Reactivity of Fe n, Co n, and Cu n Clusters with O2 and D2 Studied at

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J. Phys. Chem. 1996, 100, 12222-12234

Reactivity of Fen, Con, and Cun Clusters with O2 and D2 Studied at Single-Collision Conditions Mats Andersson,* John L. Persson, and Arne Rose´ n Department of Physics, Chalmers UniVersity of Technology and Go¨ teborg UniVersity, S-412 96 Go¨ teborg, Sweden ReceiVed: March 22, 1996; In Final Form: May 14, 1996X

This paper describes a method to study the reactivity of neutral clusters at single-collision-like conditions, which enables the determination of absolute numbers for the reaction probability (S) in a collision. A beam of clusters is produced in a laser vaporization source and skimmed and passes a cell with reactive gas, in which the clusters experience one or a few collisions with the gas molecules. The reaction products are detected with laser ionization and mass spectrometry. The depletion of pure clusters and the appearance of products are evaluated with a statistical model providing S for the first, second, etc., molecule adsorbed. The O2 and D2 reactivity of Fen, Con, and Cun has been investigated for clusters in the approximate size range 10-60 atoms. The oxidation of transition metal clusters, here exemplified by Con and Fen, shows a simple S vs n dependence, where S increases almost monotonically as n increases from 10 to 20, while for larger n, S remains high and almost constant; S ≈ 0.7 for both Fen and Con. The low O2 reactivity measured for the small transition metal clusters may be an effect of the products having a short lifetime due to the high exothermicity of the oxidation reaction. For copper clusters there are repeated minima in the O2 reactivity appearing at cluster sizes that are known to have high IP and closed electronic shells. Con is much less reactive toward D2 than O2, and S for D2 on Con exhibits large size to size fluctuations. Cun and small Fen appear unreactive (detection limit S ≈ 0.02) toward D2, whereas the larger Fen (n g 23) react with a low probability.

1. Introduction The reactivity of unsupported metal clusters has, after the introduction of the laser vaporization source for cluster production,1,2 been studied quite extensively during the last decade.3,4 Already early experiments revealed a dramatic cluster size dependence, where the reactivity of neighboring sizes could vary by orders of magnitude.5-8 These findings gave inspiration to search for models to describe the reactivity of clusters, and in many cases it has been possible to relate the reactivity patterns observed to the electronic and/or geometric structure of the clusters. Thus, the chemical reactivity has also served as a useful probe for cluster properties. To extract relevant reactivity data, various experimental configurations have been used, each of them with advantages and limitations. Many experiments have been done with fastflow or flow-tube reactors,9-16 where the clusters are exposed to a reactive gas diluted in an excess of buffer gas, at controlled temperature, pressure, and time. From the depletion of bare clusters, reaction rates (relative or absolute) have been measured, and by observation of the products equilibrium/saturation coverages can be determined. The reactor can be attached directly onto the cluster source,9-13 or the cluster beam can be allowed to expand in a wide diameter flow-tube reactor.14-16 In experiments on cluster ions it is possible to select one specific cluster size before reaction in order to assign the parent cluster for various products. Such experiments have been performed with ion drift tubes17-20 and in ion cyclotron resonance (ICR) spectrometers.21-23 An unreactive buffer gas is often used also in these experiments for thermalization of the clusters before and in between the reactive collisions. * Corresponding author. Fax: +46-31-772 3496. E-mail: f3cma@fy. chalmers.se (Mats Andersson), [email protected] (Arne Roseń). X Abstract published in AdVance ACS Abstracts, July 1, 1996.

S0022-3654(96)00889-1 CCC: $12.00

In another class of experiments, individual collisions between clusters and reactive molecules have been investigated. Examples of such experiments are ion drift tube or ICR experiments with only a low pressure of reactive gas,17,23 crossedbeam experiments with angular resolved detection,24 and scattering from collisions in a cell.25 These experiments have quite different character and include studies of such diverse, but reactivity related, subjects as the estimation of barriers, investigation of product decomposition, and determination of total or differential reactive cross sections. In the presence of buffer gas the reactions are assumed to occur at constant temperature (if the thermalization after reaction is rapid), while the single-collision reactions occur at constant energy. The experiment we present in this paper belongs to the last class of methods, although it is not strictly a single-collision experiment. A beam of neutral clusters passes through a cell with a low pressure of reactive gas only, and the reaction products and unreacted clusters are detected with photoionization and mass spectrometry. With this method we have investigated the adsorption of O2 and D2 onto clusters of iron, cobalt, and copper. Preliminary results have been published previously,26 and in this paper we give a more detailed description of the experimental methods and a more extensive analysis of the results. The description of the experimental equipment and data evaluation procedure is given in sections 2 and 3, respectively. The results, section 4, are discussed and compared with other cluster studies and surface reactions in section 5, and the discussion is summarized in section 6. 2. Experimental Methods The cluster beam apparatus is a two-chamber vacuum system with a laser vaporization source and a time-of-flight mass spectrometer, as shown in Figure 1. Both chambers are pumped by turbomolecular pumps (Balzers) with nominal pumping © 1996 American Chemical Society

Reactivity of Fen, Con, and Cun Clusters with O2 and D2

J. Phys. Chem., Vol. 100, No. 30, 1996 12223

Figure 1. Cluster beam apparatus.

Figure 2. Cross section of the cluster source.

speeds for He of 410 and 500 l/s, respectively. The cluster source is a pulsed laser vaporization source, Figure 2. The diameter of the growth zone is 3 mm, and the length is adjustable between 6 and 20 mm. The constrictions of the exchangeable nozzles are 1 mm in diameter and with lengths ranging from 3 to 12 mm. The buffer gas, He purity 99.995% or 99.9995%, is injected through a 1.5 mm diameter channel into the source by a membrane valve (R. M. Jordan Co.). For vaporization the light from a Nd:YAG laser (Continuum YG661-10) is focused with a 200 mm focal length lens onto the sample. Normally, we use the third harmonic (λ ) 355 nm) at a pulse energy of 2-20 mJ. The valve and vaporization laser puts an upper limit on the repetition rate at 10 Hz.

We use rotating disc targets with 13 mm diameter. By transferring the rotational motion through an eccentric gear device, the target will perform a translational and rotational motion and the spots exposed to the laser light will form a spirallike pattern on the target surface. As target materials we use high-purity materials in 2 mm plates or thinner foils glued onto stainless steel substrates. The cluster source is attached to a heat reservoir. Through this hollow copper body, water or liquid nitrogen can be circulated so as to control and stabilize the temperature of the cluster source. The temperature of the clusters is not known, but is assumed to be close to the source temperature. This assumption is supported by the observation that Kr atoms, when mixed in the buffer gas, condense onto the clusters if the source is cooled to liquid nitrogen temperature. Since the objective is to study the adsorption of molecules onto the clusters, it is important to have a beam of pure metal clusters with as little contamination of oxygen and carbon atoms as possible before the reactions. This can be achieved by using high-purity buffer gas and by cooling the pulsed valve. The cooling of the cluster source also reduces contamination. For some metals the rotation speed of the target is crucial for the contamination content, and generally a low speed is preferred, moving the laser focus a few cm/h over the target. After expanding from the source, the cluster beam travels 12 cm in the first vacuum chamber to the skimmer. The velocity is estimated to be close to the supersonic velocity of He, i.e. around 1500 m/s with the source at room temperature. A typical operating pressure in the first chamber is 5 × 10-4 mbar. The skimmer used in these experiments is a thin wall skimmer with a 1 mm opening. To prevent charged particles from reaching the detection system, they are deflected in the first chamber by applying a voltage to a rod mounted parallel to the cluster beam. The two reaction cells are located just behind the skimmer. Actually, the skimmer acts as the entrance aperture of the first

