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Ion K+N time-of-flight angular distributions for K beam scattering and cluster formation at graphite surfaces
Surface Science 425 (1999) 81–89
Ion K+ time-of-flight angular distributions for K beam N scattering and cluster formation at graphite surfaces J. Wang, L. Holmlid * Reaction Dynamics Group, Department of Chemistry, University of Go¨teborg, SE-412 96 Go¨teborg, Sweden Received 22 August 1998; accepted for publication 14 January 1999
Abstract Angular resolved ion time-of-flight distributions are reported for the K–graphite (0001) system over the range −90° to +90° relative to the surface normal. A low intensity K thermal atom beam strikes the graphite surface at 900 K at −45°. Ions and field ionisable Rydberg states which desorb or scatter from the surface are detected. The size distribution of clusters K* has its maximum at N=4, while N>6 is unlikely. A complex formation collision N process K+K* K* at the surface is now identified from the skewed angular distributions and the dip at ca 6°. N N+1 Such a process has not previously been identified at a graphite surface, where the rapid diffusion into the bulk keeps the surface density low. A scattering process due to collisions K++K* within the desorbing flux is observed, as symmetrically placed tails with lower velocity at increasing angle towards the normal. Both collision processes are estimated to have cross-sections in the order of 106 nm2, which is so large that resonant transfer involving Rydberg species is likely to be involved in the scattering. These collision processes take place close to the surface where the density is higher. © 1999 Elsevier Science B.V. All rights reserved. Keywords: K beam scattering; Ion time-of-flight angular distributions
1. Introduction Recently, the first time-of-flight ( TOF ) mass spectrometry based study of the K clusters formed N at a graphite surface was reported from our group [1]. This was a further step in a series of studies from our group on the formation of Rydberg species and their reaction processes at surfaces. Earlier steps include the observation of excited clusters by field ionization detectors [2] and angular distributions [3]. The scattering due to such clusters was studied in Ref. [4]. Recently, a complex formation scattering process was detected in * Corresponding author. Fax: +46-31 7723107; e-mail: [email protected].
the collisions between a K atom beam and the K cluster flux from a zirconia surface [5]. Other N studies of alkali Rydberg species at surfaces have appeared recently, like the angular distribution study at graphite (0001) in Ref. [6 ], the bulk diffusion study on the same surface in Ref. [7] and the nanosecond desorption study on graphite films in Ref. [8]. Now, more detailed results with TOF mass spectrometry are presented in the form of angular resolved TOF distributions over the full angular range. The research concerned with Rydberg clusters and Rydberg states [9,10] in clusters is diversifying and increasing in importance at present. There are several reasons for this, of which the most important may be the higher reactivity expected for the
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Rydberg clusters relative to the ground state clusters. One important aspect related to surface studies in the Rydberg cluster field is the possibility of high catalytic activity of such clusters. Fundamental studies of Rydberg clusters use modern highly resolved spectroscopic techniques like ZEKE (zero kinetic energy photoelectron spectroscopy), for example in the study of benzene–Ne Rydberg clusters [11], which gives information about structures and energy levels. Spectroscopic studies of Rydberg molecules in clusters give information on the dynamics and the interactions in van der Waals clusters [12]. The importance of Rydberg states of alkali–metal clusters is demonstrated in collision processes involving clusters [13]. Excited states of alkali clusters are studied by laser spectroscopy [14], and the structure and energetics of small alkali clusters are studied theoretically [15]. The interaction of clusters with surfaces is studied to understand adsorption, fragmentation and ion formation processes. An example is the study of collisions and fragmentation of Al clusters on a Si surface in Ref. [16 ]. The fragmentation of water clusters in collisions with a graphite surface gave information on the dynamics of the impact process in Ref. [17]. Just a few studies related to formation of Rydberg clusters and Rydberg states in clusters at surfaces have been published. The general promoter function of alkali in catalysts seems to be related to Rydberg states and Rydberg clusters [18,19], and design of the cluster properties may give entirely new possibilities to increase and modify the promoter effects. Further, the Rydberg cluster studies are closely related to the formation of so called Rydberg Matter (a condensed phase of Rydberg states). Clusters of this type have recently been observed by laser fragmentation and mass spectrometry [20] after formation outside a graphite surface by laser excitation. Rydberg Matter clusters of hydrogen and nitrogen have also been formed outside catalyst surfaces [19]. The graphite surface is of great interest from many points of view. The use of such surfaces to form Rydberg species is of course not the typical application for this material. Instead, the possibilities to form thin surface layers of carbon, diamondlike carbon and carbon nitride are the reasons why graphite is getting so much attention in surface
science and thin film science. In a recent paper [21] TOF mass spectrometry after laser ablation was used on a graphite surface to study the carbon clusters emitted.
