2804
D. A r t m a n and Ted B. F l a n a g a n
iffusion of Hydrogen in Rhodium-Palladium Alloys D. Artman and Ted 6 . Flanagan* Chemistry Department. University of Vermont. Burlington, Vermont 05401 (Received April 20. 1973)
Diffusion constants have been determined for interstitial hydrogen in a series of random face-centered cubic rhodium-palladium alloys. Diffusion parameters were determined at small hydrogen contents where they are independent of hydrogen concentration. In contrast to data for gold- and silver-palladium alloys, the presence of small amounts of rhodium leads to a decrease in the diffusion constants. This decrease arises from an increase in the energy of activation for the diffusion of interslitial hydrogen in the alloys.
Introduction This investigation represents a continuation of studies of how substitutional metals affect the diffusion constants of interstitial hydrogen in substitutional face-centered cubic (fcc) palladium alloys. The Ag-Pd1-5 and Au-Pd6 systems have been studied. The diffusion constants measured a t H-to-metal, atomic ratio, n 0, show similar trends with substituted noble metal contents. The diffusion constants remain nearly invariant with substituted metal content to about 20 atom '7'0 and then they decline approximately logarithmically 'as a function of substituted metal content to the limit of the investigations, z.e., approximately 60 atom % added metal. The closely logarithmic relationship cannot be obeyed over the whole range of contents because in both alloy systems the diffusion constants increase at the limit of pure noble metal. These two noble metal-palladium alloy systems are similar. Both metals add s electrons to the collective d hand of palladium7 and they both increase the lattice parameter of the palladium host l a t t i ~ e . There ~ , ~ have been no published accounts of how the diffusion constant of palladium is affected by substituting metals which themselves have holes in their d bands and which decrease the lattice parameter of the host palladium lattice. The Rh-Pd alloy system falls into this category and because of recent interest in the Rh-Pd-Hz systeml0J1 it was selected for study. It was found that rhodium behaves as an absorber of hydrogen a t high pressure of gaseous hydrogen when situated within the palladium 1attice.lOJl Various macroscopic techniques have been employed for the determination of the diffusion constants of hydrogen in palladium and its al1oys.l 6,12-15 The selection of an appropriate technique depends upon the magnitudes of the diffusion constants to he expected and the solubilities of hydrogen in the alloys. In general, the electrochemical techniques2,6,12-16 at their present stage of development are best suited for the temperature range from 0 to 100" and for those alloys which dissolve appreciable amounts of hydrogen. Gas-phase techniques are more widely applicable but suffer more readily from surface poisoning in the low-temperature range. In this study both techniques have been employed. The electrochemical breakthrough techn i q ~ e ~ has , ~ been ~ J ~employed for alloys of low rhodium content and the gas-phase technique4 has been used over the entire range of alloys available.
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Experimental Section Apparatus. The electrochemical technique employed was that of Kussnerl5 as modified by Maestas and FlanaThe Journalof Physicai Chemistry, Vol. 77, No. 23, 1973
g m 6 This technique involves electrochemically altering the hydrogen content of one face of a membrane and noting the time required for this perturbation to penetrate to the other side. It was found that this technique did not work well for Rh-Pd alloys with rhodium contents greater than about 10% because of the combination of difficulties in surface activation and low hydrogen solubilities. A gasphase method similar to that employed by Holleck4 was therefore employed. The membrane sample is mounted to separate two sides of a vacuum apparatus. Both sides are evacuated and then the appearance of Hz is monitored on the other side (diffusion side). The pressure was measured on both sides of the membrane with Pirani gauges (LKB, AutoVac, Type 3294B). These were frequently calibrated against a McLeod gauge. The output of the Pirani gauge on the diffusion side of the membrane was recorded with a strip chart recorder (Moseley, Model 7101B) during a diffusion run. The volume of the entry side was large (-15 1.) so that the pressure on