12224 J. Phys. Chem., Vol. 100, No. 30, 1996

Figure 3. Mass spectra of Con clusters, n ) 12-32. The upper spectrum is recorded without reactive gas in the cell, and the other ones are recorded with 0.6 × 10-3 and 1.2 × 10-3 mbar O2, respectively, in the second reaction cell.

cell. All the cell apertures have a 1 mm diameter. The first reaction cell is 106 mm long, and the second one is 50 mm; both have inner diameters of 6 mm. The distance between the cells is 20 mm. A constant pressure of reactive gas is maintained by a continuous flow through the cells. The low conductance of the cell openings compared with the pumping speed gives a large pressure ratio (>1000) between the cells and the surrounding chamber. Thus, one can assume that all reactive collisions have taken place inside the cells. The flow through the cells is controlled by leak valves outside the vacuum chamber, connected to capacitance vacuum gauges (Varian CMH4). Because of the finite conductance through the gas lines into the cells, there is a pressure difference between the cells and the location of the vacuum gauges. Correction factors for this difference have been determined with an accuracy of (10%. During a reactivity experiment, the cell pressure is varied in the range 10-4-10-2 mbar, which approximately corresponds to an average number of collisions ranging from 0.05 to 10. If the cell pressure increases, the total number of clusters exiting the cells decreases because of scattering, since there is no way to guide the neutral clusters back into the beam. This puts an upper limit on the cell pressure and the total number of collisions. To better quantify the deflected fraction of the clusters as a function of cell pressure, reference measurements with an unreactive gas are conducted in parallel with the reactivity measurements. As a reference, a gas with about the same molecular mass is used, He as a reference for D2, and N2 or Ar for O2. The main reason to have two reaction cells is the possibility of studing the subsequent adsorption of two different molecules. Also for investigation of reactions with one gas, the availability of two different geometries of the reaction cells has been very useful for investigating the influence of scattering and possible fragmentation. The reaction products are detected with photoionization and time-of-flight mass spectrometry. The distance between the exit opening of the second reaction cell and the ionizing laser beam is 8 cm, which makes the overall distance between the source and mass spectrometer 38 cm. The light from an excimer laser (Lambda Physik LPX210i) or a dye laser (Lambda Physik FL2002) is used for ionization. Normally, we use the ArF laser line (λ ) 193 nm) as the photon energy, 6.42 eV, in most cases assumed to be sufficiently above the ionization potentials of most unreacted and reacted clusters, to obtain an efficient and uniform ionization. The aperture for the ionizing laser beam measures typically 4 × 15 mm, and the laser light intensity is kept low, 20-50 µJ/cm2, to minimize effects of multiphoton

Andersson et al. absorption. The dye laser is used for control experiments, to check to what extent the relative ionization efficiency of bare clusters and products depends on photon energy. The dye laser has also been used for the determination of ionization thresholds.27 The time-of-flight spectrometer is of Wiley-McLaren type28 without a reflector, and the ions are accelerated perpendicularly to both the cluster beam and the laser beam. The ion optics consists of dual acceleration fields, deflection fields for both directions, and an einzel lens. The flight distance to the dual microchannel plate detector is 90 cm. The mass resolution (M/∆M), measured as the full width at half-maximum (fwhm), is at normal operation around 400. The detector signal is amplified 50 times in a preamplifier (Stanford Research Systems SR440) before recording and averaging in a digital 125 MHz oscilloscope (Le Croy 9400). Usually, an averaging of 3002000 cycles is needed to obtain good statistics and reduce noise. Examples of mass spectra from measurements of the Con-O2 reaction are shown in Figure 3. 3. Models and Procedures for Data Evaluation 3.1. Statistical Model To Describe Cluster Reactions at Few-Collision Conditions. The experiment is normally performed with the reaction cell pressure in a range where the clusters experience multiple collisions and several molecules can adsorb on the clusters. Thus, the experiment is not strictly a single-collision experiment, but the collisions are still so few that they can be regarded, in many respects, as independent events. To evaluate data under these conditions, we have chosen a statistical model where the average number of collisions and their statistical distribution are the important parameters. For simplicity the concept of number of collisions is used instead of cross sections, but they are, in principle, interchangeable, since the number of collisions is defined as the number of collisions with an impact parameter that is smaller than or equal to the one given by hard-sphere radii. The hard-sphere radius of an n-atom cluster, rc, is calculated as

rc ) ran1/3 + δ (1) where ra is the radius of atoms with the density of the bulk metal (ra ) 1.41, 1.38, and 1.41 Å for Fe, Co, and Cu, respectively), and δ (here δ ) 0.5 Å) is a constant to account for surface roughness and spill-out. The radii for the molecules, rm, are taken from tabulated values derived from gas kinetic properties at high pressures (rm ) 1.825 and 1.34 Å for O2 and D2, respectively).29 Thus, the hard-sphere collision cross section σHS is σHS ) π(rc + rm)2 (2) The average number of collisions, X, is calculated by deriving the gas density, number of molecules per volume N/V, from the ideal gas law: N p X ) lσHS ) (3) lσ V kBT HS where p and T are the pressure and temperature of the gas and l is the length of the reaction cell. This expression is exact only if the molecules have zero velocity. With a finite velocity of the molecules the average number of collisions is higher, and if the average velocity of the molecules is larger than the cluster beam velocity, X would better be described as the molecule impact rate at the cluster surface multiplied by the time the cluster spends in the reaction cell. In our experiment, the clusters have approximately the supersonic velocity of the He carrier gas, which in most cases is substantially higher than the room temperature average velocity of the gas molecules. The velocity difference is, however, for D2 as reactive gas not very large, especially when the cluster source is cooled with


J. Phys. Chem., Vol. 100, No. 30, 1996 12225

liquid nitrogen. Throughout this work we have maintained the direct relation between the number of collisions and the cross sections, eq 3, and do not renormalize the results for the velocity dependence of the collision frequency. This should, however, be kept in mind when the data are interpreted and uncertainties estimated. Besides the average number of collisions, the statistical distribution is needed for describing the process. The clusters traveling through the reaction cell making independent collisions can be described as a Poisson process, and the number of collisions that the clusters have experienced when exiting the cell is Poisson distributed. The frequency function of the Poisson distribution is

qx -q (4) e x! Here x is the number of collisions and the parameter q is the average number of collisions, X, as given in eq 3. The average number of collisions and their distribution are thus rather straightforward to model. We also need to describe the number of reactive collisions in relation to the total number of collisions. This can be done using eq 4 but with SX as the parameter q. S is the reaction probability or sticking probability and is defined as the probability of the cluster and molecule reacting and forming a stable product when colliding. Since X can be determined from the cell pressure and the relative frequencies of reacted species are obtained from mass spectra, these data can be fitted to eq 4 with S as the only free parameter. This rather simple model has one severe limitation. It requires that the reaction probabilities of the first, second, third, etc., molecule are the same. This is far from always the case and cannot be postulated. To solve the problem with individual reaction probabilities, S1, S2, etc., in the successive addition of a molecule A2 to a cluster Mn, f(x) )

S1

Mn + A2 98 MnA2

(5a)

S2

MnA2 + A2 98 MnA4

(5b)