2. Theory The formation of Rydberg states of desorbing K atoms from graphite surfaces has been reported in several publications [6–8,22]. Recent kinetic results [22] show that the ground state of the K atom outside the surface does not correlate with any bound state of K on the surface. Instead, the ionization of a K 4s atom approaching from a distance is rapid, and the state reached on the surface is designated K+. This state may then s easily be transformed into covalently bound states at suitable free sites on the surface. The covalent states correlate with electronically excited states outside the surface, namely the K 4p and K 3d states. The desorption from the covalent states cross the highly excited, Rydberg-like states K*, which have their potential minima at a large distance from the surface. A transfer of the desorbing atoms to the Rydberg-like states is then probable [22]. The lifetimes of free Rydberg states are rather long. The radiative lifetimes for Rydberg atoms increase with principal quantum number n, as n3 for low l quantum numbers, and as n5 for large l quantum numbers (l is the angular momentum quantum number) [9]. For an ordinary free Rydberg atom in a circular high-l state, the radiative lifetime varies with the principal quantum number n as n5, which means a lifetime of at least 1 ms for n=40 and 100 ms for n=100 [9,10]. The radiative lifetime averaged over the angular quantum momentum numbers is given by Ref. [23] to be 0.18 s for n=40 and 17 s for n=100. In Refs. [5,6,22,24], the consequences of the long-range force between a Rydberg atom and a surface were discussed. The diffusion over the surface may take the form of very long jumps due to this long-range force. The long-range interaction also means that the excited K atoms are efficiently retained in a layer outside the surface, a surface sheath similar to a Knudsen layer. One important process taking place in this layer is the formation
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of clusters by condensation of the excited K* species. The condensation means that each K* atom decreases its interaction with the surface since the Rydberg electrons are no longer in contact with the surface but instead form the bonds in the cluster. Emission of clusters from various surfaces have been reported in Refs. [2,4,5,24]. The emission of clusters is often observed as a peak in the normal direction in the angular distribution. Using field ionization detection, such a peak due to formation of excited potassium clusters was found for a potassium impregnated iron surface [4], which indicates that the clusters are in Rydberg-like states. A distribution of clusters which peaks in the normal direction requires that many atoms combine to form clusters just outside the surface in the surface sheath, that is, they combine their velocities to a common cluster velocity. The angular distribution of the cluster velocity vectors depends on the size of the cluster, which means the larger the cluster size, the more peaked the distribution becomes. A simple theoretical model which describes the cluster formation was presented by Kotarba et al. [3]. When an atom from the K atom beam approaches the surface at an angle −45° and with a velocity n , it may collide with an atom K* or a A cluster K* moving out from the surface with a N velocity n in the surface sheath. The complex C formation process has the form K+K*K* . (1) N N+1 A complex cluster of this form may be long-lived enough to reach the detector as an excited cluster, or it may de-excite by emitting radiation. The relative velocity between the two colliding particles is divided as a fraction 1/(N+1) for the cluster, and N/(N+1) for the atom. The tangent of the angle h against the normal for their common center of mass on its motion out from the surface can be derived easily as [5]: 1
. (2) n앀2(n /n )−1 C A The angle thus depends on the velocity ratio n /n , which is close to unity in the present case. C A If this ratio is assumed to be 0.95, the average
tg h=
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value found for a zirconia surface in Ref. [5], the angles are 71° (1+1 scattering, thus forming a dimer K ), 31° (1+2), 18° (1+3), 13° (1+4), 10° 2 (1+5), 8.1° (1+6), 6.8° (1+7) and 5.9° (1+8). In the case of cluster formation by collision of two ground state species, the complex may only stick together for a very short time in the order of picoseconds. This is so, since the time required for removal of the excess energy by emission in the infrared range is so long that no such deexcitation can take place before the particles separate again. In the case of one colliding partner in a Rydberg state as shown in Eq. (1), the direct interaction for the K atom is with the core ion K+. This is N likely to give a longer interaction time, since the long-range force is larger in this case. The motion of the K atom around and together with the core ion K+ inside the Rydberg orbit may couple to N the Rydberg electron, and thus remove energy from the internal motion in the core cluster K+ . There also exist processes which will remove N+1 the energy from the cluster, namely radiative deexcitation via the Rydberg electron and long-range energy transfer collision, also via the Rydberg electron. It is thus likely that such energy transfer processes can stabilize an electronically excited collision complex, as formed in Eq. (1), much faster than it would stabilize a ground state collision complex [5].
3. Experimental The experiments are carried out in an ultrahigh vacuum ( UHV ) apparatus with a base pressure of 1×10−8 mbar. It has been fully described previously [4,6 ] and a view of the present configuration is shown in Fig. 1. The K beam is a thermal beam from a two-chamber source, with the reservoir at ca 525 K and the front of the source 50– 100 K hotter. A beam flag in front of the source or a valve between the source chamber and the sample chamber are used to turn off the beam. The source chamber is separately pumped, with one further intermediate differential stage to decrease the gas load to the UHV sample chamber. The pyrolytic graphite surface studied was cut from a crystal (Grade ZYB, Advanced Ceramics
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Fig. 1. View of the apparatus. The sample is placed in the center of the UHV chamber. The potassium beam from the source can be interrupted by the valve between the chambers or by a beam flag in front of the source. No grids are used, to avoid ionization of the Rydberg species. The shield surrounding the sample (dashed circle) consists of one cylinder above and one below the plane of the figure, with a 5 mm slit in-between.