this side remained essentially constant during the run. Gold foil protected the membrane from contamination by mercury. The membrane samples (2.5 cm diameter) were placed between two stainless steel flanges each of which had circular ridges which deformed the membrane in order to make a vacuum tight seal. This seal was the most likely source of leaks and the vacuum had to be carefully tested after mounting a fresh sample. A thermocouple was affixed to the flanges which held the sample. The sample and connecting tubing were sealed to Pyrex L ' I ~ a kovar seal. Each side of the connecting tubing contained a flexible bellows tube so that some flexibility was present. The sample and connecting tubing were inserted into an air furnace which was controlled to Jt0.2". The temperature range investigated was 10-270". Materials. Hydrogen was introduced into the apparatus by a sample of palladium which had been filled with hydrogen by electrolysis and then transferred to the apparatus, evacuated, and then heated to release its H2. The Rh-Pd alloy samples were obtained from Engelhard Industries, Inc. Their thicknesses were carefully determined with a high-quality micrometer gauge and they were generally 0.01 f 0.001 cm. It has been shown previously that these alloys have the expected lattice spacings and they are nonsegregated substitutional fcc alloys.8 Sample Preparation. The samples were roughened with very fine emery cloth, briefly immersed in concentrated nitric acid, and then cleaned anodically in sulfuric acid until fine bubbles formed uniformly over the entire surface. The samples were then charged cathodically with
Diffusion of Hydrogen in Rhodium-Palladium Alloys
hydrogen for 1-6 hr. The fully charged alloys were then rinsed in distilled water and immersed in a stirred solution of PdC12(1%). The absorbed hydrogen reduced a thin layer of palladium black onto the membrane surface. The Rh(30%)Pd and Rh(4OYo)Pd alloys were made cathodic (25 mA) during this plating (0.5 to 5 min) since they absorbed only small amounts of hydrogen during electrolysis. The coated samples were rinsed and stored in water prior to mounting. The samples were mounted wet and then the system was quickly evacuated in order to avoid contact of the dry surface with oxygen. Method. In the gas-phase method the sample was thoroughly evacuated prior to a run so that the initial concentration of hydrogen was zero, co = 0. Hz was introduced to the entry side of the membrane at a constant pressure at values from 0.1 to 90 mm. Generally, however, the pressure was 2 to 5 mm. The exact time of initiation of a run was automatically indicated by a blip on the recording tracing. This method differed from that employed by Holleck4 because he evacuated continuously through a capillary on the diffusion side until a steady-state pressure was attained. In the method employed here Hz accumulated on the diffusion side. All Pirani readings were converted to pressures uia a calibration curve. The time lag was determined by extrapolation of the linear region of the pressure increase (steady-state permeation rate) to the time axis. The intercept gives the time lag, t L . 4 , 1 2 If co is zero, and if the pressures on the diffusion side are negligible compared to the entry side. then D = s2/6tL (1) The pressure difference between the two sides was large, lo2 to lo3. Alternatively the time lag can be evaluated from the time at which the permeation rate is 0.6299 times its steady-state value.12 Either procedure gave closely similar values of tL. Time lags ranged from several seconds to about 1000 sec for the various alloys. Diffusion constants can also be evaluated from the time behavior during the approach to the steady-state permeation rate. The slope of plots of In ( J , - J t ) / J . against t give as the slope l / t o , where t o is the rise time12 and Jt and J , are fixed at time t and at infinite time, respectively. The relationship between to and D is If Jt is plotted against t, the intercept of the extrapolation of J t to the time axis gives as the intercept tb, the breakthrough time which is related to by t b = s2/15.3D (3) Values of t b can also be obtained from the time a t which gas first appears on the diffusion side. In practice, the most convenient measurement of D was cia t L and data were determined from this diffusion parameter. Details of the electrochemical method are given elsewhere.6 Diffusion constants were determined from the electrochemical breakthrough time.
