Reactive scattering from solid surfaces

Surface Science Reports 3 (1984) 413-495 North-Holland, Amsterdam

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REACTIVE SCATTERING FROM SOLID SURFACES M a r k P. D ' E v e l y n a n d R o b e r t J. M a d i x

Department of Chemical Engineering, Stanford University, Stanford, California 94305, USA Manuscript received in final form 21 August 1984

Molecular beam scattering studies of reactive processes on solid surfaces have been conducted for two decades. This article presents an overview of reactive scattering, together with a brief description of the experimental requirements and a discussion of the data analysis in molecular beam relaxation spectrometry. A critical review is given of the reactive scattering studies performed to date of several catalytic reactions on metal surfaces: adsorption and desorption of hydrogen, CO and NO and the oxidation of CO and hydrogen. Also reviewed are several additional catalytic reactions, and reactions between gases and solids to form volatile products. Emphasis throughout is on the insights into the kinetics and dynamics of elementary surface reactions obtainable using molecular beam techniques.

0167-5729/84/$29.00 © 1984 N o r t h - H o l l a n d (North-Holland Physics Publishing Division)

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Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

415

1.1. R e a c t i v e processes at surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

416

2. E x p e r i m e n t a l considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

418

3. D a t a analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

421

3.1. First o r d e r reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

422

3.2. Sequential or parallel reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

424

3.3. C o u p l e d diffusion and reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

425

3.4. N o n l i n e a r reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

428

4. Catalytic reactions on metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

431

4.1. H 2 - D 2 exchange and h y d r o g e n r e c o m b i n a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

432

4.1.1. A n g u l a r and velocity distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

432

4.1.2. R e c o m b i n a t i o n kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

437

4.2. A d s o r p t i o n and desorption of C O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

441

4.3. A d s o r p t i o n and d e s o r p t i o n of N O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

445

4.3.1. Kinetics of adsorption and d e s o r p t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

446

4.3.2. Kinetic m o d e l for a d s o r p t i o n and desorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

448

4.3.3. Velocity and internal state distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

450

4.4. A c t i v a t e d a d s o r p t i o n of N 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

457

4.5. C O oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

457

4.5.1. M e c h a n i s m and kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

459

4.5.2. A n g u l a r , velocity, and internal state distributions in the CO2 product . . . . . . . . . . . . . . . .

461

4.6. H y d r o g e n - o x y g e n reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.7. D e c o m p o s i t i o n reactions of m o r e c o m p l e x molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

469

5. G a s - m e t a l reactions at e l e v a t e d t e m p e r a t u r e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

472

5.1. G e n e r a l m e c h a n i s m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

472

5.2. R e a c t i o n s with halogens, o x y g e n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

473

5.2.1. Product distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

474

5.3. M o d u l a t e d b e a m studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

476

6. R e a c t i o n s of n o n m e t a l s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

477

6.1. Silicon and g e r m a n i u m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

477

6.2. I I I - V s e m i c o n d u c t o r s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

483

6.3. G r a p h i t e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

486

7. S u m m a r y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Acknowledgements ................................................................................................

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Glossary of a b b r e v a t i o n s and symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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References ...........................................................................................................

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I. Introduction

The subject of reactive scattering of gases from solid surfaces conceivably encompasses all studies of heterogeneous reactivity. In this review, however, the term is restricted to distinguish gas-solid interactions in which reactant molecules incident on the solid can experience only a single encounter with the surface, being trapped or reflected, and the products formed are detected prior to secondary surface encounters. Under such ideal circumstances it is possible to study in detail the effect of the chemical and dynamical states of reactants on the overall reactivity and selectivity of heterogeneous reactions. Furthermore, reactants and product species such as free radicals or atoms can be studied. Whereas the conditions employed to study reactive scattering allow such detailed studies, they generally preclude the study of heterogeneous reactions of a highly complex nature which, for example, require a number of successive collisions to form products or which occur with collisional probabilities less than about 10 -4. The value of such studies is therefore primarily to provide basic understanding of heterogeneous chemical reactivity and reaction dynamics for well-chosen model systems. With this foundation, extrapolation to more complex reaction conditions may be possible. The dynamical state of the gaseous reactant is normally controlled by the use of molecular beams. A molecular beam provides a spatially controllable reactant supply as well as a convenient means for controlling the gas temperature or, separately, the velocity and the internal energy states of the molecules [1, 2]. The use of molecular beams also allows study of surface reactions without mass transfer limitations or secondary surface reactions. Low pressure collisionless flow assures that gas-phase diffusion of reactants or products cannot limit the reaction rate and that the surface interaction itself dominates the process. For studies of reaction dynamics, near collisionfree conditions also minimize complications due to intermolecular relaxation effects. In this review we will discuss reactive scattering with particular emphasis on its contribution to the current understanding of elementary reaction steps in catalytic reactions and high temperature gas-solid reactions. Most of the work described below employs periodic modulation of the reactant beam to impart phase information to the reactant molecules. Coupled with mass spectrometric detection, this technique is referred to as molecular beam relaxation spectrometry (MBRS). In order to facilitate a clear understanding of the principles involved, brief discussions of the experimental considerations and of the analytical procedures commonly employed are included. In addition, the discussion of the current state of the field utilizes examples from the literature which clearly illustrate the connection between theory and experiment. The characterization of reactive scattering at solid surfaces is still a relatively new area of chemical dynamics, and the level of sophistication of both experiment and theory in reactive gas-surface scattering is considerably less advanced than corresponding work in gas phase scattering. Nonetheless, accurate kinetic infor-

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mation has been obtained for several systems and dynamical information is also becoming available. Angular and velocity distributions have been measured for several reactive systems, and within the past four years several experiments have probed the internal states of scattered or desorbed molecules. The experimental determination of surface reaction dynamics is a particularly exciting development in surface reactivity, as it promises a fruitful interplay with theory in the elucidation of reactive surface processes at the microscopic level. In brief, studies of reactive scattering offer a wealth of information which can be used to gain a deeper understanding of heterogeneous reactivity. The interested reader is referred to several other reviews [3-6] of molecular beam surface scattering. 1.1. R e a c t i v e p r o c e s s e s at surfaces

The sequence of events in reactive scattering is (1) chemisorption of reactant(s), (2) surface migration of reactant(s), (3) reaction(s) on the surface to form product(s), (4) surface migration of product species, and (5) desorption of product(s). In some cases, as will be discussed below, (6) diffusion and solution of reactants in the bulk of the material is important also. The relative importance of these processes can be examined by molecular beam relaxation spectrometry (MBRS). The first step, chemisorption of reactants, is discussed thoroughly elsewhere [7, 8] and will not be considered in detail here. We note only that the probability of adsorption, s, can be easily measured in several ways using low pressure methods. Since chemisorption is normally assumed to occur during a "collision", its characteristic time cannot be resolved by MBRS. The reaction times measured by MBRS are thus determined solely by elementary steps subsequent to adsorption while the quantity (amplitude) of product formed is directly proportional to s. It is possible that any of the steps (2)-(6) can be rate determining, and consequently, the rate constant measured by MBRS can correspond to that for a molecular event - the elementary step. Provided the reaction conditions are appropriately linearized (see section 3), the relaxation times observed when step (5) dominates the kinetic sequence will show pseudo first order behavior. For first order reactions the relaxation time r measures the rate constant, k(1), directly, as r = 1/k(l~, and for linearized second order reactions r = (4k(2~h)-1, where k(2~ is the true second order rate constant and h is the steady-state surface coverage of reactant. In order to codify the rate constants observed in reactive scattering experiments, it seems most appropriate to utilize the formalism of transition state theory from which [9] k(i) = ~ k B ~ s e ASTIR e-AH~;/RTs,

(1)

where k(i) denotes the ith order rate constant, x is the transmission coefficient, or probability that reactants in the proper configuration in phase space will actually

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form products, k a is the Boltzmann constant, h is Planck's constant, R is the gas constant, Ts is the surface temperature, and AS* and A H * are the entropy and enthalpy of activation, respectively. The magnitude of the preexponential factor, A, where A =-- x ~

e AS*/R .~. 1013x eAS*/Rs-1 ,

(2)

is a particularly useful means of categorizing elementary reaction events [10]. For first order reactions, values of A of order 1013 s -1 imply for a simple desorption reaction either a loosely bound adsorbed state or a transition state having little freedom of motion, unless x is much less than unity. Preexponential values greater than 1013 s -1 imply that the adsorbed product is tightly held and that the transition state has appreciable freedom, probably in rotational degrees of freedom [11]. In gas phase unimolecular reactions involving simple bond fissions, preexponentials of 1016 s-1 are expected [10], and there is reason to expect similar values for desorption reactions, as discussed below. For a second order reaction the A-factor can be derived from eq. (2) to be A(2) = ~ kBTs h

f* flf2

'

(3)

where f*, fl and f2 are the partition functions per unit area of the transition state and reactants, respectively. For the simple recombination of atoms on the surface, consider f* to represent a weakly bound molecule with complete rotational and (two-dimensional) translational freedom and fl and f2 to represent freely translating atomic species on the surface. Then A(2) ~- x ~

2~tr 2,

(4)

where r 0 is the interatomic distance in the diatomic transition state. If r o is taken as 1 ,A,, A(2) is of the order of 10-2 cm 2 s -1 near room temperature. Collision partners, with a transition state bond length equal to 3 A could show a preexponential as high as 10-1 cm 2 s-1. If the transition state is more restricted in its motion, having, for example, restricted rotational motion, or if g is significantly less than unity, A(2) will be reduced below 10-2 cm 2 s -1. In the limit of hindered translational motion of the reactants and of the transition state, ignoring small contributions from torsional vibrations in the transition state, and assuming the barrier to translation for the transition state and the reactants, Vo, to be identical [9] k~_~ 4:tr~ 1 A(2) = ~¢ - (27ru) 2 ,

(5)

where u = Vo/2kBT s. Eq. (5) holds only for u > > 1. The effect of hindered translation is seen to reduce the value of the preexponential. For a value of V0 equal to 10 kcal/mol, A(2) would be reduced to approximately 10-4 x cm 2 s -1 at 500 K. T a m m

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and Schmidt [12] have determined A(2~ to be approximately 10 -2 ~ cm2 s -1 in the case where surface migration of an adatom to any other surface adatom is the rate limiting step. Values of A(z) are thus expected to lie between 10-4 and 10 -t cm2 S-1.

The migration steps (2) and (4) may show widely different behavior in MBRS depending on surface coverage and homogeneity. For a surface reaction with a characteristic time of 10-3 s (i.e., measurable at modulation frequencies of 10-1000 Hz), a chemisorption probability of unity, and a reactant flux of 1 monolayer/s, the fraction of the surface covered by product during an MBRS experiment can be estimated as 10 -3 monolayers (see section 3). It is therefore clear that unless a slow reaction process occurs in parallel to the elementary step observed by MBRS at chopping frequencies of order 10-1000 Hz, the surface coverage will be much less than a monolayer. Under these conditions adsorbed species may diffuse to specific reaction sites such as steps and grain boundaries. This random walk process occurs with characteristic time, r o (XE)/D, where (X2} is the mean square distance a migrating species must travel to encounter a reactive site, and D is the surface diffusion constant. Under conditions where a slow process does occur in parallel to rapid surface migration, the characteristic relaxation behavior can be quite different. Though the rate constant for the slow step does not appear explicitly in the amplitude or phase information, it may lead to much higher coverages than calculated above. Examples of this behavior are given in section 5. =

2. Experimental considerations Experimental studies of reactive surface scattering have been carried out for more than a decade, and there are a number of descriptions in the literature of the requisite apparatus [13-15]. We will restrict ourselves to an outline of the M B R S experiment and a brief summary of the experimental requirements. A typical modulated beam scattering experiment is illustrated schematically in fig. 1. The molecular beam issues from a source, passes through one or more stages of collimation and differential pumping, is modulated by a chopper and impinges upon the surface at angle 0i, measured from the surface normal. The fluxes of reflected reactant molecules and product molecules are then detected at angle Or (for simplicity we consider only in-plane scattering). Most of the early reactive scattering studies utilized effusive beam sources [2] while most recent work has made use of supersonic nozzle beams [1]. The main differences are the ready attainment of higher fluxes and small velocity spreads with nozzle beams, as well as the "cold" distribution of energy among the internal degrees of freedom. Typical fluxes at the surface range from 1013 to 1016 molecules cm -2 s -1 (0.01-10 monolayers/s). Modulation of the molecular beam serves two purposes: to improve the signal-

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tl

419

~f

t3L

BEAM SOURCE

CHOPPER

DETECTOR

Fig. 1. Schematicdiagram of a typical MBRS experiment, showingthe characteristic surface residence time (r), transit (tl, tz) and detection (t3)times.

to-noise ratio; and additionally, to "time-tag" the incident molecules. Rates of surface processes can then be measured directly. Most workers have utilized a rotating slotted disk for modulation because of the ease with which the frequency may be varied. Square-wave modulation is used most commonly, due to the ease of fabrication of the chopper, the high AC beam flux, and the straightforward data analysis. However, both narrow-pulse [16] and pseudorandom [17] modulation possess higher temporal resolution, and one of these is normally used if velocity distributions are to be measured. The relative merits of the different techniques are described in detail elsewhere [16-18]. A light beam and photodiode are typically employed to generate an electronic reference signal at time to, as the molecular beam is interrupted. We note that modulation of the beam p r i o r to entering the vacuum chamber gives rise to background partial pressure fluctuations that act as a source of coherent noise. Typically a shutter is also incorporated in the apparatus to block the beam prior to entry into the scattering chamber. The short switching time (~- 20 ms) of a shutter permits the use of transient techniques for determination of rate constants at lower temperatures and higher coverages than with MBRS. As the purpose of studies of reactive scattering is the basic understanding of the dynamics, kinetics, and mechanism of heterogeneous reactions, it is imperative that the surface be well-characterized and the experiment be conducted so as to minimize the likelihood of surface contamination. The techniques of Auger electron spectroscopy (AES) and low energy electron diffraction (LEED), in particular, are essential to assess the state of cleanliness and order of the solid surface [19]. Since at 10-8 Torr molecular species with a sticking probability of unity will form a monolayer in about 100 s, particular attention must be paid to achieving low partial pressures of gases which can lead to surface "poisoning". For this reason the use of ultrahigh vacuum (UHV) techniques are of paramount importance,

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although in studies of certain reaction systems with surfaces which are easily cleaned and difficult to poison less stringent conditions may be required. For example, early studies of reactive scattering, prior to the widespread of use of AES, focussed on tungsten, germanium and silicon (see sections 5 and 6) which could be cleaned continuously by heating in a reactive ambient of oxygen. Even under UHV conditions, however, it should be noted that experiments requiring hours of operation may be affected by residual gases in the vacuum system or in the beam itself. T h e need for reactant impurity is therefore critical. Generally, the product detector is a quadrupole mass spectrometer. The signal/noise ratio is often a problem in surface scattering, and one or more stages of differential pumping will improve it substantially. However, in many MBRS studies it has been unnecessary. The output signal from the mass spectrometer reflects all stages of the transformation of the reactant beam into the product species arriving at the detector. The characteristic time of interest is normally the surface residence time, designated as r in fig. 1. The transit times q and t2 will introduce phase shifts into the detected signal, and will broaden (convolute) the incident and scattered waveforms, respectively, by an extent proportional to the velocity spread of the molecules. For accurate determination of r, it is important that transit and detection times be kept small relative to r. However, since q and the detection time, t3, are insensitive to the surface temperature, beam flux, etc., they will not change significantly as reaction conditions are varied, and their effect can be subtracted out, to a good approximation, in MBRS experiments. Uncertainties in the various transit and detection times do set an lower limit on the reaction times measurable by MBRS irrespective of the modulation frequency. Depending on the detector configuration, additional dynamical scattering information may be obtained. Provision for rotation of the detector about the surface permits the measurement of angular distributions of scattered reactant and product molecules. Velocity distributions may also be measured, given a sufficient surface-to-detector distance and adequate signal-to-noise ratio. We note again that the detected signal will in general represent a convolution of the surface process and scattered molecule transit time, so that the most accurate information is obtained when one of the processes is fast compared to the other. The transit time t2 may be obtained independent of the surface residence tim e by modulation of the scattered b e a m [13]. Note that the mass spectrometer is a densitysensitive detector, while for analysis of kinetic processes the relevant distributions are weighted according to flux. Analysis of scattered waveforms thus often involves assumptions, explicit or implicit, about the velocity distributions of the scattered and desorbing species, which may or may not be justified. Ideally, of course, these are measured directly, but to date this has seldom been done. The output signal from the detector is usually analyzed either by digital acquisition of the product waveforms (time domain) [18, 20] or by a phase-sensitive lockin amplifier (frequency domain) [21, 22]. The lock-in detector is a narrow band amplifier that measures the amplitude and phase of the first Fourier component of

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the input signal relative to a reference signal. Most of the MBRS experiments performed to date have employed lock-in detection. Digital waveforms contain more information (i.e., higher harmonics), although to date this has not represented an overwhelming advantage since the modulation frequency, tOo, is easily varied and higher harmonics can be obtained from lock-in processing as well. In any case, for quantitative analysis the waveforms are normally Fourier transformed, and the subsequent analysis (section 3) is the same regardless of the mode of data acquisition. We conclude this section with a brief discussion of signal-to-noise problems. Spurious coherent (i.e., at the modulation frequency) noise can arise from modulation of the beam prior to entry into the scattering chamber or from adsorption/desorption behavior of reactant or product molecules on surfaces within the chamber, particularly within the mass spectrometer ionizer itself. The characteristic time associated with the first effect is V / S , where V is the chamber volume and S is the pumping speed. This effect can be isolated by measuring the amplitude and phase of the signal with the surface moved out of the beam. The latter effect should be suspected if phase lags greater than 90° are observed, indicating two sequential first order processes in the scattering event (see section 3). Ideally this second effect can be eliminated by using a flow-through ionizer so that the reflected reactant and product molecules pass through without suffering collisions with a surface. A spurious coherent signal can also arise if the detector signal lead is improperly shielded from the chopper motor. The principal source of incoherent noise should be the background partial pressure of the species under examination (or as a cracking fraction of a larger molecule), but noise can arise from a variety of other sources as well. Careful shielding and grounding are necessary to minimize 60-cycle pickup, which can otherwise drastically degrade the signal-to-noise ratio. Vibrational noise can be a problem in mechanically pumped systems. This type of noise can easily be detected as a rolling beat frequency superimposed on the heterodyned signal in a lock-in amplifier. With proper operation, lock-in phase-sensitive detection provides an amplification factor of about 100 in extracting the signal from the noise; the enhancement factor associated with waveform acquisition is limited only by the stability of the system and the length of time required t o obtain a sufficient number of counts. Both lock-in detection [21, 22] and waveform acquisition [18, 20] have been reviewed in connection with MBRS.

3. Data analysis As men$ioned in the previous section, analysis of MBRS data is typically carded out in the frequency domain, for all but the simplest first order processes (for which rate constants can be obtained directly from product waveforms). Lock-in detection yields the amplitude and phase of the first Fourier component at the

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422

modulation frequency directly; alternatively, time-domain waveforms may be Fourier transformed to yield the amplitude and phase of the fundamental mode and a number of higher harmonics. For surface processes that are linear the principle of superposition holds, and the system responds independently to each frequency component. Put differently, a linear surface process cannot generate frequencies not present in the driving function (i.e., the modulated incident molecular beam), but can only attenuate and phase shift the frequencies that are present. Such a system is completely characterized by a transfer function, F(m), which describes the amplitude attenuation and phase shift as a function of frequency. A nonlinear surface process will generate frequencies that are sums and differences of those of the input. If a modulation function is chosen that contains only odd harmonics (e.g., a square wave), the presence of even harmonics in the product signal is a signature of a nonlinear reaction mechanism (if noise contributions can be eliminated or subtracted out). In the frequency domain it is straightforward (in principle) to deconvolute contributions due to the transit times, t I and t2, and the detection time, t3, (fig. 1) from the measured signal. If the velocity distributions and detector response function can be measured or estimated, the surface transfer function, Fs(a0, is given by the observed F(co) divided by the product of the Fourier transforms of the aforementioned quantities. However, as the MBRS experiment is conventionally performed, the phase lag of the product molecules is measured relative to that of the reflected reactant molecules. If the differential transit and detection times are short in comparison to r, then/~s(co) ~ F(to).

