Molecular beam studies of gas-surface collision dynamics

0079-6816/91 $0.00 + .50 Copyright © 1991 Pergamon Press plc

Progress in Surface Science, Vol. 38 pp. 1-102 Printed in the U.S.A. All rights reserved.

Molecular Beam Studies of Gas-Surface Collision Dynamics Christopher R. ArumainayagamI and Robert J. Madixz3

1Department of Chemistry, Wellesley College, Wellesley, MA 02181 2Departments of Chemical Engineering and Chemistry, Stanford University, Stanford, CA 94305 3"1"owhom correspondence should be addressed

ABSTRACT Recent progress in the application of supersonic molecular beam techniques to the study of gas-surface interfacial phenomena is reviewed. The experimental and theoretical studies discussed examine fundamentalissues regarding both non-reactive and reactive scattering. Topics discussed include elastic scattering (thermal energy atom scattering and diffractive selective adsorption), inelastic scattering, u'apping-desorption, molecular chemisorption and desorption, dissociative chemisorption (direct collisional activation, precursor-mediated dissociation, and collisioninduced dissociation of adsorbed species) and chemical reactions at surfaces. The review is organized around dynamical variables rather than particular gas*surface systems to emphasize the underlying physical principles governing gas-surface interactions. An index is provided at the beginning for the reader interested in specific gas-surface systems.

1

C.R. Arumainayagam and R.J. Madix

Table of Contents I n d e x o f gas-surface systems I .................................................................................................

4

Index o f gas-surface systems II ...............................................................................................

5

A b b r e v i a t i o n s ...........................................................................................................................

6

1 I n t r o d u c t i o n ...........................................................................................................................

7

2 E x p e r i m e n t a l ........................................................................................................................ 2.1 M o l e c u l a r b e a m s .......................................................................................................... 2.1.1 E f f u s i v e b e a m s ................................................................................................... 2.1.2 N o z z l e (supersonic) b e a m s ................................................................................. 2.1.2.1 V e l o c i t y distribution .................................................................................. 2.1.2.2 S e e d i n g techniques .................................................................................... 2.1.2.3 Internal state distributions ......................................................................... 2.1.2.4 P u l s e d nozzle b e a m s .................................................................................. 2.2 E x p e r i m e n t a l setup ...................................................................................................... 2.2.1 Source c h a m b e r .................................................................................................. 2.2.2 M o d u l a t i o n c h a m b e r a n d buffer c h a m b e r s ......................................................... 2.2.3 U l t r a h i g h v a c u u m scattering c h a m b e r ............................................................... 2.2.3.1 D y n a m i c s o f scattering a n d desorption ..................................................... 2.2.3.2 D y n a m i c s o f adsorption ............................................................................ 2.2.3.3 T h e r m a l e n e r g y a t o m scattering ( T E A S ) ..................................................

7 7 8 8 8 9 9 10 10 10 12 12 13 15 16

3 N o n - R e a c t i v e Scattering f r o m Surfaces ............................................................................... 3.1 Elastic scattering .......................................................................................................... 3.1.1 Structural studies o f surfaces by b e a m diffraction ............................................. 3.1.2 D i f f r a c t i v e selective adsorption .......................................................................... 3.1.3 Q u a n t i f y i n g defect densities with T E A S ............................................................ 3.1.4 A p p l i c a t i o n o f T E A S to m o n i t o r surface c o v e r a g e ............................................ 3.1.5 T E A S investigation o f adsorbate m i g r a t i o n ....................................................... 3.1.6 T E A S investigation o f 2-D p h a s e transitions .................................................. 3.2 Inelastic scattering ....................................................................................................... 3.2.1 Z e r o - p h o n o n inelastic scattering ........................................................................ 3.2.1.1 Rotational transitions ................................................................................. 3.2.1.2 Rotationally m e d i a t e d selective adsorption ( R M S A ) ................................ 3.2.2 S i n g l e - p h o n o n inelastic scattering ...................................................................... 3.2.2.1 Inelastic He scattering to detect surface p h o n o n s ..................................... 3.2.2.2 Inelastic H e scattering to detect adsorbate vibrational m o d e s .................. 3.2.3 M u l t i - p h o n o n inelastic scattering ....................................................................... 3.2.3.1 A n g u l a r distributions ................................................................................. 3.2.3.2 V e l o c i t y distributions ................................................................................ 3.2.3.3 Internal state distributions ......................................................................... 3.2.3.3.1 Rotational state distributions ............................................................ 3.2.3.3.2 Rotational a l i g n m e n t a n d orientation ............................................... 3.2.3.3.3 V i b r a t i o n a l state distributions .......................................................... 3.2.3.4 Steric effects in scattering ....................................................................... 3.3 T r a p p i n g - d e s o r p t i o n .................................................................................................... 3.3.1 D e p e n d e n c e o f trapping o n incident translational e n e r g y .................................. 3.3.2 D e p e n d e n c e o f trapping o n incident a n g l e ......................................................... 3.3.3 D e p e n d e n c e o f trapping o n surface temperature ................................................ 3.3.4 D e p e n d e n c e o f trapping o n initial m o l e c u l a r orientation ................................... 3.3.5 D e p e n d e n c e o f trapping on adsorbate c o v e r a g e ................................................. 3.3.6 D y n a m i c s o f extrinsic precursor adsorption ....................................................... 3.3.7 D e t a i l e d b a l a n c e ................................................................................................. 3.3.8 Rotational state distributions in trapping-desorption .........................................

17 18 19 20 21 21 24 25 25 25 26 26 26 27 28 28 28 30 32 32 34 36 42 42 43 45 47 47 48 48 50 50

Molecular Beam Studies

3.3.9 Orientation o f molecular axis in desorption ....................................................... 3.4 Molecular chemisorption and desorption .................................................................... 3.4.1 Dependence on incident translational energy ..................................................... 3.4.2 D e p e n d e n c e on incident angle ............................................................................ 3.4.3 R o l e o f precursors ............................................................................................... 3.4.4 Stefic effects in molecular chemisorpfion ......................................................... 3.4.5 Rotational state distribution for dcsorption ....................................................... 3.4.6 Rotational alignment in desorption ....................................................................

51 51 51 52 52 57 57 58

4 Reactive Scattering from Surfaces ....................................................................................... 4.1 Dissociative chemisorption .......................................................................................... 4.1.1 Direct collisional activation ................................................................................ 4.1.1.1 Dependence on incident translational energy ............................................ 4.1.1.2 Dependence on incident angle ................................................................... 4.1.1.3 Dependence on surface temperature .......................................................... 4.1.1.4 Dependence on incident vibrational energy .............................................. 4.1.1.5 Dependence on incident rotational energy ................................................ 4.1.1.6 Identification and manipulation of dissociation products ......................... 4.1.2 Precursor-mediated dissociation ......................................................................... 4.1.2.1 Dependence on incident translational energy ............................................ 4.1.2.2 Dependence on incident angle ................................................................... 4.1.2.3 Dependence on incident vibrational energy .............................................. 4.1.2.4 Dependence on surface temperature .......................................................... 4.1.2.5 Dependence on surface coverage .............................................................. 4.1.2.6 C o m p l e x dissociation pathways ................................................................ 4.1.3 Collision-induced dissociation o f adsorbed species ........................................... 4.2 Chemical reactions at surfaces ....................................................................................

58 58 60 60 67 71 71 77 78 80 80 80 81 81 82 84 86 86

5 Conclusion ............................................................................................................................

89

References

90

..............................................................................................................................

C.R. Arumainayagam and R.J. Madix

Index of Gas-Surface Systems I Ag(lll) HC1, 32 Hydrogen, 26 Nitrogen, 34 NO, 32, 36, 39, 42, 47 Trifluoromethane, 51 Au(lll) Ammonia, 39 Cu

Hydrogen, 77 Cu(100) Hydrogen, 45, 68, 75 Cu(110) CO, 68 Hydrogen, 68, 75, 77 Cu(lll) Hydrogen, 68, 75, 77 Fe(111) Nitrogen, 80, 81 Ge, oxidized NO, 34, 50 Graphite He, 20 It(110)-(Ix2) CO, 71 Ethane, 43, 45, 48 Methane, 63 n-alkane, 65, 71, 80, 84 LiF(001) He, 20 Hydrogen, 20, 26 Mg(100) Hydrogen, 60 MgO(100) Hydrogen, 26 Iodine, 78 Ni(100) Carbon dioxide, 73, 77 CO, 51, 52, 57, 71 n-alkane, 65, 67 Ni(110) Nitrogen, 52

Ni(111) CO, 51, 71 Methane, 63, 67, 71, 73, 78, 86 Ni(997) Hydrogen, 80 Pd, foil Carbon dioxide, 73 Pd(lll) CO, 88 NO, 57 Pt, foil Carbon dioxide, 73 Pt(lll) Ar, 32, 43, 45, 47 CO, 24, 28, 51, 52, 57, 88 Ethane, 43, 45, 48 Hydrogen, 24, 26 Methane, 32, 43, 47, 50, 63, 71 Nitrogen, 32 NO, 57, 58 Oxygen, 80, 84 Propane, 43, 45, 48 Xe, 25, 32, 43, 45, 48, 50 Pt(997) Hydrogen, 24

Re(0001) Nitrogen, 60, 65 Rh(lll) CO, 88 Ru(001) Ne, 45 NO, 51 W, polycrystalline Ar, 30, 42 Nitrogen, 82 W(100) Ar, 30 Nitrogen, 30, 52, 71, 80 - 82, 84 W(100), Hydrogen covered Ar, 45, 50 W(110) Hydrogen, 26 Methane, 63, 67, 73 Nitrogen, 60, 65, 67, 68, 75 Oxygen, 67, 80

Molecular Beam Studies

Index of Gas-Surface Systems II Ammonia Au(111), 39 Argon Pt(ll 1), 32, 43, 45, 47 W, polycrystalline, 30, 42 W(100), 30 W(100), Hydrogen covered, 45, 50 Carbon dioxide Ni(100), 73, 77 Pd, foil, 73 Pt, foil, 73 CO Cu(110), 68 Ir(110)-(Ix2), 71 Ni(100), 51, 52, 57, 71 Ni(111), 51,71 Pd(111), 88 Pt(111), 24, 28, 51, 52, 57, 88 Rh(111), 88 Ethane Ir(110)-(lx2), 43, 45, 48 Pt(111), 43, 45, 48 See also n-Alkane HC1 Ag(lll), 32 He

Graphite, 20 LiF(001), 20 Hydrogen Ag(111), 26 Cu, 77 Cu(100), 45, 68, 75 Cu(110), 68, 75, 77 Cu(111), 68, 75, 77 LiF(001), 20, 26 Mg(100), 60 MgO(100), 26 Ni(997), 80 Pt(111), 24, 26 Pt(997), 24 W(110), 26

MgO(100), 78 Methane Ir(110)-(Ix2), 63 Ni(111), 63, 67, 71, 73, 78, 86 Pt(l 11), 32, 43, 47, 50, 63, 71 W(110), 63, 67, 73 See also n-Alkane n-Alkane Ir(110)-(Ix2), 65, 71, 80, 84 Ni(100), 65, 67 See also ethane, methane, and propane Ne

Ru(001), 45 Nitrogen Ag(111), 34 Fe(111), 80, 81 Ni(110), 52 Pt(111), 32 Re(0001), 60, 65 W, polycrystalline, 82 W(100), 30, 52, 71, 80-82, 84 W(110), 60, 65, 67, 68, 75 NO Ag(lll), 32, 36, 39, 42, 47 Ge, oxidized, 34, 50 Pd(l II), 57 Pt(ll I), 57, 58 Ru(001), 51 Oxygen Pt(111), 80, 84 W(110), 67, 80 Propane Pt(111), 43, 45, 48 See also n-Alkane Trifluoromethan¢ Ag(111), 51 Xe

Iodine

Pt(111), 25, 32, 43, 45, 48, 50

C.R. Arumainayagam and R.J. Madix

ABBREVIATIONS AES

Auger Electron Spectroscopy

FTIR

Fourier Transform Infrared Spectroscopy

HREELS

High Resolution Electn3n Energy Loss Spectroscopy

LEED

Low Energy Electron Diffraction

LIF

Laser-Induced Fluorescence

LITD

Laser Induced Thermal Desorption

MBRS

Molecular Beam Relaxation Spectrometry

MPI

Multiphoton Ionization

NEXAFS

Near Edge X-ray Absorption Fine Structure

PES

Potential Energy Surface

REMPI

Resonance Enhanced Multiphoton Ionization

RMSA

Rotationally Mediated Selective Adsorption

SIMS

Secondary Ion Mass Spectrome~-y

TEAS

Thermal Energy Atom Scattering

TOF

Time-of-Flight

TPD

Temperature Programmed Dcsorption

UHV

Ultrahigh Vacuum

UPS

Ultravioletphotoelectron spectroscopy

XPS

X-ray photoelectron spectroscopy

Molecular Beam Studies

7

] Introduction

Over the past two decades molecular beam experiments with the associated techniques of surface science have provided significant advancement in the elucidation of the dynamics of gas-surface interactions [1]. Prior to the use of molecular beam methods in the study of gas-surface collisional processes, experiments revealed only the effects of gas-surface encounters averaged over energy and angle of incidence [2]. Ideally, dynamical studies of the events at the gas-surface interface require that the translational, electronic, vibrational, and rotational levels of a molecule be independently controlled before and separately measured after collision with the surface. Scattering of nearly monoenergetic supersonic molecular beams with well defined internal state distributions from well-characterized single crystal surfaces, using time-of-flight (TOF) measurements and state selective detection techniques such as laser-induced fluorescence (LIF) and multiphoton ionization (MPI), come close to achieving this ideal. Molecular beam studies have been utilized to deduce the fundamental details of non-reactive gas-surface interactions, to probe the structures of surfaces (elastic diffractive scattering), to obtain phonon spectra of solid surfaces (inelastic scattering), and to provide insight into the fundamentals of the kinetics of heterogeneous chemical reactions (reactive scattering). Extensive reviews of molecular beam studies of gas-surface dynamics done prior to 1984 have been published [[1], [3]].

Since these compendiums, however, there has been major progress in

experiment and theory regarding molecular collisions with solid surfaces, and the goal of this review is to present a synopsis of gas-surface dynamical studies with emphasis on the more recent developments. A detailed technical description of the apparatus and procedures used in these types of experiments has been published recently [4]. Our main objective is to review material, both experimental and theoretical, that has relevance to reactive collisional processes, including surface characterization. The review is intended to be reasonably comprehensive, but not exhaustive, and regrettably, some excellent work has

been omitted. In section 2 we present a brief introduction to the experimental aspects of molecular beam studies of gas-surface dynamics. This section is not meant to be comprehensive and is included for the reader unfamiliar with molecular beam techniques. 2 Experimental 2.1 M o l e c u l a r b e a m s A molecular beam is a collimated stream of electrically neutral molecules traversing a region of sufficiently low pressure such that the effects of molecular collisions with the ambient gas and within the beam can be ignored. Molecular beams are produced by expanding a gas through an orifice into a region of low pressure and collimating the flow by several apertures along the beam line. Depending on the type of source, molecular beams can be classified into two classes: effusive beams and supersonic (nozzle) beams [5]. Below we consider some salient features of these two types of beams.

8

C.R. Arumainayagamand R.J. Madix

2.1.1 Effusive beams In effusive sources the low operational pressure ensures free molecular flow through the source. Few molecular collisions take place during the formation of an effusive beam because of the high Knudsen number (K,>>I), the Knudsen number being the ratio of the mean free path (X) of the gas in the source to the source orifice diameter (d) (I~ = ~/d). The angular distribution of molecules emanating from the orifice is cos 0. The velocity distribution of molecules along the beam axis is Maxwellian and is characterized by the source temperature (T). All other degrees of freedom are also characterized by this temperature. The flux weighted normalized velocity distribution (I(v)) of a effusive beam is given by the following expression: /(V)=

v3ex

~

(1)

where 0~2 = 2kT/m, k is the Boltzmann constant, and m is the molecular weight. The above expression contains a v 3 term rather than a v 2 term because the velocity distribution is expressed as a flux weighted distribution rather than a density distribution. By the use of multichannel capillary array sources, high fluxes can be obtained for effusive molecular beams [6].

2.1.2 Nozzle (supersonic) beams Supersonic molecular beams, originally proposed in 1951 [7] and first developed in 1954 [81, have become popular recently because they overcome two major limitations of effusive beams: wide velocity distributions and the inability to obtain a wide range of translational energies. In the adiabatic (isentropic) expansion of a free jet from a nozzle at high pressure (K, << 1) into an evacuated chamber, random thermal molecular motion is almost completely converted to directed motion, producing a nearly monoenergetic beam which is more focussed and intense than an effusive beam. Such beams also allow the translational energy to be varied over a wide range. We will now consider in more detail important aspects of supersonic molecular beams.

2.1.2.1 Velocity distribution The supersonic molecular beam is characterized by a very narrow velocity distribution. Velocity spreads of less than 0.1% can be obtained for cooled, highly expanded helium beams [9]. However, velocity spreads of approximately 10% are more typical for higher molecular weight species such as Ar, Xe, CzH~. The flux weighted normalized velocity distribution of a supersonic nozzle beam is given by: l ( v ) = A (Vo, Ct)v 3 e x p ( - ( v --Vo) z /)

(2)

Molecular Beam Studies

9

where A(vo, ~z) is the normalization constant, Vo is the flow velocity, and ~, a measure of the spread in velocities of the gas parallel to the flow direction, is: ct2 = 2kTII m

(3)

Tit,the axial translational temperature, is usually much smaller than the source temperature due to cooling during the expansion. The average translational energy of a supersonic molecular beam is approximated by the following expression: -

-

E =

RT~T

(4)

(7-1) where 7 is the heat capacity ratio (C_a,/C0of the gas, R is the universal gas constant, and T~ is the nozzle temperature. 2.1.2.2 S e e d i n g t e c h n i q u e s Supersonic nozzle beams also permit the use of seeding techniques in which a fast moving light gas (usually 1-12or He) accelerates slow moving heavier gas molecules to higher velocities [10]. Neglecting the difference in heat capacity, the translational energy of the heavy gas is:

Er=[(l-x)--~+x] CpT, m

-1

(5)

where m and M are the molecular weights of the light and heavy gas, respectively, x is the mole fraction of the heavy gas, Cp is the heat capacity at constant pressure, and To is the nozzle temperature. In the limit of infinite dilution (x = 0), the velocity of the heavy component becomes equal to the pure beam velocity of the light component. By heating the nozzle (< 3000 K ) and by increasing the mole fraction of the lighter gas it is possible to attain translational energies as high as 1390 kJ/mole for heavy species such as Xe [11]. Conversely, by cooling the nozzle and/or "anti-seeding" a light gas such as H2 in a heavier gas such as Ar or Xe, translational energies of H 2 as low as a few kJ/mole can be achieved [ 12]. Hence, by varying the nozzle temperature and the ratio of the heavy gas to the light gas, the translational energy of the molecules in a supersonic molecular beam can be varied over a large range. 2.1.2.3 I n t e r n a l s t a t e d i s t r i b u t i o n s Whereas effusive beams are characterized by Maxwell-Boltzrnann distribution of velocity and internal energy, supersonic beams exhibit extensive cooling of rotational and some relaxation of vibrational degrees of freedom. While rotational temperatures of less than 1K are possible [13], vibrational cooling is much less efficient. For a given nozzle temperature the extent of internal energy cooling is determined by the stagnation pressure (P0), nozzle diameter (dN) and the collision number (Z) [ 14]. The rotational collision number (Z~),for example, is defined as the number of hard sphere collisions

10

C.R. Arumainayagam and R.J. Madix

which occur during the characteristic rotational relaxation time. In reality, Z, is the ratio of some cross-section which determines the collision frequency to the cross-section for collisional transfer of rotational energy to translational energy. A similar definition applies for Z~, the vibrational collision number. Since the total number of collisions possible during a supersonic expansion is limited to a few hundred for typical nozzle conditions, a high Z (>1000) implies very little internal energy cooling while a low Z (< 100) implies substantial internal energy cooling [ 15]. For example, Z, has been determined to be 15 for a 300 K nozzle methane beam, indicating significant rotational cooling [14]. Vibrational relaxation, however, is negligible since Z~ for methane is about 1.5 x 104 [16]. Since most molecules have similarly high Z~, it is often assumed that the incident molecules in a supersonic molecular beam have a Maxwell-Boltzmann vibrational distribution defined by the nozzle temperature. Vibrational cooling in nozzles has been considered in detail previously [17]. 2.1.2.4 P u l s e d n o z z l e b e a m s Supersonic molecular beams can also be formed via a pulsed nozzle where gas pulses are produced by placing an electromagnetically operated valve in the nozzle [18]. This source gives pulse lengths as short as 10 microseconds and repetition rates as high as 200 Hz. The short intense pulses can provide a very high beam flux while maintaining a low gas load in the source chamber. In addition to lowering the pumping speed requirements for the source chamber, pulsed molecular beams allow high beam fluxes to be used with modest pumping speeds in the ultrahigh vacuum (UHV) scattering chamber. However, the pulsed nozzle beam source may not be the ideal choice for certain types of applications. For example, the inability to heat the pulsed nozzle precludes its use at high incident translational energies that may be necessary to study collisionally activated reactions on solid surfaces (see below). 2,2 E x p e r i m e n t a l s e t u p A typical molecular beam scattering experiment is illustrated schematically in Fig. 1. The apparatus consists of a beam source, several stages of differential pumping, and a UHV chamber containing the single crystal sample and the necessary surface analytical instruments. A detailed technical description of such an apparatus has been published recently [4]. Below we provide only a brief description of the salient features of a generic supersonic molecular beam scattering apparatus used to study gas-surface dynamics. 2.2.1 S o u r c e c h a m b e r The molecular beam issues from a source at pressures as high as 1-10 atm through a precision drilled nozzle (diameter 5-80 ~t) into the source chamber. A conical skimmer of optimum shape and diameter is placed at a strategic point along the beam line, between 100 and 500 nozzle diameters, to prevent the shockwave produced during the expansion from collapsing on itself and degrading the monoenergeticity of the supersonic molecular beam [19]. Although nozzles are usually constructed out of metal (stainless steel, tungsten, nickel, inconel), material such as alumina and quartz have been used to produce corrosive beams, such as atomic oxygen. Provision can be made to both heat (resistive) and

11

Molecular Beam Studies

source chamber chopper cmainh a m b e ~ chamber

s~immer ___,, ,~ ~__~

chopper

p°""'l _-

."'-:"-~--3"'., "~foce

l

~"-

Figure 1. Schematic view of a supersonic mol¢cular beam apparatus used to study gassurface dynamics. Rvproduced from B. Poelsema, Guntcr Mechtersheimer and G. Comsa, Surface Sci. 111, 519 (1981).

