J. Phys. Chem. 1993.97, 17461748
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Mobilities of Metal Cluster Ions AI,+ and AlN2+:Effect of Charge on Cluster Geometry Martin F. Jamold. Department of Chemistry, Northwestern University, 21 45 Sheridan Road, Euanston, Illinois 60048
J. Eric Bower AT& T Bell Laboratories, Murray Hill, New Jersey 07974
Received: November 30, 1992
The mobilities of size-selected doubly charged aluminum cluster ions, Aln2+(n = 20-142), have been measured using injected ion drift tube techniques. These results are compared to previous measurements for the singly charged clusters, Al,+ (n = 5-73). In the region of overlap, the relative mobilities of the singly and doubly charged clusters are remarkably similar, suggesting that the charge state has only a minor effect on the cluster’s geometry. The mobilities of both the singly and doubly charged clusters show an apparent correlation with the predictions of the electronic shell model. Close inspection of the results reveals that there are subtlevariations in the mobilities of Al,’ and Aln2+which suggest that it is the number of valence electrons, and not the number of atoms, that controls the cluster’s shape.
Introduction Mobility measurements can provide information about the geometries of atomic clusters.14 In a recent paper, we reported measurements of the mobilities of aluminum cluster ions, Al,+ ( n = 5-73).4 We found substantial variations in the mobilities with cluster size. Some of these variations could be attributed to the effects of electronic shell closings (in particular those with 138and 198electr~ns).s-~ In this paper we report measurements of the mobilities of doubly charged aluminum clusters. The motivation for this work is (1) to compare the mobilities of the singly and doubly charged clusters, and so determine how the charge influences the clusters’geometries, and (2) to extend these measurements to larger cluster sizes to determine whether correlation with the predictions of the electronic shell model persists. Experimental Methods The experimental apparatus used for these studies is identical to that employed in our previous work.Z4 The aluminum cluster ions were generated by pulsed laser vaporization of an aluminum rod in a continuous flow of helium buffer gas. The source was cooled to 180 f 20 K. Doubly charged clusters were generated by injecting a 1.2-kV electron beam into the buffer gas just before the exit aperture of the source. After exiting the source, the cluster ions were focused into a quadrupole mass spectrometer where a particular cluster size was selected. The size-selected cluster ions were then focused and injected into the drift tube. An injection energy of 50 eV was employed for most measurements. The drift tube is 7.62 cm long, and its temperature can be varied. Measurements were performed with an electric field of 13.1 V/cm and helium buffer gas at 10 Torr. The buffer gas pressure in the drift tube was directly measured using a capacitance manometer. After traveling across the drift tube, a small fraction of the ions leave through the exit aperture and are subsequentlyfocused into a second quadrupolemass spectrometer. At the end of the quadrupole the ions were detected by an off-axis collision dynode and dual microchannel plates. Mobilitieswere measured using an electrostaticshutter to allow a short (generally 50 ps long) pulse of size-selected cluster ions to enter the drift tube and recording the arrival time distribution at thedetector with a multichannel scaler (using IO-@ resolution). Measurements are performed both with and without the buffer gas in the drift tube, and the time the clusters spend drifting across the drift tube is determined from the difference between
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OO22-3654/93/2097-1746$04.00/0
these two measurements (plus some small correction~3.~). The mobility is then determined from’o
K = L/t@ (1) where t D is the average drift time, E is the electric field, and L is the length of the drift tube. The measured mobility is inversely proportionalto the buffer gas number density,and so by convention it is converted to a reduced mobility10 P 273.2 K O = K -760 T where P is the pressure in Torr.