S3

(5c) MnA4 + A2 98 MnA6 one has to employ a model with sequential differential equations dN0 (6a) ) -N0S1 dX dN1 ) N0S1 - N1S2 dX

(6b)

dN2 (6c) ) N1S2 - N2S3 dX for the abundances N0, N1, N2, etc., of clusters with 0, 1, 2, etc., molecules adsorbed. The solution of this system of differential equations, assuming an initial abundance of Ns pure clusters, is -S1X

N0 ) Nse

[

N2 ) NsS1S2

(7a)

S1 N1 ) Ns (e-S2X - e-S1X) S1 - S2

(7b)

e-S1X e-S2X + + (S1 - S2)(S1 - S3) (S2 - S1)(S2 - S3)

]

e-S3X (7c) (S3 - S1)(S3 - S2) This is the same as pseudo-first-order kinetics, but with S and X as the parameter and variable instead of the normally used

rate and time. In many experiments on cluster reactivity and/ or scattering only the depletion of the bare cluster intensity is followed and reactivity in the first step is determined on an absolute or relative scale. In our case we evaluate the intensity of both pure clusters and the reaction products mainly for two reasons. We hope to be able to obtain information also on the subsequent reaction steps, i.e. the adsorption of a second or third molecule. Also, measuring only the depletion of pure clusters might not be sufficient to derive product formation probabilities, since the depletion is a combination of two processes: deflection of clusters out of the beam because of scattering in reactive or unreactive collisions and depletion of pure clusters due to product formation. The scattering of clusters is a complex process and depends on the interaction between the cluster and molecule during the collision. Fundamental investigations of metal cluster scattering with the purpose to derive total or differential cross sections have been performed in several different types of experiments,24,25,30,31 and also reactive scattering has been investigated.24,25 It is not our ambition in this study to derive detailed scattering cross sections, and the experimental geometry is not well suited for that, but we need to estimate the deflection of clusters out of the beam in order to make an accurate evaluation of the product formation probability. In analogy with the analysis of the reactive collisions, it seems appropriate to define a deflection probability as the cross section for deflection out of the beam divided by the hard-sphere collision cross section. It is, however, well established that the total scattering cross sections can be substantially larger than the hard-sphere cross sections due to long-range attractive van der Waals interactions.25 This is typically the case in low-energy collisions, while collisions with impact parameters within the hard-sphere radius dominate the scattering at higher energies. Also the scattering angles differ between collisions at small and large impact parameters. Collisions with large impact parameters lead to scattering in small angles, while collisions with small impact parameters have a larger fraction of the scattering in large angles. Our experiment is characterized by collision energies that are higher, but not very much higher, than thermal energies, a high mass ratio between the cluster and the molecule, and an acceptance angle that is relatively large compared to what is used in dedicated scattering experiments.25 This probably means that most deflected and not detected clusters are deflected in collisions with impact parameters within the hard-sphere radius, and this will be more true for large clusters than for small ones. The use of a deflection probability per hard-sphere collision can thus be a useful model, if one is careful and aware of the limitations. To experimentally evaluate the deflection cross section or deflection probability, D, the transmitted fraction, NT, is modeled with an exponential decay:

NT ) Nse-DX

(8)

in analogy with eq 7a. The deflection is estimated for both unreactive and reactive gases, and for reactive gases the total intensity of all products is included in NT. The deflection probability in a (reactive) collision is needed for the evaluation of the reaction probabilities since the reacted clusters have, on average, made more collisions than the unreacted ones. Assuming the same reaction probability for all reaction steps, the product clusters have on average made one collision more (the reactive one) for every molecule adsorbed. Although the reaction probability is not equal in the successive reaction steps, this model has been used in this study since this simplification does not change the results significantly, and the uncertainties

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Andersson et al.

Figure 5. Deflection probability as a function of cluster size for Con colliding with O2 (dashed line), N2 (dotted line), and Ar (dot-dashed line) in the second reaction cell. The solid line represents the polynomial expression used for the deflection correction of product abundances.

Figure 4. Parts of the mass spectra of Figure 3 showing the region around Co29 and Co30. The full line is the experimental spectrum. The dotted lines are the individual fitted peaks, and the sum of these constitutes the model spectrum indicated by the dashed line.

in the determination of the deflection probability are often larger than the effects of not including the various reaction probabilities. 3.2. Evaluation of Mass Spectra. The output from the experiments is a series of mass spectra recorded at different pressures in the reaction cell, as shown in Figure 3. Each mass spectrum contains a number of peaks for pure clusters, reaction products, and sometimes impurities, and often all peaks are not well resolved. The basic idea behind the evaluation of peak intensities is to fit a model spectrum containing the relevant peaks to the experimental spectrum with the peak intensities as fitting parameters. First a mass scale, peak widths, and peak shapes are determined, using various nonlinear fitting procedures. Then a model spectrum with predetermined widths and positions of the peaks is fitted to the experimental spectrum with peak heights and a base line, built up of cubic splines, as the only fitting parameters. This results in an overdetermined system of equations for which the least-squares solution is calculated. An example of fitted peaks in mass spectra from the Con-O2 reaction is shown in Figure 4. 3.3. Evaluation of Reactivity Data. Before performing the reactivity analysis the deflection probabilities as discussed in section 3.1 should be determined. The total intensity of all clusters with one parent cluster is fitted to eq 8 as a function of reaction cell pressure. Normally, D should be a smooth function of size, and thus, the deflection probability as a function of cluster size is modeled with a polynomial expression adhering to the experimental data. An example of the measured D for the Con-O2 system is shown in Figure 5, together with the

smooth polynomial fit and D for Con-N2 and Con-Ar. The abundance of products is corrected for the deflected, not detected fraction by dividing the measured abundance by (1 - D)m, where m is the number of adsorbed molecules. To derive the reaction probabilities, the corrected relative product abundances are, for each cluster size, plotted vs reaction cell pressure or average number of collisions. Then curves are fitted to this data according to eqs 7 with the reaction probabilities as fitting parameters. All curves are fitted in one nonlinear fitting procedure. An example for Con and its products ConO2 and ConO4 (n ) 15, 20, 25, and 30) is shown in Figure 6. The lines represent best fits to eqs 7a, 7b, and 7c, respectively. 4. Results We have studied the reactivity of iron, cobalt, and copper clusters with O2 and D2. Clusters of all three metals react readily with O2. For larger clusters several molecules adsorb, at least on Fen and Con. Because of a mass interference between CunO4 and Cun+1 (which could be avoided by using isotope-separated Cu and 18O2), we cannot quantify any multiple product formation for the copper oxygen system or even safely detect it. Instead, the measurement had to be performed at pressures where multiple products did not form. Con showed a rather high, but very size selective, reactivity with D2, and for n g 22 ConD4 products were also detected. Fen did not show any D2 reactivity for n < 23 and above that a moderate, rather size independent reactivity. We did not observe any reactions between Cun and D2. The detection limit for the Fen-D2 reaction is estimated to be a reaction probability of 0.01-0.03 depending on size, and for Cun-D2 0.05-0.10, so we can only conclude that the reaction probability is lower than those values when a product is not observed. If the cluster source was cooled to liquid nitrogen temperature, the Con clusters became about twice as reactive with D2, while the reaction probability for O2 did not change significantly for any of the three metals. In no case was the formation of products with an odd number of adsorbed atoms, e.g. MnO, MnO3, MnD, or MnD3 (M ) Fe, Co, Cu), detected, except the small amount of oxide impurity clusters formed in the source. Values for the reaction probabilities were determined for Fen, Con, and Cun reacting with O2 and for Con reacting with D2. This was done for n ranging from 10-15 to 45-65. The lower limit of n is determined by a combination of large deflection probability and high ionization potentials. For large n, the mass resolution becomes worse and the measured intensities less reliable. In several cases data for another 10 sizes or more could


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Figure 6. Relative abundance of Con (O) and its reaction products ConO2 (+) and ConO4 (×) vs cell pressure. A pressure of 0.80 × 10-3, 0.72 × 10-3, 0.65 × 10-3, and 0.60 × 10-3 mbar corresponds to an average of one collision for Co15, Co20, Co25, and Co30, respectively. The lines (solid for Con, dashed for ConO2, and dotted for ConO4) represent the least-squares fits of the statistical model, eqs 7.