12

C.R. Arumainayagam and R.J. Madix

liquid nitrogen or liquid helium cool the nozzle. High pumping speeds in the source chamber may be required to maintain background gas pressures low enough to avoid scattering of molecules out of the molecular beam [4]. 2.2.2 M o d u l a t i o n c h a m b e r a n d b u f f e r c h a m b e r s The second chamber usually contains a variable frequency chopper (a rotating slotted disk) moving perpendicularly across the molecular beam path. Mechanical chopping of a continuous beam can be controlled to yield both higher duty cycles (e.g., 50%) and shorter pulse widths (e.g., 1 Ixsec) than electromagnetically pulsed molecular beams [4]. Modulation of the molecular beam at a fixed period serves to improve the signal-to-noise ratio, provided this period is less than the time constant for pumping in the scattering chamber. In addition, by using a narrow slot in the chopper to produce a narrow beam pulse (1-10 p.sec) and "time tagging" the incident molecules, it is possible to perform time-of-flight measurements and to obtain the velocity distribution of the scattered molecules (see below). Moreover, beam modulation using a range of frequencies permits the study of surface reaction kinetics using the technique of molecular beam relaxation spectrometry (MBRS) [3]. Since the gas load in the second chamber is two to three orders of magnitude smaller than the load in the source chamber, pumping speeds need not be as high [4]. A third and possibly fourth evacuated chambers may be used to further collimate the beam and to reduce the effusive gas load on the scattering chamber. Differential pumping ensures that the flux of the incident molecular beam is several orders of magnitude higher than the effusive flux from the background gas emanating from the last stage of differential pumping. Since the flux of the molecular beam decreases as the inverse of the square of the distance from the nozzle, great effort has been taken to minimize the nozzle-surface distance [20]. Collimating slits are placed along the beam line to define the size of the molecular beam at the sample inside the UHV chamber and to also reduce the effusive flux entering the UHV chamber. The nozzle, skimmer and collimating slits need to be carefully aligned to obtain the highest possible molecular beam flux at the crystal surface. 2.2.3 U l t r a h i g h v a c u u m s c a t t e r i n g c h a m b e r After passing through the stages of differential pumping, the molecular beam enters the scattering chamber and impinges on the crystal surface. The single crystal is mounted on a high precision manipulator with three mutually perpendicular translational degrees of freedom, which affords accurate and reproducible positioning of the crystal. For molecular beam experiments extreme care is typically taken in aligning the crystal when mounting. Ideally, the crystal is mounted such that its front face is always vertical and its rotation axis is located in the front face of the crystal midway between the sides of the crystal. Further, the crystal is positioned so that the centerline axis of the beam is incident on the center of the crystal. Under these conditions, the polar angle of incidence of the beam can be changed by simply rotating the crystal. Tilt, which is rotation about an axis perpendicular to the one described above (also lying in the crystal plane), permits measurements of out-of-plane scattering distributions (see below). More complex manipulators also permit variation of the incident azimuthal angle by rotation

Molecular Beam Studies

13

around an axis perpendicular to the crystal surface. A three-axis manipulator [21] affords control of the incident polar and azimuthal angle in addition to the till The intersection of the three mutually perpendicular axes must always be at the center of the molecular beam. A thermocouple spotwelded to the crystal is typically used to monitor the surface temperature. Radiative heating by a tungsten filament behind the sample coupled with electron bombardment or resistive heating can be utilized to heat the sample. Liquid nitrogen cooling permits the crystal to be cooled to as low as 80 K. Rapid cooling may be necessary to minimize background contamination prior to an experiment. Liquid He cooling may be used to achieve lower surface temperatures [22]. In order to study the interactions of gas molecules with a solid surface at a fundamental level, it is imperative that the surface be well characterized and remain free of contamination during an experiment. These objectives are realized by the use of standard UHV techniques. Base pressures (beam off) as low as lff n tort are achieved in the scattering chamber by using either turbo-molecular pumps or liquid nitrogen trapped diffusion pumps in combination with ion pumps and/or titanium sublimation pumps. The pressure in the scattering chamber may rise to 10.9 torr when a He seeded beam is introduced into the UHV chamber. Such a high pressure is generally not a problem for surface temperatures of 80 K or above since the background consists almost exclusively of inert He which adsorbs on surfaces only at

temperatures far below liquid nitrogen temperatures. In addition to realizing pumping speeds of 2000

liter/sec or higher in the scattering chamber, a constant pumping speed is most desirable throughout a particular experiment in order to avoid baseline drifts in signals. Argon ion sputtering followed by annealing and chemical titration methods are used to clean the surface of contaminants, such as unwanted carbon and sulfur, prior to an experiment. The cleanliness of the surface can be monitored by standard UHV methods, such as Auger electron spectroscopy (AES), and the surface order is determined by low energy electron diffraction (LEED) or by the elastic scattering of a helium beam (see below). Below we discuss some of the special experimental requirements for the three major types of molecular beam studies of gas-surface interactions: (1) scattering and desorption dynamics, (2) adsorption dynamics, and (3) thermal energy atom scattering (TEAS).

2.2.3.1 Dynamics of scattering and desorption Dynamical studies of scattering and desorption often involve the detection of molecules after they have left the surface. In contrast to ion beams, neutral beams are difficult to detect. Quadrupole mass spectrometers with electron bombardment ionizers are the most commonly used detectors. Because of their fast response time, flow-through mass spectrometers [23] are preferred over stagnation-type mass spectrometers [24]. Bolometers, too, have been used as detectors for molecular beam scattering experiments [[25], [26]]. This technique involves the measurement of the change in resistance of a semiconductor crystal held at liquid He temperatures when a beam of molecules impinges on it. Although rather slow compared to mass spectrometers, bolometers afford the possibility of measuring the internal energy of the incident and scattered molecules. One limitation of the technique is its inability to distinguish between molecules.

14

C.R. Arumainayagamand R.J. Madix In particular experiments the flux of the mattered molecules at the detector may be extremely

low; the partial pressure of the scattered species may be less than that of the same molecules present as

residual gas in the chamber. Hence, to obtain a good signal-to-noise ratio it may be necessary to reduce the background partial pressure of the molecule being studied to about 1014 torr by employing as many as three differential pumping stages at the detector, in addition to the three or four differential pumping stages along the beam line [ 1]. Cryogenic pumping may also be used to reduce the background pressure. In addition, the flux of the scattered molecules at the detector may be increased by decreasing the nozzle-to-surface distance and/or surface-to-detector distance if these adjustments are compatible with the objectives of the experiment. Rotation of the quadrupole detector about the target surface at a fixed distance permits the measurement of angular distribution of the scattered molecules (intensity vs. scattering angle) in the scattering plane. A three-axis manipulator or a detector mounted on a goniometer which permits detection outside the scattering plane is required to obtain out-of-plane scattering distributions [1]. Velocity distributions of scattered molecules may also be measured by time-of-flight using a pulsed nozzle or a very narrow chopper to mechanically modulate the incident beam if the residence time of molecules on the surface is negligible. In the case of a non-negligible residence time on the surface it may be necessary to chop the beam subsequent to scattering to obtain velocity distributions [1]. On the other hand, it is relatively easy to obtain mean surface residence times provided they are much larger than the time-of-flight (approximately 100 microseconds) by beam modulation [[1], [3]]. Recently, surface residence times as short as 100 ~ts were obtained from the time-of-arrival distributions for Xe atoms leaving a Pt(111) surface [27]. The signal due to the scattered species is usually analyzed either by the time-of-flight (TOF) technique (time domain) [28] or by a phase-sensitive lock-in amplifier (frequency domain) [29]. In the former method a narrow incident pulse is scattered from the surface and is detected by a mass spectrometer connected to a multichannel analyzer. The signalintensity as a function of the arrival time at the detector is measured over a suitable number of cycles to obtain the intensity versus time-of-flight (TOF) curve. In the latter method, a lock-in detector measures, at the modulation frequency, the amplitude and phase of the fast Fourier component of the scattered signal in response to a square wave input (beam). A digital TOF waveform can be recorded to obtain more information which can be analyzed in either the frequency or time domains. State-specific techniques such as laser induced fluorescence (LIF) [30] and multiphoton ionization (MPI) [31] can be used to determine the rotational, vibrational, and electronic distributions of incident and scattered (or desorbed) species. In addition,.fourier transform infrared spectroscopy (FI'IR) has been used to detect the infrared emission from vibrationally excited species produced in molecule- surface interactions [[32], [33], [34], [35]]. In LIF, the most commonly used method, a laser is used to excite the scattered molecule to a higher electronic state and the ensuing fluorescence is monitored to obtain the internal state distribution. Despite its high sensitivity, this technique has been utilized for only a

Molecular Beam Studies

15

few small molecules such as NO which have a high fluorescence quantum yield. In addition, the molecule must be spectroscopically well characterized with its spectral lines identified and the associated intensities as signed. The low-lying electronically excited staes of NO facilitate its detection. While molecules such as H2, N2, and CO require vacuum uRmviolet light for singie-photon electronic excitations, a single photon in the 225 nm region is sufficient to access the A 2'L'~excited state of NO. Although molecules other than NO may be detected by muldphoton spectroscopy, sensitivities may be smaller [36]. Internal energy distributions in H2 desorbing from copper surfaces have been reported, for example [37].

2.2.3.2 Dynamics of adsorption Measurement of the adsorption probability as a function of incident velocity, incident angle, incident internal energy, incident orientation, surface temperature, and coverage yields information crucial to understanding the dynamics of adsorption. The adsorption probability is defined as the fraction of the incident molecules which adsorb. In uptake methods with molecular beams, the surface coverage (0) is determined as a function of exposure (~), and the resultant curve is differentiated to obtain the adsorption probability as a function of coverage:

s(0) = dO ~

(6)

The coverage of the adsorbed molecules can be determined by one or more surface sensitive methods such as Auger (ALES),X-ray photoelectron spectroscopy (XP$), work function, iemperature programmed desorption (TPD), with the aid of one or more calibration points. The exposure is determined by the product of the beam flux (molecules/cm2/sec) and the time of exposure. The latter quantity can be controlled by a shutter or a movable flag along the beam line. For high incident fluxes (> 1 monolayer/sec) it may necessary to use a low duty cycle chopper (e.g., 1%) to facilitate accurate control of the exposure time. The flux of incident molecules is obtained by measuring the pressure rise in the UHV scattering chamber when the molecular beam is introduced into the chamber, the pumping speed of the beam gas in the UHV chamber, and the cross-sectional area of the molecular beam. The uptake method, referred to above, can be used to measure adsorption probabilities as small as 10~. The measured absolute values are accurate to a factor of about two due to the errors involved in the many measurements. For adsorption probabilities greater than 102, a direct (beam reflection) method yields more accurate values [[38], [39]]. Measurement of the partial pressure of the beam gas in the UHV scattering chamber when the beam is incident on (1) an inert surface and (2) the crystal yields the adsorption probability directly. The direct measurement has several advantages over other methods. The first is speed and ease of measurement, and the second is that the adsorption probability is determined independent of any measurements such as flux, pumping speeds, mass spectrometer sensitivities, or AE$ calibrations necessary for uptake experiments. Moreover, if the m/q ratio used to measure the partial pressure mass spectrometdcally during the uptake is solely due to the molecule under study, the presence of contaminants in the beam will not invalidate the measurement of the initial adsorption probabilities, provided the contaminant does not build up to more than about 1% of a monolayer during the fwst few

16

C.R. Arumainayagam and R.J. Madix

seconds following exposure. If the contaminant gas does not register a discernible partial pressure rise in the UHV chamber because it is pumped too effectively, the direct technique can still be used to measure initial adsorption probabilities even if the contaminant gas has a cracking fragment at the m/q ratio used to monitor the species of interest. The disadvantage of the technique is that adsorption probabilities less than one or two percent cannot be measured. In addition, if the gas of interest is pumped too efficiendy by the walls of the system, the partial pressure rise that results when the beam is admitted into the chamber is immeasurably small, precluding the use of the direct technique to accurately measure adsorption probabilities. By cooling the crystal sufficiently, the direct technique can be extended to measure trapping probabilities of weakly interacting non-dissociative gas-surface systems using supersonic molecular beam techniques. Previously, trapping probabilities were extracted from angular or velocity distributions of scattered molecules from the surface. This method involves deconvoluting the scattering distribution into two channels: (1) a lobular scattering channel peaked near the specular direction due to direct inelastic scattering, and (2) a cosine or a near-cosine distribution due to trapping-desorption. The trapping probability is approximated by the fraction of the scattered molecules directed into the cosine scattering channel.

Calculation of absolute trapping probabilities using this method requires knowledge or

assumption of (1) the in-plane and out-of-plane angular distribution of the trapped-desorbed component (which may not be cosine), (2) the in-plane and out-of-plane angular distributions of the direct inelastic component, (3) the velocity distribution of the trapped desorbed channel (which may not correspond to the average "equilibrium" value of 2kT,) as a function of polar angle, and (4) the velocity distribution of the direct inelastic component as a function of polar and azimuthal angles. Each of these quantities may depend on incident translational energy, incident angle, and surface temperature. Besides being less tedious, the direct technique yields more accurate values. In addition, the direct technique can also be used to obtain the following information in the same experiment: (1) trapping probability as a function of adsorbate coverage, (2) initial trapping probability onto the saturated monolayer, and (3) desorption kinetics. Chemical identification of the species produced as a result of adsorption is also important in studying the dynamics of adsorption in the case of dissociative chemisorption. A high resolution electron energy loss spectrometer (HREELS) [40] has been used to characterize the adsorbed product of methane dissociation on a Ni surface [41 ]. The application of species specific techniques to ascertain the identity of products in reactive gas-surface collisions is extremely important and has been slow to develop.

2.2.3.3 Thermal energy atom scattering (TEAS) In recent years the molecular beam technique of thermal energy atom scattering (TEAS) has become a powerful and versatile surface analysis tool. TEAS involves the elastic and inelastic scattering of low energy (0.2 to 17 kJ/mole) He atoms from well-characterized single crystal surfaces. It promises to be an excellent surface analysis tool for the following reasons: 1) since low energy atoms do not penetrate into the solid, it affords extremely high surface selectivity; 2) the closed shell electronic

Molecular Beam Studies

17

structure of He atoms prevents chemical interaction with the surface; 3) no surface damage occurs even for weakly bound adsorbates; 4) as a consequence of the high surface selectivity there is a very high sensitivity to surface adsorbates at very low coverages; 5) unlike some other techniques such as Auger electron spectroscopy, it can detect adsorbed hydrogen atoms; 6) no electrical charging of insulator surfaces occurs, because the incident particles are electrically neutral [[42], [43]]. In TEAS a chopped supersonic beam of He atoms with an extremely narrow velocity distribution (Av/v < 1%), collimated to approximately 0.2" (an extremely narrow beam) is directed towards a crystal mounted on a three-axis manipulator which allows control of the incident polar and azimuthal angles [[42], [43]]. The reflected beam is detected by a quadrupole mass spectrometer which can be moved in the radial direction in order to change the sample-detector distance, and in the direction perpendicular to the scattering plane to detect out-of-plane scattering. The mass spectrometer is typically operated at an extraordinarily high angular resolution of 0.15". Information is usually recorded in the pulse counting mode, and the signal intensity as a function of time is measured over a number of cycles to give an intensity versus time-of-flight curve. The technical requirements for TEAS experiments generally exceed those of typical molecular beam scattering experiments [[42], [43]]. For example, the angular resolution of the detectors of the sample must be at least an order of magnitude better for TEAS experiments than for standard molecular beam scattering experiments in order to resolve diffracted beams. Further, since high beam monoenergeticity is required for time resolution, high nozzle stagnation pressures (e.g., 160 atmospheres) and low nozzle temperatures (e.g., 78 K) are needed to produce molecular beams with a very narrow velocity distribution (e.g. Av/v = 0.7%) [43]. In order to obtain the high signal-to-noise ratio necessary to distinguish the low coherent signals from the background, additional differential pumping is utilized in the detector chamber to obtain He partial pressures in the detector chamber as low as 10t6 torr. Studying the effects of adsorbates with TEAS requires that surface structural effects be minimized. An extremely high quality close-packed metal surface (Pt(111)) with a defect density which is an order of magnitude smaller than that found on a single crystal typically used for surface science studies has been used. Due to the above mentioned additional requirements, to date TEAS studies of adsorption have been confined to only a few systems, such as CO (because of its unusually large scattering cross-section), Xe, and Hz (see below), but its use is growing.

3 Non-Reactive Scattering from Surfaces Gas surface interactions can be broadly classified as either nonreactive or reactive, depending on whether the scattered (or adsorbed) species is chemically distinct front the incident molecule. In this section we will consider nonreactive scattering from surfaces, while in the next section we will address reactive scattering.

C.R. Arumainayagam and R.J. Madix

18

Based on a large body of experimental data, four different regimes have been identified for non-reactive gas-surface interactions [44]. (I) Elastic scatteringoccurs when translationaland internal energy of the molecule is unchanged. However, elasticallyscattered molecules may have conserved theirsurface parallelm o m e n t u m only to within a surface reciprocal latticevector. 2) Inelasticscattering occurs whcn the translational and/or internal energy of the molecule has changed, but the scattered molecules stillretain some information regarding their incident trajectories. 3) Tmpping-desorption occurs whcn molecules adsorb and equilibrate with the surface before desorbing, having lost all information about theirincident trajectories.This definitionof trapping has recently been extended to include molecules which equilibrate the normal component of their translationalenergy but fail to equilibrate the parallel component before escaping the surface (scc below). 4) Molecular cbemisorption occurs when the molecules bind to the surface more strongly, and often remain adsorbed on the surface evcn at room temperature. Since at equilibrium the flux of ambient gas incident on a surface varies as the cosine of the angle from the normal to the surfacc (0), the totalflux leaving the surface at equilibrium must also yield a cos 0 angular distribution. T h e m are no constraints on the angular distribution of any single scattering proccss ifthis condition is satisfiedfor the totalflux. In addition, at equilibrium the sum over all specics leaving the surface, which, of course, includes all types of scatteringprocesses, must yield distributions of molecular quantum states (translational,electronic, vibrational and rotational) which are Maxwcll-

Boltzmann at the surface temperature. Detailed information regarding a particular scattering process can be obtained by measuring the associated internal state distributions [45].

3.1 Elastic scattering During an elastic scattering event, the incident molecules reflect from the surface with an extremely narrow angular distribution peaked at the specular angle (incident angle = reflected angle), with no energy transfer taking place during the process. This mechanism is normally thought to be confined to only light atoms such as He and molecules such as H2. Recent studies of rare gases adsorbing on a Ru(001) surface, however, suggest that substantial zero-phonon elastic scattering occurs even for rare gases as heavy as Ar [46]. Elastic diffractive scattering of light atoms (He) and molecules (H2) from well-ordered surfaces contributes to the understanding of several areas of interest. First, the intensity patterns of the diffracted beam can in principle be related to the geometric structure of the outermost layer of the surface. Second, surface scattering resonances (often called selective diffractive adsorption) identified in the scattering patterns provide information on the attractive part of the gas-surface potential. The significant progress made in both areas using 4He, 3He, H2, D2, H, D, and Ne as probes, and alkali halides, graphite, metals, semiconductors, and adsorbate covered metals as targets has been extensively discussed previously [47].