3.1. First order reaction The analysis applied to a simple reaction mechanism in which the gas molecule, A, incident on the surface adsorbs with a temperature- and surface-coverage-independent probability, So, and desorbs with rate constant k, serves to illustrate the principles involved. This mechanism is represented as so

A(g) -~ Aa, Aa k_+ A(g).

(6)

The rate of change of the concentration, hA, of Aa on the surface is given by the continuity relation hA(t) = solo(t)- knA(t ),

(7)

where Io(t ) is the time-varying incident beam flux. The steady-state desorbing "product" flux at a given frequency (neglecting, for the moment, the reflected incident flux, Ir(t)) may be obtained by Fourier transforming eq. (7) and solving the resultant algebraic equation: i~(co) = k,~A(~O) -

s0?0(~o)

i - i~Tk- '

(8)

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

423

where the tildes denote Fourier transformed quantities. To obtain the surface transfer function, or so-called reaction product vector, we divide by the incident flux:

p~(to)_ ld(to)

]o(to)

-

So

1 - ito/k

- s ° [ 1 + (w/k)2]-l/2ei~,

(9)

where tan tp = to/k.

(10)

The net result of the surface reaction is to demodulate the incident signal by the factor [1 + (to/k)2] '~ and to introduce a phase delay, described by the angle q~. Both the phase lag and amplitude demodulation factor contain information about the reactive collision, namely the desorption rate constant, k, and the reaction probability, s o. Note that in the absence of modulation only s o is measurable. The actual signal at the detector contains contributions from both the desorbed (ld) and reflected (It) molecules, with the fraction of the former given by s 0. The trapping-desorption channel typically has a diffuse angular distribution, proportional to cos 0r (cf. fig. 1), and the molecules generally have a velocity distribution characteristic of the surface temperature [23-25]. The reflected molecules scatter quasielastically or inelastically from the surfac.~ with a lobular angular distribution centered near the specular angle (0 r = 0i), and the velocity distribution depends on that of the incident molecules as well as on the surface temperature [23-26]. The two scattering channels may also be readily distinguished by the different frequency response behavior of ]d(to) (eq. (8)) and Ir(to) (= constant in the 0-1000 Hz range), since the characteristic time associated with inelastic scattering is of order 10 -12 s. If the modulation frequency can be varied over a wide enough range, the contribution of the trapping-desorption channel is simply the difference between the total signals at low (to o < < "t"-l) and high (too < < "r-l) frequencies. The sticking probability may be determined by integrating lid + Irl and lid over 0 r (note that converting density to flux distributions is complicated by the different velocity distributions in the two channels). An estimate of s o may be made much more simply by varying the surface temperature at fixed too and 0r = 0i = 45 °. Neglecting differences in the mean velocity between desorbed and reflected molecules and assuming the fraction of flux contained within the solid angle detected to be a good measure of the total amplitudes of desorbing and reflected species, s o is given approximately by the difference in the signals at high and low temperatures (such that k > > too and k < < too, respectively) divided by the high temperature signal. At frequencies where the phase angle is changing appreciably with Ts, k ~ to, and the su~ace coverage may be estimated as n A = i o s o / k ~ ]oSo/to.

(11)

This condition is precisely that which allows the value of k to be determined. For

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

424

an incident flux of one monolayer per second, a sticking probability of one, and modulation frequencies of 10-1000 Hz, the surface reactant coverage will lie in the range of 10-2 to 10 -4 monolayer. Normally, then, in the absence of provisions to boost the surface concentration (see section 3.4) rate constants determined by MBRS correspond to low surface coverage. Eq. (9) suggests a convenient means for testing whether experimentally observed phase and amplitude data represent a simple first order surface reaction. Since ]Ps(to)1-2 = So2 (1 + to2/k2)

(12)

for the reaction (6), a plot of IPsl-2 versus 092 must yield a straight line at all temperatures studied. At low temperatures or high frequencies to > > k , and I&l varies as o9-1. However, this test alone is not an absolute test of a simple first order reaction, and must be combined with measurements of the phase angle. Note that tan rp varies linearly with frequency and is independent- of incident flux, which contrasts with other reaction mechanisms discussed below. Once the first-order nature of the reaction is established, the activation energy and preexponential factor are readily extracted by plotting log k = (to/tan rp) versus 1/T~. Alternatively, with the assumption that s o and the angular distribution of desorbing product are independent of surface temperature, k(T~) may be extracted from the signal amplitude by dividing the product signal (with the reflected reactant signal subtracted out) by that obtained in the high temperature limit (k > > to), yielding the quantity [1 + (to/k)2]-vL In some cases it may prove more convenient to extract the activation energy from k(T 0 obtained in this way and to utilize the phase shift measurement to evaluate the preexponential factor. Note, however, that amplitude measurements are more sensitive to the velocity distributions of reactants and products than are phase angle measurements (as long as transit times are short), since the mass spectrometer signal for a given flux of particles varies inversely with their speed. If significant deviations from fully elastic reflection or from complete accomodation occur (see section 4), substantial errors in the inferred fluxes may result.

3.2. Sequential or parallel reactions The simple analysis presented above can readily be extended to more complex surface processes, such as sequential or parallel reactions, reactions involving diffusion, etc. For the linear sequence S

A2(g ) ~ 2 Aa, kl

(13a)

Aa

-+ Ba,

(13b)

Ba

k--~2B(g),

(13c)

M. P. D'Evelyn, R. J. Madix / Reactivescatteringfrom solid surfaces

425

the transfer function is easily calculated to be [21]

p~(~) =

2So [1+((O/kl)211/2 [l+(to/k2)2]l/2

e i~,

(14)

with go-- tan-1 (to~k1) + tan-1 (to~k2).

(15)

Comparison of eqs. (9) and (10) with (14) and (15) leads to the conclusion that for a linear sequence o f reaction events the phase lags o f each step are additive and the amplitude factors are multiplicative. This ensures that no reaction step with k 1 < < to can precede a reaction event with k2 --~ to that is observed, if the first order frequency test (eq. (12)) is obeyed. The slow initial step demodulates the resultant signal by kl/to, making observation of the reaction sequence extremely difficult. Moreover, the frequency behavior when k 1 < < to is

IPsl-= = (2~ok1)-2 [,o2 + k~2to4],

(16)

in contrast to the linear relationship between IPsl-2 and to2 for a single step pathway (eq. (12)). A polar plot of Fs provides a convenient means for evaluating the importance of multiple pathways in the reaction mechanism [21]. Fig. 2 shows polar plots for (a) simple adsorption/desorption, (b) a two-step sequence with k 1 = k 2 = k, and (c) a parallel branched reaction process with a branching probability of 0.5, illustrated schematically by

..~

2 Aa(1}

k1

~ B(g)

A2(g) &'~"~W2 Aa(2) -

k2 ÷

B{g).

(17)

These plots provide a userul "signature" for each mechanism. A comparison of figs. 2a and 2c indicates that a ratio of rate constants of at least five is necessary for a clear distinction between a simple adsorption/desorption process and a branched mechanism. One of the most important characteristics of a branched process is the production of sluggish changes in gowith surface temperature. Near constant phase lags may be observed over an appreciable temperature range. 3.3. Coupled diffusion and reaction Both bulk and surface diffusion phenomena have been found to be important in MBRS studies of heterogeneous reactivity. The reactive process at the surface involving simultaneous diffusion and solution into the bulk can be represented as [27]

426

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

90 °

d

o°

90 °

b(

E

18o*

O*

90 ° kdl/kd2=l

C

cO

~

O* 2~

Fig. 2. Polar plots of the surface transfer function/~s(~o),associatedwith (a) a simple adsorption/desorptionreaction(eq. (6)); (b) a two-stepreactionsequencewith k 1= k2 = k (eq. (13)); and (c) a parallel branched reaction (eq. (17). From ref. [21], with permission.

A2(g )

SO,

2 Aa

kd~

2 A(g)

2 A(solution) T h e c o n t i n u i t y r e l a t i o n f o r t h e s u r f a c e c o n c e n t r a t i o n o f A a is

(18)

M. P. D'Evelyn, R. J. Madix / Reactive scatteringfrom solid surfaces

(ac)

h A = 2solo(t) - kdn A -4- D ~

o'

427 (19)

where D is the bulk diffusion coefficient, c is the bulk concentration just below the surface, and x is the distance into the bulk from the surface. The relationship between c and nA is assumed to be of the form c(O,t) = HnA(t),

(20)

in analogy to Henry's law. Eqs. (19) and (20) must be applied to the solution of the time-dependent diffusion equation ac at

-

O

a2c ax 2

- - ,

(21)

subject to the appropriate boundary condition for large x. For to > > D/d2, where d is the thickness of the sample, the surface transfer function is given by [21, 27] 2S0 ei~ , /~s (~o) = {[1 + Q(o)/kd)l/2]2 + [(o)/kd) -4- Q(co/kd)l/2]2} 1/2

(22)

with q~ = tan_l[ a)/ka + Q(o)/kd)l/2 ] 1 + Q(mlkd)l/2 ]'

[

(23)

and Q =- (I-lZD/2ka) 1/2.

(24)

As k d becomes large compared to/-/2D, Q goes to zero and the phase and amplitude behavior approach that of a simple adsorption/desorption process. As Q becomes large in comparison to ¢o/k d and unity, the phase angle approaches a constant value of 45 ° and the amplitude varies as ~o-1~. It is instructive to examine the consequences of treating the bulk diffusion/solution process as if it were a simple adsorption/desorption reaction. This is done by setting the phase angle (eq. (23)) equal to tan -a [w/kaf] (cf. eq. (10)). When the characteristic times for the solution/diffusion process and desorption are nearly equal (Q of order unity) and ¢o/kd is large, kefe = ( H2 D09/2) 1/2.

(25)

The apparent rate constant shows no dependence on k d and depends on the solution/diffusion parameters only; it also varies as to1~. Only when Qz is of the order of ~O/kd or smaller can the desorption rate constant be determined. It is also possible that the surface reaction may be dominated by surface diffusion to reactive zones on the surface such as grain boundaries [28]. Under these circumstances a concentration gradient is established between the center of the zone and the reactive boundary. If the sticking probability is assumed to indepen-

428

M. P. D'Evelyn, R. J. Madix / Reactive scatteringfrom solid surfaces

dent of surface coverage, the governing continuity relation and boundary .conditions are an A Ot

n A (x, t)

02hA -- D =

- 2 D ~anA -

(26a)

~x2-x2 +solo(t),

n A

(-X, t),

(26b) (26c)

x=L = k n n ( L , t ) ,

where the reaction is envisioned to occur at parallel reactive ledges of spacing L, with a rate constant k. The amplitude, IFs(to)l, is too cumbersome to reproduce here, but the phase is given by [29]

qg(to) = tan-a

sinh 2 a - sin 2a sinh 2a + sin 2a

+ 2fl cosh 2 a - cos 2a ] sinh 2a + sin 2a '

(27)

where a ~ L(to/2D) 1/2,

(28)

and fl =- ( 2 D / k L )a.

(29)

For diffusion sufficiently slow so that fl < 0.1, the phase angle is constant at 45 ° and the amplitude varies as to_l~, provided a2 is greater than about two. More complicated linear surface processes may be analyzed using a formalism developed by Chang and Weinberg [30, 31]. The kinetic equations are written in matrix notation, with the coefficients of the surface concentrations of the various intermediates as matrix elements. The surface transfer function is then expressed in terms of the eigenvalues and eigenvector components of the kinetic matrix. 3.4. Nonlinear reactions

The analysis of an MBRS experiment becomes significantly more complex if the surface reaction sequence is nonlinear, that is, the kinetic equations contain the product of two or more time-varying quantities. Important examples of such nonlinear processes are second-order desorption and adsorption with a coveragedependent sticking probability. A nonlinear process is indicated experimentally by a phase lag that is strongly affected by the incident reactant flux or by the beam-to-background ratio at a fixed surface temperature, or by the detection of harmonics in the product flux not present in the incident flux (e.g., even harmonics of too with square wave modulation). In general a nonlinear surface kinetic model may be solved for a given set of parameters by numerically integrating the kinetic equations until steady-state be-

M. P. D'Evelyn, R. J. Madix / Reactive scatteringfrom solid surfaces

429

havior is observed, then Fourier transforming the product waveform [27]. An alternative approach is to modify the experimental conditions so as to linearize the kinetic equations [22]. For example, a simple second order reaction is represented by A k(2) Az(g ) ~ 2 A a, 2 ,'-x a ~ Az(g ).

(30)

The continuity relation for A a is then h A = 2s0/0(t ) - 2k(Z)n2,

(31)

where k(2) is the true second-order rate constant. If the experiment is conducted with a sufficiently high constant flux of reactant, such that the modulated beam represents a small perturbation in flux at the surface, then it suffices to retain only the constant and first harmonic contributions to the concentrations of each surface intermediate. The solution is readily obtained as hA = [SJo/k(2)]l/2,

(32)

cp(to) = tan-l[to/4h Ak(2)] =- tan-a[to/keff],

(33)

and

IPs(~o)L = s0/[1 +

(~o/kef02] 1/2,

(34)

where the bars refer to time-averaged quantities. Provided the surface coverage can be determined, the true second-order rate constant can be evaluated. However, both s o and ]0 must be known in order to calculate hA. To analyze many MBRS studies of nonlinear processes it appears to be adequate to linearize the equations, as above, even when the fluctuating incident flux is o f the s a m e order o f magnitude as the time-averaged flux. Such an analysis is only slightly more complicated than for a linear process, and for typical reactions the solutions are accurate to roughtly 5 - 2 0 % , depending on the nature of the nonlinearity [32, 33]. Yet another approach is to monitor the product flux at twice the modulation frequency, using an incident waveform that contains only odd harmonics. The phase shift of id(2to0) relative to ]0(to) for the reaction (30) is given by [34] q0=

2 + tan-l[ -

32k(2)2h'~t° - t°3 32k(2)3h3_ 10k(2)hA 092 ]"

(35)

In summary, a wide variety of reaction pathways including complex reaction sequences and diffusion effects have been analyzed for the amplitude and phase of the surface transfer function, Fs(~o). Ultimately the appropriate examination of the dependence of Fs(to) on frequency, temperature, beam flux, and beam-tobackground flux ratio determines the kinetics and mechanism of the reaction.

430

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

Table 1 Summary of the amplitude and phase response for surface reaction mechanisms Mechanism

Change with: Surface temperature

Frequency

Beam intensity

Beam to background

Amplitude increases with increasing surface temperature

Amplitude decreases with increasing frequency

Amplitude increases linearly

No effect

Phase decreases with increasing surface temperature

Phase increases with increasing frequency; phase > 90° possible

No effect

No effect

Amplitude increases with increasing surface temperature

Amplitude decreases with increasing frequency

Amplitude increases linearly

No effect

Phase decreases with increasing surface temperature

Phase increases with increasing frequency, response not as strong

No effect

No effect

II. Bulksolution followed by surface reaction

Amplitude increases with increasing surface temperature

Amplitude decreases as ~o-1/2;phase constant 45 °

No effect

No effect

III. Surface diffusion limited surface reactions

Amplitude increases with increasing surface temperature

Amplitude decreases

No effect

No effect

Phase generally insensitive to surface temperature

Phase constant 45 °

No effect

No effect

IV. Nonlinear adsorptiondesorption kinetics

Amplitude increases with increasing surface temperature

Amplitude decreases with increasing frequency

Amplitude increases linearly

Weak effect decreases with increasing

Phase decreases with increasing surface temperature

Phase increases with increasing frequency

Phase decreases at high beam pressure

Phase decreases with increasing

I. Linear 1. Series

2. Parallel

a s O) l/2

431

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

Table 1 (continued) Mechanism

v. Secondorder surface reaction

Changewith: Surface temperature

Frequency

Beam intensity

Beam to background

Amplitude increases with increasing surface temperature (at higher pressures-asymptotic value at highest surface temperature decreases)

Amplitude decreases with increasing frequency

Slope of order plot between 1 and 2

Slope of order plot between 1 and 2

Phase decreases with increasing surface temperature

Phase increases with increasing frequency

Phase decreases sharply with increasing beam pressure

Phase decreases sharply with increasing ratio

Table 1 summarizes useful e x p e r i m e n t a l tests for distinguishing the types of surface reactions. It must be a d m i t t e d that the most difficult aspect of M B R S is the unambiguous fitting of the d a t a to a kinetic model. O l a n d e r [35] has discussed the limitations of M B R S in this regard. It is h o p e d that the additional information available from analysis of the higher harmonics of product waveforms, perhaps together with novel techniques such as t e m p e r a t u r e m o d u l a t i o n [36, 37], or time-resolved photoelectron [38] and A u g e r electron [39] spectroscopies, will facilitate the characterization of m a n y m o r e reactive scattering processes on surfaces.

4. Catalytic reactions on metals

Molecular b e a m techniques have been used to investigate a n u m b e r of reactions on metal surfaces, most p r o m i n e n t l y the adsorption/desorption of H 2, C O and N O and the catalytic oxidation of C O and H 2. In each case the kinetic information o b t a i n e d has c o m p l e m e n t e d that derived from other techniques, but in addition, molecular b e a m studies have clearly d e m o n s t r a t e d , for example, the importance of surface h e t e r o g e n e i t y in desorption kinetics at low coverage and the d o m i n a n c e of the " L a n g m u i r - H i n s h e l w o o d " mechanism in oxidation reactions. M e a s u r e m e n t s of the angular, velocity, and internal state distributions of desorbing molecules have often shown significant deviations from those commonly assumed to be characteristic of equilibrium with the surface. The internal state

432

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

distributions of product molecules formed by exothermic surface reactions appear to contain information on the dynamics of the surface reaction and/or the desorption process. In general, the most detailed information has been obtained for reactions that are rather simple, while for several decomposition reactions the details of the mechanism and the kinetics of the elementary steps remain somewhat unclear. We attempt here to provide a fairly comprehensive review of the work to date falling within the topics considered in this section, with emphasis on the insights into the kinetic and dynamical behavior obtainable with molecular beam techniques. The interested reader is referred to other reviews that discuss molecular beam studies of catalytic reactions [3, 4] as well as to general reviews of the specific reactions considered, which are cited in each subsection.

4.1. He-D e exchange and hydrogen recombination The H 2 - D 2 exchange reaction is among the simplest surface reactions that involve the breaking of molecular bonds. The interaction of hydrogen with metals is of enormous technological importance and has received much attention, yet a number of features remain unclear or controversial. Experimental measurements of the dynamic aspects of the hydrogen recombination reaction have clearly demonstrated that desorption need not result in diffuse (cos Or) angular distributions and Maxwellian velocity distributions of desorbing species at the surface temperature, as often assumed. Surface heterogeneity, in the form of steps, has been shown to play a role in the recombination kinetics on Pt, while on Pd bulk solution/diffusion dominates the behavior. The H 2 - D 2 exchange reaction has been recently reviewed by Engel and Ertl [40].