Corp.) as a rod with thickness 0.8 mm, a width of 3.3 mm, and a length of 30 mm. It was placed in the center of the chamber in the vertical direction and clamped at the ends by Ta foils, exposing a length of 16 mm centered around the horizontal plane in which the detector is moving. The sample was heated to 990 K by passing an AC current of ca 25 A through it, and its temperature was measured with an optical pyrometer. The K beam reached the surface at an angle of −45° relative to the normal of the exposed basal surface. In the TOF experiments, the sample is connected to an electronic circuit which switches between −15 and +10 V with rise and fall times of 100 ns. Steady-state experiments with the sample connected to +10 V are also described here. The circuit for this employs optically isolated switching of MOSFET transistors, Hewlett–Packard HPWR-6503 (N-channel ) and Motorola MTP2P50 (P-channel, two in parallel ). The ion extracting pulse length at +10 V is 17 ms, with a repetition period of 600 ms. The particles from the sample move close to the beam plane (in the plane in Fig. 1) to the detector over a length of 115 mm. The detector, a dynode–scintillator–photomultiplier combination can be rotated 360° around the sample to measure angular distributions. A grounded shield in the form of two vertical collinear metal cylinders, one above and one below the beam plane, is mounted around the sample at a sample-to-shield distance of 75 mm to improve the
shape of the electric field. ( The location of this shield is shown as a dashed circle in Fig. 1.) The slit between the two cylinders is 5 mm in the vertical direction, allowing access of the beam and emission of the flux to the detector. The detector, with a 3 mm circular opening, contains a small Cu–Be dynode held at −9.5 kV, and a grounded scintillator (NE 102A) with 50 nm Al coating on one side [25]. The ions which enter the detector, or which are formed from electronically excited species inside the detector in the strong field around the dynode, are accelerated towards the dynode. The secondary electrons from the ion impact on the dynode are accelerated towards the scintillator. The light pulses from the scintillator are observed by a photo multiplier, amplified with linear amplifiers, put through a discriminator and fed into a multi-channel analyzer. Usually, 50,000 periods of the signal are averaged and output to a computer. The angle of the detector is defined to be zero in the direction of the surface normal, and increasingly positive with the specular direction at 45°. On the other side of the normal, the angles are negative, with the impinging beam at −45°. The impinging beam flux density is in the order of 2×10−8 A cm−2 or 3×1011 atoms cm−2 s−1 at the sample. The average thermal velocity is close to 500 m s−1, which gives a gas phase density of 6×1012 m−3 (5×10−10 mbar) outside the surface. The surface density can be calculated from the flux density and the desorption rate constant. The
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rate constant has been measured in Refs. [22,26 ] to be of the order of 1 s−1 for the neutral desorption with retarding field (between the TOF pulses), and 100 s−1 for accelerating field. This gives a surface coverage <10−4 of a monolayer of K on the graphite surface, making any condensation by ground state atoms to clusters at this temperature highly unlikely.
4. Results and discussion 4.1. Background The results obtained for ion TOF distributions are plotted as a function of angle in the figures. One example of a full angular TOF distribution is shown in Fig. 2, with another view in Fig. 3. These data are related to the angular distribution in Fig. 4, which is measured in the same experiment with the same detector, and with a constant accelerating field on the graphite sample. As in the other experiments presented, the incoming beam
Fig. 3. The same distributions as in Fig. 2 but from another angle of the three-dimensional plot.
Fig. 4. Angular distributions measured with the dynode detector with no TOF switching of the sample voltage at +10 V, from the same experiment as Figs. 2 and 3. Compare the form of the distribution with Fig. 3. The arrow indicates the direction of the K beam. Fig. 2. The TOF distributions at the dynode detector placed at the angles indicated relative to the normal of the graphite (0001) sample surface. The high voltage on the sample was +10 V with 17 ms extraction time, and the low voltage was −15.7 V. The sample temperature was 990 K. In the marked range, the detector blocks the incoming K beam. The basal surface in the plot is at the zero signal.
direction is at −45°. This means that the detector used will block the molecular beam in a region around this direction, which is observed in the figures.
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The previous results in Ref. [1] provide the basic understanding of the TOF data. The flux of K from the hot sample contains large amounts of K* Rydberg species, which is clearly demonstrated in several publications [6–8,22]. The emitted Rydberg species interact strongly by dispersion forces, and form a thin boundary layer just in front of the surface. Outside this layer, the gas expands and the number of collisions decreases. In the measurements in Ref. [1] and the present study, three types of ion mass peaks are observed with different flight times, corresponding to monomer, dimer and quadrumer K+ ions. The signal N was in Ref. [1] compared with the result from a trajectory calculation which assumed that a constant flux of ions K+, K+ and K+ leaves the 2 4 sample during the 17 ms long ion extraction pulse with a positive voltage on the sample. The agreement of the peak positions with the calculation was good, and also the tails of the distributions were reproduced well. The TOF distribution in Figs. 2 and 3 agrees well with the angular distribution in Fig. 4. The dip at 6°, which will be discussed further later, is visible in both sets of data, and the signal at very large angles, at 70–90°, is also found in both sets. The intensity at large angles seems to be somewhat larger in the TOF measurements than in the angular data. However, the main shape of the angular distributions is retained also in the TOF data. The sharp rise of the signal at 16 ms is due to the K+ ions which leave the sample at the switch-over from negative to positive sample voltage. Calculations show that the dimer K+ should arrive 2 at the detector with its peak at 30 ms, and K+ at 4 45 ms. Both these cluster sizes form the flat-topped peaks in the center of Figs. 2 and 3, with their tails disappearing at 60 ms. 4.2. Cluster formation scattering The angular distribution in Fig. 4 is not symmetric around the surface normal. Instead, it is tilted towards positive angles. Such a change in the angular distribution is expected if the flux has taken part in scattering processes, since the incoming beam will transfer its momentum along the surface to the flux leaving the surface. As can be