MolecularBeamStudies

19

As described below, thermal energy atom scattering (TEAS) experiments involving the elastic scattering of He have been used to study the crystallographic and electronic structures of clean and adsorbate covered surfaces, defect densities on single crystal surfaces, reconstruction of adiayer surfaces, phase transitions of adlayers, and the kinetics of adsorption, diffusion, island formation, and desorption at very low adsorbate coverages. 3.1.1 S t r u c t u r a l s t u d i e s o f s u r f a c e s b y b e a m d i f f r a c t i o n LEED has proved invaluable in deducing the atomic arrangernem of numerous clean and adsorbate covered surfaces. Because the electrons scatter from ion cores and not from the valence-electron distribution, it is not possible to determine the election distribution at surfaces [48]. In contrast to electrons, He scatters from the repulsive part of the potential due to the short range repulsive forces arising from interaction with electron distributions at the surface, whose periodic modulations reflect the valenceelectron distribution of the surface; the short range forces reflect the He 2-3 ,~ from the surface ion cores. Hence, atomic beam diffraction of thermal energy atoms offers the possibility of not only determining the atomic positions but also the periodic electronic structure of the surface. Moreover, in contrast to LEED, multiple scattering effects are negligible in atomic diffraction [49]. Nevertheless, information about nuclear positions from atomic beam diffraction studies is indirect. In addition, diffractive atom scattering, because of its high surface selectivity, does not provide information concerning interlayer spacings [50]. Hence, atomic beam diffraction and LEED should provide complementary information about the crystallographic and electronic structure of surfaces. A beam of monoenergetic parallel helium atoms at thermal energies of 2-20 kJ/mole is equivalent to a plane wave whose de Broglie wavelength ranges between 0. I and 1.0 ,~, which is ideally suited for surface structure analysis. Momentum conservation requires that:

K~= K,.+G

(7)

where K tand IQ are the finaland initialwavevectors parallelto the surface and G is the reciprocal lattice vector. Energy conservation requires that (K/+ k/.) 2 = (K i. + k,.) 2

(8)

where kf.and k~.are the finaland initialwavevectors in the directionnormal to the surface. Determining the angular position of a sufficientnumber of diffractionpeaks enables the size and shape of the surface unit cell to be deduced. This analysis requires no "dynamical theory" and is based only on kinematical equations [[47], [48]]. To extract information about structurewithin the unit cell from the intensitiesof the diffractive peaks, however, one must employ a dynamical theory of scattering which rexluims solving the Scb.fl~nger equation with boundary conditions [51]. In such a treatment, a potential function V(R,z) (R parallelcoordinate, z normal coordinate) for the gas-surface interactionis constructed assuming a surface atomic structure,and the Schfl~nger equation for the scatteringproblem is solved to obtain the scattering intensities. The attractivepart of the potential (due to van der Waals dispersion forces) has

20

C.R. Arumainayagamand R.J. Madix

been shown to have a z 3 dependence for distances far from the surface, and to a fhst approximation is assumed to be independent of R. The repulsive part of the potential (due to short-range Pauli repulsion between the orbitals of the metal and the atom) has been shown to be proportional to the local electron density p(z,R) and, hence, contains the periodicity. If p is calculated from a simple superposition of atomic charge densities [52], the diffraction pattern may be predicted without any adjustable parameters for a given arrangement of surface atoms. In the more general case, the repulsive part of the potential is adjusted by trial and error to match the experimentally observed intensities. Hence it is possible to obtain the corrugation of the gas-surface potential, which can then be related to the surface valenceelectron distribution. The application of atom beam diffraction to the determination of surface structures has been previously reviewed [[47], [51]]. Atom beam diffraction has been useful in studying ionic crystals such as LiF(100) [[53], [54], [55]], semiconductor surfaces such as Si(111) and Si(100) [[56], [57]], graphite [58], metal surfaces such A g ( l l l ) [59] and Cu(ll0) [60], adsorbate covered surfaces such as H2 on Ni(110) [[61], [62]], the thermal roughening of stepped copper surfaces [63], and reconstructed metal surfaces such as W(100) [51].

3.1.2 Diffractive selective adsorption Minima, or sometimes maxima, may be observed in the intensity of the specular and diffracted beams as a function of incident beam parameters such as incident polar and azimuthal angles [[64], [65]]. Typically the angle of incidence is varied at a fixed incident energy. This resonance phenomenon, known either as diffractive selective adsorption or bound state resonance, occurs when the total energy of the incident particle equals the energy of a bound state for the motion normal to the surface plus the kinetic energy of unbound motion parallel to the surface, according to: E, = E i - 2~- (I~ + G) 2

(9)

where m is the mass of the incident atom, E, is a bound state level of the laterally averaged potential, Ei is the total energy of the incident particle, and Ki is the initial wavevector parallel to the surface [66]. By measuring these minima or maxima, one may obtain the energies of the bound vibrational states and hence the laterally averaged attractive part of the gas-surface interaction potential, V00(z) [67]. Most diffractive selective adsorption resonance studies have focussed on highly corrugated, nonmetal surfaces. For example, the binding energies in the gas-surface potential well, V00(z), have been determined for H and D atoms on LiF(001) [68], 3He and 4He on LiF(001) [69], and 3He and 4He on graphite [[70], [71]]. In selective adsorption the incident atom converts part of its incident normal translational energy into translational energy of motion parallel to the surface. If sufficient normal translational energy is lost in the process, the incident atom is temporarily "trapped" on the surface. The average lifetime of He-surface selective adsorption resonance states is 1-5 x 10~2 sec, and the average distance the He atom travels along the surface before ejection is 10 -30/~ [72].

Molecular Beam Studies

21

3.1.3 Quantifying defect densities with TEAS Since defects sometimes play a pivotal role in the chemistry of surfaces, the study of randomly stepped surfaces has come under increasing scrutiny [73]. Steps, a primary example of defects, have been studied by LEED [74], electron microscopy [75], low energy ion scattering [76] and Xe adsorption [77]. Recently TEAS has been successfully employed to characterize the defect density of such surfaces [[78], [79], [80], [81]]. On surfaces with a random step distribution, the measured intensity of the specularly scattered beam shows periodic oscillations as a function of incident angle (Fig. 2) due to He scattered from terraces separated by monoatomic steps. The path difference (81) for diffraction from two adjacent terraces separated by an interlayer spacing h is given by 8/= n~. =

2h

cos0 i

(10)

where 3. is the de Broglie wavelength of the incident He atom and 01 is the incident angle [78]. An integer value for n corresponds to constructive interference and a half-integer value for n implies destructive interference. The positions of the maxima and minima are in good agreement with the interlayer spacing of the (111) surface used in this study. The amplitude of the peak osciliations is related to the surface step density [82]. A Pt(111) crystal polished and oriented with extreme care was shown to be free of such oscillations. Further analysis implied an average terrace width of 3000 ~ for this crystal, corresponding to a misalignment of the crystal surface of less than 0.05". Standard single crystal surfaces used in surface science studies typically show a misalignment of 0.5". Surfaces prepared by the usual methods thus would produce pronounced oscillations, as shown in Fig. 2. These studies illustrate a sensitive method for determining the surface defect density, a factor of substantial importance in molecular beam studies of surface reactions (section 4, below). Due to its sensitivity to defects, TEAS has been applied to the study of surface roughening by both ion bombardment and heating. A two layer model has been proposed for argon ion sputtering of Pt(111) [81]. He scattering studies of the thermal behavior of clean Cu(110) have shown no evidence for thermal roughening (the proliferation of atomic steps) up to a surface temperature of 900 K [83]. 3.1.4 A p p l i c a t i o n o f T E A S to monitor s u r f a c e c o v e r a g e The large total cross-section for scattering (>250 ]~2 ) of an adsorbed CO molecule for an incident thermal He atom makes TEAS sensitive to adsorbed CO even at coverages as low as 0.001 monolayers. The adsorbate-induced attenuation of the specular He beam intensity (13 c ~ therefore be exploited to monitor a variety of processes related to surface coverage [[84], [85]]. In the case of random adsorption the relative magnitude of the specular beam intensity UIo ,where I0 is the specular He beam intensity for the clean surface, depends exponentially on the coverage 0 up to at least 0 = 0.17 (Fig. 3): /L= exp(-Zn, O)

(11)

22

C.R. Arumainayagam and R.J. Madix .5

(a) Eo=16 meV

~N ~0"

it..

O

.75-

~.3" ¢-,

c ,~0-

P.1

== 25-

1

c

0-

0~., /.O*

t

.5

68* - ' ~i

7,0* 7i*" 7~* 'oi "

- 77° 'of~

(c)

~ .75-10"

E°=63meV .3-

2o

,1 04,

,a, .25-

1

~ ,

,

,

z.Oo 5'0° 6(2* 70° •Of

~ .5"

"~ .4'

Eo=63 meV

. ; 2,1 "6 r~ e

,/

/

./

i

0

80* 90 °

'of~

/ (el ,,~'~,=

5,0*

6,0*

(f)

a0" N (3

E .75c >. 50w ._c

t.'0*

85"- 'oi

83°

(='oi)

7'0°

8,0°

90*

,

q

25,'.s_ 79.5°

0 -~"

80 °

80.5* -,~f~

Figure 2. A thermal energy atom scattering (TEAS) study of step densities on a Pt(111) surface. Figures (a), (c), and (e) correspond to the specular intensity of the scattered beam as a function of incident angle (= reflection angle). Figures (b), (d), and (f) on the right correspond to the actual angular distributions of the scattered (crosses) and the incident (open circles) He beam. The bottom row corresponds to data obtained after the P t ( l l l ) crystal was precisely oriented and polished. Note the absence of interference effects. Reproduced from B. Poelserna, R.L. Palmer, G. Mechtersheimer, and G. Comsa, Surface Sci. 117, 60 (1982).

Molecular Beam Studies

1

~ ,

23

He

!

I/Io

EHe:63 meV 0.1

0.01

1 0

I

1.0

I

I

2.0

3.0

/,.0

exposure {101~molecules/cm2) Figure 3. Figure displays a thermal energy atom scattering (TEAS) study of CO adsorption on Pt(111). The relative height of the specular He beam scattered from the Pt(111) surface decreases exponentially with increasing CO exposure at constant surface temperature and a fixed partial pressure of CO. Reproduced from B. Poelsema, R.L. Palmer, and G. Comsa, Surface Sci. 136, 1 (1984).

24

C.R. Arumainayagam and R.J. Madix

where Z is the total collision cross-section of CO for noncoherent scattering and n, the number of Pt atoms per square centimeter. The coverage 0 is determined completely by the sticking probability S(0) and the exposure. If an appropriate 0 dependence is assumed for S

(e.g., S=S0(1-0) 2 in the case of a

diatomic molecule adsorbing dissociatively), experimental values can be fit to the above expression to obtain absolute values for So in addition to deducing the total cross-section [[86], [87], [88], [89]]. By monitoring the relative peak height, I/I0, as a function of CO partial pressure at fixed temperatures, the activation energy for CO desorption from Pt(111) was found to decrease linearly with increasing coverage, at least up to a coverage of 0.13 monolayers [90]. TEAS measurements in conjunction with LEED observations have revealed that CO forms islands on a Pt(111) surface saturated with hydrogen, a system which exhibits only repulsive adsorbate-adsorbate interactions [91 ]. The technique is especially useful in detecting changes in the initial sticking probability too small to be perceived by conventional techniques [85]. For example, the initial sticking probability of H 2on a nearly defect free Pt(111) surface was found to increase from 0.045 at a surface temperature of 90 K to 0.06 at a surface temperature of 240 K. This result has been taken as evidence for the migration of dihydrogen to defects at which dissociation occurs even at defect concentrations less than 10.3 [85]. TEAS has also been used to determine the origin of the low-temperature (= 150 K) hydrogen desorption from Pt(111) resulting from incorporation of hydrogen in ice layers [92]. He beam diffraction from a hydrogen covered Pt(997) surface has been used to show that adsorbed hydrogen does not change the perpendicular component of Pt surface vibrations [93]. In addition, TEAS has been used to monitor ethylene adsorption on Pt(111) [94] and also to selectively study the adsorption/desorption kinetics of H2 from the terraces of a Pt(997) stepped surface [95]. All of the experiments described thus far were conducted by monitoring the elastic coherent (00) peak intensity as a function of coverage. Measuring the elastic incoherent component in addition to the (00) peak may provide additional information regarding two-dimensional phase changes, for example [[96], [97]].

3.1.5 TEAS investigation of adsorbate migration Laser induced thermal desorption (LITD) and field ion microscopy (FIM) are two techniques currently used to study the migration of adsorbed gases on single-crystal surfaces. However, techniques such as LITD are applied at adsorbate coverages too large for adsorbate-adsorbate interactions to be considered negligible. TEAS has been recently employed to study the migration of adsorbed gases at very low coverages (= 1.5%) and also to observe island formation [98]. The method depends on the ability of TEAS to distinguish between molecules adsorbed on defect sites and defect-free regions on a single crystal surface. This is possible because He scattering into the specular beam occurs almost exclusively from the defect free low index areas, and the contribution from defect sites is negligible. Hence, if molecules migrate from the low index planes to the defect sites, the intensity of the He specular beam increases. Using this method to monitor surface coverage on the defect free areas as a function of surface temperature, it is then possible to estimate both the activation energy and the pre-exponential factor for adsorbate migration. So far only one system, CO/Pt(111), has been

Molecular Beam Studies

25

studied using this technique [98]. CO coverages of 1.5% were used to minimize CO-CO interactions. The activation energy for CO migration on It(111) was found to be 29 kJ/mole, which is approximately 20% of the value for the activation energy for desorption (==133 kJ/mole), consistent with expectations [99].

3.1.6 TEAS investigation of 2-D phase transitions Weakly adsorbed monolayers of rare gases on the basal planes of graphite have come under intense scrutiny because they represent model quasi-two-dimensional systems [100]. However, techniques normally applied to the study of phase transition on graphite, such as neutron diffraction, high-energy electron diffraction, and sychrotron x-ray diffraction are not suitable for metal substrate atoms such as Pt. In addition, the necessity to invoke multiple scattering and the large cross-section for electronsimulated desorption make LEED an inappropriate technique to study most rare-gas/metal systems. The diffraction of monochromatic, highly collimated, thermal-energy He atom beams is a technique which overcomes the above mentioned drawbacks of other techniques for the study of ordered overlayers of rare gases on metal surfaces. By measuring the specular and diffracted He beam intensities as a function of Xe coverage at a constant surface temperature, six different structural phases have been observed for the Xe on It(111), including commensurate (C), striped incommensurate (SI), hexagonal incommensurate (HI), and hexagonal incommensurate rotated (HIR) structures [[101], [102], [103], [104], [105], [ 106], [ 107]]. These studies have demonstrated that Xe monolayers adsorbed on Pt(111) exhibit all of the theoretically predicted [[108], [109]] characteristics of the commensurate-incommensurate phase transitions in two-dimensions. Moreover, thephase which exists at saturation coverage (0.41 monolayers at a surface temperature of 25 K) shows a + 3.3" rotation angle with respect to the C and I phases in agreement with predictions (the Novaco-McTague rotational epitaxy) [ 110].

3.2 Inelastic scattering Direct inelastic scattering refers to a single collision between the molecule and the surface involving energy transfer. Indirect inelastic scattering involves multiple collisions with the surface before the molecule escapes. Depending on the number of phonons excited or de.excited in the scattering event, inelastic scattering may be classified as (1) zero-phonon inelastic scattering, (2) one-phonon inelastic scattering or (3) multi-phonon inelastic scattering.

3.2.1 Zero-phonon inelastic scattering Even though experimental evidence for zero-phonon scattering is generally lacking for rotational transitions (rotationaUy inelastic diffraction) and rotationally mediated selective adsorption (RMSA), models which use a static surface have been reported to successfuUy account for the experimental findings for both processes.

26

C.R. Arumainayagam and R.J. Madix

3.2.1.1 Rotational transitions Transfer of translational energy to rotational energy in the scattering of low molecular weight diatomic molecules results in new peaks in the angular distribution of the scattered molecules. The position of the extra peaks which appear in rotationally inelastic scattering may be determined by invoking energy and momentum conservation, neglecting phonon interactions: k ~ - k~ = ~-~AE,

(12)

I~-KI= G

(13)

where A~ is the change in rotational energy, K~ and Kr are the parallel components of the initial and final wavevectors, ki and kf, and G is the reciprocal lattice vector. CollisionaUy induced rotational transitions have been observed in molecular beam studies of H 2, D2, and HD scattering from MgO(001) [111], and 1-12and D2 scattering from LiF(001) [112].

3.2.1.2 Rotationally mediated selective adsorption (RMSA) Rotationally mediated selective adsorption (RMSA) involves the conversion of translational to rotational energy leading to a bound state resonance. Minima and occasionally maxima are seen in the intensity ofrotationally inelastic transitions as a function of incident angle at a fixed incident translational energy. The condition for RMSA (neglecting phonons) is given by the following expression:

~2 E. = E, -~'mm (K~ + G) 2 - AE,.

(14)

where E. is the bound state energy, E i is the incident energy, K i is the incident wave-vector parallel to the surface, G is a reciprocal lattice vector, and AF~ is the change in energy associated with the rotational transition. This equation assumes conservation of parallel momentum of the scattered species to within a reciprocal lattice vector. Rotationally mediated selective adsorption has been reported for HD scattering from Pt(111) [ 113], HD scattering from Ag(111) [ 114], and n-H2, p-H2, n-D2, and o-D2 from Ag(111) [ 115]. The isotropic and anisotropic component of the laterally averaged molecular hydrogen/Ag(111) potential was investigated using RMSA studies, rotationally inelastic scattering studies, and diffractive selective adsorption studies [[116], [117]]. Somewhat surprisingly, rotationally mediated trapping does not contribute to dissociative chemisorption of liD on W(110) [[118], [119]]. In this case even though RMSA was observed in both the specular and rotationally inelastic scattering channels, RMSA resonance channels lead to diffuse scattering, not enhanced dissociation. 3.2.2 S i n g l e - p h o n o n i n e l a s t i c s c a t t e r i n g Whereas heavy particle scattering results in multiphonon excitations, inelastic scattering of small atoms such as He may lead to excitation of only a single phonon. Below we consider the use of

Molecular Beam Studies

27

single-phonon inelastic scattering in studying (1) phonon spectra of solid surfaces and (2) low energy adsorbate vibrational modes inaccessible to both infrared spectroscopy OR) and electron energy loss spectroscopy (EELS).

3.2.2.1 Inelastic He scattering to detect surface phonons The inelastic scattering of small atoms such as He can be used as a probe to study surface lattice dynamics. By using very high resolution TOF techniques to determine velocity distributions of scattew.A atoms from single crystal surfaces, it is possible to identify peaks corresponding to the creation (longer flight time than for elastic scattering) or annihilation (shorter flight time than for elastic scattering) of single surface phonons (Rayleigh phonons) [120]. Conservation of energy and momentum results in the following expressions: ~2k~ ~2k2 2m

=

~' ±~c0(Q)

K/=K~+G+Q

(15) (16)

where ki, kf are the initial and final wavevectors of the scattered particle, Ki, Kf are the initial and final wavevector components parallel to the surface, G is the reciprocal wavevector, co is the frequency of the phonon created (-) or annihilated (+) in the scattering, and Q is the phonon wavevector. From the measured shift in time of flight of the scattered atoms (At), one can obtain the energy of the phonon, and hence its frequency (co) with a resolution comparable to optical spectroscopies: ¢o=_~/i/1

viAt~-2 "] +TJ -']

(17)

where m is the mass of the incident atom, vi and 0t are the incident velocity and polar angle, and 1 is the target-detector distance [1]. Using the above technique it is possible to measure the momenta of the surface vibration modes over the whole Brillouin zone. Hence, by varying the incident beam parameters it is possible to find the dispersion relationship (frequency vs. wavevector) for surface phonons. Lattice dynamical analysis of these dispersion curves reveal the nature of surface forces. Inelastic He scattering is complementary to electron energy loss spectroscopy (EELS) in the stud); of surface vibrations since it can probe vibrational energies below 10 meV which EELS cannot access due to interference from elastically scattered electrons [121]. The technique has been especially useful in obtaining the surface phonon dispersion curves of alkali halide crystals such as LiF, NaF, NaCI, KC1, RbC1, KBr, RbBr, and NaI [[122], [123], [124], [125], [126], [127], [128], [129], [130], [131], [132]]. He TOF studies of close packed fcc noble metals (Cu, Ag, Au), Pt, and Pb have revealed a second surface mode in ~ddidon to the Rayleigh surface mode [[133], [134], [135], [136], [137], [138], [139]], suggesting a softening of 50% - 75% of the surface intralayer force constant. In addition to obtaining phonon dispersion curves as described above, it may also be possible to extract scattering cross-sections, phonon density of states, and thermal populations from the TOF spectra [[1], [140]]. Phonon dispersion curves of rare-gas monolayers and multilayers adsorbed on metal substrates have also been studied by using angle and velocity resolved inelastic He scattering [[141], [142], [143], [144], [145]].

28

C.R. Arumainayagamand R.J. Madix

3.2.2.2 Inelastic He scattering to detect adsorbate vibrational m o d e s The technique discussed in the previous section has been extended to the observation of low energy vibrational modes of adsorbed species, Studying the vibrational modes of adsorbates is a major endeavor in surface science because it provides insight into the nature of the bonding, the symmetry of the adsorption site, the magnitude of adsorbate-adsorbate interactions, and the geometrical structure of the adsorbate layer [146]. Because of the limited resolution of EELS (typically 4-10 meV) and the inadequate spectral range and sensitivity of IR spectroscopy, to date these techniques have proven ineffective in measuring adsorbate vibrational modes below 10 mcV. In a recent study low energy loss and gain features (6 mcV) have been detected in the TOF distribution of He atoms scattering from CO adsorbed on Pt(111) at a resolution of 0.5 meV [146] (Fig. 4). Kinematic conditions were chosen to avoid excitation of surface phonons. Based on normal mode analysis, these loss and gain features have been attributed to hindered translation of the upright CO molecule parallel to the surface. Since thermal activation of such modes is important in conversion between different adsorption sites and in surface diffusion, their detection can enhance the understanding of these processes [146].

3.2.3 Multi-phonon inelastic scattering For molecules other than H 2, D2, and HD and for atoms other than H, D, He, and perhaps Ne, elastic scattering and single Rayleigh phonon inelastic scattering become much less probable [1]. Even for H2, rotational and vibrational excitations, dissociative chemisorption and reactions may occur on some surfaces [1]. As the mass of the scattering particle increases, multiphonon inelastic scattering, participation of bulk phonons and trapping (section 3.3) on the surface become increasingly dominant [ 1]. Because of the broad velocity and angular distributions of scattered heavy particles, high resolution techniques such as those used in He scattering arc not possible [1]. 3.2.3.1 A n g u l a r

distributions

Qualitatively, during direct inelastic scattering parallel momentum is changed very little while normal momentum is approximately reversed. Hence, direct inelastic scattering is usually characterized by an angular distribution peaked near the specular angle. Corrugation of the surface potential and energy transfer between the incident molecule and the surface broaden the distribution into a lobular pattern and also cause the peak maximum to move from the specular direction. The peak may move toward the surface normal (subspecular scattering) or move toward the surface (supraspecular scattering), according to whether energy is gained from or lost to the surface in the collision. The intensity of the scattered beam decreases if the temperature of the surface is increased at a constant incident angle and incident translational energy, or if the incidence angle approaches grazing at constant incident translational energy and surface temperature [147].

Molecular

0.2

i

i

i

29

Beam Studies

~'~

I

II

i

I

,

--

-6.0

I =50

~J

u~ c"

0.1

O (J C~ t(J3

0 I

!

