On the dependence of energy exchange and corrugation in atom-surface scattering: Argon scattering from Ni(115)

Surface Science 183 (1987) 515-530 North-Holland, Amsterdam

515

ON THE DEPENDENCE OF ENERGY EXCHANGE A N D C O R R U G A T I O N IN A T O M - S U R F A C E S C A T r E R I N G : ARGON SCATrERING FROM Ni(ll5) R a l p h M. A T E N , David B L A N C H A R D , L y n n R. A L L E N , E d w a r d R. C O N R A D , M a r k N E L S O N a n d T h o m a s E N G E L Department of Chemistry, BG-IO, University of Washington, Seattle, WA 98195, USA

Received 10 September 1986; accepted for publication 2 December 1986 The scattering of Ar from Ni(ll5) has been studied for a range of incident energies and surface temperatures. Both angular distributions integrated over all outgoing energies and timeof-flight studies at selected final angles have been carried out. Lobular angular distributions are observed for in-plane scattering with the beam incident in the uncorrugated [110] azimuth whereas rainbow scattering distributions consistent with a corrugation amplitude of 0.4 A are observed in the strongly corrugated [5-52] azimuth. The dependence of the final energy on initial energy and surface temperature is well described by the hard cube equation: E f / 2 k T s = (o~gEi/2kTO+ ots. To within the experimental error, ag and a s are the same for scattering with the beam incident in both azimuths. This indicates that energy transfer in atom-surface scattering does not depend strongly on the surface corrugation. However, the angular scattering distributions are not well described by hard cube models.

1. Introduction The loss of energy of atoms a n d molecules to a surface u p o n which they i m p i n g e is of i m p o r t a n c e in a variety of processes. A m o n g these are energy a n d m o m e n t u m a c c o m m o d a t i o n a n d the kinetics of adsorption. A molecule which can be chemisorbed o n a surface must first lose sufficient kinetic energy that it is trapped n o r m a l to the surface. C h e m i s o r p t i o n at a fixed site occurs w h e n a d d i t i o n a l energy is lost so that the molecule is n o longer m o b i l e parallel to the surface. Rare gas scattering is a useful probe of the initial stage of this process since physisorption b u t n o t c h e m i s o r p t i o n can occur. F o r this reason, the complexities of the overall c h e m i s o r p t i o n process (which i n c l u d e a transition from a long-range weak i n t e r a c t i o n to short-range chemical b o n d formation) can be avoided. A n u m b e r of studies have been carried o u t recently involving energy loss or gain of heavy n o b l e gas atoms which strike a single crystal surface. These include A r scattering from P t ( l l l ) [1] i n which the direct inelastic process has been studied, t r a p p i n g desorption of A r o n P t ( l l l ) [2], a n d the study of b o t h processes in Xe scattering from P t ( l ] l ) [3]. I n addition, direct inelastic a n d trapping d o m i n a t e d scattering of N 2 a n d C H 4 from P t ( l l l ) have been investigated [4]. 0 0 3 9 - 6 0 2 8 / 8 7 / $ 0 3 . 5 0 9 Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)

516

R.M. Aten et al. / Argon scattering from Ni(115)

An important result which emerged from the direct inelastic studies is that the incoming particle energy El, the scattered particle energy El, and the surface temperature T~ are related by Ef/2kT

s = (o/ggi/2kTs)

-I--ors.

(1)