seen from the distributions in Ref. [6 ], this kind of tilted distribution is normally not observed when the entire flux is measured at higher surface temperatures. However, in cases where only the excited, or ionized species are detected, like in the case with scattering from a zirconia surface in Ref. [5], the skewed form of the distribution is the rule. The same kind of distribution is also found for total scattering if the graphite sample is held at a negative voltage, like in Ref. [7]. This means that a large fraction of the flux from the surface collides with the atoms in the beam, so that they are deflected towards positive angles. It is obvious that this requires very large cross-sections for the interactions, which directly indicates that Rydberg states exist in the flux from the surface. A conservative estimate of the collision cross-sections between Rydberg species from the surface and K atoms from the beam indicates 106 nm2, or an effective diameter of 1 mm. Very large cross-sections are expected for resonant processes involving Rydberg ˚ 2 (104–105 nm2). species [27,28], up to 106–107 A A dip close to 6° is often found in the angular distributions of desorbing K+ ions with a K beam impinging on a graphite surface. Such a dip can be expected as the result of scattering of the beam atoms from the small electronically excited clusters which are formed at the surface. As shown also in the case of K beam scattering off a zirconia surface [5], the complex formation between a K atom from the beam and a small cluster K from the N surface can give a cluster K . The cluster will N+1 normally be in an electronically excited state, which means that it will be detected by the dynode detector. According to Eq. (2), clusters with N+1=7 and 8 are expected to be observed at 6°. The dip close to 6° observed here indicates that clusters with sizes N+1=7 and larger are not formed with any large probability. In Fig. 2 it is easily seen that the tail in the distribution is longer at smaller positive angles, close to the normal direction at angles <18°, outside which another process starts (see below). This indicates that larger, slower clusters are formed by collisions at these angles. Thus, the observations of angular distributions which are slightly tilted towards positive angles must indicate a scattering process, and a dip in the distribution at a small positive angle
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indicates a complex scattering process of the form described here. The process in Eq. (1) is often difficult to distinguish from a direct ionization process like the associative ionization K+K*K+ +e−. N N+1 This type of bound-free transition may be less likely than the complex formation process in Eq. (1), but we have no possibility to distinguish between the two processes in the present experiments. In the experiments with a zirconia surface [5], however, the neutral excited clusters in Eq. (1) were observed. A direct ion formation was also observed, but only in backwards scattering. Thus, it is likely that in the present case the skewed scattering distributions are due to collision complex formation as in Eq. (1), followed by field ionization of the clusters. 4.3. Inelastic scattering in the desorbing flux In Fig. 2, another feature in the TOF angular distribution is clearly visible, namely a tail at positive angles outside 18° which moves towards longer TOF times at larger angles. A similar tail extends also to negative angles as can be seen in Fig. 3, but it is not so easily observed due to the detector blocking the beam at these angles. This feature varies continuously with the angle, and it is thus unlikely that it is due to the formation of heavier clusters at larger angles. Instead, it is likely due to scattering of ions moving out from the surface in the desorbing plume, giving slower ions at larger angles. This effect could be caused by the same processes which decrease the kinetic energy of the ions reaching the collector, demonstrated in Ref. [6 ]. There, it was proposed that the low kinetic energy of the ions was due to charge exchange processes during the expansion of the desorbing flux from the sample. Such processes will exist when the K+ ions are accelerated in the field. The ions will then overtake and collide with the slower K* atoms in the flux. Among these collisions, the ones with large impact parameters may preferentially give charge exchange, by collisions with the Rydberg electron, while small impact parameters should give rise to core ion collisions and thus substantial energy loss and angular deflection, observed as the tails in Figs. 2
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and 3. A larger deflection angle will give a smaller translation energy, as observed. The cross-sections for this process will be of approximately the same order of magnitude as the cluster formation collisions discussed above, which indicates resonant Rydberg state collisions. That scattering in the residual gases outside the surface should give the observed scattering behavior is unlikely. A typical cross-section for ionmolecule collisions is 1 nm2. This means that a pressure of at least 10−6 mbar would be needed to produce a scattering similar to what is observed, that is a much higher pressure than the one existing in the apparatus. 4.4. Surface processes The peaks at large negative angles are not very well resolved in Figs. 2 and 3. In Fig. 5, the data from another run display the details in that range much better. One new feature is then observed, namely a ridge in the signal moving towards longer flight times with increasing angle. Note the arrow in Fig. 5. This is relatively small feature, not of the size of the scattering tails observed in Figs. 2 and 3, but otherwise showing the same interdependence between angle and velocity. Thus, we
Fig. 5. The TOF distributions in a case with slightly higher intensity peaks at large angles relative to the normal. Surface temperature is 990 K. Observe the ridge on the distribution in the angular range 80–90°, at the arrow. The basal surface in the plot is at the zero signal.
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propose also this signal variation with angle to be due to an inelastic scattering process in which the ions scatter at larger angles with lower velocities. Since the intensity at large angles from the normal is likely to mainly originate from the prism faces of the graphite sample or from the edge of the sample, it is not so easy to deduce the exact form of the particle involved in this scattering at present, but the identification of the process shows the strength of the full angular distribution measurements. The different distributions of the flux from the basal surface and from the prism surfaces are shown in Refs. [6,7]. The flux from the prism surfaces is only seen at angles outside ±60°, that is, in an angular range which is well separated from the flux from the basal surface. That the processes observed here are due to the rapid interactions between K atoms and ions brought to the surface by the K beam is readily shown, by turning off the beam with the beam flag. After 2 min, the signal intensity has dropped a factor of 5, and after 10 min, the signal has disappeared completely. Thus, the clusters leaving the surface are formed rapidly during the exposure to the beam, and they are not preformed in the bulk or on the surface. It could also be interesting to observe the angular distributions with lower surface densities, so that the cluster formation is decreased. However, it is not possible to measure the angular distribution rapidly enough after turning off the beam flux. Instead, low surface density results are found in Ref. [6 ] at higher sample temperatures. There, almost symmetric angular distributions around the surface normal are observed. Thus, the observation of skewed distributions due to cluster formation is related to high surface densities. It is the strong interaction between the K atoms in electronically excited states in contact with the surface which is the driving force in the condensation to the small clusters at graphite surfaces. This was first reported in Ref. [1].
5. Conclusions By using full angular resolved TOF distributions to study the interaction between K atoms and a
graphite surface, new results have been reached for this system, where the surface density of K is considerably smaller than for other surfaces studied by similar scattering methods due to the rapid diffusion into the graphite bulk. A complex formation scattering mechanism in the surface sheath is now identified at the graphite surface, which is due to the strong interaction between the electronically excited clusters K* and the K beam N atoms. The same mechanism is known to exist at metal oxide surfaces. The size distribution of clusters K* has its maximum at N=4, while N>6 is N unlikely. An inelastic scattering process in the desorbing flux is also observed between K+ ions and neutral K* Rydberg species which leave the surface. The sizes of the cross-sections estimated for both collision processes indicate resonant energy transfer.