Figure 7. Apparent reaction probabilities for Con-O2 as a function of cluster size. The reaction probability of the first molecule (S1) is displayed for n ) 10-55 and of the second molecule (S2) for n ) 15-45. The relative errors in S2 are about twice the errors in S1.

be extracted, but with larger error bars. As this additional data seems to follow the general trend at large sizes, possibly with the exception of Cun-O2, we do not display it here. Figure 7 shows the apparent reaction probability of the first and second O2 molecule on Con. Here the term apparent reaction probability is used because product fragmentation could influence the derived values for the reaction probability, as will be discussed in the next section. A third adsorbed molecule was detected from n ≈ 20 and also a fourth one at even larger sizes. It was, however, from the data in this measurement not possible to quantify S3 or S4 with reasonable accuracy. The apparent reaction probability for O2 with Fen is shown in Figure 8. Also on Fen, a second molecule was found to adsorb for n > 15, but because of the limited mass resolution due to the Fe

Figure 8. Apparent reaction probability (S1) for Fen-O2 as a function of cluster size for n ) 12-45.

isotope distribution, the S2 values are less accurate and not shown here. The reaction probability for the first O2 molecule with Cun is shown in Figure 9. In Figure 10 (top and middle), S1 and S2 for D2 on Con are shown. Con from a liquid nitrogen cooled source were significantly more reactive with D2, as shown in the bottom panel of Figure 10. There is limited data for the reaction probability for D2 on Fen; it is lower than ∼0.02 for n < 23 and approximately 0.05 for n g 23, but it is increasingly more difficult to quantify for larger sizes because of the limited mass resolution. The error bars displayed in the figures show the relative errors for one size compared to others. Added to this, there is an uncertainty in the absolute scale of (20-30% independent or only weakly dependent on cluster size. This uncertainty mainly originates from errors in the pressure measurement and the

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Andersson et al. data evaluation. Still there is good agreement between the reaction probabilities presented here and the preliminary ones. The largest deviation is seen for the Con-O2 reaction for which S1 ≈ 0.7 was determined, rather than the previously reported S1 ≈ 1.0 for large sizes, a difference that is mainly due to a refined model for deflection correction. 5. Discussion

Figure 9. Reaction probability (S1) for Cun-O2 as a function of cluster size for n ) 15-65.

Figure 10. Reaction probabilities for Con-D2 as a function of cluster size. Top: reaction probability of the first molecule (S1). Middle: reaction probability for the first (S1) and second (S2) molecules. Bottom: reaction probabilities (S1) on clusters produced at source temperatures 80 and 300 K, respectively.

deflection correction. The choice of hard-sphere cross sections also influences the absolute probabilities. As mentioned earlier, the reaction cross section can be derived by multiplying the reaction probability with the hard-sphere cross section. Since the preliminary results were published,26 we have remeasured the reactions and further developed the models for

The discussion in this section covers the reliability and applicability of our method for reactivity studies and the models for interpretation of the reactivity results as well as an examination of the specific systems including comparisons with results from other cluster and surface reactivity experiments. 5.1. The Method for Cluster Reactivity Studies. The virtue of the method presented here for reactivity studies is that it provides a rather straightforward way to calculate the number of reactive collisions and the total number of collisions and define the ratio between them as the reaction probability. This definition is, however, not as simple as it appears, since both the reactive collisions and the total number of collisions must be clearly specified as discussed in section 3.1. Moreover, what is measured as a reactive collision is when the molecule is adsorbed onto the cluster and remains adsorbed during the transport to the ionization region and during the ionization and acceleration processes. Thus, weakly bound adsorbates, which are likely to desorb between the reaction and the ionization are not registered as adsorbed in this experiment. The impact parameter, b, has most certainly an influence on the reaction probability, as shown in molecular dynamics simulations.32,33 Often b ) 0 gives the highest S, and then S decreases as b increases. From our measurements we cannot extract information on how S depends on b. Instead, we derive an average S constant for b e rm + rc, and S ) 0 for b > rm + rc, where rm and rc are the hard-sphere radii of the molecule and cluster as defined in section 3.1. This means that S actually can be larger than 1 if the molecule is efficiently trapped in collisions with b > rm + rc. Thus, the full definition of the reaction probability or sticking probability as used in this work should be as follows: the number of collisions in which the molecule sticks to the cluster and stays there throughout the detection process divided by the number of collisions with b e rm + rc. In the reactivity evaluations we compare the abundance of reacted and unreacted clusters to obtain the reaction probability, and we must be certain that the experiment provides true ratios. There are mainly three processes that can influence the result and, thus, have to be considered carefully: scattering/deflection, photoionization efficiency, and fragmentation. Deflection. We know that some of the clusters are deflected; the problem is to find a method to quantify this scattering and to correctly adjust the product abundance. To measure the depletion of cluster intensity and fit the data to eq 8, is the straightforward method to estimate the deflection cross section or deflection probability. In this case we actually need the deflection probability in a reactive collision to be able to correct the relative intensity of the various products as described in sections 3.1 and 3.3. When the deflection probability is measured with a reactive gas, the derived deflection probability will be a combination of scattering in both reactive and unreactive collisions (unless S ) 1), while the reference measurements with unreactive gas provide the deflection probability in unreactive collisions only. The general impression is that over large cluster size ranges the deflection probability mainly depends on the mass ratio irrespectively of whether a reactive or unreactive gas was used. This observation can be interpreted in two ways, either that the deflection probability is about the same in reactive and unreactive hard-sphere collisions

