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Atom scattering from isolated molecular adsorbates on surfaces: Effects of adsorbate orientation
Volume 158, number 3,4
CHEMICAL
9 June 1989
PHYSICS LETTERS
ATOM SCATTERING FROM ISOLATED MOLECULAR EFFECTS OF ADSORBATE ORIENTATION
ADSORBATES
ON SURFACES:
G. PETRELLA DepartmentqfChemistry,
A.T. YINNON
University ofBar;, 70126 Bari, Italy
and R.B. GERBER
Department of Physical Chemistry and The Fritz Haber Research Centerfor Molecltiar Dynamics. The Hebrew University ofJerusalem, Jerusalem 91904, Israel Received 3 January
1989; in final form 2 1 March 1989
The scattering of He atoms from O2 molecules adsorbed on a flat surface is studied, and comparison is made of models in which the 0, is respectively perpendicular and parallel to the surface. The sudden approximation is used to calculate both the angular intensity distribution ofthe scattered atoms at fixed incidence energy, and the integral cross section for scattering by the adsorbate as a function of collision energy. Significant differences are found in both the cross sections and the angular intcnsitics bctwccn scattering by the parallel and by the perpendicular adsorbate. The possible use of He scattering to study adsorbate orientation is discussed in the light of the results.
1. Introduction The use of molecular beam scattering to study defects on surfaces is a novel topic, motivated by the technological importance of various types of surface defects, and by the fundamental interest in disordered surfaces. One important research direction in this field is to explore the specular scattering of He atoms, which is attenuated by the presence of the defects [ l-91. In the limit of low concentration of defects, it is convenient to describe the specular attenuation in terms of a cross section for scattering by a single defect. Extensive experimental [ l-31 and theoretical [ 4-91 studies in recent years focused on the study of this quantity for a variety of surface imperfections and as a function of collision energy and incidence angle. Another approach using He scattering to investigate surface defects pursued the angular intensity distribution of the scattered atoms. The first successful experiments on structure in the angular intensity distributions due to the effect of isolated defects have been reported only two years ago [ 101. Likewise, there have been several theoretical studies and predictions of particular features in the angular 250
intensity distribution [ IO- 15 1, and progress was achieved in understanding of the experimentally observed maxima. One important theoretical objective in this field is to quantitatively understand the relation between the observable cross sections and intensity distributions and the defect site geometry. This article deals with the dcpendcnce of the scattering data upon the orientation of a molecular adsorbate at the surface. We wish to find out if He scattering can be used as a means for learning about the orientation of isolated adsorbates with respect to the surface. This question is, of course, directly related to the role of the anisotropic part of the He/adsorbate interaction in the scattering dynamics. With very few exceptions [ 6 1, most calculations to date ignored the anisotropy of the potential between He and the adsorbed molecule in treating the scattering process. In this article we study the scattering of He from an O2 adsorbate on a smooth surface, focusing on the influence of molecular orientation on scattering data. WC assume that the He/O1 potential is the same as in the gas phase. Section 2 briefly describes the model system used, and the scattering calculations. Section
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3 gives an outline of the results. Concluding are given in section 4.
PHYSICS LETTERS
remarks
2. Model system and method
(1)
~(x,Y,z)=v,(z)+v,(x,Y,z),
where V, denotes the potential between helium and a perfect Pt surface, while V, is the interaction between He and the O2 imperfection, z is a coordinate that measures the distance of the scattered atom from the surface plane, while X, y are coordinates parallel to the surface. The assumption that the Pt surface is flat, although certainly an approximation, is reasonable for Pt ( 11 I ) [ I]. We make a much stronger approximation now in taking va to be the gas-phase interaction potential between He and 0,. This assumption was not tested for an O2 adsorbate but there is substantial evidence in the case of He interacting with CO on Pt( 1 I 1), based on quantitative interpretation of scattering data, that the Pt surface alters considerably the He interaction with the defect 181. Nevertheless, it appears reasonable to assume that using a “bare”, gas-phase potential for the atom/ adsorbate interaction will not qualitatively affect any conclusions on the role of the potential anisotropy in the scattering. Energy transfer from the atom to the adsorbate, and to the surface, is neglected in our calculations. For the interaction V,(z) between He and a (perfect) Pt surface, we use the Morse potential
-2exp[
-2a(z-z,)
where r is the distance between He and the ccnterof-mass of 0, and y denotes the angle between the molecular axis and the He/O, distance vector r. E(Y), p (r, y) and f are defined by E(Y) =&” +e2p2 (cosy)
The model system employed in the calculations represents, albeit very approximately, an isolated 0, adsorbate on a smooth platinum surface, say Pt ( 111). The interaction potential between the He atom and the target system is taken to be of the form
v,(z)=D{exp[
9 June 1989
]
-a(z-z,)]}
(2)