Acknowledgement This study was supported by the Foundation for Strategic Research (SSF ) through the Swedish Natural Science Research Council (NFR).
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Ion K+ time-of-flight angular distributions for K beam N scattering and cluster formation at graphite surfaces J. Wang, L. Holmlid * Reaction Dynamics Group, Department of Chemistry, University of Go¨teborg, SE-412 96 Go¨teborg, Sweden Received 22 August 1998; accepted for publication 14 January 1999
Abstract Angular resolved ion time-of-flight distributions are reported for the K–graphite (0001) system over the range −90° to +90° relative to the surface normal. A low intensity K thermal atom beam strikes the graphite surface at 900 K at −45°. Ions and field ionisable Rydberg states which desorb or scatter from the surface are detected. The size distribution of clusters K* has its maximum at N=4, while N>6 is unlikely. A complex formation collision N process K+K* K* at the surface is now identified from the skewed angular distributions and the dip at ca 6°. N N+1 Such a process has not previously been identified at a graphite surface, where the rapid diffusion into the bulk keeps the surface density low. A scattering process due to collisions K++K* within the desorbing flux is observed, as symmetrically placed tails with lower velocity at increasing angle towards the normal. Both collision processes are estimated to have cross-sections in the order of 106 nm2, which is so large that resonant transfer involving Rydberg species is likely to be involved in the scattering. These collision processes take place close to the surface where the density is higher. © 1999 Elsevier Science B.V. All rights reserved. Keywords: K beam scattering; Ion time-of-flight angular distributions
1. Introduction Recently, the first time-of-flight ( TOF ) mass spectrometry based study of the K clusters formed N at a graphite surface was reported from our group [1]. This was a further step in a series of studies from our group on the formation of Rydberg species and their reaction processes at surfaces. Earlier steps include the observation of excited clusters by field ionization detectors [2] and angular distributions [3]. The scattering due to such clusters was studied in Ref. [4]. Recently, a complex formation scattering process was detected in * Corresponding author. Fax: +46-31 7723107; e-mail: [email protected].
the collisions between a K atom beam and the K cluster flux from a zirconia surface [5]. Other N studies of alkali Rydberg species at surfaces have appeared recently, like the angular distribution study at graphite (0001) in Ref. [6 ], the bulk diffusion study on the same surface in Ref. [7] and the nanosecond desorption study on graphite films in Ref. [8]. Now, more detailed results with TOF mass spectrometry are presented in the form of angular resolved TOF distributions over the full angular range. The research concerned with Rydberg clusters and Rydberg states [9,10] in clusters is diversifying and increasing in importance at present. There are several reasons for this, of which the most important may be the higher reactivity expected for the
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Rydberg clusters relative to the ground state clusters. One important aspect related to surface studies in the Rydberg cluster field is the possibility of high catalytic activity of such clusters. Fundamental studies of Rydberg clusters use modern highly resolved spectroscopic techniques like ZEKE (zero kinetic energy photoelectron spectroscopy), for example in the study of benzene–Ne Rydberg clusters [11], which gives information about structures and energy levels. Spectroscopic studies of Rydberg molecules in clusters give information on the dynamics and the interactions in van der Waals clusters [12]. The importance of Rydberg states of alkali–metal clusters is demonstrated in collision processes involving clusters [13]. Excited states of alkali clusters are studied by laser spectroscopy [14], and the structure and energetics of small alkali clusters are studied theoretically [15]. The interaction of clusters with surfaces is studied to understand adsorption, fragmentation and ion formation processes. An example is the study of collisions and fragmentation of Al clusters on a Si surface in Ref. [16 ]. The fragmentation of water clusters in collisions with a graphite surface gave information on the dynamics of the impact process in Ref. [17]. Just a few studies related to formation of Rydberg clusters and Rydberg states in clusters at surfaces have been published. The general promoter function of alkali in catalysts seems to be related to Rydberg states and Rydberg clusters [18,19], and design of the cluster properties may give entirely new possibilities to increase and modify the promoter effects. Further, the Rydberg cluster studies are closely related to the formation of so called Rydberg Matter (a condensed phase of Rydberg states). Clusters of this type have recently been observed by laser fragmentation and mass spectrometry [20] after formation outside a graphite surface by laser excitation. Rydberg Matter clusters of hydrogen and nitrogen have also been formed outside catalyst surfaces [19]. The graphite surface is of great interest from many points of view. The use of such surfaces to form Rydberg species is of course not the typical application for this material. Instead, the possibilities to form thin surface layers of carbon, diamondlike carbon and carbon nitride are the reasons why graphite is getting so much attention in surface
science and thin film science. In a recent paper [21] TOF mass spectrometry after laser ablation was used on a graphite surface to study the carbon clusters emitted.