- 15.0

- 10.0

I

-5.0

0.0

5.0

!

I

10.0

15.0

20.0

Energy Transfer [meV] Figure 4. A typical time-of-flight spectrum (converW~ to an energy u'ansfer scale) for He scattering from a CO-covered Pt(111) surface. The numbers above the peaks indicate values ofhv in meV (lmeV = 8.07 cm'l). Reproduced from A.M. Laheee, J.P. Toennies and Ch. Woll, Surface Sci. 177, 371 (1986).

30

C.R. Arumainayagam and R.J. Madix

The role of surface corrugation in direct inelastic scattering has been investigated for Ar and N2 scattering from a W(100) surface at incident translational energies ranging from 2.9 kJ/mole to 530 kJ/mole, and surface temperatures between 90 K and 1800 K by obtaining the angular and velocity (see next section) distributions [148]. The W(100) surface is of particular interest in studying the role of corrugation of the interaction potential in the dynamics of gas-surface interactions because the trapping step in the precursor mediated dissociation of N2 is independent of the incident angle (see below), suggesting that the gas-surface interaction potential governing the process is corrugated, in contrast to the results of He scattering from this surface which reveal a corrugation of < 0.03 ,& [149]. The full width at half maximum (FWHM) of the angular distribution may be used as a crude measure of the corrugation, a broad angular distribution implying a relatively corrugated gas-surface interaction potential. The FWHM of the angular distribution of Ar scattering from a W(100) surface was measured as a function of incident translational energy at incident angles of 45" and 60" and surface temperatures of 800 K and 1700 K (Fig. 5). The results demonstrate a transition from "thermal scattering" at low incident translational energies to "structure scattering" at high incident translational energies [[150], [151]]. Similar trends were obtained for the direct-inelastic scattering of N2 from W(100); the onset of structure scattering occurred near 100 H/mole. The deeper penetration at high incident translational energies results in higher corrugation felt by the incident molecules, leading to broad angular distribution. However, the broad angular distributions at low incident translational energies defy a simple explanation. Traditionally, angular distributions at low incident translational energies were explained by invoking one-dimensional models of scattering such as the hard-cube model, which assume that the parallel momentum is conserved. However, the observed insensitivity of the angular distribution to surface temperature and the deviation from parallel momentum conservation seen in the velocity distribution invalidate such simple arguments for the direct-inelastic scattering of Ar and N2 from W(100). Rather, the broad angular distributions at low incident translational energies were attributed to corrugation in the attractive part of the interaction potential [ 152]. The effect of this corrugation becomes less pronounced with increasing incident translational energy, leading to narrower angular distributions until structure scattering sets in at the highest incident translational energies.

3.2.3.2 Velocity distributions In addition to angular distributions, velocity distributions are also needed to characterize inelastic scattering. In the scattering of Ar from polycrystalline W, for high incident beam energies, where trapping is negligible and inelastic scattering is dominant, a linear relationship was found for the mean final translational energy () as a function of incident translational energy () and surface temperature (T,) (equation (18)) [153]. In this analysis all the translational energies involved arc scaled by 2kT:-the average translational energy of a molecule leaving the surface in equilibrium at T,.

(e:)= a,(E,)+ a~(2kL)

(18)

31

MolecularBeam Studies J

'

I

i

I

I

1

'

I

J

I

'

80 A 7O

Ar/W(100)

m

Oi

0

•-8 60 - • o 50 w, o o 40 .== "~ 5

30

• • A o

45 8 0 0 K 60 800 K 45 1700 K 60 1700 K

0

6 zx~

20

dbeoa

-

<

~

o~

o•

•

10 m

0

l

0

T

!

1

t

!

2

t

!

3

i

!

t

4

!

5

t

t

6

Kinetic Energy (eV) Figure 5. Dependence of the full width at half maximum of the angular distribution of Ar scattering from W(100) on incident translational energy at surface temperatures of 800 K (closed symbols) and 1700 K (open symbols) for incident angles of 45" (triangles) and 60" (circles). Reproduced from C.T. Rctmer and E.K. Schwcizer, Surface Sci. 203, L677 (1988).

32

C.R. Arumainayagam and R.J. Madix

In addition, the width of the velocity distribution correlates with the surface temperature:

(2kT, ) Ot2=bl---~

(19)

where a is a measure of the width of the velocity distribution as defined previously (equation (3)). The quantities a,, a2, and b are experimentally determined parameters. Ar [ 154], Xe [ 155], N2, and Ct-L[ 156] scattering from Pt(111) also display a similar linear relationship. Hence, direct inelastic scattering leads to velocity distributions which are non-Boltzmann and strongly correlated to the incident translational energy.

3.2.3.3 Internal state distributions Although angular and velocity diswibutions of scattered molecules provide substantial information about direct inelastic scattering of heavy particles from surfaces, state specific information cannot be obtained from such studies [ 1]. Angular distributions of the scattered species are too broad to distinguish between possible energy transfer channels such as internal mode excitations or phonon excitations [ 1]. This difficulty can be overcome by using state specific detection techniques such as laser induced fluorescence (LIF), resonance enhanced multiphoton ionization (REMPI), or infrared (IR) emission to detect the internal energy distribution of molecules inelastically scattered from surfaces. Furthermore, it may also be possible to clearly distinguish between trapping-desorption (next section) and directinelastic scattering by using thcse techniques [1]. More importantly, measurement of the rotational population and thc alignment distribution of the direct inelastically scattered molecules provides additional information about the gas-surface interaction potential.

3.2.3.3.1 Rotational state distributions The rotational state distribution of direct inelastically scattered molecules is strongly affected by the anisotropy of the gas-surface interaction potential. The rotational state distribution for NO direct inelastically scattered from Ag(111) shows deviations from a Maxwell-Boltzmann distribution, and hence cannot be characterized by a rotational temperature over all J values[157]. Recently, similar results have also been obtained for HC1 direct inelasticaUy scattered from Au(111) [ 158]. Direct inelastic scattering of NO from Ag(111) was ensured by using high incident translational energies (18 - 90 kJ/mole) and by making the measurements close to the specular angle to avoid trapping-desorption. The rotational state distribution as measured by LIF for a rotationally cold NO supersonic molecular beam (rotational temperature between 5 and 50 K) scattering from Ag(111) as a function of internal energy (bottom scale) or rotational number J (top scale) is shown in Fig. 6. For an equilibrium MaxwellBoltzmann distribution, such a plot would yield a straight line whose slope is inversely proportional to the apparent rotational temperature, TR. For high incident translational energies, although the Boltzmann plot displays linear behavior at low rotational energies, the plot shows deviations from MaxwellBoltzmann behavior at high values of J; the curve displays a broad maximum as a function of J. This rotational rainbow effect, similar to rainbow scattering observed in gas phase systems [[ 159],[ 160] ],

33

Molecular Beam Studies

10.5

14

20.5

Rotational Quantum Number J 30.5 40.5

50.5 rq = P I 0 =RI @ =P2 X =R2

12

~

En=O.93eV

=,, 8

10

O

m

•

O

. Stoo m

OOOM O

xEn=0.70 eV OOO~

0

-

8

% @

ra

¢2

C

6

o¢~=

@ "1

En=0.30 eV O0~ 0II

En=0.19 eV 0

i

(2 0

I

0.1

I

I

1

I

..I

I

0.2 0.3 0.4 Internal Energy (eV)

'

i

0.5

Figure 6. Rotational state distribution of NO scattering from Ag(111) as function of internal energy (bottom scale) or rotational quantum number J (top scale). Reproduced from A. W. Klcyn, A.C. Luntz and D.J. Auerbach, Phys. Rev. Letters 47, 1169 (1981).

34

C.R. Arumainayagamand R.J. Madix

was attributed to the conversion of translational energy to rotational energy during the collisional process. A qualitative understanding of rotational rainbows has been obtained by modelling the incident gas molecule as a non-rotating hard ellipsoid (or any other non-spherical shape) and the surface as a hard flat plane. The degree ofrotationalexcitation (zhE~)displays a maximum as a function ofinitialorientation angle, y, between y = 0" and 90"; incident molecules with orientation such that ~ = 0" or 90" exhibit no rotational excitations. According to the classical picture, the term (d(zkE,)/d3t)~ causes the differential cross-section to blow up at this maximum, leading to rotational rainbows. A quantum mechanical treatment also leads to the same conclusion [161]. The translational and rotational energy distribution of NO molecules scattered from a oxidized Ge surface, however, indicate that pure translational to rotational energy transfer is not necessarily the dominant mechanism for rotational excitations in the scattering process [162]. The average final translational energy for the direct inelastically scattered molecules was found to decrease with increasing rotational excitations ( increasing J"). However, the decrease was less than what was predicted from the previously mentioned mechanism for rotational rainbows. Based on recent theoretical work [ 163], it is hypothesized that rotational excitation is due to a strongly anisotropic attractive gas- surface potential: when a NO molecule approaches with the weakly bound O-end rather than the more strongly bound N-end toward the surface, it is spun around, producing rotational excitations which remain virtually unchanged when the molecule scatters back to the gas phase [162]. Since memory of the dynamical parameters of the incident beam is retained in direct inelastic scattering, the rotational state distributions strongly depend on the beam translational energy and the angle of incidence. Only a weak dependence on surface temperature is observed [ 164], as expected for direct inelastic scattering. 3.2.3.3.2 R o t a t i o n a l a l i g n m e n t a n d o r i e n t a t i o n The majority of state specific molecular beam studies of direct inelastic scattering have concemed the rotational state distribution, a scalar quantity, to help understand the gas-surface interaction potential. However, since angular momentum is a vector quantity, the measurement of the spatial distribution of the angular momentum of direct inelastically scattered molecules can provide additional insight into the dynamics of the gas-surface collisions [ 165]. The moments of the spatial angular momentum diswibution can be related to two dynamical quantities: rotational alignment and rotational orientation. Rotational alignment is preference for "cartwheel" motion vs. "helicopter" motion (see Fig. 7). The rotational orientation is the net handedness of the rotation, i.e., clockwise vs. counterclockwise. The rotational alignment of N= direct inelastically scattered from a clean Ag(111) surface was determined using resonance enhanced multiphonon ionization (REMPI) [166]. For intermediate values of J, the degree of alignment was found to be less than perfect, indicating a corrugated surface. The degree of alignment, however, increased with increasing J. The scattered N2 molecules showed a strong preference for "cartwheel" motion, which has its rotational angular momentum vector parallel to the

35

Molecular Beam Studies

a) Helicopter

b) Cartwheel

! ,z.~

j

I

Figure 7. Rotational alignment relative to the surface plane; (a) helicopter motion (b) cartwheel motion. Reproduced from D.C. Jacobs, K.W. Kolasinski, R.J. Madix and R.N. Zare, J. Chem. Soc. Far. Trans. 2 (1989) 1325.

36

C.R. Arumainayagam and R.J. Madix

surface. Rotational alignment was independent of incident translational energy, incident angle and surface temperature. A similar preference for cartwheel motion was found for NO direct inelastically scattered from Ag(111) [167]. The angular momentum orientation of N2 scattered from Ag(111) was also determined by 2+2 REMPI [[ 168], [ 169], [ 170]]. Intuition suggests that a molecule colliding with a surface develops rotation in the "forward" sense ("topspin"). Nevertheless, the experimental results suggest that following collision some of the molecules are rotating in the "backward" sense ("backspin").

The observation of net

orientation demonstrates that in-plane forces are present during a scattering event because of the corrugation of the gas-surface interaction potential with a wavelength comparable to the dimension of the molecule [168]. Although the orientation shows a complex dependence on the final rotational state and the final scattering angle, a friction hard-cube model reproduced the qualitative features of the experimental data. The nature of the surface corrugation probed by these studies complements that obtained from angular distribution and surface diffusion studies [168].

3.2.3.3.3 Vibrational state distributions Vibrational excitation during a single gas-surface collision has been the focus of several recent supersonic molecular beam studies. Such studies are of major importance because vibrational excitations can couple directly to the dissociative reaction coordinate [171] (see below). Two mechanisms have been proposed for vibrational activation in molecule-surface collisions: (1) an electronic excitation mechanism and (2) an electronically adiabatic "mechanical" vibrational excitation mechanism. The probability for direct vibrational excitation into the v=-I level of NO for scattering from a Ag(111) surface was observed by resonant-multiphoton ionization [172]. At a surface temperature of 273 K the vibrational excitation probability (NO(v=l)/NO(v=0)) was immeasurably small (< 1 x 103) for all incident translational energies up to 135 kJ/mole. The degree of vibrational excitation increases roughly exponentially with surface temperature; the apparent activation energy for this excitation is approximately equal to the NO vibrational excitation energy (ca. 22 kJ/mole) (Fig. 8). Even though it is not as dramatic as the dependence on surface temperature, the dependence of the vibrational excitation on incident translational energy is sizable. The vibrational excitation probability was found to increase linearly with normal translational energy with no energy threshold (Fig. 9). The highest vibrational excitation obtained was ca. 7%. Even at high incident translational energy (120 kJ/mole) and surface temperature (760 K), vibrational excitation into the v=2 level was immeasurably small (< 5 x 10-3). The increase in vibrational excitation probability with increasing incident translational energy, the variation of the rotational state distribution with incident translational energy and incident angle, and the quasi-specular nature of the angular distribution for scattered NO (v=0) and NO (v=l), all indicate that the vibrational excitation for NO scattering from Ag(111) results from direct-inelastic scattering rather than from trapping-desorption [172]. In addition to being direct, the mechanism for vibrational

Molecular Beam Studies !

I

5-

I

4-

II :>

37 I

I

E.=102 kJ. mol

-I

3-

C:) Z IE:

2 I

0

_

ol -I

i

I

I

1.2

1.4

1.6

I I

1.8

_

I

2.0

103/Ts (K-') Figure 8. Arrhenius plots showing the effect of surface temperature on the vibrational excitation probability for NO/Ag(111) via the electronic mechanism. The incident angle was 15" and the incident translational energy was 9 and 102 H/mole. Reproduced from C.T. Retmer, F. Fabre, J. Kimman, and D.J. Auerbach, Phys. Rev. Lett. 55, 1904 (1985).

C.R. Arumainayagamand R.J. Madix

38 I

i

i

,

~

I

i

i

J

i

I

'

i

t

i

0.07 NO/Ag (111)

t

0.06 0.05 II

© Z

0.04

A

II ©

I

0.03

Z

T S= 760K

t

•V == 30 15"° • = 45 °

0.02 0.01 0.00

-I 0

I

t

t

v

I 0.5

i

v

i

i

I

v

v

~

v

1.0

E n = Eicos28i (eV) Figure 9. The effect of incident translational energy on the vibratio~=alexcitation probability for NO/Ag(111) at a surface temperature of 760 K and incident angles of 15", 30", and 45 ". Reproduced from C.T. Rettner, F. Fable, J. Kimman, and D.J. Auerbach, Phys. Rev. Lett., 55, 1904 (1985).

Molecular Beam Studies

39

excitation must account for the dependence on surface temperature and incident normal translational energy independently. The above conswaints were used to rule out coupling to surface phonons and to attribute the vibrational excitation to an electronic mechanism [172]. Theoretical studies have shown that vibrational excitation during gas-surface collisions may occur via the temporary formation of a negative molecular ion [ 173]. Gas phase electron-molecule scattering

studies also display a similar mechanism for vibrational excitation [174]. This mechanism is viable for NO scattering from Ag(111) because of the low-lying empty orbitals in NO. Theoretical studies of negative ion formation and the concomitant elecvron-hole-pair de-excitation on the NO/Ag(111) agree semi-quantitatively with experimental results for vibrational excitations in the same system [ 175]. The other mechanism for vibrational excitation involves direct collisional transfer of translational to vibrational energy. This electronically adiabatic "mechanical" vibrational excitation mechanism has been observed for NH 3(vffi0)scattering from Au(111) [ 176]. Up to three quanta of vibrational excitation were observed in the v2 umbrella mode of NH3 using two-photon-resonant, three-photon-ionization [(2+I)MPI] laser spectroscopy. The vibrational excitation was found to increase linearly with incident normal translational energy. The translational energy threshold was found to be close to the energy of

the vibrational energy level being excited (Fig. 10). Since the variations in the slopes for the different vibrational energies are within the experimental error of the measurements, no effort was made to ascribe a dynamical interpretation. In contrast to NO scattered from Ag(111), the vibrational excitation probability was found to be insensitive to surface temperature between 300 K and 800 K. The Arrhenius plot of the scattered NH3 vibrational distribution clearly shows that the dominant mechanism for vibrational excitation is not thermal activation by the surface (Fig. 11). The non-zero threshold behavior, the linear dependence on incident normal translational energy, and the independence on surface temperature were all cited as evidence for a vibrational excitation mechanism dominated by direct collisional translational to vibrational energy transfer [ 176]. Quasi-classical trajectory calculations reproduce the experimentally observed trends for the vibrational excitation ofNH 3colliding with a Au(111) surface [177]. The NI-I3 molecule was modelled as a one-dimensional vibrator and a three-dimensional rotor, while the surface was considered to be structureless and rigid. Because ammonia possesses a significant dipole moment, the long range dipole image-dipole potential preferentially orients the incident molecule so that its Ca symmetry axis is perpendicular to the surface plane prior to collision, facilitating translational to,vibrational energy transfer. Detailed calculations demonstrate the validity of the "light-heavy" impulsive collision model, which predicts that collisions with the light end of the molecule lead to facile vibrational energy transfer; NH 3 molecules incident with the three hydrogen atoms directed toward the surface and the symmetry axis perpendicular to the surface display the highest degree of vibrational excitation. In contrast to the NI-I~/Au(111) system, the mechanical vibrational excitation plays a negligible role for NO scattering from Ag(111) for several reasons [ 176]. The small dipole moment of NO precludes preferential orientation of the incident molecules by the long range dipole-image-dipole potential.

C.R. Arumainayagam and R.J. Madix

40

Z

NH 3 - Au ( 1 1 1 ) T s ffi 3 0 0 K 0 v=l

0

14 I-m

._1 a.

0

• •

12

v=2 v=3

10

_J I--

0

I-. LI.

8 6

0 IZ IJJ

4

0

2

(1~ /

(2)/,

(3)

I

II,

IJJ 0

I-

0

2

4

6

8

10

NORMAL KINETIC ENERGY (kcal/mole) Figure 10. Vibrational excitation ofNH 3scattered from Au(111) as a function of the normal incident translational energy. The energies of the fin'st, second, and third v2 quanta are indicated by the arrows. Reproduced from B.D. Kay, T.D. Raymond, and M.E. Coltrin, Phys. Rev. Lett. 59, 2792 (1987).

41

MolecularBeam Studies

~20

!

I

i

i

|

i

'

1,¢- - 1 5 _ NH 3 - A u ( 1 1 1 )

V-- 1

a~ =p,

--I

~

I

A ".r

10 -

O

13. ..J

,¢ 1-

5

~a. -r-r

O

V=2

a_

,I,

,

1I.L,

O 1Z

V'-3

U.I

~

C) n.. U.I n

1 1.0

i

~

t

I

,

t

m

I

2.0

1000

Ts

t

I

t

I

3.0

(K -1 )

Figure 11. Arrhcnius plot of the observed vibrational excitation of NH3 scattered from A u ( l l l ) for surface temperatures between 300 K and 800 K at an incident normal translational energy of 29 kJ/mole. Reproduced from B.D. Kay, T.D. Raymond, and M.E. Coltrin, Phys. Rev. Lett. 59, 2792 (1987).

42

C.R. Arumainayagam and R.J, Madix

Moreover, the transfer of vibrational energy due to the impulsive collision is diminished because of the match in masses between N and O. In addition, it requires twice as much energy to excite the fn'st vibrational level of NO compared to that of NH3. 3.2.3.4 S t e r i e e f f e c t s in s c a t t e r i n g Direct inelastic scattering of oriented molecules from surfaces can provide additional insight into the anisotropy of gas-surface interaction potentials. Recently the fwst observation of steric effects in gas-surface scattering was reported [[178], [179], [180]]. A well collimated pulsed molecular beam of NO with an incident translational energy of 19 kJ/mole at an incident angle of 35" was oriented using hexapole focussing techniques and scattered from a Ag(111) surface held at a temperature of 600 K. The angular distribution of the direct inelastically scattered molecules was measured for three different orientations of the incident NO molecules: 1) random orientation, 2) N-end pointedpreferentially toward the surface before the collision, and 3) O-end pointed preferentially toward the surface before collision. In all cases broad, lobular angular distributions with maximum intensity near the specular were observed. This near-specular scattering was assumed to be indicative of a flat and structureless surface, suggesting parallel momentum conservation. Hence, it was concluded that only the normal translational energy is effective in rotational excitation. The angle of the maximum intensity in the lobular distribution measured from the surface normal showed the following trend: N-end < random orientation < O-end. Since a scattering distribution peaked away from the specular angle and toward the surface indicates loss of normal momentum during collision, it was concluded that O-end collisions result in more rotational excitations than N-end collisions. This conclusion was consistent with independent experiments of trapping-desorption of the NO/Ag(111) conducted by the same group (see below). 3.3 T r a p p i n g - d e s o r p t i o n In contrast to the short interaction times involved in direct inelastic scattering of molecules, trapping-desorption is characterized by interaction times longer than the characteristic vibrational period for species adsorbed in the gas-surface potential well. Two classes of species can be envisioned; those that equilibrate only the z-component of momentum [ 181] and those that fully equilibrate with the surface. Unless otherwise specified, we consider in this section only those species that fully equilibrate. Trapping-desorption usually accompanies direct inelastic scattering of molecules and is expected to become increasingly probable as the incident translational energy and the surface temperature decrease, and the incident mass increases. Since the trapped-desorbed molecule which equilibrates x,y, and z motion loses all memory of its incident parameters, the angular distribution for desorption is symmetric and peaked about the surface normal and displays a cosine or near cosine distribution as opposed to the lobular scattering which is peaked near the specular angle for direct inelastic scattering. Velocity distributions for the trapping-desorption channel for Ar scattering from a polycrystalline W surface appear consistent with a Boltzmann distribution characterized by the surface temperature [153].