RWdQ Figure 1shows the arrival time distribution measured for Al55+ at room temperature (292 K). The larger peak at -2700 ps arises from Als5+. The second smaller peak at 1900 ps arises from Alllo2+. This second peak comes and goes as the electron gun is turned on and off. The electron gun injects a high-energy electron beam into the sourcejust before the cluster exit. Though, the doubly charged clustersare probably formed by charge transfer from He+, rather than by direct electron impact. The smallest doubly charged cluster that we observed was A1142+.Doubly charged clusters were not observed for larger clusters, however, until n = 20. The special stability of A114~+ is easily understood. It contains 40 valence electrons which corresponds to a closed electronic shell (note that aluminum is trivalent so each atom contributes three valence electrons).s The mobility is directly proportional to the charge on the cluster. Thus, if Alss+and Al~s++ were identical in every respect except the extra charge, the mobility of AIs5++would be twice as large as that for Alss+. While Alllo++has twice as many atoms as Alss+,the mobilities of these large atomic clusters are controlled by the collision cross section which is not proportional to n for a three-dimensional geometry but scales roughly as nz13. Thus, the mobility of All is around 2/W3 (- 1.26) larger than that of Alss+, and the singly and doubly charged clusters are easily separated on the basis of their different mobilities. In our previous workz4 we found it convenient to convert the measured reduced mobilities to relative mobilities by dividing by the mobility of a sphere of volume nV, (V,is the bulk atomic volume). The larger clusters have smaller mobilitiesjust because they are physicallybigger, and doubly charged clustershave larger mobilities because of the extra charge. Dividing by the hardsphere mobility removes the variation in the mobilities which
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CP 1993 American Chemical Society
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The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 1747
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Figure 1. Arrival time distribution rccorded for Alss+ and Alllo*+ at rmm temperature (292 K) with a helium buffer gas pressure of -9.5 Torr and a drift.field 13.125 V/cm. The injection energy was 50 eV. The peak due to All lo2+ comes and goes as the electron gun is turned on and off.
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Figure 3. Relative mobilities of Al,+ ( n = 5-73) (dashed line) and AI,*+ ( n = 20-142) (solid line). The arrows show the location of the electronic 0.83
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shell closings. The numbers associated with the arrows give the number of valence electrons required to completely fill the shell.
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30 40 50 60 70 80 NUMBER OF ATOMS Figure 2. Plot of the reduced mobilities of Al,+ (n = 10-71). The results 20
shown by the dashed line were taken from our previous work: and were recorded with the electron gun off. The data shown by the solid line were recorded with the electron gun on. Note the difference a t A14st.
arise from these simple physical origins and makes it easier to compare the mobilities and identify differences. The hard-sphere mobility is given bylo
where e is the charge, m~ and ntg are the masses of the cluster ion and buffer gas, respectively, and QHSis the hard-sphere collision cross section. Figure 2 shows the measured relative mobilities for AI,+ containing 10-71 atoms. The dashed line shows our previously reported measurements which were made with the electron gun off? The solid line shows the mobilities of the singly charged clusters recorded during the course of this work with the electron gun on. The agreement between these two data sets is remarkably good. There is, however, one significant difference. With the electron gun off the mobility of A145+ is similar to that of A14+, but with the electron gun on the mobility of A b + has increased significantlyand is now similar to that of AIM+. We found in our previous studies of the singly charged clusters that the A145+ clusters coming from the source are not in their lowest energy structural forma4Collisional annealing (by injecting the clusters into the drift tube at elevated kinetic energies) or thermal annealing (by changing the temperature of the drift tube) converts the higher energy, lower mobility isomer into the more stable larger mobility isomer. We found that the metastable isomer of A4s+ anneals at 345 K,only slightly above room temperature. Apparently, the high-energy electron beam heats the clusters enough to anneal Figure 3 shows plots of the relative mobilities of Al,+ clusters
containing 5-73 atoms (dashed line) and Al,++ clusterscontaining 20-142 atoms (solid line). We are able to examine larger doubly charged clusters becausethey have smaller mass-to-charge ratios. The results shown in Figure 3 are the average of at least two independent sets of measurements. The reproducibility of the independent measurements in extremely good (generally within 0.5%). In the region of overlap the relative mobilities of the singly charged and doubly charged clustersare remarkably similar. Figure 4 shows an expanded view of this region (clusters with 2&71 atoms). It appears that essentially all the small local variations reproduced. As noted above, in our previous studies of the mobilities of AI,+, isomers were observed for A45+ cluster^.^ Isomers were also observed for AI&+. With the drift tube cooled, a second Abs+ isomer appears with a mobility similar to that of A b + . The low-mobility A b + isomer anneals at 245 K,compared to 345 K for A145+. The arrival time distribution for &5++ is substantially wider than that for neighboring clusters, indicating that isomers are also present for this cluster. Note that the data for &5++ shown in the figures is an average for the two isomers, and it lies between the mobilitiesof Al#++and &++. A series of annealing experiments were performed for A145++ and AI&++,changing both the injection energy (25-100 eV) and the drift tube temperature (77-350 K). No changes were observed: isomers were always present for AI45++and never observed far Ab++. This is consistent with the conclusion reached above that the electron beam anneals the clusters in the source. The observation of two isomers for AI45++,even after annealing, indicates that these isomers must have nearly identical stabilities, in contrast to A145+, where one isomer dominates after annealing.