2. Theory The formation of Rydberg states of desorbing K atoms from graphite surfaces has been reported in several publications [6–8,22]. Recent kinetic results [22] show that the ground state of the K atom outside the surface does not correlate with any bound state of K on the surface. Instead, the ionization of a K 4s atom approaching from a distance is rapid, and the state reached on the surface is designated K+. This state may then s easily be transformed into covalently bound states at suitable free sites on the surface. The covalent states correlate with electronically excited states outside the surface, namely the K 4p and K 3d states. The desorption from the covalent states cross the highly excited, Rydberg-like states K*, which have their potential minima at a large distance from the surface. A transfer of the desorbing atoms to the Rydberg-like states is then probable [22]. The lifetimes of free Rydberg states are rather long. The radiative lifetimes for Rydberg atoms increase with principal quantum number n, as n3 for low l quantum numbers, and as n5 for large l quantum numbers (l is the angular momentum quantum number) [9]. For an ordinary free Rydberg atom in a circular high-l state, the radiative lifetime varies with the principal quantum number n as n5, which means a lifetime of at least 1 ms for n=40 and 100 ms for n=100 [9,10]. The radiative lifetime averaged over the angular quantum momentum numbers is given by Ref. [23] to be 0.18 s for n=40 and 17 s for n=100. In Refs. [5,6,22,24], the consequences of the long-range force between a Rydberg atom and a surface were discussed. The diffusion over the surface may take the form of very long jumps due to this long-range force. The long-range interaction also means that the excited K atoms are efficiently retained in a layer outside the surface, a surface sheath similar to a Knudsen layer. One important process taking place in this layer is the formation
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of clusters by condensation of the excited K* species. The condensation means that each K* atom decreases its interaction with the surface since the Rydberg electrons are no longer in contact with the surface but instead form the bonds in the cluster. Emission of clusters from various surfaces have been reported in Refs. [2,4,5,24]. The emission of clusters is often observed as a peak in the normal direction in the angular distribution. Using field ionization detection, such a peak due to formation of excited potassium clusters was found for a potassium impregnated iron surface [4], which indicates that the clusters are in Rydberg-like states. A distribution of clusters which peaks in the normal direction requires that many atoms combine to form clusters just outside the surface in the surface sheath, that is, they combine their velocities to a common cluster velocity. The angular distribution of the cluster velocity vectors depends on the size of the cluster, which means the larger the cluster size, the more peaked the distribution becomes. A simple theoretical model which describes the cluster formation was presented by Kotarba et al. [3]. When an atom from the K atom beam approaches the surface at an angle −45° and with a velocity n , it may collide with an atom K* or a A cluster K* moving out from the surface with a N velocity n in the surface sheath. The complex C formation process has the form K+K*K* . (1) N N+1 A complex cluster of this form may be long-lived enough to reach the detector as an excited cluster, or it may de-excite by emitting radiation. The relative velocity between the two colliding particles is divided as a fraction 1/(N+1) for the cluster, and N/(N+1) for the atom. The tangent of the angle h against the normal for their common center of mass on its motion out from the surface can be derived easily as [5]: 1
. (2) n앀2(n /n )−1 C A The angle thus depends on the velocity ratio n /n , which is close to unity in the present case. C A If this ratio is assumed to be 0.95, the average
tg h=
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value found for a zirconia surface in Ref. [5], the angles are 71° (1+1 scattering, thus forming a dimer K ), 31° (1+2), 18° (1+3), 13° (1+4), 10° 2 (1+5), 8.1° (1+6), 6.8° (1+7) and 5.9° (1+8). In the case of cluster formation by collision of two ground state species, the complex may only stick together for a very short time in the order of picoseconds. This is so, since the time required for removal of the excess energy by emission in the infrared range is so long that no such deexcitation can take place before the particles separate again. In the case of one colliding partner in a Rydberg state as shown in Eq. (1), the direct interaction for the K atom is with the core ion K+. This is N likely to give a longer interaction time, since the long-range force is larger in this case. The motion of the K atom around and together with the core ion K+ inside the Rydberg orbit may couple to N the Rydberg electron, and thus remove energy from the internal motion in the core cluster K+ . There also exist processes which will remove N+1 the energy from the cluster, namely radiative deexcitation via the Rydberg electron and long-range energy transfer collision, also via the Rydberg electron. It is thus likely that such energy transfer processes can stabilize an electronically excited collision complex, as formed in Eq. (1), much faster than it would stabilize a ground state collision complex [5].
3. Experimental The experiments are carried out in an ultrahigh vacuum ( UHV ) apparatus with a base pressure of 1×10−8 mbar. It has been fully described previously [4,6 ] and a view of the present configuration is shown in Fig. 1. The K beam is a thermal beam from a two-chamber source, with the reservoir at ca 525 K and the front of the source 50– 100 K hotter. A beam flag in front of the source or a valve between the source chamber and the sample chamber are used to turn off the beam. The source chamber is separately pumped, with one further intermediate differential stage to decrease the gas load to the UHV sample chamber. The pyrolytic graphite surface studied was cut from a crystal (Grade ZYB, Advanced Ceramics
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Fig. 1. View of the apparatus. The sample is placed in the center of the UHV chamber. The potassium beam from the source can be interrupted by the valve between the chambers or by a beam flag in front of the source. No grids are used, to avoid ionization of the Rydberg species. The shield surrounding the sample (dashed circle) consists of one cylinder above and one below the plane of the figure, with a 5 mm slit in-between.
Corp.) as a rod with thickness 0.8 mm, a width of 3.3 mm, and a length of 30 mm. It was placed in the center of the chamber in the vertical direction and clamped at the ends by Ta foils, exposing a length of 16 mm centered around the horizontal plane in which the detector is moving. The sample was heated to 990 K by passing an AC current of ca 25 A through it, and its temperature was measured with an optical pyrometer. The K beam reached the surface at an angle of −45° relative to the normal of the exposed basal surface. In the TOF experiments, the sample is connected to an electronic circuit which switches between −15 and +10 V with rise and fall times of 100 ns. Steady-state experiments with the sample connected to +10 V are also described here. The circuit for this employs optically isolated switching of MOSFET transistors, Hewlett–Packard HPWR-6503 (N-channel ) and Motorola MTP2P50 (P-channel, two in parallel ). The ion extracting pulse length at +10 V is 17 ms, with a repetition period of 600 ms. The particles from the sample move close to the beam plane (in the plane in Fig. 1) to the detector over a length of 115 mm. The detector, a dynode–scintillator–photomultiplier combination can be rotated 360° around the sample to measure angular distributions. A grounded shield in the form of two vertical collinear metal cylinders, one above and one below the beam plane, is mounted around the sample at a sample-to-shield distance of 75 mm to improve the
shape of the electric field. ( The location of this shield is shown as a dashed circle in Fig. 1.) The slit between the two cylinders is 5 mm in the vertical direction, allowing access of the beam and emission of the flux to the detector. The detector, with a 3 mm circular opening, contains a small Cu–Be dynode held at −9.5 kV, and a grounded scintillator (NE 102A) with 50 nm Al coating on one side [25]. The ions which enter the detector, or which are formed from electronically excited species inside the detector in the strong field around the dynode, are accelerated towards the dynode. The secondary electrons from the ion impact on the dynode are accelerated towards the scintillator. The light pulses from the scintillator are observed by a photo multiplier, amplified with linear amplifiers, put through a discriminator and fed into a multi-channel analyzer. Usually, 50,000 periods of the signal are averaged and output to a computer. The angle of the detector is defined to be zero in the direction of the surface normal, and increasingly positive with the specular direction at 45°. On the other side of the normal, the angles are negative, with the impinging beam at −45°. The impinging beam flux density is in the order of 2×10−8 A cm−2 or 3×1011 atoms cm−2 s−1 at the sample. The average thermal velocity is close to 500 m s−1, which gives a gas phase density of 6×1012 m−3 (5×10−10 mbar) outside the surface. The surface density can be calculated from the flux density and the desorption rate constant. The
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rate constant has been measured in Refs. [22,26 ] to be of the order of 1 s−1 for the neutral desorption with retarding field (between the TOF pulses), and 100 s−1 for accelerating field. This gives a surface coverage <10−4 of a monolayer of K on the graphite surface, making any condensation by ground state atoms to clusters at this temperature highly unlikely.