Molecular Beam Studies

43

Weak molecular adsorption occurs due to the attractive van der Waals' interaction between a molecule and a surface with little or no charge transfer and is typically characterized by binding energies less than 40 kJ/mole. In order for a molecule to trap on the surface, the loss in translational energy of the incoming molecule must be dissipated into other degrees of freedom; otherwise, no trapping into the potential well occurs. While dissociative chemisorption may involve energy loss via excitation of electron-holepairs [ 182] in addition to surface phonons, weak molecular adsorption is believed to involve an energy transfer process dominated by excitation of surface phonons [183]. The first step in epitaxial growth, thin film growth, and heterogeneously catalyzed reactions is the adsorption of gases on surfaces. Hence, a fundamental understanding of these technologically important processes requires the examination of the critical parameters governing the adsorption process. Since weakly interacting gas-surface systems serve as models to understand the fundamental aspects of adsorption phenomena, several studies have recently focussed on trapping dynamics using nearly monoenergetic molecular beams [[184], [ 185]].

3.3.1 Dependence of trapping on incident translational energy Very simple classical arguments predict that trapping probabilities at low surface temperatures approach unity for low translational energy beams and zero for high translational energy beams [1]. A molecule with incident translational energy E inside an attractive well of depth D has a total energy of (E+D). If it loses a fraction f of this energy on collision, where f depends on the gas/solid mass ratio, and the remaining energy (1-f)(E+D) is less than D, the particle will trap. Hence, ifE is less than fD/(1-f) the adsorption probability will be unity and zero otherwise. This argument, although a gross approximation to reality, qualitatively predicts the general trends in adsorption probabilities. Supersonic molecular beam studies show that the initial mapping probability of methane [186], ethane [187], propane [188], Ar [189], and Xe [[190], [191]] on Pt(lll) and ethane on Ir(l10)-(lx2) [ 192] decreases with increasing incident translational energy at all incident angles studied, in qualitative agreement with the classical model described above (Fig. 12). A more quantitative understanding of mapping dynamics may be obtained by modifying the original hard-cube model for gas-surface scattering [193] by incorporating a one-dimensional square well to permit mapping. The surface is modelled by a cube, constrained to move only in a direction perpendicular to the surface with a one-dimensional Maxwell-Bol~mann velocity distribution characteristic of the surface temperature. The incident gas molecules are assumed to be rigid elastic spheres with no internal degrees of freedom, thus constraining energy loss to excitations of surface phonons only. A derivation based on the above assumptions yields a closed form expression for the initial trapping probability as a function of incident translational energy, incident angle, and surface temperature [[ 186], [ 194]]. The calculated initial trapping probabilities show semi-quantitative agreement with the measured initial trapping probabilities, suggesting that excitation of surface phonons is the dominant energy loss mechanism.

44

C.R. Arumainayagam and R.J. Madix

n-Alkanes / P t ( l l l ) A 0.8

T=95K S

[]

eN

O

ou

"-

0.= 00

",,°. •%

"'.°

0.6

1

A

eg3

Jim

em

0.4

0 "..

i

A

"..

eu e l

"*°

c3-8"-

m

0.2 oCH

0 0

I 10

20

4

. C 2H 6 []

I 30

I 40

I 50

60

Incident Translational Energy (kJ/mole) Figure 12. The initial trapping probability of methane (solid circles), ethane (solid squares) and propane (solid triangles) on Pt(111) as a function of incident translational energy at normal incidence at a surface temperature of 95 K. Reproduced from C.R. Arumainayagam, Mark C. McMaster and R.J. Madix, J. Vac. Sci. Technol. A 9, 1581 (1991).

Molecular Beam Studies

45

Recent experimental studies of Ne trapping on Ru(001), however, were found to be incompatible with classical mechanical theory, requiring the energy wansfer to phonons be treated quantum mechanically [46]. At low incident translational energies, the adsorption probability was found to be 0.1 instead of one as expected from classical theories. This large quantum effect was not attributed to the wavelength of the Ne atom, but rather to the quantum mechanical response of the lattice. Quantum effects have also been observed in the weak molecular adsorption of H2 and D2 on Cu(100) [[195], [196]]. The adsorption probability was found to be on the order of 0.1 at low incident translational energy. Classical treatments are believed to be appropriate only when the typical energy transfer to the lattice exceods the phonon bandwidth [ 197]. Since for H2 on Cu the energy transfer for a single molecuie is typically 2-3 meV and the phonon bandwidth is 30 meV, the use of classickl mechanics is not justified. 3.3.2 D e p e n d e n c e o f t r a p p i n g o n i n c i d e n t angle For a constant incident translational energy (ET), the initial trapping probability increases with increasing incident angle from the surface normal due to the dominance of normal momentum exchange in the trapping process, in qualitative agreement with one-dimensional models. Nevertheless, in contrast to the assumptions of one-dimensional theories, the initial trapping probability is not a monotonically decreasing function of Ercos20t (referred to as "normal" translational energy), indicating deviation from normal energy scaling. Here 0t is the incident angle measured from the surface normal. Generally, the initial trapping probability decreases monotonically with F~os"0i, where n is a number between 2 (normal energy scaling) and 0 (total energy scaling), due to the participation of the parallel momentum in the trapping process. Such scaling corresponds to a more gradual increase in the initial trapping probability, So, with increasing angle of incidence than expected from one-dimensional models. Deviations from normal energy scaling have been recently obtained for the following weakly interacting gas-surface systems: Ar/2H-W(100) [198], Xe/Pt(ll 1) [[190], [191]], Ar/Pt(111) [189], ~ ( 1 1 1 ) [187], C~s/Pt(111) [188], and ~ 1 1 0 ) - ( I x 2 ) [192]. These observations may be rationalized by a corrugated gas-surface interaction potential which effectively couples parallel momentum into normal momentum away from the surface, thereby decreasing the adsorption probability relative to that expected from normal energy scaling [199]. The dependence of the initial adsorption probability on incident translational energy and incident angle was simulated for Xe/Pt(111) using three-dimensional stochastic trajectory calculations incorporating a corrugated gas-surface interaction potential [190]. Stochastic classical trajectory calculation techniques were developed in the past decade to circumvent the prohibitive task of integrating very large numbers of fwst-order coupled differential equations (Hamilton's equations of motion) associated with describing the large number of atoms involved in dynamical events at surfaces [200]. For the adsorption of Xe, the Pt(111) surface was modelled by a slab composed of three layers each containing 36 moving atoms. The fourth and fifth layers of atoms were fixed at their equilibrium positions. Friction and random forces were applied to account for energy flow into and out of the bulk. Harmonic interactions among the Pt atoms were assumed. It was necessary to employ a pairwise additive Morse potential

C.R. Arumainayagam and R.J. Madix

46

Xe / Pt(lll) Ts = 9 5 K

0.8 e~ N em

0

m

0

•

0.6

¥

•

Experimental

o

Theoretical (Morse Potential)

e~

0

%. 0.4 0 i

8

o~ o~

0.2 0 •

0

OI

• @

0

m 0

t

I

I

I

I

I

10

20

30

40

50

60

70

E cos O.(kJ/mole) T

1

Figure 13. Comparison of experimental So (solid squares) and thr~-dimcnsional stochastic trajectory calculations of So (open circles) as a function of E.rcos 0i for Xc trapping on Pt(111) at a surfac~ tcml~raturc of 95 K. Reproduced from C.R. Arumainayagam, R.J. Madix, Mark C. McMast~r, V.M. Suzawa and J.C. Tully, Surface Sci. 226, 180 (1990).

Molecular Beam Studies

47

instead of a Lennard-Jones potential to represent the Xe-Pt interaction in order to vary the steepness of the repulsive wall of the gas-surface potential independent of its corrugation. In all simulations parancters were chosen to produce a Xe-surface binding energy of 25.9 kJ/mole, as obtained from

experiment [201].

The calculations, employing realistic interaction parameters, reproduced the

experimental results quite well (Fig 13).

3.3.3 Dependence of trapping on surface temperature Since the direct method does not provide true initial trapping probabilities when the surface temperature exceeds the desorption temperature of the molecule of interest, an alternative method involving deconvoluting angular distribution data has been used to study the dependence of the initial trapping probability on surface temperature. This method involves deconvoludng the scattering distribution into two channels: (1) a lobular scattering channel peaked near the specular direction due to direct-inelastic scattering, and (2) a cosine or near-cosine distribution with the maximum flux at the surface normal due to trapping-desorption. The trapped-desorbed component for CI-IdPt(111) was found to be nearly invariant with surface temperature in the range of 160 to 500 K to within experimental error, suggesting that the trapping probability is rather insensitive to surface temperature over this range [ 186]. Calculations based on the modified hard-cube model also indicate that the initial trapping probability should decrease only slighdy with surface temperature for incident translational energies less than 10 ld/mole [186].

ca.

Very recent results indicate that for the Ar/Pt(111) system the dependence of the trapping probability on parallel momentum changes with surface temperature [189]. Under the conditions studied, the lifetime of the trapped species was expected to vary from approximately 10s to 10 picoseconds. Since deconvolution of either velocity or angular distributions of inelastically and trapped-desorbed species depends on a distinct separation of the two components, species which are trapped for times insufficient to produce full equilibration complicate analysis. Trajectory simulations show that there is a range of surface temperatures for which this separation is possible [ 181 ]. These trajectory simulations clearly show that normal momentum accommodation occurs much more rapidly than parallel momentum equilibration. "Hot" parallel momentum can thus give rise to translationally hot desorbing species far from the surface normal which have actually been trapped in the molecule-surface potential well. Care must be taken in the interpretation of such trapping-desorption experiments at very small surface lifetimes.

3.3.4 Dependence of trapping on initial molecular orientation The dependence of the trapping probability on the initial orientatioi~ of the incident molecules has been investigated for the wealdy interacting NO/Ag(111) system [202]. The trapping probability of NO on Ag(111) is larger for the orientation with the O-end toward'the surface than with the N-end toward the surface, despite the fact the N-end is expected to interact more strongly with the surface on the basis of its interaction with metal surfaces such as Pt(111) on which it binds with the N-end down [203]. Calculations based on classical molecular dynamics attribute this observation to the fact that the

48

C.R. Arumainayagamand R.J. Madix

anisotropy of the repulsive potential wall dominates the anisotropy of the attractive potential well in trapping dynamics [204]. Hence, rotational excitation is more efficient for molecules oriented with the O-end toward the surface than for molecules oriented with the N-end toward the surface. Since rotational excitation occurs via translational to rotational conversion, the authors concluded that those molecules with the highest rotational energy will possess the lowest translational energy and hence will trap more efficiently. Experiments involving the direct inelastic scattering of NO from A g ( l l l ) support this mechanism [[178], [179], [180]].

3.3.5 Dependence of trapping on adsorbate coverage The molecular adsorption probability of ethane [205], propane [188], and Xc [206] on Pt(111) and ethane on Ir(110)-(Ix2) [207] increases with surface coverage (0) at submonolayer coverage and hence cannot be fit by Langmuirian kinetics ( S(0)= So (1-0)) or by the original Kisliuk model [208]. By invoking weakly bound mobile precursor states, Kisliuk derived kinetic expressions for adsorption as a function of coverage using a successive site statistical model to explain cases in which the adsorption probability did not fall linearly with coverage as predicted by the Langmuir model for associative adsorption. In view of recent molecular beam results, the Kisliuk model has been modified to account for the initial increase in molecular adsorption probability with coverage before the decrease to zero at saturation coverage [[205], [207]]. Adsorption is assumed to occur either directly with probability So on unoccupied sites or indirectly with probability S~ on covered sites. Duc to better mass matching of the collision partners, S~ > S0. The adsorption probability S is given by [209]: S = So(1 - 0) + s~e

(20)

This dependence on coverage over the entire range can be understood on the basis of an extrinsic precursor state. If the rate of desorption from the extrinsic precursor state is not much smaller than the rate of conversion from the extrinsic precursor state to the adsorbed species, a more general expression for S results [[205], [207]]. For an approach that totally ignores lateral interactions and island formation, this simple model fits the experimental data remarkably well for the molecular adsorption of ethane on P t ( l l l ) [205] and Ir(110)-(lx2) [207], and X¢ trapping on P t ( l l l ) [206] at all incident translational energies and incident angles studied (Fig. 14).

3.3.6 Dynamics of extrinsic precursor adsorption Since trapping-dominated reactive processes at surfaces may be strongly influenced by the existence of precursor states, the dynamics of precursor adsorption is of fundamental importance. Ethane [210], propane [188], and Xe [206] trapping onto a saturated monolayer on Pt(111) have been studied in order to investigate the dynamics of extrinsic precursor adsorption. At all incident u'anslational energies and angles, the initial trapping probability onto the monolayer state is higher than on a clean surface despite the fact that the binding energy in the second layer is less than that in the monolayer. This behavior can be attributed to the mass of the adsorbed species, which is less than that of the Pt

Molecular Beam Studies

49

0.8

Modified Kisliuk Model Xenon/Pt(111) ~;~ 0.6

t_

.-~

qm--~° 0.4

.z

i! :oo

.< 0.2 Is

[Er= 34 kJ/m°ie

i ! i

I

I

1

I

0.2

0.4

0.6

0.8

Coverage (Fraction of a Monolayer) Figure 14. The adsorption probability of Xe on Pt(l 11) as a function of adsorbed Xe coverage at an incident translational energy of 34 kJ/mole at normal incidence at a surface

temperature of 95 K. The solidcirclesindicatethe experimental data and linesindicatethe results of the modified Kisliuk model calculations for various values of the adjustable parameter q,. Reproduced from C.R. Arumainayagam, James A. Stinnett, Mark C. McMastcr and R.J. Madix, J. Chem. Phys. 95, 5437 (1991).

50

C.R. Arumainayagamand R.J. Madix

atom, leading to increased energy transfer for the impact of an incident particle with the adsorbed species than with Pt. The match in mass of the collision partners may also enhance multiple collisions, thereby facilitating energy loss. In contrast to previous findings for weak molecular adsorption on clean surfaces which show that the initial trapping probability increases with incident angle, the initial trapping probability into the second layer is independent of incident angle, indicating total energy scaling. A dynamical corrugation of the adsorbed layer was postulated to rationalize this strong deviation from the normal energy scaling implicit in one-dimensional theories of trapping [210]. Indeed, trajectory simulations for Ar trapping on a Ar monolayer show only a very weak dependence on incident angle [211].

3.3.7 Detailed balance The observed dependence of the initial trapping probability ofCH 4 [ 186] and Xe [ 190] on incident translational energy at normal incidence is consistent with previous mean translational energy measurements for ~

[ 156] and Xe [ 155] desorbing from Pt(111) at the surface normal, in accordance with

detailed balance. For gas surface interactions at equilibrium, detailed balance predicts that the mean energy of molecules desorbing at the surface normal is given by:

where s(u,) is the trapping (sticking) probability as a function of incident normal velocity u, and a 2 = 2kBT/M where kB is the Boltzmann constant, M is the mass of the incident gas molecules, and T is the temperature of the gas and the surface [212]. Only if the trapping (sticking) probability is independent of the incident normal velocity will the molecules desorbing at equilibrium at the surface normal have the expected mean energy of 2kBT. If the trapping probability is a decreasing function of the incident normal velocity, the above equation requires that the mean energy of the desorbing molecules at equilibrium at the surface normal will be less than 2kBT (i.e., subthermal). By fitting measurements of So as a function of E, with an exponential for ease of integration and substituting into the above equation, the mean translational energy for Xe desorbing at the surface normal was estimated to be 2-4% subthermal. In accordance with detailed balance, this estimate agrees with the directly measured value of 0% to within experimental error. Similar agreement has been found for Ar trapping on a H atom covered W(100) surface [198].

3.3.8 Rotational state distributions in trapping-desorption The trapping-desorption channel has been isolated in state specific studies by lowering the incident translational energy, by using glancing angles of incidence and by making observations near the surface normal. As expected, the rotational state distributions for trapped-desorbed molecules of NO from a Ge surface were found to be independent of incident translational energy [213]. Rotational state dis-

MolecularBeam Studies

51

tribufions observed for the trapping-dcsorption channel were always Maxwell-Boltzmann in form. At surface temperauncs below approximately 250 K, the rotational temperatore was found to be equal to the surface temperature. However, at surface temperatures between 250 K and 900 K the rotational temperature was found to be less than the surface temperature, reaching a limiting value of about 400 K at a surface temperature around 600 K in the case of NO. According to a theoretical study, this iimidng value is determined only by the rotational constant of the desorbing molecule and not by its interaction potential with the surface [214]. This "rotational cooling in desorption", fwst identified for the thermal desorption of NO from Ru(100) [215], has been explained by several different theoretical studies [[216], [217], [218], [219], [220], [221]]. In the simplest scenario, the effect has been explained in terms of rotational-translational energy exchange, employing microscopic reversibility [213]. The trapping probability decreases as the incident rotational energy is increased because of the possibility of rotational energy to translational energy transfer. Assuming microscopic reversibility, this effect requires a rotational cooling on desorption, since at equilibrium direct inelastically scattered molecules have higher than average rotational energy, so that the desorbed molecules must have a lower than average rotational energy. 3.3.9 O r i e n t a t i o n o f m o l e c u l a r axis in d e s o r p t i o n The preferential orientation of the molecular axis (as opposed to the preferential direction of the angular momentum vector) for molecules desorbing from a surface has been measured recently using electrostatic focussing techniques [222]. These studies suggest CI-IF3 desorbs from Ag(ll 1) with its hydrogen atoms oriented toward the surface, while the opposite orientation was preferred for direct inelasticscattering. 3.4 Molecular chemisorption a n d desorption Stronger interactionsthan van der Waals' interactions,having the characterof chemical bonding between the molecule and the solid surface, lead to chemisorption. Chemisorption involves charge transferbetween the molecule and the surface leading to binding energies usually much largerthan 40 kJlmole. In non-dissociativemolecular chemisorption the molecule retainsits chemical identity. In contrastto weak molecular adsorption,where energy transferisthought to be confined only to excitation of surface phonons [183], electronicexcitationvia electron-holepairs may also contributeto the dissipationof incident translationalenergy in the case of chemisorption [182]. Chemisorption may be a direct or an indirect process. The latter case involves an intermediate weakly adsoflmd state (precursor state)prior to chemisorption. 3.4.1 D e p e n d e n c e on incident translational energy The initialmolecular stickingprobabilityof C O on Ni(100) [199], Ni(11 I) [223] and Pt(llI) [224] has been shown to decrease with increasingincidenttranslationalenergy, using nearly monocnergeticmolecular beams. On Ni(100),as the incidenttranslationalenergy of the C O molecules atnormal incidence isincreasedfrom 8 to 126 kJ/mole, the initialmolecular adsorptionprobabilitydecreases from

C.R. Arumainayagam and R.J. Madix

52

0.91 to 0.50 at surface temperatures between 300 and 400 K (Fig. 15). As for weak molecular adsorption, this behavior has been attributed to non-unit efficiency of trapping; fast molecules have a greater probability than slow ones of being reflected rather than being adsorbed. Molecular adsorption probabilities that decrease with increasing gas temperatures have been observed for several systems including N~,V(100) [225], and H~/Ni(110) [226]. The effect has been attributed to the incident translational energy increasing with increasing gas temperature.

The adsorption probability for strong molecular chcmisorption decreases much more slowly with incident translational energy than predicted by the cube models. For example, the sticking probability of CO on Pt(ll 1) does not decrease below 0.1 even for incident translational energies as high as 200 kJ/mole [224].

Translational-rotational conversion was invoked to explain enhanced sticking at

translational energies above the critical energy, as estimated by trajectory simulations.

3.4.2 Dependence on incident angle As in the case of weak molecular adsorption, the dependence of the sticking probability on incident angle for molecular chcmisorption demonstrates the participation of the parallel momentum in the adsorption process. For CO adsorbing on Ni(100), the initial sticking probability is independent of incident angle at an incident translational energy of 8 kJ/mole [199] (Fig. 16). At higher incident translational energies, the sticking probability decreases with increasing incident angle, in total contradiction to one-dimensional theories of adsorption. This effect was attributed to the scattering of trapped, translationally hot molecules from a corrugated potential back into the gas phase. Total energy scaling has been observed for CO chemisorption on Pt(ll 1) and has been attributed to the corrugation of the potential due to the large well depth [224]. The role of defects in these processes has not yet been determined.

3.4.3 Role of precursors At low incident translational energies and surface temperatures, adsorption of CO on Ni(100) proceeds in a fashion consistent with classical extrinsic precursor kinetics (Fig. 17) [199]. At a surface temperature of 100 K and an incident translational energy of 6.7 kJ/mole the relative molecular sticking probability is 1.0, remaining constant with coverage up to a value near 0.5 ML (1ML = 1.61 x 101~ molecules/cm2) where it falls abruptly toward zero. At higher surface temperatures, this drop is less precipitous. At a higher incident translational energy of 90 kJ/mole (21.4 kcal/mole), however, the adsorption probability decreases linearly with increasing coverage. These results were attributed to a transition from extrinsic precursor adsorption kinetics at low incident translational energies to direct (Langmuirian) adsorption at high incident translational energies. Angular distributions of scattered molecules from a CO-saturated surface indeed show that there is a transition from trapping-desorption, characteristic of extrinsic precursor kinetics, at low incident translational energies, to direct inelastic scattering, signifying reflection from the covered surface, at high incident translational energies (Fig

18).

Molecular Beam Studies

•

cr~

53

.

''

!

0.5

O.

0

I

0

I

I

I

|

I

l0

Energy

I

I

I

I

l

20

I

I

I

30

(kca]/mo])

Figure 15. The dependence of the initial molecular sticking probability So on incident ~anslational energy for CO adsorbing at normal incidence on Ni(100). The solid curve is a fit to an empirical expression, So = 0.92 exp [ -E / 235 (kJ/mol¢)]. Reproduced from M.P. D'Evclyn, H.-P. SteinrUck and RJ. Madix, Surface Sci. 180, 47 (1987).