In this equation ag and a S are constants which lie near 0.8 and 0.2, respectively. The simplicity of this relationship and the fact that only the ratios of E e and E i to T~ rather than their individual values are of importance has been shown to follow from hard cube models [5,6]. In these models, the parallel momentum is assumed to be conserved and the surface atoms are modelled by flat cubes which move independently vertical to the surface with a velocity related to the surface temperature. Thus the physical significance of the equation is easily understood. The first term takes into account the energy transfer of the incoming atom with a surface cube. The second term adds the contribution from the vibrational amplitude of the surface atoms which increases with temperature. The validity of these models has been discussed elsewhere [5-7]. Although they are not suitable for predicting the angular distribution of scattered particles, they are very useful in predicting the energy exchange with the surface. To date, all investigations of energy accommodation on single crystal surfaces have been carried out on the P t ( l l l ) surface. Due to its close packing, the corrugation of this surface as measured by helium diffraction is very small [8]. Model calculations indicate that the energy exchange with a surface should be sensitive to the surface corrugation. More open surfaces which have high corrugation amplitudes are predicted to lead to more inelastic scattering than surfaces of low corrugation [6,9]. We have investigated the dependence of inelastic scattering on corrugation amplitude by scattering_argon from the N i ( l l 5 ) surface. This surface is strongly corrugated in the'[552] azimuth and weakly corrugated in the [110] azimuth as measured with helium diffraction. This technique gives corrugation amplitudes in these directions of 0.62 + 0.02 and less than 10 -2 A respectively [10]. Therefore, by aligning the beam parallel to each azimuth in turn, and detecting only in-plane scattering, the effective corrugation can be varied while leaving all other parameters unchanged. In this way, the dependence of energy exchange on corrugation can be measured directly. In section 2 of this article, we describe the apparatus used in these experiments. In section 3 we present angular scattering distributions for scattering in the [5-5-2]and [110] azimuths. Section 4 deals with the time-of-flight data and in section 5 we discuss the results.

2. Experimental The apparatus which was used in the studies has been described in detail elsewhere [11]. The molecular beam generating portion consists 0f four dif-

R.M. Aten et al. / Argon scattering from Ni(115)

517

ferentially pumped stages. The nozzle-skimmer chamber is pumped by a ring jet ejector p u m p whereas all other stages are pumped with diffusion pumps. The beam is chopped by a 50% duty cycle chopper in the third differential stage using a vacuum compatible motor. The scattering chamber is pumped by a 510 E/s turbomolecular p u m p and a titanium sublimation pump. Base pressures of 1 X 10 -1~ Torr are achieved after a 48 h bakeout at 130~ The beam has a diameter of 1.0 m m at the point where it strikes the crystal. The N i ( l l 5 ) single crystal sample is mounted on a three axis manipulator with x y z motion and can be cooled to 80 K. The manipulator is described in detail elsewhere [12]. The scattered beam is detected using a quadrupole mass spectrometer contained within two differentially pumped vacuum chambers. The quadrupole together with the differential pumping chambers are rotated about an axis which is colinear with the sample polar rotation axis using differentially pumped spring loaded Teflon seals [13]. The N i ( l l 5 ) sample was spark eroded into a 3 m m thick disc of - 7 m m diameter and oriented using Laue backscattering techniques. To remove bulk carbon, the crystal was heated to 1100 K in 3 x 10 - 6 Torr 02 for 24 h. The crystal was then reoriented and the oxide coating was removed by mechanical polishing after which the crystal was chemically etched in a solution of 50% glacial acetic acid, 30% nitric aid, 10% sulfuric acid and 10% orthophosphoric acid. The front surface was estimated to be perpendicular to the [115] direction to within +0.3 ~ Final cleaning in vacuum consisted of cycles of 10 min sputtering with 1000 eV argon ions followed by 5 rain annealing at 1100 K. Typically 48 h of cycling reduced the oxygen, sulfur and carbon peak Auger signals (measured with a cylindrical mirror analyzer) to 0.8%, 0.2% and 0.5%, respectively, of the 848 eV nickel Auger peak. This corresponds to surface coverages of less than 0.2% C, 0.4% O and 0.3% S [14]. The surface was then annealed by cooling at a rate of 2 K s -1 from 1100 to 400 K. After this treatment, the surface could be heated to 800 K for 15 rain without any significant O, C or S diffusion to the surface. For longer heating to higher temperatures, chlorine and oxygen were found to diffuse to the surface and could only be removed by sputtering. The helium diffraction peak intensities and half widths were found to be extremely sensitive to small amounts of contaminants. Reproducible results could be obtained only for O, C and S concentrations well below 1% of a monolayer. Argon beams were produced by expansion at 2 - 3 atm through a 75 /~m nozzle. The energy of the incident Ar atoms was varied over the range 63-273 meV by seeding in helium and by heating the nozzle. For time-of-flight (TOF) measurements of the Ar energy, the beam was chopped by a 1% duty cycle chopper. This led to a typical 20 x 10 -6 S F W H M pulse at the chopper. A reference signal was generated using a helium-neon laser beam which passed through the chopper and on to a photodiode external to the vacuum system.

