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in Pd(111)
Surfade Science 90 (1979) 162-180 0 North-Holland Publishing Company
A MOLECULAR-BEAM ADSORPTION
INVESTIGATION.OF
AND ABSORPTION
THE SCAITERING,
OF H, AND D, FROM/ON/IN
Pd( 111)
T. ENGEL * and H. KUIPERS Institut fiir Physikalische Chemie der Universitrit Miinchen, Sophienstrasse Miinchen 2, W. Germany
II, D-8000
Received 23 March 1979; manuscript received in final form 5 June 1979
H2 and D2 are scattered from clean Pd(ll1) and a saturated chemisorption layer in a highly specular distribution. Evidence for an ordering of the adlayer with increasing coverage is seen. The hydrogen-deuterium exchange occurs via a Langmuir-Hinshelwood mechanism, and the temperature dependence of the rate of HD production can be understood without assuming an activation energy for equilibration. Lock-in and wave-form analyses of scattered Hz + D2 mixed beams show that equilibrium between adsorbed hydrogen and deuterium and that dissolved just below the surface is reached rapidly at temperatures above 300 K.
1. Introduction
The absorption of hydrogen and deuterium in palladium have been studied extensively [l-3] due to their technological importance. However, the difficulty in determining reproducible rates of permeation through Pd membranes at low pressures led to the knowledge that surface contamination has a marked effect on the rate of solution of H, in palladium [4,5]. A number of investigations of the chemisorption layer has been reported [6-91 but most of these were hampered by the difficulty in separating surface and volume effects. The molecular beam method is ideally suited for such an investigation since volume diffusion can easily be separated from adsorption-desorption which takes place only in the adlayer [lo]. Furthermore, by choosing a suitable modulation frequency, only the uppermost low3 mm of the sample contribute to the signal detected, such that surface and near-surface palladium can be separated from deep bulk palladium without having to work with thin wires. Molecular adsorption, dissociative chemisorption and solution of Ha and D2 formed the subject of this study. Molecular adsorption was investigated using the angular distribution of scattered H2 and D2. Chemisorption was investigated with the hydrogen-deuterium exchange reaction, and the degree to which equilibrium is achieved between chemisorbed and dissolved hydrogen was investigated using modulated molecular beam techniques. * Present address: IBM Zurich Research Laboratory, CH-8803 Riischlikon, Switzerland. 162
T. Engel, H. Kuipers /Scattering of H2 and D2 from Pd(1 I I)
163
2. Experimental The apparatus used in this study has been described elsewhere [ 111. Briefly, it consists of separate bakeable molecular beam and experimental subsystems which are connected with a straight-through valve. The nozzle beam system is threestage differentially pumped with liquid nitrogen baffled oil diffusion pumps. The 18 inch experimental chamber in which the Pd(ll1) sample is mounted contains a retarding field analyzer for LEED and AES, and an ion bombardment gun for cleaning purposes which are used to establish and check the surface cleanliness and order. The beam can be mechanically chopped after entering the experimental chamber with a four-bladed wheel magnetically coupled to a motor outside the vacuum system. The scattered beam is detected by a quadrupole mass spectrometer rotatable in the scattermg plane. The angular resolution can be varied between 1’ and 5” by varying the beam diameter between 1 and 5 mm. A high pumping speed was maintained by evaporating titanium onto a liquid nitrogen cooled cryopanel at the height of the scattering plane. With the beam on at an intensity equivalent to a pressure of 5 X lo-’ Torr, the total pressure remained below 1 X lo-” Torr.
3. Results 3.1. Scattering of Hz and 02 from Pd(ll1) Fig. 1 shows the angular scattering distribution of Hz from a Pd(ll1) surface at 250 K. At this substrate temperature and with the beam intensity used, the hydrogen coverage is approximately 6 = 0.9. The appearance of a sharp specular peak with Z/Z0 = 0.16 indicates a high degree of order in the adlayer. The fraction of total
\
\
\
\
I
I
/
/
Fig. 1. Angular distribution in polar coordinates for Hz scattered from the 250 K surface; 0i = 45”. The maximum intensity corresponds to I/IO = 0.16. The arrow designates the direction of the incoming beam.
164
T. Engel, H. Kuipers /Scattering
of Hz and D2 from Pd(1 I I)
intensity seen at the specular angle is approximately one-third of that observed for He scattering from the same sample [ 1 I]. Moreover, the specularity of Ha scattering from a hydrogen covered surface is greater than that of the clean surface, as seen in fig. 2. Initial adsorption of Ha causes a sharp decrease in the intensity at the specular angle to a value approximately one-third of the value for the clean surface. Further adsorption of Ha increases the intensity to a value whichis approximately twice that of the clean surface. This behavior is consistent with a disordered adlayer at low coverages which becomes ordered at higher coverages due to interactions within the adlayer. A similar effect is seen in the temperature dependence of the intensity at the specular angle under steady state conditions which are shown for Ha and Da in fig. 3. An increase in the substrate temperature which is coupled to a decrease in the surface coverage leads to a minimum in the intensity versus temperature curve for Ha scattering. A further increase in temperature decreases the coverage leading to a subsequent increase in the scattered intensity. The scattering behaviour for Ha and Da is quite similar to what is seen in fig. 3. However, the specular intensity for Da scattering is lower than that for Ha scattering by approximately a factor of 2, due to the higher mass of Da which makes inelastic scattering events with the surface more probable. An increase in the substrate temperature decreases the specular intensity drastically at the expense of more lobular scattering as shown in fig. 4 for Ha scattering from Pd(ll1). The angular distributions were measured by modulating the beam at 63 set-‘. As will be shown in section 3.2, the relaxation time associated with dissociation and recombination of H and D atoms is so long at the substrate temperatures of fig. 4 that it can be concluded that the broad angular distributions result from molecular scattering only. Since 19 decrease from 0.9 to 0.4 between
0
I
50
100
150 TIMEI s I
200
250
Fig. 2. H2 scattering intensity at the specular angle as a function of time for a beam intensity equivalent to -5 X lo-’ Torr, 0i = 45’.
T. Engel, H. Kuipers /Scattering of Hz and II2 from Pd(ll I)
250
300
165
350 TEMPERATURE%
Fig. 3. Hz and D2 scattering intensity at the specular angle as a function of substrate temperatUIe;Bi=45”,w=189sec-l.
Fig. 4. Angular distribution for H2 scattering for various substrate temperatures set-l. The arrow designates the direction of the incoming beam.
for w = 63
166
T. Engel, H. Kuipers /Scattering
of H2 and D2 from Pd(l1 I)
250 and 300 K, the decreased specularity seen in fig. 4 is quite likely due to a disordering of the adlayer with decreasing coverage. 3.2. Hydrogen-deuterium
exchange on Pd( I I I)
In order to investigate scattering which involves atoms in the chemisorbed layer, a distinction must be made at the detector between molecules which scatter, without losing their molecular identity, and those which have dissociated and recombined before desorption. This is mostly easily done by impinging a mixture of H2 and Da onto the surface. Any HD formed must then result from a surface recombination since an Eley-Rideal mechanism can be ruled out, as will be shown below. At steady state, the mass balance for scattering involving recombination in the chemisorbed layer can be written as J[XSH,PD,
6,)
+ (1 -
x)
sD#D,
OH)]
= kDD6
+ 2kHDeDeH
+kH&k
,
(1)
where I is the beam intensity, s(&,, 0,) the sticking coefficient as a function of the coverages, X the fraction of Ha in the total impingement rate, and the ki are the rate constants for desorption. Since the isosteric heats of adsorption for Ha and Da on Pd( 111) are ecpal to within 5% [6], it can be assumed that kDD = kHD = kHH and it can reasonably be assumed that &!$~aand SD, are only functions of the total COVerage 6 = 8H + oD. SinCe it iS assumed that kHH = kDD, the ratio Of oD t0 OH will be given by SDa/SHa and, as will be seen below, is temperature independent. With these simplifications, the rate of HD production can be written as d [HD] /dt = al S(O) = vBz exp [-_!@)/RT] , (2) , where v is the preexponential factor in the desorption rate. The effect of unequal &, and OH, and SHa and SD, as well as a deviation of X from 0.5 has been included in the factor a. The rate of production of HD is then, within the framework of the above simplifications, a direct measure of an average sticking coefficient for Ha and Da to within a multiplicative constant. Fig. 5 shows the rate of HD production as a function of substrate temperature. The data has been corrected for the change in the equilibrium constant for the reaction Ha = Da t 2HD with temperature [12] and for the variation in the detection efficiency with molecular velocity. For the latter correction, it was assumed that the HD molecules leaving the surface had a mean velocity characteristic of the substrate temperature. For temperatures below 250 K, the HD signal and therefore are extremely small. This does not imply that Ha and Da are not SHY and SD, adsorbed, but rather that the desorption rate from the chemisorbed layer is so small that effectively no exchange between incoming and adsorbed hydrogen and deuterium occurs. Between 250 and 375 K, the rate of HD production increases rapidly before approaching a saturation value above 400 K. The dashed curve shows a fit to the data assuming that the activation energy for desorption is independent of coverage and is given by the isosteric heat of desorption of Ha on Pd(ll1) [6] and that
T. Engel, H. Kuipers / Scattering of Hz and D2 from Pd(l1 I)
250
167
1
300
350
Loo
LM
550
500 TEMPERATURE[
K I
corrected experimenFig. 5. The rate of HD production as a function of temperature: ( -) tal data (see text); (- - -) calculated assuming S = S,(l - e)2 and E constant.
the sticking coefficient has a coverage dependence given by S = Se(1 - e)‘. The agreement between these results and a Langmuir-Hinshelwood mechanism for the reaction in which the activation energy for reaction is the desorption energy, rules out a possible Eley-Rideal reaction mechanism. Although the agreement is reasonable, deviations from the predicted behaviour are observed and will be discussed below. A slight increase in HD signal with substrate temperature is observed up to the highest temperatures investigated. This may be an experimental artifact due to
Fig. 6. Angular distribution for HD formed in the equilibrium reaction. T = 320 K; Bi = 45”. The arrow designates the direction of the incoming beam.
