Surface Science 222 (1989) 213246 NorthHolland, Amsterdam
DYNAMICS
213
OF MOLECULAR
CH, ADSORPTION
ON Pt(ll1)
Christopher R. ARU~INAYAGAM Departmen? of Chemists,
Stanford Universi~,
Stanfor& CA 94305, USA
Mark C. McMASTER, Gregory R. SCHOOFS * Department
of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
and Robert J. MADIX * * Department of Chemisrv and Department Stanford, CA 94305, USA
of Chemical Engineering,
Stanford University,
Received 14 March 1989; accepted for publication 31 May 1989
The dynamics of molecular methane adsorption on Pt(ll1) were probed with supersonic molecular beam techniques. Initial trapping probabilities were directly measured between 0.94 and 0.16 for incident total translational energies between 3.4 and 20.2 kJ/mol and angles of incidence (with respect to the surface normal) between 0 ’ and 45 o at a surface temperature (T,) of 100 K. The incident methane molecules were rotationally and vibrationally cold. The initial trapping probability decreases with increasing incident translational energy (ET) and decreasing angle of incidence ( ei) and varies smoothly with incident normal energy (E, = ET cOS28i ), indicating a low corrugation of the moleculesurface interaction potential. The dependence of the initial trapping probab~ty on incident normal translational energy agrees qu~ti~tively with both a modified hard cube model and Leuth&tsser’s theory at incident normal transiational energies below 8 kJ/mol. At higher incident normal translational energies the observed initial trapping probabilities are higher than the values predicted by both models. Energy loss mechauisms other than surface phonon excitations may partially account for this discrepancy. A rapid decrease in the apparent adsorption probability as the surface temperature approaches 140 K is caused by the competitive influence of desorption. The temperature at which the apparent adsorption probability goes to zero agrees well with the desorption temperature measured independently by temperaturk programmed desorption. In accordance with the aforementioned models, the measured inplane angular distributions suggest that the trapping probability is relatively independent of surface temperature in the range of 160 to 500 K. The relatively low intensity of methane found * Current address: Department of Chemical Engineering and Applied Chemistry, Columbia University, New York, NY 10027, USA. * * To whom correspondence should be addressed.
00396028/89/$03.50 0 Elsevier Science Publishers B.V. (NorthHolland Physics Publishing Division)
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et al. / Dynamics
of CH, adorption
on Pt(l I I)
near the surface normal in the angular distributions may be partially explained by a wider than cosine angular distribution for the trappeddesorbed channel, which is consistent with the observation that the trapping probability increases with angle of incidence. Comparison of our initial trapping probability versus normal translational energy data to previous mean translational energy measurements of methane molecules desorbing from Pt(ll1) at the surface normal suggests that detailed balance applies for the nonequilibrium situation involving a collimated monoenergetic molecular beam of methane incident on a Pt(ll1) surface.
1. Introduction Numerous molecular beam studies (e.g., refs. [llo]) have identified direct collisional activation as one mechanism for dissociative chemisorption, which is often the initial step in heterogeneously catalyzed reactions and is sometimes the rate determining step in such processes. Trapping precursormediated processes are also important alternate routes to dissociative chemisorption [3,5,10121. To understand this latter mechanism in complex reactive systems, it is useful to first examine energy accommodation and trapping in simple model systems that do not involve dissociative chemisorption. However, there are very few experimental studies of the dynamics of gas molecules trapping on solid surfaces for weakly interacting gassurface systems [13221. In order to molecularly adsorb a molecule must lose sufficient translational energy in the coordinate normal to the surface so that it cannot escape the attractive binding forces with the surface. Hence, an understanding of adsorption requires examination of the various energy loss mechanisms involved in gassurface collisions such as excitation of surface phonons, electronic excitations via electronhole pairs, conversion of translational energy to internal energy, and redirection of the momentum initially oriented perpendicular to the surface into momentum directed parallel to the surface [23]. Nondissociative, weakly interacting gassurface systems provide simple cases to study the role of energy transfer in gassurface collisions. Whereas dissociative chemisorption may involve energy loss via excitation of electronhole pairs [24] in addition to surface phonons, weak molecular adsorption is believed to involve an energy transfer process dominated by excitation of surface phonons [25]. The coupling of translational energy and surface phonons in such systems is most effectively studied with supersonic molecular beam techniques. In most molecular beam investigations of weakly interacting gassurface systems, the angular distributions of the scattered particles have been used to extract the trapping probabilities as functions of incident translational energy, surface temperature, and angle of incidence [1315,20,21,26,27]. This method involves deconvoluting the scattering distribution into two channels: (1) a lobular scattering channel peaked near the specular direction due to direct inelastic scattering, and (2) a cosine or a nearcosine distribution due to
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215
trappingdesorption. The trapping probability is approximated by the fraction of the scattered molecules directed into the cosine scattering channel. Calculations of absolute trapping probabilities using this method require knowledge or assumption of (1) the inplane angular distribution of the trappeddesorbed component (which may not be cosine), (2) the inplane and outofplane angular distributions of the direct inelastic component, (3) the velocity distribution of the trappeddesorbed channel (which may not correspond to the average “equilibrium” value of 2kT,) as a function of polar angle, and (4) the velocity distribution of the direct inelastic component as a function of polar and azimuthal angle. Each of these measurements may depend on incident translational energy, incident angle, and surface temperature. Such extensive measurements have been performed only for the Ar/Pt(lll) system for which the absolute trapping probability was reported for only one incident translational energy and surface temperature [15]. Moreover, it was not possible to measure even the relative trapping probability of Ar as a function of incident beam angle. Two additional factors may introduce uncertainties in the deconvolution of angular distributions into separate direct inelastic and trapping desorption channels. First, a contaminated or rough surface may scatter molecules into a diffuse, cosinelike pattern even though the scattered molecules do not accommodate completely with the surface [28]. Second, the lobular scattering channel may have a significant, but not easily quantifiable contribution near the surface normal. Estimates of trapping probabilities can also be obtained from velocity distribution data [29]. It is possible to separate trappingdesorption from direct inelastic scattering because these two channels have different velocity distributions. The trappeddesorbed component is usually characterized by a velocity distribution independent of the incident beam conditions, but strongly dependent on the surface temperature. The velocity distribution of. the direct inelastic component, however, is a sensitive function of the incident beam conditions, but only weakly dependent on the surface temperature. By measuring the velocity distribution over a range of incident beam parameters and surface temperatures, it is possible, at least in principle, to separate the trappingdesorption and direct inelastic channels and extract the trapping probability. However, only for Xe scattering from Pt(ll1) [27], Ar scattering from a 2HW(100) surface [22], and NO scattering from a Ge surface [30,31] has it been possible to unambiguously resolve the two different channels in the velocity distribution data. In this paper we present one of the first supersonic molecular beam studies of a weakly interacting gassurface system using the direct method of King and Wells [32,33]. Specifically, the initial trapping probability of methane on Pt(ll1) was measured as a function of incident translational energy, angle of incidence, and surface temperature. The initial trapping probability was found to decrease smoothly with incident normal translational energy, falling from
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close to unity to almost 0.1 as the incident normal translational energy was increased from 2 to 20 kJ/mol at a surface temperature of 100 K. Quantitative agreement was found between expe~ment~ results and theory except at incident translational energies higher than 8 kJ/mol, where significant deviations occurred. The measured angular distributions of methane scattered from Pt(ll1) suggest that the trapping probability is relatively insensitive to surface temperature between 160 and 500 K. Comparison of our initial trapping probability versus normal translational energy data with previous velocity dist~bution measurements [26] for the same system suggests that detailed balance applies for this nonequilibrium gassurface system.
