Interaction of hydrogen with polycrystalline palladium films

Interaction of hydrogen with polycrystalline palladium films

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Applied Surface North-Holland

Science

Interaction W. Lisowski

72 (1993) 149-156

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applied surface science

of hydrogen with polycrystalline

palladium films

and R. DuS

The Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44 /52, Received

........

9 February

1993; accepted

for publication

2 June

01-224 Warsaw, Poland

1993

The kinetics of hydrogen interaction with thin palladium films at 195, 298, 348 and 360 K was studied by means of surface-potential change (ASP) measurements and thermal desorption mass spectrometry (TDMS). Dissociative adsorption occurs at all temperatures, forming mobile states of the hydrogen adsorbate. The kinetics of adsorption at 298 K, at coverage 0 z 0.8, is strongly influenced by interaction within the adsorbate layer. Two TDMS peaks, well described by second-order desorption kinetics, were detected when hydrogen adsorption was carried out at 195 K. However, a small part of the hydrogen adsorbate desorbs according to the first-order kinetic equation. This effect can be attributed to the existence of interactions between adsorbed hydrogen atoms, subsurface hydrogen, or can be related to structural imperfections of the Pd film surface. A detailed analysis of the isothermal desorption of the weakly adsorbed hydrogen species was performed. The results obtained from TDMS and from isothermal desorption are compared.

1. Introduction

The interaction of hydrogen with Pd, one of the most active catalysts for hydrogenation reactions, has been extensively studied in the past. The results concerning H, interaction with Pd monocrystals have been reviewed [l]. Thermal desorption (TD) studies have indicated the existence of several TD peaks both on Pd single crystals [2-61 and on polycrystalline Pd surfaces [7-101. The dynamics of low-temperature H, interaction with Pd has been investigated using work-function measurements [2-6,10,11]. The existence of a positively polarized surface state, precursor to hydride formation, has been clearly observed on thin Pd films [lO,ll]. Hydrogen interaction with Pd has also been studied at higher temperatures in terms of kinetics of absorption [12,13] and surface reaction with oxygen k3,141. The nature of hydrogen adspecies in the distinguished surface states is not clear yet. Various explanations for the origin of the low-temperature states on Pd have been presented. The concept of “subsurface hydrogen” has been discussed by many authors [3-61 but only for hydro0169-4332/93/$06.00

0 1993 - Elsevier

Science

Publishers

gen adsorption on Pd(ll0) and Pd(100). For the most packed Pd(ll1) plane, which may be regarded as being dominating for a polycrystalline surface, the measurable incorporation of hydrogen adspecies into the bulk was not found under the applied gas-phase pressure (10-a Torr) [2]. Also, results reported for Pd thin films [lo] and wires [7] indicate the existence of adsorption states only of hydrogen adsorbed at 195 K. It is worth remembering that the heat of hydrogen adsorption is much higher than the heat of solubility in the (Yphase (23 kJ/mol) [15]. Thus, some hydrogen segregation on the surface should be expected until the critical conditions for palladium hydride formation are reached. The aim of the present work was to bring more information concerning the kinetics of hydrogen adsorption on thin Pd films at temperature 2 195 K, and the nature of the hydrogen adsorbate at these temperatures. In these studies we applied thermal desorption mass spectrometry (TDMS) to determine the parameters characteristic of hydrogen deposit in the distinguished desorption states, as well as isothermal studies of adsorption and desorption caused by changing gas-phase pressure. In the isothermal measurements, the

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150

W. Lisowski, R. Dus’ / Interaction

of hydrogen with polycrystalline palladium films

surface potential SP (SP is equal to the work function with a negative sign) was applied to monitor the population of hydrogen adspecies directly on the surface of the Pd film.