4.1.1. Angular and velocity distributions Noncosine angular distributions of desorbing hydrogen have been observed by a number of workers on a variety of surfaces. Approximating the angular density as proportional to cosd0r, values of d from 1.5 to 5.5 were obtained for H D production following H 2 - D 2 exchange on N i ( l l l ) [41], on fiat and stepped (111) surfaces of Pt [42, 43] and on the (100), (110) and stepped (310) surfaces of Cu [44]. Cosine (d = 1) distributions were observed on the stepped (997) and (553) Pt surfaces [45] (although a subsequent investigation by the same group yielded noncosine distributions [43]) and on P d ( l l l ) [46]. Peaked distributions (d > 1) have also been observed for hydrogen desorbing from single crystals of Ni and Cu and polycrystalline Ni, Cu, Pt, Pd, and Fe, following permeation through the bulk [47-52]. Stickney and co-workers [49-51] found that as the metal surfaces in the permeation studies were cleaned of S, O, and C impurities the values of d for Ni, Pt, and Fe decreased from ~ 4, ~ 3, and ~ 7 to 1.1, 1.8, and ~ 3, respectively (the latter two surfaces were still slightly contaminated), while the value of d for Cu was unchanged. Balooch et al. [44] showed that the angular distribution of H D desorbed following the catalytic exchange of H2 with adsorbed D atoms on the

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

433

(100), (110), and (310) faces of Cu was in excellent agreement with that observed in the permeation experiments [51] (see fig. 3). They also found that the dissociative sticking probability for H2 scaled with the component of translational energy normal to the surface, and increased fourfold to ~ 0.1 near an energy of 5 kcal/ mol (fig. 4). The initial interpretation of these results was in terms of a model with an activation barrier to adsorption that acts principally normal to the surface, proposed by Van Willigen [47] and subsequently modified by Balooch et al. [44] and by Comsa and David [53]. The activation barrier is assumed to be intrinsic to clean Cu, but associated with surface impurities (which were not directly monitored in the early exchange [41, 42] and permeation [47, 48] studies) in the case of the other metals. This model qualitatively explains the activated adsorption behavior, while the reverse phenomenon of non-diffuse desorption is explained using the principle of detailed balance. As an example, consider an adsorption/recombination reaction proceeding at total equilibrium [54]: A2(g ) % 2 A a

I

(adsorption),

1

I

(36a)

I

I

I

I

I

1.0 0.9 0.8

•

0.7 U.,I N d

0.6

\ -

o \\

a Io9

0.5 0.4

Cu ( I 0 0 ) Cu ( 1 1 0 )

x~-co s~, DIFFUSE k E M ISS 10N

\ka \

o z

A a

\

-

Cu (1001

-

\

0.3 _

\ o\~ a

X 8X~\

\ \

0.2

o

o \

\

\

, o

\

\

a o

o

\

0.1 ! I0

I 20

I 30

I I 40 50 8 r (deg)

I 60

I

I

70

80

Fig. 3. Angular distributions of desorbing hydrogen from the (100), (110) and (310) faces of Cu. Symbols: HD distributions following H2-D 2 exchange at T s = 850 K. Dashed lines: H 2 distributions following atomic permeation through the bulk crystals at 1100 K. The latter are given approximately by cosa0r, with d ~ 5 for Cu(100) and d ~ 2.5 for Cu(110). From ref. [44], with permission.

434

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces I ;0

i

i

~

1

i

t

(a)

I

] 0.14

o

Cu (liO)

~

013 012

oa

070068

0 II 010

a °a ~

009 908 ;007

05

0

O4

0 c3

0O6 -005 -004

o

03 02

-00:5

o~

-002 OOi

Ot [

08 o w

cv

l

L

I

I

E

I

i

I

0.10

0.7

Cu(310)

y~,

,06 a°

0.09

._J

~'

0.08

'~

007

0.5

0.06 o

0.4

o o ~

0.2

o

~c ..,:, :~

|

OJ_

o

o o

c

~003

~ ~'

I

J

i ,..h

~0.02

70 0

,~o I

I

I

5

"-}0"05 -~004

L

I

1

I

~

I

~ ),10 07~.

Cu(I00)

/

0 6 /-

of

0.5 L-

~ ~

).09

~'

0.08 0.07 0.06

/o

004 003 0.02 011 O0

~C~o I I

O.OI I

2

i

3 -

L 4 2

I 5

t 6

~

I

8

I 9

Ej= E i cos 8, (kcol/mole } Fig. 4. Dissociative sticking probability for H 2 at low coverage on several faces o f Cu, shown as a func. tion of the component of translational energy normal to the surface. From ref. [44], with permission.

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces 1- s o

435

A 2 ( g ) ~ A2(g )

(reflection),

(36b)

2 A a ~ A2(g )

(desorption),

(36c)

Since the flux of molecules incident on the surface is isotropic and has a Maxweil-Boltzmann velocity distribution, the same must be true of the total flux (reflected plus desorbed) emanating from the surface. If the reaction probability for molecules incident at angle 0 i (e.g., normal incidence) is large, there will be a deficit of reflected molecules at 0r = 0i, and the flux of desorbing molecules at that angle must be correspondingly large. Furthermore, if an activation barrier to adsorption exists, and only the molecules with sufficient translational energy to surmount the barrier adsorb, the reflected flux at 0r will be translationally colder than the incident flux (for simplicity we assume the "reflection" process to be dominated by quasielastic scattering). The desorbing flux must then be translationally hot at Or to produce the equilibrium distribution far from the surface. Conversely, if the sticking probability at 0i decreases with increasing translational or internal energy due to inefficient energy transfer, then the desorbing flux at Or = 0 i will be colder. These considerations for desorption also apply to circumstances where there are no molecules incident on the surface, provided statistical equilibrium can be maintained on the surface during desorption, and the rate limiting step for desorption does not change. Cardillo et al. [54] and Palmer et al. [41] have shown the experimental data on H 2 - D 2 exchange on Cu and Ni to be consistent with these detailed balance considerations. Gelb and Cardillo [55-57] have attempted to construct a quantitative model for the H2/Cu system [44], making use of trajectory calculations and semiempirical potential energy surfaces. They were able to obtain a reasonable fit to the low coverage sticking probability, so(E) (fig. 4) with a potential that had a minimum dissociation barrier of -~ 8 kcal/mol and a rather large barrier for surface diffusion of 10 kcal/mol [57]. However, this potential did not reproduce the experimental scaling behavior of s o with the normal component of translational energy. However, recent H 2 and D 2 permeation experiments by Comsa and co-workers [52, 58-60] have raised questions about the above interpretation. These authors measured both velocity and angular flux distributions of hydrogen following permeation and recombination on surfaces of Ni, Pd, and Cu. On N i ( l l l ) Comsa et al. [52] observed peaked angular distributions (d = 3-5) and average translational energies that depended strongly on desorption angle. In contrast to earlier work [49], they found their results to be essentially independent of sulfur coverage down to 0 s < 0.02, where 0 s is the fractional surface coverage of S (i.e., n s divided by the concentration of surface atoms. We follow the conventional notation in the surface science literature and use 0 A to denote the fractional surface coverage of species A; distinction from the angles 0 i and Or should be noted). On Pd(100), distinct "fast" and "slow" groups of desorbing D 2 were observed [58, 59]. The fast molecules were characterized by a narrow velocity distribution and

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

436

an angular distribution of ca. cos100,, while the slow molecules had a Maxwellian velocity distribution at Ts + 50 K and a cosine angular distribution [58] (see fig. 5). The relative proportions of the two groups were found to be controlled by the amount of S impurity on the surface, with the fraction of fast molecules vanishing as 0 s --->0, and to be independent of surface temperature. In the case of Cu(100) and C u ( l l l ) , Comsa and David found all the desorbing molecules to belong to the "fast" distribution [60]. The desorbing molecules had very narrow velocity and angular distributions (cos7-80r), just as the fast group on Pd(100). The "fast" distributions in each case were attributed to recombination events in which at least one of the atoms has equilibrated in a subsurface state [61, 62] (fig. 6). Support for this interpretation comes from the fact that the energy barriers inferred by comparing the observed angular and velocity distributions [52, 58, 60] with the predictions of a simple model [53] correlate with bulk permeation energies and not with the activation energies for adsorption, and from the observed temperature independence of the proportion in each channel on Pd(100). Comsa et al. [52, 60] suggest that the discrepancy between their results and those of Stickney and co-workers [49-51] for the angular distributions from Ni and Cu and in particular, the effect of sulfur on the former, may be due to surface roughness introduced during the removal of surface impurities by the latter authors. This mod-

I Pdll001-D2 Ts=360 K

Os ~ 0.5 -

0

-4 O x

3

]

20°

oC o

60 °

2

800

Cc in

I

Y

I

0 - -

0

5 time of flight[.10-Asec]

1020

Fig. 5. Time-of-flight distributions for D2 desorbing at various 0, from a sulfur-covered Pd(100) surface following atomic bulk permeation at 360 K. From [ef. [58], with permission.

M. P. D'Evelyn, R. J. Madix / Reactive scattering from sofid surfaces T ............... >~" . . . . . .

437

Cu+D

ED=58- ~

=-p=17

II IIII 'Oob eb

/

½e°o--s3

Es=11.7-

Cu÷gD2 Dad Fig. 6. Schematicpotential energydiagramfor D adsorbed and absorbedon Cu. All energiesare given in kcal per moleof D atoms. From ref. [60], with permission.

el does not explain, however, the peaked angular distributions of H D desorbing from Pt [42, 43] and Ni [41] following adsorption from the gas phase. The latter observations could be explained by assuming a small activation barrier, perhaps induced by surface impurities, and that an activated adsorption process could operate in parallel with that proposed by Comsa and co-workers. 4.1.2. R e c o m b i n a t i o n kinetics

Both the values of the kinetic parameters for hydrogen recombination on platinum and the role of surface heterogeneity have been sources of discussion and controversy. The kinetics of the H 2 - D 2 exchange reaction on the flat (111) and stepped [9(111) x (111)] and [5(111) x (111)] Pt surfaces was studied by Bernasek and Somorjai using MBRS [45]. To explain the observed phase and amplitude behavior they proposed a branched mechanism, involving diffusion of molecular hydrogen to step sites where reaction occurs, supplemented at high temperatures by an Eley-Rideal reaction between adatoms at steps and incident gas phase hydrogen molecules. Subsequently, Wachs and Madix [63] showed that a better fit to the Bernasek-Somorjai data could be obtained by postulating a two-branch mechanism in which the rate-limiting step involved recombination of adsorbed H or D atoms on either step or terrace sites. The apparent first-order rate constants for reaction at the steps and terraces were found to be: k s = 8 x 104 exp [-5.2 (kcal/mol)/RTs] s -1 k t = 3 x 102 exp [-2.7 (kcal/mol)/RTs] s -1,

M. P. D' Evelyn, R. J. Madix / Reactive scattering from solid surfaces

438

respectively. For the [9(111) × (111)] surface the branching probability, i.e., the fraction of exchange proceeding via steps as opposed to terraces, was Ps = 0.28. On the [5(111) × (111)] surface Ps was found to be 0.43. This analysis also showed the ratio of reaction probabilities on the stepped flat surfaces to be of order 10, several orders of magnitude less than originally proposed [45], indicating only a modest structure sensitivity for this reaction. Salmer6n et al. [64] demonstrated directly that the H 2 - D 2 exchange probability on stepped P t ( l l l ) surfaces is a factor of two higher when the reactants impinge upon the open side of the step than when the inner corner of the step is shadowed. The substantial angular dependence provides strong evidence that dissociative adsorption occurs directly upon impact, without significant diffusion of molecular hydrogen. The sticking probability on P t ( l l l ) was found to vary roughly as cos 0 i, which was ascribed to a small (-< 0.4 kcal/mol) activation barrier to adsorption. However, no effect was observed when the average kinetic energy of the incident molecules was varied from 0.9 to 1.7 kcal/mol. The MBRS phase and amplitude behavior was found to be qualitatively similar on the (111) an d [6(111) × (111)] surfaces, with the difference in reactivity being due to quantitative differences in the kinetic parameters [43]. Salmer6n et al. [43] interpreted their data using either of two branched reaction sequences. The first scheme, illustrated schematically by

y

2 Ha,l

kl

H2, a

k3

H2(g)

H2(g)

(37)

~Y~°-"~ 2 Ha,2

k2_

H2, a

H2(g)

is formally identical to that proposed by Wachs and Madix [63]. The second model involved adatom migration from the second to the first type of site, followed by recombination. Similar fits to the M B R S data were obtainable with either mechanism. The second-order activation energies for the low temperature branch (kl) were found to be El(2) = 16 kcal/mol and Es(2) = 13 kcal/mol on the flat and stepped surfaces, respectively. Estimating an incident flux of 1013-1014 cm -2 s -1, they obtained preexponentials of Af(2) = 10 -2 cm 2 s -1 and As(2) = 10 -3 cm 2 s -1. Salmer6n et al. were unable to obtain unique values of the kinetic parameters for branch two on either surface, but if a " n o r m a l " preexponential was assumed, the activation energy was estimated as 20-30 kcal/mol on the stepped surface for either model. The rate constant for the series step, which became important at low Ts, was estimated as k 3 = 104 exp [ - 2 (kcal/mol)/RTs] s -1. On the (111) surface the reaction rate was observed to continue to increase with temperature at high temperature, which was attributed to an activation barrier

M. P. D'Evelyn, R. J. Madix / Reactive scatteringfrom solid surfaces

439

for dissociative adsorption of 1.5 kcal/mol. This value is substantially higher than that used to explain the incident angle dependence of the reaction probability (0.2 - 0 . 4 kcal/mol) [43, 64], perhaps reflecting differing efficiencies of incident translational energy or surface temperature in surmounting the activation barrier. MBRS measurements have impacted significantly on a controversy in the literature over the kinetics of hydrogen recombination on Pt. The results from a number of investigations are summarized in table 2. Christmann et al. [65, 66] obtained low-coverage rate constants of 3 × 10-9 exp [-9.5 )kcal/mol)/RTs] cm 2 s -1, 6 x 10-8 exp [-.12 (kcal/mol)/RTs] cm 2 s -1, for hydrogen desorbing from the (111) and [9(111) × (111)] Pt surfaces, respectively, by thermal desorption and work function measurements. These preexponentials are many orders of magnitude smaller than those observed for hydrogen desorption from other Group V I I I metals [67] and from the values predicted by eqs. (4) or (5) above. A similar value was obtained by Steinbach and Hausen [69] by MBRS following H C O O H decomposition on polycrystalline Pt. However, "normal" values of the preexponential and activation energies ranging from 16 to 22 kcal/mol have been reported by McCabe and Schmidt [69], Poelsema et al. [70], and by Norton et al. [71] on flat and stepped (111) Pt surfaces. The low temperature M B R S rate constants of Salmer6n et al. [43] also fall in the latter category. Gdowski et al. [72] have observed D2CO and C H a O D to decompose rapidly on Pt(110) and Pt(S)-[9(111) × (100)], yielding CO and H E (D2, H D ) by a desorption-limited sequence of elementary steps. The MBRS rate constants for CO production were identical to those observed earlier for CO adsorption/desorption on

Table 2 Low coverage kinetic parameters for hydrogen recombinationon platinum Surface plane

A(2) (cm2s-0

E(2) (l~cal/mol)

(111) [9(lll)x(lll)] poly (111)

10-8.5 10-7.2 10-7.5 10-3

9.5 12 9.3 17

[9(111)x(lll)]

10-2±1

(111) (111) [6(111)x(11~)] (110)

10-3.5+-1.5 10-2 10-3 10° 10-2.5 10-1.1

19 (terrace) 22 (steps) 16 16 13 24 19.5 (terrace) 25 (steps)

[9(ill)x(100)]

Method

Ref.

TPD, A~ MBRS; DCOOD decomposition TPD

[65] [66] [68] [69]

He diffraction

[70]

Nuclear microanalysis

[71]

MBRS; H2-D2 exchange

[43]

MBRS;D2CO, CHaOD decomposition

[72]

440

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

the same surfaces [73, 74]. The rate constant for hydrogen evolution on Pt(110) was given by 10°-+°.5 exp [-24 ( k c a l / m o l ) / R T s ] cm 2 s -1. On the stepped surface a branched process was observed, with activation energies of 19.5 and 24.9 kcal/moi and preexponentials of 3 x 10-3 and 9 x 10-2 cm 2 s -1 (see fig. 7). Gdowski et al. were able to infer the characteristic rate on the terrace sites of the [9(111) x (100)] surface by studying the reaction in the presence of a competitor and a poison. In the presence of a background flux (1015 cm -2 s -1) of CO (which preferentially binds to the step sites [74]) the kinetic parameters for CO production from D2CO were unchanged, while a single pathway for D2 production was observed (fig. 7). The D 2 desorption rate constant was given by 3 x 10-3 exp [-19 ( k c a l / m o l ) / R T s ] cm 2 s -1, in excellent agreement with the low temperature branch in the absence of CO. Next the step sites were selectively poisoned by approximately 10% of a monolayer of sulfur, and the decomposition of D2CO again monitored. The rate constant for CO production was in good agreement with the CO desorption rate con-

2000

--

1000-500

.

'~.

--

--

~ ' %

I0000

-- 5000

2000 I000

-"-....

5o I20 F

"-CO Beom On

500

200

/ I.I

1.2

13

[4 1.5 16 I / T X 103 (K q }

17

Fig. 7. Arrhenius plots of the effective rate constant for hydrogen evolution following decomposition of D2CO on P t ( S ) - [ 9 ( l l l ) x (100)]: (a) without a CO beam and (b) with a CO beam flux of 1015 cm-2 s-1. From ref. [72].

M. P. D'Evelyn, R. J. Madix / Reactivescatteringfrom solid surfaces

441

stant previously measured on the same crystal with the same S coverage [74], and the D 2 rate constant was given by 10-3 exp [-20 (kcal/mol)/RTs] cm 2 s -1. The combination of these latter results provides strong evidence that the low temperature rate constant (faster route) on the clean stepped surface is associated with terrace sites, and the high temperature branch (slower route) with step sites, in agreement with Poelsema et al. [70]. In each case "normal" values of the preexponential were obtained, with activation energies in good agreement with other workers [69-71]. The reasons for the wide range of kinetic parameters obtained by different groups remain unclear, although most of the recent experiments have yielded "normal" results [69-72]. Perhaps differences in crystal preparation are responsible. McCabe and Schmidt [69] have noted that the H 2 TPD peak is much broader than expected for simple second-order desorption; this may be related to a strong coverage dependence of the inferred kinetic parameters. In the absence of any solid evidence for unusual features of the H/Pt interaction which could be responsible for anomalous desorption kinetics [67, 75], it seems reasonable to conclude that in fact the kinetic parameters are qualitatively similar to those for hydrogen recombination on other Group VIII metals. On Pd(111), Engel and Kuipers [46] observed rapid diffusion of hydrogen into the bulk above 300 K, as expected from the well-known facile adsorption and permeation of hydrogen in Pd. They observed a continuous rise in the H 2 - D 2 exchange probability with temperature as did Salmer6n et al. [43], which the latter authors attributed to an activation energy for hydrogen adsorption. Engel and Kuipers showed that the phenomenon could be explained alternatively by assuming that either the activation energy or sticking probability varies strongly with coverage, even in the low coverage limit sampled experimentally. They used the bulk diffusion model of eq. (18) above to interpret their results, and obtained fairly good agreement with the MBRS phase and amplitude data using literature values or reasonable estimates of the various parameters. We note that strong bulk diffusion effects were also observed by Prince and Lambert [76] in the interaction of C12with W, as Well as in a number of gas-solid reactions (sections 5 and 6). 4.2. Adsorption and desorption o f CO

The interaction of CO with Group VIII metal surfaces has been investigated by every surface technique developed to date, including MBRS. A number of common features highlight the adsorption and desorption behavior of CO on Ni [77], Pd [15], and Pt [73, 74, 78, 79]. The sticking probability at zero coverage, So, is of order unity and is insensitive to incident angle and surface temperature, over the range of Ts studied. The sticking probability declines more slowly than (1-0co) with coverage, and is well described by a precursor state model [80, 81]. The

442

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

"precursor" appears to correspond to C O molecules physisorbed above CO-covered chemisorption sites, while no MBRS evidence is seen for a distinct physisorbed state on a clean surface. The activation energy and preexponential factor for desorption are found to be 30-36 kcal/mol and ~ 1015 s-l, in good agreement with the parameters determined by work function or thermal desorption measurements, and the role of surface heterogeneity in determining the low-coverage kinetics is clearly illustrated. The kinetic parameters for adsorption and desorption of CO are summarized in table 3. Preliminary indications are that the vibrational state populations of desorbing CO molecules are given by a Boltzmann distribution at T s, but the rotational energies are less than expected on the basis of full accommodation [82]. For a more systematic account of the interaction of CO with metal surfaces, the interested reader is referred to the review by Yates et al.

[83]. The MBRS rate constant for CO desorbing from Ni(ll0) observed by Helms and Madix [77] (table 3) agreed well with earlier thermal desorption results [11], and firmly established the existence of preexponential factors well above 1013 s -1 for desorption. Sau and H u d s o n [84] obtained a similar M B R S rate constant for CO desorbing from clean N i ( l l 0 ) , but on an annealed carbided surface the preexponential and activation energy decreased to 4 x 106 s-1 and 11.6 kcal/mol, respectively. The values of the preexp0nential factor and the desorption energy are much lower than those obtained by McCarty and Madix (1012.5 s-1 and 21 kcal/ mol) [85] by T P D , but details of the experimental analysis were not given and their origin is unclear. On P d ( l l l ) , Engel [15] found the angular distribution of scattered CO to be very nearly cosine at both low (300 K) and high temperature (1020 K). In the former case the observed distribution is due to scattering from a saturated (0co = 0.5) overlayer with immeasurably short surface residence time; the cosine distribution suggests efficient trapping into a second layer, physisorbed state. At 1020 K the steady state surface coverage is 0co ~ 10-7, and the observed angular distribution is due to desorption, again with very short surface lifetime. A simple ad-

Table 3 Low-coveragekinetic parameters for adsorption and desorption of CO from Group VIII metals Surface

so

A(1) (s-0

E(O (l~cal/mol)

Ref.