Reactivity of Fen, Con, and Cun Clusters with O2 and D2 or that unreactive collisions with large impact parameters dominate. In the latter case the true deflection probability in a reactive collision would be much smaller. We believe, however, that with the comparatively large allowed deflection angles and high velocity and mass ratio, the deflection is dominated by hard-sphere collisions. The most reliable test for the deflection-correction model, which can be done in our experimental configuration, is to perform the reactivity experiment in both reaction cells. If the collisions take place in the first cell, the allowed scattering angle is smaller because the second cell acts as a blocking aperture. Thus, the deflection probabilities, D, are substantially higher. The difference between reaction probabilities measured in the respective cells was not larger than typical deviations between two series of measurements in the same cell, i.e. within (1015% of the measured values. The influence of the ratio between the number of reactive and unreactive collisions was tested by measuring the Con-O2 reactivity with air (21% O2) instead of pure O2 gas. The deviations in reaction probability were in this case also around 10%. We have also checked how uncertainties in the deflection correction influences the calculated reaction probability and found that the derived reaction probabilities vary 5-15% of the actual value (except for small sizes, n ≈ 10) when typical errors are added to the deflection probabilities. For small clusters reacting with oxygen, D is very high, close to 1, and since very low product abundance is detected, the sensitivity for variations in D is strong. This limits the cluster size range that is feasible to study and is one reason not to present values here for as small clusters as was done in our previous studies.26 When considering the errors originating from uncertainties in the deflection correction, one should note that the deflection probability is assumed to vary smoothly as a function of size. Thus, the errors mainly affect the absolute values of the reaction probability, only weakly the trends with size, and not the relative reactivity of neighboring sizes. Photoionization Efficiency. Another possible problem is the photoionization process, where the evaluation procedure used here demands that the relative ionization and detection probability is the same for pure and reacted clusters. There are several investigations of how the adsorption or incorporation of molecules and atoms in clusters can change the ionization potential (IP). For example, the IP of small transition metal clusters has been found to often increase more than 1 eV upon adsorption of hydrogen.34 Adsorption of ammonia generally lowers the IP of clusters, with a decrease per adsorbed molecule that diminishes with cluster size.35 Incorporation of oxygen atoms in Nbn36 and Yn37 could shift the IP in either direction, but with smaller shifts the larger the cluster. We have measured the IP shifts of Cun upon O2 adsorption and found that the shift can be either positive or negative, and on average the IP increased ∼0.1 eV.27 Data for ionization cross sections of pure and reacted clusters are more scarce. The general impression of photoionization efficiency curves for metal clusters36,38 is that the ionization efficiency rises sharply the first tenths of an electronvolt above the threshold, but then rises more slowly and levels off. Our conclusion from this is that there are reasons to be very careful, especially if one studies small clusters or uses photon energies near the threshold. In the measurements presented here we have used 6.42 eV photons, which is around 1 eV or more above the IP of most Fe, Co, and Cu clusters38,39 in the investigated size range. One more reason not to present data for smaller clusters is that there is a larger risk for differences in IP and ionization probability.

J. Phys. Chem., Vol. 100, No. 30, 1996 12229 We have made reference measurements using 6.0 eV photons from a frequency-doubled dye laser for ionization and recorded mass spectra both with 6.42 and 6.0 eV photon ionization at the same reaction cell pressure. There were no systematic deviations in the relative product intensity or the product distribution for any of the systems Con-O2, Fen-O2, Cun-O2, or Con-D2. The latter test is no proof that the relative photoionization efficiency is not affecting the reactivity data, but in our opinion it gives a clear indication that it is not a large source of error. A nonuniform ionization probability would also be reflected in the deflection data; if for example the ionization efficiency decreases upon oxidation, the deflection probability would appear too large because of the additional loss of signal. Besides ionization, photon absorption can also result in fragmentation. The photon energy should be sufficiently above the IP to efficiently ionize the cluster, but not so high above that the excess energy can cause fragmentation. The light intensity should be kept low to avoid multiphoton absorption. At the laser light intensity used in the reactivity measurements, there were no signs of photofragmentation, However, if the intensity was increased a factor of 5-10 or more, the relative intensity of D2 products on the Co clusters decreased and for the Cu clusters a typical fragmentation pattern started to appear with a depletion preferentially of even numbered pure Cun+ ions and especially Cu22+ and Cu42+. In the FenO2 or ConO2 reactions there is no such significant desorption/fragmentation pattern to rely on because they probably fragment by monomer evaporation, which is not as size selective for Fen or Con as it is for Cun. By doing the measurement at a laser light intensity that is at least a factor of 5 lower than the threshold for observable desorption and fragmentation effects, we believe that we have minimized the influence of multiphoton absorption. Fragmentation. The reactions we study are exothermic, and the chemisorption energy must be contained in the clusters since no buffer gas is used to thermalize them. Thus, the formed product is metastable and it will decompose with a rate that can be estimated from unimolecular decay theory. The important question for the interpretation of the results is whether the lifetime is shorter or longer than the time between reaction and detection, approximately 10-4 s. The decay path can be desorption of the adsorbed molecule or evaporation of a metal atom or some other complex, primarily depending on the energy needed for the various processes. For pure metal clusters with high internal energy the preferred decay path is evaporation of monomers,40,41 but the Aln-O2 reaction is thought to be followed by evaporation of Al2O units.42,43 The decomposition of clusters with excess energy is most often modeled using the RRKM theory44 that predicts a unimolecular decay rate, k, as

Nq(E - E0)

k)s

hF(E)

(9)

where s is the reaction path degeneracy; Nq(E - E0), the sum of states in the transition state at the excess energy; and F(E), the density of states in the reactant at the total energy. These data are normally not available for clusters. Instead, simplifying assumptions are made, such as that the vibrational frequencies can be taken from a Debye model. This procedure was outlined by Jarrold and Bower43 and has also been used by several other groups,14,40,45 sometimes with minor modifications. In our experiment there are two cases that are critical for unimolecular decomposition/fragmentation. If the chemisorption energy is too low, an adsorbed molecule will desorb before ionization and no product is detected. In the present study, this case will be observed and treated as if a reaction has not

12230 J. Phys. Chem., Vol. 100, No. 30, 1996

Andersson et al.

occurred. If, on the other hand, the chemisorption energy or the summed chemisorption energy of several molecules is high, metal atoms or some other species can evaporate from the cluster. In the fragmentation there will be a recoil between the parent cluster and the fragment, which can cause deflection of the cluster and the fragment out of the beam. If the cluster is not sufficiently deflected, it is detected as containing less metal atoms than it originally had. In both cases the experiment would yield an “incorrect” product distribution in the respect that a reaction of a parent cluster does not result in a detectable product containing the same number of metal atoms as the parent cluster. In our data this would show up as a depletion of clusters of the fragmenting size and maybe an increase of clusters of the size where detectable fragments are formed. Thus, the deflection data can be influenced also by fragmentation, and if the deflection probability for a reactive gas is unexpectedly high compared with an unreactive gas, fragmentation might be the reason. Of the here investigated reactions there is reason to believe that fragmentation can occur at least in the oxidation of Con and Fen, as will be discussed further below. 5.2. Results for the Individual Systems. Con + O2. For ConO2 there is a rather simple size dependence in the measured reaction probabilities, as shown in Figure 7. For the smallest sizes, n ) 10-14, S1 is low and then increases and levels off at S1 ≈ 0.7 for the larger sizes. For S2 the size dependence is similar, with the first products appearing at n ≈ 15, and a high reactivity is reached at n > 20. Qualitatively, the same is observed for the ConO6 products, only shifted to even larger sizes. It seems that the cluster must have reached a certain size to efficiently form products, and the more molecules adsorbed, the larger the size needed. The O2 reactivity of small (n ) 2-9) cationic Co clusters has been studied by Guo et al.20 They detected the products formed from one single size parent cluster ion and found that no cluster but the dimer showed the simple addition reaction

Con+ + O2 f ConO2+

(10a)

Instead, for the larger clusters (n ) 4-9) the dominating scheme was a switching reaction,