discussed in ref. [S], with D=4 meV and a=0.6 bohr-‘. z, is arbitrary, and only its distance from the center-of-mass position of the O2 along the z axis affects the observable quantities. For the (gas-phase) anisotropic He/O1 interaction, we use the potential given by Keil et al. [ 16 1,
V,(x,y,z)=V,(r,y)=&(Y)f[P(Y,y)l
5
(3)
with e,=2.94
meV, E*= -0.59
meV,
(4b)
3
p(r, y) =ylrm(y)
rnl(Y)=rnu
(4a)
>
( ‘y-d$Y)‘~2,
(4c)
with Y, L = 3.29 8, r,=Q.24,
flP)=exp[P(l-p)1{exp[B(l-p)l-2}, PQI >
(5a)
.oP) = (Pz-P) [SI (Pz-PF+&l + (P-P,) is2 (P-PlY+Ll, s(P)=-GP-6,
Pap2
7
PI
(5b) (5c)
where the constants in the above equations are given by [l&17]: p,=1.1175, ~~~160, SI=-3.5832, &=0.0409, S,= -0.7202, S,= -0.2727, /I= 5.90, &=2.13. The scattering calculations in this study were carried out using the sudden approximation [8,14, 15,181. This method was previously tested for scattering from surface imperfections [ 8,14,15 ] and it at least qualitativeIy describes most features ofthe scattering dynamics when the incidence energy normal to the surface is high. The condition for the validity of the sudden approximation is k,>
jK’-KI
,
(6)
where k,is the incident wave number normal to the surface. K is the component of the incident wavevector parallel to the surface, and K’ is the parallel component of any final or intermediate wavevector that plays a significant role in the scattering. It was found that for collisions at normal incidence, and in the energy range pursued here, the sudden approximation yields good agreement with numerically exact results for specular and for near specular scattering angles, and for the diffuse non-specular scattering background [ 14,15 1. The sudden approximation yields good agreement (within 10% or better) for the cross sections, which are dominated by 251
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collisions having relatively high impact parameters with respect to the defect [g]. The sudden approximation inherently fails to reproduce those features in the scattering involving double collisions of the atom with the target system [ 141. Although such effects may arise for the system studied here at some of the collision energies, our conclusion from refs. [8,14,15] is that the sudden approximation is expected to yield very good results for most features of the scattering in the case studied here, and it can therefore serve as a suitable model for obtaining the scattering intensities from the different orientations of 02. The calculation of the angular intensity distribution using the sudden approximation is as follows. Let A be the area of a large surface segment that contains the defect (A should be large enough, with the defect at the center of the segment, so that edge effects on the scattering intensity become negligible). Then the angular intensity distribution is given by I K-K 2 =
$
cxp[i(K’-K)-R]
expf2iq(R)]
dR
, (7)
where R= (x, JI), and K, &? are respectively the initial and final wavevector of the scattered atom along the surface plane. q(R) is the scattering phase shift computed for fixed R, given by
(8) where m is the mass of the atom, and z. the classical turning point corresponding to the integrand in eq. (8). To calculate the cross section for scattering by a defect, WC use the operational definition due to Comsa et al. [ I-31, I,,,=exp(
-mn,tI)
,
(9)
where u is the cross section for scattering by a single defect, 0 the surface coverage of defects, n, the number of sites that can accommodate a defect per unit surface area. n*=n,B is thus the defect concentra252
9 June 1989
tion, which equals l/A in our model, where A is the surface segment area in eq. (6).
3. Results and analysis Calculations of He scattering intensities were carried out for four types of adsorbate orientations with respect to the surface: (i) The molecular axis is perpendicular to the surface plane. (ii) The 0, molecule is parallel to the surface with orientations random in the surface plane. (iii) The molecule is parallel to the surface, having some fixed orientations in the plane. (iv} The anisotropic part of he He/O, potential was neglected (i.e. the orientation dependence of the scattering intensities was eliminated altogether), Models specified in (i)-(iii ) may all be (approximately) realized for certain types of surfaces, and in certain tcmperaturc ranges. Assumption (iv), neglecting the anisotropy of the atom interaction with the adsorbate, was made in most previous calculations of scattering from molecular imperfections. All calculations reported here are for incidence normal to the surface. The cross sections were calculated for collision wavenumbers k, in the range from k,= 1.0 bohr-’ to k,=4.5 bohr-‘. The angular intensity distribution for each type of orientation was computed for several values of the incident energy. We will discuss here the angular intensity distributions for collision wavenumbers k,=4.5 bohr-’ (high collision energy) and k,= 1.5 bohr-’ (low collision energy). 3.1. Behavior of the cross sections Fig. 1 shows the dependence of the cross section for scattering of He by the adsorbate upon the collision wavenumber, for each of the four types of orientation mentioned previously. Differences between cross sections for different types of orientation are as large as 12% at low energies (when the cross sections are large), and 25% at high energies. Such differences are definitely larger than the corresponding typical experimental uncertainty in the same energy range. A very interesting feature is that the perpendicular orientation gives cross sections which are smaller than those of the parallel orientations at low
Volume 158,number 3,4
CHEMICAL PHYSICS LETTERS
Fig. 1. Cross sections for He scattering from a O2 adsorbate on Pt( 111). The cross sections are shown as a function of k,, the collision wavenumber. The results are for normal incidence.