R.M. Aten et al. / Argonscatteringfrom Ni(ll5)

518

T O F data were taken by routing the output pulses of the continuous dynode multiplier mounted on the quadrupole mass spectrometer to a multichannel scaler of minimum channel width 1 • 10 -6 s. This was interfaced to an LSI 11/23 laboratory computer. Angular distributions were taken using a separate 50% duty cycle chopper. For both T O F and angular distributions, the resolution of the detector is 0.6 o F W H M . The detector can intercept the beam both between the chopper and sample position and after the sample position. These two positions lie 31.26 cm apart, symmetrically about the sample position. By measuring T O F spectra at both positions, instrumental parameters such as the phase angle between the beam and the reference signal can be eliminated. In these experiments, the sample-detector distance is 15.63 cm and the c h o p p e r - s a m p l e distance is - 22.6 cm. The measurement of particle energies of T O F spectra for atom scattering from surfaces has been discussed in detail elsewhere [1]. We have fit our data to the expression

R(t) d t = _ ~ e x p [ _ ( 1

112d2 ]

- t0] ./2]dt'

(2)

where d is the flight path and d/t o = vo. This quantity characterizes the flow velocity which takes on the value zero for a Maxwellian velocity distribution. In the above equation, N is a normalizing constant. The quantity 72 = m / 2 k T H, where m is the particle mass, k is the Boltzmann constant and T H is the temperature of the beam in the frame of reference moving with the beam at velocity v0. The parameter y measures the spread in arrival times of the pulse. Eq. (2) is general enough to allow fitting of Maxwellian beams as well as beams with high speed ratios using the two parameters v0 a n d 7- The average particle energy is given by the expression

( E ) = 89

2)

=

89

2 + 7~2

_

_

6y4/(av0z + 6 y 2 ) ] .

(3)

To characterize the incident beam we have measured T O F spectra at the two positions described above. The T O F spectra measured further away from the chopper are given by the convolution integral

D(t) =

f'_ G(t')R(t- t')

dr,

(4)

where G(t') is the effective gating function measured at the position nearest the chopper and R ( t - t ' ) is given by eq. (2). TII was less than 5 K for E i < 130 meV and increased to 18.3, 120 and 143 K for energies of 164, 244 and 273 meV, respectively. The nozzle temperature was 300 K for all but the two highest energies, for which heating was necessary to achieve such beam energies. In order to analyze T O F spectra taken after scattering from the surface, eq. (4) was solved numerically with G ( t ' ) calculated at the surface position using

519

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TIME (MI CROSECONDS) Fig. 1. Time of flight spectrum for the Ar beam passing directly into the detector. Best fit parameters to give the solid curve are vo = 3.91 • 104 c m / s and V = 0.66 • 104 c m / s . 0.10-.

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520

R.M. Aten et aL / Argon scatteringfrom Ni(115)

the T O F spectra taken for the direct beam at the two positions which are equidistant from the sample position. In this way the effect of broadening of the gas pulse due to the spread in beam velocities which occurs between the chopper and the surface can be separated from changes of the velocity distribution upon collision. Typical T O F spectra for the incident beam and following scattering from the surface are shown together with the best fit to the data in figs. 1 and 2.

3. Angular distribution for argon scattered from Ni(ll5) 3.1. Scattering in the [1-10] azimuth

Figs. 3 and 4 show angular scans for argon scattering with the beam incident in the weakly corrugated [110] azimuth. As is expected, based on previous studies on close packed surfaces [14,15], a lobular pattern is seen with the m a x i m u m intensity occurring near the specular angle. The distribution is consistent with direct inelastic scattering from a weakly corrugated surface. As has been observed previously [14], the half width of the lobular peak decreases with increasing beam energy. 1,

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Fig. 3. Angular distributions of backscattered Ar intensity with the beam incident in the [1i0] azimuth. E i = 63 meV, 0 i = 3 0 o a n d T s = 273 K.