2. Experimental

details

All experiments were performed in glass UHV apparatus capable of routinely reaching pressures of (l-2) X 10~“’ Torr (1 Torr = 133.3 Pa). The surface-potential change (ASP) measurements were executed applying a modified, rapidly recorded static capacitor method [16]. The capacitor was the same as described in ref. [17]. Thin palladium films were deposited under UHV conditions (routinely lower than 3 x lo-‘” Torr) on the plate of the static capacitor made of Pyrex glass and maintained at 78 K. The deposition was carried out by evaporation of Pd wire (Johnson Mathey grade I> from a tungsten heater. After evaporation the films were sintered at 400 K for 30 min. The geometrical area (A) of the films was 150 cm2 for both 360 and 348 K and 200 cm2 f$r 298 and 195 K, their average thickness = 2000 A, and their roughness factor (r) estimated by means of hydrogen-oxygen titration [8] was 16 f 2. A short response time (0.1 s> static capacitor circuit of high sensitivity (& 1 mV>, low noise level (& 1 mV) and high stability (1 mV/h) allowed measurement of the kinetics of surface processes associated with surface-potential changes. Spectroscopically pure hydrogen, additionally purified by diffusion through a palladium thimble, was introduced into the static capacitor in successive calibrated doses. The pressure (PI was measured during the adsorption by means of a MacLeod manometer to avoid hydrogen atomization on the hot filament of the ionization gauge. Knowing the volume of the static capacitor and recording ASP and P as the result of adsorption of successive hydrogen doses, the calibration curve ASP versus hydrogen uptake n (called surfacepotential isotherm) has been constructed. This afforded possibilities for transformation of experimental dependences of ASP on time (t) into a function n =f(t> to examine the mechanism of

the distinguished surface processes using the known kinetic equations. It was particularly useful for the isothermal desorption studies of hydrogen deposit obtained within the equilibrium pressure range of 1 X 10-‘-l X lop2 Torr. The TDMS experiments were performed in a separate glass UHV system, but the way the thin Pd films were prepared was the same as in the static condenser method. The TDMS measurement technique and peak analysis method were the same as described previously [18-201. The temperature CT) was measured by means of two separate chromel-constantan fine thermocouples kept in contact with the outer wall of the cell. The mass spectrometer (Topatron, Theybold) was utilized for hydrogen pressure ( PH,> monitoring during the thermal desorption process. Knowing the course of the simultaneously recorded relations: PH2 versus time and T versus time, a definite amount of hydrogen could be ascribed to each energy state of the adsorbate. The total amount of desorbed hydrogen can be compared with the amount of adsorbed hydrogen determined volumetrically. The agreement was 2 5%. By solving the kinetic equation for desorption, one can determine the order (m) of the desorption reaction and the activation energy for desorption (E,>. In this work we define the coverage 8 as the ratio of the number of adsorbed H atoms per number of surface Pd atoms. Knowing the roughness factor (r) of the film [8], its geometrical area A, and assuming the number of surface Pd atoms per 1 cm2 (n,) given as the average over the most probable low-index planes [21], the coverage can be evaluated according to the formula: 0 = n/Am,, where Ar is the real area (S) of the film.

3. Results and discussion 3.1. Analysis of the thermal desorption spectra Fig. 1 shows the TDMS spectra for hydrogen from thin palladium films obtained after various exposures at 195 K. At a hydrogen coverage around 8 = 0.1, one symmetrical peak with a maximum at temperature T,,,,, 2 404 K is registered.

W Lisowski, R. Du4 / Interaction of hydrogen with polycrystalline palladium films

200

300

400 -------T

[Kl

Fig. 1. TDMS spectra of hydrogen from palladium film at various coverages. The hatched parts of the peaks indicate the regions where the first-order kinetic equation for desorption was found.