Con+ + O2 f Con-1O2+ + Co

(10b)

with O2 replacing one Co atom. There is no reason to believe that the reaction mechanisms on cationic and neutral clusters are very different and the switching reaction can also be dominating in our experiment. It is, however, not clear whether the ejection of the Co atom occurs directly in the adsorption process or should be characterized as evaporation from a thermally equilibrated complex. To analyze various reaction paths, we start by estimating binding energies. Hales et al.46 have measured the binding energies for Co atoms in Con+ (n ) 2-18) with collisioninduced dissociation (CID) and also calculated the binding energies in neutral clusters by comparison with the IP.38 The binding energy increased from 2.41 eV for Co4 to 3.84 eV for Co18. The bulk cohesive energy is 4.39 eV.47 The chemisorption energy of O2 on bulk Co surfaces has been estimated to 4.1-4.6 eV.48,49 Probably, the O2 chemisorption energy on a cluster approaches the bulk value more rapidly than the atombinding energy does. After chemisorption the oxygen atoms tend to bind in the most favorable configuration, maximizing the binding energy, while the atom-binding energy is the energy needed to remove the most weakly bound atom. Thus, it is reasonable to assume that the O2 chemisorption energy is close to or even above 4 eV. If the emission of a Co atom is the result of unimolecular decay after equilibrating the chemisorption energy, the RRKM

model is a suitable approach to calculate lifetimes. For metal clusters a Debye model is often used to model the vibrational frequencies.43 For ConO2 we have chosen to maintain the Debye model with the frequencies for pure Con as the basis and then double the frequency of six evenly spaced modes (assumed to be associated with the oxygen atoms). We assume a tight transition state, remove the midfrequency (taken to be the translational coordinate), and reduce the two adjacent frequencies by a factor of 2, also according to the scheme of Jarrold and Bower.43 The dissociation energies are taken from ref 46 for n ) 5-18, and for the larger clusters we have in a generalized form used the expression for the binding energy in a small metal particle suggested by Miedema:50

∆H(n) ) ∆Hbulk - γn1/3

(11)

with γ here chosen to fit the experimental value for Co18 rather than insert the true materials’ properties. The decay rate was calculated using eq 9 with s ) n2/3. The sum of states and densities of states were calculated with a direct count algorithm.51 The result of the RRKM calculations is shown in Figure 11 as the lifetime (on a logarithmic scale) as a function of cluster size, with each curve representing one specific excess energy, for the ConO2 and ConO4 products. The detailed structure in the curves originates from the variations in the atombinding energies of the pure clusters46 and may not be applicable to the Con(O2)m products. Since simple models for the vibrational frequencies were used and electronic excitations were neglected, the calculated lifetimes should be regarded as order of magnitude estimates. The fragmentation rate should be compared with the time between reaction and detection, which is approximately 10-4 s, indicated by a dashed line in Figure 11. The excess energy, Ex, in the cluster after adsorption of m molecules is

Ex(m) ) E - E0 ) mEbO2 + mEc + Evib,init - E0 (12) where E is the total energy; E0, the Co atom binding energy; EbO2, the chemisorption energy of O2 (≈4.0 eV); m, the number of adsorbed molecules; Ec, the collision energy (≈0.3 eV for clusters from a room temperature source colliding with O2); and Evib,init, the initial vibrational energy (≈(n - 2)0.07 eV) assuming a vibrational temperature around room temperature. The excess energy Ex is estimated to be around 2 eV after adsorption of one molecule. After adsorption of two molecules Ex is 6-7 eV, and for m ) 3 it is estimated to be 10-12 eV. Figure 11 shows that the Ex ) 2 eV curve intersects the line indicating the experimental lifetime at n ≈ 10. For a ConO4 product with Ex ) 7 eV clusters with n g 18 are predicted to have a lifetime longer than 10-4 s. The ConO6 products, not explicitly shown, are predicted to be stable for clusters with n g 25. These numbers correspond reasonably well to the smallest cluster sizes where we detect a significant reaction probability for that number of molecules. When it comes to the evaluation of absolute numbers of S1 and S2, one should have in mind that the reaction probabilities derived from eqs 7 are dependent not only on the stability of the first product but also on higher order products. Thus, even if the ConO2 products are stable, a too low S1 will be derived if ConO4 products are formed and fragment. The atom leaves the cluster with a certain recoil energy, and the cluster and even more probably the atom may be deflected out of the beam and are thus not detected. The probability to be deflected is larger for small clusters than for large ones, because of the smaller mass difference between the cluster and the atom. If the daughter cluster reaches the detection region, it is detected as a one size smaller cluster. In the latter case, the derived reaction probabilities represent an average reaction


Figure 11. Lifetimes of ConO2 (top) and ConO4 (bottom) products as a function of n, calculated with the RRKM model. The curves represent lifetimes at one specific excess energy. In the ConO2 products the excess energy is estimated to be around 2 eV, and in the ConO4 product 6-7 eV. The dashed line at 10-4 s indicates the approximate time between reaction and detection. The structure in the excess energy curves originate from the variations in binding energy in the pure Con clusters and might not represent the conditions in the oxide products.

probability over a small size range rather than the reaction probabilities of individual sizes. The successive appearance of the various products and their increasing formation probabilities can thus be an effect of fragmentation of products, which initially were formed with a higher probability than the apparent reaction probabilities shown in Figure 7. The lower abundance of products of small clusters would then be the result of shorter lifetimes and/or higher deflection probabilities in the recoil. The reasonable agreement between the cluster sizes where efficiently detected products first appear and the calculated unimolecular decay rates is no proof that this is the correct interpretation of the reaction mechanism. It is, however, a model that can describe the measured reaction probabilities, and it is not inconsistent with the observations of Guo et al.20 that Co2-9+ react with O2 with a high reaction probability and that the O2 adsorption causes loss of a Co atom. An alternative explanation for the apparently low reactivity of small clusters could be that the IP increases and ionization cross section decreases upon oxidation, and the product detection probability becomes lower. For larger clusters, more O2 molecules might be needed before the ionization probability would be noticeably affected. This explanation is contradicted by the observation that the measured relative product abundance is about the same when 6.00 eV photons are used for ionization as when 6.42 eV photons are used. It is also possible that the measured reaction probabilities are the “true” reaction probabilities. If that is the case, one can only speculate about possible reasons. One could be insufficient energy transfer in the cluster molecule collision,

J. Phys. Chem., Vol. 100, No. 30, 1996 12231 making it an effectively elastic collision, combined with lower energy transfer probability for a smaller cluster. If a clustermolecule complex is formed, the intermediate complex for small (or hot) clusters might be so short lived that it decomposes by desorbing the O2 molecule before an equilibrated product is formed. This is to some extent similar to the fragmentation model discussed above but with a much more weakly bound complex with a much shorter lifetime. Such complexes normally require some barrier along the reaction coordinate, and those are not thought to be present in the O2 adsorption on transition metal surfaces, but for clusters the case could be different. We have not been able to find any data for sticking probabilities of specifically O2 on bulk Co surfaces, but generally S for O2 is high (0.5-1.0) on transition metal surfaces,52 so it appears as if the Con clusters in this respect have attained bulk properties already at small sizes. The comparison between sticking probabilities on bulk and cluster surfaces is, however, not straightforward to make. The cluster surface is not flat, and for example the distribution of impact parameters is different from the normal distribution of incidence angles in a surface experiment. Another difference is the impact energy, estimated to be distributed around an average of 0.3 eV in our cluster experiment, which is significantly above thermal energies. Fen + O2. The Fen-O2 reactivity pattern, Figure 8, is similar to the Con oxidation, with a high almost uniform reaction probability for large Fen, while the small Fen appear less reactive. There is no reason to believe that the qualitative mechanisms for oxidation of Fen and Con are different, so the interpretation of this reaction should be similar. Thus, we think that the apparent reaction probabilities that we observe are a result of high reactivity followed by fragmentation of small clusters as discussed for the Con-O2 reaction. The chemisorption energy for O2 on a bulk Fe surface is ∼5.0 eV,49 and the bulk surface enthalpy for a pure Fe surface is 4.28 eV.47 The binding energies in Fen (n ) 2-19) have also been measured by Armentrout's group.40,53 All values are similar to the ones for Co, but the O2 adsorption is slightly more exothermic. The Fen-O2 reaction has also been investigated by Whetten et al.10 using a fast flow reactor where oxygen was added to the buffer gas. They detected products also for the smallest sizes (except for the atom) and found that clusters of all sizes (n ) 2-15) reacted with a high rate. Nieman et al.54 have investigated the oxidation of Fen and other transition metal clusters (Vn, Crn, and Nin) and found that the reaction probability was high and that the high exothermicity of the oxidation caused fragmentation. A model with a high reaction probability for all sizes followed by fragmentation because of the excess energy is consistent also with the observations in these previous experiments.10,54 Cun + O2. The oxidation of Cun, Figure 9, appears very different from Fen or Con. There is a distinct size selectivity throughout the investigated size range, and also the absolute reaction probability is significantly lower. Minima in reactivity show up at sizes n ) 20, 30, 34, 40, 48, 57/58, which have high IP39 and/or closed electronic shells according to the jellium model.55-58 It is well established that the electronic structure of Cun, as reflected in photoelectron spectra,59,60 IP,39 and stability,61 is well described by the jellium model with the 4s electrons in delocalized orbitals. The adsorption of an O2 molecule onto a Cu cluster involves interactions between the antibonding O2 2π* orbitals and the highest occupied molecular orbital (HOMO) of Cun. As a part of the adsorption process, electrons are transferred to the O2 2π* orbital, weakening the O-O bond.