4. Results and discussion 4.1. Background The results obtained for ion TOF distributions are plotted as a function of angle in the figures. One example of a full angular TOF distribution is shown in Fig. 2, with another view in Fig. 3. These data are related to the angular distribution in Fig. 4, which is measured in the same experiment with the same detector, and with a constant accelerating field on the graphite sample. As in the other experiments presented, the incoming beam
Fig. 3. The same distributions as in Fig. 2 but from another angle of the three-dimensional plot.
Fig. 4. Angular distributions measured with the dynode detector with no TOF switching of the sample voltage at +10 V, from the same experiment as Figs. 2 and 3. Compare the form of the distribution with Fig. 3. The arrow indicates the direction of the K beam. Fig. 2. The TOF distributions at the dynode detector placed at the angles indicated relative to the normal of the graphite (0001) sample surface. The high voltage on the sample was +10 V with 17 ms extraction time, and the low voltage was −15.7 V. The sample temperature was 990 K. In the marked range, the detector blocks the incoming K beam. The basal surface in the plot is at the zero signal.
direction is at −45°. This means that the detector used will block the molecular beam in a region around this direction, which is observed in the figures.
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The previous results in Ref. [1] provide the basic understanding of the TOF data. The flux of K from the hot sample contains large amounts of K* Rydberg species, which is clearly demonstrated in several publications [6–8,22]. The emitted Rydberg species interact strongly by dispersion forces, and form a thin boundary layer just in front of the surface. Outside this layer, the gas expands and the number of collisions decreases. In the measurements in Ref. [1] and the present study, three types of ion mass peaks are observed with different flight times, corresponding to monomer, dimer and quadrumer K+ ions. The signal N was in Ref. [1] compared with the result from a trajectory calculation which assumed that a constant flux of ions K+, K+ and K+ leaves the 2 4 sample during the 17 ms long ion extraction pulse with a positive voltage on the sample. The agreement of the peak positions with the calculation was good, and also the tails of the distributions were reproduced well. The TOF distribution in Figs. 2 and 3 agrees well with the angular distribution in Fig. 4. The dip at 6°, which will be discussed further later, is visible in both sets of data, and the signal at very large angles, at 70–90°, is also found in both sets. The intensity at large angles seems to be somewhat larger in the TOF measurements than in the angular data. However, the main shape of the angular distributions is retained also in the TOF data. The sharp rise of the signal at 16 ms is due to the K+ ions which leave the sample at the switch-over from negative to positive sample voltage. Calculations show that the dimer K+ should arrive 2 at the detector with its peak at 30 ms, and K+ at 4 45 ms. Both these cluster sizes form the flat-topped peaks in the center of Figs. 2 and 3, with their tails disappearing at 60 ms. 4.2. Cluster formation scattering The angular distribution in Fig. 4 is not symmetric around the surface normal. Instead, it is tilted towards positive angles. Such a change in the angular distribution is expected if the flux has taken part in scattering processes, since the incoming beam will transfer its momentum along the surface to the flux leaving the surface. As can be
seen from the distributions in Ref. [6 ], this kind of tilted distribution is normally not observed when the entire flux is measured at higher surface temperatures. However, in cases where only the excited, or ionized species are detected, like in the case with scattering from a zirconia surface in Ref. [5], the skewed form of the distribution is the rule. The same kind of distribution is also found for total scattering if the graphite sample is held at a negative voltage, like in Ref. [7]. This means that a large fraction of the flux from the surface collides with the atoms in the beam, so that they are deflected towards positive angles. It is obvious that this requires very large cross-sections for the interactions, which directly indicates that Rydberg states exist in the flux from the surface. A conservative estimate of the collision cross-sections between Rydberg species from the surface and K atoms from the beam indicates 106 nm2, or an effective diameter of 1 mm. Very large cross-sections are expected for resonant processes involving Rydberg ˚ 2 (104–105 nm2). species [27,28], up to 106–107 A A dip close to 6° is often found in the angular distributions of desorbing K+ ions with a K beam impinging on a graphite surface. Such a dip can be expected as the result of scattering of the beam atoms from the small electronically excited clusters which are formed at the surface. As shown also in the case of K beam scattering off a zirconia surface [5], the complex formation between a K atom from the beam and a small cluster K from the N surface can give a cluster K . The cluster will N+1 normally be in an electronically excited state, which means that it will be detected by the dynode detector. According to Eq. (2), clusters with N+1=7 and 8 are expected to be observed at 6°. The dip close to 6° observed here indicates that clusters with sizes N+1=7 and larger are not formed with any large probability. In Fig. 2 it is easily seen that the tail in the distribution is longer at smaller positive angles, close to the normal direction at angles <18°, outside which another process starts (see below). This indicates that larger, slower clusters are formed by collisions at these angles. Thus, the observations of angular distributions which are slightly tilted towards positive angles must indicate a scattering process, and a dip in the distribution at a small positive angle