C.R. Arumainayagam and R.J. Madix

54 !

l

~

|

J

l

I

1.0 o

m

O

~

o

~

0

I~----.._

m

2.0

O m O B O

II ~

I

I

11.5 14.5

c~

o-)

0.5 17.0

0.0

J

0

i

t

r

r

m

I

r

r

~

30

m

I

I

I

I

60

Oj (degrees) Figure 16. The molecular adsorption probability of CO on Ni(100) at zero coverage as a

function of incident angle for various incident translational energies which are indicated beside each line (in kcal/mole). Reproduced from M.P. D'Evelyn, H.-P. Steinrfick and RJ. Madix, Surface Sci. 180, 47 (1987).

55

Molecular Beam Studies

1. O

-,,

ioo K

0.5

"~,

cn

I

0.5

~

I

%

~. ~,.~\ ~"%~.~

(a) 0.0 1.0

\~o.e

l

I

l

I

".

:

220

\ (b)

0.0 1.0 1. a

0.5

300 K

(c) 0 . 0 ~-

0.0

0. l

0.2

0.3

0.4

0.5

0.5

8c0 Figure 17. The relative molecular adsorption probability as a function of coverage forCO on Ni(100) and incident translational energy at surface temperatures of (a) I00 K, (b) 220 K, and (c) 300 K. The various incident translational energies are indicated in kc~mole beside each line. Reproduced from M.P. D'Evelyn, H.-P. Steinrfick and R.J. Madix, Surface Sci. 180, 47 (1987).

C.R. Arumainayagam and R.J. Madix

56

-."4

4.,

., _._

ir....=.--

-m- T

"T

-m-

. ....,

.~-

~J

70 GJ (_

...'{!

/

0 0

~,~t ''m

j"

-

"~.." -60

-30

\

11.5

, 0

, E

I 30

,I

,I

I, 60

t

,

t 90

Or- (degrees) Figure 18. The angular distribution of CO scattered from CO covered Ni(100) at surface temperaturesof(a) 100Kand (b)300K. Thespecularangleis60O. The incident translational energy in kcal]mole is indicated beside each line. Reproduced from M.P. D'Evelyn, H.-P. SteinriJck and R.J. Madix, Surface Sci. 180, 47 (1987).

Molecular Beam Studies

57

Although evidence was presented for the presence of an extrinsic precursor state, the very weak dependence of the initial molecular sticking probability on surface temperature was used to conclude that at surface temperatures above 100 K chemisorptiou occurs directly on a clean Ni(100), without incident molecules becoming thermalized in a identifmble intrinsic precursor state [199]. At each incident translational energy So is independent of surface temperature between 100 and 400 K, to within experimental error (± 0.02). The angular distributions of the scattered molecules obtained by using beam modulation to separate the direct inelastically scattered andltrapped-desorbed components at different surface temperatures also suggest that molecules that fail to chemisorb on the clean surface are direct inelastically scattered and do not become fully accommodated in a precursor state. For CO adsorption on Ni(100) there is absolutely no indication of a reversibly adsorbed, thermally accommodated intrinsic precursor. Using molecular beam relaxation spectrometry (MBRS) (section 4.2) three contributions to the flux of CO scattered from P t ( l l l ) between 530 K and 650 K have been identified [227]; namely, chemisorbed-desorbed CO, trapped-desorbed (physisorbed) CO, anddirect inelastically scattered CO. The trapped-desorbed (physisorbed) component is characterized by a cosine angular distribution and a Maxwell-Boltzmann velocity disa'ibution at the surface temperature, suggesting equilibration with the surface prior to desorption. However, the ratio of the chemisorbed signal to the physisorbed signal remained constant with temperature (530 K < 1", < 650 K), suggesting that the energy harder between the chemisorptiou state and the physisorption state is at the vacuum level. It was concluded that the physisorbed state does not act as precursor state to chemisorption.

3.4.4 Steric effects in molecular chemisorption The steric effects for a strongly interacting gas-surface system, NO/Pt(111), have been investigated using oriented molecular beams [228]. As discussed previously, forNO adsorption on Ag(111), a weakly interacting gas-surface system, the adsorption probability is highest for molecules approaching the surface with the orientation for which the attractive forces are the weakest. A strong anisotropy in the repulsive portion of the gas-surface interaction potential which leads to rotational excitation was invoked to explain this observation. For NO chemisorption on Pt(111), NO exhibits a slightly higher adsorption probability for molecules approaching the surface with the N-end toward the surface, the orientation for which the am active forces are strongest. This observation has been attributed to the much higher binding energy of NO on Pt(11 I). The higher binding energy causes the trapping to be dominated by phonon excitation rather than translational to rotational energy transfer.

3.4.5 Rotational state distribution for desorption Desorption of a strongly bound molecule displays rotational cooling [229] similar to that seen for the desorption of a weakly bound molecule. The rotational state distribution of NO desorbing from Pd(111) was measured by REMPI spectroscopy. The crystal was dosed with a pulsed molecular beam at the same repetition rate as the laser used to cause the desorption. Although NO binds strongly to the Pd(111) surface, no dissociation takes place [230] and desorption is not the result of atom recombination.

58

C.R. Arumainayagam and R.J. Madix

Rapid heating

via nanosecond laser pulses made possible the observation of desorption via a thermal

mechanism at high rates and high surface temperatures. Experimental conditions were optimized to minimize post-desorption collisions. Although the rotational distribution could be characterized by a Maxwell-Boltzmann form, the characteristic temperature was found to be only 640 + 40 K which was far below the surface temperature of 11(30 + 100 K at the time of desorption. These results suggest that rotational cooling is an intrinsic property of thermal desorption from surfaces.

3.4.6 Rotational alignment in desorption Since rotational alignment in the desorbing molecule provides information regarding the last gas-surface interaction prior to desorption, it is a sensitive measure of desorption dynamics [231]. By measuring the dependence of the REMPI ion production on the linear polarization of the laser beam relative to the surface normal, the rotationally-resolved alignment of NO desorbing from Pt(111) has been measured [231]. The results indicate that for high values ofJ (J > 15), 20% more molecules desorb with J pointing along the surface normal ("helicopter" motion) than those with J pointing parallel to the surface ("cartwheel" motion).

4 Reactive Scattering from Surfaces 4.1 D i s s o c i a t i v e c h e m i s o r p t i o n Dissociative chemisorption, a key step in a wide variety of catalytic processes, involves the breakage of intramolecular bonds and the formation of new bonds to the surface atoms. A sizeable activation barrier may have to be surmounted for some molecules to dissociatively adsorb on metal surfaces. Hence dissociative chemisorption is often the rate limiting step in surface reactions, and a microscopic understanding of dissociative chemisorption is thus of technological importance. A schematic representation of the one-dimensional potential energy surface for a diatomic molecule dissociatively chemisorbing on a solid surface is shown in Fig. 19 [232]. Although this depiction is a gross oversimplification of the true multidimensional gas-surface potential hypcrsurface, it provides simple insight into the basics of dissociative chemisorption. The abscissa is the potential energy and the ordinate is the distance from the surface (or the reaction coordinate). The curve corresponding to the precursor state is for the weak molecular interaction between the incident molecule and the surface. The curve corresponding to the chemisorption state represents the strong interaction of the dissociated fragments with the solid surface. Multiple curves are drawn for the potential of the precursor state to demonstrate that the repulsive part of the potential depends on the impact point on the lattice, orientation of the molecule, and the particular gas-surface system. In this simple picture, dissociative chemisorption is either non-activated or activated depending on whether the potential energy curves for the chemisorption state and the precursor state cross below or above the zero of the potential energy. For non-activated dissociated chemisorption, molecules in the precursor state have a smaller harrier to chemisorption than desorption. Hence, the dissociative chemisorption probability decreases with increasing surface temperature for non-activated adsorption.

Molecular Beam Studies

T

T

T

59

T

II111| IIIIIl 1111II 111111 II1111 lllll llll-

c"

cIII

C © r~

Chemisorption State 0

~ . ~

! L 1 2 3 4 Distance from Surface ()~)

5

Figure 19. A one-din~nsional representation of potentials for dissociative chemisorption. The different curves for the precursor state illustrate the dependence of the potential on variables such as adsorption sites, orientations, and impact parameters. Reproduced from D.J. Aucrbach and C.T. Rettncr, in Kinetics of lnterface Reactions, M. Grunze and HJ. Kreuzer Eds., Springer Series in Surface Sciences (Springer-Verlag, Berlin Heidelberg 1987).

C.R. Arumainayagam and R.J. Madix

60

For activated dissociative chemisorption, molecules in the precursor state have a higher barrier to chemisorption than for desorption, and increasing the surface temperature causes the dissociative chemisorption probability to increase. A two-dimensional hypersurface depicting the potential as a function of both distance from the surface and the interatomic distance provides additional insight into the complexities of dissociative chemisorption.

The qualitative features of a two-dimensional potential energy surface (PES) are

illustrated for the dissociative adsorption of H2 on Mg(100) [233] on an atop site (Fig. 20). The potential is depicted as a function of the distance from the surface (ordinate) and the interatomic spacing of the incident molecule (abscissa). The collisional trajectory of a molecule may be represented as a path on this figure [232]. Since the incident molecule has to turn the comer to dissociate in well B, even molecules with incident energy higher than the barrier at A and D may not dissociate [232]. A more detailed theoretical understanding of dissociation may require the representation of the PES as a function of other coordinates of the system such as orientation of the incident molecule and the impact site [234]. Furthermore, high energy collisions will result in scattering offthe repulsive wall prior to exiting the product channel, introducing the possibility of energy dissipation into the solid. Indeed, recent dynamical simulations for N 2 dissociative chemisorption on Re(0001) show very significant energy transfer to the lattice phonons [234]. Theoretical studies have also shown that the dynamical PES appears to be higher and thicker than the static PES due to recoil of nearest neighbor atoms during dissociation [235]. Due to the mismatch in masses, the effect of the motion of the lattice atoms is not pronounced for light molecules such as H 2 and D 2. Molecular beam studies have helped to identify three different mechanisms for the dissociative chemisorption of a gas phase molecule on a solid surface : (1) direct collisional activation, (2) trapping or precursor mediated dissociation, and (3) collision-induced dissociation. In the direct collisional activation mechanism, the molecule dissociates immediately upon impact with the solid surface. In the trapping or precursor mediated mechanism, the gas molecule loses sufficient kinetic energy to first trap and accommodate on the surface before dissociating or diffusing to a favorable site for dissociation. In collision-induced dissociation, high energy molecules impinging on an adsorbate-covered surface cause dissociation of the adsorbed molecules.

4.1.1 Direct collisional activation 4.1.1.1 Dependence on incident t r a n s l a t i o n a l e n e r g y In the simplest scenario for direct collisional activation the molecule dissociates immediately upon impact when the energy of the incident species in the reaction coordinate is greater than the barrier height. The molecule reflects from the surface when the energy is below the,barrier height. For a simple one-dimensional barrier accessible with translational energy, an abrupt increase in the reaction probability from zero to near unity is expected. Indeed, supersonic molecular beam studies of the dissociative adsorption of N2 on W(110) have shown that the initial dissociative sticking probability increases from 3 x 103 to 0.35 when the incident translational energy increases from 30 kJ/mole to 100 kJ/mole [[236],

Molecular Beam Studies

w

61

6

UJ

,,< GO 0

Z 0 (.9 0 "I" i-n-

O

STEP

0.6

SIZE

1'.0

0.1SeV'" ~+~~" ' ~;~z.,~.:,,~",'~, " 1.4

1.8

2.2

2.6

3.0

PARALLEL TO SURFACE (o.u.) Figure 20. Contour plot of the potential energy surface for the dissociative chemisorption of H2 on Mg(001) over an atop site. Reproduced from J.K. Norsokov, FL Houmollor, P.K. Johansson and B.I. Lunqvist, Phys. Rov. Lctt. 46, 257 (1981).

C.R. A r u m a i n a y a g a m and R J . M a d i x

62

I

I

I

I

100

Xo o x

m

. ro D t'~ O

0

•

16

>,,

0

o

1 O" I

x

•

13. ¢. ~

v ¢3

--

0 o

x = o =

30 ° 45 °

•

=

55 °

•

.--- 6 0 °

. R

co •~

# •

10-2

f

J

° ~

c-

f •

1

i i

J

J

f

I

10 -3 0

I, 50

r 100 Beam

1 150

Energy

t 200

(kJ mo1-1)

Figure 21. The initial dissociative sticking probability of Nz on W(110) as a function of incident translational energy for angles of incidence between 0" and 60". The dashed line indicates the predicted behavior for 0i=60", based on normal energy scaling of the 0" data. Reproduced from H.E. Pfniir, C.T. Rettner, J. ~ , Phys. 85, 7452 (1986).

R.J. Madix, and D.J. Auerbach, J. Chem.

Molecular Beam Studies

63

[237], [238]] (Fig. 21). These studies also reveal that the saturation coverage of nitrogen increases with increasing incident translational energy. As discussed below, translational energy is effective in surmounting the activation barrier, in many cases the dissociative sticking probability increases sharply with increasing incident translational energy. However, the reaction probabilities do not show the abrupt threshold behavior expected from the above one-dimensional model. This result is not surprising if one considers the role of a distribution of impact sites, incident orientations, and the full multidimensional PES. Interestingly, methane dissociates on W(ll0) [[239], [240]], N i ( l l l ) [[241], [242], [243]], Ir(ll0)-(lx2) [244], and Pt(111) [[245], [246]] with an initial dissociative sticking probability which increases exponentially with increasing incident translational energy. Deviation from exponential behavior was seen for methane dissociation on Pt(111) at low incident translational energies [246]. The most dramatic example of this exponential behavior was observed for W(1 I0) on which the dissociation probability was found to increase by four orders of magnitude, from ca. 10"s to ca. 0.2 as the incident translational energy was increased from ca. 10 kJ/mole to ca. 100 H/mole by using seeding techniques and changing the nozzle temperature (Fig. 22). To account for this exponential dependence of So on incident translational energy, the tunnelling mechanism originally proposed for methane dissociation on W filaments was applied [[247], [248]]. This model considers a hydrogen atom tunnelling through a one-dimensional parabolic barrier for dissociative chemisorption. A barrier height of 115 H/mole was estimated by extrapolation of the data to a value of S0=1, assuming that the exponential dependence on translational energy holds over the range of higher translational energies. Barrier heights of 99, 106, and 121 kJ/mole result from the same analysis for Ni(111), IK110)-(lx2) and Pt(111), respectively. These barrier heights are a direct consequence of the exponential dependence of So on translational energy and are not necessarily reflective of a tunnelling process. The isotope effect observed for methane activation on W(110) and Ni(111) has been cited as additional evidence for the role of quantum mechanical tunnelling in the dissociative chemisorption of methane on metal surfaces. The dissociative sticking probability of CD4 was found to be an order of magnitude smaller than that of CH4. A classical kinetic isotope effect of 4.8 was calculated for the lowest nozzle temperature (640 K) used in the Ni(111) studies. In this calculation it was assumed that the transition state for dissociation is negligibly different from the adsorbed CH 3 species which results from dissociation. The vibrational frequencies found by EELS for the adsorbed CH 3 species formed via collisional activation was used to calculate the classical kinetic isotope effect [243]. Quantum mechanical tunnelling was invoked to explain the discrepancy between the magnitude of the observed isotope effect (a factor of ten) and the value predicted by the difference in zero point energy (a factor of 4.8). The order of magnitude difference in dissociation probabilities was attributed to the facile tunneling of light H atoms as compared to the heavy D atoms. However, controversy still surrounds tunnelling as a viable mechanism for methane dissociation on metal surfaces [[249], [250], [251 ], [252]]. Dissipation of incident translational energy to lattice phonons or internal degrees of freedom may contribute to the apparent activation barrier to dissociation. Recent trajectory calculations simulating

64

C.R. A r u m a i n a y a g a m and R,J. M a d i x

100

t

a

J

J

a

I

10-1

l

w

Methane/W (110)

~A/"'~Z//

10-2 .

n

°

n

t~ m O Q,.

"/

°

°

/

/I

10-3

/

v 03

A e

/x

/~

CH4 / "

10- 4 {~//

ct~ ~

*"

m

c-

/

10-5

/ /

/ /.

9

/

/

10-6

CD4

"°° /

15 ° • 30 ° CH 4 • 45 ° _ * 60 ° O 0 °, CD4 •

/

0

50

100

El = Eicos2~ i (kJ tool -1 ) Figure 22, Initial dissociative sticking probability of CI-L (solid symbols) and CD4(open symbols) on W(110) as a function of incident normal translational energy at a surface temperature of 800 K. The incident angles arc shown in the inset. A tunneling model was used to obtain the solid and dashed lines. Reproduced from C.T. Rctmer, H.E. Pfn~, D.J. Auerbach, Phys. Rev. Lett. $4, 2716 (1985).

Molecular Beam Studies

65

the direct coUisional activation o f N z on Re(O001) indeed show that dissipation to lattice phonons is an important aspect of the reactive collision [234]. The energy required to produce a reaction probability of unity may then exceed the static barrier height. In particular, exchange of translational energy to lattice phonons or rotational motion may occur during the reactive collision for highly activated processes such as n-alkane activation on Ni(100) [253]. Incident translational energy was shown to promote activated dissociation of n-alkanes on Ni(100) well below the C-H bond dissociation energies. No measurable adsorption of the alkanes was observed for incident translational energies less than 3010/mole at a surface temperature of 500 K. Above 30 IU/mole, the initial dissociative sticking probability for each alkane increased with increasing incident translational energy. Moreover, for a given incident translational energy, the reaction probability on the clean surface decreased with increasing molecular weight of the hydrocarbon, suggesting an apparent increase in the activation barrier with molecular weight, despite the fact that the C-H bond energy in methane is at least 25 H/mole greater than that in the larger molecules studied. The apparent increase in activation barrier with molecular weight of the alkane has been attributed to energy dissipation from the reaction coordinate during collision. Indeed, at translational energies well below those needed for reaction the angular distributions of the scattered alkanes molecules show a distinct trend: the direct inelastic component decreases with increasing molecular weight while the trapped-desorbed component increases with increasing molecular weight. These angular distributions demonstrate that the heavier alkanes dissipate kinetic energy more effectively upon collision than does methane, as is expected from simple classical theories due to both their higher mass and greater well depth. When the differing losses of translational energy expected in this series of alkanes due to transfer to the solid according to the hard-cube model is subtracted from the incident translational energy, the dependence of the reaction probabilities of all alkanes studied on initial translational energy collapses into a broad hand (Fig. 23). Similar experimental results were obtained for the direct collisional activation of n-alkanes on It(110)-(lx2) [244]. On Ir(110), however, direct collisional activation competes with precursor mediated dissociation (see section 4.1.2.6). Although internal energy excitations may also play a role in collisional activation, the above results suggest that translational energy dissipation makes a substantial contribution to the apl~arent activation energy for activated adsorption. Qualitatively similar effects have been found in theoretical treatments of N2 dissociation on iron [235]. Another manifestation ofdir~t collisional activation is the dependence of the saturation coverage on incident translational energy. For the direct dissociative chemisorption of N 2 on W(110), the initial dissociative sticking probability decreases to zero at a coverage of 0.25 ML for an incident translational energy of 5 k.l/mole [[236], [237], [238]], resulting in a p(2x2) N overlayer. However, at this coverage, the initial dissociative sticking probability is approximately 0.1 when the incident translational energy is increased to

ca.

100 kJ/mole. The saturation coverage increases from 0.25 ML at low incident

translational energies, to over 0.52 ML at an incident translational energy of 100 kJ/mole. These results

66

C.R. Arumainayagam and R,J. Madix

0. 5

,"

i

i

,

i

#

i

i

1

• mthon~

•

0.4

propmne m but~nQ

2

o _o

o

a.

i

NI(IO0) . TS= 500K

• m~thone

/~

0.3

ci

/~/C2 03

E

0.2

/

f

.

'

•

~

C4

u~ o

0.1 ~

aJ

0.0 O.

II, I 1 1 1 1 ~ 1 1 1 1 , I I I ~ 25. 50. 75. I00. 125. 150. 175.

200.

Normal K i n m t i c Energy (k2/mol)

0.5

--

o .o o ~.

I

• t. •

0.4

I

I

r

'II

I~

I II ,

I

I

~

"I

T

I

Ni ¢I00) T = 500 K

mot.hc3ne Q1~hc:n~

proponQ

5

• ~)utonQ 0.3

O_ r

•

,~u 0 . 2

a.

o:

•

•b

•~

0.1

•

i,I -- 0,0

•ol,

Dill ~ 0.

I 25.

I

f 50.

n

r 75.

i

;

i

100.

125.

,

i 150.

i

1

i

175.

I 200.

Kinetic Emergy - Enmr~y l.o~t (kJ/mol)

Figure

23.

The

initial dissociative sticking probability of C1-C4 alkancs on Ni(100) as a

function of incident translationaJ energy (top flgu~) and as a function of incident translational energy minus the calculated energy transferred to tim surface using the hard-cube mod¢l (bottom figure). Reproduced from A.V. Hamza and R.J. Madix, Surface Sci. 179, 25 (1987).

Molecular Beam Studies

67

show that the effective barrier height for dissociation increases with surface coverage. A qualitatively similar dependence on incident translational energy was found for the saturation coverage of 02 on W(110) in the case of direct collisional activation [[254], [255]]. The accessibility of incident translational energies far above the mean translational energy of a MaxweU-Boltzmann gas at room temperature, makes monoenergetic molecular beams an almost unique tool to study the dynamics of direct collisional activation. Studies of gas-surface chemical dynamics at high incident translational energies ( ,= 100 kJ/mole) not only permit the study of gas-surface systems whose dynamics are governed by a narrow domain of the potential hypersurface, but they also diminish effects due to the thermal motion of solid surfaces [256].