As the coverage increases and approaches 0.4, the second peak with TmaXplaced at 260 K arises, while the position of the maximum of the hightemperature peak shifts from 404 to 354 K. The shift is consistent with second-order desorption kinetics indicative of dissociative adsorption. The estimated activation energy for desorption E, of this peak (taken as the average of four presented peaks) is 9.5 + 6 kJ/mol and agrees well with E, values reported for H, desorption from palladium films (8.5-115 kJ/mol) [8,10,22] and other Pd polycrystalline materials (92-120 kJ/mol) [7,23,24]. Studies carried out with Pd low-index single-crystal surfaces [l-3] showed that the heat of adsorption QH for the hydrogen high-temperature form ranged between 84 and 102 kJ/mol, depending significantly on the Pd crystal plane. It should be expected that QH = E,, since the activation energy for dissociative adsorption of hydrogen on Pd is very low. In all cases, the validity of the second-order desorption kinetics equation was found to be characteristic for this form of hydrogen adsorbate. The low-temperature TDMS peak is probably a superposition of two states. This can be sug-

151

gested on the basis of the analysis of this peak performed according to the Polanyi equation. It is well known that the Polanyi equation satisfactorily describes a thermal desorption process when one form of the adsorbate or its well separated forms are present on the surface. However, in the case of overlapping of several forms of the adspecies, deviations from this simple description should be expected. Thus, one should be aware of difficulties when such complex kinetic data are analyzed. Nevertheless, to get a first approximation of the parameters of the kinetic equation for desorption we applied the Polanyi relation. The analysis showed that part of the hydrogen deposit desorbs according to second-order kinetics, but in a narrow range of temperature (255-280 K) (see the hatched parts of TDMS spectra in fig. 1) the desorption of hydrogen is described by the firstorder kinetics equation. If the Polanyi equation could be applied to the analysis of this part of the deposit, the estimated E, would be = 36 kJ/mol. From fig. 1 one can conclude that the amount of hydrogen desorbing according to the first-order equation, depends only slightly on the total coverage 0. Approximately 10% and 70% of hydrogen desorbing within the low-temperature TDMS peak obeys the first-order equation at B equal to 1 and 0.5, respectively. Volumetric and ASP measurements showed that the saturation (0 = 1) of the Pd surface with hydrogen can be reached at 195 K. With this assumption, approximately 37% of the hydrogen adsorbed at 195 K desorbs in the high-temperature form. A similar saturation coverage at 300 K (0.39 H/Pd) and 200 K (0.95 H/Pd) was found for hydrogen adsorption on Pd wires [7]. The L, of the low-temperature TDMS peak of hydrogen, presented in fig. 1, shifts from 260 to 230 K as the coverage increases, which is consistent with second-order desorption kinetics. The estimated E, value (68 f 9 kJ/mol) is not far from that reported for low-temperature states of hydrogen adsorbed on Pd films (60 kJ/mol) [lo] and wires (54-59 kJ/mol) [71. It can be seen in fig. 1 that the state of the adsorbate described by the first-order kinetic equation arises when the high-temperature state is saturated. The origin of this state is not clear.

