Macroscopic measurements and microscopic information in surface science

Vacuum/volume 36/numbers 7-9/pages 427 to 432/1986

0042-207X/8653.00 + .00 Pergamon Journals Ltd

Printed in Great Britain

Macroscopic measurements and microscopic information in surface science The J Heyrovsk~ Institute of Physical Chemistry and Electrochemistry, Czechoslovak Academy of Sciences, 121 38 Prague 2, Czechoslovakia Z Knor,

The problem of microscopic interpretation of macroscopic measurements--mostly averaged over large number of nonequivalent surface atoms and large number of atomic events (spatial and time averaging)--is discussed in relation to adsorption-desorption phenomena. An example of analysis of the physical content of spatial averaging procedure in the case of work functions is presented. Dynamic effects connected with trapping of gas molecules and with exothermic processes (problem of excess energy dissipation) is briefly commented upon.

Introduction

Most interest in the field of surface science has been concentrated on the static characterization of the geometric and electronic structures of the solid surfaces and of the gas molecules prior to and after their mutual interaction. The duration of an experiment is usually in the range between 0.1 and 10 3 S, whereas the time scale of the atomic events ranges from 10 -a° to about l 0 - 1 6 S. Thus an ordinary experiment yields only time-averaged values of the measured quantities. Theoretical studies were mostly based on the solution of the time independent Schr6dinger equation, dealing thus with stationary states only. The time evolution of a particular system has been usually simulated by a sequence of stationary solutions for a gas particle at different distances from the surface plane (construction of potential energy curves or surfaces). The life-time of various states and the problem of energy dissipation and/or conversion has been either fully neglected or they were included as an additional rough approximation (energy exchange of particles, moving on a given potential energy surface, obtained in the above-mentioned way). The following example--a hydrogen molecule approaching perpendicularly the metal s u r f a c ~ s h o w s some important implications of various types of approximation (Figure 1). The above-mentioned process can be described in a quantum mechanical or quasi-classical approximation. The former treatment (in the adiabatic approximation) results in the strengthening of the intra-molecular bond, due to the polarization of the hydrogen molecule, having its axes perpendicular to the surface t. Within the same approximation, if the H - H bond is parallel to the surface plane, it is weakened, due to the screening effect of metallic electrons x. In a quasi-classical dynamic treatment of the same process--when the electronic interaction is completely neglected and only the exchange and/or conversion of translational, vibrational and rotational energies are conside r e d - t h e perpendicular configuration leads to the vibrational excitation of the hydrogen molecule (thus effectively lowering the energy needed for its dissociation) (Figure 1), whereas the parallel configuration results in a mere reflection2. Thus the two types of treatment yield qualitatively contradictory conclusions.

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i

b

•

i

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F i g u r e 1. Quasi-classical interaction of hydrogen molecule, approaching perpendicularly the metal surface (Me), with (a) molecular axes perpendicular or (b) parallel with respect to the surfaceplane. (c) Potential energy curve for the hydrogen molecule, interacting elastically with the surface.

The experimental information is also spatially averaged over the surface area of the cross-section of the primary particles beam (electrons, photons, ions, atoms), probing the surface. The spatial resolving power of most experimental techniques ranges from 10 -6 cm 2 (109 surface atoms) to 1 cm 2 (1015 surface atoms) with the sensitivity level between 101° and 1013 atoms 3. 427