168
T. Engel, H. Kuipers /Scattering
of Hz and D2 from Pdflll)
slight changes in the angular distribution with substrate temperature, although the HD angular distribution was always cosine, as shown for 320 K in fig. 6. In the framework of the model outlined above, the temperature dependence of the rate of HD production, PHD, can be written as
ve2 exp [-E(B)/RT]
.
(3)
However, additional data indicate that S does not depend explicitly on T. This is shown in fig. 7 in which the rate of HD production is plotted as a function of the H2 + D2 beam intensity in a double logarithmic representation. If the explicit temperature variation of S dominates, the slope of the plots obtained should be unity for all temperatures. If, however, S(e) decreases with coverage in the range of beam intensities and temperatures shown in fig. 7, the slope should be less than unity. The data clearly show that a slope of unity is only reached for temperatures above 400 K. It therefore appears that the variation in S with T in fig. 5 is due to an implicit variation due to the change in coverage rather than to an explicit dependence of S on T. An exact analysis of the data in fig. 5 is not possible because the coverage dependence of E, v and S are not known. However, it is instructive to carry out an anal-
. 325K A 350K .375K XLOOK o L25K
L.0
45 In P
Fig. 7. Double
logarithmic plot of the rate of HD production as a function of the beam intensity for various substrate temperatures. The slopes of the plots are indicated at the right of the figure.
T. Engel, H. Kuipers /Scattering
of Hz and D2 from Pd(Ill)
169
ysis for two simplified models. In both of these cases, v is assumed to be independent of coverage. (i) E is assumed to be independent of coverage, and the deviation of the data in fig. 5 from the dashed line is assumed to be due to a deviation of S(0) from a (1 - 0)* form. This assumption is suggested by the isosteric heat measurements of Conrad et al. [6], who found that the measured values were independent of coverage below 0 = OS. Using their value of 20.8 kcal/mole for Hz, the functional form which S(0) must have to yield, the experimental curve in fig. 5 can be determined if 6 is known at one temperature in the range investigated. We assume that 0 = 0.9 at 250 K since the very low yield of HD implies that the surface is essentially saturated. The curve obtained for ,S(e) is shown in fig. 8. In a wide range of coverage, S(e) in this model can be expressed as L?(e) = a In 0. It lies, at most a factor of 3 below the curven given by S = S,( 1 - e)*. (ii) In the second model, it is assumed that S(0) = S,(l - 0)*. This allows a determination of E(B) which must hold to describe the data in fig. 5. In this model, it has been assumed that E(B) = 20.8 kcal/mole in the midrange of coverages investigated. The curve obtained for E(0) is shown in fig. 8. E(B) varies between 21.5 kcal/mole at low and 18 kcal/mole at high coverages. In view of the simplifying assumptions made, both models given physically reasonable forms for E(B) or S(e), so that neither of the two can be ruled out on
In0
Fig. 8. S/So
and E(O) as a function of coverage to fit the data of fig. 5, see
170
T. Engel, H. Kuipers / Scattering of H2 and D2 from Pd(l1 I)
the basis of the limited amount of data available. It can be concluded that the deviation of the results in fig. 5 from the simplest model which is shown by the dashed line can be explained by a surface heterogeneity which is either present in a distribution of sites with different binding energies and/or sticking coefficients for Ha and Da, or which is induced through interactions with the adlayer. 3.3. The interaction of a modulated Hz + 02 beam with Pd(l II) As long as the palladium sample exposed to an unchopped beam has been allowed to reach equilibrium between the gas phase, the chemisorbed layer and the bulk, the adsorptiondesorption properties measured are those of the surface [6] and diffusion into the bulk can be ignored. However, if relaxation techniques are used in which the effective Hz(Dz) pressure is varied by modulating the incident beam, the extent to which equilibrium between chemisorbed and dissolved hydrogen (deuterium) is maintained will significantly affect the adsorption-desorption kinetics. As in the experiments described in the previous section, a mixture of Ha and Da was impinged onto the surface and the HD formed was detected to allow a distinction between molecules formed in the chemisorbed layer and those which are scattered without losing their molecular identity. In the following, it will be assumed that H and D are identical with regard to their heats of solution and diffusion properties and it will be assumed that the parameters for H are valid for both species. Although some evidence, obtained at higher pressure on polycrystalline palladium, indicates that this is not correct [ 131, the major simplifications in the data treatment and, as will be seen, the good agreement between the results obtained and the predictions of the model justify the assumptions. Fig. 9 shows a digitally averaged waveform for HD formed on Pd( 111) at 693 K. The HD signal only rises slowly after the beam has been turned on and the shaded area is proportional to the amount adsorbed. However, the uptake during the half cycle in which the beam is on is roughly an order of magnitude greater than the
BEAM ON
BEkM OFF
Fig. 9. Digitally averaged waveform for HD produced at 693 K; the shaded area is proportional to the amount of Hz adsorbed; w = 63 set-l.
T. Engel, H. Kuipers /Scattering of H, and D, from Pd(l I I)
171
equilibrium coverage at this temperature, showing that a rapid transfer of hydrogen atoms from the surface to the bulk has taken place. After the beam has been interrupted by the chopper, the hydrogen adsorbed in the first half cycle is again desorbed as the system relaxes to the new steady state. The volume acts as a buffer, increasing the amount of hydrogen available for surface reaction by at least an order of magnitude on a time scale of milliseconds at elevated temperatures. A detailed analysis of waveforms such as that shown in fig. 9 over a range of substrate temperatures can yield relaxation times which can be compared with possible reaction mechanisms in order to uniquely identify the mechanism involved. A more convenient data analysis can be carried out using the lock-in technique [lo]. With this technique, the first Fourier component of the signal amplitude, RE, and its phase, @, are measured as a function of the substrate temperature T and modulation frequency w. These results are compared with a reaction model in which the relevant time dependent terms have also been written in a Fourier series. A comparison of the behaviour predicted by the first term in the expansion with the experimental results is then used to establish the reaction mechanism and kinetic parameters. Experimentally determined curves for SE and C#J as a function of substrate temperature for various modulation frequencies are shown in figs. 10 and 11. The amplitude RE rises rapidly at low temperatures and then decreases after passing through a broad maximum. An increase in the modulation frequency shifts the entire structure to higher temperatures and decreases the amplitude. The phase lag $J decreases sharply from n/2 to approximately n/4 in the temperature range in which the amplitude increases. At higher substrate temperatures, $ only changes slightly. An increase in w results in an increase in 4 and in particular the asymptotic value of $I which is approached at high temperatures increases with increasing w.
300
600
760
TEMPERATURE [Kl
Fig. 10. Rate of HD production as a function of substrate temperature for various modulation frequencies: ( -) experimental results; (- - -) best fit using the parameters in table 1.
T. Engel, H. Kuipers j Scattering of Hz and D2 from Pd(l1 I)
172
*. :
:_--== _-_.*. “‘$I
loI fm
300
!%I
=0 +... ***......
600 TEMPERATURE
** . . . . . . . . . . .._ I 700 800 [K1
Fig. 11. Phase lag, @J,as a function of substrate temperature for various modulation frequencies: experimental results; (- - -) best tit using the parameters in table 1; (- l -) pre( -) dicted behaviour for D = 0. See text.