152

W. Lisowski,

R. Dus’ / Interaction

of hydrogen with polycrystalline

A similar surface state existing in a very narrow range of temperatures (220-230 K) was interpreted by Jian-Wei He et al. [6] as the result of reconstruction of the (1 x 2) phase of hydrogen adsorbed on Pd(ll0). On the other hand, no additional LEED structure (except the (1 X 1)) after hydrogen adsorption on Pd(ll1) at room temperature has been found [2]. The low-temperature experimental studies of H/Pd(lll) [25,26] reveal two distinct ordered phases at coverage near l/3 and 2/3 of the monolayers, observed at very low critical temperatures (90 and 105 K). In the light of these results one could suppose that specific sites can exist on thin Pd film surface or can be induced by the pre-adsorption of hydrogen in the form corresponding to the high-temperature TDMS peak, resulting in structural rearrangements of the topmost layer of the Pd surface. The number of these sites is small (about 5% of the total surface area) but significant in the process of arising of the major, low-temperature TDMS peak of hydrogen on Pd film at 195 K. The first-order kinetics, following desorption of the low-temperature TDMS peak, can also be interpreted as the result of lateral interactions between adsorbed hydrogen atoms at higher coverage. Such an explanation of quasi-first-order kinetics for desorption has been proposed by Behm et al. [3] for hydrogen desorption from Pd(100). The low-temperature peaks, induced by pre-adsorbed hydrogen adspecies have also been observed for adsorption of hydrogen on Fe [27], Pt [28], Co [29], and Au [30]. Careful analysis of these peaks reveals the first- and second-order desorption kinetics, depending on coverage. One might suppose that within these “induced” states hydrogen dimers Had- H,, and H,,-H,, can be formed as a result of repulsive-attractive interactions between the adsorbed (H,,) and the subsurface (Ha,) hydrogen species. Thus the order of thermal desorption can be strongly influenced by decomposition of such dimers [31]. 3.2. Analysis of the surface-potential-change suremen ts The ASP measurements the range of temperatures

mea-

were performed in 195-360 K. The mea-

palladium

films

2””

Fig. 2. Dependence of surface-potential changes on surface population (SP isotherm) for hydrogen adsorption on Pd films at 360 (line 11, 348 (line 2), 298 (line 3) and 195 K (line 41, respectively. The final equilibrium pressure was 1 X 10e5 Torr for 195 K, = 10-a Torr for both 360 and 348 K, and 1.5 X 10W2 Torr for 298 K. Open circles in the SP isotherms show reversibly adsorbed hydrogen, desorbing due to lowering of the gas equilibrium pressure by evacuation.

surements carried out at temperatures very close to the T’,, of the TDMS spectrum allowed the kinetics of the surface process accompanying the interaction of hydrogen with the palladium surface at these temperatures to be elucidated. As reported previously [8,141, one electronegatively polarized form of the hydrogen adsorbate (the negative pole of the dipole outward of the surface) appears on palladium films at temperature 2 195 K. This is confirmed by fig. 2 which presents the surface potential (SP) isotherms for hydrogen adsorption on Pd films at 195, 298, 348 and 360 K. The saturation value of ASP after adsorption of hydrogen at 298 K (-216 mV) under an equilibrium pressure 5 1 X lo-” Torr, agrees well with the maximum value of the work function obtained by Conrad et al. [2] for hydrogen adsorption on a stepped Pd(S) - [9(111) X (11 l)] surface ( - 230 mV). This surface can simulate the presence of structural imperfections on thin Pd films. Previously [S] we analyzed the character of the SP isotherm in terms of mutual interactions of hydrogen adatoms forming the adsorbed layer. The assumption of a linear relation between the dipole moment and the coverage 0 led to a good

U! Lisowski, R. DuS / Interaction of hydrogen with polycrystalline palladium films

Fig. 3. Dependence

relation with the Topping correction for depolarization) of n/ASP versus n-“* (Helmholtz adsorption on Pd films at 360 (line l), 348 (line 21, 298 (line 3) and 195 K (line 4).

153

for hydrogen

The nonlinearity of ASP versus II at room temperature can be caused by the depolarization effect due to an interaction in a planar network of dipoles. To check this assumption, the

description of the high-temperature SP isotherms for hydrogen adsorption on Pd films. In fig. 2 it can be seen that a nonlinear dependence of ASP on n is less pronounced at higher temperatures.

1

a

+

-. --__

--

-_

- ___

3.5

/T 4.0 z +

5

a

4 3 2b ~ 0

I I________r C

~ 100 -

t bl

20

3.5

I

3.0 -2 ------In

I

I

-1

_o

W [ dt

1

Fig. 4. (a) Course of ASP in time for adsorption of a large dose of hydrogen on Pd film precovered by hydrogen adsorbate (0 = 0.4) at 298 K. The arrow indicates introduction of a large dose of hydrogen. The dashed part of the line shows reversibly adsorbed hydrogen, desorbing due to lowering of the gas pressure by evacuation. (b, c) Examination of the ASP = f(t) dependence shown in (a). (d) Examination of the ASP = f(t) dependence in (a) in terms of the order m of the adsorption process. Lines indicate slopes 1 and 2 for the first- and second-order of adsorption kinetics, respectively.