Z Knot: Macroscopic measurements and microscopic information in surface science

Spatially and time averaged measured quantities and molecular mechanism of surface phenomena The experimental evidence mostly concerns the macroscopic measurements, averaged over a large number of the surface atoms and atomic events. Why should we care about the atomic details? The microscopic information about the surface is needed: (i) As a starting point for quantitative theoretical consideration (testing the reliability of the newly developed methods, obtaining parameters for semi-empirical approaches). (ii) As a basis for qualitative empirical or theoretical elucidation of the role of various factors controlling the molecular mechanism of a given interaction. Understandably, if the experimental data have to serve as a basis for further generalization, their numerical values and particularly their 'physical content' are of primary importance for both quantitative and qualitative considerations. Thus one has first to analyse the details of the spatial averaging procedure. It need not be a simple process (an arithmetic average). For example, in the case of electron emission (photoemission, thermal emission, field emission) the average electron current from a patchy surface is strongly weighted in favour of the highly emitting (low work function) areas. The physical meaning of a given average value would be clear for an ideal homogeneous surface plane, however, this is obviously not a common case. The practical importance of these considerations follows on one side from the well known extraordinary reactivity of atomic steps on the surfaces 4 (structural defects) and on the other side from the unexpectedly large dispersion of the experimental values of those quantities, resulting from kinetic studies. Examples of these quantities are the sticking probability coefficient5 or activation energies of desorption. Even those experimental data obtained on 'well defined' individual crystallographic planes (well defined within the limits of the resolution and of the sensitivity level of standard experimental methods) in renowned laboratories (Figures 2 and 3) exhibit large dispersion which sometimes

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Figure 3. Examples of adsorption heats mostly estimated from the activation energy of desorption: (a) WH1 (refs 49, 54, 57, 58, 77 86);(b) N i ~ O (refs 49, 8(~97); (c) Pd~CO (refs 86, 98-103); where the values of activation energies of desorption were not listed explicitly,the position of desorption peaks in the temperature scale has been used for their estimation 76

amounts to more than 100% of the measured value. What might be the effects of experimentally uncontrolled atomic inhomogeneities of the surfaces (atomic steps, traces of contaminant particles, etc.)--which could be eventually responsible for the above mentioned large dispersion of experimental data? It is not possible to analyse here the influence of crystallographic imperfections and of traces of contaminant particles on the results of each particular experimental technique. However, as an example of such an analysis the effect of the work function inhomogeneity is discussed in the following paragraphs. For a semi-infinite metal crystal, exposing into the gas phase a single crystallographic plane, one can define the following quantities: the 'vacuum' level (the energy of an electron at infinity with zero kinetic energy E J ; the Fermi level of the metal; the electrochemical potential of the electrons inside the metal and the work function (Figure 4). Clearly, this can be done for any crystallographic plane (Figure 4(b)). However, the situation is drastically changed, when the semi-infinite crystal exposes into the gas phase two or more crystallographic planes simultaneously (Figure 4(c)). In this case, one has a common Fermi level for all electrons inside the metal (the electrochemical potential q must have the same value for all electrons inside the crystal at equilibrium) given by the average work function (p

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Figure 2. Examples of the sticking probability coefficients, mostly measured at room temperature: (a) Ni-H z (refs45 50); (b) Ni-O 2 (refs 49 -52); (c) W-H z (refs 49, 50, 53 58); (d) Pt O z (refs 49, 59~54); (e) Pt-CO (refs 65 75). 428

(i.e. it depends both on the value of the work function of an individual patch qh and on its surface area, 0i, being the ith fraction of the overall surface). The field in the very neighbourhood of a given patch (crystallographic plane, stepped surface) is almost unperturbed by the surroundings whereas, farther from the surface, the electron 'feels' the average field. Thus, an inhomogeneous distribution of the electric field arises above the inhomogeneous surface (Figure 5), the intensity of which is extremely high (the work function anisotropy is in the range 0.1-1 eV and its variation proceeds within the distances of units of A - - t h e n the order of magnitude of the field is 10s V cm- 1). What

Z Knor. Macroscopic measurements and microscopic information in surface science

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Figure 4. Scheme of energy levels and of the potential energy of the electron, leaving perpendicularly a particular crystallographic plane (hlk~l~). q~ is the work function of an individual crystallographic plane (h~k~l~), representing a fraction of the surface O,.(E~Oi = 1); qj is the electrochemical potential of the electrons inside the metal; E~ is the energy of an electron in the infinity with a zero kinetic energy ('vacuum level'), E~ are the local 'vacuum levels' and ~Ee are the Fermi levels. consequences could such an inhomogeneity of the electric field have near the surface on a gas-metal interaction? The orientation of molecules impinging onto the surface need not be spatially random. The gas molecules near the surface may be (due to the presence of this electric field gradient) preferentially oriented into a direction either favourable or unfavourable with respect to its trapping mechanism (e.g. the orientation enabling or excluding large overlap of the relevant orbitals of the molecule and of the metal surface). This orientation depends on the