2. Experimental Since the experimental apparatus used in this study has been described in detail elsewhere [7,34], we present only a brief description here. The apparatus consists of a UHV chamber with a typical base pressure of 5 x 10l’ Torr coupled to a threestage supersonic molecular beam system. The UHV chamber is equipped with LEED/Auger electron optics and two quadrupole mass spectrometers, one stationary and the other rotatable about the center of the chamber at a fixed radius. All of the experiments were performed on a clean Pt(ll1) sample positioned at the center of the UHV chamber. LEED showed a sharp p(1 x 1) pattern characteristic of the (111) plane. The crystal was cleaned by a combination of argon ion sputtering, annealing, and oxygen treatments. Subsequent Auger analysis indicated no conta~n~ts above the noise level, corresponding to  0.01 monolayers of carbon (1 ML = 1.5 X 1O1’ atoms/ cm2). Surface order and cleanliness were further assessed by a narrow He scattering distribution characterized by a reflectivity of 24% and a FWHM of  3”, a value only slightly larger than the incident beam FWHM. These values compare favorably with previous measurements of 16% and 1.6” respectively for He scattering from Pt(ll1) [27]. However, coherent He scattering does not provide a direct quantification of the fraction of the surface which is wellordered. The surface temperature was measured by a chromelalumel thermocouple spotwelded to the back of the Pt(ll1) crystal. Although the temperatures reported in this paper are only accurate to  3 K, the temperature was controlled to within i0.3 K during the course of a single direct trapping probability experiment. The sample was cooled to  100 K with liquid nitrogen, and heated to above 1500 K by electron bombardment from a tungsten filament positioned directly behind the crystal. The methane molecular beam was formed from a variable temperature (200 < TN < 1000 K) stainless steel nozzle with a diameter of 50 pm. The
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217
beam was modulated by a variable frequency chopper with a 50% duty cycle, and was interrupted when necessary by an electromagnetically operated shutter prior to entering the UHV chamber. A flag placed inside the UHV chamber was used to prevent the molecular beam from directly hitting the crystal when the shutter was open prior to initiation of the direct trapping probability measurements and after completion of the experiment. The average translational energy of the nearly monoenergetic incident methane molecular beam was measured with the rotatable mass spectrometer in conjunction with a lockin amplifier [7]. The difference in the phase lag of the modulated molecular beam between the entrance and the back of the UHV chamber was measured to determine the translational energy. Digitized waveforms obtained at these two positions were also used to calculate the translational energies. Typically, beam energies obtained by the two methods agreed to within 5%. Based on the correlation of Anderson and Fenn [35], we estimate a velocity spread of 10% corresponding to a translational energy spread of approximately 20%. For the direct trapping probability measurements the translational energy of methane was varied between 3.4 and 20.2 kJ/mol by seeding methane into varying amounts of either argon or helium. Neither of these seed gases adsorbed on Pt(ll1) even at the lowest surface temperature employed in these experiments. The nozzle temperature was kept constant at 300 K to minimize the variation in the internal energy distributions of the incident methane molecules. For a given nozzle temperature, the extent of internal energy cooling is determined by the stagnation pressure (PO), nozzle diameter (dN) and the collision number (Z) [36]. The rotational collision number (Z,), for example, is defined as the number of hard sphere collisions which occur during the characteristic relaxation time. In reality, Z, is the ratio of some cross section which determines the collision frequency to the cross section for collisional transfer of rotational energy to translational energy. A similar definition applies for Z,, the vibrational collision number. Since the total number of collisions possible during a supersonic expansion is limited to a few hundred for typical nozzle conditions, a high Z (> 1000) implies very little internal energy cooling while a low Z (CC 1000) implies substantial internal energy cooling [37]. For a 300 K nozzle methane beam Z, has been determined to be 15, indicating significant rotational cooling [36]. Based on the product of P,,dN = (1000 Torr) x (0.05 mm) for our 300 K pure methane beam, we estimate a final rotational temperature of  90 K by comparison with previous measurements of rotational relaxation as a function of stagnation pressure in 300 K methane molecular beams [36]. Vibrational relaxation is negligible since Z, for methane is about 1.5 X lo4 [38]. However, few incident methane molecules occupy vibrationally excited states at a nozzle temperature of 300 K. Assuming no vibrational cooling occurs and that the vibrational distribution of the methane molecules is in equilibrium with the nozzle at a
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temperature of 300 K, less than 1% of the incident methane molecules occupy the first excited state of the lowest frequency vibrational mode, and the incident methane molecules have a total of 0.11 kJ/mol of energy in vibrationally excited states [39]. Hence, the incident methane molecules are both rotationally and vibrationally cold, precluding the possibility of significant rotational to translational and vibrational to translational energy transfers. The methane (Matheson, 99.99% minimum purity) beam composition was verified with the rotatable mass spectrometer placed directly in the beam path. The lockin amplifier was used to record the mass spectrum of the beam at the modulation frequency in order to discriminate species in the modulated beam from those in the background. No species other than methane monomers were observed for a pure methane beam. The sensitivity of the measurement was such that contaminant concentrations as low as 0.5% relative to the parent ion peak could be detected. Angular distributions of scattered methane molecules were measured using phase sensitive detection with the rotatable mass spectrometer rotated about the crystal at a fixed radius of 11.9 cm. The molecular beam was typically modulated at a frequency of 630 Hz. Even at the lowest surface temperature employed, the trappeddesorbed component of the scattering distribution was not demodulated. The upper limit of the angular resolution was 3”) corresponding to the FWHM of a specularly scattered thermal He beam. Since the observed angular distributions were superpositions of a cosine and a broad lobular distribution, this angular resolution was not limiting. The surface was flashed periodically to 500 K in order to minimize the effects of residual gas adsorption while obtaining the angular distribution at low surface temperatures because adsorbed residual gases would increase the intensity of the cosine scattering channel while broadening the directinelastic peak [20]. Initial trapping probabilities of methane on Pt(ll1) were measured directly by the method of King and Wells [32,33]. Fig. 1 shows data for a 3.4 kJ/mol methane beam incident at 45 o from the surface normal on a Pt(ll1) surface held at 100 K. The trace is a plot of the methane partial pressure in the UHV chamber as a function of time, measured by the stationary mass spectrometer. Initially the baseline methane partial pressure was recorded with no beam entering the UHV chamber. Approximately 10 s later the beam was admitted into the UHV chamber by opening the shutter, causing the methane partial pressure to rise. The flag in the UHV chamber prevented the beam from striking the surface. After the methane partial pressure had risen to its steady state value, the flag was removed causing the methane partial pressure to drop as the Pt(ll1) crystal adsorbed a fraction of the incident beam. The initial trapping probability equals the ratio of the methane partial pressure drop when the flag was removed to the methane partial pressure rise when the shutter was opened. Subsequent to the initial drop caused by removing the flag, the methane partial pressure rose asymptotically back to the steady state
C. R. Arumainayagam et al. / Dynamics of CH, adsorption on Pt(l1 I)
0.
20.
40. TIME
60.
80.
100.
219
120.
Fig. 1. A King and Wells direct trapping probability experiment for molecular methane adsorption on Pt(ll1). The surface temperature was 100 K; the molecular beam impinged at 45O from the surface normal with a total translational energy of 3.4 kJ/mol.
value as the rate of desorption approached the rate of adsorption. When the flag was repositioned to prevent further methane adsorption on the crystal, methane desorption produced a spike followed by a nearly exponential decay in the methane partial pressure. The desorption spike is under further investigation and will be discussed in a future publication. Finally, the shutter was closed, and the methane partial pressure returned to its original baseline value. The incident angle of the beam was varied from normal incidence (0 o ) up to 45” in a series of such experiments. By moving the rotatable mass spectrometer behind the crystal, it was verified that the entire beam hit the crystal even at the highest angle of incidence. When varying the angle of incidence, the crystal face was rotated away from the mass spectrometer to ensure that the directly reflected beam did not contribute to the methane partial pressure measured by the mass spectrometer. The UHV system was reconfigured to facilitate temperature programmed desorption (TPD) studies by placing the stationary mass spectrometer close to the crystal. The ionizer was collimated by a stainless steel cap with a 5 mm diameter hole to ensure that the methane TPD signal originated from the central portion of the crystal and not from the crystal edges or supports. Typically, the crystal was directly dosed with the methane molecular beam and the shutter was used to vary the exposure. The shutter was closed during TPD experiments to prevent the beam from entering the UHV chamber, and the
220
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~~mffinayagam et al. / Dynamicsof CH, a~or~i~~~ on Ptflll)
flag was raised to minimize adsorption of any effusive flux. Heating rates were typically 5 K/s during the TPD experiments. The coverage of adsorbed residual gases accumulated prior to the determination of the initial trapping probability was also determined by TPD. The crystal was cooled to 100 K while at the optimum position for TPD, and the methane beam was admitted into the UHV chamber for  30 s with the flag positioned to prevent direct adsorption of the beam on the crystal. This procedure simulated the condition of the crystal at the instant the initial trapping probability was measured. The crystal was then heated at 5 K/s while monitoring the pn/q ratios 2, 16, 18, 28, corresponding to H,, CFI,, H,O, and CO, respectively. In all cases the coverage of each adsorbed gas was less than 0.01 monolayers, and the upper limit of the total residual gas coverage accumulated prior to a direct trapping probability measurement was approximately 0.03 monolayers.
3. Results 3.1. Molecular versus dissociative adsorption Methane adsorbs molecularly on Pt(ll1) during the direct trapping probability measurements reported here. Flashing the crystal to 500 K restored a clean surface after every experiment, Even after a series of appro~ately 10 such experiments, no carbon a~umulation was detectable by AES, a result that implies negligible methane dissociation under these conditions. An order of magnitude estimate yields an upper limit of 10e3 for the initial dissociative sticking probability of CH, on Pt(ll1) for an incident translational energy of  10 M/mol. A similar value is obtained by linearly extrapolating the measured initial dissociative sticking probability data in a log S, versus incident translational energy, as reported previously [S]. Translationally activated dissociative chemisorption of methane on Pt(ll1) was measured (S,, 2 0.01) for incident normal translational energies greater than 56 kJ/mol. At the low incident translational energies (< 21 kJ/mol) employed in the direct trapping probabi~ty experiments described herein, dissociation of methane plays an insi~ficant role. 3.2. The dependence of the initial trapping probability energy and incident angle
on incident translational
At a constant surface temperature of 100 K and a fixed angle of incidence, the trapping probability decreases monotonically with increasing incident translational energy (fig. 2). Furthermore, the initial trapping probability increases monotonically with increasing angle of incidence at all incident
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221
CBq/Pt(lll)
_,~~,,,,,,,,..,................ ~,."",, ,_,.................~~~.~'~"" .............. (,_,,..,,,..._......,.... ET=3.4 kJ/mole i
0.8 0.6
0.0
1
I
00 (degrees
I
I
150 Incident from
300
45O
Angle surface
normal)
Fig. 2. The initial trapping probability of CH, on Pt(ll1) as a function of incident angle measured from the surface normal at different incident total translational energies. The surface temperature for these experiments was 100 K. The symbols represent the data. The dotted lines do not represent a fit, but have been drawn merely to guide the eye. For the sake of clarity, error bars of kO.06 are not drawn.
translational energies. The initial trapping probability of methane on Pt(ll1) is replotted as a function of incident normal translational energy (E, = E, cos28,) at a surface temperature of 100 K in fig. 3. The initial trapping probability decreases smoothly from 0.94 to 0.16 as the incident normal 1 .o 1,
.e s ._=
0.8 
*
Incident
n e CL
CHq/Pt(lll)
*
%
*
0.6 
0
F Oo
.g
e l3 .?Y E
0.4 0.2 
Totol
kJ/mols
0
9.1
kJ/mole
0
15.4
kJ/mole
A
20.2
kJ/mole
aA17 T=
100
A On
K
AA
S
I
0.0 0 Incident
KE
3.4
,
4 Normal
I
I
8
12 Kinetic
,
I 16
Energy
.