collision energies (up to k,z 2.6 bohr-‘), but at higher collision energies the behavior is reversed. This can be interpreted as follows: At low energies, the dominant contribution to the cross section comes from collision of large impact parameters with respect to the center-of-mass of the defect. The scattering into non-specular directions in such collisions is due to the long-range part of the He/O2 interaction that causes a weak corrugation in the total potential exerted on the He by the surface + defect system. The parallel adsorbate gives rise to higher local surface corrugations at large distances from the defect center, due to configurations in which an 0 atom is nearer to the point of impact than possible in the perpendicular orientation (for the same impact parameter). The existence of stronger long-range corrugation in the parallel orientation implies larger cross sections at low collision energies than obtained for a perpendicular adsorbate. At higher collision energies, stronger corrugations are required to produce non-specular scattering_ The cross sections then
9 June 1989
involve mainly contributions from collisions of smaller impact parameters with respect to the defect center, which probe the repulsive potential wall bctween the defect and the helium. Given that the effective corrugation at high collision energies is due to the repulsive He adsorbate potential, the corrugation is expected by geometry to be larger for a “tall and narrow” adsorbate profile on the surface than for a “low and broad” profile. This explains the larger cross sections for the perpendicular configuration at high collision energies. As expected, all the cross section curves show basically a fall-off behavior with increasing energy. Superimposed, however, on the overall fall-off behavior is an undulatory structure. The oscillations in the energy dependence of the cross section are most pronounced for the perpendicular orientation and considerably less so for the parallel orientations. Weaker undulations are also found for the isotropic adsorbate. We attribute the oscillations in the cross sections to interference effects between the wave scattered specularly from the flat surface, and the specular component of the wave scattered from the defect, probably from the smooth “top” of the adsorbate. By this interpretation, the larger the distance between the surface plane and the smooth “top” of the adsorbate potential, the more oscillatory is the cross section expected to be. This is in agreement with the result of fig. 1. Finally, an important point to be noted from fig. 1 is the relatively large difference between the cross section obtained from an isotropic He/O, potential, and the cross sections from the realistic anisotropic interaction, notwithstanding whether the orientation used is parallel or perpendicular. Only in the case of the perpendicular orientation at low collision energies do the isotropic and the anisotropic potentials yield the same interaction. In general, as fig. 1 shows, the presence of the anisotropy in the interaction potential increases the effective area for scattering by the adsorbate. The differences between the cross section for isotropic and anisotropic He/O, interactions found here are definitely large enough to be important in the interpretation of experiments. In conclusion of this part of the study, provided a reasonably reliable atom/adsorbate potential is available, then cross section measurements of the type of refs. [l-3], combined with corresponding cal253
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CHEMICALPHYSICSLETTERS
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culations, should be able to distinguish quite easily between perpendicular and parallel adsorbate orientations. On the other hand, in the case of parallel orientation, fig. 1 suggests that it will not be possible on the basis of cross section data alone to distinguish between a model in which all adsorbates have the same orientation in the plane and one in which adsorbate orientations are random.
100.0
66.7
n
1
id
3.2. Angular intensity distribution forhigh-energy collisions Fig. 2 shows calculated angular intensity distributions for a collision at incidence wavenumber k=:-=4.5 bohr- ’ which correspond to several types of adsorbate orientation with respect to the surface. Fig. 2a shows the intensity distribution when only the isotropic part of the He/O2 interaction is used for V, in ( 1). This, of course, is tantamount to neglecting any possible effect of the adsorbate orientation, and to treating the defect essentially as an atom. The results show a broadened specular peak, and at the near proximity of the specular peak, at momentum transfer in the x direction of A&a 4 1.O bohr-‘, two symmetric peaks, which we identified as first-order Fraunhofer diffraction maxima [ 10,121. Such maxima can at least be semiquantitatively understood by treating the adsorbate as a hard hemisphere [ lo], leading to a Fraunhofer-type expression for the position and intensities, as demonstrated in several previous studies [ lo,12 1. Additional peaks are seen at larger momentum transfers, for AK,= +2.0 bohr-’ and AKXz f2.5 bohr-‘. Following an analysis pursued previously for similar systems [ 12,14 1, the peaks at AK,= k2.5 bohr-’ were identified as rainbows: They correspond in the classical limit to collisions in which the incoming He atom strikes points on the potential surface which gives it a maximal force in the x direction. More precisely, rainbow scattering is dominated by contributions from the vicinity of points (x, y) in the integral eq. (7)) satisfying det
awax2
aWaxay=
a2tfia.v ax
aZ;rl/ay2
o
(10) *
The peaks at AKxz ? 2.0 bohr-’ are supernumerary rainbows. It is instructive to compare the result for an isotropic defect with the corresponding angular inten2.54
33iL 0
AK,
225
4.50
(Bohr-‘)
Fig. 2. Scattering intensity distribution for He scattered from 0, Pt( I1 1) at incident wavenumberk,=4.5 bohr-‘. Thescattering intensity (in relative units) is shown as a function ofAK,, the momentum transfer along an arbitrary direction x. (a) Results for an isotropic model of 0,. (b) Results for O2 perpendicular to the surface, (c) parallel to the surface, oriented along the x direction, (d ) parallel to the surface, averaged over all orientations of 0, in the plane.
on
sity distribution for a perpendicular adsorbate, given in fig. 2b. In the latter case, two symmetric pairs of Fraunhofer-type diffraction maxima can be seen at the vicinity of the specular peak. The added Fraunhofer peaks compared with fig. 2a stem from the fact that the equipotential for the anisotropic O2 does not correspond to a hemisphere. Also, the rainbow pattern is substantially altered for the anisotropic adsorbate: Three pronounced symmetric pairs of rainbow maxima, at bK,= k 2.0, 2 3.6, i 4.0 bohr-’ are seen in this case. While the isotropic adsorbate produced one pair of rainbows (solutions of eq. ( 10)) and one pair of supernumerary maxima, the anisotropic potential, which has lower symmetry, leads to
Volume 158, number
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CHEMICAL
additional solutions of eq. ( 10). This can be regarded as “splitting” of the rainbows of fig. 2a, as well as shifting of the latter, by the anisotropic part of the He/O, potential. The important point is that the anisotropic O2 at perpendicular orientation has more rainbow peaks than the isotropic model, and also that it yields significant peaks at much higher scattering angles (AKY values). We now turn to fig. 2c, showing the angular intensity distribution for a parallel adsorbate at a fixed orientation in the plane. As in the case of the perpendicular adsorbate, the present system gives rise to two pairs of Fraunhofer maxima, and to multiple pairs of rainbows, but both the Fraunhofer and the rainbow features differ significantly (in position and in intensities) from the corresponding values for the perpendicular defect. Finally, fig. 2d gives the results for an O2 adsorbate parallel to the surface, but of random (i.e. averaged) orientation in the plane. A much less structured intensity distribution was obtained in this case than in that of fig. 2b or 2c, since the averaging over orientations affected both the Fraunhofer and the rainbow features. The angular distribution is also much more broadly spread and uniform than the isotropic case. Accurate measurement of the angular intensity distribution for such systems presents a very difficult challenge, but it is evident from the above results that, at least in principle, such experiments can distinguish not only between the parallel and perpendicular orientations, but also between the fixed and random cases in the parallel situation. 3.3. Angular intensity distribution for low-energy scattPving Fig. 3 shows angular intensity distributions for a collision at wavenumber kz=2.5 bohr-‘, corresponding again to the cases of an isotropic adsorbate; a perpendicular 0,; a parallel 0, of fixed orientation, and a parallel O2 adsorbatc of random orientation in the plane. At the low energy of this collision, Fraunhofer maxima are the only significant non-specular feature found, hence only the nearspecular intensities are shown in the drawing. This case is much less sensitive than the high-energy one in discriminating between the various orientations. Nevertheless, the difference between the perpendicularly oriented adsorbate, fig. 3b, and all the other
9 June 1989
PHYSICS LETTERS
loo.0
(ai 66.7
-4.50
-2.25
0
2.25
AK, ( Bohr”
4.50
)
Fig. 3. Scattering intensity distribution for He scattered from O2 on Yt( 1 II ) at incident wavenumber k,=2.5 bohr-‘. (The models (a), (b), (c), (d) aredeiined as m fig. 2.)