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direction of the field gradient near the surface, on the polarizibility of a molecule and/or on its permanent dipole moment. These most active sites on the surface (atomic steps or other imperfections of the crystal lattice) might represent the 'gates' for gas molecules to become trapped. They, of course, need not stay long on the spot, they can migrate away and make the trapping centres available for further adsorption 6. The surface concentration of these minority centres could be eventually below the sensitivity level of contemporary experimental techniques and thus uncontrolled.

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Figure 5. Inhomogeneity of the electric field in the vicinity of the patchy surface, x and ~ are the coordinates perpendicular and along the surface, respectively. All other symbols are identical with those of Figure 4. 429

Z Knor: Macroscopic measurements and microscopic information in surface science

Consequently, they might at least partially explain the large dispersion of the experimental kinetic data, e.g. sticking probability coefficient. The results of UPS measurements of xenon adsorption on heterogeneous Pt, Pd and Ru surfaces support this type of consideration, based on the existence of different local 'vacuum levels' just outside the patches of different work function 7.

Dynamics of the surface phenomena The agreement between theory and experiment in characterization of stationary states (e.g. the structure of surface layers, energy loss spectra of electrons 9, distribution of states and photoemission curves) appears to be satisfactory. O n the other hand the abovementioned uncertainties of experimental values of dynamic quantities (e.g. sticking probability coefficient, activation energy of desorption) make the agreement between theory and the experiment more or less accidental 9 (Figure 6). Therefore, it seems reasonable to generalize the experimental and theoretical experience particularly in the form of qualitative models which can be used for the explanation of the observed phenomena on an atomic scale. Several basic features are now generally accepted as a basis for the interpretation of general trends of the observable quantities:

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Figure 6. Examples of comparison between theoretical and experimental results (the dashed-line frame represents the region of standard deviations of experimental values), taken from ref 9: (a) hydrogen chemisorption on nickel--© 104, ~ 105 I) lob • 1o7, x 22 ~ 10s; (b) hydrogen chemisorption on transition metals of the 5th row of the periodic system of elements-- ©22, • 12 ID~o9, & l ~o. Negative values of adsorption heats defined always as QH2= - Dn n + 2E~I mwould mean that no chemisorption of H 2 on a particular metal could take place. 430

(i) The important role of d-electrons* in chemisorption s 18 (ii) The screening effect of delocalized s (sp)-electrons 1,8.9,19.2o and their possible role in the energy dissipation processes and in the stationary bonding 21'22. The d-electrons might serve either as permanent trapping centres or transient centres (precursor states) for chemisorption of gas particles. The d-electrons might be, after some time interval, released again, due to successive relaxation and the screening effect of delocalized electrons 9. Regardless of the kind of d-electron participation in the gas metal interaction, its role should manifest itself in the trends of observable quantities both in the horizontal rows (filling of the d-band) and in the vertical columns (the spatial extension of 3d, 4d and 5d orbitals) of the periodic system. These basic features were included in the qualitative LDEI model (localized~telocalized electron interplay model) 8'9 of the surface interactions. This model has been developed on the basis of experimental and q u a n t u m chemical experience and its conclusions agree well with recent theoretical 12,14.15,18,22 24- and experimental 13'26 results. For example, when a molecule approaches the metal surface, the initial interaction is described in the LDEI model as the creation of a hole in the spatial density distribution of the delocalized electrons due to the exchange and correlation repulsive forces s'9. This process can be considered as one channel for the dissipation of the excess kinetic energy of the gas molecule, similar to the mechanism of electron-hole pair creation, suggested in literature 22,23 In the very initial stage of any surface interaction, the exchange and conversion of energy of the impinging particle plays an important role. If the gas molecule has to be trapped, it must lose the excess translational energy, corresponding to the velocity component, perpendicular to the surface. This energy would otherwise enable the molecule to escape from the potential well at the surface 21'22"27'2s. This can be accomplished via some of the following mechanisms 2~'23'27'29 31. The translational energy of the molecule can be converted into: (i) the surface migration and/or vibration and rotation of the adsorption complex (intra-molecular conversion, vibration within the adsorbed layer); (ii) the vibration of the crystal lattice i.e. the formation of phonons (this process has a low probability for light gases, because of the unfavourable mass ratio29"32); (iii) the vibration of the electron gas i.e. the formation of plasmons (this process has also a low probability, because of the high energy needed for the plasmon creation32'33); (iv) the electron-hole pair excitation (this process seems to be the most important one for simple gas metal interactions2X 23,27,29 31). The above-listed individual dissipation channels are usually treated in theoretical papers separately, in spite of the fact that, probably, several of them are operating simultaneously in a given surface interaction. Experimental studies of dynamics of surface processes have been made possible by the introduction of time resolved methods. Up until recently the experimental studies in this field were based * Note: as is common in the literature, an abbreviated formulation 'delectrons' instead of 'electrons, occupying the d-type states' will be used throughout the following text. The physical basis for such classification of transition metal electrons follows from different symmetry properties of the d-states, localized at the surface atoms, in comparison with the symmetry properties of delocalized states 8-18. This symmetry of the occupied d-states is important for surmounting the activation barrier for chemisorption, typical for the free-electron metals8'9'~6'x8.