W. Lisowski, R. Du4 / Interaction of hydrogen with polycrystalline palladium films

154

Helmholtz equation for ASP (ASP =f(n>) corrected by the well known Topping relation taking into account the depolarization effect [32], was analyzed. Taking into consideration the depolarization effect caused by interaction within the planar network of mobile dipoles, the Topping relation can be transformed into a more useful analytical form: --1

n

ASP

S 47%

9a + 47Ts”Q”

n3/2



where n is the number of adsorbed hydrogen atoms on the surface area S of the film, p0 is the normal component of the dipole moment at coverage close to zero, LYis the polarizability of the hydrogen adsorbate, and II, = 1.27 X 1015 atoms/ cm* [21] is assumed as an average value over the low-index planes corresponding to maximal surface coverage on Pd. The results of the examination of ASP =f(n> functions (fig. 2) according to eq. (1) are presented in fig. 3. The calculated values of both k0 and (Y at 195, 298, 348 and 360 K are 0.14, 0.14, 0.08 and 0.04 D and 6.7 X 10-24, 6.7 X 10-24, 5.8 x 1O-24 and 4.1 X 1O-24 cm3, respectively. It can be seen that the values of both puo and (Y diminish as the temperature increases, indicating a significant influence of the thermal disorder on the surface according to the Langevin equation

precovered by hydrogen adspecies in the amount corresponding to that characteristic of the saturated, high-temperature TDMS peak. In this case the introduction of a large dose of hydrogen into the static capacitor caused a significant increase of hydrogen uptake, slightly above the monolayer, and the decrease of ASP up to - 280 mV, whereas the equilibrium pressure increased from 2.5 X 1O-5 to 1.5 x lo-* Torr (line 3 in fig. 2). The kinetics of ASP changes accompanying this interaction was analyzed; results are presented in fig. 4. Two steps of adsorption can be distinguished. The first one, described well by a second-order kinetic equation (fig. 4b), corresponds to dissociative adsorption of hydrogen filling up the hightemperature TDMS form of the hydrogen adsorbate. The second, approximated by a first-order

- tis1 O0 2 a m Q L

400

600

800

I

a 1 -lOO-

[331. The validity of eq. (1) also indicates the mobile character of the hydrogen adsorbate at temperatures 2 195 K. This conclusion agrees with previous findings for hydrogen adsorption on Pd(100) [31. Since hydrogen was introduced into the static capacitor in successive, calibrated doses, it was possible to investigate the kinetics of adsorption at various coverages. While the ASP dependence on II is not linear within the whole uptake (fig. 2), it can be assumed that within one successive dose, the amount of adsorbed hydrogen is proportional to ASP. Thus, registration ASP =f,(t> gives n = f2(t), and known kinetic equations can be applied to examine the adsorption process. It was particularly interesting to examine at 298 K the kinetics of hydrogen adsorption on Pd film

200

2

8-

I

1

2

2-

b 00

I 200

I 400

I 600

-t

800

Is1

Fig. 5. (a) Surface-potential changes during isothermal desorption of hydrogen from palladium films exposed to hydrogen pressure = 1 x 10m3 Torr at 360 (line 1) and 348 K (line 2). (b) Examination of the ASP = f(t) dependences shown in (a).