This differs somewhat from eq 3 because in the electrochemical method the concentration at the diffusion surface is monitored rather than the total gas ev01ved.l~
Results In order to check the experimental apparatus and the method, diffusion constants were determined for a sample
2805 TABLE I: Values of D Corrected for Nonzero Concentrations 01 Hydrogen at the Diffusion Side (Ag(24%)-Pd, 245') P, m y (entry side)
0.3 0.4 2.3 2.7 3.0 4.5
13,cm2 s e c - ' (eq 1)
0.86 X 0.96 1.26 1.17 1.19
1.26
D,cm2 s e c - ' (eq 6) 1.42 1.49
x
10-5
1.54 1.39 1.41 1.44
whose diffusion behavior is well established, Ag(24%)Pd. Using values determined from the time lag a diffusion constant of 1.4 & 0.2 X 10P6 cm2 sec-I (100') was obtained compared to values in the literature of 1.4 X 10W6 and 1.21 x at the same t e m p e r a t ~ r e . ~ ? ~ Diffusion constants were determined for the Rh(5%)-Pd and Rh( 10%)-Pd alloys with the electrochemical breakthrough technique using eq 4 with samples of the same composition and thickness as used in the gas-phase method, D(25") = 5.9 X (electrochemical) and 7.0 x (gas phase) cmz sec-l for the Rh(lO%)-Pd and D(25") = 16.6 x (electrochemical) and 13.5 X (gas phase) cmz sec-l for the Rh(5%)-Pd. The agreement is not perfect but good enough to indicate the general validity of this gas-phase method. A pressure dependence was noted in the values of tL obtained, i.e., they were shorter at higher pressures. Holleck4 noted such a dependence of t L on pressure and he corrected for this dependence with17
where c2 is the concentration of hydrogen at x = 0, the diffusion side of the membrane, and c1 is the concentration at x = s, the entry side. Equation 5 allows for a nonzero concentration of hydrogen at the diffusion side in only an approximate way because the concentration on the diffusion side changes continually with time in both the present method and in Holleck's until the steady state is attained. Siererts' law18 should be applicable at these low H concentrations, i.e., cap1/2. The proportionality constant is the same for a given alloy, therefore, eq 5 can be given in terms of pressure
Holleck employed the final value for p 2 whereas the average value up to the development of the steady state is employed here. Both approaches are only approximate because pz is a function of t. Generally the average value of pressure on the diffusion side of the membrane was 0.01 mm. Typical values of F ( p ) are then 1.67 (at p1 = 0.3 mm), 1.22 (at p1 = 2.0 mm), and 1.14 (at p1 = 5.0 mm). Some values of D corrected in this way are shown in Table I. It can be seen that the correction appears to give constant values of D to within experimental error. Between about 2 and 5 mm the uncorrected diffusion constants are nearly invariant and approximately 18% smaller than the corrected values. Most data have been obtained in this pressure range because smaller pressures require larger corrections and larger pressures are somewhat inconvenient for routine measurements. Data have been corrected The Journal of Physical Chemistry, Vol. 77, No. 23, 7973
2806
D.Artman and Ted IO-^
I
I
1
Flanagan
4
I
I
B.
3
t
c
\
'A
I
tL
R h ( 4 0%) 1 6
20
2 4
2 8
32
36
$ 0
0
l / T x I Os Figure 7 .
TABLE I L : Diffusion Parameters for ilnterstitial Hydrogen ( n + 0) in a Series of fcc ~ ~ o d i u m - ~ a l S l au ~ d §~~~i i~u ~ ~Alloys onal
Pd R h (5%)--Pd Rh(lO%-Pd R h (1 0%)-Pd" Rh(ZO%)-Pd
Rh(30%)-Pd Rh (40%)-Pd
DOX 103,cm','sec 5,25
5.8 f 2.0 x
L.. I 40
d 60
% s u b s t i t u t i o n a l metal
Arrhenius plots of log D against 1 /Tat n -* 0.
Alioy
i
20
10-3
E.5 l0.4 8.0 (6.6)" 5.2
E,, kcal/rnol
5.76 6.3 rt 0.3
6.7 6.8
7.7 (8.%)O
10.4
Electrochemically determined f1 Dotaken as the average value of the Rh120%)- and Rh(40%)-Pd alloys and Ea calculated from the msasured, most reproducible, value of D (92")
by a factor of 1.18 for the pressure buildup on the diffusion side of the membrane. Runs were made over a 20-fold pressure change for the Rh(lO%-Pd alloy, 3 to 90 mm (95").Values of D were approximately 2070 greater for this alloy a t 90 mm than at 3 mm even after the correction uia eq 6 was applied. No explanation is offered for this behavior. Values of t b were generally too large compared to t1.g this may have been due to the sensitivity of the Pirani gauge in the very low-pressure range. It was not related to problems due to possible slow surface steps because the same behavior was noted for both very long and very short diffusion times measured a t the same temperature and pressure for different alloy compositions. Values of t o : on the other hand, were too small compared to tI,. (Tnterestingly, despite the discrepancy, to I- t b still was equal to t,,.) This inconsistency of the values of t o , t b , and t~ leads to the result that values of L) evaluated uia t b or to were about 15--2070smaller or 1 5 2 0 % larger, respectively, . based on t~ are bethan those obtained from t ~ Results lieved t.o give correct values of D and they are the ones reported heie. These agree with the literature values for the Ag( 2470)-Pd and the electrochemical results obtained here The Journai o f Physical Chemistry, Voi. T7, No. 23, 1973
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Comparison of D values for interstitial hydrogen at n a series of Au-Pd6 and Ag-Pd5 alloys with data for Rh-Pd alloys: 0, Rh-Pd (25"); A , Ag-Pd (25"); 0 , Au-Pd
Figure 2. 0 for
(37").
