although there is not much data available for these. DH values have also been determined as a function of H content. For alloys with XAu e 0.265, DH values decrease in magnitude with increase of r. This is consistent with the observation that ED increases for alloys with XAu e 0.265.
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(17) Chowdhury, M.; Ross, D. Solid State Commun. 1973, 13, 229. (18) Wang, D.; Flanagan, T.; Shanahan, K. J. Membr. Sci. 2005, 253, 165. (19) Luo, S.; Wang, D.; Flanagan, T. J. Phys. Chem. B 2010, 114, 6117. (20) Yukawa, H.; Morinaga, M.; Nambu, T.; Matsumoto, Y. Mater. Sci. Forum 2010, 654656, 2827. (21) Wicke, E.; Brodowsky, H. Hydrogen in Metals, II; Alefeld, G., V€olkl, J., Eds.; Springer-Verlag: Berlin, 1978. (22) Flanagan, T.; Wang, E.; Shanahan, K. J. Membr. Sci. 2007, 306, 66. (23) Flanagan, T.; Oates, W. Annu. Rev. Mater. Sci. 1991, 21, 269. (24) Morreale, B.; Ciocco, M.; Enick, R.; Howard, B.; Cugini, A.; Rothenberger, K. J. Membr. Sci. 2003, 212, 87. (25) Flanagan, T.; Wang, D. J. Phys. Chem. C 2010, 114, 14482. (26) Karger, M.; Pr€obst, F.; Sch€uttler, B.; Wagner, F. Metal-Hydrogen Systems; Veziroglu, T., Ed.; Pergamon Press: Oxford, 1982; p 187.
’ ACKNOWLEDGMENT The authors are indebted to Dr. Kirk Shanahan of Savannah River National Laboratory for help and encouragement of our research on H diffusion. ’ REFERENCES (1) Sonwane, C.; Wilcox, J.; Ma, Y. J. Chem. Phys. 2006, 125, 184714. (2) K€ussner, A. Naturforschung 1966, 21A, 515. (3) G. Bohmholdt, G.; Wicke, E. Z. Phys. Chem. 1967, 56, 133. (4) Holleck, G. J. Phys. Chem. 1970, 74, 503. (5) Z€uchner, H. Z. Naturforsch. 1970, 25A, 1490. (6) Salomons, E.; Ljungblad, U.; Griessen Diffus. Defect Forum 1989, 6669, 327. (7) Opara, L.; Klein, B.; Z€uchner, H. J. Alloys Compd. 1997, 253254, 378. (8) Serra, E.; Kemali, M.; Perujo, A.; Ross, D. Metall. Mater. Trans. A 1998, 29A, 1023. (9) Wang, D.; Flanagan, T.; Shanahan, K. J. Phys. Chem. B 2008, 112, 1135. (10) McKinley, D. Metal alloys for hydrogen separation and purification, US Patent 3,350,845, 1967. (11) Coulter, K.; Way, J.; Gade, S.; Chaudhari, S.; Sholl, D.; SemidyFlecha, L. J. Phys. Chem.C 2010, 114, 17173. (12) Chen, C.-H.; Ma, Y. J. Membr. Sci. 2010, 362, 535. (13) Maestas, S.; Flanagan, T. J. Phys. Chem. 1973, 77, 850. (14) Sakamoto, Y.; Hirata, S.; Nishikawa, H. J. Less-Common Mets. 1982, 88, 387. (15) Yoshihara, M.; McLellan, R. acta metall. 1982, 30, 251. (16) Gade, S.; Payzant, E.; Park, H.; Thoen, P.; Way, J. J. Membr. Sci. 2006, 340, 227. 11623
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