Discussion If a metal cluster with n, valence electrons is constrained to sphericalsymmetry and the electrons treated as a quantized Fermi gas, the electrons are organized into subshells or delocalized orbitals defined by a radial quantum number n and angular momentum quantum number 1.5 The subshells are 2(21+ 1)fold degenerate. With increasing cluster size, as the spacing between the energy levels diminishes, one would expect that the electronic shell structure would vanish. However, the subshells bunch together into shells with relatively large energy gaps between them," and electronic shell structure has been observed for metal clusters containing up to 1500 electrons.l2-14 When the restriction of spherical symmetry is lifted, and the clusters are permitted to undergo ellipsoidal or spheroidal distortion, the 2(21+ 1)-folddegeneracy is broken and some of the I levels move up in energy and some move down.69 Thus, a cluster with partially
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30 40 50 60 70 80 NUMBER OF ATOMS Figure 4. Expanded view of the relative mobilities of singly charged (dashed line) and doubly charged (solid line) aluminum clusters ions in the region of overlap. 10
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filled shell can lower its energy by adopting a nonspherical geometry. On the other hand, the energy of a filled shell increases as the cluster distorts, so a closed-shell cluster, with a relatively large energy gap to the next available subshell, well retain its spherical symmetry. Since clusters which undergo ellipsoidal or spheroidaldistortionshave a latger average collision cross section than a spherical cluster of the same volume, we expect to see oscillations in the mobilities of the atomic clusters, with maxima occurring at the spherical shell closings. The arrows in Figure 3 show the locations of the shell closings from the calculations of Berry and co-workers for aluminum clusters using the spherical jellium appr~ximation.'~ The numbers associatedwith each arrow gives the total number of valence electrons required to completely fill theshell. Thereis a strong correlation between theoscillations in the mobilities and the predicted shell closings, particularly for clusters with more than 40 atoms. The size of the oscillations clearly diminishes with increasing cluster size. This occurs because only the highest unfilled shell provides the driving force to distort while the total energies of the lower lying filled shells rise as the cluster distorts. Thus, the larger clusters effectively becomes stiffer. The precise ordering of the subshells and the level spacing are weakly dependent on the details of the potential used. Thus, exact quantitative agreement between predictions of the electronic shell model and the experimental results cannot be expected. Some minor deviations are apparent in Figure 3. According to the spherical jellium model calculations of Berry and c~-workers,'~ the shell closing with 256 electrons is a major shell closing and the one with 268 electrons is a minor one. Both appear in the experimental results. These shell closings have not been observed previously with aluminum; however, for both sodium and cesium the major shell closing is also predicted to be at 256 electrons, but it is observed at 263 i 5.12J3Similarly, a major shell closing is predicted to occur for aluminum clusters with 338 electronsand a minor shellclosing is expectedwith 356 electrons,14 yet there is no evidence for the shell closing with 338 electrons in the measured mobilities. Instead, the shell closing appears to be at 356 electrons. While we have explained the observed oscillations in the mobilities in terms of the tendency for clusters with unfilled shells to distort from spherical symmetry, it is worth pointing out that shape is not the only thing that changes around an electronic shell closing. For example, the dissociation energies will change, and a cluster with a larger dissociation energy may have a smaller mobility just because it has a larger cohesive energy and is physically smaller. For a cluster with around 100 atoms the change in the dissociation energy at an electronic shell closing is expected to be small, less than a few tenths of the electronvolt. The fractional change in the total cohesive energy due to this