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Fig. 4. Angular distributions of backscattered Ar intensity with the beam incident in the [110] azimuth. E i =115 rneV, 0i = 30 ~ and T~= 273 K.

3.2. Scattering in the [552] azimuth In-plane angular distributions with the beam incident in the [552] azimuth are shown in figs. 5 and 6. These patterns are characteristic for rainbow scattering which has been observed previously on strongly corrugated surfaces [14]. For a sinusoidal corrugation and an attractive well depth D, the rainbow angles 0r for an atom of " n o r m a l energy" E , = E i COS20i are given by [16] (1 + D / E , ) i / 2

= sin

(1 + D / E n ) 1/2

In this equation /3 is the m a x i m u m angle of inclination of the corrugation function within the unit cell. Since the well depth of the A r - N i ( l l 5 ) potential is not known, we have assumed it to be 1000 K which is the experimentally determined value on tungsten [17]. Since the corrugation is not expected to be perfectly sinusoidal, the rainbow angles for forward and backscattering are expected to vary somewhat. As can be seen by the arrows in figs. 5 and 6, good agreement is attained for/3 = 10 ~ + 2 ~ The forward scattering rainbow angle in fig. 5 is not fully developed and may be cut off due to shadowing effects. For a sinusoidal corrugation, the peak to peak corrugation ~max is given by

~,

=

( a/Tr ) tan/3,

(6)

522

KM. Aten et aL / Argon scattering from Ni(l l 5) I

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Fig. 5. Angular distributions of backscattered Ar intensity with the beam incident in the [552] azimuth. Ei =190 meV, 0 i = 30 ~ and T~ = 273 K.

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R.M. Aten et al. / Argon scattering from Ni(l l 5)

523

where a is the lattice constant. Using this expression, we arrive at a corrugation amplitude o~ma x = 0.36 + 0.08 ,A. This is somewhat smaller than the values of 0.62 + 0.02 A and 0.50 _ 0.02 ~, which were obtained from helium diffraction studies using a corrugated hard wall potential and a corrugated Morse potential, respectively [10].

4. Energy exchange between argon and N i ( l l 5 )

4.1. Scattering with the beam incident in the [552] azimuth Most of the data collected in this azimuth is for 8 i = 30 ~ and Of = 8 ~ This exit angle corresponds to the intensity maximum in the backscattered rainbow. The values of the fitting parameters y and v0 for different E i and T~ are shown in table 1 together with the calculated values of Ei and El. Table 2 shows additional data in which the value of Of is changed from the maximum in the backscattered rainbow to the specular angle. The data in tables 1 and 2 are shown in fig. 7 in the form of a plot of Ef/2kT~ versus E i / 2 k T~. The solid line shows the best fit for a hard cube model without an attractive potential. In this model there is only one adjustable parameter since a g = 1 - [4/x/(/x + 1) 2] cos20i ,

(7)

Table 1 Energies and best fit parameters to eqs. (2) and (3) for scattering in the corrugated direction, with 0 i = 3 0 ~ and 0 ~ = 8 ~ Ts (K)

(Ei) (meV)

(Ef) (meV)

y (10 4 c m / s )

vo (10 4 c m / s )

800 650 500 450 350 300 200 200 347 308 304 310 306 400 325 299 250

63.1 67.1 63.1 67.1 63.1 63.1 63.1 67.1 129.2 129.2 129.2 164.1 244.3 273.0 273.0 273.0 273.0

77.9 80.4 63.9 67.4 59.1 56.9 55.7 59.1 106.6 102.4 104.5 129.6 183.0 213.8 211.3 204.8 199.1

3.15 2.95 2.50 2.43 1.94 1.84 1.73 1.67 2.06 1.92 1.93 1.68 2.45 3.42 3.27 3.14 3.06

3.01 3.57 3.42 3.76 4.04 4.06 4.13 4.39 6.11 6.09 6.15 7.28 8.25 8.04 8.16 8.12 8.07

524

R.M. Aten et al. / Argon scattering from Ni(115)

Table 2 Energies and best fit parameters to eqs. (2) and (3) for scattering in the corrugated direction, with 0 i = Of = 30 ~ Ts

(El)

(El)

y

(K)

(meV)

(meV)

(104 c m / s )

o0 (10 4 c m / s )