Z Knot: Macroscopic measurements and microscopic information in surface science

mainly on spectroscopic measurements, viz. laser -3°-'~° and electron -41 induced fluorescence spectroscopy (information about the energy state of an ensemble of molecules prior to and after the interaction with the surface). Qualitative information about these processes has been obtained from the measurements of the angular distribution of particles, ejected from the surface and of their kinetic energies 42, and from the measurement of quantities related to the state of gas molecules (indication of the excited molecules, e.g. from changes of their ionization yield, either in electron-impact ionization 43 or in field ionization 44 processes). The field ionization method, developed in our laboratory, is appropriate for the indication of excited particles produced by an exothermic surface process. The gas molecules are field ionized within about 10 x6 s in the very neighbourhood of the surface of a sharp tip, prepared from the metal under investigation 44. The field ionization current is, in the low field region, roughly proportional to the field ionization probability 44, which is higher both for vibrationally and for electronically excited particles than for particles in the ground state 44. Thus, by comparing the theoretically calculated field ionization probabilities with the experimentally obtained field ionization currents one can indicate the presence of the excited particles 44. Conclusions

We have seen that even separate elementary steps of the surface interactions represent, from the experimental point of view, a rather complicated problem which is related to a detailed knowledge of the local geometry (atomic surrounding of the trapping site). Kinetics of a surface process, i.e. the rate- and route-determining steps can be influenced in a decisive way by the imperfections of the atomic structure (crystallographic defects, atomic steps, traces of contaminant particles), unobservable by standard contemporary techniques, since they may represent the 'active centres' for a particular interaction. Thus, the poor reproducibility of some experimental results in this field can be understood. When increasing the spatial resolution of the experimental techniques, an additional difficulty emerges, viz. the technique itself can strongly influence the surface process (e.g. in a field ion microscope which has atomic resolution, the presence of an extremely high electric field can seriously perturb the whole system). Gas moLecuLe in

TransLationatLy, vibrationaEy etc. 'hot' gas moLecuLe

the ground state (thermal energy)

Chemisorption

Fragments

j

the moLecuLe

r

Desorption

Heating of the sampl.

Recombination of fragments ( exothermic process )

Figure 7. Examples of an exothermic process, resulting in excited gas molecule, as evidenced experimentally42 44.

The time averaging represents another complicating factor, necessitating the use of sophisticated equipment to overcome this problem. The contemporary inability to follow directly atomic events results in one fundamental problem, viz. that we mostly do not know exactly if the initial and final states of gas molecules prior to and after the interaction with the metal surface are identical. In fact, there is already some experimental evidence 34~4 that this need not be always the case (Figure 7). Consequently, in theoretical considerations of these cases, one cannot simply apply the principle of microscopic reversibility ~J ~ which is applicable to equilibrium conditions only, since the dynamics of the adsorption and desorption processes can differ from each other.