cases is very pronounced, in a second well-resolved
since only this case results pair of Fraunhofer peaks.
4. Concluding remarks In this study, the scattering of He from an O2 adsorbate on a smooth surface was investigated theorctically, using the sudden approximation. The main question pursued was whether measured scattering data can be used to determine the orientation of the adsorbate at the surface. The observables examined were the cross section for scattering by the adsorbate as a function of the collision energy (which is related to the specular scattering only), and the angular intensity distribution at fixed collision energy. The results obtained show clearly that adsorbate orienta255
Volume 158, number 3,4
CHEMICAL
PHYSICS LETTERS
tion has a significant effect on the scattering intensities. In particular, both the cross sections and the angular intensity distribution can be used to discriminate between parallel and perpendicular adsorbate orientation with respect to the surface. In the case of a parallel adsorbate, the angular intensity distribution may be sufficiently sensitive to allow for discrimination between fixed and random orientations of the molecule in the plane. Another conclusion drawn from this study is that the anisotropy of atom/adsorbate interaction potentials is important in quantitative studies of scattering from molecular adsorb$es, and it is suggested that it should be included in all future calculations of such processes. A question that merits considerable attention is whether the effects predicted here may be washed out, or drastically reduced, by the occurrence of energy transfer between the colliding atom and the adsorbate. With regard to the results that deal with the behavior of the cross section, there is experimental evidence [ 11 that cross sections are independent of surface temperature, suggesting that these quantities are not substantially affected by energy transfer. The rainbow features in the angular intensity distribution pose a more serious question in this respect. The fact that Lahee et al. [lo] succeeded to measure such features for He scattering from CO on Pt, shows, however, that these effects are not washed out by energy transfer events in the collision. The quantitative effect of collisional energy transfer on the rainbow and Fraunhofer interference effects deserve future experimental and theoretical attention.
Acknowledgement We thank Dr. Y.M. Engel for help with the com-
256
9 June 1989
putations. This research was supported by Grant No. 840003 1 by the US-Israel Binational Science Foundation. The Fritz Haber Research Center at The Hebrew University is supported by the Minerva Gesellschaft ftir die Forschung, mbH, Munich, FRG.
References [ 1] B. Poelsema and G. Comsa,
Faraday Discussions Chem. Sot. 80 (1985) 16. [ 2 ] B. Poelsema, S.T. de Zwart and G. Comsa, Phys. Rev. Letters 49 (1982) 578; 51 (1983) 522. [ 3 ] B. Poclsema, R.L. Palmer and G. Comsa, Surface Sa. 136 (1984) 1. [4] H. Jonsson, J.H. Wcare and A.C. Levi, Phys. Rev. B 30 (1984) 2241. 151H. Jonsson, J.H. Wearc and A.C. Levi, Surface Sci. 148 (1984) 126. [6 SD Bosanac and M. Sunk, Chem. Phys. Letters I 15 ( 1985) 75. W.-K. Liu, Surface Sci. 148 (1984) 37 I. 1B. Gumhakrand A.T. Yinnon, R. Koslo~, R.B. Gerber, B. Poeisema and G. Comsa, J. Chem. Phys. 88 (1988) 3722. ]9 H. Xu, D. Huber and E.J. Heller, J. Chem. Phys., in press. [to A.M. Lahee, J.R. Manson, J.P. Toennies and Ch. W611, J. Chem. Phys. 86 (L987) 7194. [I1 R.B. Gerber, A.T. Ymnon and R. Kosloff, Chem. Phys. Letters 105 (1984) 523. [12 A.T. Yinnon, R. Kosloffand R.B. Gerber, Chem. Phys. 87 (1984) 441. 113 G. Drolshagen and R. Vollmer, J. Chem. Phys. 87 ( 1987) 4948. [14 A.T. Yinnon, R.B. Gerber, D.K. Dacol and H. Rabitr, J. Chem. Phys. 84 (1986) 5955. [I5 A.T. Yinnon, R. Kosloff and R.B. Gerber, J. Chem. Phys. 88 (1988) 7209. [ 161 A.M. Keil, J.T. Slankas and A. Kupperman, J. Chem. Phys. 70 (1979) 541. [17] B.G.C.CoreyandF.R. McCourt, J.Chem.Phys. 81 (1984) 3892. [IS] R.B. Gerber, A.T. Yinnon and J.N. Murrell, Chem. Phys. 31 (1978) 1.