450 450 250 250

67.1 115.2 67.1 115.2

66.7 91.3 58.3 88.8

2.27 2.15 1.88 1.82

3.99 5.37 4.08 5.64

and

=

-

+ 1) 2,

(8)

where I.L = m A r / t o N i . T h e b e s t f i t l i n e c o r r e s p o n d s t o a s = 0 . 1 7 + 0 . 0 4 , a g = 0 . 7 3 + 0 . 0 7 w i t h toNi = 352 + 100 amu. This must be viewed as an effective mass and since each s u r f a c e n i c k e l a t o m is c o u p l e d

to its neighbors,

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R.M. Aten et al. / Argon scattering from Ni(l l 5)

525

the mass of an individual nickel atom. N o t e that the data points for Of = 30 ~ fall on the same line as the data for Of = 8 ~ to within the experimental error. Letting a S and ag vary independently yields best fit values of 0.25 _ 0.10 and 0.70 • 0.09. These correspond to the intercept and slope of the dashed line in fig. 7. The addition of an attractive potential leads to a more complex relationship between E f and E i as has been shown by Grimmelman et al. [5]. In particular, El, E i and T~ no longer appear only as the ratios of E i and Ee to T~. We have fit our data to this model by varying # and the well depth D. N o minimum was found by varying D for D > 0 so it was set at 1000 K corresponding to the experimentally determined value for Ar on tungsten [17]. As was shown in section 3.2 this value gives reasonable agreement with the variation of the rainbow angles with 8 i. The best fit value of # for D = 1000 K gives an effective mass of 583 • 150 amu for a surface nickel atom and values of a S = 0.12 • 0.03 and ag = 0.82 • 0.06. Calculated points for these parameters can be seen in fig. 7. The fit to the data is not quite as g o o d as the cube model without a well but considering the simplicity of the models, the fit is remarkably good both with and without an attractive well.

4.2. Scattering with the beam incident in the [l fO] azimuth Table 3 shows the results obtained in the uncorrugated azimuth with 30 ~ Fig. 8 shows them plotted in the form Ef/2kT~ versus E i / 2 k T ~

O i = Of

=

Table 3 Energies and best fit parameters to eqs. (2) and (3) for scattering in the uncorrugated direction, with 8 i = Of = 30 ~ (K)

(meV)

(meV)

(10 4 c m / s )

(10 4 cm/s)

718 512 378 300 512 250 414 322 273 250 340 251 226 200 201

67.1 67.1 67.1 67.1 128.7 67.1 128.7 128.7 128.7 128.7 227.0 227.0 225.6 225.6 227.0

71.4 64.5 59.2 57.9 107.4 57.1 101.9 96.6 95.8 92.6 173.1 142.0 156.6 156.5 165.1

2.61 2.34 2.04 1.90 2.38 1.78 2.07 1.86 1.78 1.86 3.00 1.19 2.30 2.03 1.74

3.69 3.73 3.90 4.03 5.77 4.15 5.90 5.92 5.96 5.75 7.34 7.98 7.66 7.81 8.32

R.M. Aten et al. / Argon scattering from Ni(ll5)

526 5.0

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Fig. 8. Er/2kT~ versus Ei/2kT~ for Ar backscattered in the [110] azimuth. The solid circles are data points and the open squares are calculated using a hard cube model for a well depth of 1000 K. The solid line is a best fit to the data using a hard cube model for no attractive well, and the dashed line is a simple least-squares fit to the data (see text). as was done for the b e a m i n c i d e n t in the strongly corrugated a z i m u t h in fig. 7. T h e data has b e e n fit to the form of eq. (1) with ag a n d a s treated as i n d e p e n d e n t quantities a n d setting D = 0. This gives ag = 0.66 • 0.10 a n d a s = 0.24 ___0.12. F i t t i n g the data to the form of eq. (1) with ag a n d a s given b y eq. (7) a n d (8) gives ag = 0.66 + 0.06, a s = 0.21 + 0.04 a n d mar = 271 + 81. F i t t i n g the data to hard cube model with a n attractive well [5], a n d setting D = 1000 K we o b t a i n ag = 0.79 + 0.04, a S= 0.14 + 0.03 a n d mar = 478 + 133. T o within the experimental error, these values are the same as was o b t a i n e d in the more strongly corrugated [552] azimuth. 4.3. Effect o f incident a n d f i n a l angle on energy transfer