Ni(ll0) Pd(lll) Pt(ll0) Pt(lll) Pt(lll) Pt(S)-[6(Ill) ×(100)] Pt(S)-[9(lll)×(100)]

1.0 0.96 0.7 0.84 0.74 0.74 0.6

1015.4 1014.4 1014.8 1015.1 1013.5 1013-9 10150

33 32 35 35 30 34 36

[77] [15] [73] [78] [79] [79] [74]

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

443

sorption/desorption model (table 3) fit the MBRS waveforms quite well for Ts > 500 K. At lower temperatures the data suggested the presence of several adsorption states interconnected by diffusion or, additionally, possible carbon contamination effects. Fair and Madix [73] found s o for CO on Pt(ll0) to have a constant value of 0.7 from TS = 195 to 625 K, by MBRS and TPD. The MBRS desorption rate constant (table 3) predicts a much narrower thermal desorption spectrum than that observed experimentally [73]. However, Fair and Madix were able to account for the breadth of the TPD peak using a one-dimensional Ising model (motivated by the row-and-trough nature of the (110) surface as well as analytical convenience) using the low coverage rate constant together with a coverage-dependent interaction energy of 1.5 + 2.50co kcal/mol. On P t ( l l l ) , Campbell et al. [78] found s o = 0.84 to be independent of 0 i and of Ts over the range 300-400 K. These authors supplemented the usual method for obtaining angular distributions, viz., modulating the incident beam and monitoring the scattered beam using lock-in detection, with transient measurements. The latter technique, which involves measuring the scattered intensity at a given Or as a function of time following sudden introduction of the incident beam on a clean surface, permits the determination of angular distributions at coverages lower than steady-state at a particular surface temperature and beam flux. A series of distributions so obtained at room temperature is shown in fig. 8. The quasispecular lobe appears to be due to direct inelastic scattering of the untrapped fraction (l-s0), while the cosine fraction (which grows with coverage) is though to be due to trapping-desorption from a physisorbed layer above occupied chemisorption sites. The coverage dependence of s was also well described by a precursor state model [80],

s(O) =

1 --

0/0sa t

s o 1 + (K-l)

0/0sa t

(38)

with 0 s a t = 0.5 and K = 0.3. While a precursor state is important above occupied sites, the temperature-independence of So on Pt(111) [78, 79] as well as on other surfaces [15, 73, 77] suggests that above unoccupied sites chemisorption proceeds directly. This interpretation is supported by the modulated beam angular distributions from Pt(111) at 500 < -Ts < 550 K, which approximates that of fig. 8 for 0¢o = 0 [78]. In this temperature range the chemisorbed CO is completely demodulated upon desorption, but CO desorbing from a weakly held precursor should have been observable. The observed desorption rate constant of 1.2 x 1015 exp [-35

(kcal/mol)/RTs] s-l,

was attributed to interaction with sites accompanied by rapid surface diffusion of CO. The steps also manifest themselves as a high temperature shoulder in the CO thermal desorption spectrum; the aforementioned rate constant predicts a TPD peak corresponding to the shoulder rather than the main peak. Lin and Somorjai

444

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

- 20* \

\

~

0° I

20°

/

/

/

Pt (111 ) -t,0* \

310K

//~"

~.

iI

\\\

/

COSINE---~ FRACTION \\

-8oo-

CO

~

/

',)

/ - 60*

xo~,~8¢o=0,5 / t,0*

I

I

-c. --0,35 .....

0

I

\. ,

.

e** :o!

/ ;

/" /

/

60"

80.

Fig. 8. The angular distributions of CO scattered from Pt(111) at 310 K at three coverages during a series of adsorption transients. The CO beam was incident at 0 i = 55 °. The dashed circles indicate how the cosine scattering fraction was estimated. From ref. [78], with permission.

[79] obtained similar results on the flat (111) and stepped [6(111) x (100)] surface. The values of both the activation energy and preexponential were higher on the stepped surface (34 versus 30 kcal/mol and 8 x 1013versus 3 x 1013s-i). The interconversion between step and terrace binding sites was demonstrated quite clearly by Gdowski and Madix [74] on Pt(S)-[9(111) x (100)]. These authors studied the CO desorption rate as a function of sulfur coverage, using MBRS and TPD. The sulfur preferentially binds to the steps, and at 0 s > 0.1 the high temperature shoulder in the TPD spectrum was absent and the main peak shifted to lower temperature, reflecting the repulsive S - C O interaction. The sticking probability only decreased from 0.56 to 0.52 as the step sites became saturated with sulfur. As the sulfur coverage was increased further, s decreased three times more quickly with 0 s. This result shows that the sticking probability is reduced much more by sulfur on terrace sites than at step sites, and hence that most adsorption on the clean surface occurs via the terraces. Both the desorption activation energy and preexponential, as determined by MBRS, were found to decrease smoothly with 0 s. The desorption rate itself, as measured by the temperature at which the phase lag was 45 °, was found to decrease more sharply at 0 s <- 0.1 than at 0 s > 0.1. The latter observation supports the hypothesis that the low coverage kinetics is characteristic of the most tightly bound sates (i.e., the

M. P. D'Evelyn, R. J. Madix / Reactivescatteringfrom solid surfaces

445

steps). Finally, Gdowski and Madix analyzed a general two-site kinetic model and showed that the energetics of direct desorption from steps and an equilibrium between CO bound to steps and terraces followed by desorption from terraces are the same. Invoking detailed balancing, they chose the latter pathway as the dominant mechanism. The internal states of CO desorbing from an uncharacterized Pt foil have been probed by Mantell et al. [82] by Fourier transform infrared (FTIR) emission spectroscopy. The temperature range studied was 1075 to 1500 K, which corresponds to surface residence times of 10-8 to 10-10 s. They found that while the ratio of v = 2 ~ v = 1 and v = 1 ~ v = 0 emission intensities was consistent with complete vibrational accommodation to the surface temperature, the distributions of intensity in individual rotational transitions within each vibrational manifold were distinctly non-Boltzmann. The rotational accommodation coefficient for vibrationally excited desorbing molecules was found to be only 0.8 at Ts = 1365 K. At lower surface temperatures the accommodation coefficient was' higher, and the rotational distributions became more nearly Boltzmann. These results, together with others discussed below, suggest the importance of dynamical effects associated with the thermal desorption process so that rotationally cold, non-Boltzmann distributions can obtain even when the desorbing molecule has attained equilibrium with the surface. By way of contrast, Kori and Halpern [86] have used identical FTIR techniques to analyze the chemiluminescence of CO formed by reaction between chemisorbed carbon and oxygen on an uncharacterized Pt foil at surface temperatures of 1000 and 1400 K. They observed vibrational excitation in substantial excess of a distribution characterized by the surface temperature (up to v = 7). The surface residence time may be estimated to be about 5 x 10-8 s and 3 x 10-10 s at the two temperatures using kinetic parameters for the clean surface [74, 78]. However, rco may be substantially smaller on the steady state carbided surface used in this study, and may also be shorter for highly excited internal states. In any case, rco was short enough so that only partial relaxation could occur, and the observed vibrational distribution appears to contain information on the dynamics of the rather exothermic surface reaction (see further discussion below). 4.3. Adsorption and desorption o f N O

The interaction of NO with Group VIII metals, although not the subject of repeated investigations over a long period of time like CO, is nonetheless of similarly great importance for pollution control. In the past few years there has been an explosion in NO-surface studies, motivated in large part by the relative ease with which the internal states may be probed by laser-induced fluorescence or multiphoton ionization. The kinetics and dynamics of NO scattering from Pt(111) have been investigated by a number of workers [79, 87-94], and this system represents one of the first (along with the more weakly interacting N O / A g ( l l l ) system

446

M. P. D'Evelyn, R. J. Madix / Reactive scattering J~om solid surfaces

[95-102]) for which experimental information exists on the partitioning of energy into each of the degrees of freedom (translational, vibrational, and rotational) of the scattered molecules. The kinetic features of the adsorption/desorption reaction are rather similar to those of CO (section 4.2), although as we shall see, surface heterogeneity in the form of steps or defects plays a larger role. The dynamical studies yielded a few surprises, particularly in the rotational distributions, which were often considerably colder than expected from accommodation to f~. A recent review of the interaction of NO with Group VII1 metals has been published by Lambert [103].

4.3.1. Kinetics of adsorption and desorption The kinetics of the (molecular) adsorption/desorption reaction on flat and stepped (111) Pt surfaces was investigated using MBRS independently by Lin and Somorjai (LS) [79], Campbell, Ertl and Segner (CES) [87], and Serri, Cardillo and Becker (SCB) [88]. In each case, the rate of dissociative adsorption was too small to be measured. The sticking probability at zero coverage (So) is approximately constant at --~ 0.9 over the range 260 < T s < 625 K [87, 88], and the coverage dependence of s is well described by a precursor state model [80, 87], as for CO. The angular distribution comprises a quasispecular lobe, with integrated flux equal to (l-s0), and a cosine fraction [87-89], similar to the behavior of CO (fig. 8). The former is due to direct inelastic scattering of molecules which do not fully accommodate translationally, and the latter to desorption from the chemisorbed state at high temperature and low coverage or to desorption from a second-layer, precursor state at low temperature and higher coverage. The integrated intensity of the directly scattered portion has been reported to increase, implying a decrease in s 0, as the translational energy of the incident N O molecules was increased from 2 to 5 kcal/mol [89, 90]. The desorption rate constants derived from MBRS measurements reflect the presence of defects (steps) on the surface just as in the case of CO, but with NO the steps give rise to dramatic differences in the low- and high-coverage desorption kinetics as well as in the M B R S results from different laboratories. The rate constants obtained by different workers from the MBRS phase lags are shown in the form of an Arrhenius plot in fig. 9, and the derived kinetic parameters are listed in table 4. We note that Segner et al. [104] observed a rate constant for NO production identical to that of CES following dissociative adsorption of NO 2. Also included in table 4 are the kinetic parameters obtained by Gorte, Schmidt and Gland (GSG) [105] by T P D ; the rate as extrapolated to the higher temperatures of the M B R S experiments is shown in fig. 9. While each investigator obtained a similar flat-surface rate at 625 K, the observed temperature dependences are quite different, and SCB observed a substantial flux dependence. Moreover, the MBRS rate constants are more than an order of magnitude less than the extrapolation of the thermal desorption results. It is possible that differences in the crystal surface preparation and in the methods

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

14

625 K

555K

I

I

6

t

500 K L

DESORPTION RATE OF NO FROM Pt(H1)[CLEAN] FOR DIFFERENT EXPERIMENTS

~5

.~GSG (111) ~. \~ "~

°°°° FLUX(Ill)

~

O 15

447

(111j

I

I

i

I

I

16

17

la

19

zo

zl

[T(K)] -I X10 4 Fig. 9. Arrhenius plot of the apparent N O desorption rate constants from P t ( l l l ) obtained by several authors. The five lower curves were obtained by MBRS, while the highest rate was obtained by TPD. From ref. [106], with permission.

Table 4 A p p a r e n t first-order kinetic p a r a m e t e r s for desorption of N O from Pt Surface plane

~o0 (s- 0

10 (monolayer/s)

Step density

AO/ (s 1)

EO) a (kcal/mol)

Ref.

(111) (557) (111) (111) (111) (111)

31-628 63-628 119-572 1338 1338 (TPD)

~ ~ ~ ~ ~

~ 1% ~17% ~ 5% ~ 2% ~ 2%

1013-8 10 I4-1 1015.5 109.4-+1 1012±1 1016

28.6 32.3 33.1 16+2 21.5+2 25

[791 (LS) [79] (LS) [87] (CES) [88] (SCB) 1881 (SCB) [105] (GSG)

0.04 0.04 0.1 1 0.14

448

M. P. D' Evelyn, R. J. Madix / Reactive scatteringfrom solid surfaces

40

1.2 1.0

O.

30 I~ f u ~

.8

u

NO/Pt (111) f=5Hz Model A

E

E 0

z

o

20 <3

I I

.45

(D

10

oAmplitude z~Phaselag

..c ,..,,

k

.2 0 300

i

I

500

I

I

I

I

700 900 Temperature (K)

f

I

-10

1100

Fig. 10. Normalized amplitude, ]Fs[, and phase lag, q~, of the surface transfer function for NO scattered from Pt(lll). The NO beam was incident at 45° and the scattered and desorbed molecules were detected as background pressure fluctuations. The dashed curves are fits obtained using a parallel reaction model with a coverage-dependent branching probability. From ref. [79], with permission.

used in collecting and analyzing the d a t a are partly responsible for the rather large discrepancies in the kinetic p a r a m e t e r s listed in table 4. H o w e v e r , the presence of subsidiary m a x i m a in the amplitude and phase data of LS (fig. 10) is strongly suggestive of a b r a n c h e d process, and the flux d e p e n d e n c e observed by SCB indicates a nonlinear process. It was o b s e r v e d that the presence of oxygen on the surface dramatically increased the desorption rate [87, 88], and on an oxygen-saturated surface the N O desorption rate a p p r o x i m a t e d that of G S G [88, 105,106]. The latter observation, t o g e t h e r with the presence of a small high-temp e r a t u r e shoulder in the N O t h e r m a l desorption [87], suggests the importance of defect sites which bind N O m o r e tightly than the terrace sites and are p o i s o n e d by oxygen. 4.3.2. Kinetic m o d e l f o r adsorption and desorption Serri et al. [106] p r o p o s e d a relatively simple microscopic kinetic model, incorporating surface diffusion on both terrace and step sites and saturation of the step sites, which reconciled the various M B R S m e a s u r e m e n t s using reasonable values of the m o d e l kinetic p a r a m e t e r s . T h e model, with the various kinetic processes, is illustrated in fig. 11. The p a r a m e t e r s used to fit the e x p e r i m e n t a l results are summarized in table 5. A d s o r p t i o n and desorption (with rate constant kT) are assumed to occur only on the terraces, for simplicity. H o p p i n g to adjacent sites on the terrace occurs at rate k H, and conversion from a step site to an adjacent terrace at rate k s . Saturation of the steps is included by making the flux into the step

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

449

¢.//// //

/ //// / / /

J -I

/

/ / /

/

STEP

J+l

Fig. 11. Illustration of the kinetic model described by eqs. (39). The flux into any terrace site is given by the product of the sticking probability and the incident beam flux, plus the rate at which molecules on adjacent sites hop onto the location, described by the rate constant kn. The flux out is given by the diffusion rate out of the site plus the desorption rate (kw). The flux into and out of step sites is governed by the diffusion rate constant times an occupancy factor and the escape rate ks, respectively. From ref. [106], with permission.

sites proportional to [1-yr/0(t)] , where ~/0(t) is the adsorbate concentration on the steps. The concentration dependent rate equations for the concentrations in each row of sites parallel to the steps are //0(t) = - 2ksr/0(/) + 2kH[ l - yr/0(t)] r/1(/),

(39a)

ih(t) = solo(t) + ksr/0(t) - ( k v + kH[2-yrlo(t)]} r/t(t) + kHr/2(/),

(39b)

iIj(t) = s0/0(t) - ( k r + 2kH)r/j(/) + kn[~ii_x(t) + r/i+l(t)] ,

(39c)

together with the appropriate boundary condition at the midpoint of the terrace. In eqs. (39) the subscript j represents the jth row of terrace sites next to the step. This model is similar to that of Gdowski and Madix [74], although the latter model considered only overall (as opposed to microscopic) rates and did not allow for saturation of the step sites. The kinetic equations (39) are nonlinear due to the Table 5 Summary of parameters in kinetic model (after ref. [106])

kT kH ks S=l,y=4.

AO) (s-l)

E a (kcal/mol)

1016 1013-7 1012

25 5 14

450

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

step saturation term, and were solved by numerical integration. For the values of the rate parameters appropriate to P t ( l l l ) (table 5), the approximation of uniform terrace concentration (kH large) was found to be accurate. Serri et al. [106] also gave a numerical demonstration that surface hopping rates smaller than about 10 t0 sites s-1 should be experimentally measurable using MBRS on very carefully prepared and characterized surfaces.

4.3.3. Velocity and internal state distributions The aim in dynamical studies of reactive scattering is to attain a fundamental understanding of the microscopic processes involved in surface reactions (in the simplest case, desorption). In particular, the respective roles of the gas-surface interaction potential and of energy exchange in reactive scattering are of interest. Measurements of the internal energy distributions are necessary in order to fully elucidate the disposition of energy in surface reactions; they also provide the most sensitive test of theoretical models. The simplest (and long held) assumptions one can make are that desorbing molecules have a cosine angular distribution, a Maxwellian velocity distribution and Boltzmann internal state distributions, all with a characteristic temperature equal to Ts. In the case of hydrogen, the first two assumptions are often violated (section 4.1.1) and in general, one expects deviations from the above behavior, from the principle of detailed balance, unless the sticking probability is independent of angle and of translational and internal state energy. For weakly interacting systems such as N O / A g ( l l l ) , the scattering is dominated by the direct inelastic channel [95-102], and significant changes in the energy distributions of the scattered molecules are observed as the translational energy of the incident molecules is varied [98, 99, 102]. Chemisorbing systems such as NO/Pt are characterized by a well depth that is much larger than typical translational incident energies [1-5 kcal/mol], and the scattering is dominated by trapping-desorption (s o of order unity). Therefore, we expect the observed velocity and internal state distributions to be largely characteristic of desorbing molecules (particularly away from the specular angle, Or = 0i) and thus to be largely independent of the dynamical characteristics of the incident molecules, and indeed this is essentially the behavior observed [89-92]. Guthrie et al. [90] found the velocity distributions of desorbing NO to be well described by a Maxwell-Boltzmann distribution at Ts (flux mean energy = 2kBTs), although some deviations from perfect accommodation were seen at high surface temperature. This behavior is consistent with the observed cosine angular distributions of desorbing NO molecules [87-90, 92]. The flux mean energy is plotted as a function of Ts in fig. 12. The mean translational energy of the incident molecules was 2.4 kcal/mol (= 2k B × 615 K), and 0i = 51 °. The less efficient accommodation of molecules detected at the specular angle reflects the contribution of inelastically scattered molecules, which have a surface interaction time of order 10-12 s. The surface residence time of chemisorbed molecules at 1000 K, the temperature at which deviation from complete translational accommodation first

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

17_00 I

~

:

-

~

"

]

--

i

451

T /j--

!

/.

I000

////I • C) / i// ©

800 A OJ N" V

0

///~/ / coo

"B =

/

0 Specular

,/

//

400

//

K

/

• 7 ° from Normal

/

/ 3oo

i

!