I 20
(kJ/mole)
Fig. 3. The initial trapping probability of CH, on Pt(ll1) scales with incident normal translational energy (E, = ET c&9) to within experimental error ( f 0.06). The data in figs. 2 and 3 are identical; they merely have been plotted in different ways. The symbols represent the data.
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of CH, adsorption on Pt(Il1)
translational energy is increased from 1.7 to 20.2 kJ/mol. To within experimental error ( f 0.06 absolute), all data points on this plot lie on a single curve. 3.3. Injluence
of surface defects on the initial trapping probability
In order to assess the role of defects in the trapping of methane, the initial trapping probability was measured on a clean, argon bombarded, but unannealed, Pt(ll1) surface. An AES scan exhibited only trace amounts of carbon following argon bombarding. Argon ion sputtering roughened the Pt(ll1) surface as evidenced by a twofold reduction in the intensity of a specularly scattered thermal He beam. A direct quantification of the defect density is not possible based on this observation alone. An order of magnitude estimate may be obtained by comparison to a previous estimation of defect concentration induced by Ar+ bombardment of a Pt(ll1) crystal under similar conditions. Poelsema et al. estimated a few times 1Ol3 point defects/cm2 as a result of bombarding the surface at room temperature with  1 X 1014 Ar+ ions/cm2 . s with a crystal bias of 600 V [40]. For a 9.1 kJ/mol methane beam incident at 45 O, the initial trapping probability equalled 0.4 on an argon bombarded surface compared with 0.6 for the subsequently annealed surface. This surprising result indicates that methane trapping on Pt(ll1) is more efficient on a flat surface than on a rough surface. This feature is discussed further below. 3.4. Methane
TPD
Kinetic parameters for methane desorption from Pt(ll1) were obtained by TPD. One binding state at approximately 140 K was observed for molecular methane adsorption on Pt(ll1) for surface temperatures above 100 K (fig. 4). At a constant heating rate of 5 K/s, the peak temperature remains unchanged within experimental error when the initial surface coverage is varied from 0.001 to 0.01 monolayers, indicating that CH, desorption from Pt(ll1) is governed by firstorder kinetics without significant lateral interactions in this range of coverage. An asymmetric peak shape about the peak maximum confirmed first order desorption kinetics. A lower limit to the activation energy for desorption of 25 kJ/mol, corresponding to a preexponential factor of 2 x lo9 si, was obtained using the methods of McCarty et al. [41], Chan et al. [42], and Edwards [43]. However, low pumping speeds and readsorption during a flash may broaden the TPD curve leading to artificially low activation energies and preexponential factors since these methods rely on the FWHM of the TPD peak. Desorption rate parameters were also estimated from a plot of ln(rate/coverage) versus l/T,, which yielded a straight line with a slope of  E,/R consistent with firstorder desorption kinetics. This analysis gave an activation energy of 30 kJ/mol and a preexponential of
C.R. Arumainayagam et al. / Dynamics of CH, ahorption
I1 110.
11 140.
1
I
I 170.
TEMPERATURE
I
’
11 200.
on
Pt(ll1)
223
J
Fig. 4. Thermal desorption spectra of CH, on Pt(ll1) as a function of exposure. The adsorption temperature was  100 K, and the heating rate was 5 K/s.
1 x 10” sl. Assuming a preexponential of 1013 sl for a peak temperature of 140 K provided an upper limit to the activation energy of 35 kJ/mol. Thus, we estimate an activation energy of 2535 kJ/mol for methane desorption from Pt(lll), which, given the high adsorption probability, must also be its binding energy to the surface (see note added in proof). Bond order conservation theory yields a binding energy of 38 kJ/mol for molecular methane adsorption on Pt(ll1) [44]. Activation energies for desorption of 25,29, and 34 kJ/mol have been previously measured for methane molecularly adsorbed on Rh films [45], W(100) [46], and W(lll) [47], respectively. 3.5. Influence of surface temperature
on initial trapping probability
measurements
Fig. 5 displays the measured initial trapping probability of methane on Pt(ll1) as a function of surface temperature for several incident translational energies with the beam incident at 45” from the surface normal. At all temperatures except 140 K, increasing the incident translational energy caused the measured trapping probability to decrease. The measurements at 140 K were plagued by large uncertainties because the observed trapping probabilities were very small. The rapid decrease in the measured trapping probability
224
Arumainayagam
... . ,
0.8
0.6
F
et al. / Dynamics of CH, ahorption
CH*/Pt(lll)
incident Total KE
,._
‘Y..._ %_ Y.
“x.
Surface
on Pt(l II)
Temperature
*
3.4 kJ/mole
0
9.1 kJ/mole
0
15.4 kJ/mole
A
20.2
kJ/mole
(K)
Fig. 5. The apparent trapping probability of methane on Pt(lll) as a function of surface temperature at different incident total translational energies. The molecular beam impinged at 45’ from the surface normal. The rapid decrease in the measured trapping probability with increasing surface temperature reflects the influence of desorption rather than a trapping probability strongly dependent on Z’I,.
near the surface temperature of 140 K, the desorption temperature of methane on Pt(lll), reflects the competitive influence of desorption as shown by detailed calculations for the molecular ethane/Pt(lll) system [48], rather than a trapping probability strongly dependent on surface temperature. The King and Wells method provides only an estimate of net adsorption rather than the true initial trapping probability when the surface temperature approaches the desorption temperature. Competitive desorption is unlikely to influence the initial trapping probability measurements at a surface temperature of 100 K, since at that temperature a trapping probability close to unity was measured for a 3.4 kJ/mol beam incident at 45 O_ 3.6. Angular distributions
of CH4/ Pt(l I I)
The inplane angular distribution of scattered methane molecules as a function of incident translational energy and surface temperature was also measured to provide a complementary, yet less direct, probe of trapping. Even for experimental conditions which most enhance trappingdesorption (low incident beam energy and low surface temperature), the scattering distributions exhibit only moderate intensity near the surface normal. At first sight, methane appears to scatter from a clean Pt(ll1) surface predominantly by direct inelastic scattering according to these distributions. However, as dis
C. R. ~~ainayaga~
_.
40
et al. / Dynamics of CH, ~orptia~
20
0
20
40
60
on Pt{I 11)
225
80
Scattering Angle (Degrees from surface normal) Fig. 6. The angular distribution of methane scattered from a clean Pt(ll1) surface held at 500 K as a function of incident total translational energy. The angle of incidence is 45O. The angular resolution is 3” as assessed by He atom scattering.
cussed later, care must be taken in relating the angular distributions
to the initial trapping probability. The angular distributions for methane scattered from a clean Pt(ll1) surface for three different incident translational energies at a surface temperature of 500 K and an incident angle of 45” are displayed in fig. 6. As the incident translational energy is increased from 4.2 to 45 kJ/mol, the intensity near the surface normal decreases in agreement with the trend seen in the direct trapping probability measurements at lower surface temperatures; the trapping probability decreases with increasing incident translational energy. The lobular peak also shifts away from the surface normal toward higher scattering angles, and the FWHM of the lobular fraction decreases with incr&ing incident translational energy. Similar behavior has been observed for the directinelastic scattering of rare gases [13,14,49], and can be semiquantitatively understood in terms of the hard [50] or soft [51] cube models. The surface temperature dependence of the angular distributions for a 4.2 kJ/mol methane beam incident at 45’ is shown in fig. 7. As the surface temperature is increased from 160 to 500 IS, the lobular peak maximum shifts towards the surface normal while the FWHM increases slightly in agreement
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5 c
IJ1
0.8 0.7
*;
0.6
=: 4:
0.5
;
0.4
.E 
0.3
g
0.2
z
0.1
0.0’ 40
’
’
’
20
’
’
0
’
Scattering (Degrees
from
’
20
’ 40
’
’
60
’
’ 80
Angle surface
normal)
Fig. 7. The surface temperature dependence of the angular dist~bution of methane from a clean Pt(lll) surface. The incident total tr~~ation~ energy was 4.2 kJ/mol, and the incident angle was 45O from the surface normal.
with the predictions of the cube models. The trappeddesorbed component remains approximately constant, suggesting that the trapping probability does not decrease significantly when the surface temperature is increased from 160 to 500 K. This feature will be discussed further.