;‘,
CHEMICAL
9 June 1989
PHYSICS LETTERS
ATOM SCATTERING FROM ISOLATED MOLECULAR EFFECTS OF ADSORBATE ORIENTATION
ADSORBATES
ON SURFACES:
G. PETRELLA DepartmentqfChemistry,
A.T. YINNON
University ofBar;, 70126 Bari, Italy
and R.B. GERBER
Department of Physical Chemistry and The Fritz Haber Research Centerfor Molecltiar Dynamics. The Hebrew University ofJerusalem, Jerusalem 91904, Israel Received 3 January
1989; in final form 2 1 March 1989
The scattering of He atoms from O2 molecules adsorbed on a flat surface is studied, and comparison is made of models in which the 0, is respectively perpendicular and parallel to the surface. The sudden approximation is used to calculate both the angular intensity distribution ofthe scattered atoms at fixed incidence energy, and the integral cross section for scattering by the adsorbate as a function of collision energy. Significant differences are found in both the cross sections and the angular intcnsitics bctwccn scattering by the parallel and by the perpendicular adsorbate. The possible use of He scattering to study adsorbate orientation is discussed in the light of the results.
1. Introduction The use of molecular beam scattering to study defects on surfaces is a novel topic, motivated by the technological importance of various types of surface defects, and by the fundamental interest in disordered surfaces. One important research direction in this field is to explore the specular scattering of He atoms, which is attenuated by the presence of the defects [ l-91. In the limit of low concentration of defects, it is convenient to describe the specular attenuation in terms of a cross section for scattering by a single defect. Extensive experimental [ l-31 and theoretical [ 4-91 studies in recent years focused on the study of this quantity for a variety of surface imperfections and as a function of collision energy and incidence angle. Another approach using He scattering to investigate surface defects pursued the angular intensity distribution of the scattered atoms. The first successful experiments on structure in the angular intensity distributions due to the effect of isolated defects have been reported only two years ago [ 101. Likewise, there have been several theoretical studies and predictions of particular features in the angular 250
intensity distribution [ IO- 15 1, and progress was achieved in understanding of the experimentally observed maxima. One important theoretical objective in this field is to quantitatively understand the relation between the observable cross sections and intensity distributions and the defect site geometry. This article deals with the dcpendcnce of the scattering data upon the orientation of a molecular adsorbate at the surface. We wish to find out if He scattering can be used as a means for learning about the orientation of isolated adsorbates with respect to the surface. This question is, of course, directly related to the role of the anisotropic part of the He/adsorbate interaction in the scattering dynamics. With very few exceptions [ 6 1, most calculations to date ignored the anisotropy of the potential between He and the adsorbed molecule in treating the scattering process. In this article we study the scattering of He from an O2 adsorbate on a smooth surface, focusing on the influence of molecular orientation on scattering data. WC assume that the He/O1 potential is the same as in the gas phase. Section 2 briefly describes the model system used, and the scattering calculations. Section
0 009-2614/89/$ 03.50 0 Elsevier Science Publishers ( North-Holland Physics Publishing Division )
B.V.
Volume 158, number
3,4
CHEMICAL
3 gives an outline of the results. Concluding are given in section 4.
PHYSICS LETTERS
remarks
2. Model system and method
(1)
~(x,Y,z)=v,(z)+v,(x,Y,z),
where V, denotes the potential between helium and a perfect Pt surface, while V, is the interaction between He and the O2 imperfection, z is a coordinate that measures the distance of the scattered atom from the surface plane, while X, y are coordinates parallel to the surface. The assumption that the Pt surface is flat, although certainly an approximation, is reasonable for Pt ( 11 I ) [ I]. We make a much stronger approximation now in taking va to be the gas-phase interaction potential between He and 0,. This assumption was not tested for an O2 adsorbate but there is substantial evidence in the case of He interacting with CO on Pt( 1 I 1), based on quantitative interpretation of scattering data, that the Pt surface alters considerably the He interaction with the defect 181. Nevertheless, it appears reasonable to assume that using a “bare”, gas-phase potential for the atom/ adsorbate interaction will not qualitatively affect any conclusions on the role of the potential anisotropy in the scattering. Energy transfer from the atom to the adsorbate, and to the surface, is neglected in our calculations. For the interaction V,(z) between He and a (perfect) Pt surface, we use the Morse potential
-2exp[
-2a(z-z,)
where r is the distance between He and the ccnterof-mass of 0, and y denotes the angle between the molecular axis and the He/O, distance vector r. E(Y), p (r, y) and f are defined by E(Y) =&” +e2p2 (cosy)
The model system employed in the calculations represents, albeit very approximately, an isolated 0, adsorbate on a smooth platinum surface, say Pt ( 111). The interaction potential between the He atom and the target system is taken to be of the form
v,(z)=D{exp[
9 June 1989
]
-a(z-z,)]}
(2)
discussed in ref. [S], with D=4 meV and a=0.6 bohr-‘. z, is arbitrary, and only its distance from the center-of-mass position of the O2 along the z axis affects the observable quantities. For the (gas-phase) anisotropic He/O1 interaction, we use the potential given by Keil et al. [ 16 1,