J

500

I 700

I

I

t

900

I IIoo

i

1300

Surface temperalure (K) Fig. 12. Flux m c a n k i n e t i c e n e r g y o f N O m o l e c u l e s s c a t t c r c d f r o m Pt(111), as a f u n c t i o n o f T~. T h e N O b e a m h a d a n a v e r a g e k i n e t i c e n e r g y o f 2.4 k c a l / m o l a n d w a s i n c i d e n t at 0~ = 51 °. T h e s c a t t e r e d m o l e cules w e r e d e t e c t e d e i t h e r at 0, = 0 i (circles) o r at 0, = 7 ° (filled circles). F r o m ref. [90], with p e r m i s sion.

becomes noticeable, is about 10 -9 s, as calculated using the kinetic model of Serri et al. [106]. At higher incident energy (5.5 kcal/mol), mean translational energies of scattered molecules slightly higher than 2k BTSwere also observed. This behavior may be due to contributions from directly scattered molecules, though this would require direct inelastic scattering far from the specular angle. Measurements of the vibrational energy of NO desorbing from Pt [91-93] have yielded somewhat cold distributions, although the temperature dependence of the populations of the v = 1 and v = 2 levels suggests that accommodation is efficient nonetheless [91, 92]. Asscher et al. [91, 92] found that the population ratio of the first excited and ground vibrational states was well described by

P(v= 1)/(P(v=O) = 0.67 exp (-E,,/kBTs),

(40)

over the range 450 < T s < 950 K (fig. 13), where Ev = 1876 cm -1 is the energy difference between the two states. At temperatures greater than 1000 K, somewhat lower ratios were obtained. The vibrational state populations were assumed to be proportional to the populations of the bandhead (i = ~1 - ~ 1) of the Q21 + P21 rotational branch, as determined by two photon ionization [91, 92]. The vibrationally excited molecules all resulted from desorption, as evidenced by a purely cosine angular distribution. The simplest explanation for the above behavior is that the desorption rates for molecules for adsorbed molecules in the v -- 1 or v -- 0 states are slightly different, and that the factor 0.67 represents the ratio of the preexpo-

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

452

1.0

o

Iv

I

i

o
I

I

o °

u

008

o

_o

'i 0 z Q6

/

BOLTZMANN DISTRIBUTION Ev=1876cm'l " " /

z Lo z o

6 o z

0.04 "> o 7-

400

800

1200 Tcrystol (K)

0 1400

Fig. 13. Vibrational distribution of NO molecules scattered from Pt(111), as a function of Ts. Open circles: experimental N O (v = 0) signal. Crosses: ratio of N O ( v = 1) to N O ( v = 0) signals. Heavy solid line: ratio corresponding to a Boltzmann distribution at Ts. Dashes line: eq. (40). From ref. [92], with

permission.

nentials [92]. Mantell et al. [93] obtained a somewhat higher coefficient, 0.88, for the population ratios of the v = 2 and v = 1 levels, in which case E v = 1848 cm -t. The latter result was obtained using FTIR emission spectroscopy with an unchar acterized Pt foil, at a single temperature of 1430 K. In contrast to the behavior of translational and vibrational energy, the rotational distributions of desorbing N O at low surface coverage, as obtained by Asscher et al. [91, 92], by Segner et al. [89] (using laser-induced fluorescence), and by Mantell et al. [93], have been found to be considerably colder than expected for complete accommodation. Two typical rotational distributions of N O in the ground vibrational state are shown in fig. 14. For 400 < TS < 850 K, Boltzmann distributions were found in desorbing molecules, as shown by the linear dependence on the logarithm of the populations divided by the degeneracy factor on rotational energy (fig. 14), but at temperatures of only 350-450 K (fig. 15). At room

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces 6

I

I

I

453

I 0 i" 62",

Tcrystoi = 5 8 0

K

Of <:~ _

rot =480--+ 45 K

0

62 °

•

NORMAL

+

Z Z d

Trot =4004- 4 0 K ~

~. ~.

"-t.

I 200

I 600

-.

I I000 E r o t (cm -I )

-

~

I 1400

1800

Fig. 14. Boltzmann plot (i.e., logarithm of the populations divided by the degeneracy factor versus energy) of the rotational distributions of NO molecules scattered from Pt(111) at 580 K. Open circles: 0r

= 0i = 62°. Filled circles: 0r = 0°. From ref. [92],with permission. temperature and below, the steady state N O coverage is large, varying from 0NO = 0.3 to 0.5 [89], and the scattered N O molecules had a Boltzmann rotational energy distribution at T s [89, 92, 94], consistent with trapping in a precursor state (section 4.3.1). Segner et al. [89] found the rotational distributions to be essentially unchanged in the presence of an oxygen overlayer, with 0 o = 0.6 (fig. 15). The rotational temperature detected at the specular angle may be somewhat higher than at 0 r -- 0 ° [89, 91, 92], due to translational-to-rotational energy transfer in the direct-inelastically scattered fraction (as has been seen for NO/Ag(111) [98, 99, 102]). At higher temperatures (870 K, 1430 K), significant departures from Boltzmann behavior were found, with the populations of states with j > 20 being substantially higher than expected from an extrapolation of the Boltzmannlike results for smaller] [91-93]. The accommodated behavior seen in the translational and vibrational distributions for 450 K < T s < 950 K suggests that the cold rotational distributions are due to dynamical effects in the desorption process, rather than to a failure to accommodate. This is strongly supported by other observations, both experimental and theoretical, of cold rotational and/or translational energy in desorbing molecules (see beloW') and by the determination, by Asscher et al. [107], that N O formed by oxidation of N H 3 was cold both rotationally and vibrationally. The distributions at T s = 804 K were identical, within experimental error, with those observed for NO desorbing molecularly [92]. The reaction

454

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surjaces

i

Trot

,

r

,I

y

,

,

[K] 500 [2°O

olo//

O(

/

l.O0

300

200

System / lOO

/

Incidenceangle 30°

56 °

NO/Pt(111)

0

[]

NO-He/Pt(111)

•

NO/Pt(111)*O

0

[]

NO-HeJPt(lll)*O

260 360

760 860

Tsuaace[K] Fig. 15. Rotationaltemperature (slope of Boltzmannplots, cf. fig. 14) of NO moleculesscattered from clean and oxygen-coveredPt(lll), as a functionof T,. Open and filledcircles: 0i = 30° = 0f. Open and filledcirclcs: 0i = 30° = 0r. Open and filledsquares: 0. = 56°, 0r = 0°. From ref. [89], with permission.

NH 3 + 0 2 ~

NO + H 2 0

has an overall exothermicity of 53 kcal/mol, with the surface reaction being exothermic by ~ 27 kcal/mol, based on estimates of the adsorption energies of NH 3 [108], O2 [109], NO [105], and HeO [110]. Given the excited vibrational states observed following oxidation reactions of carbon [86] (section 4.2) and of CO (section 4.5 below), one might have expected to see excited distributions of desorbing NO which could yield information on the dynamics of the surface reaction. However, the surface residence time of the product N O may be estimated to be about 10-9 s, assuming the step sites to be poisoned by adsorbed oxygen [87, 88, 106] and neglecting the possibility of faster desorption rates for an internally excited transition state. Given the rapid apparent equilibration rate of adsorbed N O (essentially complete accommodation for rNO ~> 10-9 S), the observed N O distributions following N H 3 oxidation are perhaps not so surprising.

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

455

Cold rotational energy distributions have also been observed for molecules desorbing from other surfaces, as have cold translational energy distributions. Cavanagh and King [111,112] have found the characteristic temperatures of the distributions of both rotational energy and of translational energy (for motion of molecules parallel to the surface, in the v = 0, j = ~ state), for NO thermally desorbing from Ru(001) at Ts = 455 K, to be approximately equal to 235 K. Thorman and Bernasek [113] observed accommodated vibrational distributions, but cold rotational distributions (with a characteristic temperature of 400 K), of N 2 following (atomic) bulk permeation and subsequent associative desorption from a clean iron surface at 1086-1239 K. By way of contrast, Talley et al. [114] found the characteristic temperatures of both the rotational and vibrational distributions to be equal to Ts for O H radicals desorbing from a Pt wire at 1130 K. In a series of time-of-flight studies of molecules scattered from a P t ( l l l ) surface, Wharton and co-workers obtained, for the desorbing fraction, Maxwellian velocity distributions near Ts in the case of Xe (T~ = 185 K) [24] and N 2 (175-300 K) [25], while the mean translational energies for Ar (100 K) [115] and C H 4 (180-250 K) [25] were distinctly subthermal. Tully [116] observed cold translational energy distributions of Ar and Xe (at elevated temperatures) desorbing from P t ( l l l ) (fig. 16) in stochastic classical trajectory computer simulations. For NO desorb-

1.0

i

i

i

0.9

0.8 fx V

0.7 A

0.6

1000

2000

SURFACE TEMPERATURE Ts (K)

Fig. 16. Mean translational energy of Ar and Xe desorbing isothermally from Pt(lll), as observed in stochastic classical trajectory computer simulations. From ref. [116], with permission.

456

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

ing from A g ( l l l ) , Tully [117] found both the translational and rotational energy distributions to be cold. In each case, the semiempirical gas-surface interaction potential gave a good description of the experimental scattering behavior [24, 26, 95, 96, 99, 115]. Tully found the translational "cooling" to be due to inefficient energy transfer between surface and adsorbate, which caused s o to decrease with translational energy [116], coupled with, in the case of NO, efficient rotationalto-translational energy transfer due to the rotational anisotropy of the potential energy surface [117]. Note that, by detailed balance, a characteristic temperature less than Ts for a given degree of freedom of desorbing molecules indicates that the sticking probability should decrease with increasing energy in that degree of freedom. As noted earlier, s o for NO on P t ( l l l ) decreases with increasing translational energy. The (molecular) trapping probability for N 2 on (100) [81, 118] and polycrystalline W [119] has also been found to decrease with increasing translational and/or internal energy of the incident molecules. The most likely explanation for cold internal state and/or velocity distributions of desorbing molecules or atoms, and for the reciprocal phenomenon of s o decreasing with incident energy, appears to be energy exchange limitations. However, both the nature of the transition state and the shape of the potential energy surface along the desorption (exit) channel [113,120, 121] may be of considerable importance in determining the actual distributions. Also of possible importance is the conversion of zero-point hindered rotational energy in the adsorbed species to rotational energy as the chemisorption bond is broken [122]. Many of the details of desorption dynamics, including determination of the characteristic energy exchange rates, will require considerably more experimental and theoretical analysis for any kind of complete understanding. Nonetheless, it is well established that desorption can lead to energy distributions significantly different from MaxwellBoltzmann distributions at the surface temperature. The relatively rapid accommodation rate (or order 109 S-1, from the N O / P t ( l l l ) data), although slow on the vibrational time scale, suggests that excited internal energy distributions in the desorbing products of exothermic surface reactions will only be observed at high surface temperatures or for product molecules that interact weakly with the surface. 4.4. Activated adsorption of N 2 Molecular beam techniques have been used to study adsorption kinetics on a variety of systems. While these studies generally fall outside the scope of this review, we do mention some recent experiments on the activated adsorption of N 2. This is an important problem, for example, as dissociative adsorption of N 2 is the rate-limiting step in ammonia synthesis over iron catalysts [123], and activation barriers of 5 and 7 kcal/mol have been reported for the (100) and (110) surfaces [124, 125]. On W(100) dissociative adsorption of N2 is facile, with So = 0.6 [81, 118], while on the more densely packed (110) surface s o ~ 10-3.

M. P. D'Evelyn, R. J. Madix / Reactive scattering frorn solid surfaces

457

Auerbach and co-workers [126, 127] showed, using supersonic molecular beams, that dissociative adsorption of N 2 on W ( l l 0 ) is activated, with a barrier of roughly 20 kcal/mol. Incident translational energies from 2 to 50 kcal/mol were produced using a nozzle at temperatures from 300-1000 K and by seeding the N 2 into He or H 2. The initial dissociative sticking probability rose from 3 x 10-3 to 0.4 with the rate of increase (on a linear scale) being most rapid at a beam energy of approximately 20 kcal/mol (fig. 17). The sticking probability was found to decrease with nitrogen coverage as (1-0N) 2 at low coverage, suggesting a direct, rather than precursor-mediated, process. The saturation coverage was found to increase with beam energy, with an unusual autocatalytic desorption state being populated above ON ~ 0.25. The initial sticking probability was relatively insensitive to the incident angle, so that in contrast to the H2/Cu system [44], So scales approximately with the total kinetic energy, rather than with the component normal to the surface (fig. 17). Such behavior is completely at odds with a quasi-one-dimensional activation barrier. Auerbach et al. [127] found that the sticking probabilities obtained using an effusive source, at oven temperatures up to 2000 K, were within experimental error of the values derived by convoluting so(E) by the

I

100

i

I

I

o 6

Xo

8 •

•

ii x

0

•

o

10- I

•

-~.

x=

0 °

30*

g

o = 45 °

o i.o

• = • =

55*

60 °

•

j

ZE 10-2 J

m,. 10-3 o

I 50

I

I

1 O0

150

I 200

Beam Energy (kJ tool -1 ) F i g . 17. Initial sticking probability, So, as a function of translational energy of N 2 molecules incident on a W ( l l 0 ) surface at various angles of incidence. It is seen that s o is insensitive to 0 i for 0i <~ 45 °. The dashed curve indicates the sticking probability predicted at 0i = 60 ° by using the 0i = 0 ° data and assuming that s o scales with the normal component of kinetic energy. Clearly the actual 0i = 60 ° results lie much closer to the uncorrected 0 i = 0 ° data. From ref. [127].

458

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

effusive kinetic energy distribution. This result indicates that the reaction is primarily translationally activated. 4.5. CO oxidation The catalytic oxidation of CO on platinum metals is undoubtedly the most widely studied and best-understood surface reaction. We will confine ourselves to a discussion of the contribution of molecular beam techniques to the understanding of the reaction mechanism and of the dynamical aspects of the disposal of the reaction energy, along with a brief discussion of the change in the kinetic parameters with reactant coverage. For further details the interested reader is referred to the recent reviews by Engel and Ertl [128, 129] and to the references given below. For Ts > 200 K the reaction takes place between chemisorbed O and CO, commonly referred to as the Langmuir-Hinshelwood (LH) mechanism: sc___~o CO(g) ~-co COa'

(41a)

so

O2(g ) ~oo222 0 a ,

(41b)

C O a -'1--O a k--~ LH C O : ( g ) ,

(41c)

Under normal reaction conditions the desorption of oxygen may be safely ignored. Earlier kinetic studies of CO oxidation were not able to clearly distinguish between the above LH mechanism and an Eley-Rideal (ER) mechanism, between chemisorbed O and incident or physisorbed CO. However, modulation of the incident CO beam in an MBRS experiment allows for the unambiguous measurement of the surface residence time of the reaction intermediate (since the product CO 2 is only weakly bound to the surface), and has clearly demonstrated the dominance of the LH mechanism over all reaction conditions studied with Ts > 200 K (see table 6 below; for Ts < 200 K an additional reaction channel, between adsorbed CO and adsorbed molecular oxygen, becomes available [130]). The co-adsorption behavior of CO and O is sufficiently complex, however, that no rate expression has been given that describes the reaction rate over the full range of temperature, incident fluxes, and coverages. The CO 2 product on P t ( l l l ) desorbs with translational and internal energy substantially in excess of that expected from equilibration with the surface; the details of the distributions change with reactant coverage and promise to yield information on the dynamics of the surface reaction. 4.5.1. Mechanism and kinetics MBRS investigations of CO oxidation on Pd and Pt single-crystal surfaces, by Ertl and co-workers [131,132] and others [133], were instrumental in establishing

M. P. D'Evelyn, R. J. Madix / Reactive scattering f r o m solid surfaces

459

the dominance of the L a n g m u i r - H i n s h e l w o o d mechanism (41) and in quantifying the qualitative change in the kinetics in going from the low-coverage limit to oxygen-saturated surfaces. The results of these experiments are summarized in table 6. The kinetics in the low-coverage limit seems to be well understood, while questions remain on the high coverage behavior. Co-adsorbed CO and O interact in complex ways: chemisorbed CO inhibits the adsorption of O2, while Sco is largely unchanged by adsorbed oxygen [128, 129, 134-136]. Chemisorbed oxygen forms islands, due to attractive interactions, at coverages as low as 0.05 at T S = 300 K. CO adsorbs exterior to the oxygen islands, and at sufficiently high coverage compresses the oxygen [134-136] and may form a mixed C O - O phase, at least on Pd [134,136]. In view of this behavior it is not surprising that the detailed kinetics at intermediate and high coverage is not fully understood, and that relatively little numerical modeling of reaction kinetics over a wide range of reactant fluxes and surface temperatures has been performed to date [137,138]. In their study of CO oxidation of P d ( l l l ) , Engel and Ertl [131] alternatively modulated a CO or O 2 beam in the presence of a background pressure of the other reactant. In each case the observed CO2 phase lag and its temperature dependence was entirely consistent with the LH mechanism and contradicted the behavior predicted by an E R mechanism. When both 0co and 0 o were small, the activation energy for the reaction was found to be 25 kcal/mol, with a normal preexponential factor (table 6). The M B R S experiments were complemented by transient measurements, where the crystal was pre-saturated with Oa, and the reaction rate was followed after suddenly switching on a CO beam. The activation energy at low 0co and high temperature was found to be 28 kcal/mol, in good agreement with the M B R S result, while for 0co > 0.02 at lower temperature the activation energy decreased to 14 kcal/mol. Both sets of reactions with high 0 o were presumed to occur at the perimeter of the oxygen islands, with the change in kinetic parameters at higher coverage being associated with compression of the islands and concomitant destabilization of the metal-adsorbate bonds. This idenTable 6 Kinetic parameters for C O oxidation Surface

0co

0o

T~ (K)

A(2t (cm2 s i)

Ea (kcal/mol)

Ref.

Pd(lll)

< 0.1 < 0.02 0.06

<0.01 0.20-0.25 0.20-0.25

460-560 500-700 300-450

10-2 10-0.5 10-6

25 27 14

[131]

Pt(111)

< 0.1 < 0.02 <10- 3

<0.01 0.20-0.25 0.25

475-660 265-350 350-475

10-1 10- 7 10-5.4

24 11 12

[132]

Pt(S)-[9(ll 1) × (100)]

<10-4

480-660

10 7

10

[133]

0.23

460

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

tification is supported by temperature-programmed reaction (TPR) experiments on Pd(111) [134] and Pd(100) [136], where an additional, lower temperature CO2 product peak appears when the CO coverage is sufficient to begin to compress the oxygen islands. In the case of Pt, Fair and Madix [133] employed a background oxygen flux sufficient to nearly saturate the (stepped [9(111) x (100)] surface, and modulated the incident CO beam (see table 6). Campbell et al. [132] utilized a modulated 02 beam with a small CO background pressure to obtain the rate constant when both 0co and 0o are small. The activation energy was combined with the adsorption enthalpies of CO [78] and of O [109] to construct the reaction enthalpy diagram in fig. 18. Campbell et al. also performed transient measurements of the reaction rate on an oxygen-presaturated surface, alternatively with a continuous or modulated CO beam. The latter experiment, carried out under conditions for which the CO oxidation rate is much greater than the desorption rate, allows for the direct measurement of the CO residence time as a function of 0o. The kinetic parameters obtained from the transients were in relatively good agreement with the result of Fair and Madix. We note that the modulated experiments were conducted in two different regimes which allowed for linearization of the reaction: (i) at a high, constant value of 0 o, with a modulated CO beam, and (ii) with a modulated 02 beam, at surface temperatures such that CO desorption is rapid compared to oxidation, so that 0co ~ constant. The behavior of the transients ob-

tO

co._:_..

T

-10 T

-6 -20 E -6 o . 30 Y

>, -40

O~

-50

~-60 3 -70 -80

~.H, 67,5 kcQI.mole "1

2

C02

COo • Oa

COL,

Fig. 18. Enthalpydiagramfor the CO oxidationreaction on Pt(lll) in the lowcoveragelimit. Fromref. [131],withpermission.

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

461

served by Campbell et al. is quite similar to that seen by Engel and Ertl, suggesting a similar mechanism (island compression) at high total reactant coverage. However, in a recent TPR experiment on P t ( l l l ) [135], only one peak was seen over a wide range of initial coverages, including those sufficient to compress the oxygen. Fair and Madix have argued that the anomalously low frequency factors at high 0 o can be explained by the presence of soft vibrational modes for adsorbed CO, which result in a relatively high partition function. The effect of steps on the low-coverage desorption rate of CO was noted earlier. Recent work by Gland et al. [139] on the atomically rough Pt(321) surface indicates that oxygen adsorbed at terrace sites reacts more readily with CO than oxygen at kinked step sites. This suggests that a steady-state reaction will occur primarily on the terraces (at least at high coverage, since both oxygen [109,140] and CO [74, 78, 141] preferentially bind to step and kink sites on Pt), in accord with the agreement between the results of Fair and Madix and of Campbell et al. on oxygen-covered [9(111) × (100)] and (111) surfaces, respectively (table 6). These observations are consistent with the classification of CO oxidation as a structure-insensitive reaction [129].