small change in the dissociation energy is -0.146 (for a cluster with 100 atoms). Using a simple 6-12 potential, we estimate that this change in the cohesive energy will lead to a change in the nearest-neighbor distance of -0.01%. So changes in the mobilities arising from changes in the cohesive energyare expected to be negligible. There appears to be a structural transition associated with the shell closing with 138 electrons. Instead of gradually becoming more spherical as the shell closing is approached, an abrupt increase in the mobility occurs for clusters with -45 atoms. This behavior suggests that the electronic structure of clusters with C45 atoms departs from the predictions of the shell model, but as the shell closing is approached, the additional stabilization availablefor adopting a closed-shell configurationsnaps the cluster into a more spherical shape. Isomers were obscrved at the structural transition for both A14s+and Al*s++. For A14~++ both isomers have similar stabilities; however, for A145+the more spherical isomer is the more stable. Thus, it seems that adding a single electron to A14s++is enough to stabilizethe more spherical isomer and shift the location of the structural transition slightly. In the region of overlap the relative mobilities of the singly and doubly charged clusters are remarkably similar. This result is important for several reasons. First, it indicates that the influence of the ion-induced dipole interaction between the charged cluster and the helium buffer gas is negligible, at least for clusters with more than 20 atoms. Second, it indicates that the geometries of the clusters are essentially unaffected by the charge, suggesting that neutral clusters will have the similar geometries to the singly and doubly charged clusters. While the mobilities of the singly and doubly charged clusters are very similar, close inspection of the results shown in Figure 4 reveals that there are some subtle systematic differences: in many cases it appears that marginally better agreement between the mobilities of the singly and doubly charged clusters could be obtained by sliding the results for the doubly charged clusters slightly to the left. For example, consider the small local maxima that occur for clusters with -60 atoms. The isomers observed for A14s+and Aids++ are another example. This behavior suggests that the total number of valence electrons is more important than the number of atoms in determining the cluster's shape. While this result is consistent with the overall shape of the cluster being determined by electronic shell effects, note that the shift also occurs for small features in Figure 4 which do not have an obvious explanation within the framework of the electronic shell model.
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1986. (8) Selby, K.; Vollmer, M.; Kresin, V.; de Heer, W. A.; Knight, W. D. Phys. Reu. B 1989, 40, 5417. (9) Ekardt, W., Penzar, Z. Phys. Reo. B 1988, 38, 4273. (IO) McDaniel, E.W.; Mason, E.A. The Mobility and Difjusion o/Ions ion Gases; Wiley: New York, 1973. ( 1 1) Nishioka, H.; Hansen, K.; Mottelson, 8. R.Phys. Reu. B 1990,42, 9377. (12) Gohlich, H.; Lange, T.; Bergmann,T.; Martin, T. P. Phys. Reo. Lerr. 1990,65, 748. (13) Bjornholm, S.;Borggrecn, J.; Echt, 0.;Hansen, K.; Pedersen, J.; Rasmussen, H. D. Phys. Rev. Lerr. 1990, 65, 1627. (14) Persson, J. L.;Whetten, R. L.; Cheng, H.-P.; Berry, R. S. Chem. Phys. Leu. 1991, 186, 215.