V,(x,y,z)=V,(r,y)=&(Y)f[P(Y,y)l
5
(3)
with e,=2.94
meV, E*= -0.59
meV,
(4b)
3
p(r, y) =ylrm(y)
rnl(Y)=rnu
(4a)
>
( ‘y-d$Y)‘~2,
(4c)
with Y, L = 3.29 8, r,=Q.24,
flP)=exp[P(l-p)1{exp[B(l-p)l-2}, PQI >
(5a)
.oP) = (Pz-P) [SI (Pz-PF+&l + (P-P,) is2 (P-PlY+Ll, s(P)=-GP-6,
Pap2
7
PI
(5b) (5c)
where the constants in the above equations are given by [l&17]: p,=1.1175, ~~~160, SI=-3.5832, &=0.0409, S,= -0.7202, S,= -0.2727, /I= 5.90, &=2.13. The scattering calculations in this study were carried out using the sudden approximation [8,14, 15,181. This method was previously tested for scattering from surface imperfections [ 8,14,15 ] and it at least qualitativeIy describes most features ofthe scattering dynamics when the incidence energy normal to the surface is high. The condition for the validity of the sudden approximation is k,>
jK’-KI
,
(6)
where k,is the incident wave number normal to the surface. K is the component of the incident wavevector parallel to the surface, and K’ is the parallel component of any final or intermediate wavevector that plays a significant role in the scattering. It was found that for collisions at normal incidence, and in the energy range pursued here, the sudden approximation yields good agreement with numerically exact results for specular and for near specular scattering angles, and for the diffuse non-specular scattering background [ 14,15 1. The sudden approximation yields good agreement (within 10% or better) for the cross sections, which are dominated by 251
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collisions having relatively high impact parameters with respect to the defect [g]. The sudden approximation inherently fails to reproduce those features in the scattering involving double collisions of the atom with the target system [ 141. Although such effects may arise for the system studied here at some of the collision energies, our conclusion from refs. [8,14,15] is that the sudden approximation is expected to yield very good results for most features of the scattering in the case studied here, and it can therefore serve as a suitable model for obtaining the scattering intensities from the different orientations of 02. The calculation of the angular intensity distribution using the sudden approximation is as follows. Let A be the area of a large surface segment that contains the defect (A should be large enough, with the defect at the center of the segment, so that edge effects on the scattering intensity become negligible). Then the angular intensity distribution is given by I K-K 2 =
$
cxp[i(K’-K)-R]
expf2iq(R)]
dR
, (7)
where R= (x, JI), and K, &? are respectively the initial and final wavevector of the scattered atom along the surface plane. q(R) is the scattering phase shift computed for fixed R, given by
(8) where m is the mass of the atom, and z. the classical turning point corresponding to the integrand in eq. (8). To calculate the cross section for scattering by a defect, WC use the operational definition due to Comsa et al. [ I-31, I,,,=exp(
-mn,tI)
,
(9)
where u is the cross section for scattering by a single defect, 0 the surface coverage of defects, n, the number of sites that can accommodate a defect per unit surface area. n*=n,B is thus the defect concentra252
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tion, which equals l/A in our model, where A is the surface segment area in eq. (6).
3. Results and analysis Calculations of He scattering intensities were carried out for four types of adsorbate orientations with respect to the surface: (i) The molecular axis is perpendicular to the surface plane. (ii) The 0, molecule is parallel to the surface with orientations random in the surface plane. (iii) The molecule is parallel to the surface, having some fixed orientations in the plane. (iv} The anisotropic part of he He/O, potential was neglected (i.e. the orientation dependence of the scattering intensities was eliminated altogether), Models specified in (i)-(iii ) may all be (approximately) realized for certain types of surfaces, and in certain tcmperaturc ranges. Assumption (iv), neglecting the anisotropy of the atom interaction with the adsorbate, was made in most previous calculations of scattering from molecular imperfections. All calculations reported here are for incidence normal to the surface. The cross sections were calculated for collision wavenumbers k, in the range from k,= 1.0 bohr-’ to k,=4.5 bohr-‘. The angular intensity distribution for each type of orientation was computed for several values of the incident energy. We will discuss here the angular intensity distributions for collision wavenumbers k,=4.5 bohr-’ (high collision energy) and k,= 1.5 bohr-’ (low collision energy). 3.1. Behavior of the cross sections Fig. 1 shows the dependence of the cross section for scattering of He by the adsorbate upon the collision wavenumber, for each of the four types of orientation mentioned previously. Differences between cross sections for different types of orientation are as large as 12% at low energies (when the cross sections are large), and 25% at high energies. Such differences are definitely larger than the corresponding typical experimental uncertainty in the same energy range. A very interesting feature is that the perpendicular orientation gives cross sections which are smaller than those of the parallel orientations at low
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Fig. 1. Cross sections for He scattering from a O2 adsorbate on Pt( 111). The cross sections are shown as a function of k,, the collision wavenumber. The results are for normal incidence.