4.5.2. Angular, velocity, and internal state distributions in the C02 product The observed LH activation energies represent a significant amount of energy (see fig. 18) that must be distributed between the surface and the various degrees of freedom of the desorbing product molecule. Given the relatively weak adsorption energy of the product CO 2 (5-7 kcal/mol [130]) and its correspondingly short surface residence time under typical reaction conditions, one might expect to see a substantial fraction of the reaction energy in the various degrees of freedom of the desorbing CO 2. Hot CO 2 product molecules have indeed been seen following reaction on Pt surfaces, with energy distributions that are dependent on the surface reactant coverages. Interestingly, no such effects have been seen on Pd, despite the rather similar energetics for the reaction. Palmer and Smith [142] found that the angular distributions of CO2 produced by CO oxidation on epitaxially-grown P t ( l l l ) could be well fit by the function cosa0r. The exponent d varied from 4 - 6 on different surface samples, with higher values being obtained on smoother surfaces, as monitored by He scattering. Becker et al. [143,144] obtained d = 7 on clean P t ( l l l ) at 750 K, and somewhat broader distributions, d = 2-3, over Pt foil. In contrast, the CO 2 angular distribution above P d ( l l l ) is diffuse [131]. The peaked CO 2 angular distributions on Pt suggest an elevated product translational energy. Indeed, Becker et al. measured, by time-of-flight techniques, average kinetic energies of 14 and 7 kcal/mol for C O 2 emitted, at Or = 0° and Ts = 900 K, from P t ( l l l ) [143] and Pt foil [144], respectively. In both experiments the average kinetic energy declined away from the surface normal. Ertl and co-workers [132, 145] found significant variations in the CO 2 angular distribution with surface temperature and reactant coverages, and concluded that

462

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

differences in the accommodation probability for the product CO2 were responsible. Angular distributions were measured both using lock-in analysis of the CO2 product with a modulated reactant beam, and from the transient measurements described in section 4.5.1 [132]. Segner et al. [145] found that the distributions could all be fit by Id(0r) oc acos Or + (1 - a ) cos 7 Or,

(42)

with the coefficient a varying with the reaction conditions (actually, density rather than f l u x angular distributions were measured; this does not affect the conclusions below). The fraction, F 7, of product molecules in the COS70rchannel is given by [145] /77-

2(1-a) 2+6a'

(43)

and is shown as a function of 0 o and T s in fig. 19. The cos 0r channel was attributed to desorbing CO2 molecules that had equilibrated with the surface, and the COS70rchannel to molecules that desorbed prior to accommodation. This identification is supported by separate experiments in which the signal intensity in the trapping-desorption channel (So = 0.5) of scattered CO 2 decreased as T~ u2 up to 600 K [145], and a cos 0r CO2 distribution was seen by angle-resolved TPD [130]. F 7 was observed to increase with 0o (cf. fig. 19; T s ~> 500 K, where 0co is small) and even more strongly with 0co (fig. 19; Ts < 500 K and 0 o small). F 7 also

04 an/"

.o 560K

O

02

0.1

p~o

" ~ u~

"f"'[-~,~ ~.

0.05

01

015 "

T,=280K ]

02

00

Fig. 19. Fraction of flux of CO2 produced by CO oxidation on Pt(111) in the cos70rchannel, as a function of oxygen coverage and surface temperature. The CO flux was 3 x 1013cm-2 s-l, incident at 45°.

From ref. [145],with permission.

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

463

increased with Ts, when either 0 o = 0.25 (fig. 19) or when both reactant coverages were less than ~ 0.02 (T s > 600 K, steady state reaction). Segner et al. deduced that accommodation of CO 2 takes place primarily at step or defect sites (they estimated their crystal to have a 5% step density [78, 87, 145]) based on (i) comparison of their angular distributions with those of others on (111) [130,142, 143] and polycrystalline [130, 144] Pt surfaces; (ii) the reactant coverage effects mentioned above (further discussion below); (iii) the sharp increase in F 7 as 0co increased to ~ 2 - 5 % in the steady state reaction [145]; and (iv) the decrease in F 7 [143, 145] in the presence of unreactive subsurface oxide [146], which should increase the microscopic roughness of the surface. Segner et al. [145] argued at at low coverage and Ts ~< 500 K the oxidation reaction takes place primarily at step sites, since the binding energies of both CO and O and the sticking probability for 0 2 are higher at steps than on the terrace [78,109], and Oa is relatively immobile [147]. The accommodation probability for CO 2 formed at step sites was assumed to be much larger than for reaction at terrace sites. The observed changes in F 7 with the reaction conditions were then explained by: (i) at higher Ts and fixed 0 o and 0co, the equilibrium reactant population at terrace sites increases relative to the step sites, resulting in a higher fraction of CO 2 formed at terrace sites; (ii) an accommodation probability for CO 2 that declines with increasing Ts; and (iii) at higher 0co or 0 o the reaction shifts onto the terrace due to saturation of the steps, resulting in an increase in F 7. We note, however, that at least on the rough (321) surface, oxygen at t e r r a c e sites reacts most readily with CO [139]. The results of Segner et al. could also be explained by accommodation of the CO 2 product at step sites, even if the oxidation reaction takes place primarily on terrace sites at all reactant concentrations. The accommodation probability for CO 2 would decrease with T~ since its surface residence time, and hence its likelihood of diffusion to and trapping at a step site prior to desorption, diminishes. At higher reactant coverages, the step sites would be blocked by relatively unreactive species, and the equilibration probability for CO2 product would also decrease. A substantial fraction of the reaction energy on Pt is also released as internal excitation of the C O 2 product molecules, as shown by a series of infrared emission experiments. In a flow-tube experiment, Bernasek and Leone [148] determined from the observed infrared chemiluminescence that CO2 formed over Pt gauze has excess vibrational energy in the asymmetric stretch mode. This conclusion has been confirmed and elaborated on considerably in a series of F T I R emission experiments by Mantell et al. [149-151]. These authors found that their high resolution (0.06 cm-1) spectra could be well described by Boltzmann distributions at different temperatures for each vibrational degree of freedom together with a common distribution for the rotational populations within each band. The results of their fits (made using five vibrational bands in the asymmetric stretch portion of the spectrum) are reproduced in table 7. They found that a two-temperature distribution was necessary to describe the rotational distributions. The lower rota-

464

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

Table 7 Internal mode temperatures for CO 2 produced by CO oxidation on polycrystalline Pt (after ref. [150]) Ts

(K) 730 900

Vibrational temperature (K)

Rotational temperature (K)

vs

va

Bend

TI

T2

1300 1700

1600 1750

1500 1600

200 200

1050 1200

tional temperature was ascribed to collisionally-induced relaxation in the gas phase, based on an extrapolation to zero density. The assumption of independent Boltzmann distributions for each mode was judged to be a good one based on the good agreement between calculated and observed spectra at low resolution (4 cm-1), where more than 200 vibrational bands contribute to the spectrum. An additional intriguing observation is that while the CO 2 production rate reached a maximum at 780 K, at higher temperatures the integrated IR intensity per product molecule decreased more slowly than the reaction rate. This means that the emission signal per molecule increased, which was explained by postulating that the average translational energy of the CO 2 molecules decreased with Ts, which is consistent with the observations by Segner et al. [145] if the steady state coverage of CO decreases below the defect density in this temperature range. Unfortunately, Mantell et al. [150] made no estimate of the steady state reactant coverages or of the density of n o n - ( I l l ) sites in their experiments, so a more detailed comparison is not possible. Mantell et al. [151] have also studied the CO2 energy distribution over Pt and Pd foils in a time-resolved mode, which allows the effect of surface coverage to be explored independently of T~. They used a free 02 jet and a pulsed CO jet, and collected infrared interferograms at various intervals after the beginning of a CO pulse. The low resolution spectrum obtained with Pt at 800 K was observed to narrow near the end of a CO pulse, indicating a reduction in CO2 internal energy as O a became depleted. No effect with 0 o was observed over Pd. The steady state oxygen coverage between CO pulses may be estimated as ~ 0.2, using the sticking probability and desorption rate constant data for O2/Pt(lll ) of Campbell et al. [109], while each CO pulse consisted of approximately 1.5 monolayers. These experiments thus appear to be analogous to the titration experiments of Ertl and co-workers [132, 145], discussed in detail above. Together, these results show that both the translational and internal energy of the desorbing CO 2 molecules are lowered when both reactants are at low coverage, possibly due to trapping of the CO2 product at step or defect sites. The experiments of Mantell et al. [149-151] have yielded some very interesting results; needless to say, quantitative interpretation would be facilitated by accurate values of surface reactant coverages during the course of the experiments, as well as the use of well-characterized metal surfaces (recall the differences in both the angular and velocity distributions between (111) and polycrystalline Pt [130, 142-144]).

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465

4.6. Hydrogen-oxygen reaction The hydrogen-oxygen reaction, while of considerable importance to electrochemistry and corrosion and as a model oxidation reaction, has been studied much less extensively (both generally and by molecular beam techniques) than CO oxidation. The reaction apparently proceeds via a Langmuir-Hinshelwood mechanism, involving dissociative adsorption of both reactants and sequential addition of hydrogen to Oa: SH2

H2(g) ~

2Ha,

(44a)

O2(g) ~-- 2Oa,

(44b)

H k Ha + Oa ~-20Ha'

(44c)

Ha + OHa kL---~HH2Oa,

(44d)

kH 2 so 2 ko 2

kH20

HzOa ~

H20(g),

OH a k°--~ H OH(g).

(44e) (44f)

An OH intermediate has been observed spectroscopically on P t ( l l l ) [152] and Pd(100) [153,154] following H20 adsorption on an oxygen-covered surface. During the hydrogen oxidation reaction, noH is sufficiently low as to be unobservable by X-ray photoelectron spectroscopy (XPS) [110, 155, 156]. However, Lin and co-workers [114, 157] have observed OH desorbing from polycrystalline Pt by matrix isolation and by laser-induced fluorescence while hydrogen and oxygen, at total reactant pressures from 10-5 to 10-2 Torr, impinged on the surface. The binding energetics of the OH intermediate and the nature of the rate-limiting step(s) in different regimes of reactant coverage and surface temperature remain uncertain, however, as we will discuss below. We note that the desorption rate for OH is negligible compared to the rate of H20 formation under the conditions of the studies described below, and we will not consider it further. For a more detailed description of the hydrogen-oxygen reaction, the reader is referred to the review by Norton [158] and to the references given below. In an MBRS study on epitaxially-grown P t ( l l l ) , Smith and Palmer [42] observed an apparent reaction order of 0.8-1 in 02 flux and varying from I to 2 in DE flux depending on the conditions. They obtained an apparent activation energy of 12 kcal/mol for DzO production in the range 600 < Ts < 850 K. Interestingly, they observed an apparent activation barrier to adsorption of DE; the rate varied as cos40i exp[-3.6 (kcal/mol)/R T DE],

466

M. P. D'Evelyn, R. J. Madix / Reactive scattering frorn solid surfaces

where 0i is the incident angle of the D 2 beam and TD2 is the temperature of its oven source. Pacia and Dumesic [159] investigated the H 2 - O 2 reaction on polycrystalline Pt by a steady-state molecular beam technique, monitoring the consumption of U 2 o r 0 2 by reaction. Their results were consistent with a L H mechanism. They analyzed their data assuming a direct reaction between 2H n + Oa to form H20(g ), obtaining an activation energy of 20 kcal/mol for this step. Gdowski and Madix [160] demonstrated by MBRS that the rate of H 2 0 formation on Pt(S)-[9(ll 1) × (100)] is second order in IH2, which precludes O H a formation as the rate limiting step (cf. eq. (44)) under the reaction conditions studied, if hydrogen desorption can be neglected (see below). The experiment was performed under conditions of excess 02 so that 0 o was nearly constant at 0.20-0.25. The MBRS amplitude varied as IH21.0-1-5, depending on the conditions, and more importantly, the phase lag for H 2 0 decreased with increasing IH2. These results are inconsistent with a first order reaction in H a , and are typical of a second order reaction (cf. table 1). Gdowski and Madix found their results to be consistent with the mechanism (44) given above with k2 > > klno,kcHnH, SO that quasi-equilibrium existed between O n, Ha and O H n. The direct reaction 2 H a + O a --~ H 2 0 is also consistent with the data. A mechanism involving disproportionation of O H groups, 2 O H a ~ O a + H20(g), as has been observed in T P R experiments on Pd(100) following hydroxyl formation [153, 154], could not be unequivocally excluded by the MBRS data, but seems unlikely (see below). Their model, with an effective first order rate constant keff = 4(SH21H2kno) 1/2,

(45)

accounted for the H 2 flux dependence of q~ to within + 30% for 500 < Ts < 650 K, where k = kjkcH/k 2 if one assumes quasi-equilibrium in step (44c). The apparent activation energy, Eelt = 10.4 kcal/mol, was in fairly good agreement with Smith and Palmer [42], while the activation energy (= 2Eeff) for the rate constant k agreed well with the value obtained by Pacia and Dumesic [159]. Using estimates of SH2 on an oxygen-covered surface [158,161] and of the oxygen coverage, the preexponential was calculated to be about 1014-1 cm 4 s -1, which is consistent with "normal" values of A1, A2, and ALH. The phase lag was also observed to decrease with •o2, which is consistent with either quasiequilibrium of O H n or a concerted reaction between 2H a and O n. Above 700 K the MBRS amplitude continued to increase, although H 2 desorption should begin to complete effectively with oxidation. This behavior was attributed to the appearance of a second branch in the mechanism with a higher activation energy, which was believed to be associated with oxygen more strongly bound at step sites. The rate constant observed by Gdowski and Madix predicts a T P R peak at about 300 K, in agreement with recent T P R results [161, 162] at 0 o = 0.25 and OH < < 1. In the case of water produced by hydroxyl disproportionation on P t ( l l l ) , the T P R maximum occurs at 215 K [152]. The discrepancy between this value and that predicted by the M B R S rate constant, together with the apparently

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

467

H

~_ -4o

._o~ /

--75

- 80

H~o/H

llJll REACTION COORDINATE

Fig. 20. Enthalpy diagram for the H2-O 2reaction on PI(lll) with 0o = 0.25, and OH<< 1. The enthalpy values of the various intermediates and activation barriers are given on the right-hand side of the vertical axis.

very small O H a concentration during water formation [155,156], weights against a disproportionation reaction in the coverage regime studied by Gdowski and Madix by MBRS. A n enthalpy diagram for the reaction H z + 1 02 ~ H2 O on P t ( l l l ) , under conditions where 0 o --~ 0.25 and OH<< 1, is shown in fig. 20. The binding enthalpies for H a, Oa, and H 2 0 a w e r e taken to be 11 [72], 20 [109, 163], and 16 kcal/mol [110], respectively, relative to the gas phase molecular species (1Ha, !Oa2, and H 2 0 ). The position of O H a in the diagram is uncertain; the value shown was calculated by assuming that the difference between the enthalpy changes in the addition of H to O and to O H are the same as in the gas phase [160]. This value is consistent with the observation [152] of the reaction H 2 0 a + O a ~ 2 O H a.

(46)

Under the conditions for which reaction (46) is observed, the O H a species may be stabilized by an additional ~ 7 kcal/mol [164] relative to low coverage, due to hydrogen bonding [154]. The apparent activation energy for O H desorption (31 kcal/mol) reported by Tevault et al. [157], if used directly to evaluate the enthalpy of H a + OHa, yields a value of - 3 3 kcal/mol [160] (cf. fig. 20). Use of this value, however, predicts A H for reaction (46) to be ~ +35 kcal/mol, even taking hydrogen bonding into account, which is clearly much too large [165]. A simple steadystate kinetic analysis of the mechanism (44) indicates that a number of the rate constants appear in the expression for the rate of O H desorption, but uncertainty

468

M. P. D'Evelyn, R. J. Madix / Reactive scatteringfrom solid surfaces

in their values precludes extraction of koH. The height of the barrier between Ha + OH a and H20 a (fig. 20) was calculated using the activation energy measured by Gdowski and Madix, while the preceding barrier is constrained only to be smaller, so that quasiequilibrium between H a + O a and OH a can prevail. We note that the ambiguities in the enthalpy diagram are due in large part to uncertainties about the importance of hydrogen bonding in H2O a and in OH a at both low and high coverages. Recent work has illustrated the complexity of the H2-O 2 reaction on P t ( l l l ) under different conditions [155,161,162,166]. For example, TPR experiments at higher initial hydrogen coverages yielded not only a peak near 300 K, which is consistent with the MBRS rate constant [160], but also a peak near 200 K and a desorption-limited peak (T s ~ 180 K) [161, 162]. Hydrogen titration experiments, both at high (T s > 300 K) [166] and low (T S < 160 K) [162] temperatures have clearly shown the importance of local (as opposed to average) concentrations of reaction intermediates. These results also suggest that the detailed mechanism may change at different surface temperatures and reactant concentrations. TPR experiments at low hydrogen coverage have also provided evidence that the binding energy of H a on the oxygen-covered surface may be less than on the clean surface [161,162], and hence that hydrogen desorption during water formation may not be negligible. If this is the case, the MBRS results [160] may be alternatively explainable by a model incorporating quasi-irreversible OH a formation (i.e., k2 < < keHnu in eq. (44)). In this limit the effective MBRS rate constant is given by keff = 2[~n 2 + 4kH2 (SH2IH2 + (klk2/kLH)no)] 1/2

(47)

and the phase lag decreases with increasing H e or O2 incident flux (cf. eq. (45)), in qualitative agreement with experiment. Further study of this reaction is clearly required. On Pd(111), bulk solution/diffusion of hydrogen is found to be important, as in the H z - D 2 exchange reaction (section 4.1.2), but excess oxygen seems to block this pathway. Engel and Kuipers [167] found that under conditions of excess H2, large H20 phase lags were observed, even at high temperatures, indicating an LH mechanism and the presence of bulk diffusion effects. With O2 in excess, however, the phase lag decreased to zero at high temperatures, indicating that a high oxygen coverage blocks bulk diffusion, or at least that the rate is dominated by reaction with adsorbed H. The MBRS H20 amplitude was observed to vary as IH21.1-+0.1, from which these authors concluded H a + O a ~ OH a to be rate limiting. However, the variation of q~with IRa, which is crucial in determining reaction orders, was not reported under the same reaction conditions. In the high oxygen coverage limit (0 o ~ 0.25) the effective rate constant was calculated to be 10-7.4 e x p [ - 7 ( k c a l / m o l ) / R T s ] cm 2 s -1. The transition from surface reaction dominated behavior to reaction involving

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

469

bulk solution/diffusion of hydrogen was illustrated by measuring the water production rate at a fixed O2 flux as the hydrogen flux was increased. The rate increased sharply as the H 2 flux was increased past a threshold value. As the laydrogen flux was increased further, the reaction rate reached a maximum, and then declined. This behavior was attributed to the onset of reaction with H diffusing from the bulk, followed by depletion of OaThe H2-O 2 reaction in P t ( l l l ) is similar to CO oxidation in that there is a substantial amount of energy to be disposed of as the final activation barrier is surmounted (~ 52 kcal/mol versus ~ 37 kcal/mol, measured relative to the adsorbed product, as estimated from figs. 20 and 18, respectively). However, whereas peaked CO2 angular distributions were observed, only diffuse H20 distributions have been observed [42,167, 168]. Moreover, Ceyer et al. [168] found the velocity distribution of desorbing D20 molecules to be cold, by direct time-offlight measurement, following reaction of D2 + 02 or D + 02 at surface temperatures of 440-913 K. While the mean energies scale approximately with Ts, the values were only ~ 40% of that expected from equilibration with the surface. The observed velocity distributions did not appear to vary significantly with desorption angle. These results are qualitatively different from those of Becker et al. [143, 144] for CO oxidation, but qualitatively similar to those of Asscher et al. [107] for NO production by ammonia oxidation. The desorption rate constant for H20 at low coverage is not known accurately, but the binding energy may be estimated as ~ 15 kcal/mol [110]. Assuming a preexponential factor of 1013 s -1, the surface residence time in the above temperature range is estimated as 10-64 x 10-10 s. Based on the order-of-magnitude estimate for the equilibration rate (109 s -1) for NO on P t ( l l l ) (section 4.3.3), it is certainly plausible that the water molecules produced in the experiments of Ceyer et al. resided on the surface long enough to equilibrate, and that the observed velocity distributions are cold due to energy exchange limitations or other dynamical effects, as discussed in section 4.3.3.

4. 7. Decomposition reactions of more complex molecules Several decomposition reactions have been investigated using modulated beam techniques. In some cases, for example HECO and CH3OH on Pt [72], the decomposition is fast and the observed rate constants are characteristic of desorption of the product species. In other cases, analysis of the reaction is more complex, owing to the presence of various kinetically coupled surface intermediates. As a result, most of the reactions discussed in this section are much less well understood than those discussed in the previous subsections, and a number of kinetic parameters have'been measured whose magnitude seems peculiar. The power of MBRS in determining surface reaction kinetics lies in being able to measure one or two characteristic relaxation times directly, with a minimum of competing effects, such as adsorbate interactions. The utility of modulated beam techniques drops

470

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

off fairly rapidly as the complexity of the processes being studied increases. Wachs and Madix [169] found H C O O H to yield primarily CO 2 and H 2 upon decomposition on Ni(ll0). Below 280 K only desorbing H C O O H was observed; the decomposition probability increased rapidly to 0.9 at Ts ~ 400 K. Carbon and/or oxygen were found to be present on the surface during the steady-state reaction between 300 and 800 K. Analysis of the waveforms for desorbing H C O O H below 300 K showed that So = 1, and the apparent desorption rate constant was kd =

2 × 105 exp[-2.7 (kcal/mol)/RTs] s -1.