References

i j Mahanty and N M March, J Phys C, 9, 2905 (1976). 2 H Eyring, S H Lin and S M Lin, Basic Chemical Kinetics, John Wiley, New York (1980). 3 j p Hobson, Japan J appl Phys, Suppl 2, Pt 1,317 (1974). 4 H Wagner, Springer Tracts in Modern Physics, vol 85, Solid Surface Physics, p 151, Springer, Berlin (1979). s C T Campbell, G Ertl, H Kuipers and J Segner, Surface Sci, 107, 220 (1981). 6 Z Knor, Ch Edelmann, J Rudny and J Stachurski, Appl Surface Sci, 25, 107 (1986). 7 j Hulse, J Kfippers, K Wandelt and G ERtl, Appl Surface Sei, 6, 453 (1980). 8 Z Knor, Surface Sci, 70, 286 (1978); Surface and Defect Properties of Solids. (Edited by M W Roberts and J M Thomas), vol 6, p 139. Chem Soc, London (1977). 9 Z Knor, Catalysis Science and Technology. (Edited by J R Anderson and M Boudart), vol 3, p 231. Springer, Berlin (1983). o T E Madey, J T Yates, D R Sanderstrom and R J H Vorhoeve, Treatise on Solid State Chemistry. (Edited by N B Hannay), vol 6B, Surfaces, p 1. Plenum Press, New York (1976). xl j p Muscat and D M Newns, Surface Sci, 80, 189 (1979). 12 C M Varma and A J Wilson, Phys Rev B, 22, 3795 (1980). 13 M W Holmes and D A King, Proc R Soc Lon A, 376, 565 (1981). 14 j R Smith, F J Arlington and J G Gay, J Vac Sci Technol, 18, 411 (1981 ). 15 j Tersoff and L M Falicov, Phys Rev B, 24, 754 (1981). 16 A C Balazs and K H Johnson, Surface Sci, 114, 197 (1982). 17 C Thuault-Cytermann, M C Desjonqueres and D Spanjaard, J Phys C, 16, 5689 (1983). 18 W F Banholzer, Y O Park, K M Mak and R I Masel, Surface Sci, 128, 176 (1983). 19 j K Norskov, S Holloway and N D Lang, Surface Sci, 137, 85 (1984). 2o W Andreoni and C M Varma, Phys Rev B, 23, 437 (1981). 21 G P Brivio and T B Grimley, Surface Sci, 89, 226 (1979). 22 j K Norskov, J Vac Sci Technol, 18, 420 (1981); P Nordlander, S Holloway and J K Norskov, Surface Sci, 136, 59 (1984). 23 H Metiu and J W Gadzuk, J Chem Phys, 74, 2641 (1981). 24 j W Davenport, T L Einstein, J R Schrieffer and P Soven, The Physical Basis for Heterogeneous Catalysis. (Edited by E Drauglis and R J Jaffee), p 596. Plenum Press, New York (1975). 2s K Y Yu, C R Helms, W E Spicer and P W Chye, Phys Rev B, 15, 1629 (1977). 26 V V Gorodetskii, V A Sobyanin, N N Bulgakov and Z Knor, Surface Sci, 82, 120 (1979). 27 G Ertl, Ber Bunsen Ges Phys Chem, 86, 425 (1982). 28 j C Tully, Surface Sci, 111, 461 (1981). 29 j K Norskov and B I Lundqvist, Surface Sci, 89, 251 (1979). 30 G P Brivio and T B Grimley, Surface Sci, 131, 475 (1983). 31j W Gadzuk and H Metiu, Vibrations at Surfaces. (Edited by R Gaudena, J M Gliles and A A Lucas), p 516. Plenum Publishing Corp, New York (1982). 32 j Misewich, C N Plum, G Blyholder and P L Houston, J Chem Phys, 78, 4245 (1983). 33 C J Chen and R M Osgood, Appl Phys A, 31, 171 (1983). 34 N Zare and R B Bernstein, Physics Today, p 43 (November 1980). 35 T F George, J Phys Chem, 86, 10 (1982). 431