collision energies (up to k,z 2.6 bohr-‘), but at higher collision energies the behavior is reversed. This can be interpreted as follows: At low energies, the dominant contribution to the cross section comes from collision of large impact parameters with respect to the center-of-mass of the defect. The scattering into non-specular directions in such collisions is due to the long-range part of the He/O2 interaction that causes a weak corrugation in the total potential exerted on the He by the surface + defect system. The parallel adsorbate gives rise to higher local surface corrugations at large distances from the defect center, due to configurations in which an 0 atom is nearer to the point of impact than possible in the perpendicular orientation (for the same impact parameter). The existence of stronger long-range corrugation in the parallel orientation implies larger cross sections at low collision energies than obtained for a perpendicular adsorbate. At higher collision energies, stronger corrugations are required to produce non-specular scattering_ The cross sections then
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involve mainly contributions from collisions of smaller impact parameters with respect to the defect center, which probe the repulsive potential wall bctween the defect and the helium. Given that the effective corrugation at high collision energies is due to the repulsive He adsorbate potential, the corrugation is expected by geometry to be larger for a “tall and narrow” adsorbate profile on the surface than for a “low and broad” profile. This explains the larger cross sections for the perpendicular configuration at high collision energies. As expected, all the cross section curves show basically a fall-off behavior with increasing energy. Superimposed, however, on the overall fall-off behavior is an undulatory structure. The oscillations in the energy dependence of the cross section are most pronounced for the perpendicular orientation and considerably less so for the parallel orientations. Weaker undulations are also found for the isotropic adsorbate. We attribute the oscillations in the cross sections to interference effects between the wave scattered specularly from the flat surface, and the specular component of the wave scattered from the defect, probably from the smooth “top” of the adsorbate. By this interpretation, the larger the distance between the surface plane and the smooth “top” of the adsorbate potential, the more oscillatory is the cross section expected to be. This is in agreement with the result of fig. 1. Finally, an important point to be noted from fig. 1 is the relatively large difference between the cross section obtained from an isotropic He/O, potential, and the cross sections from the realistic anisotropic interaction, notwithstanding whether the orientation used is parallel or perpendicular. Only in the case of the perpendicular orientation at low collision energies do the isotropic and the anisotropic potentials yield the same interaction. In general, as fig. 1 shows, the presence of the anisotropy in the interaction potential increases the effective area for scattering by the adsorbate. The differences between the cross section for isotropic and anisotropic He/O, interactions found here are definitely large enough to be important in the interpretation of experiments. In conclusion of this part of the study, provided a reasonably reliable atom/adsorbate potential is available, then cross section measurements of the type of refs. [l-3], combined with corresponding cal253
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culations, should be able to distinguish quite easily between perpendicular and parallel adsorbate orientations. On the other hand, in the case of parallel orientation, fig. 1 suggests that it will not be possible on the basis of cross section data alone to distinguish between a model in which all adsorbates have the same orientation in the plane and one in which adsorbate orientations are random.
100.0
66.7
n
1
id
3.2. Angular intensity distribution forhigh-energy collisions Fig. 2 shows calculated angular intensity distributions for a collision at incidence wavenumber k=:-=4.5 bohr- ’ which correspond to several types of adsorbate orientation with respect to the surface. Fig. 2a shows the intensity distribution when only the isotropic part of the He/O2 interaction is used for V, in ( 1). This, of course, is tantamount to neglecting any possible effect of the adsorbate orientation, and to treating the defect essentially as an atom. The results show a broadened specular peak, and at the near proximity of the specular peak, at momentum transfer in the x direction of A&a 4 1.O bohr-‘, two symmetric peaks, which we identified as first-order Fraunhofer diffraction maxima [ 10,121. Such maxima can at least be semiquantitatively understood by treating the adsorbate as a hard hemisphere [ lo], leading to a Fraunhofer-type expression for the position and intensities, as demonstrated in several previous studies [ lo,12 1. Additional peaks are seen at larger momentum transfers, for AK,= +2.0 bohr-’ and AKXz f2.5 bohr-‘. Following an analysis pursued previously for similar systems [ 12,14 1, the peaks at AK,= k2.5 bohr-’ were identified as rainbows: They correspond in the classical limit to collisions in which the incoming He atom strikes points on the potential surface which gives it a maximal force in the x direction. More precisely, rainbow scattering is dominated by contributions from the vicinity of points (x, y) in the integral eq. (7)) satisfying det
awax2
aWaxay=
a2tfia.v ax
aZ;rl/ay2
o
(10) *
The peaks at AKxz ? 2.0 bohr-’ are supernumerary rainbows. It is instructive to compare the result for an isotropic defect with the corresponding angular inten2.54
33iL 0
AK,
225
4.50
(Bohr-‘)
Fig. 2. Scattering intensity distribution for He scattered from 0, Pt( I1 1) at incident wavenumberk,=4.5 bohr-‘. Thescattering intensity (in relative units) is shown as a function ofAK,, the momentum transfer along an arbitrary direction x. (a) Results for an isotropic model of 0,. (b) Results for O2 perpendicular to the surface, (c) parallel to the surface, oriented along the x direction, (d ) parallel to the surface, averaged over all orientations of 0, in the plane.
on
sity distribution for a perpendicular adsorbate, given in fig. 2b. In the latter case, two symmetric pairs of Fraunhofer-type diffraction maxima can be seen at the vicinity of the specular peak. The added Fraunhofer peaks compared with fig. 2a stem from the fact that the equipotential for the anisotropic O2 does not correspond to a hemisphere. Also, the rainbow pattern is substantially altered for the anisotropic adsorbate: Three pronounced symmetric pairs of rainbow maxima, at bK,= k 2.0, 2 3.6, i 4.0 bohr-’ are seen in this case. While the isotropic adsorbate produced one pair of rainbows (solutions of eq. ( 10)) and one pair of supernumerary maxima, the anisotropic potential, which has lower symmetry, leads to
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additional solutions of eq. ( 10). This can be regarded as “splitting” of the rainbows of fig. 2a, as well as shifting of the latter, by the anisotropic part of the He/O, potential. The important point is that the anisotropic O2 at perpendicular orientation has more rainbow peaks than the isotropic model, and also that it yields significant peaks at much higher scattering angles (AKY values). We now turn to fig. 2c, showing the angular intensity distribution for a parallel adsorbate at a fixed orientation in the plane. As in the case of the perpendicular adsorbate, the present system gives rise to two pairs of Fraunhofer maxima, and to multiple pairs of rainbows, but both the Fraunhofer and the rainbow features differ significantly (in position and in intensities) from the corresponding values for the perpendicular defect. Finally, fig. 2d gives the results for an O2 adsorbate parallel to the surface, but of random (i.e. averaged) orientation in the plane. A much less structured intensity distribution was obtained in this case than in that of fig. 2b or 2c, since the averaging over orientations affected both the Fraunhofer and the rainbow features. The angular distribution is also much more broadly spread and uniform than the isotropic case. Accurate measurement of the angular intensity distribution for such systems presents a very difficult challenge, but it is evident from the above results that, at least in principle, such experiments can distinguish not only between the parallel and perpendicular orientations, but also between the fixed and random cases in the parallel situation. 3.3. Angular intensity distribution for low-energy scattPving Fig. 3 shows angular intensity distributions for a collision at wavenumber kz=2.5 bohr-‘, corresponding again to the cases of an isotropic adsorbate; a perpendicular 0,; a parallel 0, of fixed orientation, and a parallel O2 adsorbatc of random orientation in the plane. At the low energy of this collision, Fraunhofer maxima are the only significant non-specular feature found, hence only the nearspecular intensities are shown in the drawing. This case is much less sensitive than the high-energy one in discriminating between the various orientations. Nevertheless, the difference between the perpendicularly oriented adsorbate, fig. 3b, and all the other
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loo.0
(ai 66.7
-4.50
-2.25
0
2.25
AK, ( Bohr”
4.50
)
Fig. 3. Scattering intensity distribution for He scattered from O2 on Yt( 1 II ) at incident wavenumber k,=2.5 bohr-‘. (The models (a), (b), (c), (d) aredeiined as m fig. 2.)