The crossing of the curves for the three highest frequencies at 500 K is an experimental artifact presumably due to chopper-induced cable vibrations. The nearly temperature independent phase shift observed at higher temperatures is again an indication that diffusion between the surface and the bulk is an important factor in the adsorption-desorption behaviour of Hz in Pd(lll). This is seen most clearly in fig. 11 by the dot-dashed line which shows the variation in $ with T expected in the absence of diffusion. The limiting value of 4 reached at high temperatures is zero, in contrast to the values observed. Models for adsorption-desorption with surface-to-volume diffusion have been discussed previously for linear [10,14,15] and nonlinear [16-181 systems and the derivation below follows the one used in these references. Olander and Ullman [16] have shown that linearization of a kinetic model with second-order desorption, as in the present case, leads to a negligible error in the calculation of RE and $I, and this approach will be used in the model proposed below. The diffusion equation x/at
=D
iFcla2)
(4)
where C is the volume concentration of dissolved hydrogen, D the diffusion coeffcient and x the distance perpendicular to the surface, is to be solved with boundary conditions given by the mass balance equation at the surface and the asymptotic behaviour of C for large x. Since the beam is modulated with a frequency w, the first Fourier component of C must have the form C(X, t) = d(x) exp(iwt)
,
(5)
T. Engel, H. Kuipers / Scattering of H2 and D-J from Pd(lI1)
which yields a solution
for d(x)
173
of + i) x] ,
C’(x) = C’(0) exp [-(0/2D)“~(l
(6)
which is an exponentially damped oscillation with a characteristic decay length of (2D/w)‘Z*. At the modulation frequencies used, only the uppermost lo-* mm of the solid contribute to the signal observed. This limits the contribution of the bulk relative to that of the surface, which was not possible previously for macroscopic samples [6-81 and which could only be achieved by using wires of extremely small diameter [9]. The second boundary condition is given by the mass balance equation at the surface which in linearized form can be written as dn/dt = 2SZg(t) - kn,n + D(W/ax),=,-, ,
(7)
where S is the sticking coefficient, Z the beam intensity, g(f) the chopper gating function, k the desorption rate constant, and no and n the steady state and periodically fluctuating hydrogen coverage, respectively. The surface and bulk concentrations n and Care related by C(0, t) = H n(t),
(8)
where H is to be determined and the steady state concentration beam intensity and kinetic parameters by ne = (SZ/k)1’2 . The solutions
n,, is related to the
(9)
for RE and $ are given by [lo]
(10) tan
4
=
(4)
+ ((.Jf2D/2k2)“2
2no t (wH2D/2k2)“2
(11)
’
A comparison between the predicted behaviour of RE and rp and the results shown in figs. 10 and 11 can be made if the parameters k, D, H and no are known. The various parameters involved are shown schematically in the potential energy diagram in fig. 12. If it is assumed that the adsorbed hydrogen and that immediately below the surface are in equilibrium, H can be written as H = C/n = Ho exp[+(AGa =:Ho
exp[+W&
-
- AG,,,)/RT]
~dIRT1
,
(12)
where AGS and AG,,,, AHs and AHSol are the free energies and enthalpies associated with adsorbed and absorbed hydrogen, respectively, and the constant Ho contains entropy terms. The parameters which were used to analyze the data of figs. 10 and 11, are
T. Engel, H. Kuipers / Scattering of H, and D2 from Pd(l I I)
174
-
----
Pd +
H2
%,I
Fig. 12. Potential energy as a function of distance from the surface. EH and E are the activation energies for desorption of molecularly adsorbed and chemisorbed i: ydrogen, Ediff is the activation energy for bulk diffusion and Es01 is the potential energy of a dissolved hydrogen atom. The energies are not drawn to scale.
shown in table 1 together with the values which gave the best fit to the data. The curves calculated with the best-fit parameters are shown as dashed lines in figs. 10 and 11. The agreement of the model with the data is good although not unique since absolute values of RE could not be measured. The measured and calculated maximum values of RE were normalized for w = 62.8 see-’ in making this comparison. Therefore, scaling the denominator of eq. (10) by a common factor will fit the experimental results equally well. The experimentally obtained heat of solution for hydrogen in the bulk, is somewhat lower than the commonly accepted value of 2.3 kcal/mole [20]. However, considering the simplicity of the model in which bulk properties have been assumed to hold up to the surface, and in which no distinction has been made in the parameters in table 1 for hydrogen and deuterium, the agreement with the experimental results is good and it may be concluded that a model, in which the equilibrium between chemisorbed hydrogen and dissolved hydrogen in the layers immediately below the surface is achieved on a time scale in the order of milliseconds, represents the H2-Pd interaction for substrate temperatures above 350 K. Below this temperTable 1 Parameters used in eqs. (10) and (11) to fit the experimental curves in figs. 10 and 11 Best fit for variable parameters
Parameter
Assumed known
SI
-
D = Do exp(-Ediff/RT)
2.9 X low3 exp(-5304/RT) E = 20.8 kcal/mole-’ [6]
H = HO exp(-E/2 k = v exp(-E/R
- aH,,l)/RT T)
E = 20.8 kcabmole-’
[6]
[19]
5 23 X 1013 cmd2 set-’ -’ Ho=1.59X107 --~,,I = 1.2 kcal/mole-’ V = 2.09 x 10-a
T. Engel, H. Kuipers /Scattering
175
of Hz and D, from Pd(l11)
ature, the rate of desorption completely dominates the overall kinetics, and the molecular beam method, which relies on the detection of desorbed products, is unable to establish whether equilibrium is achieved between the surface and the bulk. It is instructive to calculate the surface coverage and volume concentration of hydrogen valid for these experiments. The hydrogen coverage and the decay length (~D/w)~‘~ can be calculated from the parameters of table 1, and the volume concentration by extrapolating the data of Wicke and Nernst [20] to low pressures. Table 2 shows the results obtained. It is seen that no more than the uppermost lop2 mm of the bulk contribute to the signal observed. Since the decay length increases with substrate temperature, it offsets the corresponding decrease in solubility and the total hydrogen dissolved within a decay length of the surface changes by a mere factor of 2 between 300 and 700 K. However, the surface coverage changes by four orders of magnitude in the same range, and therefore the ratio of hydrogen at the surface to that dissolved within one decay length of the surface changes dramatically. At temperatures below 350 K, almost all the hydrogen detected in the experiment is at the surface so that the volume cannot act as a buffer, whereas at 550 K, only 1% of the hydrogen seen by the experiment is at the surface and the results show clearly the buffering action of the volume. These results are valid for a pressure of 5 X 10m7 Torr. An increases in PH2will shift the hydrogen surface-to-volume ratio in the last column of table 2 to lower values since fI can, at most, increase by a factor of 2.5 at 300 K, whereas the dissolved hydrogen can increase by almost four orders of magnitude before the transition to the fl phase takes place [ 11. These numerical values may be modified if the hydrogen concentration in the first few layers is higher than the deep bulk concentration. That this may be the case is suggested by the LEED measurements of Christmann et al. [21] who obTable 2 Surface-to-volume ture
hydrogen
concentration
and their ratio as a function of substrate tempera-
Temperature (R)
f3
(2D/w)“* (in mm) for 10 Hz
Dissolved H in one decay length (monolayers)
Ratio of surface to volume H
300 350 400 450 500 5.50 600 650 700
0.40 3.7 x 10-Z 6.2 X lo+
1.2 2.2 3.5 5.0 6.8 8.6 1.1 1.2 1.4
9.6 1.0 1.1 1.2 1.2 1.2 1.3 1.3 1.3
41 3.1 0.56 0.12 3.8 X 1.4 x 6.2 X 2.9 x 1.7 x
1.5 5.1 2.0 9.6 5.0 2.9
x x x x x x
10-J 10-4 10-4 10” 10-s 10-s
x x x x x x x x x
10-s 10-s 10-a 10-s 10-a 10-a 10-2 10-2 10-Z
X x x x x x x x x
1O-3 10-2 10-2 10-2 10-2 10-2 10-2 10” 10-2
lo-* 10” 1O-3 10-s 10-a
176
T. Engel, H. Kuipers 1 Scattering of Hz and D, from Pd(l I I)
served an increase in the interatomic layer spacing upon adsorption of Ha on Pd(ll1) in the lo-’ Torr range. However, the conclusion that the volume acts efficiently as a buffer at these pressures only for T> 3.50 K is unaffected by this deviation from a simple surface segregation behaviour.