W. Lisowski, R. Dus’ / Interaction of hydrogen with polycrystalline palladium films

equation (fig. 4~1, can be related to emergence of an “induced” state of the hydrogen adsorbate, probably resulting from the repulsive-attractive interaction between adsorbed adatoms. The order of adsorption kinetics seems to be affected by these interactions. The complex character of the kinetics of hydrogen adsorption is further confirmed by examination of the order Cm) of the adsorption process in the coordinate system ln(dASP/dt) versus In ASP (fig. 4d). The experimental points fit the straight lines, representing slopes 1 and 2 for the first- and second-order of adsorption kinetics, respectively. P?Jt of the hydrogen deposit obtained within the examined temperature range under equilibrium pressure exceeding low5 Torr (see open circles in the SP isotherm in fig. 2 and dashed line in fig. 4a) desorbed due to lowering of the H, pressure, while the temperature of the adsorbent was kept constant. This isothermal desorption of the negatively polarized adspecies is accompanied by an increase of the surface potential (figs. 5a and 6a). The kinetics of the isothermal desorp-

155

tion process was examined using an n = fi(t> relation transformed from ASP on the time course (figs. 5a and 6a) by applying the SP isotherms (fig. 2). The results of this analysis are presented in figs. 5b, 6b and 6c for 348, 360 and 298 K, respectively. Examination of the isothermal desorption of hydrogen revealed that at 348 and 360 K this process is well described by the second-order kinetic equation (fig. 5b). However, this is not the case at 298 K. The hydrogen deposit at 298 K is not homogeneous. Part of the adspecies at the beginning of the process desorbs according to the first-order equation for desorption (fig. 6b), while later the rate of desorption can be described well by the second-order kinetic equation (fig. 6~). It can be calculated from fig. 2 that the populations at 360, 348 and 298 K are: 0.10, 0.15 and y 1, respectively. Examining the isothermal desorption rates described by the second-order equation at 298, 348 and 360 K, one can obtain the Arrhenius plot (fig. 6d) by plotting the desorption rates ln((dn/n*>dt> versus the reciprocal temperature.

0

7 E-26l 5a v) Q ’ -21 O-

5-

Of I;

.-ci

-

+lOTK-'1

.2 20

.l

I

Fig. 6. (a) Surface-potential changes during isothermal desorption of hydrogen from Pd film previously exposed to H, pressure = 1.5 x lo-’ Torr at 298 K. (b, c) Examination of the ASP =f(n) dependence shown in (a). (d) Arrhenius plot of the experimentally determined isothermal rates of desorption versus reciprocal temperature.

156

W. Lisowski, R. DuS / Interaction of hydrogen with polycrystalline palladium films

The activation energy for desorption derived in this way was 98 kJ/mol, very close to that evaluated by the thermal desorption method for the high-temperature TDMS peak (95 f 6 kJ/mol). We suppose that the part of the hydrogen deposit obtained at 298 K is located in the subsurface region of the topmost Pd layer when the equilibrium pressure exceeds lo-’ Torr. The isothermal lowering of the gas pressure results in decomposition of the subsurface state, penetration of the H,, species to the surface followed by recombination of hydrogen adatoms, and H, desorption. The process of decomposition is slower than the recombination of the mobile hydrogen adatoms, present at high population, and can strongly influence the kinetics of H, desorption. The firstorder kinetics of desorption, found for part of the desorbed hydrogen (fig. 6b), can be an attribute to that form and can confirm our supposition. The estimated pre-exponential factor reaches 21 101” s-1 as should be expected for atomic hydrogen deposit on a transition-metal surface.

4. Conclusions Hydrogen adsorbs dissociatively on Pd films in the range of temperatures 195-360 K, forming mobile states of hydrogen adspecies. As the coverage exceeds 0.8 at 298 K, the kinetics of adsorption is strongly influenced by lateral interactions between adsorbed hydrogen adatoms, resulting in the emergence of “induced” states of hydrogen adspecies located on the surface and in the subsurface layer of Pd films. The TDMS spectra of hydrogen adsorbed at 195 K on Pd films consist of two peaks well described by the second-order equation for desorption. Part of the hydrogen adsorbate (= 5% of the total coverage) desorbs according to the first-order kinetic equation, probably due to interactions between adsorbed and subsurface hydrogen species. Examination of both thermally induced and isothermal desorption of strongly bound adspecies of hydrogen revealed the value of the desorption activation energy to be 95 + 6 and 98 kJ/mol, respectively.