for the 5 and 10% rhodium samples agree with the gasphase measurements based on the time-lag evaluation of the diffusion constants. In addit.ion, time lags can be more accurately evaluated than t o and t b which require obtaining values of J t from the slopes of the p-t plots. Diffusion constants were determined uin tl. values for the Rh-Pd alloys and are shown in Table I1 and Figure 1 expressed as D -. Do exp(--E,/RT). These ail refer t o conditions of n. 0. In Figure 2 these data are compared with those of other alloys.4-6 A marked contrast in behavior can be seen with the alloys in which the substituted metal is to the right of palladium in the periodic table. The decline in values of D is caused by the increase in energy of activation for mobility of the interstitial hydrogen.
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Discussion
In contrast t o the Au-Pdlg and Ag-PdzO systems, substitution of rhodium for palladium results in a greater endothermicity for solution of Hza t small hydrogen contents.z1,z2 This presumably arises from the decrease in size of the interstitial site and the smaller compressibility of rhodium as compared to pure palladium.21 The decrease in values of D cannot be explained simply by the decrease in size of the interstitial site because a decrease in D is also observed in the other type of alloy and in that case the interstitial site increases in size with added metal. Beck and coworkersz3 have carried out electrochemical diffusion constant determinations for a series of Fe-Ni alloys over a limited temperature range. In the composition range from 40 wt 70nickel to pure nickel fcc substitutional alloys are formed in this alloy system. The diffusion constant increases slightly as the percentage of nickel increases from 40 to 100% (27"). The energy of activation declines slightly with nickel content over the same composition range.z3 They have assigned the principal varia-
D i f f u s i o n of H y d r o g e n i n R h o d i u m - P a l l a d i u m Alloys
tion in D to changes in E , as was observed in the present research. Changes of E , are, on the other hand, attributed to corresponding changes of the heat of solution of H2 with alloy composition, i.e.
Dalloq= DN,exp(-A[AH,]/2RT) (7) the factor l/2 arises from a symmetry factorz3 and A[AH,] is the change in the heat of solution of H2. This interpretation of interstitial diffusion in fcc alloys cannot be generally valid, however, because such a linear correlation does not exist for palladium alloys. A[AH,] changes in different directions for Rh-Pd alloys and the Ag-Pd and Au-Pd alloys. It is not clear why the top of the energy barrier should remain nearly unaltered by alloying as implied by eq I . It must be concluded that there is at present no adequate theory to account for the behavior of the diffusion constants of interstitial hydrogen with substitutional metals in fcc palladium matrices. It is hoped that a theory along the lines of the Flynn-Stoneham theory24 for pure metals will be extended to fcc alloys. Acknowledgments. We thank Miss Geraldine Gross for helpful discussions. References and Notes ( 1 ) G. Bohmholdt and E. Wicke, Z. Phys. Chem. (Frankfurt am Main), 56, 133 (1967).
2807 ( 2 ) G. Holleck and E. Wicke, Z. Phys. Chem. (Frankfurt am Main), 56, 155 (1967).
(3) D. N. Jewett and A. C. Makrides, Trans. Faraday SOC.. 61, 932 (1965). (4) G. L. Holleck. 3. Phys. Chem.. 74, 503 (1970). ( 5 ) H. Zuchner. Z.Naturforsch. A . 25, 1490 (1970). (6) S. Maestas andT. B. Flanagan, J. Phys. Chem.. 77, 850 (1973). (7) N. F. Mott and H. Jones, "Theory of the Properties of Metals and Alloys," Oxford University Press, London, 1936. (8) B. R. Coles, J. Inst. Metals. 84,346 (1956). (9) A. Maeland and T. B. Flanagan, Can.