cases is very pronounced, in a second well-resolved
since only this case results pair of Fraunhofer peaks.
4. Concluding remarks In this study, the scattering of He from an O2 adsorbate on a smooth surface was investigated theorctically, using the sudden approximation. The main question pursued was whether measured scattering data can be used to determine the orientation of the adsorbate at the surface. The observables examined were the cross section for scattering by the adsorbate as a function of the collision energy (which is related to the specular scattering only), and the angular intensity distribution at fixed collision energy. The results obtained show clearly that adsorbate orienta255
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tion has a significant effect on the scattering intensities. In particular, both the cross sections and the angular intensity distribution can be used to discriminate between parallel and perpendicular adsorbate orientation with respect to the surface. In the case of a parallel adsorbate, the angular intensity distribution may be sufficiently sensitive to allow for discrimination between fixed and random orientations of the molecule in the plane. Another conclusion drawn from this study is that the anisotropy of atom/adsorbate interaction potentials is important in quantitative studies of scattering from molecular adsorb$es, and it is suggested that it should be included in all future calculations of such processes. A question that merits considerable attention is whether the effects predicted here may be washed out, or drastically reduced, by the occurrence of energy transfer between the colliding atom and the adsorbate. With regard to the results that deal with the behavior of the cross section, there is experimental evidence [ 11 that cross sections are independent of surface temperature, suggesting that these quantities are not substantially affected by energy transfer. The rainbow features in the angular intensity distribution pose a more serious question in this respect. The fact that Lahee et al. [lo] succeeded to measure such features for He scattering from CO on Pt, shows, however, that these effects are not washed out by energy transfer events in the collision. The quantitative effect of collisional energy transfer on the rainbow and Fraunhofer interference effects deserve future experimental and theoretical attention.
Acknowledgement We thank Dr. Y.M. Engel for help with the com-
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putations. This research was supported by Grant No. 840003 1 by the US-Israel Binational Science Foundation. The Fritz Haber Research Center at The Hebrew University is supported by the Minerva Gesellschaft ftir die Forschung, mbH, Munich, FRG.
References [ 1] B. Poelsema and G. Comsa,
Faraday Discussions Chem. Sot. 80 (1985) 16. [ 2 ] B. Poelsema, S.T. de Zwart and G. Comsa, Phys. Rev. Letters 49 (1982) 578; 51 (1983) 522. [ 3 ] B. Poclsema, R.L. Palmer and G. Comsa, Surface Sa. 136 (1984) 1. [4] H. Jonsson, J.H. Wcare and A.C. Levi, Phys. Rev. B 30 (1984) 2241. 151H. Jonsson, J.H. Wearc and A.C. Levi, Surface Sci. 148 (1984) 126. [6 SD Bosanac and M. Sunk, Chem. Phys. Letters I 15 ( 1985) 75. W.-K. Liu, Surface Sci. 148 (1984) 37 I. 1B. Gumhakrand A.T. Yinnon, R. Koslo~, R.B. Gerber, B. Poeisema and G. Comsa, J. Chem. Phys. 88 (1988) 3722. ]9 H. Xu, D. Huber and E.J. Heller, J. Chem. Phys., in press. [to A.M. Lahee, J.R. Manson, J.P. Toennies and Ch. W611, J. Chem. Phys. 86 (L987) 7194. [I1 R.B. Gerber, A.T. Ymnon and R. Kosloff, Chem. Phys. Letters 105 (1984) 523. [12 A.T. Yinnon, R. Kosloffand R.B. Gerber, Chem. Phys. 87 (1984) 441. 113 G. Drolshagen and R. Vollmer, J. Chem. Phys. 87 ( 1987) 4948. [14 A.T. Yinnon, R.B. Gerber, D.K. Dacol and H. Rabitr, J. Chem. Phys. 84 (1986) 5955. [I5 A.T. Yinnon, R. Kosloff and R.B. Gerber, J. Chem. Phys. 88 (1988) 7209. [ 161 A.M. Keil, J.T. Slankas and A. Kupperman, J. Chem. Phys. 70 (1979) 541. [17] B.G.C.CoreyandF.R. McCourt, J.Chem.Phys. 81 (1984) 3892. [IS] R.B. Gerber, A.T. Yinnon and J.N. Murrell, Chem. Phys. 31 (1978) 1.
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