4. Discussion 4.1. The scattering ofH2 and 02 from Pd(llI) Two features of the scattering behaviour of Ha and D, from Pd(ll1) will be discussed in more detail below: the intensity at the specular angle and the angular width of the scattering distribution. The emphasis will be on understanding the nature of the potential from which the molecules scatter and its relation to adsorption and desorption kinetics. Beeby [22] proposed a model for calculating the Debye-WalIer factor in atomic and molecular scattering which has been discussed in more detail elsewhere [23-2.51. The specular intensity, I/Z,,, is strongly dependent on C, the depth of the attractive potential, as seen from I/Z0 = exp [
24mAT %wb12
(COS28i
+ CJ/Ej)]
,
(13)
where I and Ze are the specular and incident beam intensities, ms and m, the masses of an incoming and surface particle, Ei and Bi the beam energy and angle of incidence, f$, the surface Debye temperature, kthe Boltzmann constant, and T the substrate temperature. Therefore, a value ofl/Ze almost equal to that for He scattering, as observed for Ha and D, on Pd(l1 l), requires that the depth of the potential well seen by these molecules must be less than a few hundred Cal/mole [26]. Eq. (13) also predicts a lower value of I/Ze for Da than for H, scattering as is observed, but the agreement is not quantitative unless C for Da is less than that for Ha. In order to illustrate the potential encountered by an incoming Ha molecule, a schematic diagram of a cut through potential energy surfaces normal to the Pd(ll1) surface is shown in fig. 12. An Ha molecule approaches the surface along the lower potential curve which has a minimum corresponding to the physisorption energy of Ha. It is then either backscattered into the gas phase from this potential or crosses over to the atomic potential curve which corresponds to chemisorption. Since no indication of an activation energy for adsorption was found in this work, the intersection of the two curves lies below the zero of potential. The high values of Z/Z,, observed in figs. 1 and 2 for scattering from a clean and hydrogen covered surface at 250 K, show that C for physisorption of H, and D, on Pd(ll1) is of the order of, at most, 500 Cal/mole if the molecules are assumed to feel the full depth of the potential. It is also reasonable that I/I,-, is lower for a clean Pd(ll1) surface than for a hydrogen saturated one, since the clean surface should have a higher physisorption energy, The angular distributions for higher substrate temperatures in
T. Engel, H. Kuipers / Scattering of H2 and D2 from Pd(I I I)
111
fig. 4 show a lower value of I/I0 and a broad lobe with appreciable cosine character. Since from the modulated-beam measurements described in section 3.3, hydrogendeuterium exchange is demodulated below 325 K, the 300 K angular distribution in fig. 4b is solely due to molecular scattering. III, decreases by an order of magnitude between 250 and 300 K which is not primarily a thermal effect since Z/Z0 for He scattering decreases by only 20% in the same temperature range [I 11. The data suggest that the decrease in this temperature range is primarily an order-disorder effect, although the observation that I/Z,, only rises slightly with temperature after the minimum in fig. 3 shows that the probability for inelastic scattering increases more rapidly with temperature than suggested by eq. (13). If the incoming H, molecule is trapped in the molecular state for a significantly long time, it can diffuse over the surface [27] and will be desorbed in a cosine distrit’ution [l l] unless it has crossed over to the chemisorption curve. Some evidence of this behaviour can be seen in the rotational asymmetry of the lobular scattering with respect to the specular direction in figs. 1 and 4. The sticking coefficient, which is approximately 0.1 for Ha on Pd [8] is determined by the relative probabilities for crossover and scattering from the physisorption potential, whereas the lifetime and mobility of the Ha molecule in the molecularly-adsorbed state can influence the form of 5’(e) in such a way that S decreases with 13more slowly than (1 - 0)2 [27-291. In view of the rather good agreement of the hydrogen-deuterium exchange results in section 3.2 with a sticking coefficient of the form Se(1 - 0)*, and a confirmation that s(e) has this form for H, adsorption on Pt(l11) [30], it appears that backscattering into the gas phase and crossover to the chemisorption potential are rapid in comparison with diffusion of H, over the surface. 4.2. Hydrogen-deuterium
exchange on Pd(lllj
Hydrogen-deuterium exchange on single-crystal samples has generally been analyzed by treating the temperature dependence of the rate of HD production as an activation energy for equilibration [30-321, without specifying the nature of the rate limiting step and the physical meaning of the activation energy. However, until evidence is presented that HD molecules are formed in a different way from H2 and D2 in the chemisorbed layer, it does not seem meaningful to speak of an activation energy for equilibration for HD without applying the same formalism for H2 and D2 molecules which result from a recombination within the chemisorbed layer. Analysis of the angular and velocity distribution of D,, H2 and HD desorbed from nickel surfaces [33], substantiates the assumption made here that alI three species are formed in the same kinetic process. The model discussed in section 3.3 also explains the temperature independence of the equilibration rate observed at high temperatures [3 1,321 since, under these conditions, the coverage is so low that E and S become essentially coverage independent.
178
T. Engel, H. Kuipers 1 Scattering of H2 and D, from Pd(l II)
4.3. The equilibrium between adsorbed and absorbed Hz for Pd(l1 I) Although the absorption of Ha in palladium has been studied extensively [I J and several investigations made of the chemisorption layer [f&9], the transition between surface and bulk hydrogen is not well understood. It is clear that the surface is vital in both the solution and removal of hydrogen from the bulk since, as seen in the kinetic scheme below. (14)
dissociation must occur before solution, and recombination before desorption, both processes taking place at the surface. It has recently been suggested [34] that desorption involves recombination of an adsorbed H adatom with one which is absorbed. The consistency of our results with the model proposed, in which desorption can only occur upon recombination in the chemisorbed layer, rules out direct desorption involving an absorbed hydrogen since the activation process in this case should lie considerably below 20.8 kcal/mole. Previous models assumed that strongly chemisorbed hydrogen is not in equilibrium with dissolved hydrogen applying a combination of thermodynamic and kinetic arguments [4]. However, these results show that this is not the case and that for low gas pressures, equilibrium between adsorbed hydrogen and that dissolved just below the surface is achieved over the entire temperature range investigated. Unfortunately, since equilibrium is attained quickly at temperatures for which Ha is desorbed, only the ratio kr/kz can be determined and not the individual rate constants.
5. Summary Both Hz and Da are scattered from their saturated chemisorbed layers bearing a high value of I/l,-,, which indicates a high degree of perfection in the adlayer. For 250 K adsorption, an ordering in the chemisorbed layer is observed as the coverage increases. For higher temperatures, 1/1c decreases more rapidly than is expected on the basis of a comparison with He scattering, indicating that the probability for inelastic scattering is much greater for Ha and Da than for He. Hydrogen-deuterium exchange takes place with a Langmuir-Hinshelwood mechanism and the HD is backscattered into the gas phase with a cosine distribution. The temperature dependence of the HD exchange can be explained by the variation of the sticking coefficient and/or the activation energy for desorption with coverage, excluding an additional activation activation energy for the equilibration. Modulated beam experiments were carried out to investigate the degree to which equilibrium between the chemisorbed and the dissolved hydrogen is reached. It is found that the chemisorbed hydrogen and that dissolved immediately below the surface reach
T. Engel, H. Kuipers /Scattering of H2 and D2 from Pd(l II)
119
equi~b~um rapidly. The attainment of equil~b~um between chemisorbed hydrogen and hydrogen dissolved well below the surface is governed by the diffusion equation.
Acknowledgements It is a pleausre to acknowledge the support and encouragement of G. Ertl throughout the course of this work. Financial support from the Deutsche Forschung~emeinscha~ through SFB 128 is also acknowledged.
References [I] [Z] [3] [4] [5]
F.A. Lewis, The PaBadium-Hydrogen System (Academic Press, London, 1967). R.V. Bucur, V. Mecca and T.B. Flanagan, Surface Sci. 54 (1976) 477. R.V. Bucur, Surface Sci. 62 (1977) 519. J.F. Lynch and T.B. Flanagan, J. Phys. Chem. 77 (1973) 2628. V.R. Kapitanskii, A.I. Livshits, J.M. Metter and M.E. Notkin, Soviet Phys.-Tech. Phys. 21 (1976) 602. [6] H. Conrad, G. Ertl and E.E. Latta, Surface Sci. 41 (1974) 435. [7] A.W. Aldag and L.D. Schmidt, J. Catalysis 22 (1974) 260. [8] A.W. Aldag and L.D. Schmidt, J. Catalysis 22 (1974) 260. [8] D.D. Eley and E.J. Pearson, Faraday Trans. I, 74 (1978) 223. [9] A. Couper and C.S. John, Faraday Trans. I, 74 (1978) 326. [lo] R.H. Jones, D.R. Olander, W.J. Siekhaus and J.A. Schwarz, J. Vacuum Sci. Technol. 9 (1972) 1429. [ 111 T. Engel, J. Chem. Phys. 69 (1978) 373. 1121 R. Fowler and E.G. Guggenheim, Statistical Thermodynamics (Cambridge Univ. Press, Cambridge, 1965). [13f G. Holleck and E. Wicke, Z. Physik. Chem. NF 56 (1967) 155. [ 141 J.A. Schwarz and R.J. Madix, Surface Sci. 46 (1974) 317. [15] H.C. Chang and W.H. Weinberg, J. Chem. Phys. 66 (1977) 4176; Surface Sci. 65 (1977) 153. [16] D.R. Olander and A. Ullman, Intern. J. Chem. Kinetics 8 (1976) 625. [17] H.C. Chang and W.H. Weinberg, Surface Sci. 72 (1978) 617. 1181 M. BaIooch and D.R. Olander, J. Chem. Phys. 63 (1975) 4772. [19] J. V61kl and G. Alefeld, in: Hydrogen in Metals, Eds. G. Alefeld and J. Volkl (Springer, Heidelberg, 1978). [20] E. Wicke and G.M. Nernst, Ber. Bunsenges. Physik. Chem. 68 (1964) 224. [21] K. Christmann, G. Ertl and 0. Schober, Surface Sci. 40 (1973) 61. [22] J.L. Beeby, J. Phys. C4 (1971) L359. [23] H. Hoinkes, H. Nahrand H. Wilsch, Surface Sci. 33 (1972) 516. [24] F.O. Goodman, Surfade Sci. 65 (1977) 37. [25] J. Lapujoulade and Y. Lejay, J. Chem. Pphys, 63 (1975) 1389; G. Armand, J. Lapujoulade and Y. Lejay, Surface Sci. 63 (1977) 143. 1261 J.P. Toennies, Appl. Phys. 3 (1974) 91. [27] P.J. Kisliuk, 3. Chem. Phys. Solids 3 (1957) 95; 5 (1978) 78.