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indicates a complex scattering process of the form described here. The process in Eq. (1) is often difficult to distinguish from a direct ionization process like the associative ionization K+K*K+ +e−. N N+1 This type of bound-free transition may be less likely than the complex formation process in Eq. (1), but we have no possibility to distinguish between the two processes in the present experiments. In the experiments with a zirconia surface [5], however, the neutral excited clusters in Eq. (1) were observed. A direct ion formation was also observed, but only in backwards scattering. Thus, it is likely that in the present case the skewed scattering distributions are due to collision complex formation as in Eq. (1), followed by field ionization of the clusters. 4.3. Inelastic scattering in the desorbing flux In Fig. 2, another feature in the TOF angular distribution is clearly visible, namely a tail at positive angles outside 18° which moves towards longer TOF times at larger angles. A similar tail extends also to negative angles as can be seen in Fig. 3, but it is not so easily observed due to the detector blocking the beam at these angles. This feature varies continuously with the angle, and it is thus unlikely that it is due to the formation of heavier clusters at larger angles. Instead, it is likely due to scattering of ions moving out from the surface in the desorbing plume, giving slower ions at larger angles. This effect could be caused by the same processes which decrease the kinetic energy of the ions reaching the collector, demonstrated in Ref. [6 ]. There, it was proposed that the low kinetic energy of the ions was due to charge exchange processes during the expansion of the desorbing flux from the sample. Such processes will exist when the K+ ions are accelerated in the field. The ions will then overtake and collide with the slower K* atoms in the flux. Among these collisions, the ones with large impact parameters may preferentially give charge exchange, by collisions with the Rydberg electron, while small impact parameters should give rise to core ion collisions and thus substantial energy loss and angular deflection, observed as the tails in Figs. 2
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and 3. A larger deflection angle will give a smaller translation energy, as observed. The cross-sections for this process will be of approximately the same order of magnitude as the cluster formation collisions discussed above, which indicates resonant Rydberg state collisions. That scattering in the residual gases outside the surface should give the observed scattering behavior is unlikely. A typical cross-section for ionmolecule collisions is 1 nm2. This means that a pressure of at least 10−6 mbar would be needed to produce a scattering similar to what is observed, that is a much higher pressure than the one existing in the apparatus. 4.4. Surface processes The peaks at large negative angles are not very well resolved in Figs. 2 and 3. In Fig. 5, the data from another run display the details in that range much better. One new feature is then observed, namely a ridge in the signal moving towards longer flight times with increasing angle. Note the arrow in Fig. 5. This is relatively small feature, not of the size of the scattering tails observed in Figs. 2 and 3, but otherwise showing the same interdependence between angle and velocity. Thus, we
Fig. 5. The TOF distributions in a case with slightly higher intensity peaks at large angles relative to the normal. Surface temperature is 990 K. Observe the ridge on the distribution in the angular range 80–90°, at the arrow. The basal surface in the plot is at the zero signal.
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propose also this signal variation with angle to be due to an inelastic scattering process in which the ions scatter at larger angles with lower velocities. Since the intensity at large angles from the normal is likely to mainly originate from the prism faces of the graphite sample or from the edge of the sample, it is not so easy to deduce the exact form of the particle involved in this scattering at present, but the identification of the process shows the strength of the full angular distribution measurements. The different distributions of the flux from the basal surface and from the prism surfaces are shown in Refs. [6,7]. The flux from the prism surfaces is only seen at angles outside ±60°, that is, in an angular range which is well separated from the flux from the basal surface. That the processes observed here are due to the rapid interactions between K atoms and ions brought to the surface by the K beam is readily shown, by turning off the beam with the beam flag. After 2 min, the signal intensity has dropped a factor of 5, and after 10 min, the signal has disappeared completely. Thus, the clusters leaving the surface are formed rapidly during the exposure to the beam, and they are not preformed in the bulk or on the surface. It could also be interesting to observe the angular distributions with lower surface densities, so that the cluster formation is decreased. However, it is not possible to measure the angular distribution rapidly enough after turning off the beam flux. Instead, low surface density results are found in Ref. [6 ] at higher sample temperatures. There, almost symmetric angular distributions around the surface normal are observed. Thus, the observation of skewed distributions due to cluster formation is related to high surface densities. It is the strong interaction between the K atoms in electronically excited states in contact with the surface which is the driving force in the condensation to the small clusters at graphite surfaces. This was first reported in Ref. [1].
5. Conclusions By using full angular resolved TOF distributions to study the interaction between K atoms and a
graphite surface, new results have been reached for this system, where the surface density of K is considerably smaller than for other surfaces studied by similar scattering methods due to the rapid diffusion into the graphite bulk. A complex formation scattering mechanism in the surface sheath is now identified at the graphite surface, which is due to the strong interaction between the electronically excited clusters K* and the K beam N atoms. The same mechanism is known to exist at metal oxide surfaces. The size distribution of clusters K* has its maximum at N=4, while N>6 is N unlikely. An inelastic scattering process in the desorbing flux is also observed between K+ ions and neutral K* Rydberg species which leave the surface. The sizes of the cross-sections estimated for both collision processes indicate resonant energy transfer.
Acknowledgement This study was supported by the Foundation for Strategic Research (SSF ) through the Swedish Natural Science Research Council (NFR).
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