As shown above in sections 4.1 a n d 4.2 energy transfer b e t w e e n an i n c i d e n t Ar a t o m a n d the surface is equally effective in the weakly a n d strongly corrugated azimuths. I n the strongly corrugated azimuth, the surface can. be viewed as locally flat with surface n o r m a l s which deviate +/3 from the n o r m a l to the (115) plane. F r o m the d e t e r m i n a t i o n of the r a i n b o w angles (see section 3.2), 13 is estimated to be 10 ~ + 2 ~ A possible reason that ag a n d a s are the same in b o t h azimuths is that energy exchange is less sensitive to O~ than the hard cube model predicts.

R.M. Aten et a L / Argon scattering from Ni(115)

527

Table 4 Energies and best fit parameters to eqs. (2) and (3) for scattering in the corrugated direction at various incident angles 0i, Of (deg)

Ts (K)

(g i> (meV)

(El > (meV)

y (104 c m / s )

v0 (104 c m / s )

15 40 60 50 70 80

274 274 274 200 200 200

64.0 64.0 64.0 109.2 109.2 109.2

62.4 60.6 57.9 94.5 100.7 102.9

1.92 1.82 2.00 1.48 1.30 1.28

4.25 4.28 3.89 6.18 6.55 6.64

Table 4 shows results obtained with the Ar beam incident in the strongly corrugated azimuth for various values of Oi. The TOF spectra were in all cases taken at the specular angle. In analyzing this data, the attractive well must be included in order to take the refraction of the incident trajectory into account. We have used D = 1000 K and mar = 583 which was the best fit to the data in tables 1 and 2. Fig. 9 shows the predicted relationship of Ef/2kT~ on E i / 2 k T~ for the above parameters for T~ = 200 K. Data points were only taken for a single energy and it is seen that although they lie roughly in the predicted region, Ef for a given E i varies less strongly with Oi than predicted by the '

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528

R.M. Aten et al. / Argon scattering from Ni(115)

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EiI2KTs (UNITLESS)

Fig. 10. E f / 2 k T s versus E i / 2 k T s for the hard cube model with D =1000 K and Ts = 273 K. The solid curves are calculated for (top to bottom) Oi = Oi = 60 o, 40 o, and 15 o. Again, the data points show the same trend, but are more closely spaced. h a r d cube m o d e l with a n attractive well. Since Ef a n d E i e n t e r this m o d e l [5] n o t o n l y in the f o r m of their ratios to 2kT~, d a t a t a k e n at different surface t e m p e r a t u r e s c a n n o t b e shown o n the same plot. Fig. 10 shows similar d a t a t a k e n f r o m table 4 for T~ = 274 K. A l l three d a t a p o i n t s lie w i t h i n the expected r a n g e but, as in the case o f the higher energy b e a m , the v~riation o f Ef with 0 i is less t h a n expected f r o m the h a r d c u b e model.

5. Discussion and conclusions T h e r a i n b o w scattering o b s e r v e d in the [552] a z i m u t h clearly shows that the surface is s t r o n g l y c o r r u g a t e d in this d i r e c t i o n w h e r e a s n o a p p r e c i a b l e corrugation is o b s e r v e d in the [110] azimuth. Based o n an a s s u m e d well d e p t h o f 1000 K, the c o r r u g a t i o n for a r g o n scattering is r o u g h l y 2 / 3 that o b s e r v e d for h e l i u m scattering. D e s p i t e the large differences in the c o r r u g a t i o n a m p l i t u d e s , energy exchange b e t w e e n an A r a t o m a n d the surface in b o t h a z i m u t h s is well d e s c r i b e d b y the h a r d c u b e e q u a t i o n either w i t h o r w i t h o u t a n attractive well. Since the effective m a s s o f a surface nickel a t o m is n o t k n o w n i n d e p e n d e n t l y , o u r results are n o t a sensitive test of the surface p o t e n t i a l . A n y value of D b e t w e e n 0 a n d 1000 K c a n b e used if the effective m a s s of nickel is allowed to v a r y b e t w e e n 250 a n d 600 ainu. T h e fitting coefficients Ctg a n d cts of eq. (1) are