12232 J. Phys. Chem., Vol. 100, No. 30, 1996 This has been analyzed theoretically by Gro¨nbeck et al.62,63 using two different approaches. Chemisorption properties, such as binding energy, charge transfer, and bond distance, were calculated with the MO-LCAO method for small clusters, Cu7Cu10,62 with atomic arrangements based on the minimum energy structure for Cu9 and Cu10.64 The corresponding analysis has also been made for n ) 7-9, 19-21, and 39-41 for O2 adsorbed onto Cun modeled as jellium spheres.63 For Cu7-9 there is good qualitative agreement between the MO-LCAO and jellium approaches, and therefore it seems reasonable to, at least on a qualitative level, rely on the jellium calculations also for larger sizes. The theoretical analysis clearly showed a much stronger interaction between the open shell Cun and O2, with a large hybridization between jellium orbitals and the O2 2π* orbitals, than between the closed shell or almost closed shell Cun and O2. The calculated chemisorption energy and charge transfer were also larger for the open shell clusters. In the final bonding of O atoms to Cun, localized bonds are expected to play a role, whereas the initial part of the adsorption process is thought to be dominated by interactions with the delocalized 4s orbitals. The relative inertness toward O2 for closed-shell Cun has previously been observed by Winter et al.65 up to the shell closing at Cu92, while Lee and Ervin66 rather observed an evenodd variation for Cun anions (n ) 5, 7-11). Electronic shell effects in the O2 reactivity have also been measured for Aln+/- 42,67 and Nan.68 The reaction probability for the most reactive clusters is 0.20.25, a value that is close to the sticking probability, S ≈ 0.2, on the most open, low-index single-crystal surface, the (110) surface.69 On the (111) and (100) surfaces the sticking probability is around 0.01 or lower.70 On the bulk surfaces the adsorption occurs via precursor states, and there are barriers along the reaction path.69,70 The height of these barriers is moderate, 0.02-0.04 eV, in comparison with the impact energy in the cluster O2 collisions in our experiment, ∼0.3 and ∼0.08 eV, for source temperatures of 300 and 80 K, respectively. It is therefore difficult to predict whether the adsorption onto the clusters is direct or proceeds via a precursor state. The reaction probabilities measured at the two source temperatures were almost identical regarding both absolute reactivity and the size variations. We note that also Lee and Ervin66 measured a reaction efficiency of the same magnitude (0.08-0.19), although a direct comparison is difficult since the size range, charge state, and reaction probability definition are all different in the two investigations. Also for the Cun-O2 system, fragmentation could occur as a result of the reaction. Although the chemisorption energy of O2 is lower on bulk Cu than on Fe and Co, the cohesive energy is also lower. We believe, however, that there is no substantial fragmentation for Cu20 and larger clusters. If there were extensive fragmentation, the distinct variations in reactivity with cluster size would diminish or disappear, since products would appear as clusters with one or a few Cu atoms less than the parent cluster. If the fragmentation was size selective, we would have measured discontinuities in the deflection vs size curve. The fluctuations in deflection probability that we observe are much smaller than the variations in the reactivity and are most likely due to statistical variations. If, however, some fragmentation still occurs, the difference in reactivity between the most and least reactive clusters would be larger than shown by the values derived from this experiment. Con + D2. The Con-D2 reaction, Figure 10, also displays a characteristic size dependence, with an enhanced reaction probability for Co11-13 and Co15-17 and minima at Co14 and Co20. This size dependence corresponds well with the observa-

Andersson et al. tions in fast-flow reactor experiments by Morse, Geusic et al.,5,6 and Ho et al.71,72 The absolute reaction probability appears to be somewhat lower than reported by Ho et al. but is within the estimated errors. The origin for the distinct size variations is, however, not clear. The D2 reactivity of clusters of several transition metals, e.g. Fen and Nbn, has been found to correlate, or rather anticorrelate, with variations in the IP,3,7,73 and comparisons have also been made with the difference between IP and electron affinity (EA).74 For Con the maxima and minima in the D2 reaction probability do not correlate well with the extrema in the IP38 or IP-EA difference.74 Theoretical investigations by Panas et al.75 for smaller Con (n ) 6-9) indicate that the orbital character (dn+1s vs dns2 states) is important for the ability to dissociate hydrogen and that the variations in IP are a secondary effect. The geometric structure of the Con has been investigated by Klots and Parks et al. using reactivity probes.76,77 They found indications for large clusters n > 50 having an icosahedral packing, but the structures for smaller sizes are less well determined. Some sizes around Co19 are thought to have fcc packing77 and Co14 to have a twinned tetrahedron structure,71 different from neighboring sizes. The binding energy for Co14, measured by CID,46 showed a distinct minimum, also indicating that Co14 has different bonding properties. The overall reaction probability is much lower for D2 than for O2, indicating that the D2 adsorption is more complex and limited by steric effects or barriers for adsorption or dissociation. For bulk Co surfaces both low and high sticking probabilities have been reported: 0.045 for the (0001) surface78 and close to 1.0 on a polycrystalline film at 77 K.79 The D2 chemisorption is exothermic by ∼1 eV80 on the bulk surface. This energy is lower than for O2 adsorption and also lower than the Co atom binding energy. Therefore fragmentation is not thought to occur as the result of adsorption of one D2 molecule. This is strongly supported by the observation that the decrease in total intensity of Con + ConD2 as a function of reaction cell pressure had a smooth size dependence. This shows that the high reactivity of, for example, Co13 and Co15 is not associated with fragmentation and that the low reactivity measured for Co14 is not a result of an inability to detect the products caused by fragmentation or less efficient ionization. ConD4 products are only detected for n > 20. This might be an effect of the exothermicity of the reaction. The adsorption of one molecule increases the internal energy by ∼1 eV, an energy that apparently is not sufficient to fragment the cluster. If multiple molecules are adsorbed, the excess energy could be sufficient to fragment the cluster up to a certain size, in analogy with the Con-O2 reaction discussed above. As the chemisorption energy of D2 is significantly lower than the atom-binding energy, the desorption of a D2 molecule is a much more probable decay path. A third possibility why ConD4 products are not observed for the smaller clusters is that the second D2 molecule has a much lower reaction probability with a cluster heated by the reaction. At present we have neither experimental nor theoretical support to point out one of the mechanisms as the correct one. For larger Con, n > 30, the reaction probability for the second molecule appears to be higher than for the first one. This effect was also observed by Morse et al.6 At this stage we can only speculate the reason for this. The enhanced reactivity for the second molecule can be an effect of a positive temperature dependence; that is, the reactivity increases with temperature. In this case the chemisorption of the first molecule heats the cluster to a “temperature” at which the reactivity is higher. The internal energy or temperature of the clusters can, however, be difficult to estimate since the measurements are, especially for