4. Discussion
4.1.1. The dependence of the initial trapping probabiliry on incident translationaf energy The initial trapping probability of methane on Pt(ll1) decreases monotoni
cally with increasing incident translational energy at a fixed angle of incidence and a constant surface temperature as shown in figs 2, 3 and 5. In agreement with this trend, the angular distributions in fig. 6 show a decrease in the intensity at the surface normal as the incident translational energy is in
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227
creased. The decrease in initial trapping probability with increasing incident translational energy is readily understood since a fast molecule has a smaller probability of losing sufficient perpendicular translational energy in order to be trapped than does a slow molecule [52]. The decrease in the initial trapping probability with increasing incident translational energy indicates that molecular adsorption of methane on Pt(ll1) is nonactivated. Although this conciusion may be intuitively obvious, a recent study of nitrogen adsorption on Fe(ll1) has indicated that trapping into a precursor state could be an activated process [ 111. 4.1.2. The dependence of the initial trapping probability on incident angie The initial trapping probability increases monoto~cally with increasing angle of incidence at a fixed incident translational energy as shown by fig. 2. This observation demonstrates the lesser importance of parallel momentum accommodation compared to normal momentum accommodation in the trapping process. All data points in the plot of the initial trapping probability as a function of incident normal translational energy (fig. 3) appear to he on a singfe curve, indicating that the trapping probabi~ty exhibits little dependence on the parallel component of the incident momentum and that “normal energy scaling” holds approximately for methane trapping on Pt(ll1). Normal energy scaling is expected for trapping processes involving a smooth (i.e., onedimensional) gassurface potential. However, some recent experimental and theoretical studies suggest that normal energy scaling is not always obeyed for trapping events. Using a semiclassical trajectory approximation, Persson and Harris calculated that the trapping probability of Ne on Cu(100) for incident translational energies between 0 and 40 kJ/mol decreases rather than increases with increases incident angle, if the criterion for trapping was net negative total energy following impact, rather than a net negative normal energy [53]. In a nozzle beam study of molecular hydrogen trapping on a 15 K Cu(100) surface, Andersson et al. concluded that the initial parallel momentum is not conserved in a trapping event, and that for most trapping events total energy rather than normal energy is transferred to the solid upon the initial collision even though the initial trapping probability is found to increase with increasing angle of incidence [X719]. For the precursor mediated dissociative che~so~tion of nitrogen on W(l~), Rettner et al. found that the dissociative chemisorption probability was independent of incident angle, suggesting that trapping into the precursor state was dependent on parallel momentum [12]. For argon trapping on a 2HW(100) surface, Rettner et al. found that the trapping probability scales more accurately with E, cos Bi rather than the normal energy (ET cos2Bi) [22]. These observations may be explained by an effective gassurface interaction potential which is highly corrugated and/or by the possibility that a molecule may lose sufficient normal energy to trap, but may retain parallel momentum that is later
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of CH, aakorption on Pt(l I I)
transferred into motion normal to the surface by surface corrugation, the molecule to scatter back into the gas phase.
causing
4.1.3. Influence of surface defects on the initial trapping probability The scattering of tangentially “hot” molecules back into the gas phase by corrugation of a rough surface potential may indeed explain the lower adsorption probabilities of CH, observed on a clean, argonsputtered surface relative to a clean annealed surface. Generalized Langevin simulations of Ar and Xe adsorbing on Pt(ll1) show that the adsorbate atoms glide hundreds of angstroms across the surface before thermalization of parallel momentum occurs [54561. Prior to this thermalization, however, steps and other defect sites on an argon sputtered surface may convert tangential momentum into perpendicular momentum oriented away from the surface, thereby scattering molecules away from the surface and decreasing the trapping probability. This “hot” precursor mechanism was postulated previously to explain the decrease in the sticking probability with increasing angle of incidence for molecular chemisorption of CO on Ni(lOO) [57]. Similar concepts have been invoked previously to rationalize observations such as the formation of ordered overlayers at temperatures below the onset of diffusion [58]. As noted by D’Evelyn et al., a clear distinction must be drawn between a “hot” precursor and a thermalized precursor state [57]. The latter requires a shallow secondary minimum in addition to an activation barrier between this minimum and the relatively deep chemisorption well. The existence of a “hot” dynamical precursor, however, places no such restrictions on the gas surface potential. 4.2. Modified hard cube model 4.2.1. Derivation For a more quantitative understanding of the experimental data presented here, the hard cube classical mechanical model of Logan and Stickney [50] for gassolid scattering was extended to include trapping by incorporating an attractive, onedimensional square well potential. Following the methodology of Grimmelman et al. [59], we have derived a simple, closedform expression for the initial trapping probability of a collimated monoenergetic beam of gas molecules as a function of incident velocity, incident angle and surface temperature. If the potential well depth is known, the model can be applied with only one adjustable parameter, the effective surface mass, which takes into account the cooperative motion among neighboring surface atoms due to long interaction times at low incident translational energies. The expression we present is very closely related to expressions derived by Steinbrtichel et al. [60], Grimmelman et al. [59], and Harkness et al. [61]. The surface is modelled by a cube of mass m, constrained to move only in a direction perpendicular to the surface with a onedimensional MaxwellBoltz
C.R. Arumainayagam
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229
mann velocity distribution characteristic of the surface temperature. Tangential momentum of the incident particles is conserved since the surface is assumed to be flat. The model precludes the possibility of multiple collisions. The incident gas molecules are assumed to be rigid elastic spheres with no internal degrees of freedom. The repulsive part of the gassurface interaction potential is assumed to be impulsive with no provisions, such as harmonic force terms, to represent interactions with the bulk. The attractive part of the gassurface potential is approximated by a onedimensional square well of the depth D. Modelling the gassurface potential by a square well may at first appear to be a gross oversimplification, but it has been argued by Weinberg and Merrill that since the attractive region of the potential is conservative, its shape and width are immaterial [62]. Hence, an impulsive potential may be a reasonable, if crude, approximation of the steep repulsive portion of the potential. A gas molecule of mass M and total translational energy E, approaches the surface at an angle Oi from the surface normal. The velocity of the gas molecule normal to the surface prior to impact is given by a,, =  [2( E, cos20i + D)/M]1’2,
(1)
The direction away from the bulk is defined to be positive. We approximate the nonnormalized probability distribution function of surface velocities at which collisions occur by the following expression [59]: P(u)
du=(u,u)
exp(a2u2)
du,
(2)
where u is the velocity of the surface atoms and a2 = m/2k,T,. The weighting factor (u,  u) accounts for the fact that collisions are more probable if the surface atom is moving up towards the incident gas molecule than if the surface atom is moving down away from the incoming gas molecule. The normal and parallel components of the gas molecule’s velocity after the collision are obtained from conservation of energy and momentum.
d=l4 P P'
(3) (4)
where ~1is the mass ratio M/m. If the gas molecule is to be trapped in the potential well, the normal component of the velocity just after the collision must be less than (2D/M)‘12. Hence, using eq. (4), u must be less than u, where
If the surface atom is moving at a velocity greater than u,, the critical velocity for trapping, the incident gas molecule will be reflected. Using eqs. (2) and (5),
C.R. Arumainayagam
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et al. / Dynamics of CH, aclrorption on Pt(I II)
we derive the following expression for the trapping probability ergetic molecular beam: 1’” (u,u) S(U”, D, 0
=
exp(a2u2)
OO /m (u,  II) exp( a2u2) m
for a monoen
du (6)
do ’
Formal integration of eq. (6) results in the following simple expression: s(u,,
D, T,) = i+:
erf(au,)
+ $(a~,&~)’
exp(a’$).
(7)
Here erf is the error function. Eq. (7) is identical in its functional form to the expression for the trapping probability derived by employing the soft cube model [51]. 4.2.2. Application to CH,/ Pt(l I I) system This simple model quantitatively reproduces our methane trapping probability measurements on Pt(ll1) reasonably well below incident normal translational energies of 8 kJ/mol (fig. 8). Since molecular methane adsorption is unactivated, the potential well depth equals the activation energy for desorption obtained from the TPD experiments of CH, on Pt(ll1) to a first approximation. An effective mass of 1.5 surface atoms gave reasonable agreement at low incident translational energies between the experimental trapping probability data and the modified hard cube model presented herein. For the direct inelastic scattering of CH, from Pt(lll), the closest agreement between the hard cubebased model of Grimmelman et al. [59] and the experimental velocity distribution data of Janda et al. [26] was obtained with an effective mass of one surface atom. Agreement between experiment and theory becomes less satisfactory as the incident translational energy increases above 8 kJ/mol (fig. 8). For example, the modified hard cube model predicts a trapping probability close to zero for an incident translational energy of approximately 20 kJ/mol in contrast to the measured value of 0.16. Whereas at low incident translational energies the interaction times will be sufficiently long to promote cooperative motion among neighboring surface atoms, at high incident translational energies short interaction times may preclude such behavior [59]. Since the surface atoms may be viewed as moving more independently at high incident translational energies (short collision times), the effective mass of the surface involved in the collision could be reduced from approximately 1.5 to one surface atom. A reduction in the effective surface mass enhances the translational energy transfer to the surface during a collision. Hence, the initial trapping probability at high incident translational energies may be underestimated in the calculations shown in fig. 8 due to the assumption of a constant effective mass of 1.5 surface atoms at all incident translational energies. For example,
C.R. Arumainayagam et nl. / Dynamics
5fCf14
a&option on Ptflil)
= 1.5 atoms

25 W/mole

30 kJ/mole
231


...‘..I... 35 kJ,/mole
0.0’
’ 0.
INCIDENT
’ 4.
’
NORMAL
’ 8,
’ 12.
KINETIC
16. ENERGY
20.