180 [28] (291 [30] [31] [32] (331 [34]
T. Engel, H. Kuipers / Scattering of H2 and D2 from Pd(l I I)
C. Kohrt and R. Comer, J. Chem. Phys. 52 (1970) 3283. D.A. King and M.G. Wells, Proc. Roy. Sot. (London) A339 (1974) 245. K. Christmann, G. Ertl and T. Pignet, Surface Sci. 54 (1976) 365. K.E. Lu and R.R. Rye, Surface Sci. 45 (1974) 677. P.R. Norton and P.J. Richards, Surface Sci. 41 (1974) 293. G. Comsa, R. David and K.D. Rendulic, Phys. Rev. Letters 38 (1977) 775. J.A. Konvalinka and J.J.F. Scholten, J. Catalysis 48 (1977) 374.
A MOLECULAR-BEAM ADSORPTION
INVESTIGATION.OF
AND ABSORPTION
THE SCAITERING,
OF H, AND D, FROM/ON/IN
Pd( 111)
T. ENGEL * and H. KUIPERS Institut fiir Physikalische Chemie der Universitrit Miinchen, Sophienstrasse Miinchen 2, W. Germany
II, D-8000
Received 23 March 1979; manuscript received in final form 5 June 1979
H2 and D2 are scattered from clean Pd(ll1) and a saturated chemisorption layer in a highly specular distribution. Evidence for an ordering of the adlayer with increasing coverage is seen. The hydrogen-deuterium exchange occurs via a Langmuir-Hinshelwood mechanism, and the temperature dependence of the rate of HD production can be understood without assuming an activation energy for equilibration. Lock-in and wave-form analyses of scattered Hz + D2 mixed beams show that equilibrium between adsorbed hydrogen and deuterium and that dissolved just below the surface is reached rapidly at temperatures above 300 K.
1. Introduction
The absorption of hydrogen and deuterium in palladium have been studied extensively [l-3] due to their technological importance. However, the difficulty in determining reproducible rates of permeation through Pd membranes at low pressures led to the knowledge that surface contamination has a marked effect on the rate of solution of H, in palladium [4,5]. A number of investigations of the chemisorption layer has been reported [6-91 but most of these were hampered by the difficulty in separating surface and volume effects. The molecular beam method is ideally suited for such an investigation since volume diffusion can easily be separated from adsorption-desorption which takes place only in the adlayer [lo]. Furthermore, by choosing a suitable modulation frequency, only the uppermost low3 mm of the sample contribute to the signal detected, such that surface and near-surface palladium can be separated from deep bulk palladium without having to work with thin wires. Molecular adsorption, dissociative chemisorption and solution of Ha and D2 formed the subject of this study. Molecular adsorption was investigated using the angular distribution of scattered H2 and D2. Chemisorption was investigated with the hydrogen-deuterium exchange reaction, and the degree to which equilibrium is achieved between chemisorbed and dissolved hydrogen was investigated using modulated molecular beam techniques. * Present address: IBM Zurich Research Laboratory, CH-8803 Riischlikon, Switzerland. 162
T. Engel, H. Kuipers /Scattering of H2 and D2 from Pd(1 I I)
163
2. Experimental The apparatus used in this study has been described elsewhere [ 111. Briefly, it consists of separate bakeable molecular beam and experimental subsystems which are connected with a straight-through valve. The nozzle beam system is threestage differentially pumped with liquid nitrogen baffled oil diffusion pumps. The 18 inch experimental chamber in which the Pd(ll1) sample is mounted contains a retarding field analyzer for LEED and AES, and an ion bombardment gun for cleaning purposes which are used to establish and check the surface cleanliness and order. The beam can be mechanically chopped after entering the experimental chamber with a four-bladed wheel magnetically coupled to a motor outside the vacuum system. The scattered beam is detected by a quadrupole mass spectrometer rotatable in the scattermg plane. The angular resolution can be varied between 1’ and 5” by varying the beam diameter between 1 and 5 mm. A high pumping speed was maintained by evaporating titanium onto a liquid nitrogen cooled cryopanel at the height of the scattering plane. With the beam on at an intensity equivalent to a pressure of 5 X lo-’ Torr, the total pressure remained below 1 X lo-” Torr.
3. Results 3.1. Scattering of Hz and 02 from Pd(ll1) Fig. 1 shows the angular scattering distribution of Hz from a Pd(ll1) surface at 250 K. At this substrate temperature and with the beam intensity used, the hydrogen coverage is approximately 6 = 0.9. The appearance of a sharp specular peak with Z/Z0 = 0.16 indicates a high degree of order in the adlayer. The fraction of total
\
\
\
\
I
I
/
/
Fig. 1. Angular distribution in polar coordinates for Hz scattered from the 250 K surface; 0i = 45”. The maximum intensity corresponds to I/IO = 0.16. The arrow designates the direction of the incoming beam.
164
T. Engel, H. Kuipers /Scattering
of Hz and D2 from Pd(1 I I)
intensity seen at the specular angle is approximately one-third of that observed for He scattering from the same sample [ 1 I]. Moreover, the specularity of Ha scattering from a hydrogen covered surface is greater than that of the clean surface, as seen in fig. 2. Initial adsorption of Ha causes a sharp decrease in the intensity at the specular angle to a value approximately one-third of the value for the clean surface. Further adsorption of Ha increases the intensity to a value whichis approximately twice that of the clean surface. This behavior is consistent with a disordered adlayer at low coverages which becomes ordered at higher coverages due to interactions within the adlayer. A similar effect is seen in the temperature dependence of the intensity at the specular angle under steady state conditions which are shown for Ha and Da in fig. 3. An increase in the substrate temperature which is coupled to a decrease in the surface coverage leads to a minimum in the intensity versus temperature curve for Ha scattering. A further increase in temperature decreases the coverage leading to a subsequent increase in the scattered intensity. The scattering behaviour for Ha and Da is quite similar to what is seen in fig. 3. However, the specular intensity for Da scattering is lower than that for Ha scattering by approximately a factor of 2, due to the higher mass of Da which makes inelastic scattering events with the surface more probable. An increase in the substrate temperature decreases the specular intensity drastically at the expense of more lobular scattering as shown in fig. 4 for Ha scattering from Pd(ll1). The angular distributions were measured by modulating the beam at 63 set-‘. As will be shown in section 3.2, the relaxation time associated with dissociation and recombination of H and D atoms is so long at the substrate temperatures of fig. 4 that it can be concluded that the broad angular distributions result from molecular scattering only. Since 19 decrease from 0.9 to 0.4 between
0
I
50
100
150 TIMEI s I
200
250
Fig. 2. H2 scattering intensity at the specular angle as a function of time for a beam intensity equivalent to -5 X lo-’ Torr, 0i = 45’.
T. Engel, H. Kuipers /Scattering of Hz and II2 from Pd(ll I)
250
300
165
350 TEMPERATURE%
Fig. 3. Hz and D2 scattering intensity at the specular angle as a function of substrate temperatUIe;Bi=45”,w=189sec-l.