Reactivity of Fen, Con, and Cun Clusters with O2 and D2 D2 reactions, performed at pressures that lead to multiple collisions, typically up to 10, and as can be seen from the reaction probabilities, most of them are not reactive. Thus, these collisions can serve as cooling buffer gas collisions in this specific case. Another possibility for observing S2 > S1 is that the ConD2 clusters can have an electronic structure that is more efficient in dissociating additional D2 molecules. If the cluster source is cooled to liquid nitrogen temperature, the reaction probability increases significantly for all clusters. The cooling of the source induces two effects that can influence the reactivity: the internal energy of the clusters is decreased, and the beam velocity is reduced. In the Con-D2 reactions there is an increase in reactivity for all cluster sizes (Co12 and Co20 still within the error bars), approximately by a factor of 2-2.5. The largest relative increase is measured for Co14, which became almost 4 times more reactive. A lower internal temperature could increase the reaction probability by increasing the lifetime of the final product or some intermediate reaction complex (precursor). This effect would probably be rather size selective and have larger influence on weakly bound systems. A reduction of the beam velocity increases the number of collisions the clusters make, due to the finite velocity of the reactive molecules, as discussed in section 3.1. With the combination liquid nitrogen cooled source and D2 as reactive gas, the beam velocity and the average two-dimensional velocity of the molecules are comparable, and the reduced beam velocity upon cooling is estimated to increase the number of hard-sphere collisions by up to 50%. The reduced velocity also makes the interaction time in a collision longer, which increases the trapping probability, especially by weak attractive interactions, as in collisions with large impact parameters. If on the other hand repulsive interactions are forming barriers, a lower impact energy would lower the probability to overcome the barrier. Since the increase in reactivity upon cooling is rather uniform, we conclude that the velocity effects, increased number of collisions and increased trapping probability, dominate. The temperature dependence (T ) 133-373 K) of the Con-D2, n ) 9-21, reaction has been investigated by Ho et al.71 They found that the most reactive clusters Co10-13 and Co15-17 had an almost temperature-independent reactivity, while the reactivity of Co20 increased at low temperatures and the reactivity of Co14 increased both at low and high temperatures. Thus, there might be some additional reaction channel that provides an additional increase in the reactivity in our experiment. Fen + D2. The Fen-D2 reaction is one of the most wellinvestigated cluster-molecule reactions, and the reaction was found to be very size selective, with the reaction rate varying almost 4 orders of magnitude for clusters with less than 25 atoms.6-8 In our experiment we cannot measure the reactivity of low-reactive systems. For Fen-D2 we estimate the detection limit to be around 0.02. The smallest cluster for which we safely can detect a reaction product is Fe23, and from this size on we measure a rather uniform reaction probability of approximately 0.05. This is consistent with the previous investigations showing that the large variations ceased for n > 20, and a relatively high reactivity, estimated to be ∼0.03,8 was reached for n g 23. Cun + D2. We did not detect any D2 products on Cun. In this case the detection limit is higher, ∼0.05, because of the Cu isotope distribution. This is not an unexpected result since the hydrogen adsorption on Cu surfaces is a demanding reaction with a very low sticking probability under normal conditions.81 Although the kinetic energy in our experiment (∼0.04 eV) is somewhat higher than at normal room temperature conditions, it is still much lower than the adsorption barrier of ∼0.5 eV for

J. Phys. Chem., Vol. 100, No. 30, 1996 12233 H2 on bulk surfaces.81 In other investigations6 copper clusters were also found to be unreactive toward D2. 6. Conclusions We have demonstrated that cluster reactions under singlecollision-like conditions, as studied in the experiment presented here, can yield data on absolute reaction probabilities with reasonable accuracy. The method is best suited for highly reactive systems, as the detection limit corresponds to a reaction probability of 0.01-0.05. Reactions that proceed with a high probability, such as the oxidation of metal clusters, are often highly exothermic. The large amount of excess energy can cause fragmentation, which is difficult to safely detect in an experiment on clusters with a broad size distribution. We believe, however, that we can measure the average O2 reaction probability for large clusters (n > 20) with good accuracy and that we can attribute the apparently lower reactivity of the smaller clusters to fragmentation of products. Also, reactions with deuterium have been performed successfully, and the results are in good agreement with results obtained in other experimental configurations. As we study the successive addition of molecules, the reaction probabilities for each step can be determined, and by varying the temperature of the cluster source, the trends in the temperature dependence of the reactivity can be investigated. The method presented here is in some respects a new approach to study the reactivity of neutral clusters. Thus, it represents a useful complement to the existing methods, and by combining data from the different techniques, we can get a more complete description of cluster reactivity. The results presented here show that there is a distinct difference in the O2 reactivity between clusters of the transition metals Fe and Co with unfilled d shells and the coinage metal Cu. The reactivity of the copper clusters is dominated by the delocalized 4s electrons, and the variations in O2 reactivity are related to the cluster electronic shell structure as described by the jellium model. The oxidation of Fe and Co clusters appear to be best characterized as a direct reaction with a high reaction probability in a collision and exothermic, possibly inducing fragmentation of the cluster. Also the reactivity toward D2 displays the difference between Cu and the transitions metals, where Cun is much less reactive than the transition metal clusters. The reaction probability for D2 on Fen is, even for the most reactive clusters, close to the detection limit of our experiment and could not be investigated in detail, whereas the Con-D2 reaction probabilities could be determined with good accuracy. Acknowledgment. The authors want to thank Henrik Fallgren, Leif Johansson, and Jan-A° ke Wiman for their contributions to the design and construction of the equipment; Martin Ja¨gersand and Kin Lui Wong for assistance with the development of numerical data evaluation procedures; and Henrik Gro¨nbeck and Lotta Holmgren for stimulating discussions. Financial support from the Swedish Council for Planning and Coordination of Research (FRN), Knut and Alice Wallenberg’s Foundation, Carl Trygger’s Foundation, the NUTEK/NFR Materials Research Consortium “Clusters and Ultrafine Particles”, and the Swedish Research Council for Engineering Sciences (TFR) is gratefully acknowledged. References and Notes (1) (a) Dietz, T. G.; Duncan, M. A.; Powers, D. E.; Smalley, R. E. J. Chem. Phys. 1981, 74, 6511. (b) Smalley, R. E. Laser Chem. 1983, 2, 167. (2) Bondybey, V. E.; English, J. H. J. Chem. Phys. 1982, 76, 2165. (3) Kaldor, A.; Cox, D. M.; Zakin, M. R. AdV. Chem. Phys. 1988, 70, 211.

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Reactivity of Fe n, Co n, and Cu n Clusters with O2 and D2 Studied at

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