Fig. 8. Comparison of the experimental Se versus incident normal translational energy data with the modified hard cube model (eq. (7)). Values for the well depth D were set equal to the activation energies obtained from TPD. Three curves are presented corresponding to well depths of 25, 30, and 35 kJ/mol. The circles represent the experimental data. The effective surface mass (N,) was 1.5 atoms. The surface temperature was 100 K for both experiments and computations.
modified hard cube model calculations show that for a well depth of 35 kJ/mol and an incident normal translational energy of 20 kJ/mol, S, = 0.13 and 0.03 for an effective mass of 1.0 and 1.5 surface atoms, respectively. At lower translational energies, however, an effective surface mass of one atom overestimates the initial trapping probabi~ty. Hence a progressive decrease in the effective mass with increasing translational energy would bring theory into better agreement with experiment. 4.3. Leuthiiurser’s theory 4.3.1. General We have also utilized the more sophisticated theory of Leuthausser [63,64] to analyze our experimental data. Based on the master equation in energy space (WeinerHopf equation), this theory consrders an adsorbate as a Brownian particle in a potential well and has been shown to yield results in agreement with Tully’s stochastic trajectory simulations of adsorption and
232
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e? al. / Dynamics of CH, a~o~~~iun on Pf(fii)
desorption for both the Ar/Pt(tll) and Xe/Pt(lll) systems [54563. The theory assumes that: (1) tangential momentum is conserved; (2) detailed balance (microscopic reversibility) applies; (3) the adsorbed particle has no internal degrees of freedom; (4) E < D  RT, for an additive Markov process, where E is the incident translational energy, D is the well depth, R is the gas constant, and T, is the surface temperature (for a well depth of 2535 kJ/mol, surface temperature of 100 K and incident translational energies less than 21 kJ/mol, this assumption holds for the CH,/Pt(lll) system discussed in this paper); (5) the transition probability P(r, c’) from state e to e’ is a Gaussian (this assumption has been found to be true foi the heavier noble gases Ar, Kr and Xe). If the energy transfer mechanism is not electronic in nature, but rather governed by surface phonons, there exists a simple linear relationship between the mean energy transfer in one transition step, p,, (the only adjustable parameter in the model) and D2 where D is the well depth. For a Gaussian transition probability, Leuthausser derives the following analytical expression for the trapping probability as a function of incident normal translational energy and surface temperature: S(E,)
= :(erfc{
[ E,/(~,
 I)](~i/4k7$‘2}

(1 
S(O)) exp(E,,W)
where
(1  S(O))= [VerfhPkT,)l + ( &/4kT,)“2
((Pl/2kT,)[erf(pl/4kT,)‘i?  I]} exp(U4W.
Here erf and erfc are the error function
and its complement,
respectively.
4.3.2. Application to the CH,/Pt(I I I) system The fit of Leuthausser’s model to our experimental data over the entire incident translational energy range is similar to that obtained with the modified hard cube model (fig. 9). The figure displays the experimental data and also plots of eq. (8) for the initial trapping probability of methane versus incident normal translational energy for three different values of pi at a surface temperature of 100 K. By utilizing the linear relationship between p, and D2 given by Leuthausser, values for the adjustable parameter p, of 6.31, 9.08, and 12.36 kJ/mol were calculated corresponding to well depths D of 25, 30, and 35 kJ/mol. Considering the disparate nature of their assumptions and formalisms, the modified hard cube and Leuthausser’s models are in surprising agreement in predicting the absolute magnitude of the initial trapping probability over the entire incident translational energy range for a given well depth (figs. 8 and 9).
CR. Arumainayagam
et al. / Dynamics of CH, aakorption on Pt(1 II)

25 kJ/mole

30 kJ/mole
233
_
2
0.
0.
INCIDENT
4.
6.
12.
NORMAL KINETIC
16. ENERGY
20.
Fig. 9. Comparison of the experimental S, versus incident normal translational energy data with Leuthlusser’s theory (eq. (8)). Values for p, of 6.31, 9.08, and 12.36 kJ/mol were used for the three curves corresponding to well depths of 25, 30, and 35 kJ/mol. The circles represent the experimental data. The surface temperature was 100 K for both the experiments and computations.
4.4. Accounting
for the differences
between theory and experiment
Even though Leuthausser’s model generally predicts slightly higher initial trapping probabilities than does the modified hard cube model, the predicted trapping probabilities are again lower than the observed values at high incident translational energies even for a well depth as high as 35 kJ/mol. This discrepancy may perhaps be explained by energy loss mechanisms not accounted for in either theory. Both models assume that all of the energy loss occurs via coupling of the incident normal translational energy and surface phonons. If other energy loss mechanisms were operative at higher incident translational energies, the models would underestimate the trapping probability of CH, on Pt(ll1). We consider below several such factors which may account for the discrepancy between these theories and the experimental observations.
234
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et al. / Dynamics
of C%I, adsorprlon on Pt(l11)
4.4.1. Translational to vibrational energy transfer Intramolecular conversion of incident translational energy to vibrational energy upon impact appears unlikely to enhance the trapping of C*H, molecules on the Ptflll) surface. For the experimental conditions described in this paper, neither of the two mechanisms proposed to date for vibrational activation in moleculesurface collisions appears likely. The electronic mechanism for vibrational excitations, a mechanism suggested for NO scattering from Ag(ll1) [65], is improbable since methane, unlike NO, has no lowlying empty orbitals to facilitate the formation of a negative molecular ion leading to vibrational excitations. Moreover, since this mechanism increases exponentially with surface temperature and is essentially nonexistent at a surface temperature of 273 K for the NO/Ag(lll) system, it is unlikely to be operative at the low surface temperatures employed in our study. The other mechanism for vibrational excitation involves direct collisional transfer of translational to vibrational energy. This “mechanical” excitation mechanism has been identified for NH, scattering from Au(lll), and the vibrational excitation was found to increase linearly with incident normal translational energy above a threshold close to the energy of the vibrational energy level being excited [66]. In our experiments, there is sufficient energy to excite the p4 (15.6 kJ/mol) and perhaps even the Ye (18.32 kJ/mol) bending modes of CH, at the highest incident translational energy of 20.2 kJ/mol. However, since methane has no dipole moment, unlike ammonia, there is no long range dipoleimage dipole potential to orient the incident molecules to facilitate T + V energy transfer. Janda et al. searched for vibrational excitation in a 29 kJ/mol CH, beam incident on Pt(l11) at a surface temperature of 180 K by looking for ~brationally inelastic peaks in the time~offight spectrum of the scattered molecules [26]. At angles close to the normal, Janda and coworkers estimated that less than 1% of incident CH, molecules undergo vibrational excitation. Although translational energy resolution may not be the best technique with which to quantify vibrational excitations upon collision, their results imply that translational to vibrational energy transfer is minimal even for a 29 kJ/mol incident beam. Hence, transfer of translational energy to vibrational energy is unlikely to contribute significantly to the trapping of methane on Pt(ll1) at incident translational energies less than 21 kJ/mol employed in the experiments described herein. 4.4.2. Translational to rotational energy transfer The role of tr~slation~rotations energy coupling in the trapping of CH, on Pt(ll1) should also be minimal. In the simplest scenario for rotational excitations [67], a hard, nonspherical molecule undergoes an impulsive collision with a hard, flat surface atom, converting part of its initial translational energy into rotational energy. Since methane is a very nearly spherical molecule this mechanism appears improbable. Another mechanism attributes rota
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235
tional excitations to a strongly orientationdependent attractive potential. In the case of NO, if the molecule approaches the surface in a metastable configuration (i.e., the 0 atom foremost), it is spun around, creating rotational excitations [30]. The absence of an orientationdependent attractive potential for the CH,/Pt(lll) system precludes efficient rotational excitations. The above hypothesis was confirmed tentatively by Janda et al., who found no evidence for the conversion of translational energy into rotational energy at a given detector angle for the CH,/Pt(lll) system [26]. Moreover, even if T + R transfer were to occur, recent studies of NO scattering from Ag(ll1) [68,69] and Ge surfaces [30,31] indicate an anticorrelation of energy transfer into phonon excitations and rotational excitations. In the case of NO scattering from graphite [70] and LiF(100) [71], the final velocity is found to be insensitive to the final rotational state. These examples suggest that if rotational excitations do occur, there is a corresponding decrease in the transfer of incident translational energy into phonon excitations. Thus the sum of the translational energy dissipation to phonons and rotational excitations is approximately constant, and enhanced trapping due to rotational excitation is not expected to be significant. 4.4.3. Other possibilities Several additional factors may also enhance CH, trapping on Pt(ll1). Even though the spread in the incident beam velocities may increase the observed trapping probability, the effect is expected to be minimal because nozzle beams have a narrow velocity .distribution. Electronic excitation via electronhole pairs is unlikely because the interaction of methane with Pt(ll1) is characterized by weak molecular adsorption rather than by dissociative chemisorption for the experimental conditions described herein.The concentration of adsorbed residual gases is believed to be too low to facilitate the trapping of CH, on Pt(ll1). While none of the five mechanisms discussed above can individually account for the observed high trapping probabilities at high incident translational energies, collectively they may explain the discrepancy between the experimental observations and the models. It is also possible that onedimensional theories do not adequately describe trapping even on a relatively smooth surface such as Pt(ll1). Due to relatively large uncertainties (k 0.06) in the methane trapping probability measurements and the limited translational energy range over which these measurements were made, it is possible that we could not detect deviations from normal energy scaling. Recent experimental studies of Xe trapping on the same Pt(ll1) crystal over a wide incident translational energy range show that the initial trapping probability decreases smoothly with increasing E, cos Bi rather than with ET cos28, [72]. Moreover, the measured initial trapping probability of Xe on Pt(ll1) decreases significantly slower with increasing incident translational energy than predicted by Leuthausser’s onedimensional theory.