The observed rate constant was attributed to desorption from a weakly adsorbed state, with a contribution due to conversion to a chemisorbed state which decomposes above 280 K. The magnitude of the preexponential is suggestive of surface migration, a second order process, or perhaps an energy-transfer-limited process [116]; we note that similar values have been obtained for H C O O H scattering from carbide, graphitic, and sulfur overlayers on Ni(ll0) [170] as well as for CH3OH scattering from polycrystalline Ni [36]. The origin of these values is not understood. Above 400 K H C O O H decomposed to yield CO2 + H2 with a branching probability of 0.7, with CO and H 2 0 as minor products [169]. The phase lags for CO2, CO, and H 2 0 all approached 25 ° at high temperature, suggesting the presence of bulk diffusion effects (most likely involving C or O [171, 172]) or of an unactivated branched pathway [169]. The phase lag for CO 2 was greater than 90 ° at low Ts and was independent of the beam intensity, indicating a linear sequence of decomposition steps. The incremental phase lags associated with the other products (H 2, CO, and H 2 0 ) were consistent with desorption-limited processes. We note that the rate constant inferred for CO desorption, 7 x 1012 exp[-23 (kcal/mol)/RTs] s -1, was in good agreement with that obtained by TPD from a carburized Ni(110) surface [85], but not with the MBRS result of Sau and Hudson [84]. On Pt, H C O O H decomposes similarly to yield CO 2 + H 2 [68, 72, 173]. Dahlberg et al. [173] observed the decomposition rate to decrease drastically below 1150 K, which they attributed to poisoning by adsorbed oxygen. Steinbach and Hausen [68] measured a MBRS rate contant of 6 X 10 7 e x p [ - 1 0 . 2

(kcal/mol)/RTs]

s -1,

for CO 2 production from a postulated formate intermediate. Production of this intermediate appeared to occur through an activated conversion of adsorbed H C O O H . Gdowski et al. [72] observed a branched decomposition process on the (110) surface. The polar plot of the transfer function revealed a cusp, which was attributed to a temperature-dependent branching probability. The observed low and high temperature rate constants, 2 x 105 exp[-3.8 (kcal/mol)/RTs] S-1, 1010 exp[-17.5 (kcal/mol)/RTs] s -1,

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

471

bracket the value obtained by Steinbach and Hausen [68]. The nature of the branched process is not understood. Molecular beam investigations of the decomposition of NH 3 on W and on Pt have lead to proposed surface reactions distinct from those in the generally accepted mechanism for ammonia synthesis and decomposition on iron, viz. [123] NH3(g)~NH3a,

(48a)

NH3a ~ NH2a + H a,

(48b)

NH2a(g) ~ NH a + H a,

(48c)

NH a ~- N a + H a,

(48d)

2Na~.-~-N2(g),

(48e)

2Ha~H2(g),

(48f)

Steinbach and Schiitte [174] ascribed the observed N 2 and H 2 product waveforms arising from decomposition on polycrystalline W to a linear sequence of steps. The authors analyzed a number of models, but the only one they found to be consistent with their data involved eqs. (48a)-(48c) and (48f) together with a step producing N 2 + 2H2 molecularly from the reaction of NH3a + NH a. We note, however, that a variety of stable intermediates have been reported on W and that the behavior depends on the surface composition [123]; Steinbach and Sch~tte did not attempt to characterize the state of their W surface during the steady state reaction. On P t ( l l l ) , Guthrie et al. [108] found the incident NH 3 molecules to adsorb with 0.7 probability, with fewer than 1% decomposing between 300 and 1300 K. The desorption rate constant for NH 3 was measured to be 1010"4-+0"9exp[-15.4 ___0.4 ( k c a l / m o l ) / R T s ] s -1. This preexponential factor is rather low for a first order desorption. The authors suggested it might be due to a surface migration process; alternatively it seems possible that a small metal-adsorbate vibrational frequency is responsible. The stepped [6(111) × (100)] surface was found to be considerably more reactive, with a maximum decomposition probability of ~ 18%. The phase lag for N2 was found to decrease with INH3while g0n2did not vary. Several models for the kinetics of the decomposition process were analyzed. The most satisfactory model, which gave a qualitatively, not not quantitatively, correct description of the observed phase and amplitude behavior, included the steps (48a)-(48f) above together with an additional adsorption site for NH 3. Recently, Foner and Hudson [175] found that N 2 produced by NH 3 decomposition on a Pt foil at 1300 K and pressures of 0.2-1.4 Torr was highly excited vibrationally. By measuring the ionization threshold, they inferred that N2 molecules with as much as 55 kcal/mol of vibrational energy (up to v = 9) must be produced

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

472

in the reaction. Based on estimates of the binding energies of N a and NHa, they suggested that the highly excited N 2 molecules might result from reaction of NH a + NH a, so that sufficient energy is liberated to excite the nitrogen. We note, however, that the surface composition was not characterized, and that the binding energies of the intermediates could vary considerably from the published values.

5. Gas-metal reactions at elevated temperatures

At elevated temperatures gas-solid reactions can lead to the formation of volatile products. The subject of high-temperature gas-solid reactions has been reviewed elsewhere [176, 177], and emphasis will be on the molecular mechanism and the distribution of products. Relatively few molecular beam investigations of these reactions have been made during the past decade, and the level of understanding is correspondingly less than for catalytic reactions. It is more difficult to characterize the structure and composition of the surface during a gas-solid reaction than for a catalytic process, due to phenomena such as pitting or buildup of nonvolatile intermediates.

5.1. General mechanism The mechanism for production of volatile products may be illustrated by Sb

A2(g ) ~ 2 Aa,b,

(49a)

Aa, b + M ~ MAa,

(49b)

$s

A2(g ) ---,2 Aa,s,

(49c)

Aa.s + MAa ~ MAza,

(49d)

MA2a ~ MA2(g),

(49e)

MA~ --~ MA(g),

(49f)

A~,~ --~ A(g),

(49g)

Aa, b ~ A(g),

(49h)

where M denotes a bare metal site, MxAy represents a surface compound with stoichiometric coefficients x and y, and the a, b and a, s subscripts indicate adsorption on a bare metal site or on the MA a "scale", respectively. At sufficiently low temperatures the coverage of a surface compound, e.g., MAa, may exceed one monolayer and lead to a buildup of a scale of tens or hundreds of/~ thickness. In this case bulk solution/diffusion of A within the scale may become an important supplement to this mechanism.

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

473

5.2. Reactions with halogens, oxygen The above mechanism was suggested by the pioneering work of McKinley [178-180] using unmodulated beams to study the reactions of F2, C12, and B r 2 with polycrystalline nickel. The same qualitative behavior was observed with each halogen. The total product flux was found to be proportional to the reactant flux, and the product distribution shifted to species with decreasing numbers of halogen atoms as the temperature was increased. The activation energy for NiA(g) formation was about 30 kcal/mol for each halogen, suggesting that a process involving Ni-Ni bond breaking was rate-determining. Reflected Cl 2 molecules were not accommodated translationally with the surface [181], indicating that the adsorption process was direct in nature, rather than proceeding through a weakly bound precursor state [80, 81]. Smith and Fite [182] estimated the activation energy for NiCl(g) production to be 35 kcal/mol for their early MBRS phase shift measurements, in fairly good agreement with the result of McKinley [178]. A similar mechanism was proposed for the oxidation of tungsten [183] and would seem to apply equally well to molybdenum [184]. The distribution of tungsten oxides observed by Shissel and Trulson [183] is shown in fig. 21. Following Berkowitz-Mattuck et al. [184], these investigators found that the oxide product distribution shifted from polymeric species of WO3 (W206, W309) at surface 1017

I015

:~ 1014

'0 '3

/

'

Xw206

i04/Ts ( K-b Fig. 21. Relative product fluxes in the oxidation of tungsten, as a function of surface temperature. From ref. [183].

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

474

temperatures near 1500 K to WO 3, WO2, O, W, and WO (not shown) successively as the temperature was increased to 3000 K. A similar product distribution was obtained by Cardillo and Look [185] following reaction of D20 or CO2 with W. Shissel and Trulson [183] found that two distinct binding states of adsorbed atomic oxygen (cf. eq. (49)), with desorption rate constants of 5 x 1913 exp[-144 (kcal/mol)/RTs] s 1, 1014 exp[- 114 (kcal/mol)/R T~] s- 1 were required in the kinetic model to fit the data. However, the mechanism was too complex to permit a unique determination of all the rate constants in the model. Steele [186] obtained a similar rate constant, 3 × 1013 exp[-138 (kcal/mol)/RTs] s -1, for the tightly bound oxygen atoms using MBRS. A mechanism involving two Oa binding sites has received additional support from the noble atom scattering study by Ollis et al. [187] of molybdenum oxidation.

5.2.1. Product distributions The simplest description of the product distributions makes use of equilibrium thermodynamics. Since the entropy change accompanying the overall reaction ½y A2(g ) + M--+ MAy(g),

(50)

is primarily associated with translational entropy, reactions producing greater numbers of gaseous product molecules per molecule of reactant gas will be favored at higher temperature, to the extent that equilibrium considerations prevail. For all published results of the product distribution from the reaction of a single gaseous species with a metal this correlation appears to hold. These considerations were put on a quantitative footing in the quasiequilibrium model of Batty and Stickney [188]. The assumptions of the model are (i) a fraction, ~i, of each molecular species i impinging on the surface adsorbs and equilibrates while the rest are reflected; (ii) the rate of desorption of each species from the surface is equal to the rate that would be established under equilibrium conditions, i.e., in the presence of a vapor phase containing the product species in equilibrium with the reactants. By detailed balancing, this latter rate is equal to the the impingement rate of each product species at the appropriate vapor pressure multiplied by its equilibration probability (~i). Batty and Stickney modeled the experimental results for the oxidation of W [183] and of Mo [186] by assuming that se = 1 for the metal oxides. Agreement with the overall oxidation rate was forced by equating ~o2 with the reaction probability to form volatile products, that is,

~y yRMxOy ~o2 -

2/o2

(51)

M. P. D'Evelyn, R. J. Madix / Reactive scatteringfrom solid surfaces

475

Ts(K) 3333 2500 2000 1667 1429 1250 IIII 10 . . . . . . >d

2 0 [12 a_

---

Z

_o _ca _J o 0.1 I.U i--

uJ zac

QUASI EQUILIBRIUM ~ CALCULATED

,

3

4

5

6

i

t

;

7

8

9

I04/Ts (K-')

Fig. 22. Comparisonof the equilibration probability for oxygenon molybdenumas calculated from a quasiequilibrium model, and the observedapparent reactionprobability. Fromref. [29].

where RMxoy is the rate of production of MxOy. The calculated ~O2for Mo oxidation is shown in fig. 22. A good qualitative fit to the observed product distributions was obtained using tabulated heats of formation; the fit could be made semiquantitative by adjusting the A H ? values within their (considerable) uncertainties. A similar result was obtained by Cardillo and Look [185] for the D20, CO 2 + W reactions, although these authors determined ~o2 through a fit to the total consumption of W, i.e., ~ XRwxoy , rather than the total oxygen consumption. Quantitative assessment of the quasiequilibrium model is made difficult by the large uncertainties in the tabulated thermodynamic data and by the difficulty in determining absolute fluxes of metal oxides with a mass spectrometer. However, Berkowitz-Mattuck et al. [184] found their product distributions to be inconsistent with equilibration. Arrhenius plots of log(R3Mo2/R~o3) yielded apparent enthalpies of reaction (between the tri- and dioxides) of 125 kcal/mol for W and Mo, decidedly lower than the equilibrium results of 176 + 20 [189] and 169 +__30 kcal/mol [190], respectively. Ullman and Madix [28] measured the 02 reaction probability with Mo directly using MBRS, as the fractional loss in scattered 0 2 flux. As shown in fig. 22, the reaction probability increased with temperature to 0.3 above about 1400 K, in general agreement with the results of Rosner and Allendorf

476

M. P. D'Evelyn, R. J. Madix / Reactive scattering frorn solid surfaces

[191] at higher pressures, but in contrast to the temperature dependence of ~o2 calculated from the quasiequilibrium analysis. These discrepancies suggest that while a quasiequilibrium approach is a useful approximation for such reactions, a quantitative account of the product fluxes should not be expected. The apparent relationship between the product desorption flux and thermodynamic free energies of formation was put on a sounder footing by Ullman and Madix [192] and, independently, Weber and Cassuto [193]. These authors noted that the free energy barrier for product desorption will tend to be least for those products with the highest negative free energy of formation. Using transition state theory [9], the ratio of the rates of formation of MxOy(g) and A(g) were shown to be equal to the rate predicted by gas phase thermodynamics multiplied by correction factors due to the energetics of adsorption and desorption and to non-equilibrium surface concentrations [192]. Only in the limit of (i) unit condensation coefficients of all product species; (ii) identical adsorbate binding energies; and (iii) desorption-limited behavior does the generalized expression reduce to the quasiequilibrium result [29]. The reactivities of tungsten with oxygen-chlorine mixtures to form a variety of oxides, chlorides, and oxychlorides is an interesting example of surface-reaction limited, as opposed to desorption limited, behavior. According to the exploratory work of Rosner and Allendorf [194], the reactivity of polycrystalline tungsten with CI2/O 2 mixtures of 33% Ci 2 at 1473 K and 10-~ Torr total pressure exceeded the additive reactivity with the pure gases to form volatile products by more than an order of magnitude. This observation was explained qualitatively by the large negative heat of formation of WO2C12, the presumed major product. Given a higher rate of desorption (because of lower energy barriers) than for tungsten oxide or tungsten chloride, the surface coverage by either oxygen or chlorine would be lower, the sticking probability of 02 could increase, thereby increasing the overall rate. Subsequent mass spectrometric analysis by McKinley [195] showed that WO2CI 2 was indeed the dominant product at ca. 10-4 Torr and temperatures of 1200-2100 K. The oxides WO2 and WO3 were observed in lesser amounts, but tungsten chlorides and WOC14 were not. Since these latter species would be expected from thermodynamic considerations [194], the reaction may have occurred on a tightly bound oxygen layer which made the tungsten inaccessible to the adsorbed chlorine atoms. In reactions of gas mixtures the surface may not achieve equilibrium conditions. 5.3. Modulated beam studies

Nearly all the investigations described above have made use of unmodulated molecular beams. When beam modulation has been employed, surface transport processes have often been found to be important. Ullman and Madix [28] demonstrated that surface diffusion of oxygen to grain boundaries on polycrystalline molybdenum precedes the formation of volatile molybdenum oxides. As predicted

M. P. D'Evelyn, R. J. Madix / Reactive scattering frorn solid surfaces

477

by eqs. (27)-(29) above, the observed phase lag for all product species increased from zero to a constant value of 45 ° as the modulation frequency was increased. At 45 ° the phase lag was also independent of surface temperature, quite unlike the case for non-diffusion-limited surface reactions. The importance of surface diffusion was confirmed by electron microscopic examination of the metal samples, which revealed preferential etching at grain boundaries. The surface diffusion coefficient for O a was estimated to be 10-4-+1exp[-10 + 5 (kcal/mol)/RTs] cm 2 s-1. Olander and co-workers have found bulk solution/diffusion to be important in the F2/Ta [196] and I2/Zr [197] reactions. At lower temperatures a scale (presumed to be TaF 3 and ZrI) was postulated to build up, with F or I diffusing through it. The scale was assumed to be depleted by reaction with F or I to form the observed volatile products TaF 5 or ZrI4, respectively, and replenished by reaction of F or I with metal atoms at the metal/scale interface. In rhe Iz/Zr case the existence of the scale was confirmed by AES and X-ray photoelectron spectroscopy. At high temperatures the ZrI scale became unstable and I(g) was observed as the dominant product. In both reactions relatively good agreement was obtained between the observed MBRS phase lag and amplitude data and that predicted by the model. In closing this section, we note that the presence of surface and bulk diffusion effects can render comparison of kinetic results of different groups difficult, due to perhaps minor differences in sample preparation (grain size, etc.).

6. Reactions of nonmetals

The reactive scattering of simple gases from silicon, germanium, and graphite has received considerable attention, but littlework has been done during the past 5-10 years. The interactions of Group III and Group V elements with I I I - V semiconductor surfaces have been studied intensely in connection with epitaxial growth by virtue of the importance of these materials to the electronics industry. Migration of species, on the surface or within the bulk, is found to play an important role in determining the reaction kinetics in a number of processes within each of these categories. As in the case of gas-metal reactions, the details of the reactive processes at the microscopic level remain poorly understood, relative to catalytic reactions.

6.1. Silicon and germanium The reaction probabilities (So) of O, 02, 03, C12, Br2, and 12 with heated singlecrystal surfaces of silicon and germanium were determined gravimetrically or by mass spectrometer by Madix, Boudart, and co-workers [198-207] using nonmodulated molecular beams. Desorption kinetics were determined for several of

478

M. P. D' Evelyn, R. J. Madix / Reactive scattering from solid surfaces

Table 8 Summary of reactions with silicon and g e r m a n i u m Reaction

So

A (s -1)

Ea Temperature (kcal/mol) range (K)

Ref.

Ge(s) + O2(g ) --~ 2 G e O ( g ) O(g) ~ G e O ( g ) O3(g) ~ G e O ( g ) + O2(g) Cl2(g)---~ GeCl~(g) Br2(g ) ~ GeBrz(g ) + GeBr4(g) I2(g) ~ (b)

0.02 0.3 0.5 0.3 0.3 0.3

1016 ,) 1016 a) 1016 107 107 --

55 a) 55 a) 55 25 20 --

750-1100 750--1100 750-1100 750-1100 750-1100 750-1100

[198] [199] [200] [201,202] [202,203] [202,204]

--108 ----

--40 ----

1100-1400 1100-1400 1100-1500 1100-1400 1000-1500 1060-1150

[205,2061 [199] [201,202] [202,204] [2071 [205]

Si(s) + 02(g) --" 2SiO(g) 0.04 O(g) --* SiO(g) 0.5 C12(g)---* SiCl2(g) 0.3 Br2(g) ~ (b) 0.5 NOCl(g)--~ NO(g) + SiC12(g ) + SiCl4(g) 0.3 CH4(g)-* SiC(s) + 2H2(g ) 0.6

al Believed to be identical to the desorption of G e O from Ge + 03. b) So measured by reduction of amplitude of reflected reactant; products not characterized.

these systems by MBRS. Table 8 lists the observed values of the high-temperature limit of So, the reactions observed by MBRS, the first-order kinetic parameters for the reaction, and the temperature range over which the reaction was studied. Incident fluxes of reactant ranged from 0.1 to 10 monolayers per second. The dependence of So on surface temperature and beam flux for the reaction between C12 and Si is shown in fig. 23. Note that the observed SiCI2 signal from the mass spectrometer has been converted to flux by multiplying by if/2, assuming thermal accommodation of the desorbing molecules. At low beam fluxes and high temperatures the reaction rate was independent of surface temperature. The reaction probability for the halogens showed a tendency to drop with increasing surface temperature at higher beam fluxes [201], and this effect was not simply due to desorption of halogen a t o m s . It is important to note that the values of s o reported above were obtained under low coverage conditions on a heavily reacted surface. The coverages were estimated to be ~ 10-2 [202], as described previously (section 3.1). The early stages of reaction appeared to take place at defect sites, which rapidly grew into pits. Electron microscopy revealed the reacted surface to be extensively faceted [206, 208]. The primary orientation of the facet planes was observed by L E E D to be (111), independent of the crystal plane originally exposed. This result is consistent with the observation that the S i ( l l l ) - ( 1 x 1) surface structure prevailed in the relevant temperature and pressure regime [209]. The surface exposed to the reactants can thus be viewed as being primarily of (111) orientation, although cer-

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

1500 I0 I

1400 I

__.lt_.~.-------~

Ts, K 1200 1

1300 I

479

I000

I100 I

A

u" (/3

I R m

0.5--

o.2

I 0.70

I 0.75

I

I

0.80 0.85 103/Ts, K

I

I

0.90

0.95

1.0

Fig. 23. Flux of SiCI2 produced by reaction of C12 with Si, as a function of surface temperature. Relative CI2 beam fluxes were 5 (O), 10 ( A ) and 20 ( 0 ) (arbitrary units). From ref. [201].

tainly there must be a substantial concentration of ledges, kinks, and large-dimension facets. The following discussion idealizes the complex surface as a single (111) crystal plane. The results given in table 8 show that the reactivity of the halogens with the semiconductor surfaces is quite high, and nearly identical for all the halogen/substrate systems investigated. Furthermore, among all the gases studied molecular oxygen was the only species whose reactivity differed appreciably from atomic oxygen - a reaction not requiring molecular bond dissociation. The low reactivity of 02 and the higher reactivity of the other gases can be explained in terms of the interaction of 02 with adjacent surface orbitals to form virtual bonds, which introduces a stringent steric requirement for the reaction to occur [202]. The constancy of So with surface temperature at low beam fluxes indicates that the dissociative adsorption of 02 or X 2 is direct in nature, rather than being preceded by molecular adsorption of a precursor [80, 81}. The values of s o therefore reflect the steric factor associated with the gas-surface collision, and the differences observed for

480

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

various gases are associated with the shapes of the potential energy contours involved. Given the magnitude of the 02 bond (118 kcal/mol), it is reasonable to suppose that both oxygen atoms must interact strongly with the surface in order for dissociative adsorption to occur. The probability of this process may be estimated by constructing virtual bonds in the vicinity of each surface atom, with bond lengths equal to the value in the gas phase oxide or halide. Such a construction for G e ( l l l ) is shown in fig. 24. Note the small overlap between the virtual bonds and an 02 molecule (the O 2 bond length is depicted in fig. 24a). It is interesting to note that the fraction of the (111) surface contained within the G e - O

02 Internuclear distance

a •

C

• Ge atom Bond length GeBr 2.30

b

Ge atom

d

• Ge atom Bond length GeCI 2 . 1 0 ~

• Ge atom Bond length Gel 2.50

Fig. 24. Virtual bond diagram for the dissociation of (a) 02; (b) C12; (c) Br 2 and (d) 12on Ge(111). From ref. [202].