Fig. 4. Angular distribution for H2 scattering for various substrate temperatures set-l. The arrow designates the direction of the incoming beam.
for w = 63
166
T. Engel, H. Kuipers /Scattering
of H2 and D2 from Pd(l1 I)
250 and 300 K, the decreased specularity seen in fig. 4 is quite likely due to a disordering of the adlayer with decreasing coverage. 3.2. Hydrogen-deuterium
exchange on Pd( I I I)
In order to investigate scattering which involves atoms in the chemisorbed layer, a distinction must be made at the detector between molecules which scatter, without losing their molecular identity, and those which have dissociated and recombined before desorption. This is mostly easily done by impinging a mixture of H2 and Da onto the surface. Any HD formed must then result from a surface recombination since an Eley-Rideal mechanism can be ruled out, as will be shown below. At steady state, the mass balance for scattering involving recombination in the chemisorbed layer can be written as J[XSH,PD,
6,)
+ (1 -
x)
sD#D,
OH)]
= kDD6
+ 2kHDeDeH
+kH&k
,
(1)
where I is the beam intensity, s(&,, 0,) the sticking coefficient as a function of the coverages, X the fraction of Ha in the total impingement rate, and the ki are the rate constants for desorption. Since the isosteric heats of adsorption for Ha and Da on Pd( 111) are ecpal to within 5% [6], it can be assumed that kDD = kHD = kHH and it can reasonably be assumed that &!$~aand SD, are only functions of the total COVerage 6 = 8H + oD. SinCe it iS assumed that kHH = kDD, the ratio Of oD t0 OH will be given by SDa/SHa and, as will be seen below, is temperature independent. With these simplifications, the rate of HD production can be written as d [HD] /dt = al S(O) = vBz exp [-_!@)/RT] , (2) , where v is the preexponential factor in the desorption rate. The effect of unequal &, and OH, and SHa and SD, as well as a deviation of X from 0.5 has been included in the factor a. The rate of production of HD is then, within the framework of the above simplifications, a direct measure of an average sticking coefficient for Ha and Da to within a multiplicative constant. Fig. 5 shows the rate of HD production as a function of substrate temperature. The data has been corrected for the change in the equilibrium constant for the reaction Ha = Da t 2HD with temperature [12] and for the variation in the detection efficiency with molecular velocity. For the latter correction, it was assumed that the HD molecules leaving the surface had a mean velocity characteristic of the substrate temperature. For temperatures below 250 K, the HD signal and therefore are extremely small. This does not imply that Ha and Da are not SHY and SD, adsorbed, but rather that the desorption rate from the chemisorbed layer is so small that effectively no exchange between incoming and adsorbed hydrogen and deuterium occurs. Between 250 and 375 K, the rate of HD production increases rapidly before approaching a saturation value above 400 K. The dashed curve shows a fit to the data assuming that the activation energy for desorption is independent of coverage and is given by the isosteric heat of desorption of Ha on Pd(ll1) [6] and that
T. Engel, H. Kuipers / Scattering of Hz and D2 from Pd(l1 I)
250
167
1
300
350
Loo
LM
550
500 TEMPERATURE[
K I
corrected experimenFig. 5. The rate of HD production as a function of temperature: ( -) tal data (see text); (- - -) calculated assuming S = S,(l - e)2 and E constant.
the sticking coefficient has a coverage dependence given by S = Se(1 - e)‘. The agreement between these results and a Langmuir-Hinshelwood mechanism for the reaction in which the activation energy for reaction is the desorption energy, rules out a possible Eley-Rideal reaction mechanism. Although the agreement is reasonable, deviations from the predicted behaviour are observed and will be discussed below. A slight increase in HD signal with substrate temperature is observed up to the highest temperatures investigated. This may be an experimental artifact due to
Fig. 6. Angular distribution for HD formed in the equilibrium reaction. T = 320 K; Bi = 45”. The arrow designates the direction of the incoming beam.
168
T. Engel, H. Kuipers /Scattering
of Hz and D2 from Pdflll)
slight changes in the angular distribution with substrate temperature, although the HD angular distribution was always cosine, as shown for 320 K in fig. 6. In the framework of the model outlined above, the temperature dependence of the rate of HD production, PHD, can be written as
ve2 exp [-E(B)/RT]
.
(3)
However, additional data indicate that S does not depend explicitly on T. This is shown in fig. 7 in which the rate of HD production is plotted as a function of the H2 + D2 beam intensity in a double logarithmic representation. If the explicit temperature variation of S dominates, the slope of the plots obtained should be unity for all temperatures. If, however, S(e) decreases with coverage in the range of beam intensities and temperatures shown in fig. 7, the slope should be less than unity. The data clearly show that a slope of unity is only reached for temperatures above 400 K. It therefore appears that the variation in S with T in fig. 5 is due to an implicit variation due to the change in coverage rather than to an explicit dependence of S on T. An exact analysis of the data in fig. 5 is not possible because the coverage dependence of E, v and S are not known. However, it is instructive to carry out an anal-
. 325K A 350K .375K XLOOK o L25K
L.0
45 In P
Fig. 7. Double
logarithmic plot of the rate of HD production as a function of the beam intensity for various substrate temperatures. The slopes of the plots are indicated at the right of the figure.
T. Engel, H. Kuipers /Scattering
of Hz and D2 from Pd(Ill)
169
ysis for two simplified models. In both of these cases, v is assumed to be independent of coverage. (i) E is assumed to be independent of coverage, and the deviation of the data in fig. 5 from the dashed line is assumed to be due to a deviation of S(0) from a (1 - 0)* form. This assumption is suggested by the isosteric heat measurements of Conrad et al. [6], who found that the measured values were independent of coverage below 0 = OS. Using their value of 20.8 kcal/mole for Hz, the functional form which S(0) must have to yield, the experimental curve in fig. 5 can be determined if 6 is known at one temperature in the range investigated. We assume that 0 = 0.9 at 250 K since the very low yield of HD implies that the surface is essentially saturated. The curve obtained for ,S(e) is shown in fig. 8. In a wide range of coverage, S(e) in this model can be expressed as L?(e) = a In 0. It lies, at most a factor of 3 below the curven given by S = S,( 1 - e)*. (ii) In the second model, it is assumed that S(0) = S,(l - 0)*. This allows a determination of E(B) which must hold to describe the data in fig. 5. In this model, it has been assumed that E(B) = 20.8 kcal/mole in the midrange of coverages investigated. The curve obtained for E(0) is shown in fig. 8. E(B) varies between 21.5 kcal/mole at low and 18 kcal/mole at high coverages. In view of the simplifying assumptions made, both models given physically reasonable forms for E(B) or S(e), so that neither of the two can be ruled out on
In0
Fig. 8. S/So
and E(O) as a function of coverage to fit the data of fig. 5, see
170
T. Engel, H. Kuipers / Scattering of H2 and D2 from Pd(l1 I)
the basis of the limited amount of data available. It can be concluded that the deviation of the results in fig. 5 from the simplest model which is shown by the dashed line can be explained by a surface heterogeneity which is either present in a distribution of sites with different binding energies and/or sticking coefficients for Ha and Da, or which is induced through interactions with the adlayer. 3.3. The interaction of a modulated Hz + 02 beam with Pd(l II) As long as the palladium sample exposed to an unchopped beam has been allowed to reach equilibrium between the gas phase, the chemisorbed layer and the bulk, the adsorptiondesorption properties measured are those of the surface [6] and diffusion into the bulk can be ignored. However, if relaxation techniques are used in which the effective Hz(Dz) pressure is varied by modulating the incident beam, the extent to which equilibrium between chemisorbed and dissolved hydrogen (deuterium) is maintained will significantly affect the adsorption-desorption kinetics. As in the experiments described in the previous section, a mixture of Ha and Da was impinged onto the surface and the HD formed was detected to allow a distinction between molecules formed in the chemisorbed layer and those which are scattered without losing their molecular identity. In the following, it will be assumed that H and D are identical with regard to their heats of solution and diffusion properties and it will be assumed that the parameters for H are valid for both species. Although some evidence, obtained at higher pressure on polycrystalline palladium, indicates that this is not correct [ 131, the major simplifications in the data treatment and, as will be seen, the good agreement between the results obtained and the predictions of the model justify the assumptions. Fig. 9 shows a digitally averaged waveform for HD formed on Pd( 111) at 693 K. The HD signal only rises slowly after the beam has been turned on and the shaded area is proportional to the amount adsorbed. However, the uptake during the half cycle in which the beam is on is roughly an order of magnitude greater than the
BEAM ON
BEkM OFF
Fig. 9. Digitally averaged waveform for HD produced at 693 K; the shaded area is proportional to the amount of Hz adsorbed; w = 63 set-l.