236
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et al. / Dynamics
of CH, adsorption on Pt(l I I)
Threedimensional stochastic classical trajectory calculations of Xe trapping on Pt(ll1) presented therein, however, give values of S, in semiquantitative agreement with experimental values. Hence the onedimensionality of the modified hardcube model and Leuthlusser’s theory may explain the discrepancy between these theories and our initial trapping probability measurements for the CH,/Pt(lll) system. 4.5. Test of detailed balance for gassurface
interactions
4.5. I. General The decrease in the trapping probability of CH, on Pt(ll1) with increasing incident normal translational energy is consistent with a previous finding of subthermal mean translational energy distributions near the surface normal for the trappeddesorbed component of a methane beam incident on a Pt(ll1) surface [26]. Detailed balance requires that transitions between any two states take place with equal frequency in either direction at equilibrium. For gassurface interactions at equilibrium, detailed balance predicts that the mean energy of molecules desorbing at the surface normal is M
/
ows( un) uzexp(
J%=~ J0
m s( u,,)u~
 u,!/a’)
exp( &/a’)
du, du,
(9) ’
where s(u,) is the trapping (sticking) probability as a function of incident normal velocity u,, and (Y’= 2k,T/M where k, is the Boltzmann constant, M is the mass of the incident gas molecule, and T is the temperature of the gas and the surface [73]. Only if the trapping (sticking) probability is independent of the incident normal velocity will the molecules desorbing at equilibrium at the surface normal have the expected mean energy of 2k,T. If the trapping probability is a decreasing function of the incident normal velocity, the above equation predicts that the mean energy of the desorbing molecules at equilibrium at the surface normal will be less than 2k,T. 4.5.2. CH,/ Pt(l11) system By assuming detailed balance and fitting our experimental S, versus E, data with an exponential for ease of integration, we can estimate the mean translational energy of the methane molecules desorbing at the surface normal. The following functional form was used to fit the observed S,, dependence on E,: SO( E, ) = SO (0) ed
 WRT,
)Y
(104
or equivalently, S,(U,)
= S,(O) exp( M&‘2RT,),
(Lob)
237
6 % Subthermal   7 % Subthermal _.... 8 % Subthermal
6. INCIDENT
NDRMAL
12.
KINETIC
16. ENERGY
20.
Fig. Ii). Expona~tid fit to our experimental S, versus incident normal translational energy data (eq. (lOa& Three curves are presented corresponding to mean ~~~at~o~~ energies which are 6, 7, and 8% subtbermal for molecubs desorbing at the surface normal. The circles represent the experimental data. The surface temperature was 100 K far both the experiments and computations.
Here S,(O) is the initial trapping probability at zero incident normal translational energy and T, is the fitting parameter 1151. Setting S,(O) to unity, which is reasonable since we obtain S,, = 0.94 at E, = 1.7 kJ/md, and T, = 156?,1329, and 1150 K, we see a surprisingly good fit to our experimental data (fig. 10). Substituting eq. (lob) into eq. (9) results in the following expression for the effective translational temperature (T,) of the molecules desorbing at the surface normal [15]: 1 =
=e
f+f. s
w
Based on our experimental S, versus E,, data, we estimate a mean translational energy which is 64% subthermal for methane molecules desorbing at the surface normal at a surface temperature at 100 K. Janda et al. measured directly a 158 subthermal translational energy distribution for methane molecules desorbing at the surface normal for a 9 kJ/mol methane beam incident on Pt(ll1) at surface temperatures between
238
C. R. Arumainayagam et al. / Dynamics of CH, aakorption on Pt(l II)
180 and 250 K 1261. The difference between our calculations and their experimental results can be attributed to the difference in surface temperatures. Consider a gas in ~~~b~urn with a surface, in which case the surface temperature (T,) is equal to the gas temperature Tg (T, = Tg = T). Since slower molecules have a higher probability of trapping, at equilibrium the desorbing molecules have a mean translational energy lower than 2k,T even though the mean translational energy of all the molecules leaving the surface is 2k,T. As T is increased while maintaining equilibrium, the mean energy of the molecules which trap on the surface decreases relative to 2k,T, causing the difference between the effective temperature of the desorbing molecules and T to increase with increasing T. This effect has been previously seen in stochastic trajectory calculations of Xe and Ar desorbing from Pt(lll) [54561 and NO desorbing from Ag(ll1) [75]. Recent experimental observations for the Ar/2HW(lOO) system confirm this trend [22]. A quantitative measure of this effect for the CH,/Pt(lll) system can be obtained by substituting eq. (8), the S, versus E, expression of Leuth&tsser, into eq. (9). For p1 = 6.31 kJ/mol, corresponding to a well depth of 25 kJ/mol, we estimate a 6, 15, and 21% subthermal mean translational energy distribution for methane molecules desorbing at the surface normal at surface temperature of 100, 180, and 250 K, respectively. These calculations suggest that detailed balance holds for methane adsorption and desorption, at least appro~mately, even for an intrinsically nonequilibrium situation involving a collimated monoenergetic beam of methane incident on a Pt(ll1) surface. Similar claims have been previously made for Ar/Pt(lll) [15], H,/Ni(lll) [75], and Ar/2HW(110) [22], among other systems. 4.5.3. Comparison to Ar/PtfIlf) and Xe/Ptfflf) system Less than perfect agreement is obtained between the S, versus E, calculations of Leuthausser [63,64] and the velocity distribution data of Hurst et al. for both the Ar/Pt(lll) [15] and Xe/Pt(lll) [27] systems, however. By appropriately integrating eq. (II), Leuttiusser obtained the trapping (sticking) probabi~ty as a function of incident energy for mon~nergetic species incident with a cos 8 angular distribution in order to compare his calculations with the stochastic trajectory simulations of Tully et al. [54561. Leuthausser obtained good agreement with Tully for the trapping (sticking) probabilities as a function of incident energy by choosing ,ul(xe,PO = 575 K and ~t(~~,,r~)= 130 K. Using the same values of II, and substituting eq. (8) into eq. (9), we calculate 41 and 21% subthe~~ mean tr~slation~ energy dist~bution, respectively, for Ar (T, = 110 K) and Xe (T, = 185 K) atoms desorbing from Pt at the surface normal. The corresponding experimental values are 20% and 0% [15,27]. Hence, if detailed balance indeed applies, Hurst and coworkers’ velocity distribution measurements predict that the trapping probability must fall off more slowly with incident normal translational energy than is indicated
C. R. Arumainayagam et al. / Dynamics of CH, adsorption on Pt(I I I)
239
by Leuthausser’s model (and, perhaps by extension, Tully’s calculations). For example, calculations based on Leuthausser’s model for the Xe/Pt(lll) system indicate that the initial trapping probability falls rather sharply from 0.87 to less than 0.05 as the incident normal translational energy is increased from 0 to 12 kJ/mol at a surface temperature of 185 K. The measured thermal mean translational distribution for Xe desorbing at the surface normal suggests, however, that the initial trapping probability is rather insensitive to incident normal translational energy. This discrepancy is consistent with that found for the CH,/Pt(lll) system for which the measured trapping probabilities were found to fall off more slowly with increasing incident translational energy than indicated by calculations based on Leuthlusser’s model. 4.6. Relating angular distributions
to trapping probabilities
The angular distributions reported in this work for CH,/Pt(lll) are in general agreement with previous measurements [26] which were done over a limited range of scattered angles, surface temperatures, and incident translational energies. However, care must be taken in relating angular distributions to trapping probabilities. Based on the angular distribution for a 9 kJ/mol CH, beam incident at 45O (E, = 4.5 kJ/mol) on a Pt(ll1) surface at 200 K, a trapping probability of 0.20.4 was calculated [26]. This estimate is somewhat lower than the value of 0.6 that we obtained from the direct trapping probability measurement for a 9.1 kJ/mol CH, beam incident at 45” on a Pt(ll1) surface held at 100 K. In addition, we calculate trapping probabilities higher than 0.6 using both the modified hard cube and Leuthausser models for a methane beam with an incident normal energy of 4.6 kJ/mol at a surface temperature of 200 K. We discuss below several possible reasons for the lower trapping probability obtained by integrating angular distributions. Several factors may contribute to the low intensity near the surface normal in the scattering distributions even for a 4.2 kJ/mol CH, beam incident at 45O on a Pt(ll1) surface at 160 K. When estimating the trapping probability by integrating the angular distribution, the outofplane direct inelastic scattering distribution is usually not measured; an assumption of the rotational symmetry about the peak angle must be made. Neither Janda et al. [26] nor we measured the outofplane scattering distribution for the CH,/Pt(lll) system. FOF all of the systems for which this measurement has been made, the outofplane direct inelastic scattering distribution has been found to be significantly narrower than the inplane scattering distribution [15,49]. Hence, assuming a rotationally symmetric lobular scattering fraction overestimates the direct inelastic component and contributes to lowering the value of the trapping probability obtained by integrating the angular distribution. Assuming a cos 6 angular distribution for the trappeddesorbed component can also underestimate the trapping probability of CH, on Pt(ll1). Detailed
bahmce ~~essitat~ that the anguiar ~st~b~tion of the molecules Ieaoing a surface and those impinging cm the surface are identical at equilibrium. By applying this principle it is easily shown that the angular distribution D(B) of molecules dexorbirzg at equilibrium has the following form: D(e)
= KS(e)
cos 8,
112)