4.1.1.2 Dependence Oil incident

angle

The dissociative sticking probability for direct collisional activation has been found to change monotonically with the normal translational energy: S0(Er, 0i) = S0(F--rCOSZ0i,0") for most gas-surface systems, including ~ ( 1 1 0 ) [239], CHdNi(111) [243], and n-alkanes/Ni(100) [253]. These results are in accord with the one-dimensional barrier to dissociative adsorption introduced by Lennard-Jones [257], which assumes that the gas-surface interaction potential depends only on the distance between the surface and the incident molecule. However, the true gas-surface potential must be a multidimensional hypersurface, and hence, the origin of this dependence is not well understood. A notable exception to this dependence has been found for the activated adsorption of N2 on W(110) [[236], [237], [238]], for which collisional dissociation probability is independent of incident angle for a given incident translational energy: S0(Er,0) - S0(F-.r,0"). Formation of a temporary negative N2 ion, leading to multiple encounters with the surface, thereby scrambling the parallel and perpendicular motions, has been invoked to explain this scaling with total energy [[258], [259], [260]]. The affinity level of the incident N2 molecules falls below the Fermi level of tungsten as the dinitrogen approaches the surface, and an electron tunnels (harpoons) into the molecule, thereby forming a negative ion. Nonlinear forces facilitate the coupling of energy associated with motion parallel to the surface with normal translational energy via vibrational excitation of the nitrogen molecule. For this mechanism to be operative, it must occur on a time scale faster than dissipation of translational energy to surface phonons [[258], [259], [260]]. Hence, a dynamical precursor state, distinct from a classical equilibrated precursor state, may mediate the direct collisional activation of nitrogen on W(110). A recent theoretical study of N2 dissociation on W(ll0) also yields the total energy scaling observed experimentally [261 ]. The full gas-surface potential energy surface was modelled by a modified four-body LEPS function [262]. This particular functional form offers considerable flexibility in varying the morphological features of a PES such as position, barter heights, and the molecular adsorption well depth. The initial dissociative sticking probability of N2 on W(110) was calculated as a function of incident translational energy and incident angle using a stochastic classical trajectory method [263]. In agreement with the experimental results, the initial dissociative sticking probability was found to increase rapidly with incident translational energy in the range 29 kJ/mole to 120 kJ/mole before levelling off at

C.R. Arumainayagam and R.J. Madix

68

higher incident translational energy (Fig. 24). More importantly, the initial dissociative sticking probability was found to be independent of incident angle for angles less than 40" (the experimental initial dissociative sticking probability shows deviations from total energy scaling for incident angles greater than 45"). Examination of the contour plot of the PES (Fig. 25) reveals the reason for total translational energy scaling for N 2 dissociation on W(110). The independence on incident angle was attributed to two features of the PES : (1) the molecular well in the entrance channel with a depth of 10 H/mole and (2) the narrowness of the PES near the activation barrier. Since this narrow region restricts the suitable geometries for dissociation, a molecule may bounce several times on the surface before finding the right orientation for dissociation.

Such a mechanism facilitates interconversion of normal and parallel

momentum leading to total energy scaling. The authors suggest that the presence of the molecular well enhances the surface residence time, affording the incident molecule more time to find the optimum configuration to overcome the restricted barrier. The angular distribution of the scattered molecules was also calculated to confirm the validity of the theoretical methodology. Since scrambling of the translational energy components occurs for N 2 molecules dissociating on W(110), a similar mechanism may be expected to also govern the scattered molecules leading to a diffuse angular distribution. In agreement with experiments, however, the angular distribution of the direct inelastically scattered molecules was found to be lobular in nature with no evidence for a diffuse component. The absence of scrambling for direct inelastically scattered molecules was attributed to the fact that these molecules encounter the surface only once. In contrast, molecules which make several encounters with the surface near the barrier eventually dissociate. Dissociative chemisorption is irreversible both for the experiments and the calculations. Since reflection and dissociation were found to be distinct processes, extreme care must be exercised in extracting information regarding activation dynamics from angular and velocity distribution of scattered, unreacted molecules. Based on experimental data on the activated dissociative adsorption and associative recombination of hydrogen on copper surfaces, it has been claimed that a one-dimensional potential for dissociative chemisorption is an oversimplification. The mean translational energy ofD 2 molecules desorbing from Cu(111) and Cu(100) single crystal surfaces does not increase with increasing angle, in apparent contradiction to the predictions of the one-dimensional model for activated dissociation and detailed balance [264]. In addition, contrary to the one-dimensional van Willigen model [265], H 2 a n d D 2 molecules desorbing from Cu(110) and Cu(111) surfaces have been found to have a high degree of vibrational excitation [266]. However, it has been shown very recently that a one-dimensional multiple-state model can account for the above observations [267]. The complex nature of the PES is evident in a recent study in which translational energy has been shown to be effective in dissociating CO on Cu(110) [268]. The dissociation probability increases rapidly above a translational energy of about 18 kJ/mole, reaching a value of 0.2 at 28 kJ/mole. Unreacted CO scatters into both direct inelastic and nondissociative adsorption-desorption channels. Both the

69

Molecular Beam Studies

N2-WC 110) I

Theor

U

0

_

~~,,

.1 /,--j + o

So .01

/¢,,: /,,,,"~° /,,"~ iII'

E x p %. ,, o ° r-q 3 0 o 45o X

',,

I

+ 55 o

A

0 60°

~' .001

, .0

0.4

,

,

,

1.2

2.0

Kinetic energy (eV) Figure 24. Experim¢ntal and theoretical initial dissociative sticking probabilities of Nz on W(110) at various incident translational energies and incident angles. Reproduced from Abdelkader Kara and Andrew E. Depristo, Surfac¢ SCI. 193, 437 (1988).

70

C.R. Arumainayagam and R.J. Madix 0 LO

Lr3

LO

b

.E 0

..0 0

i tO f'~

LU I t.D ("4

p,.,

1. S

Z.I

BOND

2.7

LENGTH

3.3

3.9

4. S

(bohr)

Figure 25. Contour plot of the potential energy surface (PES) for dissociative chemisorption of N 2 on W(110). Reproduced from Abdelkader Kara and Andrew E. Depristo, Surface Sci. 193, 437 (1988).

Molecular Beam Studies

71

deviation of the maximum from the specular angle in the scattered flux and the width of the scattered lobe arc well described by hard-cube (one-dimensional) theory with no attractive well, taking the mass of the surface to be equivalent to two copper atoms. However, the nondissociative chemisorption channel appears to be governed by total energy, rather than normal energy, though the information is limited. These observations have been used to argue that scattering from a complex potential energy surface involving electron-bole pair creation for certain incident orientations leads to molecular chemisorption, while molecules with other orientations feel only a weak interaction and hence experience direct inelastic scattering. Based on the fact that CO does not dissociate on the non-roughened surfaces of Ni(100) [269], Ni(111) [270], and It(110)-(lx2) [271] even at incident translational energies in excess of 100 kJ/mole, it was suggested that translationally activated dissociation may occur predominantly in cases for which the rotational aniso~'opy is low, as is the case for CO/Cu(110). When the rotational anisotropy is high, as for CO on Pt(111) or Ni(100), rotational steering may preclude collisions with orientations favorable to dissociation.

4.1.1.3 Dependence on s u r f a c e t e m p e r a t u r e In direct collisional activation, the surface temperature produces only small changes in reaction probability. For the direct collisional activation of methane and ethane on It(110)-(lx2), the initial dissociative sticking probability was found to be independent of surface temperature between 500 and 1300 K at all incident translational energies (Fig. 26) [244]. For the direct collisional activation of N2 on W(100), found only at incident translational energies above 39 kJ/mole [272], the initial dissociative sticking probability was found to be independent of surface temperature 'at an incident translational energy of 485 kJ/mole. Methane activation on both Ni(111) [[241 ], [242], [243]] and Pt( 111 ) [245] was also found to be independent of surface temperature. However, another study of methane activation on Pt(111) found that surface temperature was equally efficacious as incident translational energy in surmounting the barrier to dissociation at low values of So [246]. This effect may be related to a change in the relative collisional velocity of surface and gas atoms and may be particularly important at low incident translational energies where reaction probabilities are small.

4.1.1.4 Dependence on incident vibrational energy A two- dimensional hypersurface shows complex dynamical effects not displayed by the simple one-dimensional models for dissociation. If the barrier to dissociation occurs in the entrance channel of the PES, translational energy is expected to be efficacious in surmounting the barrier [273]. However, if the barrier occurs at a point further along the reaction coordinate, translational energy may not particularly facilitate dissociation. Instead, since this late or exit channel barrier prevents facile separation of the dissociation fragments, the vibrational energy may promote dissociation [273]. Molecular beam studies of several gas-surface systems suggest that vibrational efficacy is at most equal to the translational efficacy. In most studies the incident vibrational energy has been controlled by changing the nozzle temperature at a fixed incident translational energy in order to measure vibrational efficacies.

C.R. Arumainayagam and R.J. Madix

72

#

~

0.7 0.6

n ° L Q-

0.5

~

0.4

o Ii 63 o 6g x 79 o 84

kJ/mol kJlmol kJ/mol kJlmol kJlmol

i

i

methane/Ir (I I0)

0.3 0.2 "

0.1

- - x

~

- - o

o.---o

x

x

x-o-i_

E - - 0 - - 0

0.0 I

i

200.

I

i

400.

i

~

0.7

~o 0 . 6

I

Ii 7B o I00 x 110

i

600.

I

i

800.

I

i

I

I

1200.

1000.

{K)

Temperature

Sur?oce

o

O--

0

I

J

i

kJlmol kJlmol kJlmol kJlmol

l

ethonQIlr

(I i0)

~o 0 . 5

- - x

~

x

x

o

o

•

J

0.3 o

0.2 ~

0.1 0.0 I

200.

t

I

400.

i

I

BOO. Sur~acQ

i

I

i

I

BOO. fOOD. Tempera~ur~ (K)

I

I

1200.

i

1400.

Figure 26. The initial dissociative sticking probability, So, for methane and ethane on Ir(110)-( 1x2) as a function of surface temperature. The slight increase in So for ethane for 11 kJ/mole near 300 K is due to the onset of napping mediated processes. Reproduced from A.V. Harnza, H.-P. Steinriick, and R.J. Madix, J. Chem. Phys. 86, 6506 (1987).

Molecular Beam Studies

73

Supersonic molecular beam studies of the dynamics of dissociative adsorption of CO2 on clean Ni(100) to form adsorbed CO and O demonstrate that vibrational energy, in ~ddition to translational energy, is effective in surmounting the barrier to dissociation [274]. At a nozzle temperature of 300 K (no vibrational excitation), the initial dissociative sticking probability increased from approximately 10.3 to 10"1 as the incident translational energy was increased from c a . 8 ld/mole to c a . 100 kJ/mole. Increasing the nozzle temperature to 1000 K causes the initial dissociation probability to increase by a factor of 2 to 10 at each translational energy across the entire range (Fig. 27). As discussed in the next section, rotational energy is not responsible for the increase in the dissociative sticking probability with increasing nozzle temperature. These results suggest that incident CO z molecules with one or more quanta of bending mode excitation dissociate with significantly higher probability than molecules in the ground state. Based on these observations, it was concluded that the transition state for CO 2 dissociation on Ni(100) must be bent with both the C atom and one ofthe O atoms interacting strongly with the surface. Vibrational energy in the bending mode permits relatively facile access to this bent transition state, thereby promoting dissociation. On the basis of microscopic reversibility CO2 produced by CO oxidation would also be expectedto proceed via a bent transition state. Although such experiments have not been done on Ni(100), vibrationally and rotationally excited CO2 is formed on platinum [275] and palladium [276] foils. Population distributions in the bending mode and the antisymme~c and symmetric stretches arc Boltzmann with characteristic temperatures much higher than the surface temperature. On palladium the vibrational excitation of the symmetric stretch far exceeds that of the other modes, whereas on platinum the modes arc characterized by the same vibrational temperature. The effectiveness of vibrational energy in surmounting the barrier for methane dissociation on W(110) [240] and Ni(111) [243] has also been demonstrated. The initial dissociative sticking probability of methane on W(110) increased by five-fold when the nozzle temperature.was increased from ca.

300

K to c a . 700 K for constant incident translational energies of 10.7 kJ/mole and 22.3 kJ/mole. Care was taken to ensure that the observed effects were not due to wider velocity distributions at higher nozzle temperatures. The vibrational efficacy, defined as AIn(S0)/AF~=, was found to be approximately equal to the translational efficacy for methane dissociation on W(ll0), assuming equal efficacy for all vibrational modes. In the case of methane activation on Ni(111), vibrational energy, predominandy in the v4 (umbrella mode) and v2 (bending mode), appears on average to be slightly more effective than translational energy in overcoming the barrier. The almost equal effectiveness of normal translational energy and vibrational energy in activating methane on Ni(111) has been invoked as evidence for deformation of the methane molecule prior to dissociation [243]. In this model, the role of translational energy is to distort the tetrahedral methane molecule into a pyramidal configuration during the impulsive collision. In the model the deformation of the methane molecule is taken to be identical to the excitation of the v2 and v4 vibrational modes of methane. Therefore, translational and vibrational excitation is assumed to result in the same motion of the nuclei in passing over the barrier along the reaction coordinate. Hence, translational energy and vibrational energy are equally effective in activating methane. In this picture, the barrier to dissociation

C.R. A r u m a i n a y a g a m

74

I

0

a n d R.J. M a d i x

E L (kd mol "m) 40 60 80 I

2O l

I

I

I

I

I

I

120

I00 I

I

I

|

1

1

oO~._--~ rn

i0-1

/ /

o

Or.

• IA

O

@

~TN(K)

10-2 0 or)

/./

/-

10-3

300

I000

•

0

0 °

•

r~

22.5 °

•

,,

45

8i

o

0

/ 10-40

t

5

I

I0

I

15

I

20

I

25

E,: E cosZE~ (kcal

I

30 mol -t)

Figure 27. The dependence of the initial dissociative sticking probability of CO2 on Ni(100) on incident translational energy, incident angle, and nozzle temperature at a surface temperature of 407 K. Reproduced from M.P. D'Evelyn, A.V. Hamza, G.E. Gdowski and R.J. Madix, Surface Sci. 167, 451 (1986).

Molecular Beam Studies

75

is a result of the energy required to deform the molecule into the proper configuration for the transition state. Deformation of the molecule moves the hydrogen atoms away, permitting stronger Ni-C attractive interaction. The last step in this model for methane dissociation involves the quantum mechanical tunnelling of the light H atom when the barrier becomes sufficiently narrow. Vibrational energy provided at most a small enhancement in the direct collisional activation of N2 on W(110) [277]. Nitrogen is well suited for this type of study since the single vibrational mode of N2 makes the analysis of vibrational efficacy straightforward. Moreover, it is possible to make molecular beams of N2 with significant amount of vibrational energy, because the nozzle can be heated to high temperatures without dissociating nitrogen [277]. The role of vibrational energy in the dissociative chemisorption of H2 on Cu surfaces has come under increased scrutiny recently. Early experiments indicated that translational energy facilitated a small increase in the probability for H2 dissociation on copper surfaces [278]. However, more recent work has shown that the reaction probability actually increases much more dramatically [[279], [280]]. Experiments involving vibrationally hot H2(vl) in translationally cooled seeded beams suggest that the vibrational energy, in addition to translational energy, is necessary to surmount the barrier to dissociation [279]. The effect of nozzle temperature as a function of incident translational energy for the activation of 1-12on Cu(110) is shown in Fig. 28. Since the fraction of incident H2 molecules in the fast excited vibrational state approximately equals the initial dissociative sticking probability, it was deduced that only hydrogen in the fhst excited vibrational state overcomes the barrier to dissociation. However, the molecules in the fast excited vibrational state must possess a minimum of

ca.

12 kJ/mole in incident

translational energy for dissociation to take place, demonstrating the interplay between incident vibrational and translational energies in surmounting the barrier to dissociation. In a separate study, the role of vibrational energy in the dissociation of H 2 on Cu(100) and Cu(111) was investigated by comparing the dynamics of dissociation of H2 and D2 [280]. To within an experimental error of-t- 10%, no difference was observed in the dissociation of H 2 and D2 as a function of incident translational energy and incident angle, suggesting that vibrational energy plays a minor role in the dissociation of 1-12. However, this negative result has also been rationalized by taking into account the higher proportion of molecules found in the D2 (vl) over H2 (v0 at a particular nozzle temperature [279]. A very recent analysis of all of the experimental data available on the activated adsorption of hydrogen on copper surfaces suggests that both the ground vibrational state and the fast excited vibrational state contribute significantly to the dissociation process [267]. In addition, it was found that these two vibrational components have significantly different translational energy thresholds [267]. Additional theoretical calculations also suggest that vibrational energy promotes the dissociation of hydrogen on Cu surfaces. Assuming a two dimensional potential energy hypersurface for the interaction of H2 with a Cu(110) surface, the addition of the incident translational energy, zero point energy, and the vibrational excitation energy yields an overall barrier height measured from the bottom of the physisorption well of approximately 91 kJ/mole [279]. This high barrier to dissociation is in agreement with predictions ofjellium [281] and small-cluster calculations [[282], [283], [284]] which

C.R. Arumainayagam and R.J. Madix

76

0

2~

(DI ~t • f O ~ j ' ~ " -- " " ~ -- - ~

0

.....

"""

"

~

0

0

U

":o I

E.~. (meV)

Figure 28. The dissociative sticking probability ofH 2 on Cu(110) as a function of incident normal translational energy. The pure hydrogen beam results (open circles and solid line) were obtained by varying the incident translational energy using different nozzle temperatures. The He sceAed results were obtained atfixed nozzle temperatures of 1150 K (solid circle), 1100 K (solid squares), 1085 K (solid diamonds). ReproduceA from B.E. Hayden and C.L.A. Lamont, Phys. Rev. Lctt. 63, 1823 (1989).

Molecular Beam Studies

77

estimate the barrier height to be between 80 and 200 k J/mole. Further, as expected, this barrier is larger than that for H~ dissociation on transition metal surfaces [285] which do not have a filled d-band as does Cu. Moreover, the high activation barrier deduced from this experimental study agrees with the high mean translational energy for H 2molecules desorbing from Cu surfaces [264]. In Addition, the conclusion that H z molecules in the first vibrationally excited state dissociate readily on Cu(110) is in agreement with previous measurements which show that H2 molecules desorbing from Cu surfaces are vibrationally hot [266]. A model potential energy surface for H= dissociation on Cu surfaces, constructed from electronic structure calculations for Cu2H2 clusters, shows that vibrational energy is efficacious in overcoming the barrier to dissociation despite the fact that there is no discernible "late" harrier [286]. Calculations show that vibrational-translational energy transfer at the entrance channel strongly enhances dissociation. Even molecules with an incident wanslational energy much below the nominal harrier height may "bootstrap" their way up the barrier. The mechanism involves the continuous conversion of vibrational to translational energy all along the reaction coordinate. Recent classical, semiclassical, and full quantum mechanical calculations also show the efficacy of vibrational energy in promoting hydrogen dissociation on Cu surfaces [287]. Tunnelling in the vibrational coordinate was shown to be the primary pathway to dissociative chemisorption. 4.1.1.5 D e p e n d e n c e o n i n c i d e n t r o t a t i o n a l e n e r g y . Rotational energy is not expected to facilitate activated dissociative chemisorption because rotational motion is unlikely to couple effectively with motion over the dissociative barrier. Experimental evidence exists to support this hypothesis for Hz dissociation on Cu. The temperature corresponding to the mean rotational energy of both H z and I)= desorbing as the result of associative recombination from Cu(110) and Cu(111) is only slightly less than the surface temperature [266]. By invoking microscopic reversibility, it was concluded that rotational energy was not effective in surmounting the barrier to dissociation. Since only approximately 20% rotational cooling occurs for H z in hot nozzles, it was necessary to invoke the above results to discount the possibility ofrotadonal energy assisting dissociation [279]. Using a rotationally hot quasi-effusive molecular COz beam, gas phase rotational excitation was found not to facilitate CO 2 dissociation on Ni(100) [274]. Since rotational cooling is negligible for an effusive beam, the rotational energy in the incident molecules was 8.3 Ll/rnole at a nozzle temperature of 1000 K. The corresponding value for a 300 K supersonic nozzle beam is 1.2 H/mole. At the same incident normal translational energy, no difference in reactivity was observed between a supersonic beam and a quasi-effusive beam, suggesting that rotational energy is not efficient in surmounting the barrier for CO 2 dissociation on Ni(lO0).