R.M. Aten et al. / Argon scatteringfrom Ni(l l 5)

529

to within experimental error the same in both azimuths and therefore independent of corrugation amplitudes between 0 and 0.4 ,~. When viewed in terms of the variation in angle of the local normal to the macroscopic surface normal, these results can be restated as an insensitivity to angles of incidence which vary in the range __+10 o. This is borne out by the results shown in figs. 9 and 10 which indicate that the dependence of E f / 2 k T s on E i / 2 k T ~ on incident angle is less than that predicted by hard cube models. No detailed calculations have been carried out to which we can quantitatively compare this result. However, numerical calculations for an effective mass and surface geometry appropriate to the argon-tungsten geometry show that significant nonlinearities in a plot of E f / 2 k T ~ or E i / 2 k T s occur as the surface corrugation increases [6]. Similarly, sensitivity calculations indicate that surface corrugation is one of the two most important factors which should affect energy transfer between the surface and an impinging gas atom [9]. Calculations with the experimental geometry and corrugation appropriate to Ni(115) are needed to test the compatibility of hard and soft cube models with the observed lack of dependence of energy transfer on corrugation amplitude. As has been discussed previously [5-7], the hard wall model is unable to describe the angular distributions in gas surface scattering. Our experiments are consistent with the picture that angular distributions are largely determined by the corrugation within the unit cell. The occurrence of rainbow scattering angles for which the energy distribution is the same as specular angles clearly shows this. However, the width of the scattering distribution in the smooth [110] azimuth is clearly not due to corrugation effects and involves momentum transfer not strongly coupled to energy transfer in the way in which the cube models would predict.

Acknowledgements We have benefited from discussions with John Tully and from the technical assistance of Donald Braid. This research was supported by the National Science Foundation under grant C H E 8109067.

References [1] J.E. Hurst, L. Wharton, K.C. Janda and D.J. Auerbach, J. Chem. Phys. 78 (1983) 1559. [2] J.E. Hurst, L. Wharton, K.C. Janda and D.J. Auerbach, J. Chem. Phys. 83 (1985) 1376. [3] J.E. Hurst, C.A. Becker, J.P. Cowin, K.C. Janda, L. Wharton and D.J. Auerbach, Phys. Rev. Letters 43 (1979) 1175. [41 K.C. Janda, J.E. Hurst, J. Cowin, L. Wharton and D.J. Auerbach, Surface Sci. 130 (1983) 395. [5] E.K. Grimmelman, J.C. Tully and M.J. Cardillo, J. Chem. Phys. 72 (1980) 1039.

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[6] J.A. Barker and D.J. Auerbach, Chem. Phys. Letters 67 (1979) 393. [7] R.M. Logan, in: Solid State Surface Science, Vol. 3, Ed. M. Green (Dekker, New York, 1973). [8] I.P. Batra, Surface Sci. 148 (1984) 1. [9] R.R. Lucchese, J. Chem. Phys. 83 (1985) 3118. [10] D.S. Kaufman, R.M. Aten, E.H. Conrad, L.R. Allen and T. Engel, to be published. [11] E.H. Conrad, R.M. Aten, D.S. Kaufman, L.R. Allen, T. Engel, M. den Nijs and E.K. Riedel, J. Chem. Phys. 84 (1986) 1015; see also an erratum: J. Chem. Phys. 87 (1986) 1279E. [12] T. Engel, D. Braid and E.H. Conrad, Rev. Sci. Instr. 57 (1986) 487. [13] D.J. Auerbach, C.A. Becker, J.P. Cowin and L. Wharton, Rev. Sci. Instr. 49 (1978) 1518. [14] J.N. Smith, Surface Sci. 34 (1973) 613. [15] J.A. Barker and D.J. Auerbach, Surface Sci. Rept. 4 (1984) 1. [16] T. Engel and J.H. Weare, Surface Sci. 164 (1985) 403. [17] T. Engel and R. Gomer, J. Chem. Phys. 52 (1970) 5572.