Z Knor: Macroscopic measurements and microscopic information in surface science

36 D S King and R R Cavanagh, J Chem Phys, 76, 5634 (1982). 37 L D Talley, D E Tevault and M C Lin, J Chem Phys, 72, 3314 (1980). 38 A W Kleyn, A C Luntz and D J Auerbach, Phys Rev Letts, 47, 1169 (1981). 39 F Frenkel, J Hfiger, W Krieger, H Walther, C T Campbell, G Ertl, H Kuipers and J Segner, Phys Rev Letts, 46, 152 (1981). 4o M Asscher, W L Guthrie, T H Lin and G A Somorjai, J Chem Phys, 78, 6992 (1983). 41 R P T h o r m a n and S L Bernasek, J Chem Phys, 74, 6498 (1981). 42 G Comsa, R David and B J Schumacher, Surface Sci, 85, 45 (1979); Surface Sci, 95, L210 (1980). ,*3 S N Foner and R L Hudson, J Chem Phys, 75, 4727 (1981); J Chem Phys, 80, 518 (1984). ,*4 N M Vasilyev and Z Knor, Chem Phys Letts, 108, 623 (1984). 45 K D Rendulic and A Winkler, J Chem Phys, 79, 5151 (1983); Surfi~ce Sci, 118, 19 (1982). 46 K Christmann, Bull Soc Chim Bely, 88, 519 (1979). 47 j Lapujoulade and K S Nell, Surface Sci, 35, 288 (1973). 48 R J Madix, Catal Rel~Sci En(lny, 15, 293 (1977). 49 M A Morris, M Bowker and D A King, Comprehensive Chemical Kinetics, vol 19, Simple Processes at Gas Solid Interference. (Edited by C H Bamford, C F H Tipper and R G Compton), p 1. Elsevier, Amsterdam (1984). 5 ° G A Somorjai, Chemistry in Two Dimensions, Surfaces, Cornell University Press, Ithaca (1981). 51 G K Boreskov, Catalysis--Science and Technolooy. (Edited by J R Anderson and M Boudart), vol 3, p 39. Springer, Berlin (1982). 52 A Winkler, K D Rendulic and K Wendel, Appl Surface Sci, 14, 209 (1982 83). 53 p j Estrup and J R Anderson, Surface Sci, 49, 465 (1975). 54 p W T a m m and L D Schmidt, J Chem Phys, 51, 5352 (1969). 55 R R Rye, B D Barford and P G Cartier, J Chem Phys, 59, 1693 (1973). 56 T E Madey, Surface Sci, 36, 281 (1973). 5v D A King and G Thomas, Surface Sci, 92, 201 (1980). s8 L D Schmidt, Adsorption and Desorption Phenomena. (Edited by F Ricca), p 391. Academic Press, London (1972). 59 R P Norton, P E Binder and K Griffith, Surf?we Sci, 138, 125 (1984). 60 j L Gland and V N Korchak, Surface Sci, 75, 733 (1978). 61 K Schwaha and E Bechtold, Surface Sci, 65, 277 (1977). 6z R Ducros and R P Merrill, Surface Sci, 55, 227 (1976). 63 H P Bonzel and R Ku, Surface Sci, 40, 85 (1973). 64 G Kneringer and F P Netzer, Surface Sci, 49, 127 (1975). 65 L S Palatnik, A I Fedorenko, T P Gladkich and A A Ryabchun, Poverkhnost (USSR), No 1, p 37, (1984). 66 A E Morgan and G A Somorjai, Surface Sci, 12, 405 (1968). 6v R W McCabe and L D Schmidt, Surface Sci, 66, 101 (1977). 68 R J Behm, P A Thiel, R P Norton and G Ertl, J Chem Phys, 78, 7437 (1983). 69 G Brod~n, G Pirug and H P Bonzel, Surface Sci, 72, 45 (1978). 7o G Ertl, M N e u m a n n and K M Streit, Surface Sci, 64, 393 (1977).