where S is the trapping (sticking) probability and K is a factor independent of 8, the polar angle measured from the surface normal [73]. Hence Knudsen% cosine law is valid only if S is independent of the incident angle 8. Assuming detailed balance applies to CII,/Pt(lll) system, where the trapping prohability increases with increases incident angle, eq. (X2) predicts that the angular dependence of the trappingd~~~o~ ehanneI should be broader than cosine. In fact, ~~~t~us~r’s calculations for the t~app~dared component of the Ar,/Pt(lll) system show a significant noncosine behavior with the flux shifted towards large angles [64]. A quantitative measure of this effect can be readily obtained by using the following relationship between the angular distribution D( 8) = cos’‘“e and the mean translational energy, Ed, of structureless particles desaibing at the surface normal [76]: (13) The only eruption made in this q~~t~rn mechanicaf formalism by Doyen is that the ~~~tio~ of the gassurface potential pamIld to the surface is small; there is no assump~on regarding the gasphonon interactiun. For T, = 160 K and pr = 6.31 kJ/moI, we estimate a 12.6% s~~th~~ translatiunal energy distribution for methane molecules desorbing at the normal, corresponding to n = OS, according to eq. (13). Thus, the angular distribution of the trappeddesorbed component is cos”%. This effect leads to an underestimation of the trapping probability by 25% if the true angular distribution of the trappeddesorbed component is cos”.58 rather than cos 8. This effect may account partially for the discrepancy between the direct trapping probability measurements and those estimated from the angular distributions. It is also possible that the trapping ~~~b~bi~ty of CHI, on Pt(fll) actually decreases rapidly with increasing surface t~m~rature~ a ph~orne~u~ which would explain the relatively smah trap~d~~r~d ~mponent in the scattering distribution of CH, from PtQll). Both our scat%ering distributions and those of Janda et al. f2fj were done at surface temperatures at or above I60 R. We were unable to obtain scattering distributions at r, = 100 K, the temperature at which the initial trapping probabilities were determined because at that temperature the trappeddesorbed channel is demodulated. If the trapped probability decreases appreciably between surface temperatures of 100 and 160 K, it is possible to reconcile the angular distributions and the direct trapping probability measurements. There is clearly little change between 160
C.R. Arumainayagam et al. f @namics of CH, a~o~ption on Ptfl I I)
241
and 500 K in the angular ~st~butions, however, as shown in fig. 7, suggesting that S, is insensitive to surface temperature in this range. Several theoretical studies indicate that trapping probability is a decreasing function of surface temperature. Weinberg and Merrill used a classical mechanics model with an assumed attractive square well potential and an impulsive repulsive potential to obtain initial trapping probabilities from thermal accommodation data [62]. Their calculations show, for example, that the trapping probability of Ar on W decreases modestly from 0.44 at T, = 0 K to 0.28 at T, = 375 K for beam temperatures of approximately 300 K. By extending the formalism of Chandler [77] to obtain dynamical corrections to transition state theory, Adams and Doll [783 have studied the dynamical aspects of precursor state kinetics. Their c~c~ations show that the precursor sticking (trapping) probability decreases more dramatically with increasing surface temperature, from  0.7 at T, = 300 K to essentially zero at T, = 900 K. They cite Tully’s generalized Langevin calculations for Xe/Pt(lll) [54] as additional theoretical support for their calculations. However, since Tully’s results showing that the sticking (trapping) probability of Xe on Pt(ll1) decreases with increasing temperature were obtained assuming that the gas and the surface are at the same temperature, it is not possible to draw any conclusions regarding the surface temperature dependence of the trapping probability of Xe on Pt(ll1). Several experimental results have also been interpreted in terms of a trapping probability decreasing with increasing surface temperature. By integrating the diffuse fraction for incident effusive beams of rare gases scattered from W(llO), Weinberg and Merrill calculated, for example, that the trapping probability of Xe decreases rather slowly from  0.76 to 0.62 as the surface temperature increases from 375 to 1300 K for a constant incident gas temperature of 295 K [14]. Janda et al. [79] claimed that the previously observed rapid decrease in the dissociative sticking probability of N, on several crystal planes of W could be explained by a condensation coefficient (trapping probability) into the molecular precursor state decreasing significantly with increasing surface temperature. The trapping probability as a function of surface temperature was obtained by deconvoluting the tuneofflight spectrum into a trappeddesorbed component and a direct inelastic component. Alnot and King [SO], however, question the validity of this deconvolution and explain the surface temperature dependence of the dissociative sticking probabi~ty not as a result of the trapping probability decreasing with surface temperature, but rather as a consequence of the different barrier heights to dissociation and desorption from the molecular precursor state. Recent molecular beam studies of the N,/W(lOO) system confirm that the trapping probability of N, on tungsten is essentially independent of surface temperature [12]. As discussed previously, the King and Wells method does not provide true initial adsorption probabilities as the surface temperature approaches the desorption temperature of the molecule of interest (fig. 5). By deconvoluting
242
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et al. / Dynamics of CH, aabrption on Pt(I 1 t)
either the angular dist~bution or the velocity distribution data it is possible, at least in principle, to measure the trapping probability at surface temperatures near or above the desorption temperature. However, uncertainties associated with the trappeddesorbed component preclude precise comparison of the trapping probabilities at different surface temperatures based on angular distributions alone. If a density detector is used to measure the angular distribution, the measured intensity must be multiplied by the velocity to obtain the flux distribution. It is commonly assumed that the mean velocity of the trappeddesorbed component is proportional to T,‘j2 in order to make this correction. However, as discussed previousiy, the proportionality factor may also depend on the surface temperature which makes this procedure inaccurate. Moreover, recent expe~mental results for the Ar/2HW(ll~) system suggest that the deviation of the angular distribution of the trapped desorbed component from cos B becomes more pronounced as the surface temperature is increased [22]. The normalized density distribution of CH, scattered from Pt(lll) at two different surface temperatures, 160 and 500 K, is shown in fig. 7. Since the trapping probability equals the trappeddesorbed component divided by the sum of the trappeddesorbed and the direct inelastic components, the flux at large negative angles in a normalized flux distribution provides a rough measure of the trapping probability. The relative flux at  35 o was calculated by making the 7;‘j2 correction and was found to be nearly invariant with surface temperature in the range of 160500 K to within experimental error. At such a large negative angle the direct inelastic component is expected to be minimal. Hence, the above observation suggests that the trapping probability is rather insensitive to surface temperature over this range. Therefore, it is unlikely that the trapping probability decreases sufficiently between 100 and 160 K to explain the discrepancy between the angular distributions and the King and Wells measurements. This conclusion is further supported by both the modified hard cube and Leuth&usser”s models. Calculations using these models of the trapping probability of CH, on Pt(ll1) as a function of surface temperature for several different incident normal translational energies are shown in fig. 11. An effective surface mass of 1.5 surface atoms and a well depth of 30 kJ/mol (pi = 9.08 kJ/mol) were used in these calculations. Leuthausser’s model indicates that the trapping probabi~ty decreases from 0.97 to 0.93 when the surface temperature is increased from 100 to 160 K for an incident normal energy of 1.5 kJ/mol. Corresponding values for the modified hard cube model are 0.89 and 0.83. Clearly, the trapping probability estimated by these models does not decrease appreciably between q = 100 and 160 K. These calculations also reveal a surprising effect (fig. 11): namely, both models indicate that the trapping probability increases with increasing surface temperature for incident normal translational energies greater than  10 kJ/mol. A similar trend was observed for high incident translational energies
C. R. Arumainayagam
et al. / Dynamics of CH, aakorption on Pi(l1 I)
SURFACE
TEMPERATURE
243
Fig. 11. The surface temperature dependence of the initial trapping probability for incident normal translational energies of 1.5, 10 and 20 kJ/mol as predicted by the modified hard cube model (solid line) and Leuthausser’s theory (dashed line). A well depth of 30 kJ/mol tias chosen corresponding to a pt of 9.08 kJ/mol. The effective surface mass was 1.5 atoms for the modified hard cube model calculations.
by Barker et al. [Sl] in a computational study of Ne scattering from Ag(ll1). The modified hard cube model provides a simple explanation of this effect. Consider a surface at 0 K, where all of the surface atoms are frozen rigidly in space. Since the hard cube model is classical in nature, zero point energy is ignored. Suppose a beam of molecules impinges on this 0 K surface with a high velocity (u) such that none of the molecules trap ( uc < 0 hence S, = 0). As the surface temperature is increased above 0 K, increasingly more surface atoms will be moving towards the bulk with a velocity (u) whose magnitude is greater than the magnitude of u, (u < u, since the direction away from the bulk is defined to be positive), and, therefore, more incident molecules will be trapped as the surface temperature is increased. With Leuthasser’s model, a simple explanation of this trend is not immediately apparent. To the best of our knowledge no experimental data exist to confirm this effect.
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on Pt(l I I)
5. Conclusions Using supersonic molecular beam techniques, we have shown that the initial trapping probability of CH, on Pt(ll1) varies smoothly with normal incident translational energy (E, = E, cos*B), suggesting a low twodimensional corrugation of the gassurface potential. The initial trapping probability at T, = 100 K falls from close to unity at a low I?, to almost 0.1 at an E, of  20 kJ/mol in quantitative agreement with both a modified hard cube model and Leuthausser’s theory except at high incident translational energies. The measured angular distributions suggest that the trapping probability is not a sensitive function of surface temperature. A comparison of our S, versus E, data with previous mean translational energy measurements for the same system indicates that detailed balance may apply for the nonequilibrium situation involving a collimated monoenergetic molecular beam of methane incident on a Pt(ll1) surface.
Acknowledgement We gratefully acknowledge the Department of Energy, Chemical Sciences Division, Office of Basic Energy Sciences (grant DEFGO386ER13468) for financial support for this work.
Note added in proof We believe that the 140 K methane TPD peak is associated with defect sites on the Pt(ll1) surface since the saturation coverage in this state is only 0.01 monolayers. Almost all of the methane adsorbed at 100 K during a direct trapping probability experiment desorbs when the beam flux is removed, suggesting that the methane desorbs from the smooth surface (terraces) at or below 100 K. The surface defects bind trapped methane due to the higher binding energy at these sites. Competitive desorption is not expected to lead to a large underestimation of the initial trapping probability at 100 K since we were able to measure an initial trapping probability very close to unity at that temperature.
References [l] C.T. Rettner, H.E. Pfniir and D.J. Auerbach, Phys. Rev. Letters 54 (1985) 2716. [2] H.E. Pfniir, C.T. Rettner, J. Lee, R.J. Madix and D.J. Auerbach, J. Chem. Phys. 85 (1986) 7452. (31 C.T. Rettner, L.A. DeLouise and D.J. Auerbach, J. Chem. Phys. 85 (1986) 1131.