T. Engel, H. Kuipers /Scattering of H, and D, from Pd(l I I)
171
equilibrium coverage at this temperature, showing that a rapid transfer of hydrogen atoms from the surface to the bulk has taken place. After the beam has been interrupted by the chopper, the hydrogen adsorbed in the first half cycle is again desorbed as the system relaxes to the new steady state. The volume acts as a buffer, increasing the amount of hydrogen available for surface reaction by at least an order of magnitude on a time scale of milliseconds at elevated temperatures. A detailed analysis of waveforms such as that shown in fig. 9 over a range of substrate temperatures can yield relaxation times which can be compared with possible reaction mechanisms in order to uniquely identify the mechanism involved. A more convenient data analysis can be carried out using the lock-in technique [lo]. With this technique, the first Fourier component of the signal amplitude, RE, and its phase, @, are measured as a function of the substrate temperature T and modulation frequency w. These results are compared with a reaction model in which the relevant time dependent terms have also been written in a Fourier series. A comparison of the behaviour predicted by the first term in the expansion with the experimental results is then used to establish the reaction mechanism and kinetic parameters. Experimentally determined curves for SE and C#J as a function of substrate temperature for various modulation frequencies are shown in figs. 10 and 11. The amplitude RE rises rapidly at low temperatures and then decreases after passing through a broad maximum. An increase in the modulation frequency shifts the entire structure to higher temperatures and decreases the amplitude. The phase lag $J decreases sharply from n/2 to approximately n/4 in the temperature range in which the amplitude increases. At higher substrate temperatures, $ only changes slightly. An increase in w results in an increase in 4 and in particular the asymptotic value of $I which is approached at high temperatures increases with increasing w.
300
600
760
TEMPERATURE [Kl
Fig. 10. Rate of HD production as a function of substrate temperature for various modulation frequencies: ( -) experimental results; (- - -) best fit using the parameters in table 1.
T. Engel, H. Kuipers j Scattering of Hz and D2 from Pd(l1 I)
172
*. :
:_--== _-_.*. “‘$I
loI fm
300
!%I
=0 +... ***......
600 TEMPERATURE
** . . . . . . . . . . .._ I 700 800 [K1
Fig. 11. Phase lag, @J,as a function of substrate temperature for various modulation frequencies: experimental results; (- - -) best tit using the parameters in table 1; (- l -) pre( -) dicted behaviour for D = 0. See text.
The crossing of the curves for the three highest frequencies at 500 K is an experimental artifact presumably due to chopper-induced cable vibrations. The nearly temperature independent phase shift observed at higher temperatures is again an indication that diffusion between the surface and the bulk is an important factor in the adsorption-desorption behaviour of Hz in Pd(lll). This is seen most clearly in fig. 11 by the dot-dashed line which shows the variation in $ with T expected in the absence of diffusion. The limiting value of 4 reached at high temperatures is zero, in contrast to the values observed. Models for adsorption-desorption with surface-to-volume diffusion have been discussed previously for linear [10,14,15] and nonlinear [16-181 systems and the derivation below follows the one used in these references. Olander and Ullman [16] have shown that linearization of a kinetic model with second-order desorption, as in the present case, leads to a negligible error in the calculation of RE and $I, and this approach will be used in the model proposed below. The diffusion equation x/at
=D
iFcla2)
(4)
where C is the volume concentration of dissolved hydrogen, D the diffusion coeffcient and x the distance perpendicular to the surface, is to be solved with boundary conditions given by the mass balance equation at the surface and the asymptotic behaviour of C for large x. Since the beam is modulated with a frequency w, the first Fourier component of C must have the form C(X, t) = d(x) exp(iwt)
,
(5)
T. Engel, H. Kuipers / Scattering of H2 and D-J from Pd(lI1)
which yields a solution
for d(x)
173
of + i) x] ,
C’(x) = C’(0) exp [-(0/2D)“~(l
(6)
which is an exponentially damped oscillation with a characteristic decay length of (2D/w)‘Z*. At the modulation frequencies used, only the uppermost lo-* mm of the solid contribute to the signal observed. This limits the contribution of the bulk relative to that of the surface, which was not possible previously for macroscopic samples [6-81 and which could only be achieved by using wires of extremely small diameter [9]. The second boundary condition is given by the mass balance equation at the surface which in linearized form can be written as dn/dt = 2SZg(t) - kn,n + D(W/ax),=,-, ,
(7)
where S is the sticking coefficient, Z the beam intensity, g(f) the chopper gating function, k the desorption rate constant, and no and n the steady state and periodically fluctuating hydrogen coverage, respectively. The surface and bulk concentrations n and Care related by C(0, t) = H n(t),
(8)
where H is to be determined and the steady state concentration beam intensity and kinetic parameters by ne = (SZ/k)1’2 . The solutions
n,, is related to the
(9)
for RE and $ are given by [lo]
(10) tan
4
=
(4)
+ ((.Jf2D/2k2)“2
2no t (wH2D/2k2)“2
(11)
’
A comparison between the predicted behaviour of RE and rp and the results shown in figs. 10 and 11 can be made if the parameters k, D, H and no are known. The various parameters involved are shown schematically in the potential energy diagram in fig. 12. If it is assumed that the adsorbed hydrogen and that immediately below the surface are in equilibrium, H can be written as H = C/n = Ho exp[+(AGa =:Ho
exp[+W&
-
- AG,,,)/RT]
~dIRT1
,
(12)
where AGS and AG,,,, AHs and AHSol are the free energies and enthalpies associated with adsorbed and absorbed hydrogen, respectively, and the constant Ho contains entropy terms. The parameters which were used to analyze the data of figs. 10 and 11, are
T. Engel, H. Kuipers / Scattering of H, and D2 from Pd(l I I)
174
-
----
Pd +
H2
%,I
Fig. 12. Potential energy as a function of distance from the surface. EH and E are the activation energies for desorption of molecularly adsorbed and chemisorbed i: ydrogen, Ediff is the activation energy for bulk diffusion and Es01 is the potential energy of a dissolved hydrogen atom. The energies are not drawn to scale.
shown in table 1 together with the values which gave the best fit to the data. The curves calculated with the best-fit parameters are shown as dashed lines in figs. 10 and 11. The agreement of the model with the data is good although not unique since absolute values of RE could not be measured. The measured and calculated maximum values of RE were normalized for w = 62.8 see-’ in making this comparison. Therefore, scaling the denominator of eq. (10) by a common factor will fit the experimental results equally well. The experimentally obtained heat of solution for hydrogen in the bulk, is somewhat lower than the commonly accepted value of 2.3 kcal/mole [20]. However, considering the simplicity of the model in which bulk properties have been assumed to hold up to the surface, and in which no distinction has been made in the parameters in table 1 for hydrogen and deuterium, the agreement with the experimental results is good and it may be concluded that a model, in which the equilibrium between chemisorbed hydrogen and dissolved hydrogen in the layers immediately below the surface is achieved on a time scale in the order of milliseconds, represents the H2-Pd interaction for substrate temperatures above 350 K. Below this temperTable 1 Parameters used in eqs. (10) and (11) to fit the experimental curves in figs. 10 and 11 Best fit for variable parameters
Parameter
Assumed known
SI
-
D = Do exp(-Ediff/RT)
2.9 X low3 exp(-5304/RT) E = 20.8 kcal/mole-’ [6]
H = HO exp(-E/2 k = v exp(-E/R
- aH,,l)/RT T)
E = 20.8 kcabmole-’
[6]
[19]
5 23 X 1013 cmd2 set-’ -’ Ho=1.59X107 --~,,I = 1.2 kcal/mole-’ V = 2.09 x 10-a
T. Engel, H. Kuipers /Scattering
175
of Hz and D, from Pd(l11)
ature, the rate of desorption completely dominates the overall kinetics, and the molecular beam method, which relies on the detection of desorbed products, is unable to establish whether equilibrium is achieved between the surface and the bulk. It is instructive to calculate the surface coverage and volume concentration of hydrogen valid for these experiments. The hydrogen coverage and the decay length (~D/w)~‘~ can be calculated from the parameters of table 1, and the volume concentration by extrapolating the data of Wicke and Nernst [20] to low pressures. Table 2 shows the results obtained. It is seen that no more than the uppermost lop2 mm of the bulk contribute to the signal observed. Since the decay length increases with substrate temperature, it offsets the corresponding decrease in solubility and the total hydrogen dissolved within a decay length of the surface changes by a mere factor of 2 between 300 and 700 K. However, the surface coverage changes by four orders of magnitude in the same range, and therefore the ratio of hydrogen at the surface to that dissolved within one decay length of the surface changes dramatically. At temperatures below 350 K, almost all the hydrogen detected in the experiment is at the surface so that the volume cannot act as a buffer, whereas at 550 K, only 1% of the hydrogen seen by the experiment is at the surface and the results show clearly the buffering action of the volume. These results are valid for a pressure of 5 X 10m7 Torr. An increases in PH2will shift the hydrogen surface-to-volume ratio in the last column of table 2 to lower values since fI can, at most, increase by a factor of 2.5 at 300 K, whereas the dissolved hydrogen can increase by almost four orders of magnitude before the transition to the fl phase takes place [ 11. These numerical values may be modified if the hydrogen concentration in the first few layers is higher than the deep bulk concentration. That this may be the case is suggested by the LEED measurements of Christmann et al. [21] who obTable 2 Surface-to-volume ture
hydrogen
concentration
and their ratio as a function of substrate tempera-
Temperature (R)
f3
(2D/w)“* (in mm) for 10 Hz
Dissolved H in one decay length (monolayers)
Ratio of surface to volume H
300 350 400 450 500 5.50 600 650 700
0.40 3.7 x 10-Z 6.2 X lo+
1.2 2.2 3.5 5.0 6.8 8.6 1.1 1.2 1.4
9.6 1.0 1.1 1.2 1.2 1.2 1.3 1.3 1.3
41 3.1 0.56 0.12 3.8 X 1.4 x 6.2 X 2.9 x 1.7 x
1.5 5.1 2.0 9.6 5.0 2.9
x x x x x x
10-J 10-4 10-4 10” 10-s 10-s
x x x x x x x x x
10-s 10-s 10-a 10-s 10-a 10-a 10-2 10-2 10-Z
X x x x x x x x x
1O-3 10-2 10-2 10-2 10-2 10-2 10-2 10” 10-2
lo-* 10” 1O-3 10-s 10-a
176
T. Engel, H. Kuipers 1 Scattering of Hz and D, from Pd(l I I)
served an increase in the interatomic layer spacing upon adsorption of Ha on Pd(ll1) in the lo-’ Torr range. However, the conclusion that the volume acts efficiently as a buffer at these pressures only for T> 3.50 K is unaffected by this deviation from a simple surface segregation behaviour.