78

C.R. Arumainayagam and R.J. Madix

Nevertheless, a "centrifugal dissociation mechanism" involving rotational energy has been proposed as the result of combined molecular beam and theoretical studies for 12dissociating on a chemically inert insulator single crystal, MgO(100) [[288], [289], [290]]. Since conversion of incident translational energy to rotational energy during the impulsive collision produces dissociation, the dissociation probability increased from essentially zero to 0.4 as the incident translational energy increased from 97 kJ/mole to 970 kJ/mole. Even though time-of-flight measurements of the direct inelastically scattered non-dissociated I2 molecules displayed a 40% translational energy loss, calculations using a rigid surface model reproduced the experimentally determined dissociation probabilities over the entire incident translational energy range. This observation was explained by the fact that the torque for rotational excitation acts slightly before the excitation of the solid. Hence, for a very brief time interval, on the order of tens of femtoseconds following collision, the solid acts as though it was rigid. Hence, it was not necessary to consider the motion of many solid atoms for the centrifugal dissociation mechanism. 4.1.1.6 I d e n t i f i c a t i o n a n d m a n i p u l a t i o n of d i s s o c i a t i o n p r o d u c t s For the dissociation of diatomic species the product is evident, but in only one case has the product of dissociation of a polyatomic molecule been directly examined. Chemical identification of the species produced as a result of dissociative adsorption is thus essential. In this case high resolution electron energy loss spectroscopy (HREELS) has been used to characterize the adsorbed product of methane dissociation on a Ni(111) surface [[41], [242]]. The HREELS spectrum of the adsorbed species resulting from the dissociation of methane at an incident translational energy of 71 kJ/mole at a surface temperature of 140 K is shown in Fig. 29. The low surface temperature precluded thermal decomposition of the nascent dissociation product. Based on the HREELS spectrum and previous studies of metal alkyls [291], and NH 3 adsorbed on Ni(111) [292], the dissociation products were identified as an adsorbed methyl radical and adsorbed H atoms. The modes were assigned as the Ni-CH3 stretch (370 cm-l), the -CH3 symmetric deformation mode (1220 cml), and the "soft" C-H stretching mode (2660 cm'~). These studies demonstrate the utility of supersonic molecular beam techniques to produce surface intermediates not easily made by standard UHV techniques. Since activated dissociation often requires energies far higher than the average energy available in a thermal gas, new adsorbed species can be formed by molecular beams with incident translational energies sufficiendy high to overcome the barrier to dissociation [293]. The synthesis of methyl radicals permitted the study of their stability and reactivity by monitoring the high resolution electron energy loss spectrum as a function of surface temperature [[293], [294], [295]]. The methyl radicals adsorbed on Ni(lll) are stable below a surface temperature of 150 K. Above this temperature, the methyl radicals dissociate to form CH, which subsequently recombines to form adsorbed C~H2 [296]. If a sufficiently high coverage is achieved, the C~H2 trimerizes to form benzene as evidenced by the EELS spectrum being similar to the one observed when benzene is adsorbed

79

Molecular Beam Studies I

4.000

I/') LLJ C:)

I

I

I

I

I

1220

3.500

e--I

X (..J w tn

3.000 2.500

(I) I-Z

2.000

0 0

1.500

I 385 1320

I

2655 261o.1273o

1.000 0.500

0.000 -50O. O

i 0.0

i

I

500. 0

I

I

100(). 0

) 5no. 0

I

2D00. 0

I

;

2500. 0

3000. 0

3500.0

ENERGY LOSS Figure 29. HREELS spectrum of CH3 adsorbed on Ni(111) measured at the specular angle. The methyl radicals were formed by colliding CI~ at normal incidence with an incident translational energy of 71 kJ/molc on a Ni(111) surface at 140 K. Reproduced from S.T. Ceyer, Langmuir 6, 82 (1990).

80

C.R. Arumainayagamand R.J. Madix

on N i ( l l l ) [297]. Furthermore, benzene desorption at a surface temperature of 425 K was detected mass spectrometrically. Molecular acetylene adsorbed on Ni(ll 1) has been previously shown to trimerize to form benzene [298].

4.1.2 Precursor-mediated dissociation In trapping or precursor mediated dissociation, the gas molecule loses sufficient kinetic energy to fast trap and accommodate on the surface. Once trapped, the molecule may achieve a favorable orientation fordissociation or diffuse to a favorable site for dissociation. Precursor mediateddissociation may be the dominant channel to dissociative chemisorption even if the probabilities are low, for the following reasons. Although direct collisional activation may occur with high probability at high incident translational energies, only a small fraction of a Maxwell-Boltzmann gas at room temperature may possess sufficient energy to overcome the barrier for direct dissociation.' In contrast, the barrier to precursor mediated dissociation may be significantly lower. Moreover, due to the statistical preponderance of molecules possessing energies low enough to trap, precursor mediated dissociation may be an important route to dissociative chemisorption.

4.1.2.1 Dependence on incident translational energy If dissociation via a precursor mediated pathway occurs after the molecule has fully accommodated to the surface, the dynamics of precursor mediated dissociation is usually assumed to be governed by the dynamics of molecular adsorption into the precursor state. Hence, as in the case of weak molecular adsorption, the precursor mediated dissociation probability is expected to decrease with increasing incident translational energy. This trend has been demonstrated for the precursor mediated dissociation of C-.j-I8and C4Hl0 Ir(110)-(Ix2) [244], N2 on W(100) [272], 1-12on Ni(997) [299], 02 on Pt(111) [[300], [301]] and C-aI-l~on Ir(ll0)-(lx2) [302]. Less convincing evidence has been presented for the precursor-mediated dissociative adsorption of 02 on W(110) at low incident translational energies [ [254], [255]]. A notable exception to the above trend has been recently found for the dissociative chernisorption of N2 on Fe(111) [[303], [30411. Even though dissociation proceeds via a precursor state (0t-N2 state), as evidenced by the decrease in the dissociative sticking probability with increasing surface temperature, the initial dissociative sticking probability increases by approximately five orders of magnitude as the incident translational energy increases from 9 kJ/mole to 420 kJ/mole. A distribution of barriers to the molecular chemisorption of N2 into the ct-N2 precursor state was invoked to explain this observation. Simply put, adsorption into the precursor state appears to be activated.

4.1.2.2 Dependence on incident angle As in the case of weak molecular adsorption, the precursor mediated dissociative sticking probability is expected to increase with increasing incident angle such that adsorption depends only on the incident normal translational energy in a one-dimensional picture. However, for Nz/Fe(111) the observed scaling lies between normal energy and total energy for precursor mediated dissociation [[303], [304]].

Molecular Beam Studies

For N2 dissociating on W(100)

81

viaa precursor mechanism, the adsorption probability is independent of

incident angle [272]. These studies again point out the need for calculations which take account of the full dimensionality of the problem. 4.1.2.3 D e p e n d e n c e o n incident vibrational e n e r g y . The role of vibrational energy in the precursor mediated dissociation of N 2 on Fe(111) has been studied at nozzle temperatures of 300 K and 2000 K [[303], [304]]. The average vibrational efficacy was calculated by performing a weighted sum over all vibrational levels while taking into account the measured translational energy spreads. The vibrational energy was found to be only half as efficient as incident translational energy in facilitating dissociation. This relatively low vibrational efficacy was rationalized by a potential barrier in the entrance channel which impedes access to the precursor state to dissociation. 4.1.2.4 D e p e n d e n c e o n s u r f a c e t e m p e r a t u r e In con~ast to direct coUisional activation where the initial dissociation probability is independent of surface temperature, precursor mediated dissociation may display a strong dependence on surface temperature. The effect of surface temperature may manifest itself in two distinct ways: (1) the trapping probability into the precursor state may depend on surface temperature and (2) the ratio of the rate of desorption to the rate of dissociative chemisorption may change with surface temperature. The dependence of the initial dissociative sticking probability, So,

via the precursor mechanism may be

represented as follows: °dec

(22)

So = kc + kd where k~ is the rate constant for going from the precursor state to the chemisorption state, lq is the rate constant for desorption from the precursor state, and (x is the trapping probability into the precursor state [305]. The latter quantity may depend on incident translational energy, incident angle, and surface temperature. The above expression can be rewritten as: Vd -AE So=tX(Er,O~,Ta)[l +-~ex~(--~, )] -1

(23)

where v,/vo is the ratio of pre-exponentiais for desorption and chemisorption from the precursor state. I f ~ is independent of surface temperature, a plot of ln[(txlS0)-l] as a function ofT, yields a straight line with a slope of AE = Ed-Ec, where Ea and Ec are the activation energy for desorption and dissociation from the precursor state, respectively.

82

C.R. Arumainayagam and R.J. Madix

The precursor mediated dissociative chemisorption of N z on tungsten has been investigated intensively to uncover the origin of the surface temperature dependence of the dissociation probability. Studies based on the coverage dependence of the adsorption probability over a range of surface temperatures disagree on the dynamical origin of the observed decrease in sticking with increasing surface temperature. While one study attributed the reduction to a decrease in the trapping probability with increasing surface temperature [306], other studies accounted for the results by assuming that the trapping probability is invariant with surface temperature [[39], [307], [308]]. The latter studies attributed the surface temperature dependence to the desorption channel being favored over the chemisorption channel at higher surface temperatures. Based on the angular and velocity distribution of Nz scattering from a

polycrystalline tungsten surface, it was suggested that the surface temperature dependence was due to the decrease in the trapping probability with increasing surface temperature [309]. Supersonic molecular beam techniques have been recently utilized to distinguish the two processes in the precursor-mediated dissociation of N2 on a single crystal of W(100) [272]. The initial dissociative sticking probability (So), and the angular and velocity distribution of the scattered molecules from the clean surface were measured over a wide range of surface temperatures. If the trapping probability into the precursor state is 0~, the trapped-desorbed flux component I~ is given by: I J I = = ct - So, where I ~ is the incident flux, and the direct-inelastic component (I~.) is given by ~ - =

= 1 - o~. Hence the total

scattered flux ( I ~ is given by : I ~ / I = = Ia/I~ + I J I = = 1 -So. Therefore, if ¢t is independent of surface temperature, I~. will remain constant with surface temperature and I~ will reflect the change in So. The trapped-desorbed (cosine) flux distribution for N2 scattered from a W(100) surface increases as the surface temperature is increased from 150 K to 1600 K (Fig. 30). The decrease in the initial dissociative sticking probability from 0.60 to 0.05 as the surface temperature is raised from 150 K to 1600 K was used to calculate the total scattered flux as a function of surface temperature. Based on the difference of the two curves, the direct-inelastic component was estimated as a function of surface temperature, and was found to be rather insensitive to surface temperature, demonstrating that the trapping probability into the precursor state is at most weakly dependent on surface temperature. Hence, it was concluded that the primary effect of surface temperature on the precursor mediated dissociation of N2 on W(100) is to diminish the fraction of precursor molecules which dissociatively chemisorb, by facilitating the desorption of precursor state molecules at higher surface temperatures.

4.1.2.5 Dependence on s u r f a c e c o v e r a g e For dissociation via a precursor mechanism, the dissociative sticking probability may be found to be insensitive to surface coverage, in contrast to dissociation via direct collisional activation. For example the precursor mediated dissociation probability of N 2 on W(100) at an incident translational energy of 2.9 kJ/mole, an incident angle of 60", and a surface temperature of 200 K remains constant up to a coverage of 0.2 atomic monolayers, where 1ML = 1 x l0 is atoms/cm z, the density of W atoms on the surface. The effect was found to be even more pronounced at lower surface temperatures. Moreover, in contrast to the direct collisional activation of Oe and N 2 on W(110), where the saturation

83

Molecular Beam Studies

I

I

I

'

I

'

N2/W(100) Ei = 0.088 eV 1.0 - Oi=6o ° ~

'

I

I

Scattered !

0.8

_E 0.6

/

/

Inelastic Component

_

0.4 0.2

0.0 0

I

I

400

t

I

I

I

I

I

800 1200 1600 2000 SurfaceTemperature(K)

Figure 30. The total scattered flux, thv cosinv componvnt of this flux, and the direct inelastic component arc plotted as a function of surface temperature for the angular distribution of N 2 scattered from W(100) for an incident translational energy of 8.5 kJ/mole and an incident anglv of 60". Reproduced from C.T. Rettncr, E.K. Schwizcr, H. Stein and D.J. Aucrbach, Phys. Rcv. Lctt. 61, 986 (1988).

84

C.R. Arumainayagam and R.J. Madix

coverage increases with incident translational energy, the saturation coverage of N2 on W(100) was found to be independent of incident translational energy, consistent with precursor mediated dissociation; i.e.,

incident translational energy is not available as a driving force in the reaction.

4.1.2.6 Complex dissociation pathways Translationally activated, unactivated, and precursor-mediated dissociation were all observed for n-alkanes dissociating on Ir(110)-(Ix2) (Fig. 31) [244]. A low energy direct channel for dissociation was identified for all alkanes except methane. At high surface temperatures and incident translational energies below 60 kJ/mole, the initial dissociative sticking probability shows the following trend: butane > propane > ethane > methane. For certain ranges of surface temperature and incident translational energy, collisional activation v i a this mechanism is independent of both surface temperature and incident translational energy (Fig. 31(a)). This behavior demonstrates dissociation v i a passage over a barrier lower than 10 kJ/mole, the lowest translational energy employed in this study. At lower surface temperatures and/or incident translational energies trapping dominated processes occur (Fig. 31 (b)). For incident translational energies less than 100 kJ/mole, the initial dissociative adsorption probability of propane and butane increased to 0.6 with both decreasing surface temperature and decreasing translational energy of the incident alkane, indicating the importance of trapping into a precursor state in the activation process. Under these circumstances, the dissociation probability for butane increases by a factor of 3-4 above that observed for the low energy direct channel. At higher temperatures, however, the lifetime in the trapped state is too short for trapping to increase the reaction probability. Finally, at the highest translational energies studied, dissociation proceeded by direct translational activation via a second reaction channel with a higher barrier for all four alkanes. This channel dominates at the highest translational energies, and the order of reactivity of the alkanes is reversed from that observed for translational energies below 60 kJ/mole. Qualitatively similar behavior has also been seen for other dissociative gas-surface systems. For nitrogen dissociation on W(100) [272], a precursor mediated dissociative pathway was dominant at incident translational energies below ca. 20 kJ/mole, while a direct mechanism was operative at incident translational energies above 50 kJ/mole up to the highest incident translational energy studied (500 kJ/mole). As the incident translational energy is increased, a similar transition from precursor mediated dissociation to direct collisional activation has been suggested for oxygen adsorption on Pt(111) [[300], [301]]. The adsorption probability at a surface temperature of 200 K at first falls from 0.33 to 0.16 as the incident translational energy is increased from ca. 7.8 kJ/mole to 14.6 kJ/mole, and then rises to 0.28 for incident translational energies above 58 kJ/mole. Surprisingly, a more recent molecular beam study found that at surface temperatures below which oxygen is not thermally converted to the atomic state (T, < 150 K), oxygen adsorption on Pt(111) is non-dissociative over the entire range of incident translational energies from ca. 10 kJ/mole to c a 100 kJ/mole [310]. Based o;1 these and other results it was concluded that direct collisional activation was not an important mechanism at these incident translational energies. Rather, it was postulated that dissociation occurs via two distinct mechanisms which involved

Molecular Beam Studies 0.5

i

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Ir(llO) TS - 970 K

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Figure 31. (a) The initial dissociative sticking probability for each C,-C4 alkane on Ix(110)-(lx2) as a function of incident ~:anslational energy at a surface temperature of 970 K. The two points near 115 k.l/mole for ethane are for velocity determinations by phase lag and waveform time-of-flight. (h) The initial dissociative sticking probability of butane on Ix(110) as a function of surface temperature. Symbols correspond to data at the incident wanslational energies listed. Reproduced from A.V. Hamza, H.-P. Steinrfick, and RJ. Madix, J. Chem. Phys. 86, 6506 (1987).

86

C.R. Arumainayagam and R.J. Madix

two different initial steps: (1) trapping into a weakly bound state and (2) adsorption into a more surongly bound molecular chcmisorption state. Since tbe sticking probability increases with incident translational energy, it was concluded that adsorption into the molecular chcmisorption state is activated. 4.1.3 C o l l i s i o n - i n d u c e d d i s s o c i a t i o n o f a d s o r b e d s p e c i e s Molecules with high kinetic energy impinging on an adsorbatc-covcmd surface cause dissociation of adsorbed species [[311], [312]]. In the collision-induced dissociation of methane, a monolaycr of methane weakly adsorbed on Ni(111) at 46 K was bombarded by a beam of inert gas. Although the cross-section for coLlision-induced dissociation was found to increase with incident translational energy, the dependence on incident angle showed deviations from normal energy scaling and has be.on attributed to the range of impact parameters in the initial collision. A hard sphere collision model shows good agreement with experiments (Fig. 32). Based on these molecular beam studies, it has been claimed that collision-induced dissociation of adsorbatcs has significant implications for catalysis because at atmospheric conditions the adsorbatc covered catalyst is continually bombarded by a large flux of high energy molecules. 4.2 C h e m i c a l r e a c t i o n s a t s u r f a c e s Molecular beam techniques have made significant contributions to the understanding of the kinetics and mechanisms of elementary chemical reactions catalyzed by the surface under study. An extensive review of this subject was published in 1984 [3]. In the reactive scattering of molecular beams, the flux of molecules to and from the crystal arc collisionlcss, ensuring that all tbe chemical reactions result only from tbe interaction of the molecule with the surface and other adsorbatcs [313]. In addition to the information that could bc obtained by using standard procedures, molecular beam studies have clearly shown, for example, the dominance of the "Langmuir-Hinshclwood" mechanism in oxidation reactions [314]. Most of the reactive studies have been done by using periodic modulation of the reactant beam to impart phase information to tbe reactant molecules. This technique is referred to as molecular beam relaxation spectrometry (MBRS) [[315], [316], [317], [318], [319], [320], [321], [322], [323], [324]]. In such studies, the intensity I0 of the primary beam is modulated periodically, normally to produce a square wavcform. As the result of the surface reaction, the wavcform of each of the products emitted from the surface, characterized by recording the phase lag, ~0i, and tbe amplitude Ii of its i = Fourier component, contains the information on the reaction mechanism and the associated rate constants. For example, for a simple reaction mechanism involving a fh-,st-ordcr adsorption-dcsorption process with a sticking probability independent of coverage and temperature, the rate constant for dcsorption and the reaction probability arc obtained by varying the beam modulation frequency and/or the surface temperature [3]. This analysis can bc extended to more complex processes such as sequential reactions, paraUcl reactions, and surface diffusion. The analysis of nonlinear surface reactions such as adsorption

87

Molecular Beam Studies

J

I

I

I

I

0L

0. i 0 0 0

C~

o< 0.0100 Es (kcol/mole)

0.0010

15

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55

ENAr (kco I/too l e ) Figure 32. The cross-section for coMsion-induced dissociation of n~thanc weakly adsorbed on Ni(111) at 47 K as a function of the incident normal translational energy of Ar. Methane coverage is 0.3 monolaycrs. The following symbols represent the data obtained at differenttotal incident translational energies: circles (51.8 kcal/molc), diamonds (47.1 kcal/molc), wianglvs (42.3 kcal/mole), squares (37.2 kcal/molc), crosses (32.5 kcal/molc), hexagonals (27.8 kcal/molc). The solid lines arc the result of the model calculations. Reproduced from J.D. Beckcrlc, A.D. Johnson, Q.Y. Yang and S.T. Coyer, J. Chem. Phys. 91, 5756 (1989).

88

C.R. Arumainayagam and R.J. Madix

involving a coverage dependent sticking probability may require modification of the experimental conditions to lincarize the kinetic equations. An alternate approach involves the lincarization of the second order differential equations by making suitable approximations [324]. Recently, MBRS techniques have been used to study the kinetics and mechanism of CO oxidation on Rh(111) and related dynamical features [325]. Pseudo-fast-order kinetics was ensured by exposing the surface to a high continuous flux of oxygen molecules while keeping the incident modulated CO flux low in order to maintain a nearly constant oxygen adatom concentration. Time of arrival waveforms for the product CO= were obtained at various temperatures, modulation frequencies, and angles from the surface normal. The transform function of the observed signal, S(co), is given by the following expression: 5

s(o~)= FI f,(co) (i =5)

(24)

where the f~((o) represent the transforms of the disl~hution functions describing the five contributions

to the time of a_rdva]: (1) time of flight of CO from the chopper to the crystal, (2) the residence time of CO on the surface prior to reaction, (3) the residence time of CO2 on the surface prior to desorption, (4) the flight time of CO= from the crystal to the ionizer, and (5) the flight time of the CO2" ion prior to detection [326]. In these experiments the fast and last contributions were determined experimentally, while the third was assumed to be negligible because of the low binding energy of CO= to the surface and the high surface temperatures employed in the experiments. The fourth contribution was estimated by assuming that the desorbing CO2 molecules had a Maxwell-Boltzmann distribution of velocities at the surface temperature.

An Arrhenius plot of the CO surface residence time yielded an activation

energy of 103 + 2 kJ/mole for the CO oxidation reaction; the pre-exponential was calculated to be 2 + 1 x 10.3 cm=sec1. The angular distribution of CO2 was sharply peaked along the surface normal and at 550 K was described by the functional form 0.65 cos~20 + 0.35 cos 0, where the angle 0 is measured with respect to the surface normal. In a previous study of CO oxidation on Pt(111), the cos 0 term was attributed to CO= which accommodated with the surface prior to desorptign, and the sharply peaked term was assigned to CO= molecules which desorbed directly with higher velocities [327]. The velocity distribution of CO2 on Rh(111) at surface temperatures between 700 and 1000 K, however, do not show a bimodality at any angle [328]. Furthermore, even at 60" where the sharply peaked term should be negligible compared to the thermalized cosine channel, the velocity distribution was decidedly nonMaxwellian and the translational energy was substantially above that expected for CO= emitted at the surface temperature. Hence it was concluded that the observed angular distribution was not due to two distinct physical processes. In addition to studying the kinetics of CO oxidation on other metal surfaces such as Pt(111 ) [ [327], [329]] and Pd(111) [314], MBRS has also been successfully utilized to uncover the kinetics of several

MolecularBeam Studies

89

other surface reactions. The reaction of chlorine has been studied on liquid metal surfaces [[330], [331], [332]]. In addition, the reaction of oxygen, ozone, chlorine, and bromine with semiconductor surfaces has also been investigated using MBRS techniques [[333], [334], [335], [336]].

5 Conclusion The rapid growth in molecular beam technology now provides information complementary to that obtainable with LEED, AES, XPS, UPS, EELS, SIMS, NEXAFS and other established surface science probes. During the last six years there has been enormous growth in the use of beams to study the dynamics of gas-surface collisions. The surface sensitivity of molecular beam techniques is probably higher than all but SIMS of the above mentioned probes and their versatility as a surface analysis tool is perhaps unmatched. In the near future, one can expect a proliferation of molecular beam studies of gas-surface potentials and the chemical dynamics of catalytically important heterogeneous chemical reactions.

Acknowledgement The authors gratefully acknowledge the support of the Department of Energy (grant DE-FG0386ER13468) for our gas-surface molecular beam work.

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