C.R. A~ma~~yagam [4] [5] f6] [7] [8]
et al. f Dynamics of CH, adsorption on Ptflf 1)
245
A.V. Hamza and R.J. Madix, Surface Sci. 179 (1987) 25. A.V. Hamza, H.P. Steimiick and R.J. Madix, J. Chem. Phys. 86 (1987) 6506. A.V. Hamza and R.J. Madii, J. Chem. Phys. 89 (1985) 5381. M.P. D’Evelyn, A.V. Hamza, G.E. Gdowski and R.J. Madix, Surface Sci. 167 (1986) 451. G.R. Schoofs, C.R. Arumainayagam, MC. McMaster and R.J. Madix, Surface Sci. 215 (1989) 1. [9] M.B. Lee, Q.Y. Yang and S.T. Ceyer, J. Chem. Phys. 87 (1987) 2724. (lo] M.D. Williams, D.S. Bethune and AC. Luntz, J. Chem. Phys. 88 (1988) 2843. [ll] C.T. Rettner and H. Stein, Phys. Rev. Letters 59 (1987) 2768. [12] C.T. Rettner, H. Stein and E.K. Schweizer, J. Chem, Phys. 89 (1988) 3337; CT. Rettner, E.K. Schweizer, H. Stein and D.J. Auerbach, Phys. Rev. Letters 61 (1988) 986. [13] A.G. StoB, D.L. Smith and R.P. Merrill, J. Chem. Phys. 54 (1971) 163. [14] W.H. Weinberg and R.P. Merrill, J. Chem. Phys. 56 (1972) 2881. [15] J.E. Hurst, Jr., L. Wharton, K.C. Janda and D.J. Auerbach, J. Chem. Phys. 83 (1985) 1376. [16] H. Schlichting, D. Men&, T. Brunner, W. Brenig and J.C. Tuily, Phys. Rev. Letters 60 (1988) 2515. [17] S. Andersson and J. Harris, Phys. Rev. Letters 48 (1982) 545. [la] S. Andersson, L. Wilxen and J. Harris, Phys. Rev. Letters 55 (1985) 2591. [19] L. Wilzen, S. Andersson and J. Harris, Surface Sci. 205 (1988) 387. (201 H.P. Steinriick and R.J. Madii, Surface Sci. 185 (1987) 36. [21] G.R. Schoofs, CR. Arumainayagam and R.J. Madix, J. Vacuum Sci. Technol. A 6 (1988) 882. [22] CT. Rettner, E.K. Schweixer and C.B. Mullins, J. Chem. Phys. 90 (1989) 3800. [23] J.C. ‘Tully and M.J. CardiIlo, Science 223 (1984) 445. [24] H. Metiu and J.W. Gadzuk, J. Chem. Phys. 74 (1981) 2641. [25] F. Sob, N. Garcia and F. Flares, Surface Sci. 146 (1984) L577. [26] KC. Janda, J.E. Hurst, 3. Cowin, L. Wharton and D.J. Auerbach, Surface Sci. 130 (1983) 395. [27] J.E. Hurst, CA. Becker, J.P. Cowin, KC. Janda, L. Wharton and D.J. Auerbach, Phys. Rev. Letters 43 (1979) 1175. 1281 D. Auerbach, C. Becker, J. Cowin and L. Wharton, Appl. Phys. 14 (1977) 141. [29] D.J. Auerbach and C.T. Rettner, in: Kinetics of Interface Reactions, Eds. M. Grunxe and H.J. Kreuzer (Springer, Berlin, 1987). 1301 A. Miidl, T. Gritsch, F. Budde, T.J. Chuang and G. Ertl, Phys. Rev. Letters 57 (1986) 384. [31] F. Budde, A. M&B, A.V. Hamza, P.M. Ferm and G. Ertl, Surface Sci. 192 (1987) 507. [32] D.A. King and M.G. Wells, Surface Sci. 29 (1972) 454. [33] D.A. King and M.G. Wells, Proc. Roy. Sot. (London) A 339 (1974) 245. [34] GE. Gdowski, PhD Thesis, Stanford University, 1985. [35] J.B. Anderson and J.B. Fenn, Phys. Fluids 8 (1965) 780. (361 R.J. GaBagher and J.B. Fenn, J. Chem. Phys. 60 (1974) 3487. [37] D.R. Miller, in: Atomic and Molecular Beam Methods, Ed. G. Stoles (Oxford University Press, Oxford, 1988). 1381T.L. CottreIl and J.C. McCoubrey, Molecular Energy Transfer in Gases (Butterworths, London, 1961). [39] G. Herrberg, Molecular Spectra and Molecular Structure, Vol. 2 (Van Nostrand, Princeton, NJ, 1968). [40] B. Poelsema, L.K. Verheij and G. Comsa, Phys. Rev. Letters 49 (1982) 1731. [41] J.C. McCarty and R.J. Madix, Surface Sci. 54 (1976) 121. [42] C.M. Chan, R. Aris and W.H. Weinberg, Appl. Surface Sci. 1 (1978) 360. [43] D. Edwards, Jr., Surface Sci. 54 (1976) 1. [44] E. Shustorovich, Surface Sci. 176 (1986) L863.
246
CR. A~rnajnuy~gurn
et al. / Dynamics of CH, adsorption on Pt(lllf
1451 S.G. Brass and G. Ehrlich, Surface Sci. 187 (1987) 21.
[46] J.T. Yates, Jr. and T.E. Madey, Surface Sci. 28 (1971) 437. [47] T.E. Madey, Surface Sci. 29 (1972) 571. [48] G.R. Schoofs, C.R. Arumainayagam, M.C. McMaster and R.J. Madii, to be published. [49] H. Asada, Japan. J. Appl. Phys. 19 (1980) 2055. [SO] R.M. Logan and R.E. Stickney, J. Chem. Phys. 44 (1966) 195. [51] R.M. Logan and J.C. Keck, J. Chem. Phys. 49 (1968) 860. [52] J.A. Barker and D.J. Auerbach, Surface Sci. Rept. 4 (1985) 1. [53] M. Persson and J. Harris, Surface Sci. 187 (1987) 67. [54] J.C. Tully, Surface Sci. 111 (1981) 461. [55] E.K. Grimmelmann, J.C. Tully and E. Helfand, J. Chem. Phys. 74 (1981) 5300. [56] J.C. TuBy, Faraday Disc. Chem. Sot. 80 (1985) 1. [57] M.P. D’Evelyn, H.P. Steinrtick and R.J. Madix, Surface Sci. 180 (1987) 47. [58] T.A. Del&u and G. Ehrhch, J. Chem. Phys. 42 (1965) 2686. [59] E.K. Grimmelmann, J.C. Tulfy and M.J. Cardillo, J. Chem. Phys. 72 (1980) 1039. [60] Ch. Steinbrtichel and L.D. Schmidt, J. Phys. Chem. Solids 34 (1973) 13’79. (611 A. Hurkmans, E.G. Overbosch, D.R. Olander and J. Los, Surface Sci. 54 (1976) 154. [62] W.H. Weinberg and R.P. Merrill, J. Vacuum Sci. Technol. 8 (1971) 718. [63] U. Leuthausser, Z. Phys. B (Condensed Matter) 44 (1981) 101. [64] U. Leuthausser, Z. Phys. B (Condensed Matter) 50 (1983) 65. [65] C.T. Rettner, F. Fabre, J. Kimman and D.J. Auerbach, Phys. Rev. Letters 55 (1985) 1904. [66] B.D. Kay, T.D. Raymond and M.E. Cohrin, Phys. Rev. Letters 59 (1987) 2792. [67] G.D. Kubiak, J.E. Hurst, H.G. Rennagel, G.M. McClelland and R.N. Zare, J. Chem. Phys. 79 (1983) 5163. [68] J. Kimman, C.T. Rettner, D.J. Auerbach, J.A. Barker and J.C. Tully, Phys. Rev. Letters 57 (1986) 2053. [69] CT. Rettner, 3. Kimman, F. Fabre, D.J. Auerbach, J.A. Barker and J.C. Tully, 3. Vacuum Sci. Techol. A 5 (1987) 508. 1701 J. Misewich, H. Zacharias and M.M.T. Loy, J. Vacuum Technol. B 3 (1985) 1474. [71] J. HQer, Y.R. Shen and H. Walther, Phys. Rev. A 31 (1985) 1962. [72] C.R. Arumainayagam, M.C. McMaster, V.M. Suzawa, R.J. Madix and J.C. Tully, Surface Sci., submitted. [73] G. Comsa, in: Proc. 7th Intern. Vacuum Congress and the 3rd Intern. Conf. on Solid Surfaces, Vienna, 1977, p. 1317. [74] C.W. Muhlhasen, L.R. Williams and J.C. Tully, J. Chem. Phys. 83 (1985) 2594. [75] H.P. Steinruck, K.D. Renduhc and A. Winkler, Surface Sci. 154 (1985) 99. [76] G. Doyen, Vacuum 32 (1982) 91. [77] D. Chandler, J. Chem. Phys. 68 (1978) 2959. [78] J.E. Adams and J.D. Doll, Surface Sci. 111 (1981) 492. 1791 K.C. Janda, J.E. Hurst, C.A. Becker, J.P. Cowin, L. Wharton and D.J. Auerbach, Surface Sci. 93 (1980) 270. [SO] P. Alnot and D.A. King, Surface Sci. 126 (1983) 359. [Sl] J.A. Barker, D.R. Dion and R.P. Merrill, Surface Sci. 95 (1980) 15.