4. Discussion 4.1. The scattering ofH2 and 02 from Pd(llI) Two features of the scattering behaviour of Ha and D, from Pd(ll1) will be discussed in more detail below: the intensity at the specular angle and the angular width of the scattering distribution. The emphasis will be on understanding the nature of the potential from which the molecules scatter and its relation to adsorption and desorption kinetics. Beeby [22] proposed a model for calculating the Debye-WalIer factor in atomic and molecular scattering which has been discussed in more detail elsewhere [23-2.51. The specular intensity, I/Z,,, is strongly dependent on C, the depth of the attractive potential, as seen from I/Z0 = exp [
24mAT %wb12
(COS28i
+ CJ/Ej)]
,
(13)
where I and Ze are the specular and incident beam intensities, ms and m, the masses of an incoming and surface particle, Ei and Bi the beam energy and angle of incidence, f$, the surface Debye temperature, kthe Boltzmann constant, and T the substrate temperature. Therefore, a value ofl/Ze almost equal to that for He scattering, as observed for Ha and D, on Pd(l1 l), requires that the depth of the potential well seen by these molecules must be less than a few hundred Cal/mole [26]. Eq. (13) also predicts a lower value of I/Ze for Da than for H, scattering as is observed, but the agreement is not quantitative unless C for Da is less than that for Ha. In order to illustrate the potential encountered by an incoming Ha molecule, a schematic diagram of a cut through potential energy surfaces normal to the Pd(ll1) surface is shown in fig. 12. An Ha molecule approaches the surface along the lower potential curve which has a minimum corresponding to the physisorption energy of Ha. It is then either backscattered into the gas phase from this potential or crosses over to the atomic potential curve which corresponds to chemisorption. Since no indication of an activation energy for adsorption was found in this work, the intersection of the two curves lies below the zero of potential. The high values of Z/Z,, observed in figs. 1 and 2 for scattering from a clean and hydrogen covered surface at 250 K, show that C for physisorption of H, and D, on Pd(ll1) is of the order of, at most, 500 Cal/mole if the molecules are assumed to feel the full depth of the potential. It is also reasonable that I/I,-, is lower for a clean Pd(ll1) surface than for a hydrogen saturated one, since the clean surface should have a higher physisorption energy, The angular distributions for higher substrate temperatures in
T. Engel, H. Kuipers / Scattering of H2 and D2 from Pd(I I I)
111
fig. 4 show a lower value of I/I0 and a broad lobe with appreciable cosine character. Since from the modulated-beam measurements described in section 3.3, hydrogendeuterium exchange is demodulated below 325 K, the 300 K angular distribution in fig. 4b is solely due to molecular scattering. III, decreases by an order of magnitude between 250 and 300 K which is not primarily a thermal effect since Z/Z0 for He scattering decreases by only 20% in the same temperature range [I 11. The data suggest that the decrease in this temperature range is primarily an order-disorder effect, although the observation that I/Z,, only rises slightly with temperature after the minimum in fig. 3 shows that the probability for inelastic scattering increases more rapidly with temperature than suggested by eq. (13). If the incoming H, molecule is trapped in the molecular state for a significantly long time, it can diffuse over the surface [27] and will be desorbed in a cosine distrit’ution [l l] unless it has crossed over to the chemisorption curve. Some evidence of this behaviour can be seen in the rotational asymmetry of the lobular scattering with respect to the specular direction in figs. 1 and 4. The sticking coefficient, which is approximately 0.1 for Ha on Pd [8] is determined by the relative probabilities for crossover and scattering from the physisorption potential, whereas the lifetime and mobility of the Ha molecule in the molecularly-adsorbed state can influence the form of 5’(e) in such a way that S decreases with 13more slowly than (1 - 0)2 [27-291. In view of the rather good agreement of the hydrogen-deuterium exchange results in section 3.2 with a sticking coefficient of the form Se(1 - 0)*, and a confirmation that s(e) has this form for H, adsorption on Pt(l11) [30], it appears that backscattering into the gas phase and crossover to the chemisorption potential are rapid in comparison with diffusion of H, over the surface. 4.2. Hydrogen-deuterium
exchange on Pd(lllj
Hydrogen-deuterium exchange on single-crystal samples has generally been analyzed by treating the temperature dependence of the rate of HD production as an activation energy for equilibration [30-321, without specifying the nature of the rate limiting step and the physical meaning of the activation energy. However, until evidence is presented that HD molecules are formed in a different way from H2 and D2 in the chemisorbed layer, it does not seem meaningful to speak of an activation energy for equilibration for HD without applying the same formalism for H2 and D2 molecules which result from a recombination within the chemisorbed layer. Analysis of the angular and velocity distribution of D,, H2 and HD desorbed from nickel surfaces [33], substantiates the assumption made here that alI three species are formed in the same kinetic process. The model discussed in section 3.3 also explains the temperature independence of the equilibration rate observed at high temperatures [3 1,321 since, under these conditions, the coverage is so low that E and S become essentially coverage independent.
178
T. Engel, H. Kuipers 1 Scattering of H2 and D, from Pd(l II)
4.3. The equilibrium between adsorbed and absorbed Hz for Pd(l1 I) Although the absorption of Ha in palladium has been studied extensively [I J and several investigations made of the chemisorption layer [f&9], the transition between surface and bulk hydrogen is not well understood. It is clear that the surface is vital in both the solution and removal of hydrogen from the bulk since, as seen in the kinetic scheme below. (14)
dissociation must occur before solution, and recombination before desorption, both processes taking place at the surface. It has recently been suggested [34] that desorption involves recombination of an adsorbed H adatom with one which is absorbed. The consistency of our results with the model proposed, in which desorption can only occur upon recombination in the chemisorbed layer, rules out direct desorption involving an absorbed hydrogen since the activation process in this case should lie considerably below 20.8 kcal/mole. Previous models assumed that strongly chemisorbed hydrogen is not in equilibrium with dissolved hydrogen applying a combination of thermodynamic and kinetic arguments [4]. However, these results show that this is not the case and that for low gas pressures, equilibrium between adsorbed hydrogen and that dissolved just below the surface is achieved over the entire temperature range investigated. Unfortunately, since equilibrium is attained quickly at temperatures for which Ha is desorbed, only the ratio kr/kz can be determined and not the individual rate constants.
5. Summary Both Hz and Da are scattered from their saturated chemisorbed layers bearing a high value of I/l,-,, which indicates a high degree of perfection in the adlayer. For 250 K adsorption, an ordering in the chemisorbed layer is observed as the coverage increases. For higher temperatures, 1/1c decreases more rapidly than is expected on the basis of a comparison with He scattering, indicating that the probability for inelastic scattering is much greater for Ha and Da than for He. Hydrogen-deuterium exchange takes place with a Langmuir-Hinshelwood mechanism and the HD is backscattered into the gas phase with a cosine distribution. The temperature dependence of the HD exchange can be explained by the variation of the sticking coefficient and/or the activation energy for desorption with coverage, excluding an additional activation activation energy for the equilibration. Modulated beam experiments were carried out to investigate the degree to which equilibrium between the chemisorbed and the dissolved hydrogen is reached. It is found that the chemisorbed hydrogen and that dissolved immediately below the surface reach
T. Engel, H. Kuipers /Scattering of H2 and D2 from Pd(l II)
119
equi~b~um rapidly. The attainment of equil~b~um between chemisorbed hydrogen and hydrogen dissolved well below the surface is governed by the diffusion equation.
Acknowledgements It is a pleausre to acknowledge the support and encouragement of G. Ertl throughout the course of this work. Financial support from the Deutsche Forschung~emeinscha~ through SFB 128 is also acknowledged.
References [I] [Z] [3] [4] [5]
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