432

7~ R A Shigeishi and D A King, Surface Sci, 58, 379 (1976). 72 H Steiniger, S Lehwald and H Ibach, Surface Sci, 123, 264 (1982). 73 C T Campbell, G Ertl, H Kuipers and J Segner, Surface Sci, 107, 207 (1981). v4 M R McClellan, J L Gland and F R McFeeley, Surface Sci, 112, 63 (1981). 75 A J Crosley and D A King, Surface Sci, 95, 131 (1980). 76 Z Knor, Surface Sci, 154, L233 (1985). 77 p W T a m m and L D Schmidt, J Chem Phys, 54, 4775 (1971). 78 A H Smith, R A Baker and P J Estrup, Surface Sci, 136, 327 (1984). 79 T E Madey, J Z Czyzewski and J T Yates, Surface Sci, 49, 465 (1975). 80 R Jaeger and D Menzel, Surface Sci, 100, 561 (1980). 81 j T Yates and T E Madey, J Vac Sci Technol, 8, 63 (1971). 82 M Mahnig and L D Schmidt, Z Phys Chem NF, 80, 71 (1972). 83 T E Madey, Surface Sci, 29, 571 (1972). 84 R R Rye and B D Barford, Surface Sci, 27, 667 (1971). 8s R R Rye, B D Barford and P G Cartier, J Chem Phys, 59, 1693 (1973). 86 I Toyoshima and G A Somorjai, Catal Rev~Sci Engn#, 19, 105 (1979). s7 G A Sargent, J Chao and G B Freemen, Appl Surface Sci, 15, 255 (1983). 88 F P Netzer and T E Madey, J Chem Phys, 76, 710 (1982). so H Ibach, W Erley and H Wagner, Surface Sci, 92, 29 (1980). 90 H Conrad, G Ertl, J Kiippers and E Latta, Surface Sci, 57, 475 (1976). 91 K Klier, A C Zettlemoyer and H Leidheiser, J Chem Phys, 52, 589 (1970). 92 j C Tracy, J Chem Phys, 56, 2736 (1972). 93 A V Kalinkin, V I Savchenko and V I Erokhim, Izv SOAN USSR, 3, 20 (1982). 94 F Labohm, C W R Engelen, O L J Gijzeman, J W Geus and G A Bootsma, J Chem Soc, 78, 2435 (1982). 95 j C Bertolini and B Tardy, Surface Sci, 102, 131 (1981). 96 j T Yates and D W G o o d m a n , J Chem Phys, 73, 5371 (1980). 97 H H Madden, J Kfippers and G Ertl, J Chem Phys, 58, 3401 (1973). 98 G Ertl and J Kfippers, Low Eneroy Electrons and Surface Chemistry, p 227. Verlag Chemie, Weinheim (1974). oo R J Behm, K Christmann, G Ertl and M A van Hove, J Chem Phys, 73, 2984 (1980). loo T Engel, J Chem Phys, 69, 373 (1978). lol G D Halsey, Surface Sci, 64, 681 (1977). ~o2 H Conrad, G Ertl, J Koch and E E Latta, Surface Sci, 43, 462 (1974). los j C Tracy and P W Palmberg, J Chem Phys, 51, 4852 (1969). lo4 H Itoh, Japan Jappl Phys, 15, 2311 (1976). lo5 G Doyen and G Ertl, J Chem Phys, 68, 5417 (1978). 1o6 D Shopov, A Andreev and D Petrov, J Catal, 13, 123 (1969). ~o7 G Blyholder, J Chem Phys, 62, 3193 (1975). ~o8 D J M Fassaert and A van der Avoird, Surface Sci, 55, 313 (1976). 1o9 S W W a n g and W H Weinberg, Surface Sci, 77, 14 (1976). llo A J Martin, Surface Sci, 74, 479 (1978). 111 G D Kubiak, G O Sitz and R N Zare, preprint (1985).