References [l] K. Christmann, Surf. Sci. Rep. 9 (1988) 1. [2] H. Conrad, G. Ertl and E.E. Latta, Surf. Sci. 41 (1974) 435. [3] R.J. Behm, K. Christmann and G. Ertl, Surf. Sci. 99 (1980) 320. [4] M.G. Cattania, V. Penka, R.J. Behm, K. Christmann and G. Ertl, Surf. Sci. 126 (1983) 382. [5] R.J. Behm, V. Penka, M.G. Cattania, K. Christmann and G. Ertl, J. Chem. Phys. 78 (1983) 7486. [6] Jian-Wei He, D.A. Harrington, K. Griffiths and P.R. Norton, Surf. Sci. 198 (1988) 413. [7] W.A. Aldag and L.D. Schmidt, J. Catal. 22 (1971) 260. [8] R. DuS and W. Lisowski, Surf. Sci. 59 (1976) 141. [9] J.A. Konvalinka and J.J.F. Scholten, J. Catal. 48 (1977) 374. [lo] E. Nowicka, Z. Wolfram and R. Dus, Surf. Sci. 247 (1991) 248. [ll] R. DuS, Surf. Sci. 42 (1973) 324. [12] C.H.F. Peden, B.D. Kay and D.W. Goodman, Surf. Sci. 175 (1986) 215. [13] B.D. Kay, C.H.F. Peden and D.W. Goodman, Phys. Rev. B 34 (1986) 817. [14] R. Dus, J. Catal. 42 (1976) 334. [15] G. Alefeld and J. Volkl, Eds., Hydrogen in Metals II, Vol. 29 of Topics in Applied Physics (Springer, Berlin, 1978). [16] T. Delchar, A. Eberhagen and F.C. Tompkins, J. Sci. Instr. 40 (1963) 105. [17] E. Nowicka and R. DuS, Surf. Sci. 144 (1984) 665. [18] R. DuS and W. Lisowski, Surf. Sci. 61 (1976) 635. [19] W. Lisowski, L. Stobinski and R. DuS, Surf. Sci. 188 (1987) L735. UOI W. Lisowski, Appl. Surf. Sci. 35 (1988-89) 399. [211 D. Brennan, D.O. Hayward and B.M.W. Trapnell, Proc. R. Sot. London A 256 (1960) 81. f2.210. Beeck, Disc. Faraday Sot. 8 (1950) 118. [231 D.D. Eley and E.J. Pearson, J. Chem. Sot. Faraday Trans. I, 2 (1978) 223. [241 A. Couper and C.S. John, J. Chem. Sot. Faraday Trans. I, 2 (1978) 326. [251 T.E. Felter and R.H. Stulen, J. Vat. Sci. Technol. A 3 (1985) 1566. 1261T.E. Felter, S.M. Foiles, M.S. Daw and R.H. Stulen, Surf. Sci. 171 (1986) L379. [271 E. Nowicka, W. Lisowski and R. Dus, Surf. Sci. 137 (1984) L85. [281 W. Lisowski, Appl. Surf. Sci. 31 (1988) 451. [291 W. Lisowski, Appl. Surf. Sci. 37 (1989) 272. [301L. Stobihski and R. DuS, Surf. Sci. 269/270 (1992) 383. [311M. Smutek, S. Cerny and F. Buzek, Adv. Catal. 24 (1975) 343. [321J. Topping, Proc. R. Sot. London A 64 (1927) 67. to Solid State Physics (Wiley, New (331C. Kittel, Introduction York, 1966).