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

481

bond length of each lattice point (fig. 24a) is 0.6, which corresponds closely to the oxygen atom reaction probability. The higher reactivity of the halogens is explained by the larger spatial extent of the interaction with the surface and less stringent orientational requirements as well as the lower X e bond strength, which allows a weaker interaction with the surface to effect dissociative adsorption. The high reaction probabilities of 0 3 and NOC1 may be interpreted in a similar manner. A slightly different mechanism, involving a long-ranged charge transfer interaction [210,211] between the dangling surface orbitals and the impinging molecules, might also explain the differences in reactivity [202]. Other explanations for the relatively low reaction probability of 02, such as reactions at point defects or by non-adiabatic curve crossings, appear unlikely [202]. The formation of volatile G e O during germanium oxidation resulted from a desorption limited process. From the behavior of the MBRS phase and amplitude data the desorption rate constant was calculated [200] to be 1016 exp[-55 (kcal/mol)/RTs] s -1. This activation energy is similar to the heat of desorption of GeOa determined previously by Lever [212]. The preexponential factor indicates that G e O a is tightly bound to the surface and that the transition state is a loosely bound molecule with nearly two degrees of rotational freedom. In contrast, the kinetics of the high temperature reactive scattering of the halogens from germanium and silicon appears to be dominated by surface migration. The MBRS phase lag of the volatile halide increased to saturation at 90 ° with decreasing temperature, as predicted by eq. (10) above. The amplitude behavior was typical of a first-order process, and the demodulation of the signal with chopping frequency was in accord with eq. (12). The rate constants for halide formation are given in table 8. The preexponentials are orders of magnitude smaller than that expected for a desorption-limited process, and are characteristic of surface migration followed by facile desorption at special sites with a density of 101°-1012 cm -2. Identification of migration as the rate-limiting process is supported by the observations that the activation energies for formation of SiCl a and GeCl 2 are similar to those measured for surface self-diffusion of Si and Ge [213, 214]; and that their ratio is close to the ratio of the melting points of silicon and germanium, respectively. This suggests that the migration process depends on breaking Si-Si or G e - G e bonds, rather than Si-C1 or G e - C l bonds. The passivation of the Si and Ge surfaces at higher reactant fluxes appears to be due to formation of a nonvolatile oxide or halide layer on the surface, in agreement with the results of Wagner [215] for silicon oxidation. As the surface oxide coverage approached a monolayer, the oxidation rate became desorption limited an'cl the reaction probability dropped by orders of magnitude [204]. Corresponding effects occurred in reactions of halogens and oxygen/halogen mixtures, but the active/passive transition took place much more gradually at a much lower temperature. The effect of bromine on the passivation of a germanium surface in

482

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

970

~---770

T,K 670

570

I

I

I

I

• PBr2 =

• •

"~'~(~)

217~u.

0 PBr 2 = 21?FZ I'~

Poz = 250ju-

., o rr

g "d o

g~

.ol .9

I

I

I

I

I

I.I

1.3

1.5

1.7

1.9

2.1

103/T ( K -I) Fig. 25. The total reaction rate of germanium with bromine, oxygen, and oxygen-bromine mixtures, From ref. [204].

an oxygen beam is shown in fig. 25. This figure shows the total reaction probability of the (111) surface with (a) oxygen alone, (b) bromine alone, and (c) a 50-50 oxygen-bromine mixture. The surprising property of the mixture is that the dramatic passivation by oxygen was prevented by the presence of bromine on the surface; the net effect of the oxygen is to decrease only slightly the reactivity of the bromine. No oxybromides were observed in this system. Since the rapid decrease in reaction rate with oxygen at the passivation temperature has been attributed to a surface phase transition [215], it appears that the action of the bromine is to "stir" the surface sufficiently to prevent the formation of oxide nuclei. Similar resuits were observed in all Si/X2-O2 and Ge/X2-O2 systems studied [204].

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

483

6.2. III- V semiconductors

The interactions of molecular beams with I I I - V semiconductors, currently of great interest, have been well reviewed in connection with molecular beam epitaxy (MBE) [216,217], and the purpose of this section is to give an illustrative, and not remotely comprehensive, account of the phenemona observed. The kinetic growth behavior of binary compounds of Ga, A1, or In in combination with P, As, or Sb is similar to that observed with GaAs [217]. Accordingly, only the interactions of gaseous Ga, As 2, and A s 4 with GaAs are discussed here. Different crystal face orientations have been studied, but the effects of surface structure seem to be small [216,217]. The kinetics of formation of these compounds is complex since the surface composition is dependent on the incident flux of each species and on surface temperature and, in turn, the adsorption/desorption behavior of the two components depends on the surface stoichiometry. Depending on the preparation of the crystal, the surface may be "Ga-stabilized", with 0As < 0.1, or "As-stabilized", with 0As = 0.5-0.6 [218]. About 0.5 monolayer of As is desorbed as As2 from an As-rich surface at temperatures of 600-700 K, resulting in a Ga-rich surface. Above = 850 K, Ga begins to desorb at a measurable rate, accompanied by a stoichiometric quantity of As2 so as to maintain a Ga-rich surface [217, 218]. Under the conditions used for crystal growth by MBE, the sticking probability for Ga, SGa, is approximately equal to one, while SAs2 and SAs4depend strongly on 0A~, which is in turn determined by the relative fluxes of Ga and As2 or As4 [219-221]. The dependence of sAs2 on incident Ga flux is shown in fig. 26. Crystal growth may be conducted with separate molecular beams of Ga and As4, obtained by heating the pure substrates in furnaces, or alternatively using beams of Ga and As 2. An As 2 beam is generated by heating a substrate of GaAs, which always results in a flux of Ga in addition to the As2. Under typical growth conditions, IA~2 > 0.5IGa,

1.0

Ts:600K JAsz~ "}012tool cm-2 S-1 .

_

. . . . . .

A I[/

. . . . .

,,~

j~

SAs~ ~ 0.5

0.0 0.0

x

1.0

k

2.0 JGa 1012 ( a t o m s

310

~/

s

110

cm "2 S-1)

Fig. 26. Sticking probability for As 2 on GaAs(100) at 600 K as a function of the Oa flux. From ref. [221], with permission.

484

M. P. D'Evelyn, R. J. Madix I Reactive scattering from solid surfaces

which allows for stoichiometric growth, since any As in excess of the available Ga will not chemisorb (SAs2 " ( < 1 when 0G, = 0). The desorption behavior of the various species show characteristic differences. Arthur [219] found Ga desorption from a Ga-rich surface at 870-950 K to be a simple first-order process, with a rate constant of

5 X 1013 exp[-58 (kcallmol)lRT~] S-1, by MBRS. This preexponential factor is consistent with a simple desorption limited process. The desorption behavior of As is considerably more complex, and depends strongly on 0As. A model for the interaction of As 2 (with IAs2 > > IGa) with GaAs is shown in fig. 27. Above 485 K, Foxon and Joyce [221] found the surface residence time of scattered As 2 to be too small to measure. Below 600 K, a surface association process took place, and part of the excess As was observed to desorb as As4 (fig. 28). The As4 signal was strongly demodulated at 485 K even at a chopping frequency of 0.5 Hz, indicating r > 1 s. The MBRS amplitude of As4 was found to vary linearly with IAs2, but measurements of the variation of qVAs4 to determine the molecularity of the reaction were not reported. Arthur [218] has presented a kinetic model for the growth of GaAs from Ga(g) and As2(g) which gives a good account of the MBRS waveform for scattered As2 near 450 K and of the thermal desorption of As 2 from an As-rich surface. The model incorporates precursor-mediated adsorption of As 2 and a coverage-dependent activation energy for As 2 desorption. Foxon and Joyce [221] have discussed the extension of

/

(~~

.~.~o~ ,~/;

AS 2 incident flux v

~"

"%,

\o~. Q~ ~,~ -o/6 ~/ <

~/////~

Y

0

Y" %

Sur'foce migration

Dissociotive

¢

h

e

Go s t o b i l i z e d

~

coefficient ~1

Go As sur'foce

Fig, 2?. Illustration of kinetic model for the interaction of As2 with a Ga-rich GaAs surface. From t e l [217], with permission.

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces JAs2 ~ 1013 t o o l c m "2 S-1 A AS,

E L. 0

485

o

3.0

AS2

o

°~ o ~ °

o

o-.-o

J

~2.0 E .121

bm ~

0

1.(3

A

I

C c

O.C 2OO

I

I

400 600 Substrete temperoture

I

I A

8~ % (m)

Fig. 28. Relative desorption rates of As2 and As4 from GaAs(100), as a function of surface temperature, with an incident flux of As2. From ref. [221], with permisson.

A r t h u r ' s kinetic m o d e l to include the association reaction to form As4(g ) at Ts < 600 K. In the case of an incident A s 4 b e a m with 300 < Ts < 450 K, Asa was observed to adsorb molecularly and desorb via a first o r d e r process with an activation energy of 8.8 kcal/mol [220]. T h e p r e e x p o n e n t i a l factor decreased from 109 to 6 x 107 s -1 as 0Ga increased from ~ 0.5 to ~- 1. These values are suggestive of a process d o m i n a t e d by surface migration, with a site density for facile desorption that decreases with increasing G a coverage. The magnitude of E a is also consistent with such a process. A b o v e 450 K, SAsa increases from well below unity to 0.5 with increasing 0oa, and rAs4 b e c o m e s too short to measure [220]. The a p p a r e n t o r d e r (in the incident A s 4 flux) for A s 4 desorption changes from two to one a s I A s 4 increases. Since the motivation of the workers in this field has been to understand the kinetics of the growth process, it is not surprising to find that the dynamical aspects of adsorption and desorption have received less attention. M e a s u r e m e n t s of the angular distributions of scattred As2 an As4, although complicated by the nonstatic nature of the surface, might shed light on the importance of precursor states. While a d s o r b e d As2 and A s 4 are p r e s u m e d to be thermally a c c o m m o d a t e d to the surface [217,220,221], A r t h u r and Brown [222] found the velocity distribution of scattered o r e v a p o r a t e d As2 and As4 to be characterized by a t e m p e r a t u r e about

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

486

15% less than Ts, in the range 500-750 K. The corresponding distributions for scattered or evaporated Ga, however, were well described by a Maxweli-Boltzmann distribution at TS. Below 550 K arsenic began to build up on the surface, and the translational temperature of the desorbing As 2 and As4 approached Ts, in accordance with earlier work on As 4 evaporating from pure bulk As [223]. As noted earlier (section 4.3.3), a number of systems have displayed translational temperatures of desorbing species lower than Ts. The growth kinetics of GaAs seems to be well understood. In particular, it is straightforward to grow stoichiometric GaAs at temperatures higher than 450 K by impinging beams of Ga and A s 2 o r A s 4 upon the surface, with the arsenic in excess. There seems to be a rich variety of microscopic phenomena which take place; however, the details remain largely unexplored.

6.3. Graphite Diffusion of intermediates has been found by Olander and co-workers [224-227] to play a dominant role in the kinetics of the reactions of pyrolytic graphite with 02, H, and H20. Particularly striking is the coupled surface/bulk diffusion observed in the reactions of 02 [225] and H20 [227] with the prism plane. The physical basis for the model is shown in fig. 29. Reaction intermeNlole c u l o r

beorn

Groin

A d

~A

A

~A

Grophile groin

Jl

1/1

d A d A

A /I A

Fig. 29. Illustration of kinetic model for coupled diffusion within grain boundaries and the bulk of the grains and surface reaction. From ref. [225], with permission.

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

487

diates diffuse across the surface and within grain boundaries, simultaneously undergoing solution and diffusion within the bulk of the grains. In contrast to the case of either process alone (section 3.3), the saturation phase lag at high temperatures is 22.5 °, rather than 45 °. For the oxidation of the prism plane, Olander et al. [225] analyzed the reaction scheme so ½ O2(g)

k ,

0a

,

CO(g)

(s2)

It Ogb

1L 0b

where Ogb and Ob denote oxygen in the grain boundaries and bulk of the grains, respectively. The sluggish change of the phase lag (20°-30 °) with temperature or modulation frequency was in good agreement with the model. Preferential reaction at defect sites gave rise to substantial hysteresis effects in Torget 2000

162

t e m p e r o t u r e , Ts (K) 1500 1200 I t

m

B

I000

--

o5 C 2

Q"

-3

16Hz [o = 5.4.x I016

\

o Heot up • Cool down ~-

o o.

o. <

\ A

5

2

154i 5

I

6

I

7 104 / Ts

I

I

8

9

10

Fig. 30. Apparent rate of CO evolution followingreaction of oxygen with the basal plane of pyrolytic graphite, showinghysteresiseffects. From ref. [224],with permission.

488

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

the apparent reaction probability measured by MBRS, as illustrated in fig. 30 for the oxidation of the basal plane of pyrolytic graphite [224]. As the surface was heated the apparent reaction probability traced the upper curve in fig. 30, decreasing above 1500 K. When the sample was cooled from 1800 K, the signal followed the lower curve, indicating that a fraction of the surface reactivity had been "annealed out". Olander et al. [224] showed that the oxidation process gives rise to an increased number of active sites, which are in turn destroyed by thermal annealing. A two-branch, two-site model with surface diffusion of O a was found to give a good account of the MBRS phase and amplitude data. We note that the yield of CO 2 relative to CO was quite small (= 1%) and had a temperature dependence contrary to that predicted by a quasiequilibrium model [188]. While the reaction probability of H 2 with graphite was too small to be observed, hydrogen atoms reacted readily to yield CH 4 for Ts < 800 K and C2H 2 for Ts > 1000 K [226]. The reaction was analyzed using a model incorporating bulk solution and diffusion of H, sequential addition of H a to C to form CH4, or reaction between 2 CH a to produce C2H 2. Balooch and Olander [226] found the prism plane (s n = 0.02) to be slightly more reactive than the basal plane (s u = 0.006). The overall agreement of the experimental and predicted phase and amplitude behavior was excellent. Olander et al. [227] found H20 to dissociatively adsorb on the prism plane of pyrolytic graphite with s o = 0.15. The apparent activation energy for H20/D20 exchange was too small to be measured, while a value of 40 kcal/mol was obtained for the production of CO and H2, the only other products observed. The MBRS phase lags and amplitudes of the various products were analyzed by assuming double diffusion of each intermediate to take place; agreement with the model was satisfactory.

7. Summary Molecular beam techniques have been fruitfully ~mployed to study a wide variety of reactive processes on surfaces. Detection ot the phase lag between modulated reactant and product waveforms provides a direct measurement of the characteristic time associated with a surface process, and thus represents an excellent technique for characterization of reaction kinetics, normally at low coverage. The high degree of definition of the spatial and dynamical state of impinging reactant molecules obtainable with beam techniques also allows for measurement of the angular, velocity, and internal state distributions of scattered and desorbed species. Analysis of MBRS data is relatively straightforward for simple reaction sequences. For more complex reactions, however, it becomes more tedious, and assignment of a unique mechanism and evaluation of the kinetics of each individual elementary step are often not possible. While scattering chambers are not commerciably available, molecular beam, ultrahigh vacuum and surface analysis

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

489

technologies are all in widespread use. The catalytic reactions that have received the most attention are the adsorption and desorption of H 2, CO, and NO and the oxidation of CO and hydrogen on surfaces of Group VIII metals, particularly platinum. Surface heterogeneity, in the form of steps, has been shown to play an important role in desorption kinetics at low coverage. Steps also appear to be responsible for the coverage-dependent dynamical properties of CO 2 produced by CO oxidation on P t ( l l l ) . MBRS experiments have clearly demonstrated the dominance of a Langmuir-Hinshelwood mechanism in the oxidation reactions of CO and H 2 under a broad range of surface temperatures and reactant coverages. Measurements of the dynamical properties of desorbing molecules have shown that equilibration with the surface does not necessarily imply cosine angular distributions, Maxwellian velocity distributions, and Boltzmann internal state distributions, with a charactristic temperature equal to Ts. Nonequilibrium distributions thus contain information on the gassurface interaction potential and on energy exchange and, at least in the case of CO oxidation on Pt, the disposition of exoergic reaction energy. Reactions of gases with metals and nonmetals to form volatile products are often more complex. Diffusion of intermediates, on the surface, in the bulk, or within a layer of nonvolatile intermediate, often dominates the kinetic behavior. The reaction product distributions typically may be predicted qualitatively using equilibrium free energies of formation. We expect that the continued application of molecular beam techniques to the investigation of elementary surface reactions will yield kinetic information on a considerably wider range of reactions, and aid in a fuller understanding of the dynamics of selected reactions.

Acknowledgements The authors gratefully acknowledge the support of the Department of Energy and the National Science Foundation during the course of preparation of the article. We wish to thank the many collaborators of R.J.M. over the past fifteen years for their contributions to the development of MBRS. Special thanks go to G. E. Gdowski, with whom M.P.D. has benefitted from any useful discussions and who assisted in the compilation of the literature references.

Glossary of abbreviations and symbols AES FTIR LEED MBE

Auger electron spectroscopy Fourier transform infrared (spectroscopy) Low energy electron diffraction Molecular beam epitaxy

490

M. P. D'Evelyn, R. J. Madix / Reactive scattering from solid surfaces

MBRS TPD TPR UHV XPS

Molecular beam relaxation spectrometry T e m p e r a t u r e - p r o g r a m m e d desorption T e m p e r a t u r e - p r o g r a m m e d reaction Ultra-high vacuum X-ray photoelectron spectroscopy

A(0 c D Ea (i)

Preexponential factor for ith order reaction Bulk concentration Diffusion constant Activation energy for ith order reaction Partition function per unit area of reactants, transition state Transfer function, surface transfer function Planck's constant H e n r y ' s law constant Enthalpy, entropy of formation of transition state ith order reaction rate constant Boltzman constant Flux of incident, reflected, desorbing molecules Surface concentration of species A Branching probability Gas constant Sticking probability; So, at zero converage; SA, of species A Surface temperature Angle of incidence, detection Fractional surface coverage of species A Transmission coefficient (from transition state) Equilibration probability of species i Surface residence time Phase angle of Fs (co) A n g u l a r frequency Modulation (angular) frequency.

f l , f 2 , f J; F(t), Fs(t ) h H

AH*, AS* k(i) kB

Io, lr, Id hA(t) P R S, So, S A

L 0 i, O r

0A X

T

cp (D0

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